Flying Ad Hoc Networks: Cooperative Networking and Resource Allocation (Wireless Networks) 9811688494, 9789811688492

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Wireless Networks

Jingjing Wang Chunxiao Jiang

Flying Ad Hoc Networks

Cooperative Networking and Resource Allocation

Wireless Networks Series Editor Xuemin Sherman Shen, University of Waterloo, Waterloo, ON, Canada

The purpose of Springer’s Wireless Networks book series is to establish the state of the art and set the course for future research and development in wireless communication networks. The scope of this series includes not only all aspects of wireless networks (including cellular networks, WiFi, sensor networks, and vehicular networks), but related areas such as cloud computing and big data. The series serves as a central source of references for wireless networks research and development. It aims to publish thorough and cohesive overviews on specific topics in wireless networks, as well as works that are larger in scope than survey articles and that contain more detailed background information. The series also provides coverage of advanced and timely topics worthy of monographs, contributed volumes, textbooks and handbooks. ** Indexing: Wireless Networks is indexed in EBSCO databases and DPLB **

More information about this series at https://link.springer.com/bookseries/14180

Jingjing Wang • Chunxiao Jiang

Flying Ad Hoc Networks Cooperative Networking and Resource Allocation

Jingjing Wang School of Cyber Science and Technology Beihang University Beijing, China

Chunxiao Jiang School of Information Science and Technology Tsinghua University Beijing, China

ISSN 2366-1186 ISSN 2366-1445 (electronic) Wireless Networks ISBN 978-981-16-8849-2 ISBN 978-981-16-8850-8 (eBook) https://doi.org/10.1007/978-981-16-8850-8 © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2022 This work is subject to copyright. All rights are solely and exclusively licensed by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors, and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, expressed or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. This Springer imprint is published by the registered company Springer Nature Singapore Pte Ltd. The registered company address is: 152 Beach Road, #21-01/04 Gateway East, Singapore 189721, Singapore

Preface

Reliable unmanned autonomous flight control programs and unmanned aerial vehicles (UAVs) equipped with radio communication devices have been actively developed around the world. Given their low cost, flexible maneuvering, and unmanned operation, UAVs have been widely used in both civilian operations and military missions, including environmental monitoring, emergency communications, express distribution, and even military surveillance and attacks, for example. Although UAV technologies have to some degree matured, given that a range of standards and protocols used in terrestrial wireless networks are not applicable to UAV networks, and that some practical constraints such as battery power and no-fly zone hinder the maneuverability capability of a single UAV, we need to explore advanced communication and networking theories and methods for the sake of supporting future ultra-reliable and low-latency applications. Typically, the full potential of UAV network’s functionalities can be tapped with the aid of the cooperation of multiple drones relying on their ad hoc networking, in-network communications, and coordinated control. Furthermore, some swarm intelligence models and algorithms conceived for dynamic negotiation, path programming, formation flight, and task assignment of multiple cooperative drones are also beneficial in terms of extending UAV’s functionalities and coverage, as well as of increasing their efficiency. Here, we call the networking and cooperation of multiple drones as the terminology ‘flying ad hoc network (FANET)’, and there indeed are numerous new challenges to be overcome before the widespread of so-called heterogeneous FANETs. In this book, we examine a range of technical issues about FANETs from physical-layer channel modeling to MAC-layer resource allocation, and also introducing novel UAV aided mobile edge-computing techniques. With regard to communication channels in FANET, we commence with an introduction about UAV communication channel characteristics including its link budget, major channel fading, and channel impulse response and metrics, followed by three typical kinds of channel model. Moreover, with regard to multi-UAV-assisted seamless information coverage, we present three dynamic seamless coverage strategies for dense urban areas, quality of service (QoS)-guaranteed Internet of things (IoT) networks, as well v

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as for minimum delay constraint. Next, we discuss cooperative resource allocation in FANETs, where we provide two near-optimal joint UAV’s position/trajectory and resource allocation algorithms, while also presenting a resource allocation scheme for IoT nonorthogonal multiple access (NOMA) uplink transmission. Finally, we address the mobile edge computing for FANETs, where load balance-oriented, latency- and reliability-guaranteed, and energy-efficient secure UAV-assisted edgecomputing schemes are investigated. The aim of this book is to educate information technology engineers, computer and information scientists, applied mathematicians and statisticians, as well as systems engineers to carve out the critical role that analytical and experimental engineering play in the research and development of FANETs. This book emphasizes on multi-UAV networking technologies and applications in next-generation wireless networks. To summarize, the key advantages of this book are listed as follows: 1. It provides an introduction to the FANET paradigm, from both physical-layer and upper-layer perspectives, which currently has attracted substantial attention from both academic and industrial areas. 2. It discusses the state of the art for the FANET and its characteristics against other mobile ad hoc networks. It also surveys the basic UAV/FANET communication channels. 3. It highlights three hot topics in FANET, i.e., seamless information coverage, cooperative resource allocation, and mobile edge computing. A range of examples are illustrated in detail so as to provide a wide scope for general readers relying on introducing their problem formulation, solution algorithms, and simulation results in a comprehensive way. These successful cases can guide us to efficiently construct a multi-UAV heterogenous network. This book is organized as follows: Chap. 1 provides an overview of the FANET concept and discusses it against traditional mobile ad hoc networks. In Chap. 2, we introduce the UAV communication channels. In Chaps. 3–5, we provide study cases to show how to solve the key challenges in multi-UAN-aided seamless information coverage, cooperative resource allocation, and mobile edge computing in FANET, respectively. Acknowledgments Dr. Jingjing Wang and Dr. Chunxiao Jiang would like to thank those who helped to get this book published, especially our graduate students Zhengru Fang and Zonglin Li who helped to proofread the entire book. Moreover, we would like to acknowledge the support of the National Natural Science Foundation of China and the Young Elite Scientist Sponsorship Program by CAST.

Beijing, China Beijing, China November 2021

Jingjing Wang Chunxiao Jiang

Contents

1

Introduction of Flying Ad Hoc Networks . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 1.1 Basic Classification and Regulation of UAVs . . . . .. . . . . . . . . . . . . . . . . . . . 1.2 Differences Between FANET, VANET, MANET, and AANET . . . . . . 1.3 Compelling Applications of FANET . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . .

1 1 2 6 8

2 Communication Channels in FANET . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 2.1 UAV Communication Channel Characteristics . . . .. . . . . . . . . . . . . . . . . . . . 2.1.1 UAV Link Budget .. . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 2.1.2 UAV Channel Fading . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 2.1.3 Channel Impulse Response and Metrics . . .. . . . . . . . . . . . . . . . . . . . 2.2 UAV Communication Channel Modeling .. . . . . . . . .. . . . . . . . . . . . . . . . . . . . 2.2.1 Air-to-Ground Channels . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 2.2.2 Air-to-Air Channels . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 2.2.3 UAV-MIMO Channels .. . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 2.3 Challenges and Open Issues . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 2.3.1 Antennas for UAV Channel Measurement.. . . . . . . . . . . . . . . . . . . . 2.3.2 Channels of UAV Applications in IoT and 5G . . . . . . . . . . . . . . . . 2.3.3 Channels in Vertical Industrial Applications . . . . . . . . . . . . . . . . . . 2.3.4 Channels of UAV FSO Communications ... . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . .

11 11 12 15 16 18 19 29 31 34 34 35 35 36 36

3 Seamless Coverage Strategies of FANET . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 3.1 Introduction of Seamless Coverage Problems . . . . .. . . . . . . . . . . . . . . . . . . . 3.1.1 Problem Domain and Challenges . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 3.1.2 State of the Art . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 3.2 UAV Seamless Coverage Strategy for Dense Urban Areas . . . . . . . . . . . 3.2.1 System Model .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 3.2.2 Cyclic Recharging and Reshuffling Optimization .. . . . . . . . . . . . 3.2.3 Problem Formulation . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 3.2.4 Distributed Particle Swarm Optimization Aided Solution .. . .

41 41 42 42 43 44 47 50 51

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3.2.5 Simulation Results . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 3.2.6 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 3.3 UAV Seamless Coverage Strategy for QoS-Guaranteed IoT.. . . . . . . . . 3.3.1 System Model .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 3.3.2 Problem Formulation . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 3.3.3 Block Coordinate Descent Based Joint Optimization .. . . . . . . . 3.3.4 Simulation Results . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 3.3.5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 3.4 UAV Seamless Coverage Strategy for Minimum-Delay Placement.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 3.4.1 System Model .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 3.4.2 Problem Formulation . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 3.4.3 Markov Decision Process Transformation .. . . . . . . . . . . . . . . . . . . . 3.4.4 Backward Induction and R-Learning Based Optimization . . . 3.4.5 Simulation Results . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 3.4.6 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 3.4.7 The Proof of Theorem 1 .. . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . .

57 63 64 67 70 72 82 91 92 93 96 98 101 109 114 114 115

4 Cooperative Resource Allocation in FANET . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 4.1 Introduction of Cooperative Resource Allocation Problems .. . . . . . . . . 4.1.1 Problem Domain and Challenges . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 4.1.2 State of the Art . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 4.2 UAV Position Control with Interference . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 4.2.1 System Model .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 4.2.2 Problem Formulation . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 4.2.3 Hovering Altitude and Power Control Solution . . . . . . . . . . . . . . . 4.2.4 Simulation Results . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 4.2.5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 4.3 UAV Trajectory Design for Space–Air–Ground Networks . . . . . . . . . . . 4.3.1 System Model .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 4.3.2 Problem Formulation . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 4.3.3 The Solution for Optimization Problem . . .. . . . . . . . . . . . . . . . . . . . 4.3.4 Simulation Results . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 4.3.5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 4.4 Multi-UAV-Aided IoT NOMA Uplink Transmission . . . . . . . . . . . . . . . . . 4.4.1 System Model .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 4.4.2 Problem Formulation . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 4.4.3 IoT Nodes Clustering and Subchannel Assignment.. . . . . . . . . . 4.4.4 Power Allocation and Flight Height Design .. . . . . . . . . . . . . . . . . . 4.4.5 Simulation Results . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 4.4.6 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . .

121 121 122 122 123 125 128 131 144 149 149 150 154 155 161 167 167 169 171 174 175 187 192 192

Contents

5 Mobile Edge Computing in FANET . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 5.1 Introduction of Mobile Edge Computing Problems . . . . . . . . . . . . . . . . . . . 5.1.1 Problem Domain and Challenges . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 5.1.2 State of the Art . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 5.2 Load-Balance Oriented UAV-Aided Edge Computing . . . . . . . . . . . . . . . . 5.2.1 System Model .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 5.2.2 Problem Formulation . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 5.2.3 Joint UAV Deployment and Task Scheduling . . . . . . . . . . . . . . . . . 5.2.4 Simulation Results . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 5.2.5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 5.3 Latency and Reliability Guaranteed UAV-Aided Edge Computing.. . 5.3.1 System Model .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 5.3.2 Problem Formulation . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 5.3.3 Hybrid Binary Particle Swarm Optimization .. . . . . . . . . . . . . . . . . 5.3.4 Simulation Results . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 5.3.5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 5.4 Energy-Efficient and Secure UAV-Aided Edge Computing .. . . . . . . . . . 5.4.1 System Model .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 5.4.2 Problem Formulation . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 5.4.3 Energy-Efficient Secure UMEC Solution .. . . . . . . . . . . . . . . . . . . . 5.4.4 Analysis of Offloading and Computation ... . . . . . . . . . . . . . . . . . . . 5.4.5 Simulation Results . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 5.4.6 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 5.5 Transmit-Energy and Computation-Delay Optimization .. . . . . . . . . . . . . 5.5.1 System Model .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 5.5.2 Energy-Efficient Gateway Selection . . . . . . .. . . . . . . . . . . . . . . . . . . . 5.5.3 Task Scheduling and Resource Allocation Scheme .. . . . . . . . . . 5.5.4 Simulation Results . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 5.5.5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . .

ix

197 197 198 199 199 201 203 206 214 220 220 221 227 230 231 234 235 236 239 241 250 253 260 260 261 265 269 276 283 284

Acronyms

A2A A2G ABS AI AP AWGN B5G BCD BLOS C/N CAA CABR CIR CNPC CSI D2D eMBB FAA FANET G2G GA GEO GR GS ICAO IoT ITU LEO LMS LOS MANET

Air-to-Air Air-to-Ground Aerial Base Stations Artificial Intelligence Access Point Additive White Gaussian Noise Beyond 5G Block Coordinate Decent Beyond Line-of-sight Carrier-to-noise ratio Civil Aviation Administration Civil Aviation Administration Channel Impulse Response Control and Nonpayload Communication Channel State Information Device-to-device Enhanced Mobile Broadband Federal Aviation Administration Flying Ad Hoc Networks Ground-to-Ground Genetic Algorithm Geosynchronous Earth Orbit Greedy Algorithm Ground Station International Civil Aviation Organization Internet of Things International Telecommunication Union Low Earth Orbit Least Mean Square Line-of-sight Mobile Ad Hoc Networks xi

xii

MANETs MEC MIMO mMTC NOMA OFDM OFDMA PLS QoS SCA SIC SIMO SISO SWIPT TDD UAV UMENs uRLLC VANET VLOS

Acronyms

Mobile Ad Hoc Networks Mobile Edge Computing Multiple Input and Multiple Output Massive Machine-type Communication Non-orthogonal Multiple Access Orthogonal Frequency Division Multiplexing Orthogonal Frequency Division Multiple Access Physical-Layer Security Quality-of-Service Successive Convex Optimization Successive Interference Cancellation Single Input and Multiple Output Single Input and Single Output Simultaneous Wireless Information and Power Transfer Time Division Duplexing Unmanned Aerial Vehicles UAV-enabled Mobile Edge Computing Nodes Ultra Reliable Low Latency Communication Vehicular Ad Hoc Networks Visual Line-of-sight

Chapter 1

Introduction of Flying Ad Hoc Networks

Unmanned Aerial Vehicles (UAV) have been widely used both in military and in civilian applications. However, the cooperation of small and mini drones in a network is capable of further improving both the performance and the coverage area of UAVs. Naturally, there are numerous new challenges to be solved before the wide-spread introduction of multi-UAV based heterogeneous Flying Ad Hoc Networks (FANET), including the formulation of a stable network structure. Meanwhile, an efficient gateway selection algorithm and management mechanism are required as well. On the other hand, the stability control of the hierarchical UAV network guarantees the efficient collaboration of the drones. In this article, we commence with surveying the FANET structure and its protocol architecture. Then, a variety of distributed gateway selection algorithms and cloud-based stability control mechanisms are addressed, complemented by a range of open challenges. This chapter is organized as follows: We first introduce the basic classification and regulations about UAVs in Sect. 1.1, and then in Sect. 1.2 we compare the differences between FANET, VANET, and MANET. Finally, we elaborate various compelling applications of FANET in Sect. 1.3.

1.1 Basic Classification and Regulation of UAVs The networking architectures and operations of multi-UAV networks should follow the regulation and supervision of different agencies or governments. According to the Federal Aviation Administration (FAA) of America, the small or mini unmanned aircraft must indeed remain within visual line-of-sight (VLOS) of the remote pilot in command or visual observers. Moreover, small or mini drones are only allowed daylight operations and must yield right of way to other aircrafts. The person manipulating the flight should hold a remote pilot certificate. Moreover,

© The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2022 J. Wang, C. Jiang, Flying Ad Hoc Networks, Wireless Networks, https://doi.org/10.1007/978-981-16-8850-8_1

1

2

1 Introduction of Flying Ad Hoc Networks

the maximum weight, altitude, speed, etc., are strictly regulated by a range of government rules. As for the Civil Aviation Administration (CAA) of China, it stipulates certain illegal airspace for small and mini UAVs, such as civil airports, military bases, crowded areas, etc. In contrast to the VLOS only flight authorized by the FAA, CAA allows beyond VLOS (BVLOS) flight of small or mini drones. However, these drones must be controlled by the remote pilot, who has to be capable of stopping the flight in case of emergency. Moreover, the CAA regulates the use of the UAV cloud system. Meanwhile, the Japanese and European authorities have promulgated a series of regulations of small and mini UAVs.

1.2 Differences Between FANET, VANET, MANET, and AANET In contrast to classic Mobile Ad Hoc Networks (MANET) and Vehicular Ad Hoc Networks (VANET), the mobility and nimble flight attitude of UAV systems have a grave influence on their networking technologies. As a new member of the family of MANET, aeronautical Ad Hoc Network (AANET) constitutes a compelling concept for providing broadband communications above clouds by extending the coverage of Air-to-Ground (A2G) networks to oceanic and remote airspace via autonomous and self-configured wireless networking among commercial passenger airplanes [1]. More explicitly, the middle layer of objects is constituted by the aircraft of an AANET, which are capable of exchanging information with the satellite layer (top layer) and GS layer (bottom layer) via inter-layer links. Furthermore, AANETs are also beneficial for automatic node and route discovery as well as for route maintenance as aircraft fly within the communications range of each other, hence allowing data to be automatically routed between aircraft and to or from the GS. A bird’s eye perspective of AANET, MANET, VANET, and FANET is illustrated in the following Table 1.1, where issues, such as the propagation channel, speed, altitude, network scale, power constraint, node density, and security are considered. Although, the MANET has initially been designed both for mobile phones and for vehicles, we have classified vehicles into VANETs, which are specifically developed for connecting vehicles. AANET distinguishes itself from MANET, VANET, and FANET in terms of its features, such as its flying speed, network coverage, and altitude, which directly result in new propagation characteristics and impose challenges both on the data link layer and network layer design. Despite this, compared with AANET, FANET is more suitable for a variety of scenarios due to its UAV system. In rescue, search, and small-scale coverage tasks, FANET has more flexible characteristics. In [2], Zhou et al. proposed a two-layer aerial-ground cooperative networking architecture, where multiple UAVs forming an aerial subnetwork assist the

UAVs Airplanes

FANET AANET

VANET

Objects Mobile phones Vehicles

Networks MANET

Rayleigh/Rician Rician

Rayleigh/Rician

Channel Rayleigh

8–128 245–257

4–36

Speed (m/s) 0–1.5

Up to 122 9100–13,000

0.5–5

Altitude (m) 1–250

80 740

1

Scale (km) 0.25

Table 1.1 Comparison between existing networks of MANET, VANET, AANET, and FANET

Constraint Non-constraint

Non-constraint

Power Constraint

City: dense Rural:sparse Mission dependent Populated area: dense Unpopulated area: sparse

Density Dense

Medium Life critical

Life critical

Security Medium

1.2 Differences Between FANET, VANET, MANET, and AANET 3

4

1 Introduction of Flying Ad Hoc Networks

terrestrial vehicular subnetwork through UAV-to-UAV and UAV-to-ground communications. The UAVs act as intermediate relays due to their flexible mobility, when for example cell-splitting occurs in the terrestrial vehicular subnetwork. The multi-UAV system was first proposed in [3] based on the concept of Flying Ad Hoc Network (FANET), where the network-centric methodology provided the UAVs with the ability to autonomously position themselves for ideal connectivity and to be able to cooperate with other UAVs for the sake of achieving the best effective coverage. Figure 1.1 illustrated a multi-UAV system, relying on ground stations, ground or airborne relay stations, and remote network monitoring stations as backhauls. The major advantages of the multi-UAV network over its single-UAV counterpart can be summarized in terms of the networking viewpoint as well as the system viewpoint [4, 5]. Specifically, from the networking viewpoint: • Improves the attainable transmission efficiency: Their information transmission capacity, processing rates, and response capability are improved. Multi-UAV

Fig. 1.1 Multi-UAV network architecture and necessary UAV internal units. Specifically, both the small and mini drones should be equipped with sensor units, control and management units, and communication units in order to fulfil certain tasks. Except for some essential sensors, such as the gyroscope, GPS, radar, etc. the drones carry specific sensors, depending on their particular missions. Moreover, the control and management units are responsible for the stable operation and the collaboration of each part. The communication units are composed of multiple modules configured by various protocols, such as IEEE 802.11, IEEE 802.15, LTE, etc. in order to support different communication scenarios [4]

1.2 Differences Between FANET, VANET, MANET, and AANET

5

systems extend the range of airborne surveillance. Meanwhile, when the relay link encounters interruptions, to ensure seamless unobstructed communication, the packets to be relayed will be forwarded to other UAVs under the control of the ground station. Additionally, due to the coordination and collaboration among multiple drones, the multi-UAV network exhibits an improved information preprocessing capability and transmission efficiency. • Increases survivability: The multi-UAV network has a high reliability, and it can be constructed anytime and anywhere. Even if some UAV nodes are under attack, others can reconstruct the network and automatically choose the optimal routing to accomplish their missions. In other words, the ad hoc feature, distributed structure, and node redundancy improve the system’s survivability. • Self-organization and adaptive: Multi-UAV networks relying on mesh networks for example are capable of self-reorganization. This means that the multi-UAV network is resilient to node-failure, hence it is suitable for diverse circumstances. By contrast, from a system-oriented viewpoint: • High energy efficiency: The UAVs are smaller and less expensive in small and mini multi-UAV networks, which leads to a low energy consumption. Moreover, by operating in a coordinated manner, the system’s power consumption can be reduced to the minimum by relying on their sleep mode as well as on sophisticated power allocation schemes. • Convenient scalability: Considering the various mission requirements, the multi-UAV system is capable of changing the network architecture or adding more UAV nodes in order to achieve the required system capacity. • Enriches the applications: The associated diversity aided functions broaden the application-scope of the multi-UAV network. As a benefit of the UAV-to-ground station and UAV-to-UAV communication, the multi-UAV system improves the attainable load capacity and cruising capability. Moreover, the employment of different sensors and diverse data delivery strategies result in compelling valueadded functions. Although the multi-UAV network has some significant advantages over the single-UAV mechanism, the multi-UAV network has numerous challenges, such as intermittent links, power and bandwidth constraints, etc. On one hand, due to their highly dynamic topology and nimble flight attitude, how to design a beneficial multi-hop routing schemes for UAV-to-UAV communication becomes an important issue [6]. On the other hand, in the UAV-to-ground station communication associated with a relatively long distance, only delay-tolerant services can be supported. Secure transmission and protocol compatibility should also be carefully considered. As a result, powerful spread spectrum and smart antenna aided soft hand-off methods relying on an expert system lend themselves to employment in multi-UAV networks.

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1 Introduction of Flying Ad Hoc Networks

1.3 Compelling Applications of FANET Given their low cost and high-flexibility deployment, unmanned aerial vehicles (UAVs) have been widely used both in military and in civilian applications for surveillance, environmental monitoring and emergency rescue, etc. Depending on their cruising duration and action radius, UAVs may be categorized into four classes, i.e., high-altitude and long-endurance UAVs, medium-range UAVs, shortrange small UAVs and mini UAVs [7]. They are usually equipped with a variety of sensors in order to fulfill different tasks. Given the maturity of the UAV industry, small and mini UAVs have also been popularized among the public and their proliferation in diverse applications has attracted a lot of research attention. Recently, UAV communications have been extensively studied for boosting the capacity and coverage of the existing wireless networks [8–14]. Specifically, UAVs can be used both as flying base stations and as relays as discussed in [9] and [12], respectively. The optimum altitudes of UAV for achieving the maximum capacity both in static and in mobile scenarios were derived in these contributions. A similar work considering the UAV’s trajectory optimization at a fixed altitude was conducted by Zeng et al. in [10]. Moreover, UAVs have been introduced for Internet of Things (IoT) applications by Mozaffari et al. [11], where the UAVs are used for collecting data from IoT devices. Explicitly, the network association, the UAV placement, and the devices’ transmit power were jointly optimized for achieving maximum system capacity. However, their low load-carrying capacity and modest cruising capability have substantially limited the applications of small or mini UAVs. Additionally, computationally intensive tasks impose challenges on these UAVs because of their limited processing capability and battery life [15]. Hence, novel solutions should be conceived for enhancing the UAV’s computational and communications capability [16]. Considering the limitations of a single UAV, the cooperation of multiple UAVs has been developed for improving the quality of service (QoS). The UAVs relying on sophisticated sensors can be coordinated by the ground station (GS) to fulfill specific tasks. The multi-UAV system concept was first proposed in [3] based on the flying ad hoc network (FANET) philosophy, which was later expanded in [17– 19]. Although multi-UAV networks have substantial benefits over their single-UAV counterparts, they also have numerous challenges. Taking air-to-ground (A2G) communications as an example, if each UAV of the FANET is allowed to set up a communication link with the GS, they would lead to low spectral efficiency and severe interference. Hence, some superior drones should be chosen as the gateways to coordinate communications between the UAVs and the GS. Gateway selection schemes have been widely investigated in the context of mobile ad hoc networks (MANETs) [20–25]. In [21], Leng et al. proposed a k-hop compound metric based clustering scheme for selecting the gateways of a MANET, where the host connectivity and host mobility were jointly considered. Their simulation results showed that the scheme was characterized by rapid convergence despite its low control overhead. A network parameter optimization based gateway selection

1.3 Compelling Applications of FANET

7

algorithm was proposed in [22] by Bouk et al. where multiple QoS parameters, such as the path availability period, the path’s load capacity, and latency were jointly optimized. Moreover, a fuzzy QoS balancing gateway selection algorithm was proposed by Zhioua et al. for vehicular networks [24], where the fuzzy logic was utilized for making decisions on the specific choice of the gateway relying on the received signal strength, on the traffic load of the cluster head, on the gateway candidates, and on the link connectivity duration. They showed that the fuzzy scheme outperformed the deterministic scheme in terms of its adaptability. As for gateway selection in FANETs, Luo et al. [26] proposed a distributed gateway selection algorithm relying on the dynamic network partitioning concept, which considered the influence of the network topology on the gateway selection process. Mobile edge computing (MEC) and fog computing have become promising techniques for balancing and distributing the computationally intensive tasks among resource-limited devices [27–29], since the devices can offload their tasks to cloud servers that are deployed locally in their vicinity, and the cloud servers return the final computational results to the devices. In [28], Bonomi et al. defined the characteristics of mobile edge/fog computing, which make it a suitable platform for both the IoT and big data analysis. The security and resilience of edge cloud were analyzed by Shirazi et al in [29]. Relying on MEC and fog computing, both the power consumption and execution delay of the system can be substantially reduced. However, in comparison to traditional cloud computing, the computational resources in the edge cloud are typically restricted by its local configuration. Hence conceiving efficient resource allocation becomes a critical issue in MEC, which has therefore attracted much attention [30–32]. Specifically, in [30], Sardellitti et al. proposed an iterative algorithm based on successive convex approximation for jointly allocating both the radio resources and computational resources to multiple users in a multiple-input and multiple-output (MIMO) aided MEC system. Moreover, a power-vs-delay trade-off was formulated in [31] in the context of a multi-user MEC system, where the local processing capability of devices was considered and an optimal resource allocation scheme was designed with the aid of Lyapunov optimization. The power-vs-delay trade-off problems were also studied in [32, 33] with the Lyapunov optimization framework. In [34], Liu et al. studied the delay-optimal task scheduling and resource allocation problem under specific power constraints in MEC systems, where the optimal strategy was modeled by a Markov decision process. Their scheme was capable of achieving shorter average execution delay than their benchmark schemes. The computation offloading decision, the physical resource block allocation, and the MEC computational resource allocation were integrated into an amalgamated framework and were jointly optimized in [35] by Wang et al., who achieved a better integrated performance than classic resource allocation schemes. However, the existing works are focused on the interplay between the devices and edge cloud, while ignoring the interaction between the edge cloud and the powerful remote cloud. In order to further improve the QoS performance, relying on both the flexible configuration of the edge cloud and on the more powerful computational capability of the remote cloud, a beneficial architecture combining both the edge cloud and

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1 Introduction of Flying Ad Hoc Networks

the remote cloud has been developed in [36–42]. To elaborate a little further, Gelenbe et al. [37] studied the optimal load sharing problem between a local and a remote cloud, where an optimal scheme was proposed based on the analysis of the power consumption and the computing time in the context of diverse tasks and requirements. The fairness of resource allocation problems was investigated in [39] in the heterogenous cloud context, where a multi-resource allocation mechanism was designed for guaranteeing fairness, while maintaining service isolation among the users. Moreover, the delay-bounded task offloading problem of heterogenous cloud-based systems was highlighted by Zhao et al. [40] upon considering both the wireless transmission delay and the computational execution delay. They modeled the service arrival process by the classic M/M/1 queue. Based on this model, the success probability of the delay-bounded task execution was derived both in the context of a single-user and a multi-user scenario. Finally, a total power minimization based task scheduling problem was studied by Gai et al. [42].

References 1. J. Zhang, T. Chen, S. Zhong, J. Wang, W. Zhang, X. Zuo, R. Maunder, L. Hanzo, Aeronautical ad-hoc networking for the Internet-above-the-clouds. Proc. IEEE 107(5), 868–911 (2019) 2. Y. Zhou, N. Cheng, N. Lu, X.S. Shen, Multi-UAV-Aided networks: aerial-ground cooperative vehicular networking architecture. IEEE Veh. Technol. Mag. 10(4), 36–44 (2015) 3. I. Bekmezci, O.K. Sahingoz, S. ¸ Temel, Flying ad-hoc networks (FANETs): a survey. Ad Hoc Netw. 11(3), 1254–1270 (2013) 4. Y. Saleem, M.H. Rehmani, S. Zeadally, Integration of cognitive radio technology with unmanned aerial vehicles: issues, opportunities, and future research challenges. J. Netw. Comput. Appl. 50, 15–31 (2015) 5. A.E. Gil, K.M. Passino, S. Ganapathy, A. Sparks, Cooperative task scheduling for networked uninhabited air vehicles. IEEE Trans. Aerosp. Electron. Syst. 44(2), 561–581 (2008) 6. C. Yan, L. Fu, J. Zhang, J. Wang, A comprehensive survey on UAV communication channel modeling. IEEE Access 7, 107769–107792 (2019) 7. J. Wang, C. Jiang, Z. Han, Y. Ren, R.G. Maunder, L. Hanzo, Taking drones to the next level: cooperative distributed unmanned-aerial-vehicular networks for small and mini drones. IEEE Veh. Technol. Mag. 12(3), 73–82 (2017) 8. L. Gupta, R. Jain, G. Vaszkun, Survey of important issues in UAV communication networks. IEEE Commun. Surv. Tutorials 18(2), 1123–1152 (2016) 9. M. Mozaffari, W. Saad, M. Bennis, M. Debbah, Unmanned aerial vehicle with underlaid device-to-device communications: performance and tradeoffs. IEEE Trans. Wirel. Commun. 15(6), 3949–3963 (2016) 10. Y. Zeng, R. Zhang, Energy-efficient UAV communication with trajectory optimization. IEEE Trans. Wireless Commun. 16(6), 3747–3760 (2017) 11. M. Mozaffari, W. Saad, M. Bennis, M. Debbah, Mobile unmanned aerial vehicles (UAVs) for energy-efficient internet of things communications. IEEE Trans. Wirel. Commun. 16(11), 7574–7589 (2017) 12. Y. Chen, W. Feng, G. Zheng, Optimum placement of UAV as relays. IEEE Commun. Lett. 22(2), 248–251 (2018) 13. R. Duan, J. Wang, C. Jiang, H. Yao, Y. Ren, Y. Qian, Resource allocation for multi-UAV aided IoT NOMA uplink transmission systems. IEEE Internet Things J. 6(4), 7025–7037 (2019)

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14. J. Wang, C. Jiang, K. Zhang, X. Hou, Y. Ren, Y. Qian, Distributed Q-learning aided heterogeneous network association for energy-efficient IIoT. IEEE Trans. Ind. Inf. 16(4), 2756–2764 (2019) 15. J. Wang, C. Jiang, Z. Wei, C. Pan, H. Zhang, Y. Ren, Joint UAV hovering altitude and power control for space-air-ground IoT networks. IEEE Internet Things J. 6(2), 1741–1753 (2019) 16. R. Duan, J. Wang, C. Jiang, Y. Ren, L. Hanzo, The transmit-energy vs computation-delay trade-off in gateway-selection for heterogenous cloud aided multi-UAV systems. IEEE Trans. Commun. 67(4), 3026–3039 (2019) 17. O.K. Sahingoz, Networking models in flying ad-hoc networks (FANETs): concepts and challenges. J. Intell. Robot. Syst. 74(2), 513–527 (2014) 18. S. Rosati, K. Kru˙zelecki, G. Heitz, D. Floreano, B. Rimoldi, Dynamic routing for flying ad hoc networks. IEEE Trans. Veh. Technol. 65(3), 1690–1700 (2016) 19. J. Wang, C. Jiang, Z. Ni, S. Guan, S. Yu, Y. Ren, Reliability of cloud controlled multi-UAV systems for on-demand services, in IEEE Global Communications Conference (GLOBECOM), Singapore, Dec 2017, pp. 1–6 20. H. Su, X. Zhang, Clustering-based multichannel MAC protocols for QoS provisionings over vehicular ad hoc networks. IEEE Veh. Technol. Mag. 56(6), 3309–3323 (2007) 21. S. Leng, Y. Zhang, H.-H. Chen, L. Zhang, K. Liu, A novel k-hop compound metric based clustering scheme for ad hoc wireless networks. IEEE Trans. Wirel. Commun. 8(1), 367–375 (2009) 22. S.H. Bouk, I. Sasase, S.H. Ahmed, N. Javaid, Gateway discovery algorithm based on multiple QoS path parameters between mobile node and gateway node. J. Commun. Netw. 14(4), 434– 442 (2012) 23. F. Hoffmann, D. Medina, A. Wolisz, Joint routing and scheduling in mobile aeronautical ad hoc networks. IEEE Trans. Veh. Technol. 62(6), 2700–2712 (2013) 24. G. Zhioua, N. Tabbane, H. Labiod, S. Tabbane, A fuzzy multi-metric QoS-balancing gateway selection algorithm in a clustered VANET to LTE advanced hybrid cellular network. IEEE Trans. Veh. Technol. 64(2), 804–817 (2015) 25. M. Alawi, E. Sundararajan, R. Alsaqour, M. Ismail, QoS-enable gateway selection algorithm in heterogeneous vehicular network, in IEEE International Conference on Electrical Engineering and Informatics (ICEEI), Langkawi, March 2017, pp. 1–6 26. F. Luo, C. Jiang, J. Du, J. Yuan, Y. Ren, S. Yu, M. Guizani, A distributed gateway selection algorithm for UAV networks. IEEE Trans. Emerg. Top. Comput. 3(1), 22–33 (2015) 27. Y.C. Hu, M. Patel, D. Sabella, N. Sprecher, V. Young, Mobile edge computing-a key technology towards 5G. ETSI White Paper 11(11), 1–16 (2015) 28. F. Bonomi, R. Milito, J. Zhu, S. Addepalli, Fog computing and its role in the internet of things, in ACM Proceedings of the First Edition of the MCC Workshop on Mobile Cloud Computing, Helsinki, Aug 2012, pp. 13–16 29. S.N. Shirazi, A. Gouglidis, A. Farshad, D. Hutchison, The extended cloud: review and analysis of mobile edge computing and fog from a security and resilience perspective. IEEE J. Sel. Areas Commun. 35(11), 2586–2595 (2017) 30. S. Sardellitti, G. Scutari, S. Barbarossa, Joint optimization of radio and computational resources for multicell mobile-edge computing. IEEE Trans. Signal Inf. Process. Netw. 1(2), 89–103 (2015) 31. Y. Mao, J. Zhang, S. Song, K.B. Letaief, Power-delay tradeoff in multi-user mobile-edge computing systems, in IEEE Global Communications Conference (GLOBECOM), Washington, Feb 2016, pp. 1–6 32. Z. Jiang, S. Mao, Energy delay trade-off in cloud offloading for multi-core mobile devices, in IEEE 2015 Global Communications Conference (GLOBECOM), San Diego, CA, Dec 2015, pp. 1–6 33. Z. Fang, J. Wang, J. Du, X. Hou, Y. Ren, Z. Han, Stochastic optimization aided energy-efficient information collection in Internet of Underwater Things networks. IEEE Internet Things J. (2021). https://doi.org/10.1109/JIOT.2021.3088279

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34. J. Liu, Y. Mao, J. Zhang, K.B. Letaief, Delay-optimal computation task scheduling for mobileedge computing systems, in IEEE International Symposium on Information Theory (ISIT), Barcelona, July 2016, pp. 1451–1455 35. F. Wang, J. Xu, X. Wang, S. Cui, Joint offloading and computing optimization in wireless powered mobile-edge computing systems. IEEE Trans. Wirel. Commun. 17(3), 1784–1797 (2017) 36. Z. Sanaei, S. Abolfazli, A. Gani, R. Buyya, Heterogeneity in mobile cloud computing: Taxonomy and open challenges. IEEE Commun. Surv. Tutorials 16(1), 369–392 (2014) 37. E. Gelenbe, R. Lent, M. Douratsos, Choosing a local or remote cloud, in The Second Symposium on Network Cloud Computing and Applications (NCCA), London, March 2012, pp. 25–30 38. Y. Wang, W. Shi, Budget-driven scheduling algorithms for batches of MapReduce jobs in heterogeneous clouds. IEEE Trans. Cloud Comput. 2(3), 306–319 (2014) 39. W. Wang, B. Liang, B. Li, Multi-resource fair allocation in heterogeneous cloud computing systems. IEEE Trans. Parallel Distrib. Syst. 26(10), 2822–2835 (2015) 40. T. Zhao, S. Zhou, X. Guo, Z. Niu, Tasks scheduling and resource allocation in heterogeneous cloud for delay-bounded mobile edge computing, in IEEE International Conference on Communications (ICC), Paris, July 2017, pp. 1–7 41. J. Du, L. Zhao, J. Feng, X. Chu, Computation offloading and resource allocation in mixed fog/cloud computing systems with min-max fairness guarantee. IEEE Trans. Commun. 66(4), 1594–1608 (2017) 42. K. Gai, M. Qiu, H. Zhao, Energy-aware task assignment for mobile cyber-enabled applications in heterogeneous cloud computing. J. Parallel Distrib. Comput. 111, 126–135 (2018)

Chapter 2

Communication Channels in FANET

Unmanned aerial vehicles (UAVs) have stroked great interested both by the academic community and the industrial community due to their diverse military applications and civilian applications. Furthermore, UAVs are also envisioned to be part of future airspace traffic. The application functions delivery relies on information exchange among UAVs as well as between UAVs and ground stations (GSs), which further closely depends on aeronautical channels [1]. However, there is a paucity of comprehensive surveys on aeronautical channel modeling in line with the specific aeronautical characteristics and scenarios. To fill this gap, this chapter focuses on reviewing the air-to-ground (A2G), ground-to-ground (G2G), and airto-air (A2A) channel measurements and modeling for UAV communications and aeronautical communications under various scenarios [2]. This chapter is organized as follows: We give some brief introductions of UAV communication channel characteristics in Sect. 2.1. In Sect. 2.2, the related UAV communication channels are modeled. Finally, the potential challenges and open issues of UAV channel modeling are discussed in Sect. 2.3.

2.1 UAV Communication Channel Characteristics The international civil aviation organization (ICAO) decides that UAV control and nonpayload communication (CNPC) links must operate over protected spectrum. To regulate the UAV applications, international telecommunication union (ITU) has allowed the use of certain portions of the L-band: 960–977 MHz and C-band: 5030–5091 MHz for UAS CNPC link [3]. The Ku-band downlink: 10.95–12.75 GHz and uplink: 14.0–14.47 GHz, and Ka-band downlink: 19.70–20.20 GHz and uplink: 29.5–30 GHz are authorized for beyond line-of-sight (BLOS) CNPC spectrum of satellite aeronautical safety communications. The bands of 840.5–845 MHz, 1430–

© The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2022 J. Wang, C. Jiang, Flying Ad Hoc Networks, Wireless Networks, https://doi.org/10.1007/978-981-16-8850-8_2

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1444 MHz, and 2408–2440 MHz have been approved for unmanned aircraft systems relying on LOS links by China [4]. NASA has supported major UAV projects designed for terrestrial and space missions [5]. Jet Propulsion Laboratory (JPL) developed UAV communications payload for high-rate X-band links and for battlefield broadcast in the S-band [6], supporting a maximum data rate of 45 Mbps over a range up to 100 miles in the context of full duplex links. The communication capability of aircraft will be affected by the altitude, range, receiver sensitivity, transmitter power, antenna type, coax type, and length, as well as the terrain details. Lee [7] designed the UAV link budget of long-distance 200 km for Ku-band LOS wireless link at average altitude of 3 km. They calculate the system carrier-to-noise ratio (C/N) taking account of free space loss (FSL) for different geography and weather. The link between the command and control ground station and the UAV was designed in [8] at L- and Cbands for the Ecuadorian Air Force. The rest of this section is organized as follows. In Sect. 2.1.1, we analyze the link budget and get the carrier-to-noise power radio. In Sect. 2.1.2, we consider the terrestrial shadowing attenuation in UAV air-to-ground channels. Finally, we get impulse response characteristics in LOS channels in Sect. 2.1.3.

2.1.1 UAV Link Budget Before deployment of UAVs and ground station, we should evaluate the operating distance. Considering refractive √ effects of atmospheric layers, the optical horizon do can be verified to be do = 2ke Rh. Under normal weather conditions ke = 4/3 is to consider the four-third Earth effect, that is, the actual radio wave refraction behavior is described by√an Earth with an extended radius of 4/3R. This leads to a radio horizon dr ≈ 4.12 hA (hA in m and dr in km) [9], as shown in Fig. 2.1. The formula is calibrated by a statistically measured parameter by the ITU. The same distance can also be calculated using the Pythagoras’ theorem without considering Fresnel and other parameters like above the sea level (ASL) [10]. The free space path-loss model is valid only when there is an unobstructed LOS path between the transmitter and the receiver and no objects in the first Fresnel zone. As shown in Fig. 2.2, the first Fresnel zone determines the minimum separation that should exist between the UAV and the highest obstacle in the path of the radio link. For a point at a given distance along the path of propagation, the radius of the first Fresnel zone is given as  Rm =

λdAO dOG , dAO + dOG

(2.1)

where dAO is the distance in km of the point O from UAV, dOG is √ the distance of the point O from ground station. For dAO = dAG , Rm ≈ 8.656 dAG /f . As the

2.1 UAV Communication Channel Characteristics

13

Fig. 2.1 Radio horizon distance

Fig. 2.2 First Fresnel zone for A2G link

obstruction moves towards tangent to the LOS path, signal losses will be as much as 6 dB or more. Best practice is to maintain at least 60% of the first Fresnel zone radius free of obstructions to avoid fading of the received signal. Without loss of generality, we exemplify the link budget method as presented in Table 2.1. The transmitted equivalent isotropic radiated power (EIRP) equals to sum of output power of power amplifier and antenna gain: EIRP = GT + PT . Then, the received power at receiver side is computed as, PR = GT + PT − LT − LF − LR − LA − LO + GR ,

(2.2)

where LF is free space loss for LOS communication link, LR is rain attenuation loss, LA is gaseous atmosphere loss that consists of the effects of water vapor or dry air, and LO is other fading loss. The total losses LT for uplink and downlink consist of receiver feeder loss, antenna off-axis loss, polarization mismatch loss, radome loss, transmitter loss, receiver pointing loss, and receiver cable loss.

14 Table 2.1 Link budget table for UAV link

2 Communication Channels in FANET Parameters Carrier frequency Bandwidth Distance Tx power Tx antenna gain Tx EIRP = GT +PT Tx feeder and cable Antenna off-axis Radome loss Polarization mismatch Pointing loss Rx feeder and cable Implementation loss Total losses Free space loss Rain attenuation Atmospheric gases Other losses Rx antenna gain Rx power Antenna noise Rx noise Thermal noise TN = TA + TR Noise figure Rx noise power C/N = PR − PN Receiver sensitivity Excess margin Pm = PR − PS

Expression f BN d PT GT EIRP Ltf Loa Lrd Lpm Lpt Lrf Lim LT LF LR LA LO GR PR TA TR TN FN PN C/N PS Pm

Unit GHz MHz km dBm dBi dBm dB dB dB dB dB dB dB dB dB dB dB dB dBi dBm K K K dB dBm dB dBm dB

• Free space loss LF in dB is expressed as, LF = 92.45 + 20 log f + 20 log d,

(2.3)

where f is frequency in GHz, and d is the distance in km. • Rain attenuation LR can be obtained from Recommendation ITU-R P.838 [11] and procedure described in [12]. As given typically in [13], very heavy rainfall (100 mm/h) can produce 0.4 dB/km of attenuation at 5 GHz if the rain is uniformly heavy throughout the entire signal path, which is very unlikely. For Lband, rain attenuation of 30 km distance is negligible, i.e., approximately 0.3 dB (0.01 dB/km).

2.1 UAV Communication Channel Characteristics

15

• Link attenuation LA in dB due to atmospheric gases (absorption by oxygen and water vapor) is LA = γa d,

(2.4)

where γa is the specific attenuation in dB/km, being computed for a propagation path slightly inclined, i.e., low elevation angles, assuming a temperature of 15◦C, an air pressure of 1013 hPa, and a water-vapor density of 7.5 g/m3 for a standard atmosphere. For the two LOS bands, 1000 MHz (960–977 MHz) and 5000 MHz (5030–5091 MHz), γa equals to 5.4 × 10−3 dB/km and 7.4 × 10−3 dB/km, respectively. • Losses LO due to multipath, shadowing, beam spreading, and scintillation can be examined by using the method of small percentages of time in [12] to compute the fading depth. This kind of signal fading will be investigated together with the path loss in next subsection. At the receiver, the antenna noise temperature and Rx noise temperature are set as TA and TR , respectively, resulting in equivalent noise temperature TN = TA +TR . The noise power can be calculated as, PN = k(TA + TR )BN + FN ,

(2.5)

where k = −228.6 dBW/K/Hz is Boltzmann’s constant, and downlink noise figure is FN . Finally, we can get the carrier-to-noise power ratio as C/N = PR − PN , considering the signal fading margin LO . The received power PR can be compared to the receiver sensitivity PS to evaluate the flight link margin Pm . Furthermore, for the case of amplify-and-forward (AF) relay typically in FANET, the linear C/N value received at the destination node, after two consecutive links of different C/N values: γ1 and γ2 , should be calculated as C/N = γ1 γ2 /(γ1 + γ2 ).

(2.6)

2.1.2 UAV Channel Fading From the link budget above, we can roughly divide the airborne communication channel characteristics into two types: • Large-scale fading, arising from path loss of signal as a function of distance and shadowing by large objects such as buildings and hills. • Small-scale fading, resulting from the constructive and destructive interference of the multiple signal paths between the transmitter and receiver. Multipath fading can also arise from the aircraft itself, while these are typically weak and have a very small relative delay.

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Fig. 2.3 UAV flight states of pitch, yaw, roll, and heading

Compared with mobile wireless channel, UAV air-to-ground channels will often be more dispersive, incur larger terrestrial shadowing attenuation, and change more rapidly. The channel factors include reflection, scattering, diffraction, and shadowing effects together with a direct LOS path. • Reflection occurs when the elevation angle is low enough for the main lobe of the receiving antenna to “see” the ground. • Scattering is known as another type of reflection and can occur in the atmosphere or in reflections from very rough objects [14]. • Shadowing may occur due to surface-based obstacles, such as buildings, terrain, or trees but can also occur from the aircraft itself during flight maneuvers. Reliable UAV datalinks should adapt to the associated rapidly fluctuating link quality [15]. For UAVs, we express the flight states during the maneuvering: yaw, roll, pitch, and heading, as given in Fig. 2.3. Some measured results in the literature are obtained under these conditions, which critically challenge the reliability of A2G or A2A links.

2.1.3 Channel Impulse Response and Metrics Considering the channel fading, an LOS channel with both specular and diffuse multipath is characterized by the impulse response h(t) = a0 δ(t) + a1 ej Δθ1 ej Δωd,1 (t −τ1 ) δ(t − τ1 ) +ξ(t)ej Δωd,2 (t −τ2 ) δ(t − τ2 ),

(2.7)

where a0 and a1 are the amplitude of the LOS signal component and the specular reflection, respectively; Δθ1 is the phase shift of the specular reflection relative to the LOS component; Δωd,1 and Δωd,2 are the Doppler shifts of the specular reflection and diffuse multipath, respectively, relative to the LOS component; τ1 and

2.1 UAV Communication Channel Characteristics

17

τ2 are the delays relative to the LOS component; and ξ(t) is a complex zero-mean Gaussian random process. On the other hand, the time-varying complex baseband channel impulse response (CIR) [16] can be expressed generally as follows: h(t, τ ) =



ai (t)e−j φi (t ) δ[t − τi (t)],

(2.8)

i

where ai , φi , and τi denote the time-varying amplitude, phase, and delay of i-th multipath component (MPC), respectively. The power ratio between the LOS and the diffuse components, the so-called Rice factor [17], is given by   a02 a2 K = 2 , or KdB = 10 log 02 , c c

(2.9)

where a02 is the power of LOS signal, c2 is the power of the diffuse process. Delay dispersion modeling plays an important role in channel characterization. The delay dispersion can be characterized by three parameters namely, excess delay, the mean excess delay, and root mean squared (RMS) delay spread. • Power-delay profile (PDP) characterizes the multipath fading channel giving information about channel delay, amplitude, and power of individual path. • Mean excess delay (MED) is the average of delay weighting each path by its contributing power relative to the overall power of all paths. • RMS delay spread (RMS-DS) is a power-weighted standard deviation in delay. For the PDP of 3GPPs specified rural area channel model, the RMS delay spread equals to στ = 100 ns [9]. We can quantify the delay dispersion by the RMS-DS expression as follows:   L−1 2 2  a k τk − μ2τ , στ =  k=0 L−1 2 k=0 ak

(2.10)

where L denotes the number of MPCs. The mean excess delay is given by L−1

ak2 τk μτ = k=0 . L−1 2 k=0 ak

(2.11)

When either the UAV transmitter or the receiver is in high-speed motion, Doppler frequency shift is experienced by the radio signal. Doppler spread in the frequency domain is a measure of the spectral broadening caused by the time rate of change of mobile radio channel. Doppler spread is inversely proportional to the coherence time of the channel. The RMS delay spread is inversely proportional to coherence

18

2 Communication Channels in FANET

Fig. 2.4 UAV communications channel classifications of scenarios

bandwidth. The details of coherence bandwidth and coherence time are explained in [14, 18]. Considering the diverse range of categories of UAVs including the aerial platforms like aircraft, airship, balloon [19], the measured results for civil aeronautical communication would be referable for designing UAV communication, especially for large unmanned aircrafts. If it is not particularly explained, we will employ “UAV channel” for UAV communication channel modeling and “aeronautical channel” for civil aeronautical communication channel modeling in the following text. To have an intuitive understanding of the UAV channels surveyed in this chapter, we illustrate the channel classifications in Fig. 2.4 before providing detailed channel characteristics.

2.2 UAV Communication Channel Modeling Along with the progress of embedded systems, low-power radio devices, inexpensive airframes, and the miniaturization of micro-electro-mechanical systems (MEMS), UAVs have also become affordable for hitherto unexplored scientific and commercial applications. UAVs are combined with ground control stations and data links, it forms a UAS (Unmanned Aerial System). UAS must be considered in a system context that includes the command, control, and communication (C3) system [20]. For the aerial networks of space–air–ground integrated network [4], UAVs, airships, and balloons are three primary infrastructures for constructing the hybrid aerial mobile system. Generally, large UAVs, airships, and balloons

2.2 UAV Communication Channel Modeling

19

constitute the high-altitude platforms (HAPs), while low-altitude platforms (LAPs) are dominated by cooperative small drones. The use of UAVs and other aerial devices for relay links is an emerging technology and hence requires the channel to be characterized for establishing communication links, which can be broadly classified into two aspects namely, air-to-ground (A2G) communications and airto-air (A2A) communications [21]. In order to cater to this emerging technology, we summarize the characteristics of UAV communication channel, and basically covered the possible interference and impact of the UAV communication channel in various regions. The rest of this section is organized as follows. In Sects. 2.2.1 and 2.2.2, we establish the basic communication model in different areas of A2G and A2A channels, respectively. In Sect. 2.2.3, we also analyze the UAV MIMO channel characteristics and measurement methods.

2.2.1 Air-to-Ground Channels In this subsection, based on the different areas where A2G channels possibly exist, we mainly analyze the communication channel characteristics in urban areas, low attitude in cellular networks, and rural and over-water areas.

2.2.1.1 A2G Channels in Urban Areas A model-based fading statistics analysis of UAV A2G channel in an urban area was given by Simunek [22] with low elevation angle ranging from about 1◦ to 6◦ . Their remotely controlled airship has two missions, path loss and shadowing models, respectively. Their airborne transmitter uses continuous wave signal with power of 27 dBm and a monopole antenna at 2 GHz. It stores the global positioning system (GPS) position, pitch, and roll data. A four-channel receiver for performing diversity studies is used and receiver sensitivity is −126 dBm with bandwidth of 12.5 kHz. They express the distribution of the received signal by second-order statistics, the power spectral density, and the autocorrelation function, under the Rice assumption with a strong coherent component plus a diffuse contribution. They develop a narrowband time-series synthesizer containing two main blocks: one generates the diffuse component while the other one generates the direct/coherent signal. They conclude that the Loo (Rice + log-normal) model is the most suitable for the low elevation link dynamic characteristics, which lie between the purely terrestrial and the land mobile satellite channel. The path loss and shadowing models of UAV A2G channels were investigated by Kakar [9], where the shadowing model followed the shadowing path-loss study of HAP in [23] at 2.0, 3.5, and 5.5 GHz for 3G and 4G mobile systems. The path loss is described as the sum of FSL and excessive path loss. In case of NLOS, it includes two phases of propagation: from the airborne station to the first ground obstacle and

20

2 Communication Channels in FANET

Fig. 2.5 Propagation phases of UAV A2G channels [23]

from that obstacle to the ground station, as shown in Fig. 2.5. The path losses in LOS and NLOS scenarios can be expressed as (2.12),

L=

Δh 32.45 + 20 log(f ) + 20 log(d) + ξLOS , LOS , ,d = 32.45 + 20 log(f ) + 20 log(d) + Ls + ξNLOS , NLOS sin θ (2.12)

where d is the distance in km between airborne and ground station, Ls represents a random shadowing as a function of the elevation angle. Ls is computed using the normal distribution [23], μNLOS , σNLOS =

g+θ , h + iθ

(2.13)

where θ is the elevation angle in degrees and g, h, i are empirical parameters. Random components ξLOS and ξNLOS in dB are added as a location variability utilizing the log-normal distribution with a zero mean, whereas the standard deviation is 3–5 dB, 8–12 dB for LOS, NLOS connections, respectively. A statistical propagation model was developed with ray tracing simulator in [24] to predict the A2G path loss from an LAP to a terrestrial terminal in urban environments. The virtual-city environment being similar to Manhattan follows the ITU-R statistical parameters at 700, 2000, and 5800 MHz, with elevation angles above 15◦ . Their A2G path loss has LOS condition, or without LAP LOS but coverage via strong reflection and refraction. Recently, the probabilistic LAP model

2.2 UAV Communication Channel Modeling

21

was combined with a learning-based measurement technique to help plan the UAV relay trajectory. For ultra-low altitude (0–100 m) in simplified environment from Google Sketchup at Campus Sur of Technical University of Madrid, Chu et al. [25] conducted ray tracing simulation to analyzing A2G channels with path loss, Kfactor, multipath, and delay spread at 1.2 and 4.2 GHz. They reveal that the multipath components experience progress of decreasing with height ascending. To replay the measured or simulated A2G radio channels of various scenarios in lab environment in a repeatable and controlled way, Miao et al. [26] simulated the UAV A2G channel in low altitude by ray tracer, and emulated the simulated channel in multi-probe anechoic chamber (MPAC) using over-the-air (OTA) testing techniques.

2.2.1.2 Low-Altitude Channels in Cellular Networks UAV communication is also gaining attention within the 3GPP standardization activities. The path-loss exponents and shadowing of the channel models between UAVs and LTE cellular networks were investigated at 800 MHz in [27], where flying LTE UAV-UE (user equipment) with dipole antenna was connected to two real LTE networks in Denmark. They assess the effects of heights with distances 1–22 km, elevation angles 0.25◦–2.9◦, and averaged path-loss samples and distances to obtain the least square regression to fit the log-distance alpha-beta (AB) model [28]. They conclude that, as the UAV moves up with higher UE heights, there are better radio clearance and decreasing path-loss exponent, approximating free space propagation for horizontal ranges up to tens of kilometers and UAV heights around 100 m. This finding is corroborated by increasing interference level and number of detected interfering cells. The log-AB model is, LAB = α10 log(d) + β + Xσ ,

(2.14)

where d is distance in meter, α represents the path-loss exponent, β is the intercept point with the line d = 1 m, and Xσ is a random variable that accounts for shadowing variation modeled with normal distribution and standard deviation σ . Using ultra-low-altitude (5–15 m) UAVs to deliver 5G cellular mobile services, Catherwood et al. [29] investigated the channel gain, mean time delay, and the RMS spread of the delay at three different drone heights for an open area, a treelined environment, and an enclosed area at 3.4–3.8 GHz. They find that it is Rician distributed for the received signal strength, whereas mean time delay and RMS-DS for the open and tree-lined environments are Weibull distributed with the enclosed area tests being lognormally distributed. Cellular base stations (BSs) usually feature down-tilted antennas in order to reduce the co-channel interference and to confine the cell coverage area. The propagation characteristics of cellular LTE-to-UAV channel for flying altitude at 15–120 m [30] are presented with the path loss being a function of the depression angle and the terrestrial coverage beneath the UAV. They conclude that increasing depression angle will lead to a reduction in the obstacles

22

2 Communication Channels in FANET

between the UAV and the tower and thus a reduction in the path loss, which starts to increase as the effect of down-tilted antenna pattern dominates (4◦ –8◦ ). For low-altitude A2G channel investigations, Cai et al. [31–33] investigated the path loss, shadow fading, fast fading, delay spread, and Doppler frequency spread with passive channel sounding approach for different heights (15–300 m) and horizontal distances (100–500 m) in a suburban scenario at campus of Tongji University, Shanghai. Their air part with quasi-omnidirectional packaged discone antenna onboard the six-wing UAV receives the 18 MHz bandwidth of the LTE downlink signals with a complex sampling rate of 25 MHz at the carrier frequency of 2.585 GHz. They also present physical interpretation of the UAV channels by exploiting the propagation graph modeling approach. The channel in low heights exhibits much more MPCs, and less MPCs are observed with increasing height. For horizontal and vertical flights, they modify the close-in log-distance free path-loss models respectively as Lh = 10(nh ) log(d) + Xh + Bh ,

(2.15)

Lv = 10(nd ) log(h) + Xd + Bd ,

(2.16)

where path-loss exponent nh negatively correlates with height: nh = −0.02 · h + 3.42 + nσ , the standard deviation of nσ is calculated as 0.48, nd is affected by both link distance positions and BS antenna pattern, Xh and Xd denote the shadow fading, and Bh and Bd represent the intercept. • For horizontal flights, normal distribution N (0, 2.7) is found to best fit the empirical distribution of Xh in dB. Due to the downward BS antenna radiation pattern, Rice K-factor at the height of 15 m is larger than that of the other heights from 30 to 100 m, where N (12.6, 5.1) and N (7.6, 5.6) are found to best fit their empirical distributions. Similarly, N (−7.4, 0.2) and N (−7.1, 0.3) are found to best fit delay spreads in logarithm scale for these two cases of heights. • For vertical flights, the shadow fading is similar, with N (0, 3.0) fitting the empirical distribution of Xd in dB. For positions d = 100, 200 m, and d = 300– 500 m, N (15.2, 4.7) and N (8.4, 3.8) are found to fit the empirical distributions of K-factor, respectively. For positions d = 100–400 m, and d = 500 m, N (−6.97, 0.25) and N (−7.33, 0.13) are found to fit the delay spread empirical distributions, respectively. Similarly, Qiu et al. [34] carried out vertical (0–100 m) and horizontal (20– 100 m) flight measurements in low altitudes with continuous wave transmitter installed at the lower part of a small hexacopter UAV, providing path-loss exponent at different altitudes and a height-dependent Rice K-factor model. Their two cloverleaf antennas are circularly polarized with omnidirectional radiation pattern on the horizontal plane and a 3 dB beamwidth of 60◦ and 55◦ at 1200 MHz for Lband and 4200 MHz for C-band. Their ground station antenna is vertically polarized with a gain of 3–5 dB, and its half-power beamwidth in elevation is 50◦.

2.2 UAV Communication Channel Modeling

23

2.2.1.3 A2G Channels in Rural and Over-Water Areas Recently, Matolak et al. [16, 35, 36] modeled the UAS wideband A2G channels of CNPC links under three environments: suburban and near-urban scenarios, hilly and mountainous terrains, and over-water scenario. Their elevation angles range from 1.6◦ to 40◦ , and aircraft pitch and roll angles, and aircraft heading are recorded. The path loss, small-scale fading, spatial and inter-frequency correlations for multiple aircraft antennas, RMS-DS, and wideband TDL models are investigated. The path loss is described by either log-distance with a correction for flight direction (2.17), or two-ray models (2.18). Llog = A0 + 10(ne ) log

d + X + αF d0

(2.17)

In (2.17) and (2.18), A0 are the constants at the minimum valid link distances d0 ,F

L2ray =

FE2R(d) − 20 log[a(d)], ϕmin < ϕ CE2R(d) + BL + αF − 20 log[a(d)], ϕmin < ϕ < π/2

(2.18)

denotes the small adjustment factors for direction of travel, X are zero-mean Gaussian random variables, BL is the average difference between the measured path loss and the CE2R (curved earth two-ray) model, ϕ is the grazing angle, a(d) is a unit-energy Rician fading variable, and α = −1, +1 for travel towards or away from the receiver, respectively. The FE2R (flat-earth two-ray) or CE2R models are path-loss models considering the ground roughness influence [16]. For the first two environments, the TDL models include up to nine taps, accounting for the LOS component, a ground reflection, and up to seven MPCs, whereas the intermittent rays are termed as the third ray for the over-water environment. The equation for the complex baseband CIR for the AG channels is (2.19),

h(t, τ ) =

⎧ ⎪ −j ϕ (t ) ⎪ ⎪aLOS (t)δ(τ − τ1 (t)) + a2 (t)e 2 δ(τ − τ2 (t)) ⎪ ⎪ ⎨+ 9 z (t)α (t)e−j ϕk (t )δ(τ − τ (t)), suburban k=3 k

k

k

⎪ aLOS (t)δ(τ − τ1 (t)) + a2 (t)e−j ϕ2 (t )δ(τ − τ2 (t)) ⎪ ⎪ ⎪ ⎪ ⎩+z3 (t)α3 (t)e−j ϕ3 (t )δ(τ − τ3 (t)), over-water

(2.19)

where α, ϕ, τ denote the amplitude, phase, and delay, respectively, zk ∈ {0, 1} denotes the k-th MPC on/off parameter described by the occurrence probability. The first two terms are computed from the CE2R model. They use channel stationarity distance (SD) and equal width sliding window to calculate small-scale Rice K-factor. Assuming wide-sense stationary channel, their SD is 15 m for all environments. Their measurements show that the median values of K-factor range from 12 to 14.7 dB for L-band and 27 to 30 dB for C-band in the suburban, hilly, or over-water settings, which are almost independent of link range and

24

2 Communication Channels in FANET

environment due to the presence of a strong LOS component. For the aircraft flying over mountains or hills, the ground station (GS) local terrain may still be flat, hence allowing for a strong specular reflection, and scattering as well. Multiple aircraft antennas on the bottom of the aircraft provide almost no diversity gain for the A2G channels in strong LOS conditions, for the moderate values of antenna separation. A 3-ray multipath model was employed by Lei and Rice [37] to characterize the aeronautical telemetry channel frequency responses over the Pacific Ocean. Their measurement signal of equal power tones is received by a 4 ft parabolic reflector antenna operating at 8 GHz. Their model consists of an LOS path and two reflected propagation paths. The strong specular reflection is determined by the geometry defined by the airborne transmitter, the ground-based receiver, and the sea surface. Its delay lies between 10 and 50 ns. For smaller random reflection, mean excess delay is 57 ns with an RMS-DS of 25 ns. They conclude that the roughness of seawater not only reduces the energy for both of these reflections but also causes these two paths to be less pronounced. For rough sea, short delay reflections contribute more to the second ray than longer delay reflections. For calm sea, the second reflection is more random and has a smaller amplitude and larger delay, as described in Fig. 2.6. The Rayleigh criterion is used to characterize

Fig. 2.6 Physical interpretation of multipath propagation over calm and rough sea

2.2 UAV Communication Channel Modeling

25

whether a given surface is rough or not. The sea surface is considered rough only if σr > λ/(8 cos θi ), where σr is the surface roughness, λ is the wavelength of the signal, and θi is the incident angle of the incoming wave. As altitude decreases, the incident angle increases, and thus, the sea surface appears to be with stronger specular reflections. Meng and Lee [38] conducted experimental study of A2G channels at 5.7 GHz over sea surface at the South China Sea with low airborne altitudes (0.37–1.83 km). Their wideband channel measurements use BPSK and spread-spectrum signals with a rate of 20 Mcps. A vertically polarized omnidirectional blade antenna is mounted on the head of an aircraft with an effective radiated power of 40 dBm. To create diversity receptor, their receiver uses two identical directional antennas with a beamwidth of 20◦ in azimuth and 25◦ in elevation. However, space diversity at the ground station may not be helpful for overcoming the signal obstruction induced by the aircraft body during aircraft maneuvering [39]. The path-loss exponents are estimated through the least mean square (LMS) curve fitting from measured data. Their measured results follow a similar trend to the predicted results from the 2-ray model. The typical UAV channel measurements we described above for A2G links at rural and urban scenarios, and over sea or water areas are summarized in Table 2.2. We compare them in terms of scenario, sounding, signal and channel models. The air-to-ground links have common low elevation angle down to 1◦ , which will challenge the wideband communication system performance.

2.2.1.4 Evaporation Duct for Over Sea The considerations of ducting and atmospheric gas attenuation were not accounted for in Matolak’s work [16, 40], while the measurements in [38, 41] were reported with average elevated duct height of more than 1 km, and occurrence probability of more than 10% of the time. The FSL and 2-ray models are then found to overestimate the propagation loss. The air immediately adjacent to the ocean is saturated with water vapor. When there is a temperature increase or rapid decrease in vapor pressure, the evaporation or surface ducts arise and enhance propagation for very low-altitude UAS flights over the sea [42]. The height at which the refractivity gradient equaling zero is defined as the evaporation duct height. Evaporation duct and elevated duct over the sea surface are the two important factors that can significantly affect the over-water A2G communication link, as described in Fig. 2.7. Therefore, the UAV communication with low-altitude flight should take ducting into account during the system design and application mission. The airborne transmitter heights are 0.37–1.83 km, and receiver heights are 2.10 and 7.65 m. They find that, as the airborne altitude decreases to 0.37 km, there is a huge increase (more than ten times) in the estimated RMS-DS, due to the significant evaporation ducting effect, which results in multi-reflections with longer propagation paths. Evaporation duct above the sea surface can lead to a substantial increase in the RSS at frequencies above 3 GHz, and their results show more than

Frequency 2 GHz

2.0/3.5/5.5 GHz

0.7/2.0/5.8 GHz

0.8 GHz

2.585 GHz

3.4–3.8 GHz

0.97/5 GHz

0.97/5 GHz

0.97/5 GHz

8 GHz

5.7 GHz

Literature [22]

[23]

[24]

[27]

[31]

[29]

[36]

[35]

[16]

[37]

[38]

0.37–1.83 km msl, over sea

Mountainous, hilly terrains Over sea/freshwater Rough/calm sea Geometry PDP, RMS-DS PDP, LMS curve fitting

PDP, RMS-DS

PDP, RMS-DS

PDP, RMS-DS

1.62–20.54◦

0.25–2.9◦

h: 15–300 m, d: 100–500 m h: 5–15 m

Sounding Path loss, shadowing Shadowing ITU statistical parameters Path loss, shadowing PDP, RMS-DS, Doppler PDP, RMS-DS

>15◦

0–90◦

Scenario 1–6◦

Table 2.2 UAV channel measurements and modeling for A2G links

Equal power tones (100 kHz apart) Spread-spectrum BPSK

SIMO, DS-SS

SIMO, DS-SS

SIMO, DS-SS

5G cellular

LTE downlink

Continuous wave simulation Ray tracing simulation LTE

Signal Continuous wave

FSL and 2-ray

3-Ray

Channel model Loo (Rice + log-normal) Elevation dependent channel LOS, strong reflection, refraction Log-distance alpha-beta model Close-in path-loss models Rician, Weibull, lognormal TDL: LOS, ground reflection, 7 MPCs CE2R, TDL with 9 taps CE2R, TDL 3-ray

Beachcraft C-12 airplane Learjet 35A

S-3B Viking

S-3B Viking

S-3B Viking

Commercial drone

Six-wing UAV

Commercial UAV

LAP

HAP airship

Aircraft Airship

26 2 Communication Channels in FANET

2.2 UAV Communication Channel Modeling

27

Fig. 2.7 Evaporation duct and elevated duct over the sea surface

8 dB for 50% of the propagation time at 5.7 GHz and less than 5 dB for around 15% of the time. They find that the distance-dependence of the ducting induced enhancement PE in dB is linearly modeled, and the physical variations of the ducting layers are found to be Gaussian distributed, PE = A × d + Pdo ,

(2.20)

where A is ducting coefficients on the order of 0.1 dB/km, d is distance in km, and Pdo is empirical distance-offset signal enhancement. They also find that the seawind-driven roughened sea surface would reduce the specular sea-surface reflection in a ducting environment. Without flight with UAV, the early measurement in [43] conducted the experiment at seven frequency points from 3 to 94 GHz to investigate the influence of evaporation duct. The transmitter heights are 8.5 m above average tide, and the receiver heights 10.5 m. Transmission path over sea has a length of 27.7 km. They observe that duct heights range from 1 to 12 m during more than 67% of the time, and duct height from 12–15 m during 7% of the time. No ducting conditions exist for a high percentage of time (24%). The 10.5 and 16 GHz signals have experienced the largest enhancement: more than 16 dB during 50% of the time. At 3 GHz, the enhancement factor is larger than 5 dB during 50% of the time. Enhancements larger than 10 dB are observed at 3 GHz, 5.6 GHz, 10.5 GHz, 16 GHz, 35 GHz and 94 GHz for 19%, 48%, 70%, 70%, 50% and 21% of the time, respectively. The over-the-horizon propagation path loss from 0.6 to 18 GHz was measured in [44] based only on long-term meteorological measurements in the Aegean Sea and

28

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Table 2.3 Evaporation duct works comparison Literature Scenario [43] Tx 8.5 m, Rx 10.5 m, length 27.7 km [44] Tx 4.8 m, 4.5 m; Rx: 19.2 m, 17.8 m [45] 10 m

Frequency 3–94 GHz

[38, 46]

5.7 GHz

Tx: 0.37–1.83 km

0.6–18 GHz

8 GHz

Enhancement 50% time > 16 dB, (10.5/16 GHz) 20–30 dB (7–18 GHz)

Duct heights 67% time: 1–12 m

Site Lorient France

0–40 m

Influence is negligible as wind speed 8 dB

10 m, 20 m, 30 m

Aegean Sea, North Sea Simulation

10% time: 0.9–1 km

South China Sea

North Sea area. They install transmitters at 4.5 or 4.8 m above mean sea level (msl), and receivers at from 17.8 to 19.2 m above msl. The path is 35.2 km in length and entirely over water. They give the accumulated frequency distributions of path loss by combining annual frequency distributions of evaporation duct height with the waveguide path-loss versus duct-height results. Their results show that evaporation duct is the dominant over-the-horizon propagation mechanism at frequencies above 2 GHz, and a net gain of 20–30 dB or more will be observed at 7–18 GHz. The influence of sea-surface roughness on the propagation in the duct environment was studied at 8 GHz in [45]. The authors use a Gaussian antenna pattern in experiment, and assume horizontal polarization with elevation angle 0◦ and the beamwidth 1◦ . They model propagation by the parabolic equation method. The roughness of the sea surface is computed by modifying the smooth surface Fresnel reflection coefficient by a roughness parameter. Their experiments show that, in the evaporation duct environment, relative errors between smooth sea surface and rough sea surface enlarge with the increment of sea wind speeds, operating frequencies, and evaporation duct height. Communications over maritime environment have propagation problems that are substantially different from those arising in the land environment. We present the summarized measurements and simulations for evaporation duct in Table 2.3. For this kind of elevation angle approximating 0◦ over the sea, the UAS CNPC links at ITU C-band (5030–5091 MHz) may fall into the ducting environment, especially for the UAV-aided networking.

2.2.1.5 Aircraft Shadowing in A2G Channels Wing shadowing occurs while the aircraft makes a “U-turn,” in which the LOS link will be blocked by a wing during a large roll angle, as given in Fig. 2.3. Severe shadowing could cause a total loss in link synchronization and connection. Airframe shadowing characteristics are independent of the local ground conditions

2.2 UAV Communication Channel Modeling

29

and link distance. The shorter wavelength can be blocked and reflected by the metallic aircraft body easily. C-band signal has a significantly shorter wavelength (e.g., 0.06 m at 5 GHz) as compared to very high frequency (VHF) signal (e.g., 2.4 m at 125 MHz). At elevation angles between 1.4◦ and 2.9◦, the UAS LOS signal can be easily obstructed by the airplane itself, for which Sun et al. [47] gave results of shadowing depth, duration, multiple antenna diversity gain, and small-scale fading with a medium-sized aircraft. They model shadowing loss as a function of aircraft roll angle, but it is essentially uncorrelated with shadowing duration. Median measured shadowing loss is on average 15.5 dB in C-band and 10.8 dB in L-band. Meng and Lee [48] also conducted experimental study of the shadowing effect induced by aircraft body during maneuvering for A2G communication at C-band 5.7 GHz. They carry out linear flight route and circular flight route with aircraft orientation recorded. A vertically polarized, omnidirectional blade antenna is mounted on an aircraft, and two receivers with identical directional antennas are placed separately at the ground station. Their results show that, for linear flight route with roll and pitch orientations, the original LOS link can be shadowed up to 9.5 dB by the aircraft tail or wings with slight maneuvering. Transmitted signal undergoes significant shadowing attenuation up to 28 dB with forced turning maneuvering, at an altitude of 3.2 km, link distance from 35 to 46 km. Channel measurements at 5.12 GHz for a large aircraft flying were conducted in [49] at an altitude of 11 km over a distance exceeding 100 km. They mount the antenna on the fuselage and observe the impact of the aircraft structure on the LOS path. They simulate this shadowing and find a shadowing attenuation up to 15 dB, which fits well with empirical data. The measurements of above shadowing work share the similar results. The airframe shadowing is reported to be the primary shadowing mechanism for short to medium-range A2G links. The spatial diversity at the ground station is unable to eliminate this shadowing effect caused by the aircraft during maneuvering. Deployment of multiple airborne antennas is shown helpful to mitigate this shadowing and ensure a clear communication path for all flight scenarios. Multiple aircraft antennas can provide significant diversity gain up to 16 dB in the shadowing area, and the diversity gain is typically less than 5 or 6 dB outside the shadowing region [47].

2.2.2 Air-to-Air Channels A ray tracing simulation for UAV A2A channel modeling at 2.4 GHz was performed in [50] over the land and over the sea with different altitudes. To model path loss, they perform simulations with fixed transmitter and circularly flying receiver with 100 m radius and 3 km distance. They derive the log-distance path-loss model and characterize the small-scale fading by Rician fading. The path loss computed with the transmit-receive (Tx-Rx) distances for horizontal-horizontal (H-H) and verticalvertical (V-V) polarizations is given as L = a + 10(ne ) log d, where a refers to the Y-intercept from the least squared error fit, taking values of 77.48 dB and 63.75 dB

30

2 Communication Channels in FANET

for V-V polarization at altitude 150 and 500 m over sea, respectively. The typical values for the K-factor lie between 10 to 15 dB for all the propagation scenarios. To characterize delay dispersion, they consider the excess delay of the MPCs within 6, 12, and 18 dB below the LOS component, and all the excess delayed paths arrive within 570 ns for 3 km distance and 500 m height. The RMS-DS and coherence bandwidth are compared with the OFDM guard interval and subcarrier spacing of IEEE 802.11g/n and 802.16 WiMAX, i.e., 312.5 kHz and 10.94 kHz, respectively. Their results show that the subcarrier spacing of WiMAX systems is smaller than the coherence bandwidth, while 802.11g/n systems exhibit frequency selective fading for its subcarriers. The Doppler shift differs for each MPC and depends on the direction of movement, and will affect the carrier spacing or the symbol duration. Therefore, for WiMAX system, the possible synchronization errors will result in inter-carrier interference (ICI) due to its large symbol duration. The A2A channel between fixed-wing small UAVs at C-band 5110 MHz was modeled in [51] above both ground and sea in Japan. The on-board transceiver uses time division duplexing (TDD) TDMA minimum shift keying (MSK) signal with 7 MHz bandwidth, the transmit power is 30 dBm, and the receiver sensitivity is around −95 dBm. Their vertical polarization dipole antennas have gains of 2.14 dBi. They use received signal strength (RSS) and PDP to evaluate the channels of enroute. Their channel consists of the LOS and multipath components. The first delay wave above the sea is clearer than above the ground. The maximum incoming pathdelay time above the ground at an altitude less than 700 m is within 4 μs. They also characterized the A2A channel at S-band 2.3 GHz with altitude lower than 1.5 km in Hawaii [52], where the measurements used the same type of antenna, but examined five types ground conditions: urban, suburban, trees, mountains, and over sea areas. They use OFDM signal with 20 MHz bandwidth, subcarriers spacing of 3.8147 kHz, symbol duration of 262.1 μs, and guard interval of 32.8 μs. Transmit power at antenna terminal is 20 dBm, and receiver sensitivity is −84 dBm. They calculate CIR using IFFT and then get PDPs by averaging CIRs. They reveal that ground reflection gives an impact on the CIR for over the sea, but not for over urban areas due to obstacle of tall buildings. The diffuse components spread over 40 μs in every ground type while the case of over-the-sea is less than 10 μs. The cooperative relay-based UAVs network over generalized fading channels were studied. Results show that Rayleigh fading is suitable for low-altitude crowded area, while Nakagami-m and Weibull fading with high fading parameters fit well for high-altitude open space. The measurements of an IEEE 802.11 link at 2.4 GHz in [53] extended the Rice channel model to account for multipath effects introduced by the flight altitude of UAVs. The A2A channel is characterized to have a large Doppler shift due to high speed of the UAVs, short coherence time, and large ICI. Their results show that there is a 2 dB loss for OFDM over a frequency selective Rayleigh fading channel. The typical UAV A2A channel measurements at S- and C- bands for various scenarios we reviewed above are summarized in Table 2.4. Their results of channel models and path delay will be helpful in designing link budget, transmission

2.2 UAV Communication Channel Modeling

31

Table 2.4 UAV channels measurements for A2A links Literature Frequency Altitude [50] 2.4 GHz 500– 1500 m [52]

2.3 GHz

[51]

5.06 GHz

Scenario Urban, over sea

Nj .

3.2.3 Problem Formulation In this subsection, first of all, we denote the UAV deployment strategy as A and the UAV CRRS strategy as B. Given a fixed value of N, A represents the strategy conceived for determining the N specific UAV hovering locations, while B represents the policy determining the J flight circles, including the value of Nj +1

d

Nj and Mj in each flight circle. Let Tj  k=1Vt j,k + Nj Tjh + Thome be the charging-and-discharging period of the UAV in the j -th flight circle. We assume that only one UAV can provide information services when multiple UAVs overlap in a target location. Hence, from Eq. (3.15) and Fig. 3.3, Tj also indicates the total service duration of Mj UAVs at each target point in the j -th flight circle. Moreover,

3.2 UAV Seamless Coverage Strategy for Dense Urban Areas

51

the system’s energy efficiency, where M UAVs serve a total of N target locations relying on J flight circles, can be defined as J

j =1

η(A, B) =

Nj

J

n=1 Tj Cn (R)

,

(3.17)

j =1 Mj W

where Cn (R) is the downlink capacity of the UAV hovering at the n-th target location, which is formulated by Eq. (3.5). The numerator of Eq. (3.17) shows the amount of transmitted information, while each UAV completes a charging-anddischarging operation. The denominator of Eq. (3.17) indicates the total expended energy. Observe from Eq. (3.17) that the deployment locations directly determine the capacity of UAVs, since the user density in the covered zone directly affects the capacity, but at the same time the overlapping of covered zones potentially reduces the capacity, while users connect the nearest drone. Moreover, in Eq. (3.16), Dj is jointly determined by the specific deployment locations as well as by the CRRS strategy, and the CRRS strategy in turn also determines Nj . Therefore, the deployment locations and the CRRS strategy jointly determine the number Mj of UAVs required. Hence, strategy A and strategy B jointly affect the system’s energy efficiency η. Our objective is to maximize the energy efficiency η. Hence, the joint UAV deployment as well as UAV cyclic recharging and reshuffling optimization problem can be formulated as P1 :

max η(A, B) A,B



Tjd

s.t. C1 :

Pj (t)dt ≤ W, ∀j = 1, 2, . . . , J,

0

C2 : Mj Tjh ≥ Tj > 0, ∀j = 1, 2, . . . , J,

(3.18)

C3 : Mj > Nj , ∀j = 1, 2, . . . , J, C4 :

J 

J 

Mj = M,

j =1

Nj = N.

j =1

3.2.4 Distributed Particle Swarm Optimization Aided Solution 3.2.4.1 Analysis and Simplification Considering the homogeneity of the drones, Eq. (3.17) can be rewritten as

η(A, B) =

J 

Nj

n=1 Tj Cn (R)  Tjd j =1 Mj 0 Pj (t)dt

 Td J  Mj 0 j Pj (t)dt ηj δj ,  · J j =1 Mj W j =1

(3.19)

52

3 Seamless Coverage Strategies of FANET

where ηj 

Nj

n=1 Tj Cn (R)  Tjd Mj 0 Pj (t )dt  Tjd Mj 0 Pj (t )dt J j j=1 Mj W

represents the specific energy efficiency of the j -th flight

circle, while δ 

denotes the j -th flight circle’s energy consumption

ratio against the system’s total energy. Moreover, it may be readily inferred that we have Tj = Mj Tjh in (3.15), when η reaches its maximum value. Let us define  Td the energy consumed by a UAV in the j -th flight circle as Wj  0 j Pj (t)dt. Furthermore, we have ηj =

Mj Tjh

Nj

n=1 Cn (R)

Mj Wj δj =

where at

J

j =1 δj

Nj

n=1 Cn (R)

Wj

,

Mj Wj , MW

(3.20)

(3.21)

= 1, 0 < δj ≤ 1. Upon combining Eqs. (3.13) and (3.20), we arrive

ηj = where Dj =

=

Tjh

 Wj −

Dj Vt

Pt − Pa VHa − Pd VHd

 N

j

n=1 Cn (R)

Nj Ph Wj

Nj +1 k=1

,

(3.22)

dj,k . ∂η

It can be readily seen that ∂Wjj > 0 and maximizing η(A, B), we have to satisfy

∂δj ∂Wj

> 0. Hence, for the sake of

Wj = W, ∀j = 1, 2, . . . , J.

(3.23)

Furthermore, upon relying on Eqs. (3.13), (3.15), and (3.23), we obtain Tjh = as well as ⎡

⎛

W − Pa VHa − Pd VHd − Pt Nj Ph

D

Ph Vjt + Ph Thome

Dj Vt

, j = 1, 2, . . . , J,

(3.24)

⎞⎤

⎝ + 1⎠⎥ Mj = ⎢ ⎢Nj ⎥ , j = 1, 2, . . . , J, D ⎢ ⎥ W − Pa VHa − Pd VHd − Pt Vtj

(3.25)

where · is the ceiling function representing the upper integer value. Moreover, Eq. (3.25) satisfies the constraint of C3 in the optimization problem P 1. In practice,

3.2 UAV Seamless Coverage Strategy for Dense Urban Areas

53

we can adjust the charging duration of Tcharge , which is a function of Thome , to realize the integer ceiling operation. Therefore, problem P 1 can be reformulated as P2 :

max η(A, B) = A,B

J 

ηj δj

j =1

s.t. C1 : Mj Tjh ≥ Tj > 0, ∀j = 1, 2, . . . , J, C2 :

J 

Mj = M,

j =1

where ηj = Tjh

Nj

n=1 Cn (R)/W

J 

(3.26)

Nj = N,

j =1

and δj = Mj /M.

3.2.4.2 Distributed-PSO Algorithm Design PSO is a stochastic optimization algorithm, which is inspired by the swarming behavior of collective foraging for food by birds, bees, or fish. In a PSO algorithm, M particles fly in an n-dimensional solution space, where {Xm (l) = (xm,1 (l), xm,2 (l), . . . , xm,n (l)), m ∈ {1, 2 . . . , M}} represents the position of the mth particle in the l-th iteration, while {Vm (l) = (vm,1 (l), vm,2 (l), . . . , vm,n (l)), m ∈ {1, 2 . . . , M}} represents the current velocity of the m-th particle. Assuming that the objective function of η is employed as the fitness function, each particle has a hitherto best position {Pm (l) = (pm,1 (l), pm,2 (l), . . . , pm,n (l)), m ∈ {1, 2 . . . , M}} associated with its hitherto best fitness value, while the current globally optimal position of all particles is expressed by {Pg (l) = (pg,1 (l), pg,2 (l), . . . , pg,n (l))}. In order to converge to the globally optimal position, the update functions of the velocities {Vm , m ∈ {1, 2 . . . , M}} as well as the positions {Xm , m ∈ {1, 2 . . . , M}} are formulated as ⎧ ⎪ Vm (l + 1) = wVm (l) + c1 ζ1 (Pm (l) − Xm (l)) ⎪ ⎪ ⎨ + c2 ζ2 (Pg (l) − Xm (l)), m ∈ {1, 2 . . . , M}, (3.27) ⎪ ⎪ ⎪ ⎩ Xm (l + 1) = Xm (l) + Vm (l + 1), m ∈ {1, 2 . . . , M}, where w is the so-called inertia coefficient, while c1 and c2 represent the influence of the hitherto best position and the globally optimal position, respectively. Finally, ζ1 and ζ2 are a pair of random coefficients. For solving problem P 2 in Eq. (3.26), we propose a two-stage joint optimization algorithm termed as the distributed-PSO algorithm for the UAV deployment and CRRS problem. First of all, given the fixed N-location deployment strategy A, the capacity Cn (R), n = 1, 2, . . . , N within each service circle area can be determined. Then, problem (3.26) reduces to a single-strategy optimization problem in terms of

54

3 Seamless Coverage Strategies of FANET

Algorithm 1 Distributed particle swarm optimization algorithm input: user distribution, number of target locations (N), location of charging station, UAV altitude (H ), UAV coverage radius (R), propagation parameters (ηlos , ηnlos , a, b), iteration numbers (IA , IB = OB ∗ N), particle numbers (MA , MB ); start: Randomly initialize coordinates of N target locations (strategy A) as A∗ (0); Initialize strategy B as B ∗ (0) of N flight circles; Initialize iteration count: k = 1; repeat Stage-A start: Save current best strategy A: X1A = A∗ (k − 1); A (m = 1); Randomly generate rest particles’ position:Xm Randomly generate particles’ velocity: VmA ; A )  η(X A , B ∗ (k −1)), Calculate each particle’s fitness value according to Eq. (3.17): FA (Xm m and get current PmA and PgA ; while l < IA do A according to Eq. (3.27); Update velocity VmA and particles’ position Xm Update each particles’ private best position PmA ; Update global best position PgA ; end while Update best strategy A: A∗ (k) = PgA ; Stage-A end; Stage-B start: Save current best strategy B: X1B = B ∗ (k − 1); B (m = 1); Randomly generate rest particles’ position:Xm B Randomly generate particles’ velocity: Vm ; B according to Eq. (3.28); Discrete Xm B )  η(A∗ (k), X B ), Calculate each particle’s fitness value according to Eq. (3.17): FB (Xm m B B and get current Pm and Pg ; while l < IB do B according to Eq. (3.27); Update particles’ velocity VmB and position Xm B according to Eq. (3.28); Discrete Xm Update each particles’ private best position PmB ; Update global best position PgB ; end while Update best strategy B: B ∗ (k) = PgB ; Stage-B end; Update k = k+1; until The fractional increase of the objective value over Ls iterations is below the threshold g > 0; output: Optimal strategy A and Optimal strategy B: A∗ , B ∗ .

3.2 UAV Seamless Coverage Strategy for Dense Urban Areas

55

B = {J, Nj , Mj }. Furthermore, when relying on Eq. (3.22) to (3.25), minimizing Dj yields the maximization of ηj . Let us define the shortest Dj of j -th flight circle as Dmin,j , where Dmin,j and Nj in each flight circle can be calculated for a specific assignment strategy of the N target locations, respectively. Given that ηj is a function of both Dmin,j and Nj , the single-strategy optimization problem considered can be viewed as a generalized assignment problem, which is NP-hard. We can use a powerful discrete particle swarm optimization (DPSO) algorithm for finding a near-optimal solution of the CRRS strategy given a fixed A, say B ∗ = {J ∗ , Nj∗ , Mj∗ }. We define this stage as stage-B. On the other hand, when the strategy B = {J, Nj , Mj } is given, the problem P 2 becomes a so-called point deployment problem, which is a kind of facility location problems and is NPhard. Hence, we apply the PSO algorithm for finding a near-optimal deployment strategy A∗ . We name this stage as stage-A. Upon invoking a sufficiently high number of iterations, we arrive at a near-optimal strategy {A∗ , B ∗ } of the joint UAV deployment and UAV recharging and reshuffling problem. Algorithm 1 summarizes the flow of our proposed distributed-PSO algorithm. In the algorithm, A∗ (k) and B ∗ (k) represent the current optimal strategy A∗ and B ∗ in the k-th iteration. Each iteration in the external loop includes two stages, namely stage-A and stage-B. Specifically, stage-A is composed of a PSO relying on IA number of iterations, while stage-B represents a DPSO having IB number of iterations. The algorithm ends when the fractional increase of the objective function value over Ls iterations is below the threshold g > 0. The details of the two stages are described as follows. Stage-A The objective of stage-A is to find a near-optimal strategy A in conjunction with a given fixed CRRS strategy B, which can be initialized or be calculated by the iterative result of stage-B. We use the PSO algorithm for optimizing strategy A = (x A , x A , . . . , x A ) is defined as an N-dimensional variable. A, where Xm m,1 m,2 m,N A = (x A Moreover, xm,n m,n , ym,n ) in Xm represents the horizontal coordinate of the n-th target location of the m-th particle, where we have m ∈ {1, 2, . . . , MA }, with MA representing the number of PSO particles at this stage. Furthermore, the fitness function of the PSO is η in Eq. (3.26). Stage-B The objective of stage-B is to optimize the CRRS strategy B, while the fixed A is either the original strategy or the one calculated by the iterative result of stage-A. However, the objective function is actually equivalent to that of an optimal assignment problem allocating N target locations to a total of J flight circles. In order to find the optimum relying on the B = (x B , x B , . . . , x B ) as an N-dimensional DPSO algorithm, we define Xm m,1 m,2 m,N B = j (j ∈ {1, 2, . . . , J }) indicates that the n-th target location is variable, where xm,n B assigned to the j -th flight circle. Furthermore, considering the integer nature of Xm B in our DPSO algorithm, we discretize Xm in Eq. (3.27) and use the ceiling function: B B Xm,l = Xm,l

.

(3.28)

56

3 Seamless Coverage Strategies of FANET

Additionally, considering that the choice of N may affect the convergence efficiency, the number of iterations is set to IB = OB · N, where OB represents a scaling factor. Moreover, the fitness function of the DPSO is η in Eq. (3.26).

3.2.4.3 Algorithmic Convergence Analysis The proposed Algorithm 1 has two stages, i.e., stage-A and stage-B, which are reminiscent of block coordinate descent methods, where each stage can be viewed as a block. In the algorithm, strategy A and strategy B are alternately optimized while always fixing the other strategy. Moreover, the strategies obtained in the current iteration are the input of the next iteration. In Algorithm 1, each stage adopts the PSO method, yielding a near-optimal solution. Hence, the convergence of Algorithm 1 cannot be directly analyzed by the classical block coordinate descent method, which can be proved as follows. In stage-A, the current optimal strategy A∗ (k − 1) obtained in the previous iteration is saved in the initial particles of the PSO algorithm. As for the convergence properties of the PSO algorithm, given fixed B ∗ (k − 1), we have η[A∗ (k − 1), B ∗ (k − 1)] ≤ η[A∗ (k), B ∗ (k − 1)].

(3.29)

Similarly, in stage-B, given fixed A∗ (k), B ∗ (k − 1) follows η[A∗ (k), B ∗ (k − 1)] ≤ η[A∗ (k), B ∗ (k)].

(3.30)

Hence, based on Eqs. (3.29) and (3.30), we have η[A∗ (k − 1), B ∗ (k − 1)] ≤ η[A∗ (k), B ∗ (k)].

(3.31)

Equation (3.31) points out that the objective function value of Eq. (3.26) is nondecreasing in each iteration. Since η is upper bounded by a finite value, the convergence of Algorithm 1 is guaranteed. Given that the PSO algorithm in stage-A and the DPSO algorithm in stage-B are reinitialized in each iteration, the proposed Algorithm 1 is capable of avoiding local optima. Hence, Algorithm 1 closely approximates the optimal value, even if the PSO algorithm and DPSO algorithm normally arrive at a sub-optimal solution.

3.2.4.4 Algorithmic Complexity Analysis The complexity order of the distributed-PSO algorithm can be estimated as ! " O Ig · [(IA · MA · TA ) + (IB · MB · TB )] ,

(3.32)

3.2 UAV Seamless Coverage Strategy for Dense Urban Areas Table 3.2 Simulation parameters [29, 33]

Parameters Channel parameters (ηlos , ηnlos , a, b) Carrier frequency (f ) Bandwidth (B) Variance of noise (σ 2 ) UAV transmit power (Ptr ) UAV’s altitude (H ) UAV’s coverage radius (R) UAV’s hovering power (Ph ) UAV’s flying power/speed (Pt /Vt ) UAV’s ascending power/speed (Pa /Va ) UAV’s descending power/speed (Pd /Vd ) UAV’s battery capacity (W ) Charging duration (Tcharge ) a

Table 3.3 Parameters of distributed-PSO algorithm

57 Values (1,20,9.61,0.61) 2.4 GHz 1 MHz 5 × 10−15 W/Hz 0.5 W 100 m 100 m 200 W 240 W/10 m/s 250 W/5 m/s 180 W/5 m/s 97.58 Wh 5 mina

In reality, we can replace the battery of drones for achieving a sharp reduction in charging duration

Parameters L s , g Stage-A (IA , MA , c1 , c2 , w) Stage-B (OB , MB , c1 , c2 , w)

Values 10, 10−4 (100, 100, 1.49 , 1.49, 0.729) (20, 50, 1.49, 1.49, 0.729)

where TA and TB represent each particles’ operation time in the PSO algorithm of stage-A and stage-B, respectively, while Ig is the number of iterations in the external loop of Algorithm 1. Since the number of dimensions of the particles defined as A = (x A , x A , . . . , x A ) in stage-A equals the number of the target locations Xm m,1 m,2 m,N (N), TA linearly increases with the number N. Similarly, TB linearly increases with N. Moreover, we have IB = OB · N. Hence, the complexity of Algorithm 1 can be expressed as T (N) = O(N 2 ), which obeys a polynomial complexity order (Table 3.2).

3.2.5 Simulation Results In our simulations, we consider a 500 × 500 m rectangular area, where the users are distributed following the Poissonian clustering process. The center of the rectangular service area is located at the origin [0, 0]. The essential parameters are summarized in Table 3.2 [29], where some UAV parameters are those of the drone Matrice 100 produced by DJI [33]. Table 3.3 shows the parameters of distributedPSO algorithm. The numerical simulations are developed by using MATLAB R2017a.

58

3 Seamless Coverage Strategies of FANET

3.5

x 10

5

N=3 N=4 N=5 N=6 N=7

Energy efficiency η (bit/J)

3

2.5

2

1.5

1

0.5

0 −5000

−2500

0

2500

5000

The X−coordinate of charging station (m) Fig. 3.4 Energy efficiency η versus the position of the charging station parameterized by the total number of target service locations N

Figure 3.4 shows the energy efficiency η versus the X-coordinate of the charging station (y = 0), parameterized by the total number of target service locations N. Observe from the figure that the communication energy efficiency near linearly decreases with the distance between the origin [0, 0] and the charging station. Explicitly, since Tj = Mj Tjh as well as bearing in mind Eq. (3.17), the energy efficiency η is a linear function of the hovering duration Tjh , which is in turn a nearlinear function of the distance of the charging station from the area center according to Eq. (3.24). Hence, the distance between the charging station and the center of the service area imposes a substantial impact on the deployment and cyclic recharging of the UAVs. Moreover, when the number of target service points N is increased, the energy efficiency is degraded. This is because the target service areas may overlap, which results in an energy efficiency reduction. The performance of the energy efficiency η versus the number N of target points is portrayed in Fig. 3.5, where we can see that the energy efficiency η is reduced as a function of the number of target points. Moreover, the larger the number of target points, the more slowly the rate decreases, which is a consequence of the

3.2 UAV Seamless Coverage Strategy for Dense Urban Areas

59

5

6

x 10

X−coordinate=0 X−coordinate=1000 X−coordinate=2000 X−coordinate=3000 X−coordinate=5000

Energy efficiency η (bit/J)

5

4

3

2

1

0

0

2

4

6

8

10

12

Number of target points N Fig. 3.5 Energy efficiency η versus the number of target points parameterized by the X-coordinate of charging station

linear relationship between the energy efficiency η and the hovering duration Tjh as well as the reciprocal relationship between Tjh and Nj in Eq. (3.24). As shown in Fig. 3.5, the curve associated with the scenario, when the X-coordinate of the charging station is 5000 m, is more flat than those of the others, which implies that the influence of the number of target points N on the energy efficiency η reduces, when the charging station is farther away from the origin. Figure 3.6 illustrates the influence of the total number of drones required, namely M versus the X-coordinate of the charging station, where the Y-coordinate is fixed. The figure shows that the required number of drones M nonlinearly increases when the charging station is located far away from the origin [0, 0]. More explicitly, having a long distance between the charging station and the service area results in a short hovering duration for the UAV, which determines the longest affordable reshuffling interval of the UAVs in each flight cycle and can be corroborated by Eqs. (3.24) and (3.25). Therefore, in order to guarantee that each target point is supported by a hovering UAV at any moment, more UAVs are needed.

60

3 Seamless Coverage Strategies of FANET 30

N=3 N=4 N=5 N=6 N=7

Requried number of drones M

25

20

15

10

5

0 −5000

−2500

0

2500

5000

The X−coordinate of charging station (m) Fig. 3.6 Required number of drones M versus the position of the charging station parameterized by the total number of target service locations N

Figure 3.7 shows the required number of drones M versus the number of target points parameterized by the X-coordinate of the charging station. The required number of UAVs M linearly increases with the number N of target points. Furthermore, the slope of the curves M becomes steeper as the distance between the coverage area center and the charging station becomes longer. Figure 3.8 portrays the iterative performance improvement of our proposed optimization algorithms, indicating that convergence is attained after about 70 iterations. Moreover, the subfigure in Fig. 3.8 provides an example of near-optimal results for the UAV deployment as well as for the CRRS strategy, where the blue dots show the target locations used, while the brown lines indicate the flight paths of UAVs. Finally, the red star shows the location of charging station. Explicitly, given a fixed charging station location of [500, 0] and a total of N = 5 target service

3.2 UAV Seamless Coverage Strategy for Dense Urban Areas

61

45

X−coordinate=0 X−coordinate=1000 X−coordinate=3000 X−coordinate=5000

40

Requried number of drones M

35 30 25 20 15 10 5 0 0

2

4

6

8

10

12

Number of target points N Fig. 3.7 Required number of drones M versus the number of target points parameterized by the X-coordinate of charging station

locations, we arrive at the optimal UAV deployment strategy A∗ associated with the coordinates of [−129.7, 12.91], [125.4, 88.67], [189.1, 48.11], [36.38, −63.86], and [125.4, −75.45], respectively. Furthermore, as for the optimal UAV CRRS B ∗ , a total of J ∗ = 3 independent flight route circles and M ∗ = 9 UAVs are required for covering all the 5 target locations within each flight route circle associated with N1 = 3, M1 = 5, N2 = 1, M2 = 2, and N3 = 1, M3 = 2, respectively. Figure 3.9 illustrates the convergence of the proposed algorithm associated with various PSO and DPSO parameters, where w, c1 , and c2 are set to the same values for the PSO and DPSO. The figure portrays that the change of parameters has little effect on the convergence of the algorithm, while the parameters fall into the convergence area [34]. Furthermore, the objective function values associated with

62

3 Seamless Coverage Strategies of FANET 1

N=5 N=10 N=15

0.9 Target locations Users

0.7

100

0.6

j=1

50

Charging station

Y−axis (m)

Normalized energy efficiency

0.8

0.5 0.4

0

[500 , 0] −50

j=2 j=3

−100

0.3

j = 1: N = 3, M = 5 1 1 j = 2: N = 1, M = 2 2 2 j = 3: N3 = 1, M3 = 2

−150

0.2

N = 5, M = 9, J = 3 −200 −200

0.1

−100

0

100

200

300

400

500

X−axis (m)

0 0

20

40

60

80

100

Iteration number Fig. 3.8 The performance benefits of iterations and an example of the UAV deployment and CRRS associated with N = 5, M = 9, and J = 3

various parameters all converge to a similar value, which verifies the convergence of the proposed algorithm. For benchmarking the performance of the proposed algorithm, we opt for the classic Genetic Algorithm (GA) and the classic Greedy Algorithm (GR) for both stage-A and stage-B in Algorithm 1. In the GA, the population sizes and generation numbers are the same as the particle numbers and the iteration numbers of the PSO and DPSO in Algorithm 1, while the crossover probability and the mutation probability of GA are set as Pc = 0.8 and Pm = 0.1, respectively. Figure 3.10 contrasts our results, where the position of the charging station is set to (500, 0). Observe from Fig. 3.10 that the distributed-PSO algorithm converges faster than both the GA and the GR in the context of both N = 5 and N = 10, which is because the search trajectory of PSO is better guided than that of the GA and GR as a benefit of its memory. Recall that the energy efficiency of N = 5 is much higher than that of N = 10, which is also seen in Fig. 3.5.

3.2 UAV Seamless Coverage Strategy for Dense Urban Areas

63

5

x 10 3.05

Energy efficiency η (bit/J)

(w,c ,c )=(0.729,0.5,0.5) 1 2

(w,c ,c )=(0.729,2.5,2.5) 1 2

3

(w,c ,c )=(0.1,1.49,1.49) 1 2

(w,c ,c )=(0.729,1.49,1.49) 1 2

(w,c ,c )=(0.98,1.49,1.49) 1 2

2.95

2.9 0

10

20

30

40

50

60

70

80

90

Number of iterations Fig. 3.9 Convergence analysis with different parameters at the condition of N = 3, X-coordinate = 500

3.2.6 Conclusions Providing seamless long-term coverage in emergency situations is of vital importance. In this section, we aimed for optimizing the energy efficiency of multi-UAV communication systems with the goal of providing seamless long-term coverage in urban areas. Firstly, we introduced a novel UAV energy consumption model and defined our energy efficiency objective function. Secondly, our energy-efficient rechargeable UAV deployment strategy was optimized under the constraint of providing seamless coverage. Thirdly, relying on PSO, we designed a two-stage joint optimization algorithm for finding the near-optimal deployment strategy as well as UAV CRRS. Finally, our simulation results have confirmed the convergence of the two-stage joint optimization algorithm.

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3 Seamless Coverage Strategies of FANET 5

x 10 2.5

Energy efficiency η (bit/J)

2

1.5

1

Distributed−PSO (N=5) GA (N=5) GR (N=5) Distributed−PSO (N=10) GA (N=10) GR (N=10)

0.5

0 0

20

40

60

80

100

Iteration Index Fig. 3.10 The energy efficiency performance comparison among distributed-PSO, GA, and GR

3.3 UAV Seamless Coverage Strategy for QoS-Guaranteed IoT Connecting a large number of smart devices, the promising Internet of Things (IoT) networks are capable of improving the quality of human life, which allow for automation anywhere [35, 36]. In some remote management and control scenarios, such as smart farming, the IoT nodes may be sparsely distributed, which imposes a critical challenge for data collection and diffusion. With the ever-accelerating progress of unmanned aerial vehicle (UAV) technology, UAVs have been widely applied in civilian scenarios as well as in military scenarios [1]. Due to their high flexibility and high maneuverability, UAV has been foreseen to play a key role in the IoT applications, where UAV can alternately serve IoT nodes in the context of no ground infrastructures [37, 38]. Particularly, UAV-assisted communication can provide high-quality line-of-sight (LOS) links because air–ground communications can avoid blockages of trees and buildings on the ground [39–41]. However, the limited battery capacity of a UAV limits its cruising and hovering duration, which may be difficult for providing seamless and long-term information services. Hence, how to design an effective cooperative strategy of multi-UAVs for providing seamless and long-term services becomes a crucial problem [42].

3.3 UAV Seamless Coverage Strategy for QoS-Guaranteed IoT

65

In the state of the arts, UAV-assisted communications have been widely investigated, such as UAV-assisted coverage, UAV-aided relaying, UAV-assisted IoT, etc. As for UAV-assisted information coverage, UAVs serve as aerial base stations in order to provide uplink/downlink information services for ground users [10– 12, 16, 43, 44]. Specially, for maximizing the coverage area, Hourani et al. [10] investigated the altitude optimization in various environments, while Mozaffari et al. [11] jointly analyzed the altitude and the distance between two UAVs. Lyu et al. [16] focused on the efficient deployment algorithm for multiple UAVs for the sake of minimizing the required number of UAVs covering a set of ground users. Moreover, Alzenad et al. [12] studied the high-capacity UAV deployment based on an ergodic capacity analytical model, where the user distribution and environment conditions were jointly considered. Zhao et al. [43] established a UAV-assisted network framework for emergency network recovery in disasters. Furthermore, many network technologies can be exploited in the UAV-assisted cellular network for improving the quality of services [45, 46]. As to UAV-aided relaying, UAVs were used to relay two or more distant nodes for enhancing their connectivity [20, 21, 47, 48]. To elaborate, Zhang et al. [21] studied on the energyefficient UAV-aided relaying system upon jointly optimizing the UAV trajectory and communication time while considering both the spectrum efficiency and UAV flight energy. Ono et al. [47] investigated the variable-rate relaying approach for increasing the communication rate as well as for decreasing the outage probability of a fixed-wing UAV-enabled relaying system. Li et al. [20] aimed at maximizing the energy efficiency of multi-UAV-assisted relaying system for extending the lifetime of the network, while struck a trade-off between the energy consumption and the packet success rate. Considering the communication security, Cheng et al. [48] proposed a security cache and broadcast scheme, where both the UAV trajectory and the time scheduling were optimized for maximizing the minimum average secrecy rate. In UAV-assisted Internet of Things (IoT) systems, UAVs act as mobile central nodes for collecting and diffusing data to ground sensors [31, 49–52]. Xu et al. [49] proposed an efficient energy transfer scheme for a UAV-aided wireless power transfer system in order to lengthen the lifetime of ground sensors, where the maximization of sum-energy as well as min-energy was separately achieved by optimizing the trajectory of the drone. Considering wireless power transfer in UAV-aided IoT systems, Xie et al. [50] aimed at maximizing the common throughput for a UAV-assisted IoT network jointly considering the UAV’s trajectory and transmission resource allocation, with the constraints of maximum speed of UAV and the users’ energy neutrality. Yu et al. [51] investigated the data sampling and reconstruction infrastructure for the UAV-assisted large-scale IoT system for improving the sampling accuracy and efficiency, where a spatial data sampling scheme by exploiting the cluster-based spatial data correlation was proposed. Wang et al. [31] studied the power control and hovering altitude of multiple UAVs in the context of a space–air–ground heterogeneous networks for supporting highthroughput performance for IoT applications. Furthermore, Mozaffari et al. [18] and Sharma et al. [53] further focused on the UAV-assisted device-to-device (D2D) networks and heterogeneous cellular networks, respectively. More explicitly, in [18],

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3 Seamless Coverage Strategies of FANET

Mozaffari et al. studied the deployment of UAVs for maximizing the sum-rate of the system considering both downlink users served by UAVs and D2D users, where the static UAVs and mobile UAVs were separately considered. Sharma et al. [53] considered UAVs as intermediate aerial base stations for enhancing coverage and for boosting capacity in the heterogeneous cellular networks. There have been two scenarios for studying the energy efficiency of UAV networks, namely static-UAV-aided wireless networks and dynamic-UAV-based wireless networks. In the static-UAV-aided wireless networks, many researches focused on the UAV deployment optimization, which either separately or jointly concerned the altitude as well as the horizontal position [27–29, 54]. Specifically, Alzenad et al. [27] studied the energy-efficient placement in three-dimensional (3D) space of a UAV for minimizing the transmit power as well as maximizing the number of covered users. Wang et al. [54] focused their attention on minimizing the transmit power of UAVs in downlink communication networks by properly adjusting the UAVs’ deployment. Considering the flight-time constraint of UAVs, Mozaffari et al. [28] investigated the optimal cell partitions associated with the UAVs for optimizing the system’s performance as well as the service duration of UAVs, while separately considering the fair resource allocation as well as the user requirement-based resource allocation. Furthermore, Lu et al. [29] minimized the UAV-recall-frequency (UAV-RF) by adjusting the deployment of UAVs while considering both static and time-varying user densities. By contrast, as for the dynamic-UAV-based wireless network, extensive researches concerned the flight path planning, which fully took advantage of the flexibility of the UAV, where the UAV could fly close to the users by appropriately adjusting the flight trajectory of UAVs as well as user assignment [55, 56]. Zeng et al. [57] studied the UAV trajectory optimization in UAV-assisted relaying networks and point-to-point communication networks, where only one UAV and one user were concerned. For multiple users, Wu et al. [58] proposed a convex optimization based alternate algorithm for maximizing the minimum throughput of ground users jointly considering the user communication assignment, trajectories of UAVs, and transmit power control. Furthermore, Bayerlein et al. [55] proposed a reinforcement learning method for UAV trajectory programming in order to maximize the sum-rate of the ground users. Considering heterogeneous network combined with ground base stations, both Cheng et al. [2] and Lyu et al. [59] aimed at enhancing the quality of services (QoS) for the cell-edge users by jointly optimizing the UAV flight path as well as user assignment. However, many wide-range IoT applications, such as the power control and management in smart grids, require non-intermittent communication services in some emergency situations [35]. Long-range movement as well as the limited flight duration of the UAV in some state-of-the-art contributions may cause intermittent communication, which is not capable of providing seamless and longterm information services. Motivated by these, in this section, we study the energy-efficient cooperative strategy of multiple rechargeable UAVs for supporting seamless information services for low-mobility ground IoT nodes, where the recharging operation of UAVs is considered. Since a single UAV cannot continuously serve a node because of its

3.3 UAV Seamless Coverage Strategy for QoS-Guaranteed IoT

67

Table 3.4 Summary of notations Symbol [Xc , Yc ] H M K T N μ η0 B σ2 Pmax Smax Pc Vmax dmin DI dm,k [n] Lm,k [n] qm [n] αm,k [n] pm [n] Rk

Description Horizontal coordinate of the charging station Flight altitude of UAVs Number of UAVs Number of ground IoT nodes Flight duration of the UAV Number of time slots in the flight duration Duration of a time slot Attenuation factor corresponding to the LOS UAV-node channel Bandwidth of the UAV-node channel Variance of noise of the received signal of the IoT nodes Maximum transmit power of the UAV Maximum number of simultaneously served nodes of a UAV Average cruising power of the UAV Maximum flight speed of the UAV Minimum distance for collision avoidance of the UAV Number of interval slots of departure of each UAV from the charging station Distance between the m-th UAV and the k-th node in the n-th time slot Path loss of the channel from the m-th UAV to the k-th node in the n-th time slot Horizontal position of the m-th UAV in the n-th time slot The assignment status of the channel of the m-th UAV to the k-th node in the n-th time slot The transmit power of the m-th UAV in the n-th time slot The achievable average rate of the k-th node

limited cruising duration, the cooperation of multiple UAVs can formulate a closed chain for alternately providing seamless and long-term services to IoT nodes. The rest of this section is organized as follows. In Sect. 3.3.1, the system model and the cooperative strategy of multiple UAVs are introduced. Moreover, the energy-efficient optimization problem is formulated in Sect. 3.3.2. Section 3.3.3 proposes a block coordinate descent based algorithm and proves its convergence. In Sect. 3.3.4, numerical simulation results are presented and discussed, followed by our conclusion in Sect. 3.3.5 (Table 3.4).

3.3.1 System Model As shown in Fig. 3.11, we consider a multi-UAV-aided IoT system, where M UAVs serve as aerial base stations for providing downlink data services to a set of K ground IoT nodes, and we have M > 1 and K > 1. We assume that all UAVs are homogeneous and have the same cruising duration T > 0, while cruising at the same altitude H . Because of the constrained battery capacity, all UAVs

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3 Seamless Coverage Strategies of FANET

Fig. 3.11 UAV-aided seamless coverage

start from the charging station and end at the same station when they complete the cruising mission. We consider the UAV–UAV links as LOS channels assigned with independent frequency bands. Considering the relatively sufficient capacity of UAV–UAV LOS channels, in this section we focus more our attention on the UAVnode channels with the orthogonal frequency division multiplex access (OFDMA) scheme. Furthermore, we assume that each UAV can simultaneously connect at most Smax > 1 nodes, and all UAVs share the same frequency bands. In order to provide seamless and long-term services, we propose a scheme that the IoT nodes are served by cooperation of multiple UAVs, when one UAV terminates its services, the next UAV will in turn replace the previous UAV. At the charging station, the UAV will experience three processes, i.e., vertical landing, charging, and vertical ascending. In addition, we assume that when one UAV returns to the position above the charging station, another full-energy UAV already arrives at the specific position replacing the former UAV, where multiple standby UAVs staying at the charging station can guarantee the seamless replacement. Hence, UAVs construct a closed chain in the plane of altitude H . We assume that the time interval of departure of each UAV from the charging station is the same, which is denoted by TI . Moreover, the TI can impact the performance of the system. If the TI is small, the energy efficiency may be reduced because of the large required number of UAVs. By contrast, if the TI is large, quality of services (QoS) of ground IoT nodes cannot be guaranteed because of the long waiting time of the next UAV. In addition, with the access constraint of each UAV, i.e., Smax , the required number of UAVs in service M has a lower boundary for providing seamless and long-term services to a certain number of K ground IoT nodes, which can be expressed by M ≥ max(2, Smax

).

3.3 UAV Seamless Coverage Strategy for QoS-Guaranteed IoT

69

In order to simplify the analysis, we separate the cruising duration T into N T time slots, and each time slot has the same time slice of μ = N . Assuming that the μ is smaller enough, and we can assume that UAVs are static at each time slot. The horizontal trajectories of UAVs can be expressed as Q = {qm [n] = [xm [n], ym [n]], m = 1, 2 . . . , M, n = 1, 2, . . . , N} in the Cartesian coordinate # $ system. Meanwhile, the departure interval TI can also be expressed by DI = TμI , where · indicates the ceiling operation. Then, considering M UAVs, DI can be reformulated by % DI =

& N . M

(3.33)

Since all UAVs need to cyclically return to charging station for energy supplement, the trajectories of UAVs ought to satisfy the constraints defined as follows: ⎧ ⎪ ⎪ q1 [1] = q1 [N] = [Xc , Yc ], ⎪ ⎪ ⎪ ⎪ q2 [1 + DI ] = q2 [N + DI ] = [Xc , Yc ], ⎪ ⎪ ⎨ ..., ⎪ qm [1 + (m − 1)DI ] = qm [N + (m − 1)DI ] = [Xc , Yc ], ⎪ ⎪ ⎪ ⎪ ..., ⎪ ⎪ ⎪ ⎩ qM [1 + (M − 1)DI ] = qM [N + (M − 1)DI ] = [Xc , Yc ],

(3.34)

where [Xc , Yc ] indicates the coordinate of the charging station. In addition, the flight speed constraint as well as the collision avoidance constraint of UAVs can be formulated as

qm [n + 1] − qm [n] 2 ≤ (Vmax μ)2 , ∀m, n,

(3.35)

2 , ∀m, j = m, n,

qj [n] − qm [n] 2 ≥ dmin

(3.36)

as well as

where Vmax and dmin denote the maximum flight speed and the minimum collision avoidance distance for UAVs, respectively. Furthermore, we assume that the IoT nodes are fixed at {uk = [xk , yk ], k = 1, 2, . . . , K}. Then the distance between the m-th UAV and the k-th node can be obtained by dm,k [n] =



qm [n] − uk 2 + H 2 .

(3.37)

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3 Seamless Coverage Strategies of FANET

In this section, we consider the UAV-ground channel model as LOS propagation model. Therefore, the path loss can be formulated as  Lm,k [n] = η0

4πf c

2 dm,k [n]2 ,

(3.38)

where η0 is the attenuation factor, while f and c denote the carrier frequency and the speed of light, respectively. Furthermore, we define the binary node assignment variables {αm,k [n] = {0, 1}, ∀m, k}, where αm,k [n] = 1 indicates that the k-th node is associated with the m-th UAV in the n-th time slot, and αm,k [n] = 0 otherwise. Since one UAV can simultaneously serve at most Smax IoT nodes, we have K 

αm,k [n] ≤ Smax , ∀m, n.

(3.39)

k=1

For the purpose of maintaining seamless and long-term services to all IoT nodes, each node should be served by one UAV at any time, and hence we have M 

αm,k [n] = 1, ∀k, n.

(3.40)

m=1

3.3.2 Problem Formulation Let the maximum transmit power of each UAV be Pmax . Then the instantaneous adjustable transmit power of the m-th UAV can be denoted by pm [n], where 0 < pm [n] < Pmax . Considering equal power allocation scheme [60], the allocated transmit power associated with each node can be shown as Kpm [n] , where k=1 αm,k [n] K α [n] denotes the number of connected IoT nodes of the m-th UAV in the m,k k=1 n-th time slot. Assuming each node is allocated with the same bandwidth B, then the link capacity at the n-th time slot between the m-th UAV and the k-th node can be formulated by cm,k [n] = B log2 (1 + γm,k [n]),

(3.41)

pm [n]/(Lm,k [n] · K k=1 αm,k [n]) γm,k [n] = M . 2 j =1,j =m pj [n]/Lj,k [n] + Bσ

(3.42)

where

Specifically, γm,k [n] represents the signal-to-interference-plus-noise ratio (SINR) of the k-th node, while σ 2 represents the variance of Gaussian noise at the receiver.

3.3 UAV Seamless Coverage Strategy for QoS-Guaranteed IoT

71

Then, due to the cyclical service mode of multiple UAVs, analyzing the performance in any T duration can evaluate the entire system performance. Hence, we choose the period from the time that the first (m = 1) UAV leaves the charging station to the time that the first UAV returns to the charging station after cruising. Let rm,k [n] = αm,k [n] · cm,k [n] be the instantaneous communication rate. Then, the achievable average rate of the k-th node within N time slots can be formulated by N M 1  αm,k [n] · cm,k [n] Rk = N n=1 m=1

N M 1  rm,k [n]. = N

(3.43)

n=1 m=1

Let P c be the average cruising power of each UAV, where we neglect the transmit power considering the transmit power is much less than the flight power. Then, the total energy consumption of each UAV within one flight cycle can be denoted by W = P c · T . Finally, the energy efficiency of the multi-UAV cooperation system can be formulated as K N M K rm,k [n] · μ Rk (3.44) ς = k=1 n=1 m=1 = k=1 (bit/J), M · T · Pc M · Pc where the numerator indicates the total transmitted bits and the denominator is the total energy consumption. Our goal is to maximize the energy efficiency by jointly optimizing the node assignment A = {αm,k [n], ∀m, k, n}, UAV trajectory Q = {qm [n], ∀m, n}, and UAV transmit power P = {pm [n], ∀m, n}. The optimization problem can be formulated as K max ς =

A,Q,P

s.t.

k=1 Rk

M · Pc

qm [1 + (m − 1)DI ] = qm [N + (m − 1)DI ] = [Xc , Yc ], ∀m,

(3.45a)

(3.45b)

qm [n + 1] − qm [n] 2 ≤ (Vmax μ)2 , ∀m, n,

(3.45c)

2

qj [n] − qm [n] 2 ≥ dmin , ∀m, n, j = m,

(3.45d)

K 

αm,k [n] ≤ Smax , ∀m, n,

(3.45e)

αm,k [n] = 1, ∀k, n,

(3.45f)

k=1 M  m=1

0 < pm [n] < Pmax , ∀m, n,

(3.45g)

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3 Seamless Coverage Strategies of FANET

where (3.45b) indicates that each UAV starts and ends at the charging station, i.e., charging location constraint. Equation (3.45c) is the maximum flight speed constraint, and (3.45d) indicates the collision avoidance constraint. Moreover, (3.45e) and (3.45f) are node assignment constraints, while (3.45g) constrains the transmit power of UAVs.

3.3.3 Block Coordinate Descent Based Joint Optimization In the optimization problem (3.45), {αm,k [n], ∀m, k, n} are integer variables, and thus constraints (3.45e) and (3.45f) are both integer constraints. Meanwhile, constraint (3.45d) is non-convex. Hence, the problem (3.45) is a mixed-integer nonconvex problem. For the sake of simplification, we relax the integer variables {αm,k [n], ∀m, k, n} into continuous variables {0 < αm,k [n] < 1, ∀m, k, n}. In the following, we divide the problem (3.45) into three subproblems, which can be efficiently solved.

3.3.3.1 Node Assignment Scheduling Assuming the flight trajectory Q and the transmit power control scheme P of all UAVs are determined, we can obtain the node assignment problem as K N max ς =

k=1

M

m=1 rm,k [n]

(3.46a)

M · N · Pc

A

s.t.

n=1

0 < αm,k [n] < 1, ∀m, k, n, K 

(3.46b)

αm,k [n] ≤ Smax , ∀m, n,

(3.46c)

αm,k [n] = 1, ∀k, n.

(3.46d)

k=1 M  m=1

For simplification, based upon Eqs. (3.41) and (3.42), we rewrite the cm,k [n] in rm,k [n] of problem (3.46) as 

Am,k [n]

cm,k [n] = B log2 1 + K

k=1 αm,k [n]

 ,

(3.47)

3.3 UAV Seamless Coverage Strategy for QoS-Guaranteed IoT

73

as well as pm [n]/Lm,k [n]

Am,k [n] = M

j =1,j =m pj [n]/Lj,k [n] + Bσ

2

.

(3.48)

Problem (3.46) is a non-convex problem because of its non-convex objective function with {αm,k [n], ∀m, n, k}. Here, we introduce slack variables: ⎧ ⎫ K ⎨ ⎬  A SA = Sm [n] ≥ αm,k [n], ∀m, n . ⎩ ⎭

(3.49)

k=1

A,r [n], ∀m, n} be the given SA in the r-th iteration. Given that the Let SA,r = {Sm convex function can be lower bounded by its first-order Taylor expansion, Eq. (3.47) obeys

*  r A A,r cm,k [n] ≥ cm,k [n] + cm,k [n]*S A,r [n] · (Sm [n] − Sm [n]), m

(3.50)

where  r cm,k [n]

= B log2 1 +

Am,k [n] A,r Sm [n]

 ,

(3.51)

and we have *  cm,k [n]*S A,r [n] m * ∂cm,k [n] ** = A [n] * A,r ∂Sm Sm [n] = +

(3.52)

−B · Am,k [n]

A,r [n])2 (Sm

, . A,r + Am,k [n] · Sm [n] · ln(2)

Then, based on Eqs. (3.43), (3.50), (3.51), and (3.52), we have r rm,k [n] ≥ cm,k [n] · αm,k [n] *  A,r − cm,k [n]*S A,r [n] · Sm [n] · αm,k [n] m *  A + cm,k [n]*S A,r [n] · Sm [n] · αm,k [n] m

=

lb1 rm,k [n].

(3.53)

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3 Seamless Coverage Strategies of FANET

A [n] · α Equation (3.53) is non-concave due to the third term. Moreover, Sm m,k [n] can be reformulated as A [n] · αm,k [n] Sm

=

, + A [n] + α 2 A 2 2 (Sm m,k [n]) − (Sm [n]) + (αm,k [n]) 2

(3.54) .

Then, relying on the first-order Taylor expansion of a convex function, we have its lower boundary: A A,r r (Sm [n])2 + (αm,k [n])2 ≥ (Sm [n])2 + (αm,k [n])2 A,r A A,r + 2Sm [n](Sm [n] − Sm [n]) r r [n](αm,k [n] − αm,k [n]) + 2αm,k

(3.55)

= Fm,k [n], r [n], ∀m, n, k} denotes the given node assignment in the r-th iteration. where {αm,k Hence, from (3.50) to (3.55), we obtain (a)

lb1 rm,k [n] ≥ rm,k [n]

*  r A,r ≥ cm,k [n] · αm,k [n] − cm,k [n]*S A,r [n] · Sm [n] · αm,k [n] m *  , cm,k [n]*S A,r [n] + m A (Sm + [n] + αm,k [n])2 − Fm,k [n] 2

(b)

(3.56)

lb2 [n], = rm,k

where the equalities of (a) and (b) in Eq. (3.56) are achieved when Ar = A as well as SA,r = SA . lb2 Proposition 1 rm,k [n] in the objective function of problem (3.46) is a concave A [n]) in the context of 0 < α function with regard to (αm,k [n], Sm m,k [n] < 1 and K A Sm [n] ≥ k=1 αm,k [n]. lb2 A [n]) can be formulated as [n] in (αm,k [n], Sm Proof The Hessian matrix of rm,k 

lb2 ∇ 2 rm,k [n] = cm,k

* [n]*

A,r Sm [n]

-

. 11 . 11

(3.57)

3.3 UAV Seamless Coverage Strategy for QoS-Guaranteed IoT

75

A,r Considering the constraints of (3.46b) and (3.46c), we can obtain Sm [n] > *  0, ∀m, n. Then, from Eq. (3.52), we have cm,k [n]*S A,r [n] < 0, ∀m, n, k. By introm ducing ∀x, y ∈ R, we can obtain

[x

lb2 y]∇ 2 rm,k [n]

- . *  x = cm,k [n]*S A,r [n] (x + y)2 ≤ 0. m y

(3.58)

lb2 lb2 [n] is a negative semidefinite matrix. Then, rm,k [n] Hence, the Hessian matrix of rm,k is a concave function.  

According to Eq. (3.56), the lower bound problem of (3.46) can be given by K N max ς

lb1

A,SA

k=1

=

A s.t. Sm [n] ≥

M

n=1

lb2 m=1 rm,k [n]

M · N · Pc K 

αm,k [n], ∀m, n,

(3.59a)

(3.59b)

k=1 A Sm [n] ≤ Smax , ∀m, n, M 

αm,k [n] = 1, ∀k, n,

(3.59c) (3.59d)

m=1

0 < αm,k [n] < 1, ∀m, k, n.

(3.59e)

Fortunately, problem (3.59) is a convex optimization problem, which can be efficiently solved by classical algorithms, such as interior-point method.

3.3.3.2 UAV Trajectory Planning With regard to the fixed node scheduling A and UAV transmit power P, the optimization problem (3.45) with UAV trajectory Q can be formulated as K N max ς =

k=1

n=1

Q

s.t.

M

m=1 αm,k [n] · cm,k [n]

M · N · Pc

qm [1 + (m − 1)DI ] = qm [N + (m − 1)DI ] = [Xc , Yc ], ∀m,

(3.60a)

(3.60b)

qm [n + 1] − qm [n] 2 ≤ (Vmax μ)2 , ∀m, n,

(3.60c)

2

qj [n] − qm [n] 2 ≥ dmin , ∀m, n, j = m.

(3.60d)

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3 Seamless Coverage Strategies of FANET

Problem (3.60) is non-convex because of the non-concave objective function and the constraint of (3.60d). Based on Eqs. (3.38), (3.41), and (3.42), we reformulate the cm,k [n] as ⎡



cm,k [n] = B ⎣log2 M 

+

j =1,j =m

⎛ − log2 ⎝

O · pm [n] 1 · K 2 2

qm [n] − uk + H k=1 αm,k [n] ⎞ O · pj [n] 2⎠ + Bσ

qj [n] − uk 2 + H 2 M 

j =1,j =m

where O =

 η0

1 4πf c

2

O · pj [n]

qj [n] − uk 2 + H 2

(3.61)

⎞⎤ ⎥ + Bσ 2 ⎠⎦ ,

is a constant. The first log term is convex against qm [n] −

uk 2 . Hence, referring to the first-order of Taylor expansion of a convex function r [n], ∀m, n} in the r-th iteration, we can get its lower bound, and given Qr = {qm that is, γm,k [n] = log2

+



O · pm [n] 1 · K

qm [n] − uk 2 + H 2 k=1 αm,k [n] ⎞ M  O · pj [n] + Bσ 2 ⎠

qj [n] − uk 2 + H 2

j =1,j =m

≥

r [n] Em,k

(3.62)

r [n] Cm,k r − K ( qm [n] − uk 2 − qm [n] − uk 2 ) α [n] m,k k=1

−

M 

r Cj,k [n] · ( qj [n] − uk 2 − qjr [n] − uk 2 )

j =1,j =m lb = γm,k [n]. r [n] and C r [n] can be expressed by Here, Em,k m,k r r Em,k [n] = log2 (Dm,k [n]), ∀m, n, k,

(3.63)

3.3 UAV Seamless Coverage Strategy for QoS-Guaranteed IoT

77

as well as r [n] Cm,k

=

O·pm [n] r [n]−u 2 +H 2 )2 ( qm k r [n] · ln(2) Dm,k

, ∀m, n, k,

(3.64)

where r Dm,k [n] =

O · pm [n] 1 · r [n] − u 2 + H 2 K

qm k k=1 αm,k [n] M 

+

j =1,j =m

(3.65)

O · pj [n] + Bσ 2 . r

qj [n] − uk 2 + H 2 Q

Furthermore, by introducing slack variables SQ = {Sj,k [n] ≤ qj [n] − uk 2 , ∀j = m, n, k} for the second log term of Eq. (3.61), we can obtain ψm,k [n]

⎛

= − log2 ⎝ ⎛

M 

j =1,j =m

⎞ O · pj [n] + Bσ 2 ⎠

qj [n] − uk 2 + H 2

M 

O · pj [n] Q 2 j =1,j =m Sj,k [n] + H

≥ − log2 ⎝

⎞

(3.66)

+ Bσ 2 ⎠

lb [n]. = ψm,k

Then, based upon (3.62) and (3.66), we can get the lower bound of Eq. (3.61), which can be given by lb2 lb lb cm,k [n] = B(γm,k [n] + ψm,k [n]).

(3.67)

lb2 [n] in the objective function of problem (3.60) is a concave funcProposition 2 cm,k Q

Q

Q

tion with regard to ({q1 [n], . . . , qM [n]} , {S1,k [n], . . . , Sm−1,k [n], Sm+1,k [n], . . . , Q [n]}). SM,k

Proof It is obvious that qm [n]−uk 2 is convex with regard to qm [n], and Q

O·pj [n] Q

Sj,k [n]+H 2

is log-convex with regard to Sj,k [n]. According to Eqs. (3.62), (3.66), and (3.67), lb2 [n] is composed of the negative weighted summation of convex functions. cm,k lb2 [n] is a concave function. Hence, the cm,k  

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3 Seamless Coverage Strategies of FANET

Therefore, from Eq. (3.67), the lower bound problem of (3.60) can be formulated as K,N,M max ς

Q,SQ

s.t.

lb2

=

lb2 k=1,n=1,m=1 αm,k [n] · cm,k [n]

M · N · Pc

Q Sj,k [n] ≤ qj [n] − uk 2 , ∀j = m, n, k,

qm [1 + (m − 1)DI ] = qm [N + (m − 1)DI ] = [Xc , Yc ], ∀m,

(3.68a) (3.68b) (3.68c)

qm [n + 1] − qm [n] 2 ≤ (Vmax μ)2 , ∀m, n,

(3.68d)

2

qj [n] − qm [n] 2 ≥ dmin , ∀m, n, j = m.

(3.68e)

Based on Proposition 2, we can obtain that the objective function (3.68a) is a concave function. However, due to the non-convex constraints (3.68b) and (3.68e), problem (3.68) is still non-convex. In the following, we tackle with these nonconvex constraints by using successive convex optimization techniques. Similarly, given the first-order Taylor expansion of a convex function, we have the lower boundaries [58]:

qj [n] − uk 2 ≥ qjr [n] − uk 2 + 2(qjr [n] − uk )T (qj [n] − qjr [n]), ∀j = m, n, k,

(3.69)

and r [n] 2

qj [n] − qm [n] 2 ≥ − qjr [n] − qm r + 2(qjr [n] − qm [n])T (qj [n] − qm [n]), ∀j = m, n, k.

(3.70)

Then, problem (3.68) is equivalent to max ς lb2

Q,SQ

(3.71a)

Q

s.t.

Sj,k [n] ≤ qjr [n] − uk 2 + 2(qjr [n] − uk )T × (qj [n] − qjr [n]), ∀j = m, n, k, qm [1 + (m − 1)DI ] = qm [N + (m − 1)DI ] = [Xc , Yc ], ∀m,

qm [n + 1] − qm [n] 2 ≤ (Vmax μ)2 , ∀m, n, 2 r r dmin ≤ − qjr [n] − qm [n] 2 + 2(qjr [n] − qm [n])T

× (qj [n] − qm [n]), ∀m, n, j = m.

(3.71b)

(3.71c) (3.71d) (3.71e)

3.3 UAV Seamless Coverage Strategy for QoS-Guaranteed IoT

79

According to Proposition 2 and (3.68a), the objective function of problem (3.69) is a concave function. Moreover, (3.71b), (3.71c), and (3.71e) are linear constraints, while (3.71d) is a convex quadratic constraint. Hence, problem (3.69) is a convex optimization problem, which can be solved by low computational complexity algorithms.

3.3.3.3 UAV Transmit Power Control If the node assignment A and UAV trajectory Q are fixed, the problem (3.45) associated with UAV transmit power P can be expressed by K N max ς =

k=1

m=1 αm,k [n] · cm,k [n]

(3.72a)

M · N · Pc

P

s.t.

M

n=1

0 < pm [n] < Pmax , ∀m, n.

(3.72b)

In problem (3.72), the objective function is non-concave. From Eq. (3.61), we can see that the second log term of Eq. (3.61) is concave in (p1 [n], . . . , pM [n]). Then, based on that the first-order Taylor expansion of a concave function serves its upper boundary, we obtain ⎡ lb3 [n] cm,k



= B ⎣log2

+

M  j =1,j =m

⎛

− log2 ⎝

1 O · pm [n] · K 2 2

qm [n] − uk + H k=1 αm,k [n] ⎞ O · pj [n] + Bσ 2 ⎠

qj [n] − uk 2 + H 2 M 

j =1,j =m

−

M 

⎞

O · pjr [n]

qj [n] − uk 2 + H 2

(3.73)

+ Bσ 2 ⎠

⎤

Grj,k [n] · (pj [n] − pjr [n])⎦ ,

j =1,j =m

where Grj,k [n]

=  M

O

qj [n]−uk 2 +H 2 O·pjr [n]

j =1,j =m qj [n]−uk 2 +H 2

 . + Bσ 2 · ln(2)

(3.74)

lb3 Proposition 3 cm,k [n] in the objective function of problem (3.72) is a concave function with regard to (p1 [n], . . . , pM [n]).

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3 Seamless Coverage Strategies of FANET

Algorithm 2 Joint IoT node assignment and UAV configuration algorithm Initialize [Xc , Yc ], T , μ, N, M, H , P c . Initialize f , B, η0 , σ 2 , Smax . Initialize Vmax , dmin , Pmax . Initialize A1 , SA,1 , Q1 , P1 . Set iteration indicator r := 1. repeat Step 1: Given Ar , SA,r , Qr and Pr , get the Ar+1 and SA,r+1 by solving problem (3.59). Step 2: Given Ar+1 , Qr and Pr , get the Qr+1 by solving problem (3.69). Step 3: Given Ar+1 , Qr+1 and Pr , get the Pr+1 by solving problem (3.77). until The fractional increasing value of ς is below the threshold  > 0. output: Optimal A∗ , Q∗ , P∗ .

lb3 [n] in (p [n], . . . , p [n]) is a diagonal matrix, Proof The Hessian matrix of cm,k 1 M i.e., lb3 ∇ 2 cm,k [n] = diag(a1 , a2 , . . . , am , . . . , aM ),

where am = Um,k [n] ·

K

1

k=1 αm,k [n]

(3.75)

, aj = Um,k [n], ∀j = m, and

Um,k [n] =

−



(O·pm [n]

qm [n]−uk 2 +H 2 )

K

O·pm [n]/ k=1 αm,k [n]

qm [n]−uk 2 +H 2

+

2

/ ln(2)

M

O·pj [n] j =1,j =m qj [n]−uk 2 +H 2

2 .

(3.76)

+ Bσ 2

lb3 Furthermore, the Hessian matrix of cm,k [n] is negative definite because its eigenvallb3 ues are all negative. Hence, cm,k [n] is a concave function.  

Then, according to Eq. (3.73), problem (3.72) can be lower bounded by K N max ς P

s.t.

lb3

=

k=1

n=1

M

lb3 m=1 αm,k [n] · cm,k [n]

M · N · Pc

0 < pm [n] < Pmax , ∀m, n.

(3.77a) (3.77b)

We can conclude that the problem (3.77) is a convex optimization problem, which can be solved by interior-point method.

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81

Algorithm 3 Initialization algorithm Input: N, M, K, Vmax , dmin , Pmax , Smax , [Xc , Yc ]. Q1 Initialization: 1: Get the geometric center of all ground nodes defined as Pg = [Xg , Yg ]. Y −Y 2: Get the angle θi = arctan( Xcc −Xgg ) as the origin angle of the beginning of the circular trajectory. 3: Get the angle fragment of the circular trajectory as Δθ = 2π N . √ (Yc −Yg )2 +(Xc −Xg )2 Vmax μ 4: Set the radius of the circular trajectory as R = min( , Δθ ). 2 5: Set the center of the circular trajectory as Pc = [Xc + R ∗ cos(θi ), Yc + R ∗ sin(θi )]. 6: Determine the circular trajectories of UAVs according the center Pc , starting point [Xc , Yc ], angle fragment Δθ and interval DI , which is defined as Q1 . 1 A and S A,1 Initialization: K 7: Each UAV connects M

ground nodes sequentially until all nodes are covered, which is 1 1 defined as A = {αm,k [n], ∀m, n, k}. A,1 1 8: SA,1 = {Sm [n] = K k=1 αm,k [n], ∀m, n}. P 1 Initialization: 1 [n] = P 9: P1 = {pm max /2, ∀m, n}. 1 Output: A , SA,1 , Q1 , P1 .

3.3.3.4 Algorithmic Architecture and Convergence Analysis According to the block coordinate descent method [61], Algorithm 2 illustrates an iterative algorithm for searching the optimal node assignment A∗ , UAV flight trajectory Q∗ , and UAV transmit power scheduling P∗ . In Algorithm 2, by fixing the other two variables, the A, Q, and P are alternatively optimized. In each iteration, the outputs of the three steps are served as inputs for the next iteration. Finally, the algorithm ends when the fractional increasing value of ς is within the threshold  > 0. In order to start up the process of Algorithm 2, the initialization A1 , SA,1 , Q1 , and P1 should be defined first. Since the feasible solution of a convex optimization problem may eventually converge to the optimal solution, the initialization of the strategy should satisfy the constraints, which is detailed in Algorithm 3. For the node assignment strategy A, assuming Ar and SA,r are the optimal solutions in the r-th iteration of Step 1, given fixed Qr and Pr , we have (a)

ς (Ar , Qr , Pr ) = ς lb1 (Ar , SA,r , Qr , Pr ) (b)

≤ ς lb1 (Ar+1 , SA,r+1 , Qr , Pr )

(3.78)

(c)

≤ ς (Ar+1 , Qr , Pr ),

where (a) holds since the equalities in (3.50) and (3.55) are satisfied at the local position Ar , while the equality in (3.49) is valid at the optimal position of the r-th iteration, (b) holds since Step 1 in Algorithm 2 finds the optimal solutions Ar+1 and

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3 Seamless Coverage Strategies of FANET

SA,r+1 with given Ar , SA,r , Qr , and Pr , and (c) holds since that the ς lb1 serves as a lower boundary of ς . Similarly, given fixed Ar+1 and Pr , Q follows ς (Ar+1 , Qr , Pr ) = ς lb2 (Ar+1 , Qr , Pr ) ≤ ς lb2 (Ar+1 , Qr+1 , Pr )

(3.79)

≤ ς (Ar+1 , Qr+1 , Pr ). Moreover, given fixed Ar+1 and Qr+1 , we can obtain ς (Ar+1 , Qr+1 , Pr ) = ς lb3 (Ar+1 , Qr+1 , Pr ) ≤ ς lb3 (Ar+1 , Qr+1 , Pr+1 )

(3.80)

≤ ς (Ar+1 , Qr+1 , Pr+1 ). Hence, based on (3.78), (3.79), and (3.80), we have ς (Ar , Qr , Pr ) ≤ ς (Ar+1 , Qr+1 , Pr+1 ),

(3.81)

which proves that ς in problem (3.45) is non-decreasing with the iterations of the proposed Algorithm 2. It is obvious that the value of ς has an upper boundary. Hence, we can guarantee the convergence of the proposed Algorithm 2. From this point, we can get the near-optimal solution for problem (3.45). In terms of the computational complexity of Algorithm 2, the subproblems solved in three steps are all convex optimization problems. Moreover, the time complexity of interior-point√method for solving a convex optimization problem is upper bounded by O( I ), where I indicates the number of inequality constraints [61]. Relying on problems (3.59), (3.71), and (3.77), the number of inequality constraints grows with the order of N ·M ·K. Hence, the complexity of Algorithm 2 in the worst √ case can be expressed by T (N, M, K) = O( N · M · K), which is in polynomial order.

3.3.4 Simulation Results In the simulations, we consider an area of 600 × 500 m with a charging station located at (0, 0). Moreover, the flight altitude H of UAVs is 100 m and the average cruising power P c is assumed to be 100 W, where the maximum flight speed Vmax and the maximum transmit power Pmax of UAVs are set to 10 m/s and 0.5 W, respectively. For the sake of avoiding collision, we restrict the minimum distance dmin between any two UAVs to 10 m. Furthermore, the maximum number

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83

Table 3.5 Simulation parameters [29] Parameters Channel attenuation factor (η0 ) Carrier frequency (f ) Bandwidth (B) Variance of noise (σ 2 ) Maximum transmit power of UAVs (Pmax ) Flight altitude of UAVs (H ) Average cruising power of UAVs (P c ) Maximum flight speed of UAVs (Vmax ) Minimum distance for collision avoidance (dmin ) Maximum number of simultaneously served nodes (Smax ) Time slot (μ) Stopping threshold for Algorithm 2 ()

Values 1 2.4 GHz 1 MHz 5 × 10−15 W/Hz 0.5 W 100 m 100 W 10 m/s 10 m 3 10 s 10−4

of simultaneously serving nodes of each UAV is set to Smax = 3. The stopping threshold for Algorithm 1 is defined as  = 10−4 . For the sake of clarity, our detailed parameters for the system are shown in Table 3.5. Let 0 ≤ t ≤ T indicate the flowing time, and our proposed method based upon the above settings is simulated by MATLAB R2017a. In this subsection, firstly, we analyze the resulting strategies of our proposed Algorithm 2 with regard to various characters. Secondly, the energy efficiency as well as the average throughput with various input is evaluated. Finally, the nearoptimality of our proposed Algorithm 2 is verified.

3.3.4.1 Resulting Strategies In this simulation part, we consider two situations with the achievable durations of T = 200 s and T = 120 s, where three IoT nodes (K = 3) are randomly distributed. With the time slot of μ = 10 s, we can get the number of time slots N = Tμ = 20 and N = Tμ = 12, respectively. Figure 3.12 shows the comparison of the resulting trajectories solved by Algorithm 1 for three UAVs (M = 3) with achievable durations of T = 200 s and T = 120 s. It can be seen that the three UAVs all follow a very similar trajectory in each achievable duration, even if they have the different initial time at the charging station. Figure 3.13 depicts the changing flight speed of UAV1 with time t associating with T = 200 s and T = 120 s. Since UAV2 and UAV3 have the similar speed curve with different time phases due to the similar trajectory, their

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3 Seamless Coverage Strategies of FANET

450 Node2 Node3

400

UAV1(T=200s) UAV2(T=200s) UAV3(T=200s)

350

Y-axis (m)

300

UAV2 (t=0s,T=200s)

250

Node1

200 150

UAV3 (t=0s,T=200s)

100 50 UAV1(t=0s,T=200s)

0 Charging station

-50 -100

0

100

200

300

UAV1(T=120s) UAV2(T=120s) UAV3(T=120s) 400

500

600

X-axis (m) Fig. 3.12 The UAV trajectories in the context of both T = 200 s and T = 120 s when the number of UAVs is M = 3

speed curves are omitted in the figure. From Figs. 3.12 and 3.13, it can be aware of that UAVs have stayed stationary on top of the nodes for better communications, e.g., for both durations, UAV1 has stopped on top of the node2 and node3 from t = 120 to 130 s for T = 200 and t = 50 s for T = 120 s, respectively, and UAV1 with T = 200 s has also stopped on top of node3 from t = 60 to t = 70 s. Since longer duration enlarges the mobility range, UAVs with T = 200 s can visit all nodes, but the UAVs with T = 120 s can only visit node2 and node3. Furthermore, UAVs always fly fastest when being far from the nodes, in order to save time for better services on top of the nodes. Figure 3.14 shows the designed node assignment associating with the trajectory of T = 200 s in Fig. 3.12. It can be observed that each node always has a connected UAV at any time, while the closest UAV is selected for low path loss, for example, the connected UAV of node1 handovers from UAV3 to UAV1 at the time t = 40 s, when UAV3 is farther than UAV1. Furthermore, multiple nodes will be assigned to one UAV, when the UAV is on top of a swarm of IoT nodes, e.g., UAV3 simultaneously connects node2 and node3 from t = 60 to t = 80 s. Figure 3.15

3.3 UAV Seamless Coverage Strategy for QoS-Guaranteed IoT

85

10 9

Flight speed (m/s)

8 7 6 5 4 3 2

T=200s T=120s

1 0 0

50

100

150

200

Time t (s) Fig. 3.13 The flight speed of UAV1 in the context of both {K = 3, M = 3, T = 200 s} and {K = 3, M = 3, T = 120 s}

depicts the transmit power control associating with the trajectories in Fig. 3.12 for T = 200 s as well as the node assignment in Fig. 3.14. In Fig. 3.15, UAV1, UAV2, and UAV3 alternately transmit with maximum power in order to guarantee seamless and long-term service provision to ground IoT nodes. When the UAVs disconnect from the nodes, they sharply reduce their transmit power to avoid interference on the nodes, e.g., UAV2 shuts down transmission from t = 60 to t = 80 s. The UAV trajectories with various number of UAVs are shown in Fig. 3.16, where the flight duration of each UAV is fixed at T = 200 s. From Fig. 3.16, we can see that the total length of the operation UAV trajectory obtained from Algorithm 1 becomes longer when more UAVs are exploited. Since the larger number of UAVs has smaller time interval, longer trajectories can increase the distance between adjacent UAVs to alleviate interference. Figure 3.17 portrays the iterative performance of our proposed Algorithm 1 in the context of K = 3, M = 3, T = 200 s. It can be seen that the proposed Algorithm 1 converges within about 20 iterations. And with the increasing number of iterations, the energy efficiency rapidly increases.

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3 Seamless Coverage Strategies of FANET

Index of connected UAV

3

2

1 Node1 Node2 Node3

0

50

100

150

200

Time t (s) Fig. 3.14 The performance of node assignment in the context of K = 3, M = 3, T = 200 s

0.6

UAV transmit power (W)

0.5 UAV1 UAV2 UAV3

0.4

0.3

0.2

0.1

0 0

50

100

150

200

Time t (s) Fig. 3.15 The performance of UAV transmit power in the context of K = 3, M = 3, T = 200 s

3.3 UAV Seamless Coverage Strategy for QoS-Guaranteed IoT

87

500 Node2 400

Node3

Y-axis (m)

300 200

M=3

Node1

M=5

100 0 -100

Charging station

-200 -100

0

M=7

100

200

300

400

500

600

X-axis (m) Fig. 3.16 The UAV trajectories in the context of M = 3, M = 5, and M = 7 when the flight duration of UAV is T = 200 s

3.3.4.2 Energy Efficiency Figure 3.18 depicts the changes of energy efficiency and average throughput of our system with the employed number of UAVs in the context K of T = 200 s, K = 3, where the average throughput is defined as R  k=1 Rk . In the figure, with the increasing number of UAVs, the energy efficiency reduces, but the average throughput increases by contrary. Furthermore, the growth rate of the average throughput gets slower with a larger number of UAVs. The reason is that each IoT node is served by only one UAV at any moment, even though there may be several UAVs on top of the node as the number of UAVs increases. We select one ground IoT node (K = 1) located at (500, 0) to analyze the energy efficiency and the average throughput against the flight duration T , where Fig. 3.19 shows the results. From Fig. 3.19, we can conclude that the energy efficiency and the average throughput both increase with the flight duration T as S-curves. Moreover, the energy efficiency with a few UAVs is larger than that with many UAVs, while the average throughput R is contrary and converges to the same value. This is because the UAV can fly more close to the node with the increase of the flight duration

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3 Seamless Coverage Strategies of FANET

5500

Energy efficiency (bit/J)

5000

4500

4000

3500

3000

0

10

20

30

40

50

Iteration index Fig. 3.17 The convergence performance of Algorithm 1 in the context of K = 3, M = 3, T = 200 s

10 3

6000

6

Energy efficiency (bit/J)

Energy efficiency Average throughput 5000

2.5

4000

2

3000

1.5

2000

1 2

3

4

5

6

7

Number of UAVs M Fig. 3.18 The performance of both energy efficiency and average throughput versus the number of UAVs in the context of K = 3, T = 200 s

3.3 UAV Seamless Coverage Strategy for QoS-Guaranteed IoT

89

Fig. 3.19 The performance of both energy efficiency and average throughput versus the flight duration T of UAVs in the context of K = 1

T . Moreover, there will always be a UAV on top of the ground node to provide seamless services when the flight duration T is sufficiently large, and then the energy efficiency as well as the average throughput will stabilize according to Eqs. (3.43) and (3.44). Furthermore, the energy efficiency and the average throughput with many UAVs reach the ceiling value earlier than that with a few UAVs, as the flight duration T increases. Figure 3.20 compares the performance of the optimal energy efficiency among three trajectory designs with the same flight altitude H = 100 m, i.e., the static UAV scheme, the circular trajectory scheme, and the proposed trajectory scheme. In the static UAV scheme, all UAVs are fixed on the geometric center of all ground IoT nodes, and only one UAV transmits with maximum power at any time. In the circular trajectory scheme, the trajectories of UAVs are a same circle passing through the node1, the center of node2, node3, and the charging station from the 2D down-look view, where the corresponding node assignment and transmit power are jointly optimized according to Step 1 and Step 3 in Algorithm 1, respectively. From Fig. 3.20, for all three schemes, the energy efficiency decreases with the number of UAVs. Moreover, the proposed trajectory scheme gets better achieved

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3 Seamless Coverage Strategies of FANET

6000 Proposed trajectory Circular trajectory Static UAV

Energy efficiency (bit/J)

5000

4000

3000

2000

1000

0 2

3

4

5

6

7

Number of UAVs M Fig. 3.20 The performance of energy efficiency versus number of UAVs in terms of different trajectory schemes in the context of K = 3, T = 200 s

energy efficiency than both circular trajectory scheme and static UAV scheme for all number sets of UAVs, where the achieved energy efficiency for static UAV scheme is between 4.24 and 14.86 bit/J.

3.3.4.3 Optimality Analysis In order to verify the near-optimality of our proposed solution, we have exploited the ergodic search (ES) method to find the near-optimal solution of our problem, where the search step size of the way points in the trajectory is represented by g. In the ES method, the transmit power of the UAV is fixed at Pmax when the UAV is associated with the ground node, otherwise the transmit power is zero. The optimal node assignment in the ES method is determined by binary ergodic searching. Generally, the smaller the search step size g is, the closer to the optimal solution the result of the ES method will be. Considering the exponential time complexity of the ES method, we compare our proposed Algorithm 1 with the ES method with small-score examples in Fig. 3.21. Moreover, the control scheme of the transmit power of UAV in our proposed method is the same with the ES method because the UAV is far from the ground nodes in small-score trajectories. Then, from Fig. 3.21, we can observe that the iterative value of our proposed Algorithm 1 can reach the

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91

Fig. 3.21 The near-optimality convergence of Algorithm 1 in the context of different K, M, N

near-optimal value within a reasonable number of iterations, which have verified the near-optimality of our proposed solution.

3.3.5 Conclusions Supporting seamless and long-term information services by employing multiple UAVs gains important significance. Considering the limited cruising duration of the UAV, we investigated the cooperative strategy of multiple rechargeable UAVs in order to provide seamless and long-term information coverage to ground IoT nodes. In this section, a joint node assignment and UAV configuration optimization problem has been proposed for the energy efficiency maximization of the system. Since the problem was a mixed-integer non-convex problem, we divided the problem into three subproblems associating with node assignment scheduling, trajectory planning of UAVs, and transmit power control, respectively. Then, based on the sequential convex optimization techniques, we solved the subproblems by reformulating non-convex problems into convex optimization problems. For the

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3 Seamless Coverage Strategies of FANET

sake of maximizing the energy efficiency, we proposed a block coordinate descend based iterative algorithm. Simulation results showed that the proposed trajectory scheme got better energy efficiency than both circular trajectory scheme and fixed UAV scheme, and the average throughput of the system increased with the number of employed UAVs. Moreover, the convergence of the proposed algorithm has been verified.

3.4 UAV Seamless Coverage Strategy for Minimum-Delay Placement Given their agility, the on-demand deployment, and the bird’s-eye perspective of unmanned aerial vehicles (UAVs) [62], they have been exploited in diverse military and civilian areas. Particular to wireless networking, the decreasing cost and increasing sophistication of consumer UAVs combined with miniaturization of BS electronics have made it technically feasible to deploy base stations (BSs) on flying UAVs [63]. In practice, UAVs may carry BSs for supporting emergency communications in scenarios, where the communications infrastructure is destroyed [43] and for assisting the terrestrial cellular network in remote areas and at hotspots (e.g., stadiums) [64]. In order to further exploit the potential of this threedimensional (3D) infrastructure, extensive research contributions have been made in air–ground channel modeling [65–67], propulsion power conservation [68], and link-level implementations [69–71]. Among the design metrics in UAV-enabled communications systems, the placement and trajectory planning of UAVs play a crucial role [72]. The existing research contributions to UAV communications mainly focus on the static networks, where a set of constant throughput values are required by the users. In practice, however, the wireless tele-traffic may vary extensively over time, which leads to dynamically fluctuating queuing delay for the users. Therefore, it is imperative to address these wireless tele-traffic dynamics by conceiving a dynamic aerial BS (ABS) placement scheme relying on a cross-layer perspective. Bearing in mind that the attainable throughput is directly dependent on the distance-related path loss [73], we may resort to dynamically adjusting the distances between the ABS and the devices supported for the sake of adapting their transmission throughput to the prevalent wireless tele-traffic dynamics. Intuitively, the ABS can be moved close to the devices, which have numerous queuing packets in their buffers. However, this may increase the delay of other devices. Therefore, it is desirable to propose an appropriate dynamic ABS placement strategy for minimizing the average queuing delay of the overall network. The investigations specific to UAV communications concerning the queuing delay are still in their infancy in the open literature. Concretely, based on the analytical results obtained from queuing theory, a resource allocation scheme was proposed for UAV-aided networks for minimizing the time-averaged queuing delay [74]. The knowledge of

3.4 UAV Seamless Coverage Strategy for Minimum-Delay Placement

93

the instantaneous wireless traffic was not exploited in this scheme, which inevitably limited the system performance attained. A dynamic trajectory control algorithm was conceived for multi-UAV-enabled networks [75], where the adjacent UAVs were moved one step closer to the specific UAV, whose queue length is higher than a pre-set threshold. However, since this threshold was not optimized, the proposed system was incapable of attaining the minimum delay. A queue-lengthaware trajectory design of UAV-mounted computing nodes was proposed for serving multiple devices having limited computational capability [76], while relying on the classic Lyapunov optimization theory [77]. These impressive studies inspired us to pursue the minimum-delay design of UAV-enabled networks using the MDP approach. Against this background, we have conceived a dynamic ABS placement scheme for minimizing the queuing delay of UAV-enabled networks. Specifically, the placement of the ABS is dynamically adjusted for adapting the distance-dependent transmission throughput in response to the fluctuating wireless tele-traffic dynamics. As a benefit, the average queue length in the buffer can be minimized. Given that the dynamic fluctuation of wireless tele-traffic is considered, we have investigated three different scenarios. Explicitly, the first one is when the tele-traffic is predictable [78]. The second one is when the specific probability density function of the packet arrival process is known by the ABS [79], while in the third case neither the exact number of arriving packets nor its statistical knowledge is known by the ABS. For each scenario, we have provided a specific dynamic ABS placement strategy for minimizing the average queuing delay. The rest of this section is organized as follows. In Sect. 3.4.1, the system model and ABS placement scheduling are introduced. And the problem is formulated in Sect. 3.4.2. In Sect. 3.4.3, we discuss the Markov decision process and the transformation conditions. Then, in Sect. 3.4.4, we propose backward induction and reinforcement learning method to solve the MDP problem. Finally, we give the simulation results in Sect. 3.4.5 and conclude in Sect. 3.4.6.

3.4.1 System Model As illustrated in Fig. 3.22, we consider the uplink of a UAV-enabled network in a 3D Cartesian coordinate system, where a single-antenna rotary-wing ABS1 maintaining aloft serves K devices on the ground over T time slots (TSs).2 We assume that the ABS is linked with the core network via terrestrial base stations using high-capacity 1

This section aims for verifying the effectiveness of the proposed delay-minimum ABS placement strategies in a single-ABS scenario. Multi-ABS systems can be realized by appropriately designing both the user association and the resource management with the aid of a multi-agent MDP framework, which is beyond our current scope. 2 In this section, the locations of the ground users are assumed to be static for simplicity, which is applicable to the nodes of wireless sensor networks.

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Fig. 3.22 Illustration of the system model. A UAV-enabled network comprises an ABS located at (ux , uy , h) and a number of devices located at (dxk , dyk , 0). Each device is equipped with a buffer for storing its queuing packets. The movement of the ABS follows the rule as depicted in the top-right figure

millimeter-wave communications [80]. The backhaul link is assumed to be capable" ! of fully supporting the ABS-enabled network. We use U [t] = ux [t], uy [t], h[t] and (dxk , dyk , 0) to represent the coordinates of the ABS at the t-th TS and of the k-th device, respectively. Each TS lasts τ seconds. The whole spectrum is partitioned into K non-overlapping equal-bandwidth subchannels, while each device is connected to the network via a single subchannel relying on the classic frequency division multiple access (FDMA). Each device is equipped with a buffer for storing its queuing packets to be transmitted. The placement of the ABS is updated on the temporal basis of a TS. In the following, we detail the system model from the perspectives of the physical layer as well as of the wireless tele-traffic dynamics and then formulate a minimum average-delay ABS placement problem.

3.4.1.1 Physical Layer Model of the UAV-Enabled Network Here we assume that the channel between the ABS and devices obeys the probabilistic LoS model, where the link can be either of LoS or of non-LoS (NLoS) nature. The probability of the LoS link is given by Al-Hourani et al. [67] 1 k / 0, PLoS = 1 + ψ exp − β(θk − ψ)

(3.82)

where ψ and β are constant values that are determined ! ] "by the carrier frequency and denotes the elevation angle, × sin−1 Dh[t the surrounding environments, θk = 180 π k [t ] ! "2 ! "2 and Dk [t] = ux [t] − dxk + uy [t] − dyk + h[t]2 corresponds to the distance

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between the ABS and the k-th device at the t-th TS. Then, the NLoS probability can k k be calculated as PNLoS = 1 − PLoS . Hence the channel gain between the ABS and the k-th device at the t-th TS is readily given by −1 1 2−2  k k PLoS , μLoS + PNLoS μNLoS gk [t] = Dk [t]

(3.83)

c where we have  = 4πf c , fc and c represent the carrier frequency and the speed of light, respectively, and μLoS and μNLoS are the attenuation ! factors considered " for LOS and NLOS links, respectively. Here we use G[t] = g1 [t], . . . , gK [t] to denote the channel state information (CSI) between the ABS and these K devices. For the sake of simplicity, we assume that an idealized-capacity-achievingcoding scheme [81] is invoked and that the coordinates of the ABS and those of the devices are perfectly known. Then, the transmission rate of the communications link between the ABS and the k-th device at the t-th TS is given by

  Pt gk [t] Rk [t] = B log2 1 + , Bσ 2

(3.84)

where B, Pt , and σ 2 denote the subchannel bandwidth, the transmit power, and the power spectral density of the zero-mean white Gaussian noise at the receiver, respectively.

3.4.1.2 Queuing Model and System Dynamics The number of packets in the buffer (also termed by the queue length) at the beginning of the (t + 1)-th TS is jointly determined by the queue length at the beginning of the t-th TS as well as by the number of arriving and departing packets during the t-th TS. Here let us denote the number of the k-th device’s arriving packets during the t-th TS by Bk [t]. We assume that the packet arrival process is independent and identically distributed (i.i.d.) over the TSs and its mean value is denoted by λk = E{Bk [t]}, for ∀k ∈ {1, 2, . . . , K}. Here we use Qk [t] to denote the ! queue length of"the k-th device at the beginning of the t-th TS and Q[t] = Q1 [t], . . . , QK [t] to represent the joint queue length state information (QSI) for these K devices. More particularly, Qk [t] evolves by obeying the equation below: Qk [t + 1] = min

1

Qk [t] −

2 Rk [t]τ + + Bk [t], NQ , Nk

(3.85)

for ∀t ∈ {0, 1, . . . , T − 1}, where we define x + = max(x, 0), Nk is the packet size of the k-th user, and NQ represents the maximum number of packets that can be stored in the buffer. Without loss of generality, we assume Qk [0] = 0, for ∀k ∈ {1, 2, . . . , K}.

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3.4.1.3 ABS Placement Scheduling The ABS is equipped with a placement scheduler, which is capable of dynamically adjusting its placement in accordance with the joint CSI and QSI on the temporal basis of a time slot τ . Specifically, we realize the scheduling strategy relying on a 3D grid associated with the horizontal basis of δh = vh τ and with the vertical basis of δv = vv τ , where vh and vv represent the horizontal and vertical velocity of the ABS, respectively. As depicted in Fig. 3.22, at each TS, the ABS can be scheduled to stay at the previous location or to move to one of its six surrounding points on the grid.3

3.4.2 Problem Formulation Our minimum-delay ABS placement problem is formulated under the following constraints: • Power consumption constraint: since the ABS is typically equipped with a capacity-limited battery [72], our proposed scheduling scheme has to satisfy a realistic energy consumption constraint. Specifically, the total energy consumption of the ABS is the sum of both the communications-related and decision-making signal processing dissipation as well as of the mechanical propulsion. Here let us use Et ot to represent the total energy in the battery of the ABS. We denote its power consumption of communications, horizontal movement, vertically up movement, vertically down movement, maintaining aloft, and decision-making by Pc , Pmh , Pmv+ , Pmv− , Ph , and Pd , respectively. To elaborate, Pc represents the power consumption on communications, including the carrier frequency down conversion, power amplifying, and baseband signal processing; if the ABS stays at the previous location, its power consumption on mechanical propulsion is given by Ph , whereas if the ABS moves from the previous location to one of four possible locations in the same horizon, its power consumption on mechanical propulsion is formulated by Ph + Pmh ; if the ABS moves one step vertically up, the power consumption on mechanical propulsion is Ph +Pmv+ . To this end, we may formulate the average power constraint as (3.88) in the next page, where we define Pavg = ETtotτ − Ph − Pc − Pd and the operations as ⎧ ⎨x, if x > 0, (3.86) (x)+ = ⎩0, otherwise,

3 Without any loss of generality, our proposed framework and solutions are also applicable to the ABS scheduling strategies that are based on more complex movement patterns, e.g., following the hexagonal grid, where the delay can be further reduced.

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and ⎧ ⎨|x|, if x < 0, (x)− = ⎩0, otherwise.

(3.87)

* * *4 3 ** T ux [t] − ux [t − 1]* *uy [t] − uy [t − 1]* Pmh  E + T δh δh t =1

"+ 4 "− 4 3! 3! T T h[t] − h[t − 1] h[t] − h[t − 1] Pmv+  Pmv−  + E E + T δv T δv t =1

t =1

≤ Pavg .

(3.88)

• Grid constraint: The ABS dynamically moves among the points on the grid associated with the basis of {δh , δv }. Hence, at each TS, the coordinate of the ABS has to satisfy the constraint ux [t] ∈ {x, . . . , −δh , 0, δh , . . . , x}, uy [t] ∈ {y, . . . , −δh , 0, δh , . . . , y}, and h[t] ∈ {h, h + δv , . . . , h − δv , h}, where the bounds x, x, y, y, h, and h restrict the 3D placement of the ABS. • Speed constraint: As illustrated in Sect. 3.4.1.3, at each TS, the ABS can stay at the location of the previous TS or move to other horizontally surrounding locations at the velocity of vh or other vertical surrounding locations at the velocity of vv . Given that we have defined δh = vh τ and δv = vv τ , the speed **2 ** constraint is formulated by **U [t] −U [t −1]** ∈ {0, δh2 , δv2 }, ∀t ∈ {1, 2, . . . , T }. We focus our attention on the queuing delay in the network layer, which is defined as the temporal interval between the instant when a packet arrives at the transmitter and the instant when it is delivered. Our objective is to minimize the average queuing delay over T TSs in the ABS-enabled network. By Little’s Law [82], the relationship among the average delay denoted by D, average queue length, and packet arrival rate is given by Lau and Cui [83] 6 5 4 3 E Qk [t] Qk [t] . Dk = =E λk λk

(3.89)

Now, given an initial state of X[0] = {U [0], Q[0]}, the minimum-delay ABS placement problem is readily formulated as * 3 4 T K 1  wk Qk [t] ** P0 : arg min E X[0] λk * U [t ] T K t =1 k=1

s.t.

(3.88)

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** ** **U [t] − U [t − 1]**2 ∈ {0, δ 2 , δ 2 }, ∀t ∈ {1, 2, . . . , T }, h v

(3.90a)

ux [t] ∈ {x, . . . , −δh , 0, δh , . . . , x}, ∀t ∈ {0, 1, . . . , T },

(3.90b)

uy [t] ∈ {y, . . . , −δh , 0, δh , . . . , y}, ∀t ∈ {0, 1, . . . , T },

(3.90c)

h[t] ∈ {h, h + δv , . . . , h − δv , h}, ∀t ∈ {0, 1, . . . , T },

(3.90d)

where the positive weighting factor wk indicates the relative importance of the queuing delay of the k-th device, which is dependent on the device’s priority.

3.4.3 Markov Decision Process Transformation In a stochastic dynamic control problem, the controller can make decisions in accordance with the environment’s state. If the states satisfy the Markov property, this decision process can be termed as a Markov decision process (MDP) [84]. As a special case of the MDP, the constrained MDP (CMDP) [85] has multiple objectives. It enables minimizing one of the objectives, while satisfying the constraints imposed on the others. In this section, the minimum-delay control problem formulated in Sect. 3.4.2 is transformed to its corresponding CMDP problem. By further exploiting the Lagrangian approach, we then reformulate this CMDP problem as an unconstrained MDP problem, which can then be readily solved using various approaches, as detailed in Sect. 3.4.4.

3.4.3.1 Constrained Markov Decision Process In general, a CMDP can be characterized by four elements, namely the state space, the action space, the state transition probability, and the constrained optimization problem [85], which are specified for our minimum-delay control problem formulated in Sect. 3.4.2 as follows: • State space: Let us denote the system state at the t-th TS by X[t], which is defined as the aggregation of the ABS’s location and the global QSI, i.e., X[t] = {U [t], Q[t]}, where ∀t ∈ {0, 1, . . . , T }. Here let us use X to represent the set X |. including all possible states. The number of elements in X is denoted by |X It can be readily inferred that the future states of both the ABS location U [t] and the joint QSI Q[t] are only dependent on their current states, but not on the states at the previous TSs. Hence, the states evolved as a controlled Markov chain and this decision process is an MDP. • Action space: We use A[t] to represent the action taken at the beginning of the tth TS. For ∀t ∈ {1, 2, . . . , T − 1}, one of the seven actions can be taken from the action space denoted by A = {A0 , A1 , A2 , A3 , A4 , A5 , A6 }, where A0 means u[t] = (ux [t −1], uy [t −1], h[t −1]); A1 , A2 , A3 , A4 , A5 , and A6 refer to u[t] =

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(ux [t − 1] − δh, uy [t − 1], h[t − 1]), u[t] = (ux [t − 1] + δh, uy [t − 1], h[t − 1]), u[t] = (ux [t − 1], uy [t − 1] − δh , h[t − 1]), u[t] = (ux [t − 1], uy [t − 1] + δh , h[t − 1]), u[t] = (ux [t − 1], uy [t − 1], h[t − 1] − δv ), and u[t] = (ux [t − 1], uy [t − 1], h[t − 1] + δv ), respectively. The total number of actions is denoted A |. Furthermore, the CMDP formulated in this section aims for finding the by |A optimal ABS placement policy Ω ∗ : X → A that minimizes the average delay subject to the power constraint, from the set denoted by Ω, which includes all possible policies. • Transition kernel: Again, since the MDP is a controlled Markov chain, the state transition is determined both by (3.85) and by the actions taken at the beginning of the TSs. The state transition probability is formulated by + * ! ", (3.91) Pr X[t + 1]*X[t], Ω X[t] + * * ! ", + ! ", = Pr U [t + 1]*U [t], Ω X[t] Pr Q[t + 1]*Q[t], Ω X[t] .

Ω

P (X0 ) =

T 

3 E

Ω

t =1

* * * * Pmh *ux [t] − ux [t − 1]* *uy [t] − uy [t − 1]* + T δh δh

! "+ ! "− * 4 Pmv+ h[t] − h[t − 1] Pmv− h[t] − h[t − 1] ** + + *X[0] = X0 . T δv T δv (3.92) • Constrained optimization problem: Commencing from an initial state X[0] = X0 ∈ X and following a policy Ω ∈ Ω, the average expected delay and power consumption are defined as Ω

D (X0 ) =

* 3 4 T K 1   Ω wk Qk [t] ** X[0] = X E 0 TK λk *

(3.93)

t =1 k=1

and (3.92) in the next page, respectively, where EΩ (•) represents the expectation value of • under the policy Ω. Then, we may formulate the constrained optimization version of the minimum-delay ABS placement control problem as Ω

Ω

P1 : min D (X0 ) subject to P (X0 ) ≤ Pavg . Ω∈Ω

(3.94)

Remark 1 There is a one-to-one correspondence between Problem P0 and Problem P1. Specifically, the constraint (3.88) in Problem P0 corresponds to the constraint in Problem P1, while the constraints (3.90a), (3.90b), (3.90c), and (3.90d) restrict the action taken at each TS into the afore-specified action space in Problem P1.

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3.4.3.2 The Lagrangian Approach As analyzed in [86], the MDP problem falls into the class of convex programming problems. Therefore, solving the constrained MDP problem is equivalent to solving the unconstrained MDP associated with its Lagrangian dual problem. In this subsection, we reformulate the CMDP in (3.94) to be an unconstrained MDP by introducing a Lagrange multiplier γ , following the theorem below. Theorem 1 There is a one-to-one correspondence between the constrained MDP formulated in (3.94) and the unconstrained MDP formulated below: 1 Ω ,2 + Ω ∗ C (X0 ) = inf sup D (X0 ) + γ P (X0 ) − Pavg Ω∈Ω γ ≥0

= sup inf

γ ≥0 Ω∈Ω

1 ,2 + Ω Ω D (X0 ) + γ P (X0 ) − Pavg ,

(3.95)

and a policy Ω ∗ is optimal for the CMDP if and only if + Ω∗ 1 Ω∗ ,2 ∗ C (X0 ) = sup D (X0 ) + γ P (X0 ) − Pavg . γ ≥0

(3.96)

K ! "  wk Qk [t + 1] Cγ X[t], X[t + 1], A[t] = T Kλk k=1 * * * 3 h  ** Pm ux [t + 1] − ux [t]* *uy [t + 1] − uy [t]* +γ + T δh δh ! " ! "− 4 + Pmv+ h[t + 1] − h[t] Pmv− h[t + 1] − h[t] + + − Pavg . (3.97) T δv T δv

 

Proof See Sect. 3.4.7.

With the aid of Theorem 1, we may transform the CMDP of Sect. 3.4.3.1 to an unconstrained MDP. Specific to a fixed γ , we use Cγ (X[t], X[t + 1], A[t]) to denote the per-stage cost function of the corresponding unconstrained MDP that emerges from the state X[t] to the state X[t + 1] following the action A[t]. Its expression is given by (3.97) in the next page. To this end, we may readily formulate the corresponding unconstrained MDP problem as ∗

C (X0 ) = sup inf

T −1

γ ≥0 Ω∈Ω t =0

1 ! 2 "** EΩ Cγ X[t], X[t + 1], A[t] *X[0] = X0 , (3.98)

where we have Ω : X → A .

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3.4.4 Backward Induction and R-Learning Based Optimization Since the actions described in Sect. 3.4.3.1 may impose causality constraints on the consecutive states, we have to solve this MDP problem by using dynamic programming instead of solving it in each TS independently. In general, an MDP problem can be solved by the techniques of backward induction, policy iteration, value iteration, and reinforcement learning4 [84]. Specifically, backward induction is appropriate for the problem associated with a finite number of TSs, while both the policy iteration and the value iteration aim for providing the policy for the MDP problem associated with an infinite number of TSs. The a priori knowledge of the state transition probability is required by all of these three techniques. By contrast, reinforcement learning interacts with the environment through the “trial and error” mechanism and hence does not require the exact mathematical model of the MDP problem. Given the finite number of TSs in the problem formulated in (3.98), we provide a set of solutions for diverse assumptions of the prior knowledge of wireless tele-traffic in this subsection, by using the techniques of backward induction or of reinforcement learning. The key idea both of the backward induction and of the reinforcement learning techniques is to invoke the so-called value functions for finding appropriate policies [84]. Given a fixed γ and a policy Ω, let us denote the state-value function at the state X by vγΩ (X), which satisfies the Bellman expectation equation as follows [84]: vγΩ (X) =

 A A∈A

PrΩ (X, A)



Pr(X |X, A)

X X ∈X

/ 0 · Cγ (X, X , A) + vγΩ (X ) ,

(3.99)

where PrΩ (X, A) refers to the probability of choosing the action A at the state X under the policy Ω. To elaborate a little further, since PrΩ (X, A) is determined by a specific policy and the term Cγ (X, X , A) in (3.99) can be readily calculated by (3.97), we focus our attention on Pr(X |X, A). Specifically, given a state and an action taken at the t-th TS, the state at the (t + 1)-st TS is solely determined by Bk [t] in (3.85). Hence, once we have the knowledge of Bk [t], the state transition probability of Pr(X |X, A) can be readily determined. Without any loss of generality, again we consider three different assumptions in terms of the knowledge of Bk [t] as detailed below: • Case 1: The exact value of Bk [t] for ∀t ∈ {0, 1, . . . , T − 1} and ∀k ∈ {1, 2, . . . , K} is known by the ABS placement scheduler. 4

Machine learning techniques can be generally classified into supervised and unsupervised learning as well as reinforcement learning [87]. Specifically, both the supervised and unsupervised learning techniques are typically used for classification and clustering, while reinforcement learning aims for assisting decision-making for the MDP problem, where the state transition probability is unknown.

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Algorithm 4 Backward induction based approach for Case 1 Input: Simultaneous knowledge of wireless tele-traffic dynamics Output: Minimum-delay ABS placement policy 1. Initialization initialize γ arbitrarily for each state X ∈ X do vγT (X) ← 0 end for 2. State-value table generation for each TS t from T −/ 1 to 0 do 0  t+1  vγt (X) ← minA∈A A Cγ (X, X , A) + vγ (X ) end for 3. Average cost evaluation and γ update if C γ (X0 ) cannot be improved then v∗t (X) ← vγt (X), ∀t ∈ {0, 1, . . . , T } go to step 4) else update γ using the bisection search algorithm and go to step 2) end if 4. Policy output for each TS t from 0 to T −/ 1 do 0  t+1  Ω t (X) ← arg minA∈A A Cγ (X, X , A) + v∗ (X ) end for

• Case 2: The specific probability density function of Bk [t] for ∀k ∈ {1, 2, . . . , K} is available at the ABS placement scheduler. • Case 3: Neither the exact value nor the statistical information of Bk [t] for ∀k ∈ {1, 2, . . . , K} is known at the ABS placement scheduler. Remark 2 The stochastic process of wireless tele-traffic dynamics is assumed to be accurately predicted in Case 1. It can be realized relying on wireless tele-traffic prediction techniques [88]. Additionally, some periodic data transmission schemes also fall into this category. Case 2 is suitable for the scenario, where the devices’ wireless tele-traffic dynamics are accurately modeled. Finally, Case 3 considers the scenario, where we do not have any prior information. In the following, a set of solutions are provided for these three cases, respectively.

3.4.4.1 Solution to the Problem in Case 1 Given the exact value of Bk [t] for ∀t ∈ {0, 1, . . . , T − 1} and ∀k ∈ {1, 2, . . . , K}, the problem formulated in (3.98) can be simplified to a deterministic form T −1 " 1 1 ! C (X0 ) = sup inf Cγ X[t], X[t + 1], A[t] Ω∈Ω T γ ≥0 t =0 * 2 * *X[0] = X0 , Ω . ∗

(3.100)

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This can be solved by the technique of backward induction [89]. The basic idea is to establish a trellis that comprises all possible states at each TS and then obtain a table that contains the aforementioned state-value functions for all the states in each TS sequentially from the final TS to the beginning. Based on this table, the policy can be implemented, commencing from the initial TS. Here let us denote the state-value function of the state X at the t-th TS by vγt (X), given a specific γ . We may follow the steps below for establishing a table containing all vγt (X). 1. Since the delay is characterized in terms of a finite number of TSs T as formulated in (3.100), the states at the T -th TS do not impose further cost.5 Therefore, we set the state-value functions at the T -th TS to 0, i.e., vγT (X) = 0, ∀X ∈ X . 2. Given that Bk [t] is pre-acknowledged in each TS, its randomness vanishes in the decision-making process. In other words, the state at the next TS is solely determined both by the state at the current TS and by the action taken. Therefore, in this case we may update vγt (X) for the TS t = T − 1, . . . , 0 sequentially relying on the Bellman optimality equation [84] as follows: 0 / vγt (X) = min Cγ (X, X , A) + vγt +1 (X ) . A A∈A

(3.101)

3. For a fixed γ , the average cost C γ (X0 ) can be readily obtained by C γ (X0 ) = vγ0 (X0 ). 4. Following (3.100), we update γ using the classic bisection search algorithm and ∗ go to Step 2 until a maximum average cost C (X0 ) is obtained. Here we denote its corresponding optimal state-value function by v∗t (X), for ∀t ∈ {0, 1, . . . , T } and ∀X ∈ X . ∗

Based on the optimal average cost C (X0 ) and the corresponding v∗t (X), we may then carry out the policy by setting X[0] = X0 and then by solving the equation below: 0 / Ω t (X) = arg min Cγ (X, X , A) + v∗t +1 (X ) , A A∈A

(3.102)

from the TS t = 0 to t = T − 1 sequentially. The pseudocode of the backward induction based solution of the problem in Case 1 is given by Algorithm 4.

3.4.4.2 Solution to the Problem in Case 2 Given the finite number of TSs and the statistical information concerning the packet arrival process, the problem of Case 2 can be solved by the technique of backward

5

This is in accordance with the convention that costs occur at the next TS. Therefore, the states at the T -th TS do not impose further cost.

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Algorithm 5 Backward induction based approach for Case 2 Input: Statistical knowledge of wireless tele-traffic dynamics Output: Minimum-delay ABS placement policy 1. Initialization initialize γ arbitrarily for each state X ∈ X do vγT (X) ← 0 end for 2. State-value table generation for each TS t from T − 1 to 0 do /   vγt (X) ← minA∈A A X Pr(X |X, A) · Cγ (X, X , A) X ∈X 0 t+1  +vγ (X ) end for 3. Average cost evaluation and γ update if C γ (X0 ) cannot be improved then v∗t (X) ← vγt (X), ∀t ∈ {0, 1, . . . , T } go to step 4) else update γ using the bisection search algorithm and go to step 2) end if 4. Policy output for each TS t from 0 to T − 1 do / t+1   Ω t (X) ← arg minA∈A X Pr(X |X, A) · v∗ (X ) 0 A X ∈X  +Cγ (X, X , A) end for

induction. However, instead of following the deterministic formulations specified in (3.101) and (3.102) in Case 1, in Case 2, we have to update the state-value functions and implement the policies using the statistical information available. The steps required for establishing a table containing all vγt (X) are detailed as follows: 1. Again, we set the state-value functions at the T -th TS to 0, i.e., vγT (X) = 0, ∀X ∈ X. 2. Given the probability density function of Bk [t], we are ready to calculate Pr(X |X, A). Then, the state-value functions vγt (X) can be updated from the TS t = T − 1 to t = 0 by sequentially invoking the Bellman optimality equation of [84] as follows: vγt (X) = min A A∈A



Pr(X |X, A)

X X ∈X

/ 0 · Cγ (X, X , A) + vγt +1 (X ) .

(3.103)

3. For a fixed γ , the average cost C γ (X0 ) can be readily obtained by C γ (X0 ) = vγ0 (X0 ). 4. Following (3.98), we update γ using the bisection search algorithm and go to ∗ Step 2 until a maximum average cost C (X0 ) is obtained. Here we denote its

3.4 UAV Seamless Coverage Strategy for Minimum-Delay Placement

105

corresponding optimal state-value function by v∗t (X) for ∀t ∈ {0, 1, . . . , T } and ∀X ∈ X . ∗

Based on the optimal average cost C (X0 ) and the corresponding v∗t (X), we may then implement the policy by setting X[0] = X0 and by solving the equation below: Ω t (X) = arg min A A∈A



Pr(X |X, A)

X X ∈X

/ 0 · Cγ (X, X , A) + v∗t +1 (X ) ,

(3.104)

from the TS t = 0 to t = T − 1 sequentially. Note that Pr(X |X, A) = 0 for the set of {X, X , A}, where the state X cannot reach state X after executing the action A. The pseudocode of the backward induction based solution to the problem in Case 2 is given by Algorithm 5.

3.4.4.3 Solution to the Problem in Case 3 As for the case where Pr(X|X , A) is unknown to the scheduler, we have to rely on the technique of reinforcement learning [84], which enables the scheduler to carry out the policy by interacting with the environment. As a classic reinforcement learning technique, Q-learning [84] has been leveraged in diverse research areas. However, its cost is accumulated in a discounted manner for future TSs and may not solve the MDP problem formulated in (3.98) that is associated with undiscounted costs. To address this issue, we invoke the technique of R-learning [90], which has been tailored for the problem associated with the undiscounted costs. In generally, the horizon of a reinforcement learning problem is assumed to be infinite. The problem formulated in (3.98), however, is readily observed to be a finite-horizon MDP. As detailed in Remark 3, we have to train the scheduler in an offline manner, and hence it can be trained over many episodes for approaching the infinite-horizon performance. In infinite-horizon problems associated with undiscounted costs, the state-value function in (3.99) becomes infinite, which cannot be used as a comparative basis, when we implement the policy. In order to tackle this issue, the concept of the action value R Ω (X, A) is introduced into the technique of R-learning [90], which represents the average-adjusted value of carrying out an action A in state X once and then following the policy Ω [90]. Mathematically, R Ω (X, A) is given as follows [90]: RγΩ (X, A) = Cγ (X, X , A) − ργΩ  + Pr(X |X, A)vγΩ (X ), X

(3.105)

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3 Seamless Coverage Strategies of FANET

Algorithm 6 R-learning based approach for Case 3 Input: Neither simultaneous nor statistical knowledge of wireless tele-traffic dynamics Output: Reduced-delay ABS placement policy 1. Initialization initialize γ arbitrarily, X[0] ← X0 for each state X ∈ X and A ∈ A do Rγ0 (X, A) ← 0 end for 2. Action-value table generation for each TS t do set X ← X[t] select an action A following the -greedy method execute the action A observe the next state X receive the immediate cost Cγ (X, X , A) update the Rγ (X, A) by Rγt+1 (X, A) ← (1 − η)Rγt (X, A) / 0 +(X, A) + η Cγ (X, X , A) − ργt + minA ∈A Rγt (X , A ) / update ργ by ργt+1 ← (1 − α)ργt + α Cγ (X, X , A) 0 t   t + minA ∈A A Rγ (X , A ) − minA∈A A Rγ (X, A) update X[t + 1] ← X end for 3. Policy output Ωγ (X) = arg minA∈A Rγ (X, A) 4. Constraint satisfaction evaluation and γ update if the equality of (3.88) holds then R∗t (X, A) ← Rγt (X, A) Ω∗ (X) ← Ωγ (X) else update γ using the bisection search algorithm and go to step 2) end if

where ρ Ω is the average cost of the policy Ω. Given a specific value of γ , let us detail the steps of generating a table containing R Ω (X, A) as follows: 1. We set the initial average-adjusted value to Rγ0 (X, A) = 0, ∀X ∈ X , and ∀A ∈ A. The initial state is set to X[0] = X0 . 2. The actions are chosen using the exploration/exploitation selection mechanism [84]. Specifically, the term exploitation means that we opt for an action following the policy, which minimizes the average-adjusted value functions. MathematΩ ically, we have Ωγ (X) = arg minA∈A A Rγ (X, A). However, before obtaining a set of reliable RγΩ (X, A) values, the action taken following this policy is not deemed to be satisfactory. To overcome this hindrance, the concept of exploration is introduced to randomly select an action in A . This is capable of discovering better policies and of improving the estimate of RγΩ (X, A). In particular, we invoke the -greedy action selection method, which either takes actions randomly (exploration) with a probability of  or follows the policy (exploitation) with probability (1 − ) at each TS, where 0 <  < 1 [91].

3.4 UAV Seamless Coverage Strategy for Minimum-Delay Placement

107

3. After executing an action A at a state X, we may observe its subsequent state X and the immediate cost Cγ (X, X , A), both of which are used for updating the average cost ργt +1 and the average-adjusted value Rγt +1 (X, A). Specifically, the average-adjusted value is updated by Schwartz [90] / 0 Rγt +1 (X, A) = η Cγ (X, X , A) − ργt + min Rγt (X , A ) A ∈A

+(1 − η)Rγt (X, A),

(3.106)

where η is the learning rate for the average-adjusted value. Furthermore, if the t action A obeys Ωγ (X) = arg minA∈A A Rγ (X, A), i.e., a non-exploratory action is taken, the average cost is updated by Schwartz [90] / ργt +1 = α Cγ (X, X , A) + min Rγt (X , A ) 0

A A ∈A

− min Rγt (X, A) + (1 − α)ργt , A A∈A

(3.107)

where α is the learning rate of the average cost. 4. Set the current state to X and go to Step 2. Based on the R value Rγ (X, A) obtained, we may carry out a stationary policy by solving the equation below: Ωγ (X) = arg min Rγ (X, A). A∈A

(3.108)

Given a sequence of wireless tele-traffic over T TSs, we dynamically adjust the ABS’ placement following the policy Ωγ (X) and observe the total number of movements, which can be used for checking the satisfaction of constraint (3.88). If the equality of constraint (3.88) does not hold, we then update the value of γ using the bisection search algorithm and then carry out the policy Ωγ (X) until the equality holds. Remark 3 Policies designed for the problems in both Case 1 and Case 2 belong to the Markov policy [85], where the action taken at the t-th TS is a function of the state at the t-th TS. The policy conceived for the problem in Case 3 belongs to the stationary deterministic policy [85], where the action taken at a specific state is only determined by this state, regardless of which TS it is. Furthermore, since the satisfaction of constraint (3.88) has to be checked before carrying out the policy, the R-learning aided scheduler proposed for Case 3 has to be trained in an offline manner.

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3.4.4.4 Analysis of Computational Complexity The computational complexity of the backward induction method and the Rlearning method is dominated by generating the tables of the state-value function {v t (X)} and of the action value function R(X, A ), respectively. Hence we focus our attention on analyzing the computational complexity of the table generation for each case as follows: • Solution to the Problem in Case 1: The Bellman optimality equation (3.101) represents a series of equations, whose total number is determined by the number X |. In each equation, all |A A | actions have to be tried for finding of states, |X the appropriate action that maximizes the value function in (3.101). As a result, X ||A A |) at each TS. Given the computational complexity is on the order of O(|X that the total number of TSs is T , the overall computational complexity is X ||A A |). O(T |X • Solution to the Problem in Case 2: Similar to Case 1, the Bellman optimality X | equations and all |A A | actions have to be tried for equation (3.103) comprises |X X | state-value/ functions at (t +1)-st have each state. Note that at the t-th TS, all |X 0   t +1  to be accessed for calculating X ∈X X Pr(X |X, A) · Cγ (X, X , A) + vγ (X ) . Hence the overall computational complexity is given by O(T |X|2 |A|). • Solution to the Problem in Case 3: At each training TS, the operation Ω arg minA∈A A Rγ (X, A) dominates the computational complexity, which is the A |). Then, upon setting the total number of training TSs to Ttrain , order of O(|A A |). we may obtain the overall computational complexity as O(Ttrain |A Remark 4 The size of the table including all action values of the learning approach X ||A A |, which increases along with the joint queuing proposed for Case 3 equals |X Q |, the ABS’ location space |U U |, and the action space |A A |. state information space |Q U | and the action space It can be readily seen that both the ABS’ location space |U A | are limited in the problem considered, while the joint queuing state information |A Q | increases exponentially along with the number of ground devices. Three space |Q approaches can be considered for addressing this complexity issue. Firstly, by using the value-function approximation, the original value function can be replaced by a value-function approximator, which may help to find a sub-optimal policy associated with a reduced complexity. The second approach is deep reinforcement learning, where the original action–state-value function is replaced by the value function weighted by the deep neural network having multiple layers, which is capable of handling very large state spaces. The third approach is multi-agent reinforcement learning. Specifically, if dense ground devices have to be served, a single ABS may not be able to accommodate the erratically fluctuating wireless tele-traffic dynamics due to its limited buffer space and agility. Alternatively, the ground devices can be clustered into a number of groups, each of which is assigned to an ABS. Under the framework of multi-agent reinforcement learning, we may view each ABS as an agent. As a benefit, the space size of each agent is reduced.

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109

3.4.5 Simulation Results In this subsection, we characterize the performance of our proposed minimum-delay dynamic ABS placement strategies by numerical results, in terms of the average delay per user and of the buffer 5 overflow 6 probability. Specifically, the average delay per user is given by K E ω Q [t] /K. It reflects the overall delay performance k k 1 of the system. The buffer overflow probability characterizes the probability that the buffer size is incapable of storing the queue length, and it plays a crucial role in devices equipped with limited buffer sizes. For comparison, we also consider two benchmark schemes, detailed as follows: • CSI-only scheme: The placement of the ABS is optimized for maximizing the summation of the ground devices’ throughput. Mathematically, the objective function of Problem P0 is replaced by − K k=1 Rk . This algorithm represents the state-or-the-art schemes, where the wireless traffic dynamics are not considered when scheduling the ABS’ placement. • MaxWeight scheme [92, 93]: This is a classic delay-aware scheduling algorithm in wireless communications, which has hitherto not been investigated in UAV communications. We dynamically schedule the ABS placement to the specific points in harmony with the dynamic wireless traffic using this scheme, for maximizing the sum of the queue-length-weighted throughput. Mathematically, the objective function of Problem P0 is replaced by − K k=1 Qk [t]Rk [t]. This scheme is capable of achieving throughput-optimal performance, while maintaining the queue’s stability [92]. Without loss of generality, the ground devices are located on the rectangular area bounded by its vertexes [x, y, 0], [x, y, 0], [x, y, 0], and [x, y, 0]. The height of the ABS is adapted in the range of [h, h]. These minimum and maximum heights have to comply with relevant regulations [68], e.g., FAA. The energy consumption of the UAV mobility is based on the model proposed in [68]. As illustrated in Sect. 3.4.1.1, a probabilistic LoS model is considered for the link between the ground devices and the ABS, while data transmission is contaminated by additive white Gaussian noise associated with a zero mean and a power spectral density of σ 2 . The default settings are specified in Table 3.6. Under this parameter setting, the received signalto-noise ratio at the vertex on the ground can be tuned from −6.92 to 24.31 dB by dynamically adjusting the placement of the ABS in this 3D space. As for the wireless tele-traffic, we model the packet arrival process of each ground device by a two-state hidden Markov process, where states S1 and S2 represent the states of a low packet arrival rate and of a high packet arrival rate, respectively. The transition probability between two states is set as pt h = 0.1. We assume that the packet arrival process of both states obeys the Poisson distribution [82] and the packet arrival rates of the two states are λSk 1 and λSk 2 , respectively. The implementation of reinforcement learning consists of two steps, namely offline training and online policy operation. As for the offline training step, we initialize the parameter settings as  = 0.8, α = 0.1, and β = 0.2. The value of  is gradually reduced during the training process.

110 Table 3.6 Default simulation parameter settings

3 Seamless Coverage Strategies of FANET Description Bandwidth Scheduling slot Carrier frequency Path loss exponent LoS probability setting Attenuation factor

Parameter and value B = 500 KHz τ =2s fc = 2.4 GHz 2 β = 0.14 ψ = 11.95 μLoS = 3 dB μNLoS = 23 dB

UAV altitude The area of ground devices

σ 2 = −170 dBm/Hz Pt = 0.1 mW Pc = 5 W Pmh = 10 W Pmv+ = 20 W Pmv− = 15 W Ph = 170 W Pd = 5 W NQ = 5 packet Nk = 290 Kbyte/packet T τ = 30 min vh = 20 m/s vv = 5 m/s [h, h] = [60, 80] m x = y = 0, x = y = 160 m

Weight factor

w1 = w2 = 1

Noise Power consumption [68]

Buffer size Packet size [83] Service time UAV moving speed

We stop the training when neither the average delay nor the overflow probability can be reduced during the performance evaluation. Note that we set  = 0 during the performance evaluation because our reinforcement learning algorithm is trained in an offline manner. Using the R-table obtained, we may carry out the policy by solving (3.108) at each TS. Let us now study the performance of the proposal in various simulation environments, compared to that of benchmark schemes.

3.4.5.1 Impact of the ABS’ Total Energy Figure 3.23 shows the average delay per user and the buffer overflow probability versus the total battery energy of the ABS. Specific to the parameter settings, as detailed in Table 3.6, the total power required for remaining airborne is Pc + Ph + Pd = 180 W. Hence, given that the total service time is 30 min, the ABS cannot be moved when its total battery charge is 90 Wh. By contrast, it can be inferred that the ABS may be scheduled for travel in any direction at each time slot, when its battery life is 100 Wh. Our observations are as follows. Firstly, the performance

3.4 UAV Seamless Coverage Strategy for Minimum-Delay Placement 1.0 CSI-only MaxWeight Case 1 - BI Case 2 - BI Case 3 - RL

3.0 2.8 2.6

0.9 0.8 0.7

2.4

0.6

2.2

0.5 0.4

2.0

0.3

1.8 Average Delay Overflow Prob

1.6 1.4

90

92

94

96

98

Overflow probability

3.2

Average delay per user (packet)

111

0.2 0.1 100

Energy (Wh)

Fig. 3.23 Simulation results of the average delay per user and of the buffer overflow probability versus the total battery energy of the ABS in a two-device system, where the devices’ locations are (0, 80, 0) m and (160, 80, 0) m. The packet arrival rate of two states is λSk 1 = 0.2 pck/τ and λSk 2 = 3.0 pck/τ, respectively

of the CSI-only scheme does not change upon increasing the ABS’ total energy. This is because the maximum-throughput placement pursued by the CSI-only scheme is static, once the locations of the ground devices are fixed. Secondly, upon increasing the ABS’ total energy, both a lower average delay and a lower overflow probability are achieved by using the MaxWeight scheme and using our proposed algorithms for the three cases. This implies that these queue-aware dynamic ABS placement scheduling schemes are indeed capable of reducing both the system delay and the overflow probability, when the battery energy is sufficient for the ABS’ movement. Thirdly, equipped with sufficient battery energy for movement, the delay is the lowest for the backward induction aided scheme in Case 1, followed by the backward induction aided scheme in Case 2, the reinforcement learning aided scheme in Case 3 and the MaxWeight scheme. As illustrated in [94], the MaxWeight scheme aims for achieving the maximum throughput, while maintaining a stable queue, whose delay is higher than that of the minimum-delay schemes conceived for Case 1, 2 and 3. As for the order in Case 1, 2, and 3, this is due to their different a priori knowledge of the wireless tele-traffic dynamics. Specifically, the exact number of arriving packets is known in Case 1, and the probability mass function of the arrival packets is known in Case 2, while in Case 3 the wireless tele-traffic dynamics have to be learned during the training process. Fourthly, the increase of the ABS’ total energy drastically reduces both the average delay and the overflow probability in the queue-aware ABS placement scheduling schemes, when the ABS’ total energy is below a certain threshold, say 94 Wh, while the reduction becomes much smaller afterward. It can be inferred that the minimum delay can be achieved without adjusting the ABS’ placement for every TS.

3 Seamless Coverage Strategies of FANET 4.2 4.0 3.8 3.6 3.4 3.2 3.0 2.8 2.6 2.4 2.2 2.0 1.8

0.5 CSI-only MaxWeight Case 1 - BI Case 2 - BI Case 3 - RL

Overflow probability

Average delay per user (packet)

112

0.4

CSI-only MaxWeight Case 1 - BI Case 2 - BI Case 3 - RL

0.3

0.2

0.1 1

2

3

1

2

Scenario index

Scenario index

(a)

(b)

3

Fig. 3.24 Simulation results of the average delay per user (a) and of the buffer overflow probability (b) in various wireless traffic scenarios in a two-device system, where the devices’ locations are (0, 80, 0) m and (160, 80, 0) m. The total battery energy of the ABS is 100 Wh. The wireless traffic scenarios are specified as follows: scenario 1: λSk 1 = 0.2 pck/τ, λSk 2 = 3.0 pck/τ, scenario 2: λSk 1 = 0.8 pck/τ, λSk 2 = 2.4 pck/τ, and scenario 3: λSk 1 = 1.6 pck/τ, λSk 2 = 1.6 pck/τ

3.4.5.2 Impact of the Asymmetry Wireless Tele-Traffic Figure 3.24 presents both the average delay and the buffer overflow probability of a two-device system, where various packet arrival rates are set for the two traffic states in three different scenarios. The expectation values of the packet arrival rates in these three scenarios remain the same. Having a higher difference between the values of λSk 1 and λSk 2 implies a more asymmetric packet arrival process in the simulations. We have the following observations. Firstly, as for the average delay, the advantage of the queue-aware dynamic ABS placement schemes over the CSI-only scheme becomes higher upon increasing the difference between the values of λSk 1 and λSk 2 . This is because a higher difference between the values of λSk 1 and λSk 2 implies having more substantially fluctuating wireless tele-traffic dynamics, while the queue-aware schemes are capable of tracking these dynamic fluctuations. Secondly, although the average delay performance increases upon reducing the difference between λSk 1 and λSk 2 for both our proposed algorithms and the benchmark schemes, the overflow probability of our proposed algorithms remains almost the same, which demonstrates the efficiency of our proposed algorithms.

3.4.5.3 Impact of the Wireless Tele-Traffic Rate Figure 3.25 plots the average delay per user and the buffer overflow probability versus the packet arrival rates in a two-device system. Our observations are as follows. Firstly, as expected, both the average delay per user and the buffer overflow probability increase upon increasing the packet arrival rate. Specific to

3.4 UAV Seamless Coverage Strategy for Minimum-Delay Placement

3.6 3.2

CSI-only MaxWeight Case 1 - BI Case 2 - BI Case 3 - RL

1.0

Average Delay Overflow Prob

0.9 0.8 0.7

2.8

0.6

2.4

0.5

2.0

0.4 0.3

1.6

Overflow probability

Average delay per user (packet)

4.0

113

0.2

1.2

0.1

0.8 1.4

1.6 S

1.8

0.0

S

λk 1 = λk 2 (packet/τ )

Fig. 3.25 Simulation results of the average delay per user and of the buffer overflow probability versus the packet arrival rate in a two-device system, where the devices’ locations are (0, 80, 0) m and (160, 80, 0) m. The total battery energy of the ABS is 100 Wh

the average delay per user, with reference to (3.85), the value ranges from the mean value of the packet arrival process λ and NQ . Secondly, the advantage of our proposed algorithms over the CSI-only and MaxWeight schemes becomes lower, upon increasing the packet arrival rate. This is because the average delay is saturated by NQ , when the packet arrival rate is high.

3.4.5.4 Impact of the Ground Devices’ Location Figure 3.26 illustrates both the average delay and the buffer overflow probability in two different device location settings for a three-device system. Specifically, the distance among the devices in Scenario 4 is higher than that in Scenario 5. It can be observed that both the average delay and the buffer overflow probability can be significantly reduced, if the locations of the ground devices are closer, because in this case the transmission throughput of ground devices may be beneficially adjusted by adapting the ABS placement in a single TS. This provides an important insight for engineering design. For a system where many ground devices have to be served, we may cluster the devices based on their distance and assign an ABS for each device cluster for attaining a reduced delay. Multi-ABS systems can be realized by appropriately designing both the user association and the resource management with the aid of a multi-agent MDP framework, which is beyond our current scope.

114

3 Seamless Coverage Strategies of FANET 0.32 CSI-only MaxWeight Case 1 - BI Case 2 - BI Case 3 - RL

2.8 2.6 2.4 2.2 2.0 1.8 1.6

CSI-only MaxWeight Case 1 - BI Case 2 - BI Case 3 - RL

0.28 Overflow probability

Average delay per user (packet)

3.0

0.24 0.2 0.16 0.12 0.08 0.04

4

5

0.0

4

5

Scenario index

Scenario index

(a)

(b)

Fig. 3.26 Simulation results of the average delay per user (a) and of the buffer overflow probability (b) for a three-device system under two different devices’ locations settings. The locations of three devices are specified as follows: scenario 4: device 1 (3, 76, 0) m, device 2 (4, 7, 0) m, and device 3 (38, 75, 0) m and scenario 5: device 1 (3, 76, 0) m, device 2 (4, 47, 0) m, and device 3 (38, 75, 0) m. The total battery energy of the ABS is 100 Wh. The packet arrival rate is set as λSk 1 = λSk 2 = 1.6 pck/τ

3.4.6 Conclusions A beneficial architecture has been proposed for a UAV-aided network from a delayminimization perspective. We have formulated a minimum-delay ABS placement problem, subject to practical constraints imposed on the ABS’ battery life and velocity. We then transformed the primal problem to the corresponding CMDP problem and provided solutions to the problems formulated under various assumptions concerning our knowledge about wireless tele-traffic. The numerical results demonstrated that our proposed solutions are capable of reducing the delay compared to the benchmark scheme under the various scenarios considered. As for future work, the mobility of the ground users will also be addressed, for rendering our cross-layer optimization framework applicable to general cellular networks. Furthermore, the increasing number of ground users imposes a higher complexity on the learning aided approach, which will be tackled with the aid of value-function approximation, of deep reinforcement learning, and of multi-agent reinforcement learning.

3.4.7 The Proof of Theorem 1 The problem formulated in Sect. 3.4.3.1 is readily observed to be a CMDP problem associated with the average expected cost. The feasibility of applying the Lagrangian approach to this type of problems has been richly documented

References

115

5 wk Qk [t ] 6 in [85]. Here we aim for proving that the immediate costs, i.e., K k=1 λk ! |ux [t ]−ux [t −1]| |uy [t ]−uy [t −1]| " and Pm + , are bounded from below and the average δ δ expected cost of the objective satisfies the so-called grow condition of [85], which are the prerequisites of Theorem 1. Specifically, wk , Qk , and λk are all non K 5 wksince Qk [t ] 6 k negative, we have wkλQ ≥ 0 and hence ≥ 0. Furthermore, given an k=1 λ k ! |ux [t ]−ux [t −1]| |uyk [t ]−uy [t −1]| " equals either 0 or 1. + action specified in Sect. 3.4.3.1, δ δ ! |u [t ]−u [t −1]| " ≥ Bearing in mind that Pm is positive, we have Pm |ux [t ]−uδ x [t −1]| + y δ y 0. In this case, we have proved that the immediate costs related both to the objective and to the constraint are lower bounded by 0. In terms of the so-called growth condition [85], since the state space X[t] = {U [t], Q[t]} is finite, we have

3

wk Qk [t + 1] the set X[t] ∈ X : inf A λk

4

7 <  is finite,

(3.109)

∀ ∈ R. This is a sufficient condition for the so-called growth condition [85]. Hence, the two prerequisite conditions have been proved to be true and the proof is complete.

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Chapter 4

Cooperative Resource Allocation in FANET

With the development of the Internet of Things (IoT) and artificial intelligence (AI), the IoT system with UAVs are becoming the main body as it has been widely used in civil and military fields [1, 2]. Moreover, as the demands of smart devices increase, the channel capacity of the increasingly prosperous Internet of Things also needs to be improved. As the UAV-aided space–air–ground network is provided, the problems of cross-tier interference, power control, and system capacity are waiting to be optimized. To summarize, these issues can be generalized as a kind of cooperative resource allocation problems. Hence, how to design a UAV-aided space–air–ground network and make most cooperative resource allocation becomes a pivotal issue. In this chapter, we first discuss the problems of cooperative resource allocation relying on UAV in Sect. 4.1, and then study the joint UAV position and resource allocation optimization in Sect. 4.2. Considering the effect of trajectory, we propose a joint UAV trajectory and resource allocation scheme in Sect. 4.3. Finally, in Sect. 4.4, we investigate a staged optimization algorithm for joint optimizing the NOMA aided subchannel assignment.

4.1 Introduction of Cooperative Resource Allocation Problems Considering the rapid development of IoT devices and communication networks, a series of requirements such as high data rate, low cost, and low communication delay have become more and more stringent. Whether it is the communication between UAVs or the communication connection with other smart devices, when there are smart device scenarios, the issue of system capacity needs to be considered. Hence, the problem of collaborative resource allocation is a key issue that needs to be studied for network resource allocation, smart device connection scheduling, and © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2022 J. Wang, C. Jiang, Flying Ad Hoc Networks, Wireless Networks, https://doi.org/10.1007/978-981-16-8850-8_4

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system capacity maximization [3]. In this section, we first investigate the challenges of resource allocation problems in UAV-aided networks and then introduce the state of the art in the following subsection.

4.1.1 Problem Domain and Challenges The cooperative resource allocation problems can be mainly described in the following three parts in UAV networks: communication interference, connection scheduling, and system capacity. In this subsection, we consider UAVs as an aerial base station and use space–air–ground network as the communication scenario. We first discuss the challenges faced by the cooperative resource allocation as follows: (1) Communication interference: Equipped with diverse communication payloads, UAVs cooperating with satellites and base stations constitute a space– air–ground three-tier heterogeneous network, which are beneficial in terms of both providing the seamless coverage as well as of improving the capacity for increasingly prosperous Internet of Things networks. However, cross-tier interference may be inevitable among these tightly embraced heterogeneous networks when sharing the same spectrum. The power association problem in satellite, UAV, and macrocell three-tier networks becomes a critical issue. (2) Connection scheduling: The connection scheduling can be described as a method to maintain the cooperative resource allocation. Given the limited transmission power of smart devices in Internet of Remote Things, UAVaided space–air–ground networks become a beneficial remedy for uplink data transmission. However, when the network consists of many smart devices, if we do not consider the influence of connections between networks, it will cause low system capacity and transmission efficiency. (3) System capacity: System capacity is the crucial issue to solve the research of cooperative resource allocation. When considering the cooperative resource allocation problem in UAV networks, one of the challenges is that how to maximize the system capacity. As a common sense, since the UAV network contains a large number of smart devices, as for the cooperative resource allocation problem, if there are not enough methods to maximize the system capacity, the collaborative optimization task will become more difficult.

4.1.2 State of the Art In order to optimize the cooperative resource allocation in UAV networks, the state-of-the-art studies are provided. Zeng et al. proposed an energy-efficient UAV communication model by optimizing the trajectory of drones, which jointly

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123

considered both the energy consumption and the communication throughput in [4]. Reference [5] proposed a low-complexity adaptive algorithm for optimizing the multi-agent trajectory by adjusting the upper limit of the queuing length. Furthermore, an effective dynamic trajectory control mechanism for multi-UAV network was proposed by Fadlullah et al. [6], which was beneficial in terms of both improving the network throughput as well as of reducing the communication delay. Mozaffari et al. [7] considered a coexistence between the UAVs and an underlaid device-to-device communication network and studied the coverage performance as well as data rate. In terms of UAV’s power allocation based on NOMA, Fang et al. [8] proposed a sub-optimal power allocation scheme based on the difference of convex functions programming approach, showing that their scheme achieved superior energy efficiency. In [9], Nasir et al. considered a more user case and studied a max–min rate optimization problem for jointly optimizing the power allocation, bandwidth allocation, UAV altitude, and antenna beamwidth. Liu et al. [10] proposed an effective scheme for jointly optimizing the placement and power allocation of UAVs in a NOMA–UAV network. Zhao et al. [11] introduced a comprehensive framework for realizing effective UAV-base station cooperation for UAV-assisted NOMA networks. The authors also focused on the UAV static deployment and dynamic coverage to solve the problem of maximizing the system capacity in cooperative resource allocation. In [12], a novel iterative algorithm is proposed to optimize system capacity with UAV at the different heights in a collision situation. In [13], the horizontal position deployment of UAVs is optimized to achieve the minimal UAV number by fixing height and the maximal UAV network’s system capacity. In [14] and [15], the trajectory design is formulated as a convex optimization problem. And the trajectories for both single UAV and multiple UAVs are also discussed, respectively [14].

4.2 UAV Position Control with Interference Given the substantial success of unmanned aerial vehicles (UAVs) in surveillance and monitoring tasks, it has become vitally important to bring drones into wireless communications considering their low cost, fast deployment, fully controllable mobility, and the line of sight (LOS) communication links. These drones are usually equipped with diverse payloads for receiving, processing, and transiting signals, which can be viewed as the aerial mobile base station (AMBS) constituting UAV communication networks [16, 17]. UAV communication networks along with traditional satellite networks and ground cellulars construct a space–air–ground three-tier heterogeneous network, which is capable of both providing seamless coverage and of further improving the channel capacity for increasingly prosperous Internet of Things (IoT) networks [18, 19]. More explicitly, the ground macrocell base station (MBS) provides

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the basic broad-band information services for the IoT nodes. Small drones act as on-demand aerial access points for the sake of offloading the ground MBS and of constructing emergency links in the context of contingency. Moreover, UAV network can be viewed as a promising solution to support energy-efficient uplink and location in energy-constrained IoT-centric networks [20]. By contrast, the satellite is used for providing a global coverage benefitting from its broadcast services and broad sight [21]. Hence, relying on such three-tier heterogeneous network, the connectivity, capacity, and energy efficiency of IoT networks can be significantly improved. In particular, as a beneficial communication enhancement facilitator, UAV network is characterized by flexibility, cost-saving, and energy efficiency. Specifically, in remote regions not seamlessly covered by macrocells on the ground, the UAV network may economically provide information services for IoT nodes compared with the high cost of satellite connections. Furthermore, in crowded places the UAV network may relieve the channel congestion of the microcell and guarantee the quality of service (QoS) of latency- and throughput-sensitive IoT applications [22, 23]. More importantly, UAVs can help to quickly construct an emergency information system or even act as the IoT sensing nodes, which is beneficial of supporting the disaster relief when a large part of cellular and Internet infrastructures on the ground are destroyed by a calamity [24]. UAV-aided hybrid communication techniques have been widely investigated in the literature. However, the aforementioned articles mostly focused their attention on how to improve the communication performance such as throughput, delay, and coverage, by designing the mobility of drones, while few considered the intra- and inter-interference and cross-tier resource allocation among different networks. Due to spectrum scarcity, it is possible to share the spectrum among different kinds of communication subsystems. More specifically, the C-band, Ku-band, and Ka-band have been well utilized for air-to-ground reliable wide-band communications. Particularly, a range of compelling applications of the fifth generation wireless systems (5G) attempt to use higher frequency band for providing lowlatency and high-throughput services, such as C-band and Ka-band, which are originally assigned to the airborne communications [25–27]. It is worth noting that mmWave communications [28] have been already adopted in both UAV and satellite scenarios [29]. Hence, a well-implemented network association mechanism of space–air–ground heterogeneous systems is beneficial in terms of both improving the resource utilization and of reducing the cross-tier interference [30–32]. Moreover, they obtained upper bounds of the heterogeneous network’s performance. Furthermore, a distributed joint allocation algorithm is proposed for band selection and power allocation in order to maximize total capacity of a multi-mode and multi-band user terminal (MMT) by Choi et al. in [33]. Moreover, considering the aspect of energy efficiency, Xie et al. in [34] formulated an energy-efficient resource allocation problem as a Stackelberg game for heterogeneous cognitive femtocells, followed by a gradient based iteration solution. In [35], Ye et al. focused their attention on the relationship between the user association and load balancing for heterogeneous networks with picocells and femtocells solved by a

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low-complexity and fast convergence distributed algorithm. Furthermore, in [36], a mixed-integer programming problem was formulated for allocating subchannel and power resources in orthogonal frequency-division multiple access (OFDMA) hybrid networks with femtocells. However, these resource allocation mechanisms may not be suitable for the applications for the UAV-aided space–air–ground heterogeneous network, because few of them considered the characteristics of UAVs in designing resource allocation algorithms, such as dynamic topology, flexible deployment, etc. Given a general space–air–ground heterogeneous communication scenario jointly served by the satellite, low-altitude UAVs, and the ground MBS, users served by UAV networks may severely influence or be inevitably affected by the operation of satellite communication systems and macrocells. Therefore, the resource allocation of different kinds of users should take into account the inevitable cross-tier interference in space–air–ground hybrid networks [37]. Moreover, as the aerial base stations, UAVs play a critical role in offloading the ground MBS and in enhancing ultrareliable communication links. Given the coverage of each drone network, frequently changing UAVs’ horizontal hovering position in the same altitude may result in server inter-interference between adjacent UAV networks and increase the risk of flight collision. Additionally, considering the power constraint of small drones, it may be unrealistic to make the drone adaptively move around for supporting the bursty traffic of the ground users. Hence, a delicately designed UAVs’ hovering altitude distribution is capable of improving the user’s QoS by deploying more drones in different hovering altitudes as well as of guaranteeing their flight safety. The rest of this section is organized as follows. The system model and problem formulation are detailed in Sects. 4.2.1 and 4.2.2, respectively. A two-stage joint hovering altitude and power control solution for UAV networks is elaborated in Sect. 4.2.3. In Sect. 4.2.4, simulation results are provided for characterizing our proposed uplink resource allocation model for UAV networks, followed by our conclusions in Sect. 4.2.5.

4.2.1 System Model In this subsection, as show in Fig. 4.1, we consider a three-tier hybrid network including a satellite network with a geosynchronous earth orbit satellite (GEO), a macrocell with a MBS and M UAV networks sharing the same channel. Each UAV network is served by a hovering drone. Let hm represent the hovering altitude of the m-th drone. The coverage of M UAV networks are overlaid within the coverage of the GEO as well as the macrocell. We focus our attention on the uplink power control of the users in the UAV networks. We assume that the uplink power of both satellite users and of macrocell users is equal.

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Fig. 4.1 The structure of satellite, UAV, and macrocell three-tier hybrid network

The bandwidth of the channel is B, which is divided into K subchannels. The channel fading between the MBS and users on the ground is the frequency-selective Rayleigh fading, while the communication channel between the hovering drone and users is dominated by the line of sight (LoS) path. The channel fading between the GEO and users on the ground is the Rice fading. Let NS and NC denote the number of active users served by the GEO and by the MBS in a macrocell, respectively. Moreover, NU is the number of active users camping on each UAV network. We assume that the satellite users and the macrocell users are uniformly distributed in each coverage area. In our model, two kinds of users with different QoS requirements are served in each UAV network. Specifically, the number of QoS-sensitive users requiring a high transmission rate of Rh is Nuh , while the number of QoS-tolerant users with a low transmission rate requirement of Rl is Nul , where Nuh + Nul = NU . Let Nuh and Nul represent the set of QoSsensitive users and QoS-tolerant users, respectively. Then, we have |Nuh | = Nuh 8 and |Nul | = Nul , and Nuh Nul = ∅. U →C U →U Let gnU1→S ,m,k , gn1 ,m,k and gn1 ,m,k denote the channel gains on k-th subchannel from user n1 in m-th UAV network to the GEO, to the MBS, and to the hovering drone, respectively, where n1 ∈ {1, 2, . . . , NU }, m ∈ {1, 2, . . . , M} and k ∈ {1, 2, . . . , K}. In our model, gnU1→S ,m,k can be viewed as a constant because the UAV users locate far away from the GEO satellite, while gnU1→C ,m,k depends on the channel state and the distance between each UAV user and the MBS. For the sake of analysis, we assume that the service radius of each drone can be neglected compared with its altitude,

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and hence gnU1→U ,m,k is only sensitive to the hovering altitude hm of the m-th drone, which can be formulated as gnU1→U ,m,k =

κ , h2m

(4.1)

where κ denotes the unit power gain in terms of the reference distance hr = 1m. Furthermore, let gnC→U represent the channel gain on k-th subchannel from user n2 2 ,m,k in the macrocell to the m-th hovering drone, while gnS→U denotes the channel gain 3 ,m,k on k-th subchannel from user n3 in the satellite network to the m-th hovering drone, where n2 ∈ {1, 2, . . . , NC } and n3 ∈ {1, 2, . . . , NS }. Moreover, let pnC2 ,k and pnS3 ,k represent the uplink transmission power of user n2 in the macrocell and of user n3 in the satellite network on k-th subchannel, respectively, while pnU1 ,m,k is the uplink transmission power of user n1 in the m-th UAV network on k-th subchannel. In our model, we define PNU ×M×K as the power allocation matrix for the users served by total M UAV networks, and we have [P]n1 ,m,k = pnU1 ,m,k . Here, we define a channel indicator matrix as ANU ×M×K , where [A]n1 ,m,k = an1 ,m,k . To elaborate, an1 ,m,k = 1 represents that the k-th subchannel is occupied by user n1 in the m-UAV network, otherwise, an1 ,m,k = 0. We consider the additive white Gaussian noise (AWGN) with the variance of σ 2 . Hence, as for the m-th UAV network, the received signal-to-interference-plus-noise ratio (SINR) of the hovering drone from user n1 accessing the k-th subchannel can be calculated by γn1 ,m,k =

pnU1 ,m,k gnU1→U ,m,k gnC→U pC + gnS→U pS + σ 2 2 ,m,k n2 ,k 3 ,m,k n3 ,k

,

(4.2)

pC is the interference from the user in the macrocell sharing the where gnC→U 2 ,m,k n2 ,k same subchannel, while gnS→U pS is the interference caused by the user in the 3 ,m,k n3 ,k satellite network occupying the k-th subchannel. Remarkably, at most one user is capable of accessing the same subchannel at one moment in the macrocell, in the satellite network as well as in a UAV network. For the sake of simplification, in our model we assume that the users served by the drones are equipped with a directional antenna and the co-interference between different UAV networks is negligible compared with the cross-tier interference from the macrocell and the satellite network. Relying on the Shannon formula [38], the uplink capacity of m-th UAV network from its user n1 on k-th subchannel can be calculated by Cn1 ,m,k =

! " B log2 1 + γn1 ,m,k . K

(4.3)

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4 Cooperative Resource Allocation in FANET

4.2.2 Problem Formulation In this subsection, we will formulate the uplink resource allocation problem for the UAV network. Furthermore, we assume that the channel state information (CSI) as well as the result of uplink resource allocation can be forwarded to the users by the hovering drone based on the channel reciprocity.

4.2.2.1 Constraints In our uplink resource allocation problem, our objective is to maximize the total capacity in M UAV networks under the following constraints: • UAV user’s power constraint: The users in each UAV network have a maximum U . Hence, for ∀n ∈ {1, 2, . . . , N } and ∀m ∈ transmission power limit of Pmax 1 U {1, 2, . . . , M}, we have K 

U an1 ,m,k pnU1 ,m,k ≤ Pmax .

(4.4)

k=1

Furthermore, the non-negativity of power yields pnU1 ,m,k ≥ 0. • UAV safety flight and hovering altitude constraint: In order to guarantee the safety of M cooperated drones, we consider a hierarchical deployment of these drones with different hovering altitudes. Moreover, the hovering altitudes of them are distributed within a specified safe range of [hmin , hmax ] and subjects to 

(hi − hj )2 ≥ χ 2 ,

(4.5)

i,j ∈M,i =j

where χ 2 is the minimal variance of the altitude of M drones for safety flight and hovering, while M represents the set of M hovering drones. For ∀i, j ∈ M, we have hmin ≤ hi , hj ≤ hmax . • QoS guarantee: For the QoS-sensitive users, the requirement of a high transmission rate of Rh can be expressed as K  k=1

anuh ,m,k Cnuh ,m,k ≥ Rh ,

(4.6)

4.2 UAV Position Control with Interference

129

where ∀nuh ∈ Nuh and ∀m ∈ {1, 2, . . . , M}. By contrast, for the QoS-tolerant users, we have K 

anul ,m,k Cnul ,m,k ≥ Rl ,

(4.7)

k=1

where ∀nul ∈ Nul and ∀m ∈ {1, 2, . . . , M}. • Interference constraint of macrocell: UAV networks share the same frequency with the macrocell. Hence, the macrocell may suffer a cross-tier interference from M UAV networks. Let IkC denote the threshold of the interference on the k-th subchannel and ∀k ∈ {1, 2, . . . , K}, i.e., NU M   m=1 n1 =1

C an1 ,m,k pnU1 ,m,k gnU1→C ,m,k ≤ Ik .

(4.8)

• Interference constraint of satellite network: Similar to the interference constraint of macrocell, let IkS represent the threshold of the interference from UAV networks to the satellite network on the k-th subchannel. Thus, we have NU M   m=1 n1 =1

S an1 ,m,k pnU1 ,m,k gnU1→S ,m,k ≤ Ik ,

(4.9)

where ∀k ∈ {1, 2, . . . , K}. • Subchannel allocation constraint: In each UAV network, one subchannel can be allocated to at most one user, which can be formulated by NU 

an1 ,m,k ≤ 1,

(4.10)

n1 =1

where ∀k ∈ {1, 2, . . . , K} and ∀m ∈ {1, 2, . . . , M}. Moreover, the channel indicator variable an1 ,m,k ∈ {0, 1}.

4.2.2.2 Uplink Resource Allocation Formulation The total capacity of M UAV networks can be given by Ct ot al =

NU  M  K  m=1 n1 =1 k=1

an1 ,m,k Cn1 ,m,k .

(4.11)

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4 Cooperative Resource Allocation in FANET

Hence, the uplink resource allocation problem can be formulated as NU  M  K 

max

an1 ,m,k Cn1 ,m,k

{an1 ,m,k ,pnU ,m,k ,hm } m=1 n =1 k=1 1 1

s.t.

(4.12a) :

K 

U an1 ,m,k pnU1 ,m,k ≤ Pmax ,

∀n1 , m,

k=1

(4.12b) : pnU1 ,m,k ≥ 0, ∀n1 , m, k,  (4.12c) : (hi − hj )2 ≥ χ 2 , i,j ∈M,i =j

(4.12d) : hmin ≤ hm ≤ hmax , (4.12e) :

K 

∀m,

anuh ,m,k Cnuh ,m,k ≥ Rh ,

∀nuh , m,

k=1

(4.12f) :

K 

(4.12) anul ,m,k Cnul ,m,k ≥ Rl ,

∀nul , m,

k=1

(4.12g) :

NU M   m=1 n1 =1

(4.12h) :

NU M   m=1 n1 =1

(4.12i) :

NU 

C an1 ,m,k pnU1 ,m,k gnU1→C ,m,k ≤ Ik ,

∀k,

S an1 ,m,k pnU1 ,m,k gnU1→S ,m,k ≤ Ik ,

∀k,

an1 ,m,k ≤ 1,

∀m, k,

n1 =1

(4.12j) : an1 ,m,k ∈ {0, 1},

∀n1 , m, k.

To elaborate further, (4.12a) and (4.12b) in problem (4.12) are users’ power constraints, while (4.12c) and (4.12d) are hovering altitude constraints. As for the QoS constraints (4.12e) and (4.12f), considering the QoS-tolerant users with a low transmission rate requirement of Rl , where 0 < Rl  Rh , hence we can neglect the constraint (4.12f) in problem (4.12) without loss of generality. Furthermore, (4.12g) and (4.12h) are interference constraint from macrocell and satellite network, respectively. Finally, the subchannel allocation constraints are given by (4.12i) and (4.12j). Unfortunately, however, our optimization objective is a function of (an1 ,m,k , pnU1 ,m,k , hm ), and the form of an1 ,m,k Cn1 ,m,k is not concave in (an1 ,m,k , pnU1 ,m,k , hm ). Moreover, the hovering altitude constraint of (4.12c) and the integer programming constraint of (4.12j) are not convex as well.

4.2 UAV Position Control with Interference

131

In the following, we will reformulate the optimization problem (4.12) as a convex optimization problem with the aid of relaxing the integer constraints and provide its solution relying on a two-stage joint optimization.

4.2.3 Hovering Altitude and Power Control Solution In this subsection, we propose a two-stage joint optimization algorithm for our uplink resource allocation problem. Since there are a total of three kinds of optimization variables in problem (4.12), i.e., an1 ,m,k , pnU1 ,m,k , and hm , it is prohibitive to find the globally optimal solution and thus a near-optimal algorithm with low computational complexity is desirable. In the following, we first fix the hovering altitude hm = h0m , m ∈ M and search the optimal joint subchannel and power control scheme in Stage 1. Then, relying on the result of Stage 1, we try to find the optimal hovering altitude of each drone in Stage 2.

4.2.3.1 Stage 1: Joint Subchannel and Power Control Constraint Relaxation Here, we first study the joint subchannel and power control problem with given hovering altitude, where the initial h0m constitutes an arithmetic progression ranging from hmin to hmax . In the following, we convert the non-convex problem (4.12) into a tractable convex problem [36, 39, 40]. First of all, we relax the inter programming constraint an1 ,m,k ∈ {0, 1} in (4.12j) to a continuous convex constraint an1 ,m,k ∈ [0, 1]. Furthermore, let us introduce the auxiliary variable ρn1 ,m,k = an1 ,m,k pnU1 ,m,k , and hence the uplink capacity of Eq. (4.3) can be converted to ⎛

ρn1 ,m,k gnU1→U ,m,k

⎞

B ⎟ ⎜  ⎠ , log2 ⎝1 + Cˆ n1 ,m,k = K an1 ,m,k gnC→U pC + gnS→U pS + σ 2 2 ,m,k n2 ,k 3 ,m,k n3 ,k (4.13) κ 0 where gnU1→U ,m,k = h2m and hm  hm , m ∈ M. Now we introduce Lemma 1 to show the concavity of our objective function.

Lemma 1 Assume f (x) is a concave function of x when x ∈ [0, X]. Let us introduce a variable a as a = tx, t ∈ [0, 1]. Then, g(t, a) = tf (a/t) is concave in (t, a) when t ∈ [0, 1] and ∀a ∈ [0, tX].

132

4 Cooperative Resource Allocation in FANET 

Proof Since f (x) is a concave function, f (x) ≤ 0. The Hessian matrix of g(t, a) can be calculated as .  f (a/t) a 2 −at 2 ∇ g(t, a) = . −at t 2 t3 Furthermore, for ∀x, y ∈ R and t ∈ [0, 1], we have +

- .  f (a/t) x = (ax − yt)2 ≤ 0. x y ∇ g(t, a) y t3 ,

2

Hence, the Hessian matrix ∇ 2 g(t, a) is a negative semidefinite matrix. Thus, g(t, a) = tf (a/t) is a concave function [41, 42].   Relying on Lemma 1, our optimization objective an1 ,m,k Cˆ n1 ,m,k is concave in (an1 ,m,k , ρn1 ,m,k ), based on which our joint subchannel and power control problem can be reformulated as NU  M  K 

max

{an1 ,m,k ,ρnU ,m,k } m=1 n =1 k=1 1 1

s.t.

(4.14a) :

K 

an1 ,m,k Cˆ n1 ,m,k

U ρn1 ,m,k ≤ Pmax ,

∀n1 , m,

k=1

(4.14b) : ρn1 ,m,k ≥ 0, (4.14c) :

K 

∀n1 , m, k,

anuh ,m,k Cˆ nuh ,m,k ≥ Rh ,

∀nuh , m,

k=1

(4.14d) :

NU M   m=1 n1 =1

(4.14e) :

NU M   m=1 n1 =1

(4.14f) :

NU 

(4.14) C ρn1 ,m,k gnU1→C ,m,k ≤ Ik ,

∀k,

S ρn1 ,m,k gnU1→S ,m,k ≤ Ik ,

∀k,

an1 ,m,k ≤ 1,

∀m, k,

n1 =1

(4.14g) : an1 ,m,k ∈ [0, 1],

∀n1 , m, k.

Obviously, our joint subchannel and power control problem in (4.14) is a convex optimization problem.

4.2 UAV Position Control with Interference

133

4.2.3.2 Lagrangian Dual Decomposition Method In this subsubsection, we use the Lagrangian dual decomposition method to solve our joint subchannel and power control problem in (4.14) [43]. Let L(A, ρ, λ, μ, ν, ω, ξ ) be the Lagrangian function, which can be written as L(A, ρ, λ, μ, ν, ω, ξ ) =

NU  M  K 

an1 ,m,k Cˆ n1 ,m,k

m=1 n1 =1 k=1

+

NU M  

⎛

U λn1 ,m ⎝Pmax −

m=1 n1 =1

K 

⎞ ρn1 ,m,k ⎠

k=1

⎛ ⎞ Nuh M  K   + μnuh ,m ⎝ anuh ,m,k Cˆ nuh ,m,k − Rh ⎠ m=1 nuh =1

+

K  k=1

+

K 

νk ⎝IkC −

ωk ⎝IkS −

M  K 

NU M   m=1 n1 =1

⎛

k=1

+

k=1

⎛

NU M   m=1 n1 =1

⎛

ξm,k ⎝1 −

NU 

⎞

(4.15)

⎠ ρn1 ,m,k gnU1→C ,m,k ⎞ ⎠ ρn1 ,m,k gnU1→S ,m,k ⎞ an1 ,m,k ⎠ ,

n1 =1

m=1 k=1

where λ, μ, ν, ω, and ξ are the Lagrange multipliers associated with the corresponding constraints, while A = {an1 ,m,k } and ρ = {ρn1 ,m,k }. The constraints of (4.14b) and (4.14g) will be considered after obtaining the optimal solution of an1 ,m,k ρn1 ,m,k . Hence, the Lagrangian dual function can be expressed as g(λ, μ, ν, ω, ξ ) = sup L(A, ρ, λ, μ, ν, ω, ξ ).

(4.16)

A,ρ

The Lagrangian dual problem can be formulated as min g(λ, μ, ν, ω, ξ )

λ,μ,ν,ω,ξ

s.t.

(4.17) λ, μ, ν, ω, ξ  0.

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4 Cooperative Resource Allocation in FANET

Equation (4.15) can be reorganized as L(A, ρ, λ, μ, ν, ω, ξ ) =

M  K 

Φ + Ψ,

(4.18)

m=1 k=1

where Φ=

NU 

an1 ,m,k Cˆ n1 ,m,k −

n1 =1

+

Nuh 

NU  n1 =1

λn1 ,m ρn1 ,m,k

n1 =1 NU 

μnuh ,m anuh ,m,k Cˆ nuh −

nuh =1

−

NU 

n1 =1

ωk ρn1 ,m,k gnU1→S ,m,k −

NU 

νk ρn1 ,m,k gnU1→C ,m,k

(4.19)

ξm,k an1 ,m,k ,

n1 =1

and Ψ =

NU M  

U λn1 ,m Pmax

−

m=1 n1 =1

+

K  k=1

νk IkC +

Nuh M  

μnuh ,m Rh

m=1 nuh =1 K 

ωk IkS +

k=1

M  K 

(4.20) ξm,k .

m=1 k=1

Relying on Eq. (4.18), the dual problem can be divided into (M × K) parallel subproblems. Let an∗1 ,m,k and ρn∗1 ,m,k represent the optimal solutions of maximizing the Eq. (4.19). Take the partial derivative of Eq. (4.19) with respect to an1 ,m,k and ρn1 ,m,k , and for the QoS-sensitive user i ∈ Nuh , we have ⎞ ⎛ U →U U →U ∂Φ B ⎝ ai,m,k gi,m,k + μi,m ai,m,k gi,m,k ⎠ = − Θi , ∗ ∂ρi,m,k K ln 2 ai,m,k Δ + ρi,m,k gnU →U ,m,k

(4.21)

1

while for the QoS-tolerant user j ∈ Nul , i.e., ⎛ ⎞ U →U aj,m,k gj,m,k B ⎝ ∂Φ ⎠ − Θj , = U →U ∗ ∂ρj,m,k K ln 2 aj,m,k Δ + ρj,m,k gj,m,k

(4.22)

pC + gnS→U pS + σ 2 and Θn1 = λn1 ,m + νk gnU1→C where Δ = gnC→U ,m,k + 2 ,m,k n2 ,k 3 ,m,k n3 ,k U →S ωk gn1 ,m,k , n1 ∈ {1, 2, . . . , NU }. Considering the constraint of (4.14b), as Φ is also

4.2 UAV Position Control with Interference

135

a concave function, the optimal solution ρn∗1 ,m,k , ∀n1 , m, k obeys: ⎧ ⎪ ⎪ ∗ ⎪ ⎪ ⎨ ρn1 ,m,k = 0 ⎪ ⎪ ∗ ⎪ ⎪ ⎩ ρn1 ,m,k > 0

and

∂Φ |ρ =0 < 0, ∂ρn1 ,m,k n1 ,m,k

and

∂Φ |ρ = 0. =ρ ∗ ∂ρn1 ,m,k n1 ,m,k n1 ,m,k

(4.23)

Then, the optimal solution of the power allocation pnU1∗,m,k = ρn∗1 ,m,k /an1 ,m,k in m-th UAV network on the k-th subchannel for user n1 can be given by

pnU1∗,m,k

⎧ ⎧ ⎫ ⎪ ⎨ ⎬ ⎪ ⎪ B(1 + μ ) Δ i,m ⎪ ⎪ max 0, − , n1 ∈ Nuh , ⎪ ⎪ U →U ⎭ ⎩ K ln 2 × Θn1 ⎪ gj,m,k ⎨ = ⎫ ⎧ ⎪ ⎪ ⎬ ⎨ ⎪ Δ B ⎪ ⎪ ⎪ − max , n1 ∈ Nul . 0, ⎪ U →U ⎭ ⎪ ⎩ K ln 2 × Θn1 gj,m,k ⎩

Similarly, considering an∗1 ,m,k is given by

an∗1 ,m,k , ∀n1 , m, k

(4.24)

∈ [0, 1] in (4.14g), the optimal solution

⎧ ⎪ ∂Φ ⎪ ⎪ an∗1 ,m,k = 0 and |a =0 < 0, ⎪ ⎪ ∂an1 ,m,k n1 ,m,k ⎪ ⎪ ⎪ ⎪ ⎨ ∂Φ |an ,m,k =an∗ ,m,k = 0, an∗1 ,m,k ∈ (0, 1) and 1 1 ⎪ ∂a n1 ,m,k ⎪ ⎪ ⎪ ⎪ ⎪ ∂Φ ⎪ ∗ ⎪ |an1 ,m,k =1 > 0, ⎪ ⎩ an1 ,m,k = 1 and ∂a

(4.25)

n1 ,m,k

where for the QoS-sensitive user i ∈ Nuh ,   U∗ U →U pi,m,k gi,m,k ∂Φ B = (1 + μi,m ) log2 1 + ∂ai,m,k K Δ − (1 + μi,m )

U∗ U →U gi,m,k Bpi,m,k

K

U ∗ g U →U ) ln 2 × (Δ + pi,m,k i,m,k

U∗ − λi,m pi,m,k

U∗ U →C U∗ U →S − νk pi,m,k gi,m,k − ωk pi,m,k gi,m,k − ξm,k ,

(4.26)

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4 Cooperative Resource Allocation in FANET

and for the QoS-tolerant user j ∈ Nul , we have ⎛ ⎞ U ∗ g U →U pj,m,k B ∂Φ j,m,k ⎠ log2 ⎝1 + = ∂aj,m,k K Δ −

U ∗ g U →U Bpj,m,k j,m,k U∗ U →U K ln 2 × (Δ + pj,m,k gj,m,k )

U∗ − λj,m pj,m,k

(4.27)

U∗ U →C U∗ U →S − νk pj,m,k gj,m,k − ωk pj,m,k gj,m,k − ξm,k .

In our model, at most one user is allowed to access the same subchannel at one moment in a UAV network. In order to maximize the Lagrangian function, we have n∗1 = arg max n1

∂Φ , ∂an1 ,m,k

∀m, k,

(4.28)

where an∗∗ ,m,k = 1 represents the sub-optimal channel indicator variable. 1

The Update of Lagrangian Multipliers Since the Lagrangian dual function in Eq. (4.16) is not differentiable, we use the subgradient method to update the Lagrangian multipliers λ, μ, ν, ω, and ξ [44–46]. The Lagrangian multipliers can be updated as follows: ⎡

⎛

⎢ (i) (i) ⎝ U λ(i+1) Pmax − n1 ,m = ⎣λn1 ,m − α1

K 

⎞⎤+ ⎥ ρn1 ,m,k ⎠⎦ , ∀m, n1 ,

(4.29)

k=1

⎡

μ(i+1) nuh ,m

⎛ ⎞⎤+ K  ⎢ ⎥ (i) ⎝ = ⎣μ(i) anuh ,m,k Cˆ nuh ,m,k − Rh ⎠⎦ , ∀m, nuh , nuh ,m − α2

(4.30)

k=1

⎡

⎛

⎢ νk(i+1) = ⎣νk(i) − α3(i) ⎝IkC −

NU M   m=1 n1 =1

⎡

⎛

⎢ ωk(i+1) = ⎣ωk(i) − α4(i) ⎝IkS −

NU M   m=1 n1 =1

⎞⎤+ ⎠⎥ ρn1 ,m,k gnU1→C ,m,k ⎦ , ∀k,

(4.31)

⎞⎤+ ⎠⎥ ρn1 ,m,k gnU1→S ,m,k ⎦ , ∀k,

(4.32)

4.2 UAV Position Control with Interference

137

where i is the indicator of the iteration, and α represents the step size, while [·]+ = max{0, ·}. Moreover, to guarantee the convergence of the subgradient method, the step sizes should satisfy: ∞ 

α (i) = ∞,

and

i=1

lim α (i) = 0.

(4.33)

i→∞

In order to speed up the convergence, an adaptive step size is set as α = 1/I , where I represents the 1iteration index. Relying on Eqs. (4.25)–(4.33), we can obtain the 2 U ∗ ∗ optimal solution an∗ ,m,k , pn1 ,m,k of joint subchannel and power control for each 1 user in UAV networks considering a fixed deployment altitude of hovering drones. Denote the obtained total capacity of UAV networks as Ct ot al (an∗∗ ,m,k , pnU1∗,m,k , h), 1

where h  [h1 , h2 , . . . , hM ]T . 4.2.3.3 Stage 2: Hovering Altitude Optimization

Difference of Convex Programming Based Hovering Altitude Formulation As mentioned before, in Stage 1, we fix the deployment altitude of each hovering drone and search for the optimal joint subchannel mechanism 1 and power control 2 U∗ ∗ for each user in UAV network, denoted as an∗ ,m,k , pn1 ,m,k , where n1 ∈ 1 {1, 2, . . . , NU }, m ∈ {1, 2, . . . , M} and k ∈ {1, 2, . . . , K}. In the following, we try to determine the optimal hovering altitude of each drone based on the results obtained from Stage 1. Considering the safety hovering altitude constraints of (4.12c) and (4.12d) in our original problem formulation in (4.12), we have ⎛ ⎞ NU  K M  U∗  κp B ,m,k n 1 ⎠ max an∗∗ ,m,k log2 ⎝1 + 1 {hm } K h2m Δ m=1 n1 =1 k=1

s.t.



(4.34a) :

(hi − hj )2 ≥ χ 2 ,

(4.34)

i,j ∈M,i =j

(4.34b) : hm ≤ hmax ,

∀m,

(4.34c) : hm ≥ hmin ,

∀m.

The hovering altitude optimization problem in (4.34) can be reformulated as a difference of convex (DC) programming [47, 48], which can be given by min 0 − g0 (h) h

s.t.

(4.35a) : χ 2 − g1 (h) ≤ 0, (4.35b) : hm ≤ hmax ,

∀m,

(4.35c) : hm ≥ hmin ,

∀m,

(4.35)

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4 Cooperative Resource Allocation in FANET

where the objective function can be expressed as g0 (h) =

NU  M  K  m=1 n1 =1 k=1

⎛ ⎞ U∗ κp B ,m,k n 1 ⎠, an∗∗ ,m,k log2 ⎝1 + 1 K h2m Δ

(4.36)

and g1 (h) can be given by g1 (h) =



(hi − hj )2 .

(4.37)

i,j ∈M,i =j

Algorithm 7 CCP aided iterative algorithm for optimal hovering altitude 1: 2: 3: 4: 5: 6: 7: 8: 9: 10: 11:

Initialize an initial feasible h∗(0) , and a stopping threshold δ. Set iteration indicator n := 0. repeat Calculate g0 (h∗(n) ). gˆ 0 (h; h∗(n) )  g0 (h∗(n) ) + ∇g0 (h∗(n) )T (h − h∗(n) ). gˆ 1 (h; h∗(n) )  g1 (h∗(n) ) + ∇g1 (h∗(n) )T (h − h∗(n) ). Solve the convex subproblem in (4.41). Obtain h∗(n+1) and calculate g0 (h∗(n+1) ). Update iteration indicator n := n + 1. until g0 (h∗(n) ) − g0 (h∗(n−1) ) ≤ δ is satisfied. Set h∗  h∗(n) .

Specifically, g1 (h) is a quadratic form, which can be rewritten as g1 (h) = hT Qh, where Q = diag(M) − 1. Moreover, diag(M) denotes a diagonal matrix with all diagonal elements equaling M and 1 is an M × M matrix with all elements being 1. Hence, both g0 (h) and g1 (h) in (4.35) are convex functions. Hence, we can use the CCP method to solve the problem in (4.35), where we are capable of achieving the locally optimal result of the non-convex problem through solving a series of iterative convex subproblems as shown in Algorithm 7. CCP Aided Iterative Solution To elaborate a litter further, let gˆ0 (h) and gˆ1 (h) approximatively be the first-order Taylor expansion of g0 (h) and g1 (h), respectively, i.e., gˆ0 (h; h(n) )  g0 (h(n) ) + ∇g0 (h(n) )T (h − h(n) ) = g0 (h(n) ) + Γ (h(n) )T (h − h(n) ),

(4.38)

and gˆ1 (h; h(n) )  g1 (h(n) ) + ∇g1 (h(n) )T (h − h(n) ) = h(n)T Qh(n) + (2Qh(n) )T (h − h(n) ),

(4.39)

4.2 UAV Position Control with Interference

139

where h(n) is the value of h in the n-th iteration. Moreover, the M × 1 vector Γ = dg0 (h) dh , and the m-th element of Γ can be calculated as Γm = −

NU  K  n1 =1 k=1

2κBan∗∗ ,m,k pnU1∗,m,k .  1 K ln 2 × h3m Δ + hm κpnU1∗,m,k

(4.40)

Thus, the value of h(n+1) can be achieved from solving the following series of convex linear-constraint subproblems: min 0 − gˆ 0 (h) h

(4.41)

s.t.(4.41a) : χ 2 − gˆ1 (h; h(n) ) ≤ 0. Note that, the constraints of (4.35b) and (4.35c) in problem (4.35) will be considered in solving the above-mentioned convex subproblem. The stopping criterion of the iteration can be given by g0 (h(n+1) ) − g0 (h(n) ) ≤ δ,

(4.42)

where δ is the stopping threshold. Here, we also use the Lagrangian dual decomposition method to solve the convex problem (4.41). The Lagrangian function can be given by L(h, ψ) = −gˆ0 (h) + ψ(χ 2 − gˆ1 (h)),

(4.43)

where ψ is the Lagrangian multiplier. Hence, the Lagrangian duality function is denoted as z(ψ) = inf −gˆ0 (h) + ψ(χ 2 − gˆ1 (h)). h

(4.44)

Then, the Lagrangian duality problem can be formulated as max z(ψ) ψ

(4.45)

s.t. ψ ≥ 0. Take the derivative of Eq. (4.44) against hovering altitude vector h, and we have dL(h, ψ) = −Γ (h(n) ) − 2ψQh(n) . dh

(4.46)

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4 Cooperative Resource Allocation in FANET

For ∀m = {1, 2, . . . , M}, we have ⎛ ⎞ M  dL(hm ) (n) ⎠ = 2ψ ⎝ hi − (M − 1)h(n) m dhm i=1,i =m

+

NU  K  n1 =1 k=1

2κBan∗∗ ,m,k pnU1∗,m,k 1 ,  3(n) (n) K ln 2 × hm Δ + hm κpnU1∗,m,k

(4.47)

(n)

where hm is the value of hm in the n-th iteration. Hence, considering the fact that L(hm ) is a convex function, we have ⎧ dL(hm ) ⎪ ⎪ > 0, ⎪ ⎨ hmin , if dh m (n+1) hm = (4.48) ⎪ dL(hm ) ⎪ ⎪ < 0. ⎩ hmax , if dhm Given that the dual function z(ψ) is not differentiable, the Lagrangian multiplier ψ can be updated by ψ (n+1) = [ψ (n) + β (n) (χ 2 − gˆ 1 (hn )]+ ,

(4.49)

where β (n) is the step size of Lagrangian multiplier. Then, we can achieve the optimal h(n+1) for the convex subproblem in (4.41). Hence, relying on the CCP aided iterative algorithm, given fixed {an∗∗ ,m,k , pnU1∗,m,k }, 1 we obtain the optimal hovering altitude vector represented by h∗ . Moreover, for the sake of reducing computational complexity, numerous Boolean optimization algorithms can also be invoked in order to solve the near optimum of h. Thus, the total capacity of UAV networks can be recalculated as Ct ot al (an∗∗ ,m,k , pnU1∗,m,k , h∗ ). 1

However, the pseudo-optimal capacity Ct ot al (an∗∗ ,m,k , pnU1∗,m,k , h∗ ) is not the final 1 optimal capacity of our proposed uplink resource allocation problem in (4.12), namely Ct∗ot al . In the following, we will combine the aforementioned two stages in order to search for the optimal network capacity jointly considering the hovering altitude and the subchannel and power control.1

(i) Hereafter, we use Ctotal (an∗∗ ,m,k , pnU1∗,m,k , h∗ ) to represent the pseudo-optimal capacity of the i-th 1 two-stage iterative joint resource association for a more clear expression.

1

4.2 UAV Position Control with Interference

141

4.2.3.4 Joint Hovering Altitude and Power Control Two-Stage Joint Resource Allocation In Sects. 4.2.3.1 and 4.2.3.3, we have studied the optimization problem of both the power control (Stage 1) and the hovering altitude (Stage 2). In this subsubsection, we combine these two stages and jointly optimize the hovering altitude and power control scheme. Specifically, in the i-th iteration, the optimal subchannel and power control of {an∗∗ ,m,k , pnU1∗,m,k }(i) can be achieved in Stage 1 based on fixed 1

h(i−1) , yielding the total capacity of UAV networks of Ct ot al (an∗∗ ,m,k , pnU1∗,m,k , h). (i)

1

Then, relying on given subchannel and power control of {an∗∗ ,m,k , pnU1∗,m,k }(i) , in 1

Stage 2, we can obtain the optimal hovering altitude vector h∗(i) and the pseudoU∗ ∗ ∗ optimal capacity Ct(i) ot al (an∗1 ,m,k , pn1 ,m,k , h ) in the i-th iteration of the two-stage joint resource allocation algorithm. In return, we conduct the optimization in Stage 1 based on the latest h∗(i) and update the {an∗∗ ,m,k , pnU1∗,m,k }(i+1) as well as 1

U∗ ∗ ∗(i+1) and Ct(i+1) ot al (an∗ ,m,k , pn1 ,m,k , h). Then, relying on Stage 2, we can obtain the h 1

the pseudo-optimal capacity Ct ot al (an∗∗ ,m,k , pnU1∗,m,k , h∗ ). (i+1)

1

Algorithm 8 Joint hovering altitude and power control 1: Initialize an initial feasible h(0) , and a stopping threshold Λ. 2: Set iteration indicator i := 0. 3: repeat 4: Update iteration indicator i := i + 1. 5: Obtain {an∗∗ ,m,k , pnU1∗,m,k }(i) by solving (4.14) in Stage 1. 1

6:

(i) Calculate Ctotal (an∗∗ ,m,k , pnU1∗,m,k , h). 1

7: 8:

Obtain h∗(i) by solving (4.35) in Stage 2. (i) (an∗∗ ,m,k , pnU1∗,m,k , h∗ ). Calculate Ctotal 1

(i) (i−1) ∗ 9: until Ctotal (an∗∗ ,m,k , pnU1∗,m,k , h∗ ) − Ctotal (an∗ ,m,k , pnU1∗,m,k , h∗ ) ≤ Λ is satisfied. 1

∗ 10: Set Ctotal  Ctotal (an∗∗ ,m,k , pnU1∗,m,k , h∗ ). (i)

1

1

11: Set {an∗∗ ,m,k , pnU1∗,m,k }  {an∗∗ ,m,k , pnU1∗,m,k }(i) . 1

12: Set h∗  h∗(i) .

1

Let Λ be the stopping threshold of our two-stage resource allocation scheme. If the following condition is satisfied: Ct ot al (an∗∗ ,m,k , pnU1∗,m,k , h∗ ) − Ct ot al (an∗∗ ,m,k , pnU1∗,m,k , h∗ ) ≤ Λ, (i+1)

(i)

1

1

(4.50)

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4 Cooperative Resource Allocation in FANET

the final optimal uplink total capacity of M UAV networks can be given by Ct∗ot al  Ct ot al (an∗∗ ,m,k , pnU1∗,m,k , h∗ ), (i+1)

(4.51)

1

where the optimal subchannel and power control result is given by {an∗∗ ,m,k , pnU1∗,m,k } 1

 {an∗∗ ,m,k , pnU1∗,m,k }(i+1) as well as the optimal hovering altitude h∗  h∗(i+1) . The 1 procedure of the two-stage joint hovering altitude and power control optimization scheme for UAV networks is summarized in Algorithm 8.

4.2.3.5 Algorithm Implementation In this subsubsection, we will elaborate more on the algorithm implementation of our proposed UAV hovering altitude aided resource allocation mechanism described in Sect. 4.2.3, namely TSJ-RA as shown in Algorithm 9 for space–air–ground threetier heterogeneous networks. Furthermore, to reduce the computational complexity we propose a heuristic resource allocation algorithm in Algorithm 10, i.e., PPC-RA, which has lower computational complexity compared with the exhaustive search algorithm as well as with TSJ-RA.

4.2.3.6 Supplementary Analysis In this subsubsection, we provide a further explanation for our proposed two-stage resource allocation scheme in the face of both the optimization algorithm and the practical system design. As for solving the optimal power control problem in Eq. (4.24), the transmission power of both QoS-sensitive users and QoS-tolerant U →U users is related to Δ/gnU1→U ,m,k and Θn1 , where Δ/gn1 ,m,k represents the interference level from outside UAV networks, while Θn1 measures the interference level that the UAV users impose to other networks. We can conclude that the large Δ/gnU1→U ,m,k may result in less power assigned to subchannel k. Furthermore, Θn1 also limits the power allocation for the sake of reducing influence to other communication systems. In contrast to the power allocation for QoS-tolerant users, μn1 ,m tends to allocate more power for QoS-sensitive users, which yields a high data transmission rate. As for the subchannel allocation based on Eq. (4.28), due to the Lagrangian multiplier μn1 ,m of Eq. (4.26), more subchannel resources may be assigned to the QoS-sensitive users. Hence, in practical system design, we should to a large degree use the subchannels having less interference from outside UAV networks and also imposing less interference to other networks, and allocate more such “clean” subchannels and more power to QoS-sensitive users. Moreover, the optimal hovering altitude of M drones can be obtained by solving a series of reduced convex problems with the aid of CCP algorithm. According to Eqs. (4.47) and (4.48), the optimal hovering altitude must be the boundary value of

4.2 UAV Position Control with Interference

143

Algorithm 9 Two-stage joint resource allocation (TSJ-RA) 1: 2: 3: 4: 5:

Initialize K, M, NU , NS , NC , Nul and Nuh . Initialize IkC , IkS , Rh , Rl and Pmax . U →C U →S C→U S→U C S Initialize gnU1→U ,m,k , gn1 ,m,k , gn1 ,m,k , gn2 ,m,k , gn3 ,m,k and pn2 ,k , pn3 ,k . (0) (0) (0) (0) (0) Initialize Lagrangian variables λ , μ , ν , ω and ψ . Set the maximum number of iteration indicators imax and jmax . Let i := 0 and j := 0, respectively. 6: Initialize hovering altitude h(0) and subchannel-power control {an1 ,m,k , pnU1 ,m,k }(0) . (0)

7: Calculate Ctotal ({an1 ,m,k , pnU1 ,m,k }(0) , h(0) ) 8: repeat 9: j := j + 1. 10: repeat 11: i := i + 1. 12: for k = 1 to K do 13: for m = 1 to M do 14: for n1 = 1 to NU do 15: i. Update the power allocation pnU1 ,m,k of QoS-sensitive and QoS-tolerant UAV users relying on Eq. (4.24). 16: ii. Calculate the partial derivative of Eq. (4.26) and Eq. (4.27), respectively. 17: end for 18: Update the subchannel allocation an1 ,m,k of the UAV network relying on Eq. (4.28). 19: end for 20: end for 21: Update Lagrangian variables λ, μ, ν and ω relying on Eq. (4.29), Eq. (4.30), Eq. (4.31) and Eq. (4.32), respectively. 22: until i = imax or arrive the convergence. 23: Get {an1 ,m,k , pnU1 ,m,k }(j ) . 24: Calculate Ctotal ({an1 ,m,k , pnU1 ,m,k }(j ) , h(j −1) ). 25: Update the hovering altitude of M UAVs relying on Algorithm 7. 26: Get h(j ) . (j ) 27: Calculate Ctotal ({an1 ,m,k , pnU1 ,m,k }(j ) , h(j ) ). 28: until j = jmax or satisfying Eq. (4.43). (j ) ∗ 29: Denote Ctotal  Ctotal ({an∗∗ ,m,k , pnU1∗,m,k }(j ) , h∗(j ) ). (j )

1

feasible region. To elaborate,

M i=1,i =m

hi − (M − 1)hm in Eq. (4.47) measures the

difference between the hovering altitude of the m-th UAV and the average altitude of others. Our algorithm aims to enlarge the gap between the hovering altitude of the m-th UAV and the average altitude of others. In terms of the computational complexity, Algorithm 9 combines jmax iterations of the update of power control and the update of hovering altitude. Specifically, the computational complexity of the update of power control is O(imax KMNU ), while the computational complexity of the update of hovering altitude is O(nmax M), where imax and nmax are the maximum number of iteration for each step, respectively. Therefore, Algorithm 9 has a computational complexity of O(jmax (imax KMNU + nmax M)). By contrast, Algorithm 10 is a low-complexity

144

4 Cooperative Resource Allocation in FANET

Algorithm 10 Proportionable power constrained resource allocation (PPC-RA) 1: 2: 3: 4: 5: 6: 7: 8: 9: 10: 11: 12: 13: 14: 15: 16: 17: 18: 19:

Initialize K, M, NU , NS , NC , Nul and Nuh . Initialize IkC , IkS , Rh , Rl and Pmax . U →C U →S C→U S→U C S Initialize gnU1→U ,m,k , gn1 ,m,k , gn1 ,m,k , gn2 ,m,k , gn3 ,m,k and pn2 ,k , pn3 ,k . Set the power allocation scale parameter θ. for m = 1 to M do Let the subchannel set be K = {1, 2, . . . , K}. Let UAV user set be NU and the QoS-sensitive user set be Nuh . while Nuh = Ø, i ∈ Nuh do i. Choose i ∈ Nuh . U →U /Δ). ii. Find k ∗ = arg max(gi,m,k k∈K

iii. Set ai,m,k ∗ = 1, and K := K − {k ∗ }. U U →U iv. Set pi,m,k ∗ = θ(gi,m,k ∗ /Δ). if Eq. (4.14c) is satisfied then Nuh := Nuh − {i}. NU := NU − {i}. end if end while while K = Ø, n1 ∈ NU do i. Find {n1 , k}∗ = arg max (gnU1→U ,m,k /Δ). k∈K,n1 ∈NU

20: ii. Set an1 ,m,k |{n1 ,k}={n1 ,k}∗ = 1. 21: iii. Set an1 ,m,k∗ = 1, and K := K − {k ∗ }. 22: iv. Set pnU1 ,m,k∗ = θ(gnU1→U ,m,k ∗ /Δ). 23: end while 24: end for 25: Update the power allocation scale parameter θ relying on (4.14a), (4.14d) and (4.14e), i.e.,

θ = min

⎧ ⎪ ⎪ ⎪ ⎪ ⎨

U Δ Pmax

K ⎪ ⎪ ⎪ an1 ,m,k gnU→U ⎪ ⎩ 1 ,m,k k=1

,

IkC Δ M N U m=1 n1 =1

an1 ,m,k gnU→C g U→U 1 ,m,k n1 ,m,k

,

IkS Δ

M N U m=1 n1 =1

⎫ ⎪ ⎪ ⎪ ⎪ ⎬

⎪ ⎪ an1 ,m,k gnU→S g U→U ⎪ ⎪ 1 ,m,k n1 ,m,k ⎭

.

26: Update the hovering altitude h of M UAVs relying on Algorithm 7. ∗  Ctotal (an1 ,m,k , pnU1 ,m,k , h). 27: Denote Ctotal

greedy scheme aiming to preferentially satisfy the QoS-sensitive users, which gets rid of the update of a range of Lagrange dual. It has a much lower computational complexity of O(M(NU2 + (K − NU )2 ) + nmax M) compared with Algorithm 9.

4.2.4 Simulation Results In our simulation, three kinds of users are located in a 500m × 500m square region. NC = 10 macrocell users and NS = 10 satellite users are randomly distributed in the area. Moreover, the coverage radius of each drone is 50m and UAV users are randomly distributed in each coverage area. The altitude of GEO is 36000km, and

4.2 UAV Position Control with Interference

145

only one MBS is considered in the simulation. The carrier frequency is 2.4GHz and the total number of the subchannel is K = 128, each of which has a bandwidth of 15kHz. The AWGN power spectrum density is −174dBm/Hz. Furthermore, the channel between users and the MBS follows Rayleigh fading. By contrast, the channels between users and UAVs and the GEO follow Rician fading with 5dB Rician factor. Let the reference-distance unit power gain be κ = 1.4 × 10−4 [49]. The hovering altitude of drones spans from 200m to 400m. In the following, we consider two scenarios with 4 UAVs and 9 UAVs, respectively. Each drone serves NU = 4 UAV users. In the 4-UAV scenario, there are total 8 QoS-sensitive users and 8 QoS-tolerant users, while there are total 24 QoSsensitive users and 12 QoS-tolerant users in the 9-UAV scenario. Moreover, the minimum data rate requirement of QoS-sensitive users is Rh = 30kbps. We define the spectrum efficiency (SE) of UAV networks to evaluate the effectiveness of our proposed algorithm as SE = Ct ot al /B (bps/Hz). U on the Figure 4.2 shows the impact of the maximum transmission power pmax UAV network’s SE, where the maximum interference limit of both the MBS and the GEO is 0dBm, i.e., I C = 0dBm and I S = 0dBm for all subchannels k ∈ {1, 2, . . . , K}. It can be observed that our proposed TSJ-RA algorithm outperforms 700

Spectral Efficiency (bps/Hz)

600

500

Average Allocation in 9-UAV Scenario TSJ-RA Algorithm in 9-UAV Scenario Average Allocation in 4-UAV Scenario TSJ-RA Algorithm in 4-UAV Scenario

400

300

200

100

0 1000

1500

2000

2500

3000

3500

4000

4500

5000

Maximum Transmission Power of Each UAV User P max (mW) Fig. 4.2 Spectrum efficiency versus maximum transmission power of UAV users parameterized by different number of UAV networks

146

4 Cooperative Resource Allocation in FANET 500

Spectral Efficiency (bps/Hz)

450 400

Average Allocation in 9-UAV Scenario TSJ-RA Algorithm in 9-UAV Scenario Average Allocation in 4-UAV Scenario TSJ-RA Algorithm in 4-UAV Scenario

350 300 250 200 150 100 50 0 -60

-50

-40

-30

-20

-10

0

10

20

Maximum Interference Limit on MBS I C (dBm) Fig. 4.3 Spectrum efficiency versus maximum interference limit of the MBS parameterized by different number of UAV networks

the average resource allocation scheme2 in terms of the SE. It is because the proposed TSJ-RA algorithm jointly optimizes the altitudes of the drones and transmission power of all users, achieving a decent SE performance and satisfying all the constraints all the time. As a comparison, the comparison algorithm is not aware of system configuration and introduces significant SE loss. Besides, higher SE is obtained with a loose transmission power constraint. Meanwhile, a dense UAV deployment is capable of substantially increasing the network’s SE. Figure 4.3 demonstrates the performance of UAV network’s SE characterized U = by the maximum interference limit of the MBS, i.e., I C , with respect to Pmax S 1000mW and I = 0dBm. Since the average resource allocation scheme does not rely on the interference limit, the spectrum efficiency is not improved with the increase of MBS’s interference limit. As for the TSJ-RA algorithm, a loose interference limit on the MBS yields a high SE of UAV networks to some extent. It is because that with a loose interference limit, UAV users are capable of using higher transmission power, while with a strict interference limit, UAV users have to properly decrease the transmission power to satisfy the pre-set constraint. Besides, it can be seen that when the interference limit is loose enough, such as I C = 0dBm for 9-UAV scenario and I C = −20dBm for 4-UAV scenario, the SE remains 2

In this subsection, the average resource allocation scheme means that subchannels as well as power are uniformly allocated to two kinks of users without considering the interference limit of the MBS and the GEO under the constraint of a secure hovering altitude of each drone.

4.2 UAV Position Control with Interference

147

Probabilities of Violating Interference Limit

1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 -70

TSJ-RA Algorithm Average Allocation in 9-UAV Scenario Average Allocation in 4-UAV Scenario -65

-60

Maximum Interference Limit on MBS I C (dBm)

-55

Fig. 4.4 Probabilities of violating the maximum interference limit on the MBS

unchanged. It is because with a loose threshold, the pre-set interference constraint can be always satisfied with the given maximum available transmission power. To elaborate a little further, Fig. 4.4 portrays the probabilities of violating the maximum interference limit on the MBS, which is defined as the ratio of the number of subchannels with interference higher than pre-set maximum limit to the total number of subchannels. We can conclude that our proposed algorithm satisfies the interference limit for all subchannels k ∈ {1, 2, . . . , K} at all given I C values. However, the average algorithm has a high probability of violating the interference limit when the interference requirement is stringent. In Fig. 4.5, we evaluate the performance of SE versus different minimum hovering altitudes in different scenarios. It can be seen that a lower minimum hovering altitude is beneficial in terms of improving the SE of the total UAV networks relying on both our proposed TSJ-RA algorithm and on the average algorithm. Furthermore, Fig. 4.6 demonstrates the probabilities of satisfying the pre-set capacity requirement for QoS-sensitive users versus different values of Rh , which is defined as the ratio of the number of QoS-sensitive users with satisfied capacity to the total number of QoS-sensitive users. It can be seen that our proposed algorithm always outperforms the comparison algorithm at all given Rh values. It is because that our proposed algorithm considers the capacity requirement of QoSsensitive users, making the QoS-sensitive users have high priorities to obtain the channels. As a result, the probability of satisfying capacity requirement for QoSsensitive users equals to 1 all the time. By contrast, the average allocation is not aware of the pre-set capacity constraint. Especially when the capacity requirement

148

4 Cooperative Resource Allocation in FANET 500

Spectral Efficiency (bps/Hz)

450 400 350

TSJ-RA Algorithm in 4-UAV Scenario Average Allocation in 4-UAV Scenario TSJ-RA Algorithm in 9-UAV Scenario Average Allocation in 9-UAV Scenario

300 250 200 150 100 50 0 100

120

140

160

180

200

220

240

260

280

300

Minimum Altitude of Drones h min (m)

Probabilities of Satisfying the Capacity Requirement

Fig. 4.5 Spectrum efficiency versus minimum hovering altitude parameterized by different number of UAV networks

1 0.9

TSJ-RA Algorithm Average Allocation with hmin =200 m

0.8

Average Allocation with hmin =300 m

0.7 0.6 0.5 0.4 0.3 0.2 0.1 15

20

25

30

35

40

45

Capacity Requirement of QoS-Sensitive Users Rh (kbps) Fig. 4.6 Probabilities of satisfying capacity requirement of QoS-sensitive users in terms of different minimum hovering altitude of drones

4.3 UAV Trajectory Design for Space–Air–Ground Networks

149

is stringent, i.e., 40kbps, only around 10% of QoS-sensitive users can achieve decent capacity higher than the pre-set constraint.

4.2.5 Conclusions In this section, we formulated a two-stage joint hovering altitude and power control for UAV networks considering the feasible deployment of drones in the context of a space–air–ground three-tier heterogeneous network for supporting IoT applications. After appropriate convex relaxation, we used Lagrange dual decomposition and CCP method to provide a near-optimal solution for our proposed problem, followed by a low-complexity proportionable power constrained resource allocation algorithm. Finally, extensive simulations were conducted in order to show the performance of our resource allocation mechanism, which yielded an improved UAV network’s throughput.

4.3 UAV Trajectory Design for Space–Air–Ground Networks Given the limited transmission power of smart devices in Internet of remote things (IoRT), unmanned aerial vehicle (UAV) aided space–air–ground (SAG) networks become a beneficial remedy for uplink data transmission in IoRT networks [50]. In this section, we propose a SAG-IoRT framework, where drones act as relays to upload the data from smart devices to low earth orbit (LEO) satellites. Considering the large number of smart devices, we maximize the system capacity by jointly optimizing smart device connection scheduling, power control, and UAV trajectory, where the joint optimization is a non-convex optimization problem. The formulated problem is a mixed-integer non-convex optimization problem, which is challenging to solve directly. Hence, an efficient iterative algorithm is proposed for solving the above-mentioned non-convex optimization problem by applying variable substitution, successive convex optimization (SCA) techniques, and the block coordinate decent (BCD) algorithm. In particular, we alternately iterate smart device connection scheduling, power control, and UAV trajectory design to obtain the maximum system capacity. Numerical simulation results show that our proposed algorithm substantially improves the system capacity in comparison to the static UAV scheme, and achieve a gain of at least 22.3% in terms of the capacity against dynamic UAV scheme with a circular trajectory. The rest of this section is organized as follows. Sections 4.3.1 and 4.3.2 elaborate the system model and optimization problem formulation, respectively. Section 4.3.3 further gives the solution and elaborates the solution of three blocks. A resource allocation algorithm jointing smart device connection scheduling, power control, and UAV trajectory design is proposed, and the complexity analysis of the algorithm

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4 Cooperative Resource Allocation in FANET

is also given. Then, in Sect. 4.3.4, simulation results prove that our algorithm has good convergence and effectiveness. Finally, the conclusion is given in Sect. 4.3.5.

4.3.1 System Model As shown in Fig. 4.7, we consider a communication problem of uplink transmission in a three-layer heterogeneous network composed of the space layer supported by LEO satellites, the air layer supported by UAV relays, and the ground layer for end smart devices. The satellite communication capabilities can provide seamless coverage for very large areas [51]. And the high mobility of UAV guarantees the efficient and effective communication support for some extreme situations. We assume that the LEO satellite does not switch within the time process T , thus we consider a scenario where one LEO satellite serves. We assume that M UAVs with AF relays are flying in the air, and they are only used for data forwarding, without considering direct communication between them. Suppose there are K The LEO satellite

UAV relays mobile

Smart devices

Fig. 4.7 System model

4.3 UAV Trajectory Design for Space–Air–Ground Networks

151

smart devices on the ground. The set of UAVs and smart devices are denoted by M = {1, 2, . . . , M} and K = {1, 2, . . . , K}, respectively. To simplify the problem, the LEO satellite, UAVs, and the smart devices share the identical frequency band within a time process T . The height of LEO satellite is Hs , and the horizontal 0T / ∈ R2×1 , k ∈ K . coordinate of smart devices on the ground is wk = xk , yk It is assumed that the UAV is at a fixed minimum height H required for safety and coverage considerations. The entire time process T is divided into N time T slots, n ∈ N = {1, 2, . . . , N }, and the length of each time slot is δt = N . The horizontal position of the mth UAV in the nth slot is expressed as qm [n] = 0T / xm [n] , ym [n] ∈ R2×1 , m ∈ M , n ∈ N . Then UAVs flight trajectory can be 5 6**N expressed as qm [n] * , and the UAV trajectory needs to meet the following n=1 constraints: / 0 / 0 qm 1 = qm N , ∀m,

(4.52)

which implies that each UAV needs to return to the original position within the whole time process T to ensure that ground smart devices can be served in the next time process T . Assuming that the maximum flight rate of the UAV is Vmax , the maximum distance of each time can be expressed as Smax =Vmax δt , thus the UAV trajectory is restricted by the maximum flight rate as ;2 ; / 0 ; ; 2 , ∀m, n = 1, 2, . . . , N − 1. ;qm n + 1 − qm [n]; ≤ Smax

(4.53)

In addition, we consider a multi-UAV system. Considering the security issues among UAVs to avoid collisions, a certain safety distance dmin must be guaranteed among different UAVs. The safety constraint of UAVs can be expressed as ; ; ;qm [n] − qj [n];2 ≥ d 2 , ∀m, n, j = m. (4.54) min In the nth time slot, the uplink transmission power of the kth ground smart device D→U D→U to the mth UAV is Pk,m [n], the distance is dk,m [n], and the channel gain is D→U hk,m [n]. The uplink transmission power of the mth UAV to the LEO satellite U →S [n], and the channel gain is hU →S [n]. h is is PmU →S [n], the distance is dm 0 m the channel gain at a reference distance of 1m from the smart device to the UAV. D→U D→U D→U [n], Further, Pk,m [n] is subject to the constraint 0 ≤ Pk,m [n] ≤ Pmax D→U where Pmax [n] represents the maximum transmission power of smart devices. Interference among smart devices is not considered in order to simplify the analysis. Therefore, in the nth time slot, the transmission channel gain and signal-to-noise ratio expression of the kth smart device to the mth UAV can be given by −2  D→U d = hD→U = h [n] [n] 0 k,m k,m

H2

h0 ; ;2 , ; + qm [n] − wk [n];

(4.55)

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4 Cooperative Resource Allocation in FANET

and D→U γk,m [n] =

D→U Pk,m [n] hD→U k,m [n]

σk2

(4.56)

.

U →S [n], where Similarly, PmU →S [n] is subject to the constraint 0 ≤ PmU →S [n] ≤ Pmax U →S Pmax [n] represents the maximum transmission power of UAVs. In the nth time slot, without considering the interference among UAVs, the transmission channel gain and signal-to-noise ratio expression of the mth UAV to the LEO satellite can be given by

 −2 →S U →S = hU [n] = G0 dm [n] m

G0 (Hs − H )

2

≈

G0 , Hs2

(4.57)

and γmU →S [n] =

→S [n] PmU →S [n] hU m , 2 σm

(4.58)

where G0 is the channel gain at a reference distance of 1m from the UAV to the LEO satellite, which is larger than the h0 . Therefore, according to the Shannon formula and AF protocol [52], in the nth time slot, the data from the kth smart device is amplified and forwarded to the LEO satellite through the mth UAV, and the uplink transmission rate can be expressed as  Rk,m [n] = W log2 1 +

D→U γk,m [n] γmU →S [n] D→U 1 + γk,m [n] + γmU →S [n]

 .

(4.59)

Meanwhile, a binary variable ak,m [n] is introduced to indicate whether the kth ground smart device is connected to the mth UAV in the nth time slot. If connected, ak,m [n] = 1, otherwise ak,m [n] = 0. We assume that at each time slot, each UAV serves at most one smart device, and each smart device is served by at most one UAV, which can be expressed as M  K 

ak,m [n] ≤ 1, ∀n,

(4.60)

ak,m [n] ∈ {0, 1} , ∀k, m, n.

(4.61)

m=1 k=1

and

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153

Considering that the UAV angle is θ , and its coverage radius can be represented by H tan θ , the coverage constraint of the UAV can be represented as ; ; ak,m [n] ;qm [n] − wk [n]; ≤ H tan θ, ∀k, m, n.

(4.62)

Thus, the average system throughput in the entire time process T can be given by Rk,m =

N 1  ak,m [n] /Rk,m [n]. N

(4.63)

n=1

For the convenience of reference, the notation summary of system model is given in Table 4.1. Table 4.1 Notation summary Symbol K, M Hs , H wk , qm [n] T , N, δt Vmax , Smax , θ dmin D→U Pk,m [n], hD→U k,m [n], →S [n], PmU →S [n], hU m D→U U →S [n] dk,m [n], dm

h0 , G0 , W D→U [n], P U →S [n] Pmax max D→U γk,m [n], γmU →S [n]

σk2 , σm2 Rk,m [n] ak,m [n] Rk,m R2×1

.

Description /The number of smart devices and UAVs /The height of the LEO satellite and UAVs The horizontal position of the kth / smart device and the trajectory of the mth UAV in the nth time slot The entire time process, the number of / time slots, the length of each time slot Maximum UAV flying speed, / the maximum distance in time δt , the UAV angle /Safety distance among different UAVs In the nth time slot, uplink transmission power / and channel gain from the kth ground smart device to the mth UAV In the nth time slot, uplink transmission / power and channel gain from the mth UAV to the LEO satellite In the nth time slot, the distance from the kth ground smart device to the / mth UAV, the distance from the mth UAV to the LEO satellite Channel gain at a reference distance of 1m from the smart device to the UAV / and from the UAV to the LEO satellite, system bandwidth The maximum transmission power of smart / devices and UAVs in the nth time slot In the nth time slot, the signal-to-noise ratio from the kth smart device to / the mth UAV, and the signal-to-noise ratio from the mth UAV to the LEO satellite Noise power spectral density of / additive Gaussian white noise Transmission rate of the kth ground smart device to the LEO satellite / through the mth UAV in the nth time slot Connection scheduling between the kth / ground smart device and the mth UAV in the nth time slot Average system throughput in / the entire time process 2 × 1 dimensional real / number space Euclidean norm / (vector norm)

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4 Cooperative Resource Allocation in FANET

4.3.2 Problem Formulation 6

5

6

5

1

2

D→U Let A = ak,m [n] , ∀k, m, n , Q = qm [n] , ∀m, n , PD→U = Pk,m [n] , ∀k, m, n , 1 2 and PU →S = PmU →S [n] , ∀m, n . Given the known horizontal coordinates of ground smart devices, the goal of this subsection is to both maximize the system capacity, and to jointly optimize the smart devices scheduling connection (A), the UAV relays trajectory design (Q), the transmission power of smart devices (PD→U ) and the transmission power of UAV relays (PU →S ). Thus, the optimization problem can be formulated as follows:

5

s.t.

max

6

M K

A,Q,PD→U ,PU→S m=1 k=1

C1:

K M

Rk,m

ak,m [n] ≤ 1, ∀n,

m=1 k=1

C2:ak,m [n] ∈ {0, 1} , ∀k, m, n, D→U D→U [n] , ∀k, m, n, C3:0 ≤ Pk,m [n] ≤ Pmax U →S [n] , ∀m, n, C4:0 ≤ PmU →S [n] ≤ Pmax

/ 0 / 0 C5:qm 1 = qm N , ∀m,

(4.64)

; / ;2 0 ; ; 2 , ∀m, n, C6:;qm n+1 −qm [n]; ≤ Smax ; ; C7:ak,m [n] ;qm [n] − wk [n]; ≤ H tan θ, ∀k, m, n, ; ;2 2 , ∀m, n, j = m, C8:;qm [n] − qj [n]; ≥ dmin C9:

M K N n=1 m=1 k=1

s , ∀k, m, n. ak,m [n] /Rk,m [n] ≤ Cmax

C3 and C4 represent the transmission power limits of smart devices and UAVs, respectively, which are all non-negative and have a maximum constraint. C9 is the LEO satellite capacity constraint, which guarantees that the total amount of data s transmitted cannot exceed the LEO satellite capacity. Cmax represents the maximum capacity of the LEO satellite. Solving the problem (13) is challenging due to the following reasons. First, the concavity and convexity of the objective function in multivariate variables cannot be determined. Second, the connection scheduling constraint ak,m [n] in C2 is a binary variable, which is an integer constraint. Finally, C8 and C9 are non-convex constraints. Therefore, the problem (13) is a mixed-

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155

integer non-convex optimization problem, which is difficult to obtain the optimal solution in general.

4.3.3 The Solution for Optimization Problem Since the optimization problem (13) is a non-convex optimization problem, it is challenging to obtain its optimal solution directly. In general, there is no standard way to solve this non-convex optimization problem. In this subsection, an effective iterative algorithm will be proposed through block coordinate descent (BCD) (also called alternating iteration method) [53], variable relaxation, successive convex approximation (SCA) [54], and variable substitution [55]. More specifically, given the UAV trajectory (Q), the transmission power of smart devices (PD→U ), and the transmission power of UAVs (PU →S ), the smart device connection scheduling (A) is optimized by solving a linear programming (LP) problem. Through given smart device connection scheduling (A) and the UAV trajectory (Q) (the transmission power of smart devices (PD→U ) and the transmission power of UAV relays (PU →S )), the transmission power of smart devices (PD→U ) and the transmission power of UAVs (PU →S ) (the UAV trajectory (Q)) can be optimized by applying SCA. Then, three blocks can be alternatively iterated to obtain the resource allocation scheme. 4.3.3.1 Smart Devices Connection Scheduling Optimization In this subsubsection, in order to make the optimization problem (13) tractable, we relax the binary variable into continuous variable aˆ k,m [n], i.e., ak,m [n] ∈ {0, 1} → N / 0 aˆ k,m [n] ∈ 0, 1 , then the system capacity Rˆ k,m = N1 aˆ k,m [n] /Rk,m [n]. n=1

Given the UAV trajectory, the transmission power of smart devices and UAVs, i.e., 1 2 Q, PD→U , PU →S , the problem (13) can be transformed into the problem P1, which can be expressed as P1 :

s.t.

K M max Rˆ k,m {A} m=1 k=1 K M

aˆ k,m [n] ≤ 1, ∀n,

m=1 k=1

/ 0 aˆ k,m [n] ∈ 0, 1 , ∀k, m, n, ; ; aˆ k,m [n] ;qm [n] − wk [n]; ≤ H tan θ, ∀k, m, n, M K N n=1 m=1 k=1

s , ∀k, m, n. aˆ k,m [n] /Rk,m [n] ≤ Cmax

(4.65)

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4 Cooperative Resource Allocation in FANET

Since the problem P1 is a standard LP problem, it can be solved by using the optimization toolbox CVX [56].

4.3.3.2 Power Control Optimization In this subsubsection, 5 6 we fix smart device connection scheduling and the UAV trajectory, i.e., A,Q , then the system capacity Rk,m [n] can be expressed as   U→S [n] P D→U [n]PmU→S [n]hD→U k,m [n]hm Rk,m [n]=W log2 2 2 k,m D→U [n]hD→U [n]+σ 2 P U→S [n]hU→S [n] σk σm +σm2 Pk,m m k,m k m <   D→U U →S = W log2 Pk,m [n] PmU →S [n] hD→U [n] k,m [n] hm =  D→U 2 P U →S U →S [n] −log2 σk2 σm2+σm2 Pk,m h . [n] hD→U [n]+σ [n] m k m k,m

(4.66)

The objective function Rk,m [n] is neither convex nor concave with respect to D→U Pk,m [n] and PmU →S [n]. The variable substitution is then applied to determine its concavity and convexity. It is further transformed into a convex optimization problem by applying SCA. D→U Since Pk,m [n] , PmU →S [n] > 0, ∀k, m, n, we introduce auxiliary variables Δ

Δ

D→U αk,m [n] and βm [n]. Let Pk,m [n] = eαk,m [n] , PmU →S [n] = eβm [n] , the system capacity Rk,m [n] can be given by

<   U →S [n] /e αk,m [n] e βm [n] Rk,m [n] = W log2 hD→U k,m [n] hm  = α 2 U →S β [n] [n] m k,m − log2 σk2 σm2 + σm2 hD→U + σ h /e /e [n] k,m [n] k m <   U →S = W log2 hD→U [n] /eαk,m [n]+βm [n] k,m [n] hm  = αk,m [n] + σ 2 hU →S [n] /e βm [n] − log2 σk2 σm2 + σm2 hD→U /e [n] k m k,m

(4.67)

Δ

= W (Φ1 − Φ2 ) ,   U →S αk,m [n]+βm [n] , h /e where Φ1 =log2 hD→U [n] [n] m k,m   αk,m [n]+σ 2 hU →S [n] /e βm [n] . It is not difficult and Φ2 =log2 σk2 σm2+σm2 hD→U k,m [n] /e k m to determine that both Φ1 and Φ2 are convex functions. Therefore, Rk,m [n] is difference of convex (DC) programming problem, the concavity and convexity of which is uncertain. We can transform it into an equivalent DC programming problem

4.3 UAV Trajectory Design for Space–Air–Ground Networks

157

P2, which can be expressed as P2 : s.t.

K M min −Rk,m {α,β } m=1 k=1 D→U [n] , ∀k, m, n, 0 ≤ eαk,m [n] ≤ Pmax

(4.68) 0≤

≤

eβm [n]

M K N

U →S Pmax

[n] , ∀m, n,

s , ∀k, m, n. aˆ k,m [n] /Rk,m [n] ≤ Cmax

n=1 m=1 k=1

The problem P2 is also a non-convex optimization problem due to the non-convex objective function −Rk,m and non-convex constrain. In order to make the problem P2 tractable, we apply SCA to approximate Φ1 in each iteration. Specifically, a ˜ first-order Taylor expansion is applied toapproximate  Φ1 to a linear function Φ1 at Δ any point iteratively. Let R˜ k,m [n] = W Φ2 − Φ˜ 1 , it is a convex function. Define 1 2 r D→U r PD→U = Pk,m [n] , ∀k, m, n to represent the transmission power value of 1 2 r smart devices to UAVs in the rth iteration, then α r = αk,m [n] , ∀k, m, n is the variable substitution2value given by PD→U in the rth iteration. Similarly, PU →S = 1 r PmU →S [n] , ∀m, n is defined as the transmission power value of UAVs to the 5 r 6 LEO satellite in the rth iteration, then β r = βm [n] , ∀m, n is the substitution value r of PU →S variable given by the rth iteration. Thus, the lower bound Φ˜ 1 of Φ1 can be obtained by applying SCA, i.e.,   r [n]+β r [n] αk,m U →S m Φ1 ≥ Φ˜ 1 =log2 hD→U h /e [n] [n] m k,m    ! (4.69) " 1 r r [n] αk,m [n] − αk,m [n] + βm [n] − βm . + ln 2 r

Then the system capacity R˜ k,m =

1 N

N

r

ak,m [n] /R˜ k,m [n]. Thus, the problem P2

n=1

can be approximated as the problem P3, which can be given by P3 : s.t.

K M R˜ k,m min {α,β } m=1 k=1 D→U 0 ≤ eαk,m [n] ≤ Pmax [n] , ∀k, m, n,

(4.70) 0≤

eβm [n]

≤

M K N n=1 m=1 k=1

U →S Pmax

[n] , ∀m, n,

s , ∀k, m, n. aˆ k,m [n] /R˜ k,m [n] ≤ Cmax

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4 Cooperative Resource Allocation in FANET

It can be seen that the problem P3 is a convex optimization problem, which can be solved by applying the CVX toolbox [56]. ⎞

⎛ ρ

⎠, Rk,m [n] = =W log2 ⎝ ; ;2 ϕ ;qm [n] − wk [n]; +ψ ⎡ ⎢ Rk,m [n] ≥ R˙ k,m [n] =W ⎣log2



ρ r [n] + ψ ϕΞk,m

 −

ϕ

 r [n] + ψ ln 2 ϕΞk,m

(4.71)

⎤   ⎥ r Ξk,m [n] − Ξk,m [n] ⎦ .

(4.72) ; ; ; ; ! " ! " ;qm [n] − wk [n];2 ≥ ;qr [n] − wk [n];2 + 2 qr [n] − wk [n] T qm [n] − qr [n] . m m m

(4.73) ;2 ;! ; ; ; ; " ; ; ; ;qm [n] − qj [n];2 ≥ ; ;qrm [n] − qrj [n]; + 2 ;qrm [n] − qrj [n]; qm [n] − qrm [n] ; ;  ; ; −2 ;qrm [n] − qrj [n]; qj [n] − qrj [n] ; ;2 T !  " ; ; = − ;qrm [n] − qrj [n]; + 2 qrm [n] − qrj [n] qm [n] − qj [n] .

(4.74) P6 :

s.t.

K M R˙ k,m max {Q,Ξ } m=1 k=1

; ;2 "T ! " ! Ξk,m [n] ≤ ;qrm [n] − wk [n]; + 2 qrm [n] − wk [n] qm [n] − qrm [n] , ∀k, m, n, C5, C6, ; ; aˆ k,m [n] ;qm [n] − wk [n]; ≤ H tan θ, ∀k, m, n, ; ;2 T !  " ; ; 2 , ∀m, n, j = m, − ;qrm [n] − qrj [n]; + 2 qrm [n] − qrj [n] qm [n] − qj [n] ≥ dmin M K N n=1 m=1 k=1

s , ∀k, m, n. aˆ k,m [n] /R˙ k,m [n] ≤ Cmax

(4.75)

4.3 UAV Trajectory Design for Space–Air–Ground Networks

159

4.3.3.3 The UAV Trajectory Optimization In this subsubsection, given the connection scheduling of 1smart devices, the 2 transmission power of smart devices and UAVs, i.e., A,PD→U , PU →S , the system capacity is then denoted by Eq. (4.71) on next page, where D→U ρ=Pk,m [n] PmU →S [n] / h0 2 , ϕ=Hs2 σk2 σm2 + σk2 PmU →S [n] / h0 , D→U ψ=Hs2 σk2 σm2 H 2 +σk2 PmU →S [n] / h0 H 2 +σm2 Pk,m [n] / h0 Hs2 . Then Rk,m can be N aˆ k,m [n] /Rk,m [n]. Therefore, the optimization problem indicated by Rk,m = N1 n=1

can be represented as P4, i.e., P4 : s.t.

K M Rk,m max {Q} m=1 k=1

C5, C6, C7, C8, M K N n=1 m=1 k=1

(4.76)

s , ∀k, m, n. aˆ k,m [n] /Rk,m [n] ≤ Cmax

Considering that the concavity and convexity of Rk,m [n] in qm [n] cannot be determined, and constraints C8 and C9 are non-convex constraints, the problem P4 is also a non-convex optimization problem. Then, the problem P4 is transformed below by applying variable substitution. By 2 introducing an auxiliary variable Ξ = 1 ; ;2 ; ; Ξk,m [n] = qm [n] − wk [n] , ∀k, m, n , the system capacity can be expressed   as Rk,m [n] /=W log2 ϕΞk,m ρ[n]/+ψ , and the problem P4 can be rewritten to the problem P5, which can be given by P5 : s.t.

K M max Rk,m {Q,Ξ } m=1 k=1

; ;2 Ξk,m [n] ≤ ;qm [n] − wk [n]; , ∀k, m, n, (4.77) C5, C6, C7, C8, M K N n=1 m=1 k=1

s , ∀k, m, n. aˆ k,m [n] /Rk,m [n] ≤ Cmax

The objective function of the problem P5 is convex with respect to Ξk,m [n]. C6 and C8 in P5 are non-convex constrains. Therefore, the problem P5 is a nonconvex optimization problem. 5Then, the problem P5 is transformed below by 6 applying SCA. Define Qr = qrm [n] , ∀m, n as the UAV trajectory in the rth

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4 Cooperative Resource Allocation in FANET

iteration. Further, a first-order Taylor expansion is applied to approximate Rk,m [n] to a linear function R˙ k,m [n] at any point iteratively, where R˙ k,m [n] is the lower bound of Rk,m [n], which is indicated by Eq. (4.72) on the page. Then the system N capacity can be denoted by R˙ k,m = N1 ak,m [n] /R˙ k,m [n]. n=1 ; ;2 For the new constraint, because ;qm [n] − wk [n]; is a convex function for qm [n], we can obtain its lower bound by applying a first-order Taylor expansion on qrm [n], which is indicated by Eq. (4.73) on the page. For the non-convex constraint C8, it is a convex function with respect to qm [n] and qj [n], a first-order Taylor expansion is applied at any given qrm [n] and qrj [n] to obtain its lower bound, which is indicated by Eq. (4.74) on the page. Therefore, the problem P5 can be transformed into the problem P6, which can be indicated by Eq. (4.75) on the page. It can be seen that the problem P6 is a convex optimization problem, which can be solved by applying the CVX toolbox [56].

4.3.3.4 Optimization of Joint Smart Device Connection Scheduling, Power Control, and UAV Trajectory Design In this subsubsection, in view of the results of solving the above three blocks, we propose an overall iterative algorithm to obtain the results of the resource allocation problem by BCD. Specifically, the optimization variables of the optimization 2 1 D→U , PU →S , Q . Then, problem (13) are divided into three blocks, namely A,P the connection scheduling of smart devices A, the transmission power of smart devices and UAVs PD→U , PU →S , and the trajectory of UAVs Q are alternately optimized by fixing the other two blocks to solve the problem P1, P3, and P6. Furthermore, the solution obtained by each iteration1 is taken as the input of2the ∗ ∗ next iteration, and the resource allocation scheme A∗ ,PD→U , PU →S , Q∗ is finally obtained. The resource allocation algorithm for joint smart device connection scheduling, power control, and UAV trajectory design is shown in Algorithm 11.

4.3.3.5 Computational Complexity Analysis In this subsection, we analyze the computational complexity of the proposed joint smart device connection scheduling, power control, and UAV trajectory design. In the problem P1, the optimal smart device connection scheme is solved by applying the CVX toolbox with given power control and UAV trajectory design, and the computational complexity is O(KMN )3.5 . Similarly, solutions of the problem P3 and the problem P6 are obtained by applying the CVX toolbox, thus the computational complexity of both are O(KMN)3.5 and O(M)3.5 , respectively. In addition, we use κ to update the system capacity. Therefore, the computational

4.3 UAV Trajectory Design for Space–Air–Ground Networks

161

Algorithm 11 Resource allocation algorithm for joint smart device connection scheduling, power control and UAV trajectory design 1: Let r = 0, initialize A0 ,PD→U , PU →S , Q0 . 2: repeat r r 3: Given Ar ,PD→U , PU →S , Qr , solve the problem P1, and the optimal solution is r+1 represented by A . r r 4: Given Ar+1 , PD→U , PU →S , Qr , solve the problem P3, and the optimal solution is r+1 r+1 D→U U →S represented by P ,P . r+1 r+1 5: Given Ar+1 , PD→U , PU →S , Qr , solve the problem P6, and the optimal solution is represented by Qr+1 . 6: Update r = r + 1. 7: until The difference of the iteration of the objective function satisfies the threshold and reaches convergence. 0

0

complexity of joint smart device connection  scheduling, power control, and UAV  3.5 3.5 3.5 trajectory design can be represented by O κ (KMN) +(KMN) +(M) .

4.3.4 Simulation Results In this subsection, we evaluate the performance of the proposed resource allocation algorithm for joint smart devices scheduling connection, power control, and UAV relays trajectory design through numerical simulation. The performance of the simulation algorithm is mainly considered from the convergence for the proposed resource allocation algorithm; the system capacity changes with the optimization variables, compared with other schemes to improve the system capacity and trajectory optimization and other aspects. The simulation tool in this subsection is a convex optimization toolkit based on Matlab, which can effectively solve optimization problems such as linear programming, quadratic programming, and integer programming. The simulation parameters of this subsection are as follows [14, 57]. We set the channel bandwidth W = 5MHz, and consider that K= 6 smart devices are randomly distributed in a circular area with a radius of 300m. Consider that the LEO satellite height Hs = 200km and M = 3 UAVs are distributed in three-division circular areas with a fixed height of H = 100m and a safety distance of dmin = 100m. The noise power spectral density is −174dBm/Hz. Consider the channel gain h0 = 1.42 × 10−4 when the reference distance is 1m. The maximum D→U =1W. The maximum transmission transmission power of smart devices is Pmax U →S power of UAV relays is Pmax = 50W. In addition, the maximum capacity of s the LEO satellite is set to Cmax =100Mbps. We assume that the Algorithm 11 convergence threshold is ε=10−3 , and the number of slots is N = 20. The detailed simulation parameters are shown in Table 4.2. We first evaluate the convergence of the proposed resource allocation algorithm for joint smart device connection scheduling, power control, and UAV trajectory

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Table 4.2 Simulation parameters Parameters System bandwidth Number of smart devices Number of time slots Radius of circular area The height of the LEO satellite The height of UAVs The safety distance among UAVs Noise power spectral density Channel gain at a reference distance of 1m Maximum transmission power of smart devices Maximum transmission power of UAVs Maximum capacity of the LEO satellite Convergence threshold

Value 5MHz 6 20 300m 200km 100m 100m −174dBm/Hz 1.42 × 10−4 1W 50W 100Mbps 10−3

14.5

System Capacity(Mbps)

14

13.5

13

12.5 T=20s, =2s T=40s, =2s T=60s, =2s

12

11.5 2

4

6

8

10

12

14

Number of Iterations Fig. 4.8 The system capacity versus the number of iterations in different time processes

design. The variation of the system capacity versus the number of iterations with different time processes T and different time slots N is shown in Fig. 4.8. It can be seen that the resource allocation algorithm can converge quickly and has relatively good convergence performance. In addition, it can be concluded that as long as the time process T , the UAVs can satisfy smart devices in the area to be traversed once, and the system capacity value is less affected by time process T .

4.3 UAV Trajectory Design for Space–Air–Ground Networks

163

600 smart devices T=20s, =2s T=60s, =2s T=80s, =2s

500

y(m)

400

300

200

t=0s

100

0

-100 -100

0

100

200

300

400

500

600

700

x(m) Fig. 4.9 Optimized trajectory of single-UAV system in different time processes T

In Fig. 4.9, we consider the trajectory design scheme of single UAV. The optimized trajectories under different time processes T and different time slots N are shown in Fig. 4.9. In this subsection, the trajectory design of the UAV is initially designed as a circle. Through optimization, it can be seen that the overall outline of the UAV trajectory in the case of different time processes T and different time slots N is different, and cover smart devices as much as possible. With the condition that the UAV speed is constant, the number of smart devices covered by the UAV increases with the time process T and the number of time slots N. And the more comprehensive the UAV covers smart devices, the more accurate and smooth the trajectory, which also verifies the effectiveness of the proposed algorithm. Similarly, the trajectory design of the multi-UAV system described below can be generalized from the trajectory design of a single UAV. Next, we analyze the transmission power of the UAV and smart devices versus the time process T . Figure 4.10 demonstrates the change of the transmission power of UAVs and smart devices with time process T . It can be seen that the UAVs and smart devices always transmit at the maximum transmission power during the entire time process T . Considering the optimization problem P3, it is not difficult to prove that the objective function is a monotonically decreasing function. At the same time, the transmission power constraints of the UAV and smart devices are considered. Therefore, the maximum transmission power is taken to optimize the problem P3. According to the above conclusions, the UAV and smart devices work at the maximum transmission power during the entire process T , so the maximum transmission power of both have an impact on the system capacity. Then the

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4 Cooperative Resource Allocation in FANET 70

Transmit Power(W)

60

50

40

30

20

Transmit power of UAV relay Transmit power of smart devices

10

0 0

2

4

6

8

10

12

14

16

18

Time t(s) Fig. 4.10 The transmission power of the UAVs and smart devices versus time process T

impact is discussed next. Figure 4.11 indicates the system capacity versus the different maximum transmission power of smart devices and different maximum transmission power of UAVs. It can be seen that when the maximum transmission power of the UAV is constant, the system capacity increases as the maximum transmission power of smart devices increases. Similarly, when the maximum transmission power of smart devices is constant, the system capacity increases as the maximum transmission power of the UAV increases. Because when the maximum transmission power increases, the capacity of a single link increases, and the system capacity increases accordingly. Furthermore, we compare the resource allocation algorithm in this subsection with two more common trajectory optimization algorithms, where the smart devices scheduling optimization and power optimization of the three are consistent. Scheme 1: The UAV is statically hovering in the center of the circular area during the entire time process T . Scheme 2: The UAV works as a circular trajectory during the entire time process T . Figure 4.12 indicates the system capacity versus the number of smart devices with different schemes. It can be seen that the proposed resource allocation algorithm has a very significant gain compared to scheme 1 and has a gain of at least 22.3% compared to scheme 2. This is mainly because the UAV in scheme 1 is statically hovering in the regional center, and sometimes it may not be able to cover all smart devices, so the system capacity is lower. For scheme 2, the UAV relay can only fly according to a fixed circular trajectory. It is difficult to dynamically adjust, which limits the ability of the UAV and reduces the system capacity.

4.3 UAV Trajectory Design for Space–Air–Ground Networks

165

17

System Capacity(Mbps)

16 15 14 13 12 11 10 Maximum transmit power of UAV=25W Maximum transmit power of UAV=50W Maximum transmit power of UAV=75W

9 8 1

1.5

2

2.5

3

3.5

4

4.5

5

5.5

6

Maximum Transmit Power of Smart Devices(W) Fig. 4.11 The system capacity versus the maximum transmission power of the UAV and smart devices

System Capacity(Mbps)

30 Scheme 1 Scheme 2 Proposed Algorithm

25

20

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5

0 6

8

10

12

14

Number of Smart Devices Fig. 4.12 The system capacity versus the number of smart devices with different schemes

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4 Cooperative Resource Allocation in FANET 600

400 t=0s

y(m)

200

0

t=0s

-200 t=0s -400 smart devices -600 -400

-200

0

200

400

600

800

x(m) Fig. 4.13 Optimized trajectory of multi-UAV system in the same time process T

Through the analysis on the single UAV mentioned above, we consider a multiUAV system to analyze the performance of the algorithm. Figure 4.13 demonstrates the optimized trajectory of multi-UAV system in the same time process T . The initialization trajectories of the three UAVs are all circular trajectories, and the circular areas are equally divided. It can be seen that with the constraint of the safety distance dmin , there is no cross collision with each other. The three UAVs are responsible for the smart devices within their respective coverage areas. As long as the time process T and the number of time slots are sufficient, they can cover as many smart devices as possible, and the trajectories of each UAV are optimized. Finally, we compare the proposed algorithm for multi-UAV system with schemes 1 and 2 mentioned above. Figure 4.14 shows the capacity of a multi-UAV system versus the number of smart devices with different schemes. It can be seen that the algorithm proposed has a significant gain compared to scheme 1 and has a gain of at least 16.4% compared to scheme 2. And with the increase in the number of smart devices, the proposed algorithm has an increasing gain compared to the other two schemes. This is mainly because with the continuous increase in the number of smart devices, it is increasingly difficult for UAVs of scheme 1 and scheme 2 to cover all smart devices, which makes the system capacity growth slow down.

4.4 Multi-UAV-Aided IoT NOMA Uplink Transmission

167

90 Scheme 1 Scheme 1 Proposed Algorithm

System Capacity(Mbps)

80 70 60 50 40 30 20 10 20

25

30

35

40

Number of Smart Devices Fig. 4.14 The capacity of a multi-UAV system versus the number of smart devices under different schemes

4.3.5 Conclusions In this section, we have investigated a resource allocation problem for SAG-IoRT networks. Specifically, the smart device connection scheduling, power control, and UAV trajectory design have been jointly optimized to maximize the system capacity. By applying BCD, SCA, and variable substitution, an effective resource allocation algorithm has been proposed to solve the challenging problem. Then, the computational complexity of the proposed algorithm has been given. Finally, numerical simulation results have shown the effectiveness of the algorithm. Compared with the other two schemes, the proposed algorithm has a significant performance gain and can significantly increase the system capacity of the SAG-IoRT networks.

4.4 Multi-UAV-Aided IoT NOMA Uplink Transmission Unmanned aerial vehicle (UAV) communication is an emerging technology for the fifth generation (5G) networks and beyond. On one hand, UAVs can be quickly and efficiently deployed to support existing cellular networks and enhance ground users’ quality of service (QoS) by establishing line-of-sight (LoS) links. On the other hand, given the popularization of civilian UAVs, they are also expected to be

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4 Cooperative Resource Allocation in FANET

important users of the future network. With their inherent attributes such as high mobility, low cost and flexible deployment, UAVs can be beneficially applied to some key potential applications in next generation wireless networks. To elaborate a little further, UAVs can be used as aerial base stations (ABSs) for providing reliable uplink and downlink communications for ground users. They can also act as airborne relays for connecting the dead zone users with the terrestrial BSs and enlarging the communication coverage. Moreover, their ability to provide LoS connections can mitigate the signal blockage and shadowing, thus greatly improving the spectrum efficiency. A range of new compelling applications are also being developed for further tapping the potentials of UAVs in wireless communications. The Internet of Things (IoT), which leads to massive connections between physical things such as vehicles, wearable devices, and various sensors, is a key component of future networks. However, in many application scenarios, the reliable transmission between IoT devices remains a challenge since IoT devices cannot support long distance transmission due to their power constraints. Fortunately, UAVs are expected to provide effective solutions. UAVs can flexibly navigate to the IoT devices, collect the data, and then efficiently transmit the data to other IoT devices or directly to the data center. The high probability of LoS connections is capable of improving the transmission efficiency as well as decreasing the transmit power of the IoT devices, thereby prolonging their service life. Despite the considerable benefits of applying UAVs to IoT systems, the limited cruise time of UAVs presents as a bottleneck. Existing UAVs typically have an endurance time of less than one hour. Therefore, improving the transmission efficiency is of utmost importance. Non-orthogonal multiple access (NOMA) is a promising technology for the future network; it has superior spectrum efficiency by allowing simultaneous transmissions of different users within the same channel, which relies on the superposition coding (SC) at the transmitters and the successive interference cancellation (SIC) at the receivers. The combination between UAVs and NOMA technology will bring about predictable benefits. Therefore, in this work, a multi-UAV-aided NOMA system is established for the uplink transmission of IoT applications. Specially, UAVs are used as flying BSs to collect data from various IoT nodes, and NOMA is assumed for the uplink transmission between the UAVs and the IoT nodes for promoting spectrum efficiency. And we propose a staged optimization algorithm for joint optimizing the subchannel assignment, the uplink transmit power of IoT nodes, and the flight heights of UAVs. The rest of this section is organized as follows. The system model and problem formulation are detailed in Sects. 4.4.1 and 4.4.2, respectively. Section 4.4.3 introduces IoT nodes clustering algorithm based on the K-means clustering method and a subchannel assignment algorithm relying on many-many matching theory. In Sect. 4.4.4, distributed IoT nodes’ uplink transmit power and UAVs’ flight heights solutions as well as an AO algorithm are presented. Numerical simulations are conducted in Sect. 4.4.5, followed by our conclusions in Sect. 4.4.6.

4.4 Multi-UAV-Aided IoT NOMA Uplink Transmission

169

4.4.1 System Model In this subsection, as shown in Fig. 4.15, we consider a multi-UAV-aided IoT NOMA uplink transmission system, which consists of M UAVs and N IoT nodes. The UAVs are small or mini rotary wing UAVs controlled by ground station (GS) to collect information from IoT nodes. The examples of IoT nodes are various devices used for monitoring the information of buildings, roads, farmlands, etc. We assume that those IoT nodes are static and their locations are known by the0 GS. / The sets of the M UAVs and N IoT nodes are denoted as M = 1, 2, . . . , M and / 0 N = 1, 2, . . . , N , respectively. In this system, each UAV serves a group of IoT nodes while each IoT node can only access one UAV. We assume that all of the N IoT nodes can be covered by the M UAVs. Let Sm denote the set of IoT nodes M > 8 served by UAV m, and we have Sm = N and Sm1 Sm2 = ∅, ∀m1 , m2 ∈ m=1

M , m1 = m2 . Moreover, for further improving the spectrum efficiency, NOMA is invoked for the uplink transmissions between the IoT nodes and the UAVs, where the bandwidth of each UAV-enabled / 0subsystem is B, which are divided into K subchannels. Let K = 1, 2, . . . , K denote the set of the subchannels. Without loss of generality, we consider a 3D Cartesian coordinate system and the locations ! uav " uav , h of UAV m ∈ M and IoT node n ∈ N are denoted as xm , ym m and

Fig. 4.15 The structure of the multi-UAV-aided IoT NOMA uplink transmission system

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4 Cooperative Resource Allocation in FANET

  xnnode, ynnode , respectively. Hence, the distance between UAV m and IoT node n is ! ! " " uav − x node 2 + y uav − y node 2 + h2 . calculated by dm,n = xm n m n m 4.4.1.1 Channel Model Let gm,n,k denote the channel gain on kth subchannel from IoT node n to UAV m, where m ∈ M , n ∈ N , and k ∈ K . We assume that the communications between UAVs and IoT nodes are dominated by line-of-sight (LoS) links, where the channel quality only depends on the communication distance. Thus, gm,n,k follows the freespace path-loss model, which can be quantified by gm,n,k =

η 2 dm,n

,

(4.78)

where η denotes the unit power gain at the reference distance d0 = 1 m.

4.4.1.2 Interference Model In NOMA, at the transmitters, each IoT node can transmit data through multiple subchannels and each subchannel can be allocated to multiple IoT nodes, while at the receivers, each UAV adopts SIC to demodulate the targeted message. In our scenario, we assume that the decoding order at the UAV is always from the IoT node with a better channel quality to the IoT node with a worse channel quality; otherwise a significant power has to be consumed at the node with worse channel quality for compensating the path loss. Let us take UAV m and its corresponding IoT nodes Sm as an example to analyze the interference conditions. Without loss of generality, we assume n ∈ Sm . For signals received from IoT node n, the main interferences are composed of three parts, namely intragroup interferences, inter-group interferences, and additive noise. The intra-group interferences come from the other IoT nodes in Sm whose channel qualities are worse than that of IoT node n, while the inter-group interferences come from the other co-tier UAV-enabled subsystems. We first define a power/ allocation matrix 0 PM×N×K and a channel allocation matrix AM×N×K , where P m,n,k = pm,n,k denotes the uplink / 0transmission power between IoT node n and UAV m on kth subchannel and A m,n,k = am,n,k is the subchannel indicator. We set am,n,k = 1 if the kth subchannel is occupied by the transmission between IoT node n and UAV m, otherwise, am,n,k = 0. Then, the intra-group interferences for the uplink transmission between IoT node n and UAV m on kth subchannel can be given by Im,n,k =

 i∈Sm,n

am,i,k pm,i,k gm,i,k ,

(4.79)

4.4 Multi-UAV-Aided IoT NOMA Uplink Transmission

171

1 * 2 where Sm,n = i *i ∈ Sm , gm,n,k > gm,i,k denotes the set of IoT nodes in Sm whose channel qualities are worse than that of IoT node n. Moreover, the intergroup interferences can be given by I˜m,n,k =

N M  

ai,j,k pi,j,k gm,j,k .

(4.80)

i=1, j =1 i =m

Thus, the signal to interference and noise ratio (SINR) of the received signal from IoT node n on kth subchannel and the corresponding uplink capacity can be denoted as γm,n,k =

pm,n,k gm,n,k Im,n,k + I˜m,n,k + σ 2

,

(4.81)

and Rm,n,k =

! " B am,n,k log2 1 + γm,n,k , K

(4.82)

respectively, where σ 2 is the variance of the additive white Gaussian noise (AWGN).

4.4.2 Problem Formulation In this subsection, we will formulate the resource allocation problem for the multiUAV-aided IoT NOMA uplink transmission system. Our goal is to maximize the total uplink transmission capacity, which is expressed as R total =

M  N  K  ! " B am,n,k log2 1 + γm,n,k . K

(4.83)

m=1 n=1 k=1

The considered constraints are listed as follows: The IoT Nodes’ Power Constraint For maintaining the fairness of the IoT nodes and considering the practical limit of the battery size, each IoT node in this system has a minimum uplink transmit power constraint of pmin and a maximum constraint of pmax . Therefore, for ∀n ∈ N , we have pmin ≤

M  K  m=1 k=1

am,n,k pm,n,k ≤ pmax .

(4.84)

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4 Cooperative Resource Allocation in FANET

Moreover, the non-negativity constraint of power yields: pm,n,k ≥ 0, ∀m ∈ M , ∀n ∈ N , ∀k ∈ K .

(4.85)

The UAVs’ Flight Height Constraint For the safety of the UAVs, each UAV in our scenario is assumed to have a minimum flight height constraint of hmin ; otherwise, these UAVs may run into trees or buildings. Furthermore, they are also assumed to have a maximum flight height constraint of hmax as an excessive height will lead to fast battery consumption and a more difficult flying control. Hence, for ∀m ∈ M , we have hmin ≤ hm ≤ hmax .

(4.86)

In practice, the UAVs should also satisfy the collision avoidance constraint, i.e., 

! "2 hi − hj ≥ χ 2 ,

(4.87)

i,j ∈M ,i =j

where χ 2 is the minimum variance of the altitudes of the UAVs. The Channel Allocation Constraint Note that the UAVs adopt SIC technique to demodulate the collected message, and this may result in considerable complexity at the receiver because as the number of IoT nodes over the same subchannel grows, the implementation complexity of SIC increases. For decreasing the decoding complexity, we assume that each subchannel can be allocated to at most D1 IoT nodes. Given a proper value of D1 , the decoding complexity can be reduced to a tolerable level. Furthermore, considering the scarce spectrum resource, we also assume that each IoT node can occupy at most D2 subchannels. By choosing a proper value of D2 , all the IoT nodes can be scheduled and the user fairness is guaranteed. We assume that ND2 < KD1 . Therefore, we have N 

am,n,k ≤ D1 , ∀m ∈ M , ∀k ∈ K ,

(4.88)

am,n,k ≤ D2 , ∀m ∈ M , ∀n ∈ N .

(4.89)

n=1 K  k=1

Moreover, the channel allocation indicator satisfies am,n,k ∈ {0, 1} , ∀m ∈ M , ∀n ∈ N , ∀k ∈ K .

(4.90)

4.4 Multi-UAV-Aided IoT NOMA Uplink Transmission

173

Hence, the resource allocation problem for the multi-UAV-aided IoT NOMA uplink transmission system can be formulated as M  N  K  ! " B am,n,k log2 1 + γm,n,k K

max

P ,A,vm

s.t.

pmin ≤

(4.91a)

m=1 n=1 k=1 M  K 

am,n,k pm,n,k ≤ pmax , ∀n ∈ N ,

(4.91b)

m=1 k=1

pm,n,k ≥ 0, ∀m ∈ M , ∀n ∈ N , ∀k ∈ K ,

(4.91c)

hmin ≤ hm ≤ hmax , ∀m ∈ M ,  ! "2 hi − hj ≥ χ 2 ,

(4.91d) (4.91e)

i,j ∈M ,i =j N 

am,n,k ≤ D1 , ∀m ∈ M , ∀k ∈ K ,

(4.91f)

am,n,k ≤ D2 , ∀m ∈ M , ∀n ∈ N ,

(4.91g)

n=1 K  k=1

am,n,k ∈ {0, 1} , ∀m ∈ M , ∀n ∈ N , ∀k ∈ K ,

(4.91h)

" ! uav uav where vm = xm , ym , hm denotes the location vector of UAV m. Unfortunately, problem (4.91) is generally non-convex and NP-hard, thus it is challenging to find the global optimal solution. To solve problem (4.91) efficiently, we decouple the subchannel assignment, the power allocation of IoT nodes, and the trajectory design of UAVs and propose a staged optimization algorithm to obtain a sub-optimal solution. The block diagram of the proposed algorithm is shown in Fig. 4.16. To elaborate, firstly, the IoT nodes are clustered into M groups based on their locations, and the horizontal coordinates of the corresponding UAVs are fixed relying on the clustering results. Secondly, for each UAV-enabled uplink transmission subsystem, we adopt a many-many matching algorithm to assign subchannels to the IoT nodes with given UAVs’ heights and IoT nodes’ power allocation method. Thirdly, we alternatively optimize IoT nodes’ transmit power

Fig. 4.16 The block diagram of the proposed solution to problem (4.91)

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4 Cooperative Resource Allocation in FANET

and UAVs’ flight heights to maximize the uplink transmission capacity. Finally, we give a sub-optimal solution based on the results obtained from the preceding steps. Note that unlike most of the existing works [4, 58], we focus on optimizing UAVs’ flight heights instead of the horizontal locations. That is because optimizing the flight heights is much simpler to analyze in comparison to optimizing the 2D coordinates of horizontal locations. Moreover, given the fixed UAV-device association, frequently changing the horizontal locations of UAVs may lead to severe inter-interferences between adjacent uplink transmission subsystems and increase the risk of flight collision. Additionally, considering the limited battery size, changing the flight heights is more energy-saving comparing with adaptively moving around for supporting the bursty traffic of the IoT nodes.

4.4.3 IoT Nodes Clustering and Subchannel Assignment In this subsection, we propose a simple but effective sub-optimal algorithm to assign subchannels to IoT nodes with given UAVs’ locations and IoT nodes’ power allocation method. Before that, we first determine the indexes of the IoT nodes served by each UAV. Since the locations of the IoT nodes are known by the GS, a natural and practical approach will be that each UAV serves a group of IoT nodes which are located in proximity of each other. This approach can significantly shorten the communication distance between the IoT nodes and the corresponding UAV as well as mitigate the possibility of having strong interference between two closely located uplink transmission subsystems. Since the locations and distances are the main considerations when grouping the IoT nodes into different clusters, we adopt the classic K-mean clustering method, which can effectively group the IoT nodes into M clusters while merely bring low implementation complexity. The M clusters correspond to {S1 , S2 , . . . , SM }. Moreover, we fix the horizontal location of UAV m at the mean location of IoT nodes in Sm , which can be denoted as !

" 1   node node uav uav * , ym = * xn , yn , xm *Sm *

(4.92)

n∈Sm

* * where *Sm * represents the cardinality of Sm . As mentioned before, the benefits are that it can significantly decrease both the inter-interferences between the adjacent uplink transmission subsystems and the risk of flight collision. Next we will assign the K subchannels for each UAV-enabled uplink transmission subsystem. After clustering IoT nodes into M clusters, we have / Sm . am,n,k = 0, ∀n ∈

(4.93)

Therefore, we only need to focus on the subchannel assignment in each subsystem. In the following, we will take UAV m and its corresponding IoT nodes Sm as an example to show our channel assignment strategy.

4.4 Multi-UAV-Aided IoT NOMA Uplink Transmission

175

Since the horizontal location of UAV m is fixed by Eq. (4.92), we assume that the flight height of UAV m is fixed at h0 . Moreover, each IoT node is assumed to adopt the equal power allocation method, in which the maximum power pmax is equally allocated to the assigned subchannels. Under these assumptions, we model the subchannel assignment process as a many-many matching process between the IoT nodes and the subchannels. We assume that the kth subchannel prefers to be allocated to IoT node n1 over n2 if gm,n1 ,k > gm,n2 ,k . Then we can obtain preference lists of all subchannels, which is given by P = {P1 , P2 , . . . , PK },

(4.94)

where Pk denotes the preference list of the kth subchannel, which is in the decreasing order of channel gains of IoT nodes in Sm . Then we design a manymany matching algorithm for finding the sub-optimal subchannel assignment strategy, which is described in Algorithm 11. To elaborate, each subchannel is first allocated to its most preferred IoT node, if the number of this node’s assigned subchannels is less than D2 , then this assignment is accepted. Otherwise, this subchannel is compared with the assigned subchannel which has the lowest uplink transmission capacity, and it will replace the assigned subchannel if it has higher uplink transmission capacity. This match process will terminate if all IoT nodes are assigned with D2 subchannels. The complexity of Algorithm 11 mainly comes from the sorting phase and the matching phase. In the sorting phase, each subchannel   obtains its preference list of |Sm | users, in which the complexity is O K|Sm |2 , while in the matching phase, each subchannel will be assigned at most K |Sm |  times, resulting in the total complexity of O K|Sm |2 . Comparing with the optimal   exhaustive search, which has a complexity order of O K2|Sm | , the proposed algorithm is more suitable for practical applications.

4.4.4 Power Allocation and Flight Height Design In this subsection, we provide solutions to the joint optimization problem in terms of the IoT nodes’ power allocation and UAVs’ flight heights. Given the horizontal locations of UAVs obtained from Eq. (4.92) and the channel allocation matrix obtained from Algorithm 12, problem (4.91) can be reduced to max P ,H

s.t.

pmin ≤

N  K M   ! " B am,n,k log2 1 + γm,n,k K

(4.95a)

m=1 n=1 k=1 M  K  m=1 k=1

am,n,k pm,n,k ≤ pmax , ∀n ∈ N ,

(4.95b)

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4 Cooperative Resource Allocation in FANET

Algorithm 12 Sub-optimal subchannel assignment algorithm 1: Initialize the preference lists P according to the channel gains. 2: Initialize LC,k = ∅ to denote the set of IoT nodes assigned with the kth subchannel, where k∈K. 3: Initialize LN,n = ∅ to denote the set of the subchannels assigned to IoT node n, where n ∈ Sm . 4: Initialize Lm = Sm to denote the IoT nodes which have not been assigned with D2 subchannels. 5: while Lm = ∅ do 6: for k = * 1 to*K do 7: if *LC,k * < D1 then 8: Select * the* most preferred IoT node n1 from Pk . 9: if *LN,n1 * < D2 then 10: Add k into LN,n1 , add n1 into LC,k , set am,n1 ,k = 1. 11: else ! " 12: Select k1 from LN,n1 , where k1 = argmin Rm,n1 ,k . k∈LN,n1

13: 14: 15: 16: 17: 18: 19: 20: 21: 22: 23: 24:

if Rm,n1 ,k > Rm,n1 ,k1 then Remove k1 from LN,n1 , remove n1 from LC,k1 , add k into LN,n1 , add n1 into LC,k , set am,n1 ,k1 = 0, set am,n1 ,k = 1. else Select the next IoT node n2 from Pk and return step 7. end if end if end if end * for * if *LN,n * = D2 then Remove n from Lm . end if end while

pm,n,k ≥ 0, ∀m ∈ M , ∀n ∈ N , ∀k ∈ K ,

(4.95c)

hmin ≤ hm ≤ hmax , ∀m ∈ M ,  ! "2 hi − hj ≥ χ 2 ,

(4.95d) (4.95e)

i,j ∈M ,i =j

/ 0T where H = h1 , h2 , . . . , hM . However, problem (4.95) is still non-convex. Considering the structure of problem (4.95), in the following, we use an alternative optimization (AO) method to solve it. To elaborate, we first fix the UAVs’ flight heights and design IoT nodes’ power allocation matrix P . Then, relying on the power allocation matrix P obtained, we optimize the UAVs’ flight heights. Also an AO algorithm is proposed to further increase the total uplink transmission capacity.

4.4 Multi-UAV-Aided IoT NOMA Uplink Transmission

177

pm,n,k = ep˜m,n,k ⎡

⎤+

⎢ ⎥ ⎢ ⎥ ⎢ ⎥ am,n,k αm,n,k ⎢ ⎥ =⎢ ⎥ . N M ⎢ ⎥ a a g g K m,n,k m,n,k m,n,k m,n,k ⎢ ⎥ a α + a α + ln 2(−λ + ω )a m,i,k m,i,k i,j,k i,j,k n n m,n,k B ⎣ ⎦ Im,i,k [t]+I˜m,i,k [t]+σ 2 Ii,j,k [t]+I˜i,j,k [t]+σ 2 i∈S¯m,n

i=1, j=1 i =m

(4.96)

4.4.4.1 Power Allocation Design of IoT Nodes Given the fixed UAVs’ flight heights of h0 , problem (4.95) can be reformulated as a power allocation problem: max P

s.t.

N  K M   ! " B am,n,k log2 1 + γm,n,k K

(4.97a)

m=1 n=1 k=1

M  K 

am,n,k pm,n,k ≥ pmin , ∀n ∈ N ,

(4.97b)

am,n,k pm,n,k ≤ pmax , ∀n ∈ N ,

(4.97c)

m=1 k=1 M  K  m=1 k=1

pm,n,k ≥ 0, ∀m ∈ M , ∀n ∈ N , ∀k ∈ K .

(4.97d)

However, although the constraints of problem (4.97) are convex, the objective is still non-convex in terms of P . To overcome this problem, we adopt successive convex approximation (SCA) approach to find a near-optimal solution. The!objective of " problem (4.97) is non-convex because of the non-convex term log2 1 + γm,n,k , thus we first approximate this non-convex term by logarithmic approximation as follows: ! " ! " αm,n,k ln γm,n,k + βm,n,k , (4.98) log2 1 + γm,n,k ≥ ln 2

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4 Cooperative Resource Allocation in FANET

which is tight at γm,n,k = γ¯m,n,k when the approximation constants are chosen as αm,n,k = " ! βm,n,k = ln 1 + γ¯m,n,k −

γ¯m,n,k , 1 + γ¯m,n,k

" ! γ¯m,n,k ln γ¯m,n,k . 1 + γ¯m,n,k

(4.99)

(4.100)

Moreover, let pm,n,k = ep˜ m,n,k , then the objective of problem (4.97) can be approximated by a concave lower bound, which is given by R total ≥

+ ! ", N  K M  p ˜ + βm,n,k α ln γ  m,n,k m,n,k m,n,k B am,n,k , K ln 2

(4.101)

m=1 n=1 k=1

where ! " γm,n,k p˜m,n,k = gm,n,k ep˜ m,n,k . N M am,i,k gm,i,k ep˜ m,i,k + ai,j,k gm,j,k ep˜ i,j,k + σ 2

(4.102)

i=1, j =1 i =m

i∈Sm,n

And now, problem (4.97) can be approximated by a convex problem, which is denoted as + ! ", N K M p ˜ + βm,n,k α ln γ   B m,n,k m,n,k m,n,k max am,n,k (4.103a) P K ln 2 m=1 n=1 k=1

s.t.

−

M  K 

am,n,k ep˜ m,n,k + pmin ≤ 0, ∀n ∈ N ,

(4.103b)

m=1 k=1 M  K 

am,n,k ep˜ m,n,k − pmax ≤ 0, ∀n ∈ N .

(4.103c)

m=1 k=1

Note that the solution to problem (4.103) is only the lower bound of the optimal solution to problem (4.97). To further approach the optimal solution, we can update the parameters in Eqs. (4.99) and (4.100) in the following iterations until the results are converged.

4.4 Multi-UAV-Aided IoT NOMA Uplink Transmission

179

Problem (4.103) is a standard convex optimization problem, which can be efficiently solved by the standard convex optimization solvers. To further reduce the computational complexity, we adopt Lagrangian dual method to solve this problem.   Let L ep˜ m,n,k , λ, ω be the Lagrangian function, which can be written as   L ep˜ m,n,k , λ, ω = + ! ", M  N  K αm,n,k ln γm,n,k p˜m,n,k + βm,n,k  B − am,n,k K ln 2 m=1 n=1 k=1 ⎛ ⎞ K N M    + λn ⎝− am,n,k ep˜ m,n,k + pmin ⎠ n=1

+

N 

⎛ ωn ⎝

n=1

m=1 k=1 K M  

(4.104)

⎞

am,n,k ep˜ m,n,k − pmax ⎠,

m=1 k=1

where λ = [λ1 , λ2 , . . . , λM ]T and ω = [ω1 , ω2 , . . . , ωM ]T are the Lagrangian multipliers associated with the constraints. And the Lagrangian dual function is calculated by   L(λ, ω) = sup L ep˜ m,n,k , λ, ω .

(4.105)

ep˜ m,n,k

Since problem (4.103) is a convex optimization problem, the optimal solutions of the original problem and the dual  problem  should satisfy the Karush–Kuhn–Tucker ∂L ep˜ m,n,k ,λ

conditions, thus by solving = 0, we can obtain the optimal solution ∂ p˜ m,n,k in the form of Lagrangian multipliers. Note that p˜m,n,k can show up as the wanted signal, the intra-interference, and the inter-interference, hence p˜ m,n,k exists in four parts of Eq. (4.104), which can be given by ! " Φ1 p˜ m,n,k =

+ ! ", αm,n,k ln γm,n,k p˜m,n,k + βm,n,k

B am,n,k K ! " Φ2 p˜ m,n,k = −

ln 2

,

+ ! ", αm,i,k ln γm,i,k p˜m,i,k + βm,i,k  B am,i,k , − K ln 2 i∈S¯m,n

(4.106a)

(4.106b)

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4 Cooperative Resource Allocation in FANET

! " Φ3 p˜ m,n,k =

+ ! ", M  N p ˜ + βi,j,k α ln γ  i,j,k i,j,k i,j,k B ai,j,k , − K ln 2

(4.106c)

i=1, j =1 i =m

! " Φ4 p˜ m,n,k = −λn am,n,k ep˜ m,n,k + ωn am,n,k ep˜ m,n,k ,

(4.106d)

2 1 * where S¯m,n = i *gm,i,k > gm,n,k . Therefore, by solving   ∂L ep˜ m,n,k , λ ∂ p˜ m,n,k

(4.107)

∂Φ1 ∂Φ2 ∂Φ3 ∂Φ4 = + + + = 0, ∂ p˜ m,n,k ∂ p˜ m,n,k ∂ p˜ m,n,k ∂ p˜ m,n,k we can achieve the optimal solution as shown in Eq. (4.121), where [x]+ = max{x, 0},

(4.108)

and we let Im,n,k [t] =



am,i,k gm,i,k ep˜ m,i,k [t ] ,

(4.109)

i∈Sm,n

I˜m,n,k [t] =

M  N 

ai,j,k gm,j,k ep˜ i,j,k [t ] ,

(4.110)

i=1, j =1 i =m

which are calculated using the results obtained in the tth iteration. Moreover, since L(λ, ω) is not differentiable, we can use the subgradient method to obtain the optimal Lagrangian multipliers in Eq. (4.121), where the Lagrangian multipliers are updated as follows: / 0 λn t + 1 = ⎡ /

0

⎛

⎢ ⎣λn [t] − δn t+1 ⎝

M  K 

m=1 k=1

am,n,k pm,n,k

⎞⎤+ ⎥ − pmin ⎠⎦ ,

(4.111)

4.4 Multi-UAV-Aided IoT NOMA Uplink Transmission

/ 0 ωn t + 1 = ⎡

⎛

/ 0 ⎢ ⎣ωn [t] − δn t+1 ⎝pmax −

M  K 

⎞⎤+ ⎥ am,n,k pm,n,k ⎠⎦ ,

181

(4.112)

m=1 k=1

/ 0 where t and δn t+1 denote the iteration step and the step size, respectively. Till now, we can use a SCA based iterative algorithm to find a near-optimal solution to problem (4.97). The algorithm is summarized in Algorithm 13. To elaborate, in the outer loop of Algorithm 13, problem (4.97) is approximated as a convex optimization problem, and the outputs obtained from the previous loop are used as inputs in the coming loop. Moreover, in the inner loop of Algorithm 13, the approximated convex optimization problem is solved with the Lagrangian dual method. Since the problem in the inner loop is solved optimally, Algorithm 13 is guaranteed to converge. In each round of Algorithm 13, a total number of MNK parameters need to be updated, thus Algorithm 13 has a worst-case complexity order of O (MNKL1 L2 ), where L1 and L2 are the maximum number of the iterations for the inner loop and outer loop, respectively. However, considering the relatively small L1 and L2 , Algorithm 2 actually shows fast computational performance. Algorithm 13 SCA based power allocation algorithm for Problem (4.97) / 0 / 0 / 0 1: Initialize s = 1, αm,n,k 1 = 1, βm,n,k 1 = 0 and pm,n,k 1 = 0. 2: repeat / 0 3: Initialize λn 1 > 0 and δn = 1. Set t = 1. 4: repeat 5: for m = 1 to M do 6: for n = 1 to N do 7: for k = 1 to K do 8: Update Im,n,k [t] according to Eq. (4.109). 9: Update I˜m,n,k [t] according to Eq. (4.110). 10: Update pm,n,k [t] according to Eq. (4.121). 11: end for 12: end for 13: end for 14: for n = 1 to N/ do 0 15: Update λn t + 1 according to Eq. (4.111). / 0 16: Update ωn t + 1 according to Eq. (4.112). 17: end for 18: Update t = t + 1. 19: Update δn = 1t . 20: until pm,n,k converges. / 0 21: Update pm,n,k s + 1 = pm,n,k . 22: Update s = s + 1. 23: Update αm,n,k [s] and βm,n,k [s] according to Eq. (4.99) and Eq. (4.100). 24: until pm,n,k converges.

182

4 Cooperative Resource Allocation in FANET

4.4.4.2 Flight Heights Design of UAVs As mentioned before, in Sect. 4.4.4.1, we optimize the uplink power of IoT nodes with fixed heights. In this subsubsection, with the power allocation results obtained, we will optimize the flight heights of UAVs. Given the power allocation matrix P , the flight height optimization problem can be formulated as N  K M   ! " B am,n,k log2 1 + γm,n,k K

max H

s.t.

(4.113a)

m=1 n=1 k=1

hmin ≤ hm ≤ hmax , ∀m ∈ M ,  ! "2 hi − hj ≥ χ 2 .

(4.113b) (4.113c)

i,j ∈M ,i =j

Problem (4.113) is a non-convex optimization problem in terms of H because of ! " the non-convex term log2 1 + γm,n,k and constraint Eq. (4.113c). In the following, we still adopt the SCA approach to overcome this problem. Note that the horizontal locations of the UAVs are fixed by Eq. (4.92), thus the horizontal distance between UAV m and IoT node n can be given by  ! " " ! uav − x node 2 + y uav − y node 2 . xm lm,n = (4.114) n m n Substituting Eq. (4.114) into Eq. (4.78), gm,n,k can be rewritten as η . 2 + lm,n ! " Therefore, the non-convex term log2 1 + γm,n,k can be written as ! " log2 1 + γm,n,k ⎛ ⎞ gm,n,k =

⎜ ⎜ ⎜ ⎜ = log2 ⎜1 + ⎜ ⎜ ⎝ ⎛

h2m

pm,n,k η 2 h2m +lm,n

i∈Sm,n



am,i,k pm,i,k η 2 h2m +lm,i

a

p

η

+

N M i=1, j =1 i =m N M

ai,j,k pi,j,k η 2 h2m +lm,j

⎟ ⎟ ⎟ ⎟ ⎟ ⎟ + σ2 ⎟ ⎠ ⎞

ai,j,k pi,j,k η 2 h2m +lm,j

m,i,k m,i,k ⎜ + + σ2 ⎟ 2 ⎜ i∈Sm,n ∪{n} h2m +lm,i ⎟ i=1, j =1 ⎜ ⎟ i =m ⎜ ⎟ = log2 ⎜ ⎟ N M ⎜ ⎟ am,i,k pm,i,k η ai,j,k pi,j,k η 2 ⎟ ⎜ + + σ 2 2 2 2 ⎝ ⎠ hm +lm,i hm +lm,j

i∈Sm,n

= Rˆ m,n,k + R˜ m,n,k ,

i=1, j =1 i =m

(4.115)

(4.116)

4.4 Multi-UAV-Aided IoT NOMA Uplink Transmission

183

where Rˆ m,n,k = ⎛ ⎜ ⎜ log2 ⎜ ⎝

⎞ M N ⎟ am,i,k pm,i,k η   ai,j,k pi,j,k η 2⎟ + + σ ⎟, 2 + l2 2 + l2 ⎠ h h m m m,i m,j i=1, j =1 ∪{n}



i∈Sm,n

(4.117)

i =m

and R˜ m,n,k = ⎛

⎞

M  N ⎜  a ⎟  ai,j,k pi,j,k η m,i,k pm,i,k η ⎜ 2⎟ − log2 ⎜ + + σ ⎟. 2 2 ⎝ ⎠ h2m + lm,i h2m + lm,j i=1, j =1 i∈S m,n

(4.118)

i =m

Note that Rˆ m,n,k and R˜ m,n,k are still non-convex in terms of H . Let us introduce a set of slack variables τ = [τ1 , τ2 , . . . , τM ]T , where τm = h2m . Replace the h2m in R˜ m,n,k with τm , then R˜ m,n,k can be rewritten as R˜ m,n,k = ⎛

⎞

M  N ⎜ a ⎟  ai,j,k pi,j,k η m,i,k pm,i,k η ⎜ 2⎟ − log2 ⎜ + + σ ⎟, 2 2 ⎝ ⎠ τm + lm,i τm + lm,j i∈S i=1, j =1 m,n

(4.119)

i =m

and problem (4.113) can be reformulated as max H ,τ

s.t.

N  K M     B am,n,k Rˆ m,n,k + R˜ m,n,k K

(4.120a)

m=1 n=1 k=1

hmin ≤ hm , ∀m ∈ M ,

(4.120b)

hm ≤ hmax , ∀m ∈ M , ,  ! "2 χ2 ≤ hi − hj ,

(4.120c) (4.120d)

i,j ∈M ,i =j

τm ≤ h2m , ∀m ∈ M .

(4.120e)

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4 Cooperative Resource Allocation in FANET

⎛

⎞

⎜ ⎜ Rˆ m,n,k = log2 ⎜ ⎝



i∈Sm,n ∪{n}

M N ⎟ am,i,k pm,i,k η   ai,j,k pi,j,k η 2⎟ + + σ ⎟ 2 2 ⎠ h2m + lm,i h2m + lm,j i=1, j =1 i =m

⎞

⎛ =

⎜ 1 ⎜ ln ⎜ ln 2 ⎝

M N ⎟ am,i,k pm,i,k η   ai,j,k pi,j,k η 2⎟ + + σ ⎟ 2 2 ⎠ h2m + lm,i h2m + lm,j i=1, j =1



i∈Sm,n ∪{n}

i =m

⎛ ≥

⎜ 1 ⎜ ln ⎜ ln 2 ⎝

⎞ 

i∈Sm,n ∪{n}

M N ⎟ am,i,k pm,i,k η   ai,j,k pi,j,k η 2⎟ + + σ ⎟ 2 2 ⎠ h2m [r] + lm,i h2 [r] + lm,j i=1, j =1 m i =m



am,i,k pm,i,k η  2 2 i∈Sm,n ∪{n} h2m [r]+lm,i

  M N h2m − h2m [r] +

ai,j,k pi,j,k η 2 2 i=1, j =1 h2m [r]+lm,j i =m

⎛

−

⎜ ln 2 ⎜ ⎝

i∈Sm,n ∪{n}

am,i,k pm,i,k η 2 h2m [r]+lm,i

+

M N i=1, j =1 i =m



ai,j,k pi,j,k η 2 h2m [r]+lm,j

  h2m − h2m [r] ⎞

⎟ + σ 2⎟ ⎠

lb = Rˆ m,n,k .

(4.121) It can be verified that the constraints in Eq. (4.120e) can be met with the equality, otherwise we can always increase τm without decreasing R˜ m,n,k , thus problem (4.120) actually shares the same optimal solution with problem (4.113). It is easy to find out that R˜ m,n,k is now concave with respect to τ . However, Rˆ m,n,k is still non-concave. Moreover, the constraints are not convex because the resulting set is not a convex set. To overcome this problem, we use the first-order Taylor expansions to approximate them. Specifically, since Rˆ m,n,k is convex with respect lb to h2m , we can approximate it with the lower bound Rˆ m,n,k , where H [r] is the given local point, which equals the result obtained in the rth iteration in SCA approach. Moreover, the constraint in Eq. (4.120d) can be written as χ2 ≤



!

hi − hj

"2

= H T QH ,

(4.121)

i,j ∈M ,i =j

where Q = diag(M) − 1, in which diag(M) denotes a diagonal matrix with all diagonal elements equaling M and 1 is an M × M matrix with all the elements equaling 1. Therefore, by applying the first-order Taylor expansion at the given point H [r], the constraint can be lower bounded by χ 2 ≤ H T [r]QH [r] + 2H T [r] Q (H − H [r]) .

(4.122)

4.4 Multi-UAV-Aided IoT NOMA Uplink Transmission

185

Similarly, the constraints in Eq. (4.120e) can also be lower bounded by τm ≤ h2m [r] + 2hm [r] (hm − hm [r]) .

(4.123)

Therefore, problem 4.113 can be approximated by the following problem: max H ,τ

s.t.

N  K M     B lb am,n,k Rˆ m,n,k [r] + R˜ m,n,k [r] K

(4.124a)

m=1 n=1 k=1

hmin ≤ hm , ∀m ∈ M ,

(4.124b)

hm ≤ hmax , ∀m ∈ M , ,

(4.124c)

χ 2 ≤ H T [r]QH [r] + 2H T [r] Q (H − H [r]) ,

(4.124d)

τm ≤ h2m [r] + 2hm [r] (hm − hm [r]) , ∀m ∈ M .

(4.124e)

lb and R˜ m,n,k are now joint concave with respect to H and τ , and Obviously, Rˆ m,n,k the constraints are all linear constraints. Therefore, problem (4.124) is now a convex problem. However, comparing with problem (4.103), it is too complicated to be ∂L solved with the Lagrangian dual method for the existence of τ . And solving ∂τ =0 m will not result in intuitional solutions like Eq. (4.121). Fortunately, considering the relatively small dimensions of H and τ , problem (4.124) can be efficiently solved by standard convex optimization solvers such as CVX. Till now, we can use a SCA based iterative algorithm to find a near-optimal solution to problem (4.113). The algorithm is summarized in Algorithm 14. To elaborate a little further, in the rth iteration, we solve problem (4.124) with given local point H [r], while in the (r + 1) th iteration, the optimal result obtained in the rth iteration is used as a local point to further approach the optimal solution. Algorithm 3 is guaranteed to  3.5 converge and it has a worst-case complexity order of O M L3 , where L3 is the maximum number of the iteration rounds.

4.4.4.3 Joint Power Allocation and Flight Height Optimization In Sects. 4.4.4.1 and 4.4.4.2, we have decomposed problem (4.95) into two subproblems in order to achieve the near-optimal power allocation matrix of IoT nodes and the flight heights of UAVs. However, the results obtained from the two subproblems are only the feasible solutions to problem (4.95), since we only optimize one set of variables in each subproblem. In this subsubsection, we design an AO algorithm to further approach the optimal solution to problem (4.95), where we alternatively optimize one of the two set of variables, while keeping the other set of variables fixed. The algorithm is summarized in Algorithm 15. It should be noticed that the AO algorithm requires that the subproblem must be solved optimally to guarantee convergence, which unfortunately cannot be met by Algorithm 15 since we only obtain the near-optimal solution for each subproblem. However, it is easy

186

4 Cooperative Resource Allocation in FANET

Algorithm 14 SCA based flight heights optimization algorithm for Problem (4.113) / 0 1: Initialize an initial feasible solution H 1 , set r = 1. 2: repeat 3: Obtain H ∗ by solving arg max

N  K M     B lb am,n,k Rˆ m,n,k [r] + R˜ m,n,k [r] K

m=1 n=1 k=1

s.t. (4.124b), (4.124c), (4.124d) and (4.124e). /

0 4: Update H r + 1 = H ∗ . 5: Update r = r + 1. 6: until H converges.

to prove that Algorithm 15 is converged. Let Θ (P [z] , H [z]) denote the objective of problem (4.95) in zth iteration, we will have   / 0 Θ (P [z] , H [z]) ≤ Θ P z+1 , H [z] (a)

 / 0 / 0 ≤ Θ P z+1 , H z + 1 ,

(4.125)

(b)

where (a) and (b) hold because the problems we solved in Algorithms 13 and 14 are only lower bounds to problem (4.97) and problem (4.113), for we approximate these two problem with the logarithmic approximation and the firstorder Taylor expansion, respectively. Eq. (4.125) indicates that the objective of problem (5.134) is non-decreasing after each iteration. Since the objective of problem(4.95) is upper bounded by a finite value, Algorithm 4 is guaranteed to coverage. Since Algorithms 13 and 14 have the complexity orders of O (MNKL1 L2 ) and O (MNKL 15 has a worst-case complexity order   1 L2 ), respectively, Algorithm of O MNKL1 L2 + M 3.5 L3 L4 , where L4 is the maximum number of the iterations. Algorithm 15 Alternative algorithm for solving Problem (4.95)

/ 0 1: Initialize an initial flight height H 1 = {h0 }, set z = 1. 2: repeat / 0 3: For given H [z], solve problem (4.97) with Algorithm 13, denote the solution as P z + 1 . / 0 4: For given P z + 1 , solve problem (4.113) with Algorithm 14, denote the solution as / 0 H z+1 . 5: Update z = z + 1. 6: until H and P converge.

4.4 Multi-UAV-Aided IoT NOMA Uplink Transmission

187

4.4.5 Simulation Results In this subsection, numerical results are presented for evaluating the performance of the proposed algorithms. In the simulations, we assume that all the IoT nodes are randomly distributed in a squared area of size 2000 m × 2000 m. The maximum and minimum uplink transmit power of each IoT node are set to be pmax = 500 mW and pmin = 100 mW, respectively. The flying heights of the UAVs are assumed to span from hmin = 100 m to hmax = 500 m, and the minimum variance of the altitudes is χ 2 = 100. Furthermore, we assume that the total bandwidth of each UAV-enabled subsystem is B = 120 kHz, which is divided into K = 16 subchannels. The AWGN power spectrum density is −174dBm/Hz. Each subchannel can be assigned to at most D1 = 3 IoT nodes and each IoT node can access D2 = 2 subchannels. The reference-distance unit power gain is set to be η = 1.4 × 10−4 . We first evaluate the convergence performances of the proposed algorithms. The results are shown in Fig. 4.17, where we assume that there are M = 3 UAVs serving N = 30 IoT nodes. It can be shown in Fig. 4.17 that all the iterative algorithms described in Algorithms 13, 14, and 15 have fast convergence speed. Specifically, relying on the SCA approach, the algorithms proposed in Algorithms 13 and 14 converge within 12 and 6 steps, respectively. Moreover, relying on the near-optimal solutions obtained by Algorithms 13 and 14 in each iteration, the AO algorithm described in Algorithm 15 is capable of achieving convergence in as few as 4 steps, which validates our proof in Sect. 4.4.4.3. Figure 4.18 shows one snapshot of the system realization relying on the proposed approaches. In this figure, there are N = 30 IoT nodes randomly distributed in a 2000 m × 2000 m squared area. It is shown that these IoT nodes are clustered into three groups (identified by colors) using the K-means clustering method. Furthermore, by fixing the horizontal location of the UAVs using Eq. (4.92), these IoT nodes are evenly distributed in the surrounding area of the corresponding UAV, which can in fact minimize the total horizontal transmission distance. Moreover, Fig. 4.18 reveals that, for the sake of maximizing the total uplink capacity, the system trends to maximize the uplink transmit power of the near IoT nodes while minimize the uplink transmit power of the remote IoT nodes. This is due to the fact that the nearer IoT nodes have higher channel gains and maximizing the uplink transmit power of these IoT nodes can simply increase the total capacity. By contrast, minimizing the uplink transmit power of remote IoT nodes can decrease the intra-group interferences as well as the inter-group interferences since the remote IoT nodes are usually nearer to the IoT nodes in other subsystems. Figures 4.19 and 4.20 depict the total system capacity versus the maximum transmit power of IoT nodes and the number of IoT nodes, respectively. In Fig. 4.19, we set N = 30 and pmin = 0.2 × pmax . It is observed that the system capacity increases with the maximum transmit power of IoT nodes, which appeals to our general knowledge. Moreover, the growth of the system capacity becomes slower as the maximum power increases, which is due to the increment of the interferences. It is shown in Fig. 4.20 that the system capacity increases with the number of IoT

4 Cooperative Resource Allocation in FANET 4.8

6.78

4.785

6.76

Total system capacity (bps/Hz)

Total system capacity (bps/Hz)

188

4.77 4.755 4.74 4.725 4.71 4.695 4.68 4.665 4.65

6.74 6.72 6.7 6.68 6.66 6.64 6.62

1

2

3

4

5

6

7

8

9 10 11 12 13 14 15

1

2

3

4

5

6

7

Number of iterations

Number of iterations

(a)

(b)

8

9

10

Total system capcity (bps/Hz)

6.795 6.79 6.785 6.78 6.775 6.77 6.765 1

2

3

4

5

Number of iterations

(c) Fig. 4.17 The convergence performances of the proposed algorithms with (M, N) = (3, 30), where (a), (b), and (c) represent the convergence performance of Algorithms 13, 14, and 15, respectively

nodes. Similarly, as the number of IoT nodes increases, the rate of growth becomes slower, which fits the Shannon’s formula. Figure 4.20 also demonstrates that a larger number of UAVs leads to a higher system capacity, and the gap becomes larger as the number of IoT nodes increases. The reason is that the total transmission distance decreases as the number of UAVs increases since each UAV serves less IoT nodes. Moreover, an increment of UAV-enabled subsystems also results in a decrement of both the intra-group interferences and inter-group interferences since subchannels are assigned to less IoT nodes. In Fig. 4.21, we compare our scheme with other schemes in terms of system capacity with M = 3. Specifically, the “NOMA scheme” is the method described in Algorithm 12, 13, 14, 15 and the “NOMA scheme with fixed aerial BS” is a modified method relying on0 Algorithm 12, 13, where the flying heights of the UAVs are fixed / to 100, 150, 200 m for satisfying the collision avoidance constraint. By contrast, in the “OMA scheme” and the “OMA scheme with fixed BS”, each subchannel can

4.4 Multi-UAV-Aided IoT NOMA Uplink Transmission

189

2000

y-coordinate (m)

1500

500

500 500 500

500

1000

500 UAV 1 UAV 2 100 UAV 3 IoT node IoT node IoT node

500

0

500

500 Transmit power 500 500 500 100

500

500

500

100

500

0

100

100

500 500

100 500 100 500

500 500 500 1000

500

500 1500

2000

x-coordinate (m) Fig. 4.18 One snapshot of the system realization with (M, N) = (3, 30)

Total system capcity (bps/Hz)

9

8

7

6 M=3 M=5 5

4 100

200

300

400

500

600

700

800

900

1000

Maximum transmission power of IoT nodes (mW) Fig. 4.19 The total system capacity versus the maximum uplink transmit power of IoT nodes parameterized by different number of UAVs with N = 30

only be assigned to one IoT node and each IoT node can access one subchannel. We adopt a simple subchannel assignment approach, in which the subchannels are assigned to the IoT nodes in the decreasing order of channel gains. It can be observed that the proposed scheme outperforms other schemes and both the NOMA

190

4 Cooperative Resource Allocation in FANET

Total system capcity (bps/Hz)

11 10 M=3 M=5

9 8 7 6 5 4 10

20

30

40

50

60

Number of IoT nodes Fig. 4.20 The total system capacity versus the number of IoT nodes parameterized by different number of UAVs

9

Total system capcity (bps/Hz)

8 7 6 5 NOMA scheme NOMA scheme with fixed aerial BS OMA scheme OMA scheme with fixed aerial BS

4 3 2 10

20

30

40

50

Number of IoT nodes Fig. 4.21 The total system capacity versus the number of IoT nodes with M = 3

60

4.4 Multi-UAV-Aided IoT NOMA Uplink Transmission

191

100

Number of accessed IoT nodes

90 80 70 60 50 OMA scheme NOMA scheme with D 1 = 3 NOMA scheme with D 1 = 4

40 30 20 50

100

150

200

250

Number of IoT nodes Fig. 4.22 The number of accessed IoT nodes versus the number of IoT nodes

schemes have higher system capacity than the OMA schemes. To explain, we show the number of accessed IoT nodes versus the number of IoT nodes of different schemes in Fig. 4.22. It shows that, when the number of IoT nodes is small, all the IoT nodes can access at least one subchannel, while the NOMA schemes outperform OMA schemes for their higher spectrum efficiency. By contrast, when the number of IoT nodes grows larger than the number of subchannels, more IoT nodes can access the UAVs in the NOMA schemes than in OMA schemes since each subchannel can only be assigned to one IoT node in OMA schemes. Therefore, the NOMA schemes still outperform the OMA schemes although they have higher interferences. Finally, Fig. 4.23 compares the average rate of accessed IoT nodes versus the number of IoT nodes of different schemes. It is shown that in general, the average rate of accessed IoT nodes decreases with the number of IoT nodes. The reason is that the increment of IoT nodes results in higher interferences. Additionally, Fig. 4.23 demonstrates that when the number of IoT nodes is smaller than a threshold, i.e., the total number of subchannels, the NOMA schemes still outperform the OMA schemes. Moreover, when the number of IoT nodes exceeds the threshold, comparing with the OMA schemes, the NOMA schemes achieve same performance in terms of average rate, but more IoT nodes can be served, which validates the superiority of the NOMA schemes.

4 Cooperative Resource Allocation in FANET

Average rate of accessed IoT nodes (bps/Hz)

192

0.45 NOMA scheme NOMA scheme with fixed aerial BS OMA scheme OMA scheme with fixed aerial BS

0.4 0.35 0.3 0.25 0.2 0.15 0.1

10

20

30

40

50

60

Number of IoT nodes Fig. 4.23 The average rate of accessed IoT nodes versus the number of IoT nodes with M = 3

4.4.6 Conclusions In this section, we studied a resource allocation problem in the context of a multi-UAV-aided IoT NOMA uplink transmission system. Specifically, we jointly optimized the channel assignment, the uplink transmit power of IoT nodes, and the flying heights of UAVs for maximizing the system capacity. We proposed an efficient subchannel assignment algorithm relying on the K-means clustering method and matching theory. And an AO algorithm for finding near-optimal uplink transmit power of IoT nodes and flying heights of UAVs was proposed relying on the SCA approach. Numerical results showed that the proposed algorithms have fast convergence speed, and the system has higher capacity than the OMA schemes. These results confirm that combining UAV communication and NOMA techniques is beneficial for constructing high-performance IoT systems.

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Chapter 5

Mobile Edge Computing in FANET

Characterized by their ease of deployment and bird’s eye view, unmanned aerial vehicles (UAVs) may be widely deployed both in surveillance and traffic management. In addition, UAVs have been widely used to provide enhanced information coverage as well as relay services for ground Internet of Things (IoT) networks. Considering the substantially limited processing capability, the IoT devices may not be able to tackle with heavy computing tasks. This impediment may be mitigated by employing the mobile edge computing (MEC) paradigm for offloading demanding and load-balance computational tasks from the UAV through a wireless transmission link. However, the offloaded information may become compromised by eavesdroppers, and latency and reliability should also be considered. Hence, how to design a UAV-aided mobile edge computing system that can achieve load-balance and efficient offloading has become a crucial issue. In this chapter, we first introduce the problems of mobile edge computing relying on UAV in Sect. 5.1 and then optimize the workload of UAV-aided MEC system in Sect. 5.2. For the sake of guaranteeing the latency and reliability of networks, we propose a heuristic algorithm to jointly optimize computing, communications, and caching resources in Sect. 5.3. Moreover, we formulate an energy-efficient computation offloading problem in the presence of both active and passive eavesdroppers and find the optimal solutions for the problems in Sect. 5.4. Finally, relying on queuing theory and Lyapunov optimization, we strike a powerdelay trade-off by jointly optimizing the computational task scheduling and resource allocation for multi-UAV networks in Sect. 5.5.

5.1 Introduction of Mobile Edge Computing Problems The UAV has witnessed its substantial success in both military and civilian applications due to its easy deployment, low cost, and feasible mobility [1–4]. © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2022 J. Wang, C. Jiang, Flying Ad Hoc Networks, Wireless Networks, https://doi.org/10.1007/978-981-16-8850-8_5

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Constrained by its computation and battery capability, computational-intensive tasks may be difficult to be tackled locally. Moreover, the damage to the terrestrial communication infrastructure also makes the cloud-based computation offloading disabled. Therefore, the issue of mobile edge computing (MEC) based on UAV has been raised. UAV-aided communication technology providing on-demand communication service has drawn great attention [5–7], where UAV-aided base stations can be flexibly deployed in disaster areas to support the rescue workers. However, offloading the computational tasks via UAV-aided base station to the remote cloud data center may lead to excessive latency. Considering their harsh operational environments in disaster, it is essential to study how to provide this kind of mobile edge computing system with low latency as well as high reliability. In this section, challenges and state of the art are for further discussion in mobile edge computing problems.

5.1.1 Problem Domain and Challenges The mobile edge computing problem can be described as how to provide better and reliable QoS for users in limited UAV communication resource and system capacity. In this subsection, we mainly focus on the load balance, latency and reliability, and high-efficiency offloading under the mobile edge computing framework supported by multiple UAVs. We first elaborate the following challenges: (1) Load balance: To improve the QoS of ground IoT nodes, the UAV-aided MEC network should achieve load-balance task. Since computing resources on a UAV are also limited due to its constrained carrying capacity, some UAVs may overload, while others are free [6]. Hence, it is necessary for these UAVs to conduct an efficient load-balance scheme to make better of the UAV resources and tackle with numerous tasks offloaded for the sake of reducing the overall task processing time. (2) Latency and reliability: When the UAV-aided MEC system is used in rescue activities, for example, in hostile environments, only optimizing communication performances is not enough considering computing and caching capability constraints. So it is essential to study how to provide this kind of mobile edge computing system with low latency as well as high reliability. (3) Offloading: In UAV-MEC systems, to prevent the problem that the offloaded information may become compromised by eavesdroppers, especially on physical-layer security, the offloading technique for UAV-MEC system is facing challenge. If we do not promote the computational offloading of UAVs to edge nodes and do not increase the offloading efficiency, it may be under a risk of being intercepted, which jeopardizes data security and privacy [8].

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199

5.1.2 State of the Art For the problems of mobile edge computing, there are state-of-the-art studies as follows. With the combination of UAV and MEC, to improve the QoS for users and maximize the computing rate, Jeong et al. [9] used a moving UAV to offer computing offloading services to mobile users, which aimed at minimizing the total mobile energy consumption and satisfying the QoS requirements. In [10], UAVenabled wireless powered MEC system was studied, with computing bits as well as harvesting causality requirement satisfied. Furthermore, Zhou et al. [11] studied a UAV-enabled wireless powered system, where the energy harvesting causal as well as the UAV speed constraint was considered. In [12], for the sake of improving coverage and increasing rate, Zhao et al. used UAVs to help small-cell base stations offload traffic via wireless backhaul. In [13], a UAV-aided MEC system with a threelayer integrated architecture was established over the social Internet of vehicles. By jointly optimizing the transmit power of the vehicle and the UAV, an optimization framework for the total utility maximization was proposed. The authors also focus more attention on the improvement of reliability and latency performance from different layer perspectives. Shariatmadar et al. proposed a link adaptation optimization scheme in [14] as well as a downlink transmission scheme in [15] for ultra-reliable low-latency communications. Moreover, Hu et al. [16] presented a novel unified radio frame structure and a device-to-device medium access control protocol for high reliability and low-latency vehicle-to-X communication services. Additionally, some researchers explored to use MEC as a middleware to achieve joint optimization of both computation and communication. Specifically, Liu et al. [17] utilized Lyapunov stochastic optimization to present a dynamic latency- and reliability-aware scheme for task computation and offloading. Azimi et al. [18] discussed the mobile cloud aided task offloading for the sake of saving the energy consumption.

5.2 Load-Balance Oriented UAV-Aided Edge Computing MEC is characterized in terms of low energy consumption, low latency, and relatively high security. Meanwhile, UAVs can be well-equipped with MEC devices to provide mobile edge services in large-scale IoT scenarios for the sake of improving users’ quality of service (QoS), where the ground IoT nodes can offload heavy computing tasks to the mobile cloudlet via uplink/downlink communication with the UAVs [19]. In this section, we propose a UAV-aided MEC system as shown in Fig. 5.1, where multiple UAVs cooperate to provide MEC services for ground IoT nodes. In this case, some tasks in IoT nodes may be offloaded to the UAVs for the sake of satisfying their QoS requirement. Considering the non-uniform distribution of ground IoT nodes, both communication performance and the load balance of the

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5 Mobile Edge Computing in FANET

Fig. 5.1 Multi-UAV-aided IoT scenario

tasks from the ground IoT nodes can be substantially affected by the deployment of UAVs [20]. Since computing resources on a UAV are also limited due to its constrained carrying capacity, some of the UAVs may overload, while others are free [6]. Hence, it is necessary for these UAVs to conduct an efficient task scheduling scheme in order to tackle with a large number of tasks offloaded for the sake of reducing the overall task processing time. Therefore, both multi-UAV deployment and task scheduling impose a severe impact on the efficiency of MEC network. Specifically, a proper drone’s deployment is capable of reducing the transmission delay and of balancing the load of UAVs. In addition, the effective task scheduling strategy among the UAVs is able to reduce the waiting time of tasks and improve the processing efficiency. Hence, our scenario aims at the load balancing deployment and the effective task scheduling in the multiUAV-aided MEC system. The remainder of this section is organized as follows. In Sect. 5.2.1, the channel model is defined. Moreover, the load-balance multi-UAV deployment and the latency-aware task scheduling optimization problem are formulated in Sect. 5.2.2. In Sect. 5.2.3, DE based multi-UAV deployment algorithm and the DRL based task schedule algorithm are elaborated. Section 5.2.4 shows our simulation results, followed our conclusions in Sect. 5.2.5.

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201

5.2.1 System Model 5.2.1.1 Network Model A MEC system model is illustrated in Fig. 5.2, which consists of K IoT nodes and N UAVs. Meanwhile, IoT nodes on the ground can offload their tasks to the UAVs. Let ψ = {m1 , m2 , · · · , mK } denote the set of IoT nodes and η = {u1 , u2 , · · · , uN } be the set of the UAVs. In our system, the IoT nodes are constituted by heterogeneous types of devices with different offloading levels. We assume that there are Z types of IoT nodes represented by 5 e = {ε1 , ε2 , · ·6· , εZ }, where the corresponding offloading level is denoted by e˜ = ε˜ 1 , ε˜ 2 , · · · , ε˜ Z . Without loss of generality, we assume all IoT nodes are fixed on the ground and all UAVs fly at/a fixed altitude H (H > 0). 0 m m The position of the k-th IoT node is denoted by m = x , y , 0 , and the position k k k / 0 of the n-th UAV is denoted by un = xnu , ynu , H . Let αn,k indicate the connection between UAV and IoT nodes, where αn,k = 1 means the k-th IoT node is connected to the n-th UAV. Considering that each IoT node can only connect to one UAV simultaneously, we have N 

αn,k = 1, ∀k = 1, 2 . . . , K.

(5.1)

n=1

Moreover, the distance between un and mk can be calculated by d (un , mk ) = [H 2 + "2 ! "2 1 ! u xn − xkm + ynu − ykm ] 2 . For an offloaded task Fz (un , mk ) , ∀z = 1, 2, · · · , Z, between mk and un , given the required computing resource cz (un , mk ), the required

Fig. 5.2 Network architecture

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5 Mobile Edge Computing in FANET

execution time tz (un ,/mk ), and the required communication0 traffic hz (un , mk ), we define Fz (un , mk ) = cz (un , mk ) , tz (un , mk ) , hz (un , mk ) .

5.2.1.2 Communication Model Figure 5.1 shows the multi-UAV-aided IoT scenario. Every UAV has a fixed coverage with radius Rc . Moreover, ground IoT nodes can access the UAV via orthogonal frequency division multiplex access; hence, the interference among the UAV node links is neglected. We assume that the communication channels from UAVs to IoT nodes are dominated by LOS channel [21], and thus the channel gain between mk and un can be derived as g (un , mk ) = β0 d (un , mk )−2 =

H2

β0 " "2 , ! ! m 2 u + xn − xk + ynu − ykm

(5.2)

where β0 denotes the channel gain at the reference distance of 1 meter. Let p˜ (un ) represent the transmission power of un . Then, the uplink data rate between un and mk can be formulated by   p˜ (un ) g (un , mk ) v˜ (un , mk ) = B log2 1 + σ2 ⎛ ⎜ = B log2 ⎝1 +

⎞

β0 p˜ (un ) ⎟  "2 ! "2  ⎠ , ! m m 2 2 u u σ H + xn − xk + yn − yk

(5.3)

where σ 2 denotes the white Gaussian noise variance, and B denotes the channel bandwidth. The transmission delay between mk and un for task Fz (un , mk ) can be shown as tzT (un , mk ) =

hz (un , mk ) . v˜ (un , mk )

(5.4)

Let φ (un ) represent the set of IoT nodes connected to un , so it follows: N ? n=1

φ (un ) = ψ.

(5.5)

5.2 Load-Balance Oriented UAV-Aided Edge Computing

203

Then, the total offloading level of un can be denoted by Ωn =

K 

ε˜ (mk ) αn,k , ∀n = 1, 2, . . . , N,

(5.6)

k=1

where ε˜ (mk ) represents the offloading level of mk and ε˜ (mk ) ∈ e. ˜

5.2.1.3 Computation Model In our system, P types of resources in UAV are concerned, such as CPU, memory, hard disk, etc. Figure 5.3 shows an example of the task scheduling. For the task Fz (un , mk ), its ideal completion time is tz (un , mk ), so we calculate the total execution time of task Fz (un , mk ) according to delay

tzA (un , mk ) = tz (un , mk ) + tz

(un , mk ) ,

(5.7)

delay

where tz (un , mk ) denotes the delay time of task Fz (un , mk ). Hence, delay tz (un , mk ) is 0 when task Fz (un , mk ) is executed immediately, or more than 0 when the current processing queue of UAV is full and task needs to wait.

5.2.2 Problem Formulation In this subsection, we aim at optimizing the average slowdown for offloaded tasks, where the load balance for UAVs is guaranteed. Since the distribution of IoT nodes is generally non-uniform, the deployment strategy of UAVs will have substantially impact on the performance of the MEC system. Generally, UAVs need to be as close to the IoT nodes as possible to reduce transmission cost. Furthermore, excessive load in the UAV will increase the number of tasks in the processing queue, which will increase the total processing time of the tasks and further affect system performance. Therefore, for the multi-UAV MEC system, it is necessary to achieve load balance, in order to avoid the overall system performance degradation when some of the UAVs take too many tasks and others are free of tasks. Specifically, our problem concerns two aspects, namely the load balancing multiUAV deployment and the latency-aware task scheduling on the UAVs. As for the load balancing multi-UAV deployment, our objective is to achieve the load balance for all UAVs, where the degree of load balance can be expressed as   N  2 1  SO (Ω) =  Ωi − Ω , N i=1

(5.8)

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Fig. 5.3 A toy example for explaining the task scheduling scheme

5.2 Load-Balance Oriented UAV-Aided Edge Computing

205

where Ω=

N 1  (Ωi ) . N

(5.9)

i=1

Note that SO (Ω) ≥ 0. Hence, the larger SO (Ω) is, the more non-uniform the distribution of tasks among UAVs is. Meanwhile, the average transmission cost between UAVs and IoT nodes is considered, and we aim at minimizing the average transmission cost according to Eq. (5.4), which can be calculated by K N 1  T tz (un , mk ) αn,k . tc (un , mk ) = K

(5.10)

k=1 n=1

As for the latency-aware task scheduling, according to Eq. (5.7), we can get the task slowdown, which can be calculated by td (un , mk ) =

tzA (un , mk ) , tz (un , mk )

(5.11)

where td (un , mk ) ≥ 1. Then, according to Eqs. (5.8), (5.10), and (5.11), the load balancing multi-UAV deployment as well as latency-aware task scheduling optimization problem can be formulated as K N 1  P 1 : min td (un , mk ) αn,k (xnu ,ynu ) K k=1 n=1

+ 1 [SO (Ω)] + 2 [tc (un , mk )] s.t. d (un , mk ) ≤ Rc , mk ∈ ψ, ∀k = 1, 2 . . . , K,

(5.12)

un ∈ η, ∀n = 1, 2, . . . , N, αn,k ∈ {0, 1}, ∀k = 1, 2 . . . , K, n = 1, 2, . . . , N, N 

αn,k = 1, ∀k = 1, 2 . . . , K,

n=1

where 1 and 2 denote the weight factors for load balancing requirement and average transmission cost, respectively. Specifically, 1 = 0 means that the influence of load balance for UAVs is not considered, and 2 = 0 means that the influence of average transmission cost is not considered.

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5.2.3 Joint UAV Deployment and Task Scheduling In this subsection, we will elaborate on the proposed multi-UAV deployment algorithm and task scheduling schema. Multi-UAV deployment problem is a NPhard problem [22]. In order to find a satisfactory solution, we propose a differential evolution aided multi-UAV deployment algorithm to solve this problem. Initially, all UAVs are randomly positioned, and then we assign the maximum load for each UAV based on the location of UAVs and IoT nodes. In this way, the access problem between UAVs and IoT nodes can be modeled into a generalized assignment problem. After that, we use an approximation algorithm to determine all the connections between UAVs and IoT nodes. Meanwhile, a deep reinforcement learning algorithm is used to schedule tasks for incoming tasks. Finally, the nearoptimal positions of UAVs are obtained through iterations of differential evolution algorithm.

5.2.3.1 Load Balance for UAVs Since there are a total of Z types of IoT nodes5represented by 6e = {ε1 , ε2 , · · · , εZ } and the corresponding offloading level is e˜ = ε˜ 1 , ε˜ 2 , · · · , ε˜ Z , the total offloading level Et can be formulated as Et =

K 

ε˜ (mk ) ,

(5.13)

k=1

where ε˜ (mk ) represents the offloading level of mk . Ideally, each UAV carries a task load of Eavg = Et /N to achieve load balance. However, since the distribution of IoT nodes is generally non-uniform, balancing load for all UAVs will lead to excessive transmission consumption of these IoT nodes when some nodes are far from connected UAV, thus failing to achieve the optimization goal of Eq. (5.12). Hence, according to the location of all UAVs and IoT nodes, let elb (un ) be the lower bound of the set of IoT nodes, in which the IoT nodes can only be connected to un due to the distance. The total offloading level of elb (un ) can be formulated as e˜lb (un ) =



ε˜ (mk ) , ∀k = 1, 2 . . . , K.

(5.14)

mk ∈elb (un )

Similarly, let eub (un ) be the upper bound of the set of IoT nodes which un can cover. The total offloading level of eub (un ) can be formulated as e˜ub (un ) =

 mk ∈eub (un )

ε˜ (mk ) , ∀k = 1, 2 . . . , K.

(5.15)

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207

Then, let the reference load of UAV un be E˜ (un ), and we can achieve e˜lb (un ) ≤ E˜ (un ) ≤ e˜ub (un ).

(5.16)

Considering Eavg , e˜lb (un ), and e˜ub (un ), if Eavg ≥ e˜ub (un ), the best setting for ˜ E (un ) is E˜ (un ) = e˜ub (un ) for satisfying the total load requirement of un . Similarly, if Eavg ≤ e˜lb (un ), the best setting for E˜ (un ) is E˜ (un ) = e˜lb (un ). In the case of e˜lb (un ) ≤ Eavg ≤ e˜ub (un ), un has more exclusive IoT nodes when Eavg is close to e˜lb , where E˜ (un ) needs to be appropriately increased. When Eavg is close to e˜ub , more IoT nodes covered with un will also be covered by other UAVs, where E˜ (un ) needs to be appropriately reduced. Hence, we can get ! " E˜ (un ) = Eavg + λ1 e˜ub (un ) − Eavg " ! − λ2 Eavg − e˜lb (un )

(5.17)

= (1 − λ1 − λ2 )Eavg + λ1 e˜ub (un ) + λ2 e˜lb (un ) , where λ1 and λ2 indicate the influence factors of e˜ub (un ) and e˜lb (un ), respectively. Then, the reference load E˜ (un ) can be expressed by ⎧ ⎪ e˜lb , Eavg ≤ e˜lb (un ) , ⎪ ⎪ ⎨ e˜ub , Eavg ≥ e˜ub (un ) , E˜ (un ) = ⎪ (1 − λ1 − λ2 )Eavg + λ1 e˜ub (un ) ⎪ ⎪ ⎩ + λ2 e˜lb (un ) .

(5.18) otherwise,

N ˜ Then, the sum of all reference loads can be expressed as E˜ t = i=1 E (un ). ˜ Sometimes, it can be aware of that a gap exists between Et and Et in the case of E˜ t < Et , which needs to be filled. Hence, in the case of E˜ lb (un ) ≤ Eavg ≤ E˜ ub (un ), we fill the gap by adding E˜ gap to E˜ (un ), and the reference load remains unchanged otherwise. Then, we have Et − E˜ t , E˜ gap = n∗

(5.19)

where n∗ is the number of UAVs that under the case of E˜ lb (un ) < Eavg < E˜ ub (un ). Finally, we rewrite the Eq. (5.18) and get the final reference load of all UAVs ⎧ ⎪ e˜lb , Eavg ≤ e˜lb (un ) , ⎪ ⎪ ⎨ e˜ub , Eavg ≥ e˜ub (un ) , E˜ (un ) = ⎪ (1 − λ1 − λ2 )Eavg + λ1 e˜ub (un ) ⎪ ⎪ ⎩ + λ2 e˜lb (un ) + E˜ gap .

(5.20) otherwise.

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5.2.3.2 GAP Based Node Assignment In this subsubsection, we aim at optimizing the node assignment among UAVs according to the reference load in the previous subsection. Given the known position of all UAVs, the node assignment problem can be formulated as a kind of generalized assignment problem. In the GAP, both tasks and agents have sizes, where the size of each task is different with different agents [23]. In our scenario, each UAV can be seen as an agent, and each IoT node has a kind of tasks. Define wn,k as the cost of the task offloaded from the k-th IoT node to the n-th UAV, where wn,k is only determined by the type of the task. As a result, wn,k = ε˜ (mk ). Furthermore, let fn,k be the profit of the task, which is primarily affected by the distance between un and mk and the required communication traffic hz (un , mk ). According to Eq. (5.4), we can get

fn,k =

ϕtzT (un , mk ) , d (un , mk ) ≤ Rc , −∞, d (un , mk ) > Rc ,

(5.21)

where ϕ > 0 denotes the influence factor. In general, the closer the distance between un and mk , the bigger the fn,k is. When the distance between un and mk exceeds the service radius Rc , fn,k will be close to −∞. In order to maximize the total profit, we formulated this assignment problem as an integer programming (IP) problem, which can be written as P 2 : min xn,k

s.t.

K 

N  K 

−fn,k xn,k

n=1 k=1

wn,k xn,k ≤ E˜ (un ) , ∀n = 1, 2, · · · , N,

k=1 N 

(5.22)

xn,k = 1, ∀k = 1, 2, · · · , K,

n=1

xn,k ∈ {0, 1}, ∀n = 1, 2, · · · , N, k = 1, 2, · · · , K. Since the problem P 2 is a GAP, problem P 2 is NP-hard. Here, we propose an approximate algorithm to find its near-optimal solution, which is described as three steps: • Step 1: Linear programming relaxation Convert the integer programming problem into the following linear programming (LP) relaxation:

5.2 Load-Balance Oriented UAV-Aided Edge Computing

P 3 : min xn,k

s.t.

K 

N  K 

−fn,k xn,k

n=1 k=1

wn,k xn,k ≤ E˜ (un ) , ∀n = 1, 2, · · · , N,

k=1 N 

209

(5.23)

xn,k = 1, ∀k = 1, 2, · · · , K,

n=1

xn,k ≥ 0, ∀n = 1, 2, · · · , N, k = 1, 2, · · · , K. Then, solving this LP gives us a fractional solution. • Step 2: Bipartite graph construction Convert the fractional solution into a bipartite graph with fractional edge weights where one side represents IoT nodes and the other side represents slots in UAVs. ˆ B), ˆ where Kˆ = [K] and Bˆ = {(n , s  )|n ∈ Define a bipartite graph C = (K, [N], s  ∈ [sn ]}. We illustrate the edges in the bipartite graph by only looking at the case n = 1. For n = 1, consider only the IoT node mk such that x1,k > 0 and assume this is [K] without loss of generality. Assume that f1,1 ≥ f1,2 ≥ · · · f1,K  and sort them if necessary. For each k  ∈ [K], we track the partial sum kk=1 x1,k .   −1 If kk=1 x1,k ≤ s  , and kk=1 x1,k ≥ s  − 1, then add an edge (k  , (1, s  )) with k   −1 x1,k < s  , then add an weight x1,k  . Otherwise, if k=1 x1,k > s  , and kk=1  −1 x1,k and an edge (k  , (1, s  )) with edge (k  , (1, s  − 1)) with weight s  − kk=1 k  weight k=1 x1,k − s  . • Step 3: Deterministic rounding Note that the bipartite graph is a fractional min-cost perfect matching of the underlying cost function C(k  , (n , s  )) = −fn,k . It can be shown that all extreme points of the polytope are integral. Through finding a cycle or augmenting path in the previous bipartite graph, we can convert the fractional solution into an integral one within polynomial time, without increasing the objective value. Call all edges with weight in the range (0, 1) unsaturated and {0, 1} saturated. We represent an iterative method such that after one loop, the number of unsaturated edges decreases by at least 1, and the sum of weights attached to a left vertex is preserved as 1. Since at the end there is no unsaturated edge left and each left vertex is attached to edges with weights summing up to 1, each left vertex is mapped to a right vertex via the unique edge with weight 1. We will see shortly that this map is also injective, proving that it is a perfect matching on the left side. Consider the following two cases: Case 1: If there is a cycle of unsaturated edges, color them by blue and red alternately. By increasing the weights of all red edges by a small amount δ and decreasing the weights of blue ones by δ, no LP constraints are violated provided that δ is sufficiently small. We can thus move δ toward that direction

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until one of the red edges comes to 1 or one of the blue edges comes to 0. Either way we decreased the number of unsaturated edges by at least 1. Case 2: Call a vertex single if it is only attached to an unsaturated edge, and then the weight on the vertex is easily seen as equal to the weight of the edge. Note that no left vertex can be single since they all have weight exactly 1. Suppose now there is no cycle of unsaturated edge left, then each maximum path of unsaturated edge must start and end at single vertices. Choose a maximum path and color the edges by blue and red alternatively. Similar to case 1, perturbing the weight of all blue and red edges by a small amount δ does not violate any of the LP constraints, and we can freely move δ until one red edge reaches 1 or one blue edge reaches 0. It should be noted that, after deterministic rounding, the actual offloading level of a few UAVs may be slightly higher than the reference load, but it will not cause negative effects because it will not exceed the maximum processing capacity of the UAV.

5.2.3.3 Deep Reinforcement Learning Aided Task Scheduling In this subsubsection, we study the task scheduling scheme for incoming tasks relying on deep reinforcement learning algorithm. DRL combines deep learning and reinforcement learning in order to achieve end-to-end learning from perception to action. The agent first of all senses the state from the environment and then performs an action. The environment may move to another state with the time. At the same time, the agent can obtain a feedback according to the reward function. It can be seen that DRL is a model of human–environment interaction [24–26]. The Q-learning algorithm is a classical reinforcement learning algorithm, and it can find the nearoptimal action by interacting with the environment. Moreover, for the step t, the states can be represented as St , the policy space can be defined as π, and then the accumulated rewards V π (St ) can be calculated as V π (St ) = Rt + γ Rt +1 + γ 2 Rt +2 + · · · ,

(5.24)

where Rt is the instant reward in step t, and γ (0 < γ < 1) represents the discount factor, which reflects the influence of the future reward. In Q-learning algorithm, the Q-value is the function of states St and action At , which can be formulated as ! " Qt (St , At ) = Rt + γ V π St +1 .

(5.25)

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211

Q-learning is a kind of algorithm with the iteration of value. Since we can only get a limited series of samples and only limited samples can be used for operation, we update the Q-value according to Qt +1 (St , At ) = (1 − ϑ)Qt (St , At ) + ! ", + ϑ Rt + γ max Qt St +1 , At +1 ,

(5.26)

where the learning rate ϑ (0 < ϑ < 1) controls the learning speed. Deep Q-network (DQN) combines Convolutional Neural Network (CNN) with Q-learning, which uses the target function of Q-learning to construct deep learning tags [27]. In addition, DQN uses an experience replay mechanism to solve data correlation problems. At the same time, a CNN (MainNet) is used to generate the current Q-value, and another CNN (Target) is used to generate the target Q-value. Furthermore, the loss function of DQN can be given by + , L(θ ) = E (QT − Q(St , At ; θ ))2 ,

(5.27)

where the target function QT can be formulated as ! " QT = Rt + γ max Q St +1 , At +1 ; θ ,

(5.28)

where θ is the parameter of the neural network. Algorithm 16 Deep reinforcement learning based task scheduling Input: states, S; maximum number of iteration, tmax ; Output: action-value function, Q(S, A); 1: initialize action-value function Q with random weights; 2: for t = 1; t < tmax ; t + + do: 3: divide step t into bt sub-steps; 4: select a random sub-action in each sub-step, and all sub-actions make up action at ; 5: execute action at , then obtain the reward rt , and arrive at the next state st+1 ; 6: calculate target Q-value according to Eq. (5.28); 7: update the deep Q-network by minimizing the loss Lθ according to Eq. (5.27); 8: end for

In this subsubsection, we exploit the DRL algorithm shown as Algorithm 16 to solve the task scheduling problem, for the sake of minimizing the average slowdown of tasks in UAVs. Considering that a set of φ(un ) IoT nodes have been accessed to the n-th UAV according to Eq. (5.5), three key factors of the deep Q-network are given as follows: • State space: The resource states of UAV include the current allocated computing resources and the required computing resources of the possible scheduled tasks as shown in Fig. 5.3. We assume that the resource

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/ 0 demand of task Fz (un , mk ) / = cz (un , mk ) , tz (un , mk ) , hz (un , mk ) is0 given, where cz (un , mk ) = cz,1 (un , mk ) , cz,2 (un , mk ) , . . . , cz,p (un , mk ) and the cz,p (un , mk ) , p = 1, 2, · · · , P indicates the p-th type of resources. Furthermore, the current allocated computing resources of the n-th UAV is Gn,z . Hence, , of N UAVs + the system states with a total

can be given by Γ = S1S , S2S , · · · , SnS , n = 1, 2, · · · , N , where SnS = 2 1> K k=1 Fz (un , mk ) αn,k , Gn,z , z = 1, 2, · · · , Z . • Action space: Assuming in the t-th step, a number of Mn,t tasks are queued in the n-th UAV. Then the size of the action space in the n-th UAV can be represented by 2Mn,t , which makes challenges on the DRL. the action space, 6 5 In order to simplify we redefine the action space as An,t = ∅, 1, 2, . . . , Mn,t and divide each step into bn,t sub-steps, where bn,t denotes the total number of sub-actions that will be scheduled in the t-th step. Then, in each sub-step, only one sub-action will be scheduled, and the size of the action space is reduced to M + 1. Since a task is scheduled in the cluster as shown in Fig. 5.3, this task will be removed from the waiting queue. The agent then observes a state transition, where the scheduled task is moved to the appropriate position. Once the agent picks ∅ or an invalid sub-action, it indicates that the agent does not wish to schedule further tasks in the current step, and time actually proceeds, in other words, go to the next step t + 1. • Reward: The reward function is designed for directing the agent to minimize the average slowdown in the UAVs. Specifically, we set the reward in each timestep as Mn tz (u−1 , where Mn is the set of tasks currently in the n-th UAV. n ,mk ) As for the complexity of our proposed DRL aided task scheduling algorithm, in the training process, the time complexity is O(E ∗ D/B ∗ T ), which mainly depends on the CNN training complexity of DQN, where E represents the epochs, D denotes the data set size, B denotes the batch size, and T represents the time complexity of a single iteration. Moreover, the computational complexity of the algorithm is O(n) relying on its mainly matrix operation.

5.2.3.4 Differential Evolution Based Multi-UAV Deployment Differential evolution is a random model that simulates biological evolution. Through repeated iterations, the populations that are adapted to the environment are preserved. In our scenario, the dimension of each population is 2N, which is twice as much as the number of UAVs. Let Xd (i), d = 1, 2, . . . , D, indicate the deployment location of the i-th generation of UAVs, where D is the total number of populations. At the beginning of the algorithm, we randomly determine the deployment position of UAVs in all populations as Xd (1), d = 1, 2, . . . , D. In the g-th iteration, each population Xd (g) mutates and generates a mutation vector Hd (g) by randomly

5.2 Load-Balance Oriented UAV-Aided Edge Computing

213

selecting three other populations from the generation, for example, Xda (g), Xdb (g), Xdc (g), while da = db = dc = d. Then we have ! " Hd (g) = Xda (g) + ξ Xdb (g) − Xdc (g) ,

(5.29)

where ξ indicates the factor used to control the influence of different vectors. Then, the crossover vector Vd (g) can be calculated by

Hd (g), rand(0, 1) < Pcr , Xd (g), else,

Id (g) =

(5.30)

where Pcr is the crossover probability. Finally, according to the value of fitness function, we select the best population between crossover vector Vd (g) and the original vector Xd (g) as the next generation, which can be formulated as

Xd (g + 1) =

! " ! " Id (g), f Id (g) > f Xd (g) , Xd (g), else,

(5.31)

where function f (∗) is the objective function of Eq. (5.12). Algorithm 17 DE based multi-UAV deployment Input: the set of (IoT nodes), φ; objective function; the number of UAVs, N; maximum number of iteration, lmax ; Output: deployment of UAVs, [xnu , ynu ], n = 1, 2, . . . , N; best IoT node assignment, φ(u(n)); 1: randomly initialize populations Xd (1); 2: for i = 1; i < lmax ; i + + do: 3: obtain mutation populations through differential strategy according to Eq. (5.29); 4: obtain crossover populations according to Eq. (5.30); 5: determine reference load for multiple UAVs according to Eq. (5.20); 6: get the fractional solution of node assignment problem in Eq. (5.23); 7: construct the bipartite graph based on the fractional solution; 8: deterministic round the fractional solution; 9: find the optimal task scheduling scheme according to Algorithm 16; 10: calculate the fitness for all populations according to the objective function of Eq. (5.12); 11: get the next generation of DE according to Eq. (5.31); 12: end for

According to the characteristics of DE, after a certain number of iterations, we can get the converged populations, from which we can get the near-optimal deployment of all UAVs. As for the complexity of our proposed differential evolution based multi-UAV deployment algorithm, in each decision round, we have to update the generation of each population according to Eq. (5.31). Hence, the complexity of each decision round is on the order of O(n). The flow of our proposed DE based multi-UAV deployment algorithm is shown in Algorithm 17.

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5.2.4 Simulation Results In our simulations, a 400×400 m rectangular area is considered, where ground IoT nodes are random distributed. The channel bandwidth is B = 1 MHz and the transmission power is p˜ = 0.5 W. The variance of white Gaussian noise is σ 2 = 5 ∗ 10−15 . All UAVs fly at a fixed altitude H = 100 m with a maximum 2 coverage Rc = 100 m. The channel gain is set as β0 = ηlos ( 4πf c ) , where ηlos = 1 is the attenuation factor corresponding to LOS [28], the carrier frequency is f = 2.4 GHz, and c is the velocity of light. And there are a total of 100 IoT nodes and 5 UAVs. Figure 5.4 shows an example of near-optimal result for the multi-UAV deployment. There are some different colors of UAVs, and the smaller pointers indicate the IoT nodes, while each IoT node is connected to the UAV of the same color. Explicitly, given a total of N = 5 UAVs and K = 100 IoT nodes, we arrive at a near-optimal multi-UAV deployment strategy associated with the coordinates of [171.41,126.49], [149.50,245.87], [270.68,253.43], [284.26,152.94], and [227.91,181.27] for each UAV. As for the task scheduling, we use a neural network to construct our deep Qlearning network with learning rate 0.0025. And the task generation of IoT nodes follows the Poisson distribution, while the arrival rate is λ. There are a total of three kinds of tasks and two kinds of resources requirement for each task in the system. Meanwhile, the ideal completion time and resource requirement of each task are randomly generated from [1,15] and [1,10]. Figures 5.5 and 5.6 plot the

Fig. 5.4 Simulation result of the multi-UAV deployment in the context of N = 5 and K = 100

5.2 Load-Balance Oriented UAV-Aided Edge Computing

Fig. 5.5 Reward for task scheduling the UAV network

Fig. 5.6 Average slowdown of offloaded tasks of the UAV network

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Fig. 5.7 Average slowdown versus Poisson arrival rates in the context of λ = (0.3, 0.5, 0.7, 0.9)

reward and the average slowdown, respectively, at each iteration. As expected, both values increase with iterations improve. It clearly shows in Fig. 5.5 that as iterations increase, the total reward of DRL will gradually get bigger and converge to an ideal value. And Fig. 5.6 shows that as iterations increase, UAVs have learnt to better schedule incoming tasks, so the average slowdown will gradually approach the minimum value. Figures 5.7 and 5.8 indicate the influence of the quantity of tasks on the scheduling performance of UAVs. Since the task generation of IoT nodes follows the Poisson distribution, we can obtain that with the increase of the task arrival rate, the average slowdown increases and reward decreases owing to the limited processing capability of each UAV. We compare our proposed DRL aided task scheduling algorithm against three classic task scheduling algorithms, i.e., First Come First Serve (FCFS) algorithm, Shortest Job First (SJF) algorithm, and Round Robin (RR) algorithm, as shown in Fig. 5.9. Specifically, SJF schedules the smaller tasks first in comparison to both FCFS and RR. The performance of RR algorithm largely depends on the choice of the length of the time quantum. If time slot is longer, it tends to exhibit the same behavior as FCFS. However, if time slot is shorter than it is needed, more task switching can reduce the efficiency of task scheduling. By contrast, DRL aided task scheduling algorithm can learn from experience and can reserve the network resources. Hence, the recent arriving small tasks can be dealt with at once, and the average slowdown is minimized. Figures 5.10 and 5.11 show the influence of different weight factors 1 and 2 according to Eq. (5.12). Since 1 and 2 denote the weight factors for load balancing requirement and average transmission cost, respectively, appropriate 1 and 2 will

5.2 Load-Balance Oriented UAV-Aided Edge Computing

Fig. 5.8 Reward versus Poisson arrival rates in the context of λ = (0.3, 0.5, 0.7, 0.9)

Fig. 5.9 The average slowdown comparison among DRL, FCFS, SJF, and RR

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Fig. 5.10 Average slowdown versus weight factors (1 , 2 ) for the DE algorithm

Fig. 5.11 Reward versus weight factors (1 , 2 ) for the DE algorithm

5.2 Load-Balance Oriented UAV-Aided Edge Computing

219

Fig. 5.12 The fitness comparison among DE, PSO, and GA

give the MEC system better performance. It can be seen in Figs. 5.10 and 5.11 that, when 1 = 0.06 and 2 = 0.0015, it will get the best overall performance in our system. Furthermore, whether 1 and 2 are too small or too large, the average slowdown will increase and the reward will decrease. That is because underestimating 1 will lead to unbalanced load among UAVs, while sometimes some MEC nodes cannot meet the quality of service requirements, as well as overestimating 1 will lead to an increase in transmission cost of UAVs. In the same way, underestimating 2 will resulting in high transmission cost, and overestimating 2 will result in unbalanced load. Figure 5.12 shows the comparison to the classic genetic algorithm (GA) and the particle swarm optimization (PSO) in Algorithm 17. In the DE, the population size is 10, and the crossover probability and the mutation probability of DE are set as 0.7 and 0.2, respectively. In the PSO, the particle number is 10, which is the same as DE. Moreover, the weight factors of velocity, best position, and globally optimal position are 0.2, 0.5, and 0.5, respectively. And in the GA, the population size is 64, and one population is eliminated per generation, where the crossover probability as well as the mutation probability is the same as DE. Obviously, as iterations increase, the DE algorithm has the best fitness in comparison to the other two algorithms.

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5.2.5 Conclusions The development of UAV technology has provided a new solution for the task offloading of IoT devices. Compared with fixed ground base stations, UAVs can approach ground IoT devices efficiently due to its easy deployment, low cost, and feasible mobility. In this section, we aim for designing a multiple UAV-aided MEC system with the goal of global load balance and slowdown minimization. We introduce differential evolution algorithm to search for near-optimal locations of UAVs. Besides, the GAP aided approximation algorithm is conceived to determine each connection between UAV and IoT nodes. Moreover, a DRL based task scheduling scheme is used to schedule offloaded tasks effectively. Finally, simulation results verify the effectiveness and superiority of our proposed algorithm.

5.3 Latency and Reliability Guaranteed UAV-Aided Edge Computing Recently, the intelligent emergency rescue equipment has been widely used in the context of emergency rescue relying on the advance in Internet of Things (IoT), artificial intelligence (AI) techniques, etc. [3, 24, 29]. However, constrained by its computation and battery capability, computational-intensive tasks may be difficult to be tackled locally. Moreover, the damage of the terrestrial communication infrastructure also makes the cloud-based computation offloading disabled. UAV-aided communication technology providing on-demand communication service has drawn great attention [5–7], where UAV-aided base stations can be flexibly deployed in disaster areas to support the rescue workers. However, offloading the computational tasks via UAV-aided base station to the remote cloud data center may lead to excessive latency. Hence, inspired by the concept of mobile edge computing (MEC) [30, 31], UAV-enabled mobile edge computing nodes (UMENs) can be used to provide proximity computing services for rescue activities. Considering their harsh operational environments in disaster, it is essential to study how to provide this kind of mobile edge computing system with low latency as well as high reliability. State-of-the-art literatures focus more their attention on the improvement of reliability and latency performance from different layer perspectives. Yilmaz et al. [32] investigated an OFDM based 5G radio interface for satisfying and serving the sensitive IIoT business owning reliability and latency. Shariatmadari et al. proposed a link adaptation optimization scheme in [14] as well as a downlink transmission scheme in [15] for ultra-reliable low-latency communications. Moreover, Hu et al. [16] presented a novel unified radio frame structure and a device-to-device medium access control protocol for high reliability and low-latency vehicle-to-X communication services. Additionally, some researchers explored to use MEC as a middleware to achieve joint optimization of both computation and communication. Specifically, Liu et al. [17] utilized Lyapunov stochastic optimization to present a

5.3 Latency and Reliability Guaranteed UAV-Aided Edge Computing

221

dynamic latency- and reliability-aware scheme for task computation and offloading. Azimi et al. [18] discussed the mobile cloud aided task offloading for the sake of saving the energy consumption. However, considering the constraint of the caching capacity, simply jointly optimizing computing and communication resource is not enough. Hence, we jointly optimize computing, communications, and caching resources to further enhance the latency and reliability performance. The rest of this section is organized as follows. Sections 5.3.1 and 5.3.2 demonstrate the system model and problem formulation, respectively. In Sect. 5.3.3, a heuristic algorithm is given to solve the formulated NP-hard problem. Section 5.3.4 discusses the simulations results, followed by our conclusions in Sect. 5.3.5.

5.3.1 System Model In this subsection, the architecture of LR-UMEN is shown in Fig. 5.13. And given the service Ψ initiated by user u,1 consisting of N independent tasks, it can be represented by a set Ψ = {ψ1 , ψ2 , . . . , ψN }. Moreover, considering M UAVenabled MEC nodes (UMENs), it can be denoted by a set V = {v1 , v2 , . . . , vM }, and the CPU frequencies of the UMENs can be represented by a set F = {f1 , f2 , . . . , fM }. For brevity, we denote N = {1, 2, . . . , N} as the subscript indicator of the tasks, and M = {1, 2, . . . , M} as the subscript indicator of the UMENs. Assume that each UMEN occupying orthogonal wireless channels; hence, the signal from different UMENs cannot bring interference to each other.

5.3.1.1 Joint Communications and Computing Optimization These N tasks are partitioned into M disjoint sets and allocated to M UMENs for distributed parallel processing. Hence, to achieve service Ψ with low latency and high reliability, an optional task assignment strategy is needed considering the latency and reliability performance, i.e., a matrix A with N rows and M columns, ⎡

a11 a12 ⎢ a ⎢ 21 a22 A=⎢ .. ⎢ .. . ⎣ . aN1 aN2

1

⎤ · · · a1M ⎥ · · · a2M ⎥ . ⎥ .. ⎥, . .. ⎦ · · · aNM

(5.32)

Actually, we only consider one user, but for multi-user problems, it can be decoupled into independent single-user problems, which is practicable in several real systems assigning nonoverlapping resource blocks for each user. This assumption is commonly given in many similar works about task allocation problems.

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Fig. 5.13 The architecture of LR-UMEN

where aij can be assigned a value of 0 or 1, which indicates whether task ψi is allocated to UMEN vj , ∀i ∈ N , j ∈ M , i.e., ⎧ ⎨1, if task ψ i is allocated to UMEN v i, i j aij = ⎩0, otherwise.

(5.33)

For convenience, each task ψi can be processed by one UMEN, i.e., M j =1 aij = 1, ∀i ∈ N . According to the allocation matrix A, the tasks ψi ∈ Ψ are allocated to UMENs for distributed processing. As long as all of them are completed and return the results to the user u, the service Ψ is completed. To evaluate the reliability and latency performance with different task assignment schemes and find the optimal one, the specifical mathematical model of the LR-UMEN system processing the service flow Ψ is introduced in detail.

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223

Latency Model " ! " ! Given UMEN vj located at xj , yj , zj as well as user u located at xu , yu , zu , the distance between UMEN vj , ∀j ∈ M , and user u can be given by 1

du,j = [(xu − xj )2 + (yu − yj )2 ] + (zu − yj )2 ] 2 .

(5.34)

Because of the special environments in emergence rescue scenarios, the path loss between UMEN vj and user u cannot be reliable light-of-sight links [33]. Instead, considering the shielding of barriers after the disaster, the communication links in emergence communications should be the probabilistic superposition of line-ofsight (LOS) channel and non-line-of-sight (NLOS) channel. The path loss between UMEN vj and user u can be given by ⎧   ⎪ 4πg 2 2 ⎪ LOS ⎪ L (u, j ) = η du,j , if LOS link, ⎪ LOS ⎨ c   ⎪ ⎪ 4πg 2 2 ⎪ NLOS ⎪ (u, j ) = ηNLOS du,j , if NLOS link, ⎩ L c

(5.35) (5.36)

where ηLOS and ηNLOS denote the attenuation factors corresponding to the LOS and NLOS links, respectively, while c denotes the speed of light and g is the carrier frequency. According to [34], the probability of having a LOS link between UMEN vj and user u can be expressed as pLOS =

1 , 1 + δe−[θ−δ]

(5.37)

where δ and  denote the coefficients related to the environment, while θ is ⎛ ⎞ zj − zu 180 ⎠. tanh ⎝ θ= (5.38) 1 π [(xu − xj )2 + (yu − yj )2 ] 2 The probability that having an NLOS link can be represented as pNLOS = 1 − pLOS .

(5.39)

Hence, the average path loss can be denoted by ¯ L(u, j ) = pLOS LLOS (u, j ) + pNLOS LNLOS (u, j ).

(5.40)

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5 Mobile Edge Computing in FANET

The average transmission rates of the uplink and downlink between UMEN and users can be formulated as ⎧   ⎪ ⎪ p TX ⎪ UL UL ⎪ R (u, j ) = W log2 1 + , (5.41) ⎪ ⎪ ¯ ⎨ L(u, j )σ 2 W UL   ⎪ ⎪ p ⎪ RX DL DL ⎪ R (u, j ) = W log2 1 + ⎪ , (5.42) ⎪ ¯ ⎩ L(u, j )σ 2 W DL where W UL and W DL represent the uplink and downlink bandwidths the UMEN vj allocated to the user, respectively, while σ 2 is the white Gaussian noise variance. We use a tuple {di , αi , ri } to represent task ψi ∈ Ψ , in which di represents the input data size (in bits), αi represents the computational complexity (in cycles/bit), Comp , and ri denotes the data size of computing result (in bits). Denoted by TijUL , Tij and TijDL the upload, computation, and download latency, respectively, when task ψi offloaded to UMEN vj , which can be represented as ⎧ βdi ⎪ ⎪ TijUL = UL , ∀i ∈ N , j ∈ M , ⎪ ⎪ ⎪ R (u, j ) ⎪ ⎪ ⎪ ⎨ αi di Comp = , ∀i ∈ N , j ∈ M , Tij fj ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ βri ⎪ ⎪ T DL = ∀i ∈ N , j ∈ M , ⎩ ij R DL (u, j )

(5.43) (5.44) (5.45)

where β (β ≥ 1) represents a ratio of the transmitted data size to the original task data size caused by the transmission overhead. Reliability Model In disaster areas, harsh and complex working environments may greatly challenge the normal operation of the LR-UMEN system, specifically, the outages of UMEN caused by hardware failure or software failure, as well as the intermittent of communication links between UMENs and users. Therefore, it is intensely needed to pay attention to the reliability performance of the system, which is the probability that the system achieves the service Ψ successfully. In this paragraph, the evaluation of the reliability adopts the widely accepted reliability evaluation approach [35]. The failure of UMENs and communication links between UMENs and users is assumed to follow the Poisson process [36]. And we denote the failure rates of UMEN and communication links between user u and UMENs as λj , λuj , respectively, Comp while ReijUL , Reij , ReijDL as the upload, computation, and download reliability,

5.3 Latency and Reliability Guaranteed UAV-Aided Edge Computing

225

respectively. When task ψi is assigned to UMEN vj , the reliability can be analyzed as ⎧ UL ⎪ ⎪ ReijUL = e−λuj Tij , ∀i ∈ N , j ∈ M . (5.46) ⎪ ⎪ ⎪ ⎨ Comp Comp −λj Tij = e , ∀i ∈ N , j ∈ M . (5.47) Re ij ⎪ ⎪ ⎪ ⎪ DL ⎪ ⎩ ReijDL = e−λuj Tij , ∀i ∈ N , j ∈ M . (5.48) Expected Latency Our goal is to obtain the optimal task allocation strategy to minimize the processing latency as well as maximize the reliability. Obviously, this is a typical multiobjective optimization problem. To implement it, the weight sum method2 is a widely adopted approach due to its easiness. However, owing to the lack of physical meaning, this method cannot effectively correspond to the real situation, and the setting of the weights is also difficult. Therefore, in this paragraph, we propose a new physical concept expected latency, which derives from processing latency and reliability, reflecting the latency and reliability of a processing unit directly. Definition 1 Expected latency is defined as the mathematical expectation of the processing latency of the operation unit with a given statistical reliability. If the processing latency of the processing unit is T , the reliability of the unit during the processing procedure will be Re. The expected latency ET is given as ET =

T . Re

(5.49)

Proof Communication links and computing nodes are referred as a processing unit. Assume that the processing reliability of the unit is Re. Thus, the failure probability of that unit for processing the task can be given by F = 1 − Re.

(5.50)

X is defined as the number of processing times that requires to successfully process the task, which follows the geometry distribution. Therefore, the probability that requires k times to process the given task successfully can be expressed as P {X = k} = F (k−1) Re,

2

k = 1, 2, 3, . . . .

(5.51)

By summing the two optimization targets with different weights, a single optimization problem without any physical meanings is obtained.

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5 Mobile Edge Computing in FANET

The mathematical expectation of X can be calculated as E(X) =

∞ 

F (k−1) Rek =

k=1

1 . Re

(5.52)

Equation (5.52) means that the statistical average time of the processing unit to 1 process the task successfully is Re , while the processing latency of the unit is T . Therefore, the statistical average latency can be given by Eq. (5.49).   Actually, the expected latency ET represents the mathematical expectation of the latency of the processing unit to complete the assigned task successfully. Observing its expression, we can know that the decrease in latency and the increase in reliability will reduce expected latency. Benefiting from by this characteristic, we set expected latency as the optimization goal, which will help us find the optimal strategy with the best trade-off of latency and reliability. Comp We define ETijUL , ETij , ETijDL as the expected latency of upload, computation, and download, respectively, when task ψi offloaded to UMEN vj , for ∀i ∈ N , j ∈ M , according to Eqs. (5.43–5.45), (5.46–5.48) and (5.49), and the expected latency of upload, computation, and download can be expressed as ⎧ βd ⎪ λuj UL i ⎪ UL UL ⎪ R (u,j) T T ⎪ e βd ij ij i ⎪ ⎪ ETijUL = , = = ⎪ UL ⎪ R UL (u, j ) ⎪ ReijUL ⎪ e−λuj Tij ⎪ ⎪ ⎪ ⎪ α d ⎪ Comp Comp λj i i ⎨ Tij Tij αi di e fj Comp ETij = = = , Comp Comp ⎪ fj −λj Tij ⎪ Re ⎪ e ij ⎪ ⎪ ⎪ ⎪ βr ⎪ ⎪ λuj DL i DL DL ⎪ R (u,j) T T ⎪ e βr ij ij i ⎪ ⎪ . ETijDL = = = ⎪ DL ⎪ ⎩ R DL (u, j ) ReijDL e−λuj Tij

(5.53)

(5.54)

(5.55)

Thus, when task ψi offloaded to UMEN vj , the expected latency of processing task ψi can be formulated as Comp

ETijnc =ETijUL + ETij

+ ETijDL ,

∀i ∈ N , j ∈ M .

(5.56)

According to A, the expected latency of that UMEN vj , ∀j ∈ M processing the offloaded tasks, can be represented as ETjnc =

N 

aij ETijnc

i=1

=

N  i=1

  Comp aij ETijUL + Tij + ETijDL .

(5.57)

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227

And due to the distributed parallel processing for service Ψ on the LR-UMEN system, the total expected latency ET nc can be given by ET nc = =

max

j ={1,...,M}

max

j ={1,...,M}

ETjnc N 

  Comp aij ETijUL + ETij + ETijDL .

(5.58)

i=1

In order to minimize the latency as well as maximize the reliability, the expected latency (i.e., ET nc ) is set as the optimization target function to obtain the optimal task allocation strategy with low latency and high reliability.

5.3.2 Problem Formulation In fact, some computation tasks are with relatively higher popularity, and they may be processed many times. Considering certain quantity of low cost caches equipped at UMENs currently, we are motivated to introduce task result caching into the LRUMEN. When the computing task result is cached, the user does not need to offload the task to the UMEN, while the UMEN does not need to process the task. The user can download the computing task result from UMEN directly. It is worthily noted that if the cached results can be transformed to the requested ones, it can also be seen as the computing task results cached. For instance, the AR aided rescue helmet [37] needs to constantly render and encode the corresponding scene as the wearer moves and the viewing angle changes [38]. Nevertheless, such a transcoding and rendering task is computationally-intensive, and lots of repetitive computation is existed, which is a big challenge to satisfy the latency requirements. Besides, there is a negative correlation between the reliability of the service and the operation time of each working procedure. Therefore, to reduce the latency as well as enhance the reliability of the computation service, computing task result caching is introduced. Task Result Caching Model Obviously, caching all the computing task results is the best approach to shorten the processing latency as well as improve the reliability of the completion of the service. However, the limited caching capacities of UMENs force us to derive an appropriate caching strategy to minimize the expected latency with limited caching resources. To determine whether the computing task result of ψi caches on UMEN vj , a decision matrix X with N rows and M columns is given, as shown in Eq. (5.59). ⎡ ⎤ x11 x12 · · · x1M ⎢ ⎥ ⎢ x21 x22 · · · x2M ⎥ X=⎢ (5.59) . ⎥ .. . . ⎢ .. ⎥ . .. ⎦ . ⎣ . xN1 xN2 · · · xNM

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5 Mobile Edge Computing in FANET

For X, the element xij can be assigned a value of 0 or 1, which indicates whether the computing result of task ψi is cached on the UMEN vj . For ∀i ∈ N , j ∈ M , it can be represented by ⎧ ⎨1, if the result of ψ is cached on v , i j xij = ⎩0, otherwise.

(5.60)

The result of task ψi cached on UMEN vj means that the task must have been assigned to compute on UMEN vj in advance; hence, the decision variable xij should satisfy xij ≤ aij ,

∀i ∈ N , j ∈ M .

(5.61)

Moreover, since the caching resource in each UMEN is limited, we assume that the caching capacity of UMEN vj is Cje , and to guarantee the results caching in each UMEN cannot exceed the maximal caching capacity, the task results caching matrix X should satisfy N 

xij ri ≤ Cje ,

∀j ∈ M .

(5.62)

i=1

Expected Latency Model with Task Result Caching When the computing results exit in UMENs, the user can download the computing result directly from the UMEN without the procedure of upload and computation. The expected latency of task ψi can be given as ETijc =ETijDL ,

∀i ∈ N , j ∈ M .

(5.63)

The expected latency of the tasks executed by UMEN vj can be represented as ETjc =

N 

ETijc =

i=1

N 

ETijDL ,

∀j ∈ M .

(5.64)

i=1

And due to the distributed parallel processing for the service ψ on the LR-UMEN system, the total expected latency ET c can be given by ET c =

max

j ={1,...,M}

ETjc =

max

j ={1,...,M}

N  i=1

ETijDL .

(5.65)

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229

The caching decision matrix X determines whether task ψi cached on UMEN vj , and according to the Eqs. (5.58) and (5.65), the total expected latency of service Ψ can be denoted by ET =

N  

max

j ={1,...,M}

xij ETijDL

i=1

  Comp + (1 − xij )aij ETijUL + ETij + ETijDL .

(5.66)

Corresponding to the task set Ψ = {ψ1 , ψ2 , . . . , ψN }, it is assumed that the popularity distribution of them is denoted by P = {p1 , p2 , . . . , pN }, which represents the requested probability of each task. The popularity distribution P follows the Zipf distribution, which can be represented by [39] pi =

i −γi , N −γ i i

∀i ∈ N ,

(5.67)

i=1

where γi is the Zipf parameter of the ith task. Therefore, the total expected latency considering the popularity distribution can be represented as ET = p

N 

max

j ={1,...,M}

 pi xij ETijDL + (1 − xij )aij ∗

i=1



Comp ETijUL + ETij

 + ETijDL .

(5.68)

The optimization problem is formulated for minimizing the expected latency of the LR-UMEN processing the service, which can be represented as P1 : min max ET p s.t.

M 

aij = 1,

∀i ∈ N ,

(5.69a)

(5.69b)

j =1

xij ≤ aij , ∀i ∈ N , j ∈ M , N 

xij ri ≤ Cje ,

∀j ∈ M ,

(5.69c)

(5.69d)

i=1

aij ∈ {0, 1}, ∀i ∈ N , j ∈ M ,

(5.69e)

xij ∈ {0, 1},

(5.69f)

∀i ∈ N , j ∈ M .

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5 Mobile Edge Computing in FANET

5.3.3 Hybrid Binary Particle Swarm Optimization Since the problem is non-convex and NP-hard, the exact algorithms may have the worst computational complexity to tackle it. In this subsection, hybridization operation based HBPSO is conceived for addressing the local optimum of traditional particle swarm optimization algorithms. Denote I ∈ {1, 2, . . . , Imax } as the iteration number of the algorithm, where Imax is the maximum iteration number. And u ∈ {1, 2, . . . , U } denotes the index of the uth particle, in which U is the total number of particles. The position and the flying speed of the uth particle in the I th iteration can be represented as u Y u (I ) = {y1u (I ), · · · , ytu (I ), · · · , y2NM (I )} u u = {a11 (I ), · · · , aiju (I ), · · · , aNM (I ), u x11 (I ), · · ·

, xiju (I ), · · ·

(5.70)

u , xNM (I )}

u V u (I ) = {V1u (I ), · · · , Vtu (I ), · · · , V2NM (I ),

(5.71)

respectively. And the updates of the flying speed of the uth particle are denoted by u V u (I + 1) = ηV u (I ) + ξ1 ζ1 (pbest (I ) − Y u (I ))

+ξ2 ζ2 (gbest (I ) − Y u (I )),

(5.72)

where η is the inertia weight, and ξ1 and ξ2 are the learning factors, while ζ1 u and ζ2 are the random values; pbest (I ) and gbest (I ) represent the historical optimal positions of the uth particle and the whole particle swarm until the I iteration. Given that ltu (I ) represents the probability that the value of ytu (I + 1) is 1, which can be calculated by ltu (I ) =

1 . u 1 + e−Vt (I )

(5.73)

ltu (I ) ranging from [0, 1] determines the changes of the position of the uth particle, i.e., yt =

⎧ ⎨1, ⎩0,

if κ ≤ ltu (I ), otherwise,

(5.74)

5.3 Latency and Reliability Guaranteed UAV-Aided Edge Computing

231

where κ is a random value. The fitness function that evaluates the performance of the particles’ position is defined as ⎧ ! " ⎪ ⎪ p u Yu ∈ H, ! u " ⎨ET Y , (N+1)M+N %Y = ! u" " p! p ⎪ ETt Y u , Y u ∈ N , ⎪ ⎩ET Y +Λ

(5.75)

t =1

in which Λ is the penalty factor, while H and N are the feasible region and p infeasible region, respectively. ETt is denoted by ⎧* * * * N ⎪ ⎪ * * ⎪ e ⎪ y d − C * s t +NM+(s−1)M ⎪ t * , 1 ≤ t ≤ M, ⎪ * * ⎪ s=1 ⎨ ! " p! u" ETt Y = max yt +MN−M − yt −M , 0 , M + 1 ≤ t ≤ M  , * * ⎪ ⎪ * * ⎪ M ⎪ * * ⎪ ⎪  (y − 1 * * , 1 + M  ≤ t ≤ M  + N, ⎪ ⎩*s=1 M(t −M −1)+s *

(5.76)

where we have M  = (N + 1)M. However, BPSO easily falls into local optimum because each particle keeps learning to get close to its own best position as well as the global best position by adapting to its own position and velocity, but if the global best particle location approaches a local optimal solution, it may lead all the particles to fly into local optimal solution. Hence, to solve the problem that BPSO algorithm easily falls into local optimum, we introduce the hybrid operation to improve its global search ability. Pick o particles at random to form the hybrid pool, and any two particles are selected from the hybrid pool for hybridization operation. Given that the positions of the two selected particles are Y o1 (I ) and Y o2 (I ), and the corresponding velocities are V o1 (I ) and V o2 (I ), respectively. The position, i.e., Y n1 (I ), and the velocity, i.e., V n1 (I ), of the new particles are given by ⎧ ⎪ ⎨Y n1 (I ) = ϑY e1 I + (1 − ϑ)Y e2 (I ); ⎪ ⎩V n1 (I ) = ϑV e1 I + (1 − ϑ)V e2 (I ),

(5.77)

respectively, where ϑ is a random number on interval (0, 1). Repeat o times, and the generated o new particles are used to replace the o old particles of the hybrid pool. The algorithm is summarized in Algorithm 18.

5.3.4 Simulation Results To validate the effectiveness of our proposed scheme, extensive experiments are needed to perform. According to [25, 39–41], the essential parameters are summa-

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5 Mobile Edge Computing in FANET

Algorithm 18 BPSO algorithm Input: input a particle swarm with Imax , η, ξ1 , ξ2 , hp, o, Λ 1: " ! Output: gbest , % gbest 2: for each particle u do 3: Initialize Y u (0), V u (0) 4: Evaluate fitness function of particle u using (5.75) u (0) 5: Set current position as the best position of particle pbest 6: end for 7: Choose the particle position with the best fitness of all u particles as the global best position gbest (0) 8: while (Generation 1 to Imax ) do 9: for each particle u do 10: Update the velocity of particle u using (5.72) 11: Update the position of particle u using (5.73–5.74) 12: Evaluate the fitness with new position using (5.75–5.76) " function ! u (I )) then 13: if % Y u (I + 1) < %(pbest u (I + 1) = Y u (I + 1) 14: pbest 15: end!if " 16: if % Y u (I + 1) < %(gbest (I )) then 17: gbest (I + 1) = Y u (I + 1) 18: end if 19: if random(0, 1) < hp then 20: Select o old particles to form the hybrid pool 21: Generate o new particles using Eq. (5.77) 22: Replace the selected o old particles with o new particles 23: end if 24: end for " ! 25: end whilereturn gbest , % gbest

rized in Table 5.1. We consider there are 3 UMENs that are randomly deployed in 500 m3 area, and the user needs to process 15 tasks. The parameter of the algorithm is set as follows: the amount of the particles are Imax = 100; the inertia weight is η = 0.5, while the learning factors ξ1 and ξ2 are 1.5 and 2.5, the probability hp of hybrid operation is 0.3, and the number of selected particles, i.e., o is 25. The penalty factor Λ is set as 20. Figure 5.14 compares the expected latency performances of different algorithms, including standard binary particle swarm optimization (BPSO), BPSO with linear decreasing weight (LWBPSO), BPSO with adaptive weight (AWBPSO), simulated annealing binary particle swarm optimization (SABPSO), and hybrid binary particle swarm optimization (HBPSO). We can observe that the proposed HBPSO is with the optimal expected latency all along compared with other algorithms, while the standard BPSO is with the worst performance. And the SABPSO, which combines the advantages of simulated annealing algorithm to avoid local optimum, can also achieve relatively lower expected latency. As for LWBPSO and AWBPSO, which make some operations on the weights so as to improve the convergence performance, they also achieve some good results, and the AWBPSO that adopts adaptive weight is relatively better than the LWBPSO with linear decreasing weight.

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233

Table 5.1 System parameters Parameter ηLOS g WUL PTx σ2  λj fj (xj , yj , zj )

Value 1 2.4 GHz 1MHz 1.258 W 5 ∗ 10−15 0.61 U([0, 0.005]) U([0, 0.9]) Randomly in 500 m3 area

Parameter ηNLOS c WDL PRx δ β λuj (xu , yu , zu ) Cje

Value 20 3 ∗ 108 m/s 1MHz 1.181 W 9.61 1 U([0, 0.005]) (0, 0, 0) U([50, 100]) Mb

di ri

U([15, 20]) Mb 0.8di

αi γi

1900/8 cycles/bit U([0.5, 1.5]) Mb

1 HBPSO SABPSO AWBPSO LWBPSO BPSO

Expected Latency /s

0.8

0.6

0.4

0.2

0 1

2

3

4

5

6

7

8

9

10

Input Data Size /Mb Fig. 5.14 Algorithm performances versus input data size in terms of expected latency

Figure 5.15 shows the expected latency performance comparison of joint optimization of communication and computing (corresponding to the legend without caching in Fig. 5.15) and joint optimization of communication, computing, and caching (corresponding to the legend with caching in Fig. 5.15), when processing different kinds of computation tasks (i.e., with different computational complexities) [42]. We can see that with the increase of the input data size, the benefit that is taken account of caching resource is more larger. For instance, in Fig. 5.15, when processing the X264 CBR encode tasks, i.e., the computational complexity is

234

5 Mobile Edge Computing in FANET 1

0.6 with caching without caching

Expected Latency /s

Expected Latency /s

0.5 0.4 0.3 0.2

0.6 0.4 0.2

0.1 0

0 2

8 10 12 14 16 18 20 Input Data Size /Mb (a) Computational complexity, i.e., i = 330/8 cycles/bit

4

6

2

8 10 12 14 16 18 20 Input Data Size /Mb (b) Computational compelxity, i.e., i = 1300/8 cycles/bit

4

6

2

1.2

with caching without caching

with caching without caching

Expected Latency /s

1

Expected Latency /s

with caching without caching

0.8

0.8 0.6 0.4

1.5

1

0.5

0.2 0

0 2

4

6 8 10 12 14 16 18 20 Input Data Size /Mb (c) Computational complexity, i.e., i = 1900/8 cycles/bit

2

4

6

8 10 12 14 16 18 20 Input Data Size /Mb

(d) Computational complexity, i.e., i = 5900/8 cycles/bit

Fig. 5.15 Expected latency performance comparison between joint optimization of communication and computing and joint optimization of communication, computing, and caching, when processing different kinds of tasks (i.e., with different computational complexities)

1900 8

cycles/bit, and the input data size is 20 Mb. The expected latency that jointly optimizing communications, computing, and caching is only 71.46% lower than that only jointly optimizing communications and computing.

5.3.5 Conclusions In this section, we proposed a multi-UAV-enabled latency and reliability guaranteed mobile edge computing framework for intelligent emergency rescue equipment. Moreover, communications, computing, and caching resources are jointly optimized in order to reduce the latency and enhance the reliability. Relying on the concept of expected latency, the HBPSO algorithm was conceived for solving the abovementioned non-convex problem. Simulation results showed the effectiveness of our proposed algorithm in terms of the latency and reliability performance.

5.4 Energy-Efficient and Secure UAV-Aided Edge Computing

235

5.4 Energy-Efficient and Secure UAV-Aided Edge Computing Given the advantages of prompt deployment and their bird’s eye perspective, unmanned aerial vehicles (UAVs) have been widely invoked for environmental monitoring and data collection [2, 6, 43], in the fields of agriculture [22], disaster sensing [44], emergency management [45], border control [46], intelligent transportation systems [47], and crowd surveillance [48]. However, the decision-making applications relying on real-time video streaming and image processing tend to exceed the local data processing capability of low cost UAVs or may excessively prolong the time required for executing their actions [49]. To address this issue, mobile edge computing (MEC) [8] may beneficially cooperate with UAVs [47, 48] for facilitating computational offloading from the UAV to the edge nodes. The cooperation between UAVs and MEC systems can be exemplified by crowd surveillance [48]. More explicitly, UAV-mounted highresolution cameras are capable of streaming real-time video, which facilitates the detection of criminals using face recognition. However, both the moderate computational capability and limited power supply of UAVs stifle the aforementioned real-time recognition on board. To tackle these challenges, the assistance of MEC systems can be invoked for offloading a number of computational tasks for improving the face recognition performance in a timely manner [50]. To be specific, the data collected are partitioned into two segments, one to be computed at the UAV and the other to be offloaded to the edge node through a gateway or access point (AP). Specific to the part to be offloaded, the data may also be valuable to a third party; hence, it is under a risk of being intercepted, which jeopardizes data security and privacy [51]. To overcome this security risk of the MEC, extensive work has been carried out in [52–55]. However, the current state of the art is focused on improving the cyber-security, while there is a paucity of contributions on their physical-layer security (PLS) at the time of writing. Against this background, we conceive a PLS-aided energy-efficient computational offloading scheme for UAV-MEC systems (UMEC) operating in the presence of an eavesdropper. Specifically, with the advent of an advanced full-duplex mechanism, the AP acts as a gateway for the edge nodes to receive the computational tasks offloaded from the UAV but also plays the role of a jamming source in order to impose artificial noise on the eavesdroppers. Moreover, depending on the availability of the eavesdropper’s channel state information (CSI) and location information (LI), we consider three different types of eavesdroppers [56], namely, active eavesdroppers for which we have both CSI and LI knowledge, passive eavesdroppers for whom the LI is known but the CSI is not, and passive eavesdroppers at a random location for whom we have no CSI or LI. In this context, we provide the optimal solution to the energy-efficiency problems satisfying both the offloading and security requirements by answering the following three questions: (1) What is the volume of the computational tasks to be offloaded? (2) What is the suitable duration of offloading? (3) How much power should be assigned to the offloaded signal?

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The rest of the section is organized as follows. The system model is elaborated in Sect. 5.4.1, and the energy-efficient computation offloading problem of UMEC is formulated in Sect. 5.4.2. Section 5.4.3 transforms the original problems into convex problems and provides the optimal offloading strategy, while Sect. 5.4.4 presents the conditions for the three offloading options from a physical perspective. Our numerical results are discussed in Sect. 5.4.5, while our conclusions are offered in Sect. 5.4.6.

5.4.1 System Model As shown in Fig. 5.16, we consider a hovering single-antenna UAV capable of offloading computational tasks to an edge computing node via an AP on the ground through the wireless transmission link, which is intercepted by a single-antenna eavesdropper (Eve) on the ground. In order to combat eavesdropping, the AP relying on full-duplex techniques [57] imposes artificial noise for degrading Eve’s reception quality. Since the transmitted artificial noise is known by the AP and the CSI between the AP’s transmit and receive antennas is known, we invoke the idealized simplifying assumption that the self-interference of the AP is canceled.

Fig. 5.16 Illustration of the secure UAV-edge hybrid system model

5.4 Energy-Efficient and Secure UAV-Aided Edge Computing

237

Let us denote the channel between the UAV and the AP as well as the channel between the UAV and Eve by g U →A and g U →E , respectively, which are assumed to be dominated by the line-of-sight (LoS) path, yielding −η1

g U →A(E) = κ1 d1

,

(5.78)

where d1 denotes the hovering altitude of the UAV,3 while κ1 corresponds to the unity channel gain at the reference distance of d1 = 1 m and η1 represents the path-loss exponent of the LoS path. Moreover, the channel between the AP and Eve consists of both the large-scale path loss and small-scale fading, i.e., g A→E = ξ hA→E . As for the large-scale fading, it is modeled as −η2

ξ = κ2 d 2

,

(5.79)

where d2 denotes the distance between Eve and the AP, while κ2 corresponds to the unity channel gain at the reference distance of d2 = 1 m and η2 represents the path-loss exponent of the NLoS component. Finally, the small-scale fading envelope is assumed to obey quasi-static Rayleigh distribution, and hence, the Cumulative Density Function (CDF) of hA→E obeys FhA→E (x) = 1 − e−λx ,

(5.80)

0 / where λ−1 = E hA→E .

5.4.1.1 Local-Computing Model We use L and  to denote the total number of bits to be processed and the number of bits to be offloaded to the edge node, respectively. In this case, the number of locally computed bits is L − . Moreover, as for the local computing at the UAV, CU corresponds to the number of central processing unit (CPU) cycles required for processing 1-bit of input data, while PU represents the energy consumption of each CPU cycle. In this case, the energy consumption of the local computation is expressed as Eloc = CU PU (L − ). Furthermore, assuming that the UAV has a computational capability of DU quantified in terms of the number of CPU cycles per second, the time required for carrying out the local computation is expressed as CU (L − )/DU .

3 The drone may potentially be laser-charged as detailed in [58] for supporting sustained operations.

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5 Mobile Edge Computing in FANET

5.4.1.2 Jamming Model Various jamming schemes have been proposed for PLS based on various strategies [59], such as nonself-cooperative [60] versus self-cooperative [61], omnidirectional [62] versus directional scenarios [63], relying on either perfect or imperfect eavesdropper CSI [59]. Since the design of the jamming scheme is not within our main focus in this section, the self-cooperative jamming strategy using an omnidirectional antenna [59] is invoked at the AP side for simplicity. Accordingly, given a jamming power of pJ , the artificial noise received by Eve is given by NJE = pJ g A→E . 5.4.1.3 Secure Offloading Model Let us denote the power of the natural noise at the AP and Eve by N0A and N0E , respectively. As for a wiretap channel, the secrecy capacity denoted by S can be obtained as the difference between the main channel’s and the wiretap channel’s capacity [64]. Specifically, given the offloading power of pO and the jamming power of pJ , S(pO , pJ ) in the system considered is formulated as [64]     pO g U →A pO g U →E S(pO , pJ ) = B log2 1 + − B log 1 + , 2 N0A N0E + NJE (5.81) where B refers to the bandwidth of the channel. Another metric quantifying the quality of service (QoS) is the secrecy outage probability (SOP), which corresponds to the probability that the secrecy capacity fails to meet the secure transmission rate required. Given the offloading power of pO , jamming power of pJ ,  offloaded bits, and the offloading transmit duration of t, the SOP is formulated as [64] .  . Pout (pO , pJ , , t) = 1 − Pr S(pO , pJ ) ≥ t -

S

(5.82)

Moreover, the energy consumption of offloading from the UAV is given by Eoff = pO t.

5.4.1.4 Edge Computing Model As for edge computing, we use DE and CE to represent the computational capability quantified in terms of the number of CPU cycles per second and the number of CPU cycles required for processing one bit of input data, respectively. Taking advantage of parallelism [65], the computational loads can be partitioned into tasks of minimal volume; hence, the edge computing node is capable of executing the

5.4 Energy-Efficient and Secure UAV-Aided Edge Computing

239

computations along with all the receiver’s tasks. Then, the time duration required for edge computing is formulated as CE /DE .

5.4.2 Problem Formulation The total energy consumption of UAVs is constituted by the sum of the local computation-related and computation offloading-based dissipation as well as that of the propulsion. As for the scenario where the UAV acts as a flying base station [66] and as a floating relay [67], the flight trajectory and the placement of the UAV can be optimized for improving the communication performance, respectively. By contrast, the mobility of the UAVs used for environmental monitoring and surveillance is controlled by a specific user instead of a communication service provider. Therefore, we have to exclude the propulsion-related energy optimization in our problem formulation. Specifically, the total energy is calculated as Etot = Eloc + Eoff. We note that Eoff substantially depends on the availability of the eavesdropper’s CSI, as we will demonstrate by considering both active and passive eavesdroppers. More explicitly, the active eavesdropper (i.e., listening and transmitting) may be a user being served by the AP; hence, the CSI between the AP and Eve can be estimated in a near-instantaneous manner. By contrast, the passive eavesdropper is listening but not transmitting. Hence, its CSI cannot be extracted. Therefore, at best we can assume the knowledge of statistical information of the channel between the AP and Eve. Furthermore, both the total volume of computational loads and the computingrelated energy per bit on the UAV’s board are assumed to be signaled by the AP using its feedback link. Based on the above information, the small-cell cloud manager of the AP aims for determining both the UAVs’ offloading data volume of , as well as the offloading transmit power of pO and the offloading duration of t, for maintaining both a high energy efficiency and high transmission secrecy. In the rest of this section, our energy-efficient computation offloading problems are formulated in the presence of both an active and a passive eavesdropper, one after the other.

5.4.2.1 Problem 1: Active Eavesdropper Our energy-efficient computation offloading problem is formulated in the presence of an active eavesdropper under the following constraints: • Latency constraint: The computation has to be executed within a maximum tolerable latency, which is denoted by T . Then, the temporal constraints of the local and of the edge computing can be formulated as CU (L − )/DU ≤ T and CE /DE ≤ T , respectively. Moreover, assuming that the offloading duration is t, it should not exceed the latency constraint, i.e., 0 ≤ t ≤ T .

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5 Mobile Edge Computing in FANET

• Offloaded data volume constraint: The volume of data offloaded to the AP is naturally a non-negative integer and does not exceed the total computational loads, i.e.,  ∈ {0, 1, · · · , L}. • Power consumption constraint: The UAV has a maximum transmission power max , i.e., 0 ≤ p ≤ pmax . limit of pO O O • Secrecy constraint: Provided that the instantaneous CSI of Eve is known, the AP is able to ensure that the received power of artificial noise remains constant by forcing pJ = p J /g A→E . In order to support secure offloading in the presence of an eavesdropper, the secrecy capacity should not be lower than the offloading rate, given the offloading duration of t, i.e., S(pO , pJ ) ≥ /t. The computational offloading problem is formulated for minimizing the energy consumption of the UAV’s data processing in the secure UMEC intercepted by an active eavesdropper as P1 : arg min CU PU (L − ) + pO t ,pO ,t

s.t.

CU (L − ) ≤ T, DU

(5.83a)

CE  ≤ T, DE

(5.83b)

 S(pO , pJ ) ≥ , t

(5.83c)

 ∈ {0, 1, · · · , L},

(5.83d)

max , 0 ≤ pO ≤ pO

(5.83e)

0 ≤ t ≤ T,

(5.83f)

where the first and second terms of the objective function (OF) correspond to the energy consumption of the local computation and the computation offloading, respectively. As for the constraints, (5.83a), (5.83b), and (5.83f) ensure the latency requirement to be met. Furthermore, (5.83c) guarantees the secure offloading, while (5.83d) and (5.83e) restrict the feasible sets of  and pO .

5.4.2.2 Problem 2: Passive Eavesdropper The constraints of the energy-efficient computation offloading problem in the presence of a passive eavesdropper are elaborated on as follows: • The latency, the offloaded data volume, and the power consumption constraints are the same as those in the presence of an active eavesdropper. • Secrecy constraint: Since the instantaneous CSI is unknown in this case, the secrecy capacity cannot be always ensured for supporting the secure target

5.4 Energy-Efficient and Secure UAV-Aided Edge Computing

241

offloading rate in the face of the channel’s fluctuation. Therefore, we impose S (p , p , , t) a SOP requirement of  on the offloading transmission, i.e., Pout O J ≤ . The energy-efficient computing offloading problem is formulated for the UMEC intercepted by a passive eavesdropper as P2 : arg min CU PU (L − ) + pO t ,pO ,t

s.t.

CU (L − ) ≤ T, DU

(5.84a)

CE  ≤ T, DE

(5.84b)

S (pO , pJ , , t) ≤ , Pout  ∈ {0, 1, · · · , L},

(5.84d)

max , 0 ≤ pO ≤ pO

(5.84e)

0 ≤ t ≤ T,

(5.84f)

(5.84c)

where (5.84a), (5.84b), and (5.84f) correspond to the latency constraint. Moreover, (5.84c) ensures the SOP requirement to be satisfied, while (5.84d) and (5.84e) restrict the feasible set of  and pO , respectively. Additionally, since the large-scale path loss is a component of g A→E , the fact whether the passive eavesdropper’s LI is acknowledged by the AP influences the S (p , p , , t) in (5.84c). distribution of g A→E and hence further influences the Pout O J Therefore, we consider two types of passive eavesdroppers, i.e., one at a fixed location whose LI is acknowledged by the AP, while the other at a random location whose LI is unknown to the AP—and the corresponding problems are denoted by P2-1 and P2-2, respectively.

5.4.3 Energy-Efficient Secure UMEC Solution In this subsection, we present the optimal solution to the problems for both the active and passive eavesdroppers at a fixed location as well as the asymptotically optimal solution to the problem, where the passive eavesdropper is at a random location. In short, the problems are solved in three steps: 1) having multiple variables, Problem P1, P2-1, and P2-2 cannot be solved directly and here we transform them into problems having a single variable; 2) we prove the convexity of the problems; 3) the optimal solutions are conceived for the three problems considered.

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5.4.3.1 Case 1: Active Eavesdropper Transformation of Problem P1 Problem P1 is transformed into Problem P1-E having a single variable as follows. Proposition 1 Constraint (5.83c) is strictly binding for the optimal solution of Problem P1, i.e., the secrecy capacity of S to satisfy  S(pO , pJ ) = . t

(5.85)

Proof It may be readily seen that S(pO , pJ ) in (5.81) is monotonically increasing with pO in our considered case where the SNR at the AP is higher than that at the eavesdropper. Assuming that the constraint of (5.83c) is slack at the optimal solution of Problem P1, we can then reduce pO for reducing the objective function values, without violating any constraints. This completes the proof.   Theorem 2 Given  number of bits to be offloaded, the offloading duration yields t = T for the optimal solution to Problem P1. Proof Defining γ U →A = g U →A /N0A and γ U →E = g U →E /(N0E + pJ g A→E ), and substituting (5.81) into (5.85), pO can be expressed as a function of  as 

pO () =

1 − 2− Bt γ U →A 2− Bt − γ U →E 

(5.86)

.

Then, Eoff can be formulated as (1 − 2− Bt )t 

Eoff = pO ()t =



γ U →A 2− Bt − γ U →E

.

(5.87)

It can be observed that the denominator in (5.87) increases with t. In this case, if the numerator in (5.87) decreases with t, the offloading energy can be shown to be monotonically decreasing along with t. Taking the partial derivative of the numerator of t, we have     ∂ 2 Bt − 1 · t ln(2) ·    = 1− 2 Bt − 1, (5.88) ∂t Bt whose polarity is still difficult to observe. Defining ψ = /Bt, where ψ ≥ 0, and denoting (5.88) by Ψ , the derivative of Ψ (ψ) with respect to ψ is expressed as / 02 dΨ (ψ) = − ln(2) ψ2ψ , dψ

(5.89)

5.4 Energy-Efficient and Secure UAV-Aided Edge Computing

243

which is non-positive and hence Ψ (ψ) is monotonically decreasing with ψ. In other words, when ψ = 0, Ψ (ψ) reaches its maximum that is equal to 0. In this way, the partial derivative of the numerator of (5.87) with respect to t is non-positive and hence Eoff has been shown to monotonically decrease in t ∈ [0, T ].   With the aid of Theorem 2 and (5.86), Problem P1 can then be reformulated to Problem P1-E as follows: 

P1-E : arg min CU PU (L − ) + 

s.t.  ≥ L − ≤

T (1 − 2− BT ) γ U →A 2− BT − γ U →E 

T DU , CU

T DE , CE

 ≤ −BT log2

(5.90a) (5.90b)



 max γ U →E 1 + pO max γ U →A , 1 + pO

(5.90c)

0 ≤  ≤ L.

(5.90d)

Here (5.90a), (5.90b), and (5.90c) are reformulated by taking into account (5.83a), (5.83b), and (5.83d), respectively, while (5.90d) is obtained by relaxing the integer programming constraint of (5.83d) to a continuous constraint. Convexity of Problem P1-E Problem P1-E is proved to be a convex problem in the following proposition. Proposition 2 Problem P1-E is a convex problem. Proof Denoting the first derivative of the objective function of Problem P1-E by Φ1 (), we have Φ1 () = −CU PU +

 ln(2) U →A − γ U →E )2− BT B (γ ! "2  γ U →A 2− BT − γ U →E

.

(5.91)

It can be readily observed that the increase of  results in an increased Φ1 (), and hence, the objective function of Problem P1-E is a convex function. Moreover, the constraint functions of (5.90a), (5.90b), (5.90c), and (5.90d) are all of linear forms. In this way, Problem P1-E is shown to be a strictly convex problem.  

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5 Mobile Edge Computing in FANET

5.4.3.2 Case 2–1: Passive Eavesdropper at a Fixed Location Transformation of Problem P2 Similar to the process of solving Problem P1 in Sect. 5.4.3.1, Problem P2-1 is herein transformed into Problem P2-1-E having a single variable. In short, the method is to link the SOP of (5.82) with the CDF of hA→E in (5.80). Specifically, substituting (5.81) into S(pO , pJ ) ≥ /t in (5.82), we have    pO g U →E pO g U →A − Bt 1 + − 1, ≤ 2 N0E + pJ ξ hA→E N0A

(5.92)

where ξ is known by the AP for the case of the eavesdropper at a fixed location. In order to obtain the feasible set of hA→E satisfying S(pO , pJ ) ≥ /t, first the polarity of the right side of (5.92) has to be clarified. Particularly, under the condition of S(pO , pJ ) ≥ /t, we have 1 + pO g U →A /N0A ≥ 2/Bt based on the observation of (5.81), and hence, the right side of (5.92) is proved to be positive. Then, the range of hA→E can be obtained by reformulating (5.92) as +

hA→E ≥ ξpJ

N0E pO g U →E   , − .  U→A ξpJ 2− Bt 1 + pO g A −1

(5.93)

N0

Upon denoting the right side of (5.93) by hA→E req (pO , pJ , , t), (5.84c) becomes equivalent to + , FhA→E hA→E req (pO , pJ , , t) ≤ ,

(5.94)

where FhA→E (x) corresponds to the CDF of hA→E as illustrated in (5.80). In this way, under the given values of , t, and pJ , the required pO attaining the targeted SOP of  can be obtained by substituting (5.80) and (5.93) into (5.94) as + pO ≥

−

ξpJ ln(1−) λ

 g U→A − Bt 2 N0A

+

−

+ N0E

ξpJ ln(1−) λ

,+

,  1 − 2− Bt , . + N0E − g U →E

(5.95)

Again, the polarity of the denominator of (5.95) is clarified in the following proposition. Proposition 3 The denominator of (5.95) can be proved to be positive under the S ≤ . condition of Pout

5.4 Energy-Efficient and Secure UAV-Aided Edge Computing

245

Proof Since log2 (x) is a monotonically increasing function of x, we have 

pO g U→A N0A

B log2



 > B log2

pO g U→E N0E +pJ g A→E

1+ 1+

pO g U→A N0A

 .

pO g U→E N0E +pJ g A→E

(5.96) Then, with the aid of (5.84c), we have -



Pr B log2

pO g U→A N0A pO g U→E N0E +pJ g A→E



 ≤ t

.

-

 < Pr S(pO , pJ ) ≤ t

. ≤ . (5.97)

The left side of the above equation can be reformulated as  A→E

Pr h

g U →E · N0A  N0E Bt − ≤ 2 ξpJ g U →A ξpJ

 < .

(5.98)

Then, replacing the left side of (5.98) by hA→E ’s CDF of (5.80), the denominator S ≤ . of (5.95) can be proved to be positive under the condition of Pout   Then, pO can be expressed as a function of  through the following proposition. Proposition 4 (5.95) is strictly binding for the optimal solution to Problem P2-1, i.e., ,+ , +  E 1 − 2− Bt − ξpJ ln(1−) + N 0 λ + , pO () = U→A .  g ξpJ ln(1−) − Bt E − g U →E 2 + N − A 0 λ N0

(5.99) Proof Similar to the proof of Proposition 1.

 

The optimal offloading duration of t is obtained from the following theorem. Theorem 3 Given  number of bits to be offloaded, the offloading duration becomes t = T for the optimal solution to Problem P2-1 for the eavesdropper at a fixed location.

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5 Mobile Edge Computing in FANET

dE

off (t) dt    U →A   α g A 2− Bt α − g U →E + α2− Bt g U →E − N0

=  α ≤  α =

+

 g U →A − Bt 2 N0A

 g U →A − Bt 2 N0A

+

α − g U →E



α − g U →E  g U →A − Bt 2 N0A

 g U →A − Bt 2 N0A

  + α2− Bt g U →E − +



 g U →A − Bt 2 N0A

 1 − 2− Bt − ln(2) Bt 

α − g U →E

,2

α − g U →E

 g U →A − Bt 2 N0A

 g U →A − Bt 2 N0A

    g U →E 2− Bt − α + α ln(2) Bt ,2

   g U →E − α + α ln(2) Bt

α − g U →E

,2

 g U →A − Bt 2 nA 0

 g U →A − Bt 2 nA 0

 α

 α



(5.100)

.

Proof Upon introducing α = − ξpJ ln(1−) + N0E , the energy consumed by λ computation offloading in the presence of a passive eavesdropper at a fixed location may be expressed with the aid of (5.99) as

Eoff (t) =

+ ,  α 1 − 2− Bt t  g U→A − Bt 2 N0A

α − g U →E

(5.101)

.

Then, the derivative of Eoff(t) with respect to t can be obtained as (5.100), where

 the inequality of 1 − 2− Bt − ln(2) Bt ≤ 0 can be proved in the feasible set of /Bt ∈ [0, +∞). In this way, the energy consumption of computation offloading Eoff(t) is monotonically decreasing along with t, and hence, t = T yields the optimal solution to Problem P2-1.   

With the aid of Proposition 4 and Theorem 3, Problem P2-1 can be reformulated to a single-variable problem for the passive eavesdropper at a fixed location, i.e.,

P2-1-E : arg min CU PU (L − ) + 

s.t.

, +  α 1 − 2− BT T  g U→A − BT 2 N0A

α − g U →E

(5.90a), (5.90b), (5.90d) . max g U →E α + pO  ≤ −BT (1 − ) log2 maxαg U→A . pO α+ NA

(5.102a)

0

Herein the constraints of (5.84a) and (5.84b) in Problem P2 are transformed into (5.90a) and (5.90b), respectively. Moreover, (5.90d) is obtained by relaxing (5.84d) to a continuous constraint, while (5.84e) is rewritten by (5.111a).

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247

Convexity of Problem P2-1-E The convexity of Problem P2-1-E is discussed in the following proposition. Proposition 5 Problem P2-1-E is a convex problem. Proof Denoting the first derivative of the objective function of Problem P2-1-E with respect to  by Φ2 (), we have

Φ2 () = −CU PU +

 − g U →E < =2 .  g U→A − Bt α − g U →E A 2

 α ln(2) − BT B 2



g U→A α N0A

(5.103)

N0

It can be readily observed that the increase of  results in the increase of Φ2 (), and hence, the objective function of Problem P2-1-E is a convex function. Moreover, the constraint functions of (5.90a), (5.90b), (5.90d), and (5.102a) are all of linear form. In this way, Problem P2-1-E is proved to be a strictly convex one.  

5.4.3.3 Case 2–2: Passive Eavesdropper at a Random Location In this subsubsection, we consider the case of a passive eavesdropper at a random location, which is assumed to obey uniform distribution within the circle having a radius of R served by the AP. Transformation of Problem P2 The transformation process is similar to that in Sect. 5.4.3.1, with the only difference being that of linking the SOP constraint of (5.84c) to the CDF of g A→E . More explicitly, given the values of pO , pJ , , and t, the specific range of g A→E satisfying S(pO , pJ ) ≥ /t can be obtained by reformulating (5.92) as +

g A→E ≥ pJ

N0E pO g U →E   , . −  U→A pJ 2− Bt 1 + pO g A −1

(5.104)

N0

A→E (p , p , , t), (5.84c) becomes Then, denoting the left side of (5.104) by greq O J equivalent to , + A→E Fg U→A greq (5.105) (pO , pJ , , t) ≤ ,

where Fg U→A (·) corresponds to the CDF of g U →A , while the feasible set of pO satisfying S ≥ /t can be obtained after further mathematical manipulations as

pO >

, +  (pJ θ + N0E ) 1 − 2− Bt (1−)  g U→A − Bt (1−) 2 (pJ θ N0A

+ N0E ) − g U →E

,

(5.106)

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5 Mobile Edge Computing in FANET

where θ yields

θ=

2 2+η2

−



4 (2+η2 )2 1 λR η2 1+η2 κ2

−

2 1+η2

(5.107)

.

Here the polarity of the denominator of (5.106) is clarified in the following proposition. Proposition 6 The denominator of (5.106) can be proved to be positive under the S ≤ . condition of Pout Proof Similar to the Proof of Proposition 3, with the aid of (5.96) and (5.97), the left side of (5.97) can be reformulated as  Pr g

A→E

g U →E · N0A  N0E Bt − ≤ 2 pJ g U →A pJ

 (5.108)

< .

Rewriting (5.108) with the aid of the CDF function and after some further mathematical manipulations, we have NE g U →E · N0A  2 Bt − 0 < θ. U →A pJ g pJ

(5.109)

Then the denominator of (5.106) can be proved to be larger than 0 by reformulating (5.109), and hence, Proposition 6 is proved.   Here, pO can be expressed as a function of  in the following proposition. Proposition 7 The optimal pO approximates the minimum value obtained in (5.106), yielding

pO () →

, +  (pJ θ + N0E ) 1 − 2− Bt (1−)  g U→A − Bt (1−) 2 (pJ θ N0A

+ N0E ) − g U →E

.

(5.110)

Proof The relationship > in (5.106) is asymptotically close to ≥. Then, the rest of the proof is similar to the proof of Proposition I.   The optimal offloading duration of t is obtained by the following theorem. Theorem 4 Given  number of bits to be offloaded, the offloading duration is t = T for the optimal solution of Problem P2-2. Proof Upon introducing β = pJ θ + N0E , this theorem can be proved by replacing α in (5.100) by β.  

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249

With the aid of Proposition 7 and Theorem 4, Problem P2-2 can be reformulated as a single-variable problem for the case of a passive eavesdropper at a uniformly distributed location, i.e., + ,  β 1 − 2− BT T P2-2-E : arg min CU PU (L − ) + U→A  g − BT  β − g U →E A 2 N0

s.t.

(5.90a), (5.90b), (5.90d) . max g U →E β + pO  ≤ −BT (1 − ) log2 . p max βg U→A β+ O A

(5.111a)

N0

Herein the constraints of (5.84a), (5.84b), and (5.84d) in Problem P2 are transformed into (5.90a), (5.90b), and (5.90d), respectively, while (5.111a) is rewritten by (5.84e). ˆopt =

−BT log2

!

2CU PU γ U→A

@

+

!

2CU PU γ U→A γ U→E + ln(2) γ U→A −γ U→E B

4 ln(2) U→A γ U→E B C U PU γ

!

"

!

2CU PU γ U→A

"2

- 2CU PU αgU→A gU→E ˆopt =

−BT log2 

+

2 (2) B2

γ U→A −γ U→E + ln

4CU PU αg U→A g U→E α ln(2) B NA 0

N0A

! gU→A NA 0

!

γ U→A −γ U→E

+ α ln(2) B

! gU→A

N0A 2CU PU α 2 (g U→A )2 (N A )2 0

"

α−g U→E + α

"

"2

2 ln2 (2) B2

"2 . .

α−g U→E

! gU→A NA 0

(5.112)

"

α−g U→E

"2 . .

2CU PU α 2 (g U→A )2 (N A )2 0

(5.113)

Convexity of Problem P2-2-E The convexity of Problem P2-2-E is discussed in the following proposition. Proposition 8 Problem P2-2-E is a convex problem. Proof The process is similar to the proof of Proposition 5 by replacing α in (5.103) by β.  

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5.4.3.4 Optimal Offloading Strategy for the Secure UMEC As illustrated in Sect. 5.4.3, Problems P1-E, P2-1-E, and P2-2-E are proved to be convex, and hence, there exist optimal solutions to the problems. Let us use I = {1, 2-1, 2-2} to represent Problems P1, P2-1, and P2-2, respectively, and •i , where i ∈ I , to represent the variable of • in Problem i. Then, the optimal offloading strategy for the secure UMEC is formulated as follows: • Offloading duration: According to Theorems 2, 3 and 4, the offloading duration opt is ti = T , where i ∈ I , for the optimal solutions. • Offloading computational load size: Let us denote the feasible set of  ], which is determined by the constraint functions by  ∈ [imin , max i of (5.90a), (5.90b), (5.90c), and (5.90d) for Problem P1-E, (5.90a), (5.90b), (5.102a), and (5.90d) for Problem P2-1-E, and (5.90a), (5.90b), (5.111a), and (5.90d) for Problem P2-2-E. Moreover, we denote the solution to opt opt Φ1 () = 0 by ˆ1 , the solution to Φ2 () = 0 by ˆ2-1 , and the solution opt to Φ2 () = 0, where α is replaced by β by ˆ2-2 , which can be obtained from (5.112), (5.113), and (5.113), where α is replaced by β, respectively. Then, opt the optimal offloading data volume of i can be obtained differently in three specific cases: opt opt – If ˆi < min , then we have4 i = min

, where i ∈ I . i i opt opt max min ˆ – If i ∈ [i , i ], then we have i = arg min opt ∈{ ˆopt ,ˆopt} i i i ! opt opt " Etot pO (i ), i , T , where i ∈ I . opt opt , then we have i = max , where i ∈ I . – If ˆi > max i i opt • Offloading transmit power: The optimal offloading power of pO i can be obtained from (5.86) and (5.99) for i = 1, 2-1, respectively, while the asympopt totically optimal power of pO 2-2 is obtained from (5.110), by substituting the opt opt values of pJ , ti , and i .

5.4.4 Analysis of Offloading and Computation In Sect. 5.4.3, we have provided the optimal solutions to the secure computation offloading problems from a mathematical perspective with the aid of strict proofs. To further augment our understanding, additional physically tangible insights are offered in this subsection. Specifically, we refer to the results obtained from the

4

Here we use · and · to represent the floor and ceiling operations, respectively.

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optimization in Sect. 5.4.3.4 for  = 0,  = L, and 0 <  < L as the zero, full, and partial offloading, respectively. Moreover, we use the terminology of computational overload to refer to the event, when the problems formulated in Sect. 5.4.3 cannot be solved owing to the UAV’s limited hardware capability. In the following, the conditions both of selecting one of the three offloading options and of the computational overload event are explicitly detailed.

5.4.4.1 Zero Offloading The zero offloading scenario requires the following necessary condition and one of the following optional conditions to be simultaneously satisfied: • Necessary condition: The UAV is capable of executing all the computational tasks subject to the latency constraint, i.e., we have CU L/DU ≤ T , which corresponds to  ≥ 0 in (5.90a). • Optional conditions: – (a) The edge node is unable to carry out a bit calculation within the temporal constraint, i.e., CE /DE > T , which corresponds to  < 1 in (5.90b). – (b) The offloading is unable to transmit a bit within the maximum tolerable time interval subject to our specific security constraint, corresponding to  < 1 in (5.90c), (5.102a), and (5.111a). – (c) The edge node is capable of computing a bit, and the offloading link is secure, and simultaneously the energy consumption of computing a bit at the UAV is lower than the energy cost of offloading a bit, i.e., we have CU PU ≤ pO (1)T ,

(5.114)

where pO (1) can be obtained by substituting  = 1 into (5.86), (5.99), and (5.110) for Problems P1, P2-1 and P2-2, respectively. The associated reason is explained as follows. When the energy consumption of offloading a bit is lower than that of computing it locally, the UAV would definitely offload the bit to the edge node. Hence, zero offloading is not a valid option in this scenario.

5.4.4.2 Full Offloading The activation of full offloading requires the necessary condition and one of the optional conditions to be simultaneously accommodated as follows: • Necessary conditions: The edge node is capable of completing all the computational tasks subject to the latency constraint, i.e., CE L/DE ≤ T , while L bits can be transmitted into the AP within the same time interval subject to the

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specific security constraints, which correspond to  ≤ L in (5.90b) and  ≤ L in (5.90c), (5.102a), and (5.111a), respectively. • Optional conditions: – (a) The UAV is incapable of computing a bit within the temporal constraint, i.e., CU /DU > T , corresponding to  ≥ L in (5.90a). – (b) The average energy consumption per bit of offloading all bits is lower than that of the combination of offloading (L − 1) bits and locally computing a bit, i.e., pO (L)T CU PU + pO (L − 1)T > , L L

(5.115)

where pO (·) can be obtained from (5.86), (5.99), and (5.110) for Problems P1, P2-1, and P2-2, respectively, and the associated reason is explained as follows. When the average energy consumption per bit for offloading all bits is higher than that for the combination of offloading (L − 1) bits and locally computing a bit, the associated bit would be processed at the UAV side and hence full offloading cannot be achieved in this scenario.

5.4.4.3 Partial Offloading The occurrence of partial offloading requires the necessary condition and one of the optional conditions to be simultaneously met, detailed as follows: • Necessary condition: The joint computational ability of the UAV and of the edge node exceeds the total computational requirement of processing all L bits, subject to the latency constraint, i.e., CU (L − )/DU ≤ T and CE /DU ≤ T , for an  ∈ (0, L), while  bits can be offloaded subjected to the security constraint. This condition corresponds to the 5 6 situation, when there exists an intersection between (5.90a), (5.90b), (5.90d) and (5.90c), (5.102a) and (5.111a) for Problems P1, P2-1, and P2-2, respectively. • Optional conditions: – (a) The UAV and the edge computing are incapable of completing the computational tasks satisfying the temporal constraint, respectively, i.e., we have CU L/DU > T and CE L/DE > T , which indicates that 0 <  < L for (5.90a) and (5.90b). – (b) The energy consumption of locally computing a bit falls in the supplementary set of (5.114) and (5.115), i.e., pO (1)T < CU PU ≤ pO (L)T − pO (L − 1)T ,

(5.116)

where pO (·) can be obtained from (5.86), (5.99), and (5.110) for the Problems P1, P2-1, and P2-2, respectively.

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5.4.4.4 Computational Overload A computational overload may occur due to either of the following two conditions: • The joint computational capability of both the UAV and the edge does not meet the requirement of computing all the bits within the latency constraint, i.e., CU (L − )/DU > T or CE /DU > T , for any  ∈ [0, L], which corresponds to the situation that there is no intersection between (5.90a) and (5.90b). • The UAV is incapable of executing all the computational tasks within the temporal requirement, i.e., CU L/DU > T , while the offloading fails to transmit L − T DU /CU bits within the maximum tolerable time interval subject to the security constraint, which corresponds to the situation that there is no intersection between (5.90a) and (5.90c).

5.4.5 Simulation Results In this subsection, we evaluate the performance of the proposed energy-efficient computation offloading strategy conceived for secure UMEC, by answering the following questions: (1) Which offloading option should be selected for optimal offloading? (2) What is the impact of different secrecy requirements on both the maximum number of bits that can be processed and the total energy consumption in UMEC? (3) What is the influence of the UAV’s altitude and of the eavesdropper’s location on the performance of the total energy consumption and of the maximum number of bits that can be proceeded? The parameters are selected according to the existing industrial data sheets and standards. Their default values are listed in Table 5.2.

5.4.5.1 Selection of Offloading Options One of the three offloading options (i.e., zero offloading, partial offloading and full offloading) is selected for the non-overloaded computational scenarios after carrying out the proposed optimization as discussed in Sect. 5.4.4. In this subsection, we aim for investigating the selection of these three offloading options under various numerical relationships between the local computation and the offloading in terms of the energy consumption per bit while relying on the numerical results. Figure 5.17 depicts the results of our offloading strategy proposed in Sect. 5.4.3 for the three considered scenarios5 under various values of PU , where the total 5

Here p J refers to the averaged jamming power for Case 1, while pJ refers to the constant jamming power for Cases 2–1 and 2–2. In the following, we use pJ to represent both pJ and pJ .

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Table 5.2 Simulation parameters Description AP coverage radius UAV hovering altitude The location of Eve Bandwidth UAV-to-ground channel [68] AP-to-Eve channel [68]

Noise [69]

Parameter and value R = 100 m d1 ∈ [200, 400] m d2 ∈ [0, R] m B = 50 MHz κ1 = 1.42 × 10−4 η1 = 2 κ2 = 1.42 × 10−4 η2 = 3.5 λ=1 N0A = 1.99 × 10−10 mW

N0E = 1.99 × 10−10 mW

UAV computation [70]

Edge computation Power consumption

L ∈ [0, 20] MB DU = 2.0 GHz PU ∈ [0, 20 × 10−11 ] J/cycle CU = 500 cycle/bit DE = 200 GHz CE = 500 cycle/bit pJ ∈ [0, 3.5] W pmax = 250 mW, pmin = 0 mW O

Temporal constraint [70] Secrecy constraint [71]

O

T = 100 ms  ∈ [0.001, 0.1]

number of bits to be computed is equal to the maximum number of bits that can be processed within the maximum tolerable time interval of T at the UAV, but below that in the edge node. It can be observed that zero offloading (i.e.,  = 0) is selected when PU is of a small value, which corresponds to the optional condition (b) of Sect. 5.4.4.1. When PU increases, the computational tasks start to become offloaded to the edge node (i.e., 0 <  < L, corresponding to the optional condition (b) of Sect. 5.4.4.3), until reaching full offloading (i.e.,  = L, corresponding to the condition (b) of Sect. 5.4.4.2). Numerically, the cut-off values of PU for zero, partial, and full offloading reflected from Fig. 5.17 are also consistent with the analysis of (5.114), (5.116), and (5.115) in Sect. 5.4.4, respectively. Moreover, it can be seen that partial and full offloading occur in conjunction with a smaller value of PU in Case 1, compared to Cases 2–1 and 2–2, which is because the AP is capable of exploiting the knowledge of the channel between itself and the eavesdropper in Case 1. Furthermore, Case 2–1 has a similar advantage over Case 2–2, which is because the eavesdropper has a higher probability to be roaming further away from the AP under the uniform distribution of Case 2–2. Hence, the received jamming power at the eavesdropper is likely to be low. In this case, it imposes a higher energy consumption per bit for offloading, whereas partial and full offloading occur only when CU PU exceeds the above-mentioned offloading energy consumption.

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400

 L−

350

Case 1 Case 2-1 Case 2-2

250

L −  (Kbits)

 (Kbits)

300

200 150 100 50 0 2e-15

4e-15

6e-15

8e-15

1e-14

1.2e-14

P U (J/Cycle) Fig. 5.17 Locally computed number of bits  and offloaded bit volume of L −  versus the energy consumption for each CPU cycle of PU , in Case 1, Case 2–1, and Case 2–2. The results are obtained according to the proposed strategy in Sect. 5.4.3.4. The parameters are set as follows: L = 400 Kbits; pJ (p J ) = 3.5 W; d1 = 300 m; d2 = 50 m for Cases 1 and 2–1;  = 10−3 for Cases 2–1 and 2–2. The remaining parameters are listed in Table 5.2

Figure 5.18 presents the results of our offloading strategy proposed in Sect. 5.4.3 for the three scenarios considered under various values of PU , where the total number of bits to be offloaded is beyond the maximum number of bits that can be processed in the UAV, but below the maximum processing limitation of the edge node within the interval of T . It can be observed that zero offloading does not occur, regardless of the value PU , which corresponds to the optional condition (a) for partial offloading in Sect. 5.4.4.3. Moreover, comparing the results in Fig. 5.17 to those in Fig. 5.18, we can see that the cut-off value of PU for full offloading increases along with the total amount of bits to be processed, which is because it requires a higher offloading energy consumption per bit to offload more bits within a certain time interval, while full loading happens only when the energy consumption per bit for local computation is higher than that for offloading. Figure 5.19 characterizes our offloading strategy for Case 2–2 for various values of PU , where the jamming power of pJ is set differently. It can be observed that increasing pJ results in reduced cut-off values of partial and full offloading, which is because it requires lower offloading power of pO to achieve the same secrecy capacity, when a higher jamming power is invoked; hence, a lower cut-off PU is obtained. This observation is consistent with the analysis of (5.115) and (5.116). Moreover, it can be seen that the difference of the cut-off values of PU for partial and full offloading between the pJ = 3.5 W and pJ = 2.5 W scenarios is much smaller than that between pJ = 2.5 W and pJ = 1.5 W, which is explained as

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 (Kbits)

600

L −  (Kbits)

 L−

700

Case 1 Case 2-1 Case 2-2

500 400 300 200 100 0 2e-15

4e-15

6e-15

8e-15

1e-14

1.2e-14 1.4e-14 1.6e-14 1.8e-14

P U (J/Cycle) Fig. 5.18 Locally computed number of bits  and offloaded bit volume of L −  versus the energy consumption for each CPU cycle of PU , in Case 1, Case 2–1, and Case 2–2. The results are obtained according to the proposed strategy in Sect. 5.4.3.4. The parameters are set as follows: L = 1000 Kbits; pJ = 3.5 W; d1 = 300 m; d2 = 50 m for Cases 1 and 2–1;  = 10−3 for Cases 2–1 and 2–2. The remaining parameters are listed in Table 5.2

400

 L−

 (Kbits)

300 250

pJ = 3.5W pJ = 2.5W pJ = 1.5W

200 150

L −  (Kbits)

350

100 50 0 5e-15

1e-14

1.5e-14

2e-14

2.5e-14

3e-14

P U (J/Cycle) Fig. 5.19 Locally computed number of bits  and offloaded bit volume of L −  versus the energy consumption for each CPU cycle of PU parameterized by different jamming power of pJ in Case 2–2. The results are obtained according to the proposed strategy in Sect. 5.4.3.4. The parameters are set as follows: L = 400 Kbits; d1 = 300 m;  = 10−3 . The remaining parameters are listed in Table 5.2

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follows. When pJ is of a low value, the performance is jamming-power-limited. In other words, a slight increase on pJ results in a substantial increase of the secrecy offloading capacity defined in (5.81). By contrast, it requires a substantial increase of pO to achieve the same secrecy offloading capacity.

5.4.5.2 Impact of SOP Requirements The attainable computational performance can be characterized both by the maximum computational loads that can be processed within the affordable time interval and by the energy consumption imposed by processing a certain number of bits. These performance metrics are evaluated for our proposed offloading strategies, with a concern on the impact of secrecy capacity and of SOP. Figure 5.20 plots the maximum number of bits Lmax that can be processed, using our proposed offloading strategy for Cases 1, 2–1, and 2–2 for various values of both pJ and SOP requirement of . Our observations are as follows. First, the advantage of Case 1 over Cases 2–1 and 2–2 is an explicit benefit of exploiting the knowledge of the channel between the AP and the eavesdropper, while the advantage of Case 2–1 over Case 2–2 is granted by the fact that the eavesdropper, whose location obeys uniform distribution, has a higher probability of being located more than 50 m away from the AP. Second, for Case 2–1 and Case 2–2, a more stringent SOP

60

Case 1 Case 2-1 Case 2-2

 = 0 .1  = 0 .01  = 0 .001

L max (Mbits)

50 40 30 20 10 0 0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

pJ (W) Fig. 5.20 Simulation results of maximum computational load of Lmax versus jamming power of pJ parameterized by different values of SOP requirement of  in Case 1, Case 2–1, and Case 2–2. The parameters are set as follows: PU = 10 × 10−11 J/Cycle; d1 = 300 m; d2 = 50 for Cases 1 and 2–1. The remaining parameters are listed in Table 5.2

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max is incapable of supporting requirement results in a reduction of Lmax because pO a high secrecy capacity while meeting the more stringent SOP requirement. Third, the increase of jamming power results in a higher value of Lmax because a higher secrecy capacity can be achieved for a higher pJ , facilitating more bits to be offloaded to the edge node. Fourth, the increase of pJ is capable of drastically increasing Lmax when pJ is of a small value, whereas the increase of Lmax becomes smaller when pJ reaches a certain threshold value because the performance is jamming-power-limited when pJ is of a small value, whereas the performance becomes offloading-power-limited, when pJ reaches a high value. Figure 5.21 evaluates the total energy consumption of our proposed offloading strategy for Cases 1, 2-1 and 2-2 for various values of computational loads, given a specific value of pJ . The observations are illustrated as follows. First, a more stringent SOP requirement results in an increase of Etot because it requires higher offloading power to meet more stringent SOP requirements, when offloading a certain volume of computational bits. Second, Etot of Case 2-2 exhibits a sharp increase within the L range of 1.5 − 3 Mbits, which can be explained with the aid of Fig. 5.20. Explicitly, it is observed in Fig. 5.20 that when pJ reaches 3.5 W, the Lmax value of Case 2–2 having  = 10−3 gradually saturates a little above 3 Mbits, whereas Lmax represented by the other curves tends to saturate much higher than 6 Mbits. In general, we require much higher offloading power for approaching the performance limit. Third, the performance tends to degrade in the order of Cases 1,

0.1

E tot (mJ)

0.08 0.07

0.012

0.06

0.01

0.05

0.008

0.04

0.006

0.03 0.02

 = 0.1  = 0.01  = 0.001

Case 1 Case 2-1 Case 2-2

0.09

0.004 2.4

2.5

2.6

2.7

2.8

2.9

3.0

0.01 0.0 0.0

0.5

1.0

1.5

2.0

2.5

3.0

L (Mbits) Fig. 5.21 Simulation results of energy consumption of Etot versus the computational load L, parameterized by different SOP requirements of  in Case 1, Case 2–1, and Case 2–2. The parameters are set as follows: pJ = 3.5 W; PU = 10 × 10−11 J/Cycle; d1 = 300 m; d2 = 50 for Cases 1 and 2–1. The remaining parameters are listed in Table 5.2

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2–1, and 2–2, which is consistent with the trend observed in Fig. 5.20. Furthermore, the advantage of Case 1 over both Case 2–1 and Case 2–2 in terms of the total energy consumption is marginal when we set L as a small value, while the advantage becomes increasingly substantial upon increasing L.

5.4.5.3 Impact of the UAV’s Altitude and of the Eavesdropper’s Location

60

0.14

50

0.12 0.1

40

Etot (mJ)

Lmax (Mbits)

Let us now characterize the performance of our proposed offloading strategy for different values of the UAV’s altitude with the calibration of both Lmax and Et ot in Fig. 5.22. It can be observed that the increase of the UAV’s altitude results in the reduction of Lmax and in the increase of Et ot because the path loss between the UAV and the receiver on the ground decreases along with the increase of the UAV’s altitude; hence, the secrecy capacity is reduced. In this case, less bits can be offloaded given the values of pJ as well as pO and more energy is expended by offloading a bit. In Fig. 5.23, we show the Lmax and Et ot performance of our proposed offloading strategy for different eavesdropper locations. It can be seen that the increase of the distance between the eavesdropper and the AP results in a reduction of Lmax and the increase of Et ot . This is because the increase of d2 leads to the reduction of the path loss between the AP and the eavesdropper and hence further reduces the jamming power received at the eavesdropper. In this case, the secrecy capacity is degraded. The sharp increase of Etot for Case 2-1 at the right of Fig. 5.23 is because it experiences a jamming-power-limited region when the eavesdropper is located at d2 = 100 m; hence, a much higher offloading power is required for processing the computational loads encountered.

30 20

0.08 0.06 0.04

10 0

Case 1 Case 2-1 Case 2-2

0.02 200

300 UAV Altitude d1 (m)

400

0.0

200

300

400

UAV Altitude d1 (m)

Fig. 5.22 Simulation results of the maximum computational load of Lmax (left) and the total energy consumption of Etot (right) versus the UAV’s altitude of d1 in Cases 1, 2–1, and 2–2. The parameters are set as follows: pJ = 3.5 W; d2 = 50 m for Cases 1 and 2–1;  = 0.01 for Cases 2–1 and 2–2; PU = 10 × 10−11 J/Cycle. For the right, L = 10 Mbits. The remaining parameters are listed in Table 5.2

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0.2 Case 1 Case 2-1

50 Etot (mJ)

Lmax (Mbits)

0.15 40 30

0.1

20 0.05 10 0.0

0 25

50

75

Eve Location d2 (m)

100

25

50

75

100

Eve Location d2 (m)

Fig. 5.23 Simulation results of the maximum computational load of Lmax (left) and the total energy consumption of Etot (right) versus the eavesdropper’s location of d2 in Cases 1 and 2–1. The parameters are set as follows: pJ = 3.5 W. d1 = 300 m for Cases 1 and 2–1;  = 0.01 for Case 2–1; PU = 10 × 10−11 J/Cycle. For the right, L = 8 Mbits. The remaining parameters are listed in Table 5.2

5.4.6 Conclusions A beneficial architecture has been proposed for secure UMEC from the perspective of the PLS. We have formulated an energy-efficient computation offloading problem in the presence of both active and passive eavesdroppers. We then provided the optimal solutions to the problems formulated and analyzed the conditions of both the three offloading options and the computational overload event from a physical perspective. The numerical results verified the accuracy of our mathematical analysis and quantified the performance of the proposed optimal offloading strategy for the secure UMEC under various scenarios considered.

5.5 Transmit-Energy and Computation-Delay Optimization Unmanned aerial vehicles (UAVs) have been widely used in a range of compelling applications. In this section, we integrate both the networking techniques and cloud computing tasks of multi-UAV systems. We commence by proposing an energyefficient scheme for selecting the gateway of UAVs invoked for relaying data to the heterogenous cloud [72]. The remainder of this section is organized as follows. The system model, including the UAV model, the channel model, and the cloud execution model, is introduced in Sect. 5.5.1. In Sect. 5.5.2, our energy-efficient gateway selection scheme is characterized based on the analysis of the energy consumption and data transmission time. In Sect. 5.5.3, the power-vs-delay trade-off is improved based on Lyapunov optimization. Moreover, an iterative algorithm is invoked for finding the optimal strategy in each time slot. Finally, our simulation results are provided in

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Sect. 5.5.4 for evaluating the performance of our proposed scheme, followed by our conclusions in Sect. 5.5.5.

5.5.1 System Model In this subsection, we consider a heterogeneous cloud-based multi-UAV system, which consists of multiple UAV clusters, an edge cloud, and a remote cloud, as shown in Fig. 5.24. The UAVs in different clusters carry sensed data related to different tasks, while the UAVs in the same cluster constitute a FANET. We assume that these tasks are computationally-intensive; hence, the UAVs have to offload the tasks to the clouds for their execution. The UAVs are able to communicate with the clouds through a radio access network (RAN). In our model, the edge cloud can be viewed as a small processing center with limited computational capabilities at the wireless access point (AP), while the remote cloud is a large-scale processing center with powerful processing capabilities with the aid of its high-rate, low-delay Internet backbone. The system is operated under dynamically fluctuating conditions because of the high mobility of the UAV nodes. For the simplicity of analysis, the dynamic fluctuations of the system are discretized into time slots, i.e., t ∈ T = {1, 2, 3, . . .}. We assume that the topology of different UAV clusters remains relatively timeinvariant in one slot. In each time slot, first a gateway is selected to relay the sensed data of different UAVs within the same FANET to the AP over the air, and then the

Fig. 5.24 The structure of the heterogeneous cloud aided multi-UAV system

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data is processed by the virtualized machines (VMs) either within the edge cloud or in the remote cloud.

5.5.1.1 The UAV Model We assume that there are I FANETs executing I tasks in the multi-UAV system, which are denoted as {G1 , G2 , . . . , GI }, while Gi = [1, 2, . . . , Ni ] represent all the UAVs in FANET i. The tasks are assigned by the GS. Once being assigned a task, the related UAVs will fly to certain area according to the pre-defined path, collect the related data, and then offload the data to the nearest AP. These UAVs are equipped with sensor units, control units, management units, and communication units to fulfill their tasks. Specifically, the communication units are composed of multiple modules configured by various protocols [73], so that the UAVs can communicate with the AP via Wi-Fi, long-term evolution (LTE) transceivers, etc., as required. We assume that the gateways are allocated orthogonal resources (e.g., OFDMA systems) so that the interferences between different gateways can be neglected and that the bandwidth allocated to each gateway is B. The UAVs in the same FANET communicate with each other using the IEEE protocol 802.11b/g (WiFi). Since the inter-FANET communication is beyond the focus of this subsubsection, we assume that the energy consumption and the delay between UAVs and the gateway can be neglected compared to that caused by air-to-ground (A2G) communication and cloud-based computations. Under this assumption, we only consider the packet arrivals from the selected gateway. Let Ai (t) denote the number of/ packets arriving at the AP 0 from the gateway of Gi in time slot t, while A(t) = A1 (t), A2 (t), . . . , AI (t) denotes the vector of arrivals in time slot t, where Ai (t) in the different time slots is independent and identically distributed (i.i.d.). We also assume that the number of packet arrivals is bounded by Ai,min 0 ≤ / Ai (t) ≤/Ai,max0 and that Ai (t) is uniformly distributed between Ai,min , Ai,max . Let λi = E Ai (t) denote the rate of packet arrival from the gateway of Gi in time slot t.

5.5.1.2 The Channel Model In contrast to cellular networks, in A2G communications, each UAV typically has a line-of-sight (LoS) path toward the AP with a given probability. The probability of LoS propagation depends both on the environment and on the elevation angle, which may be quantified by [74, 75]: f LoS =

1  / 0 , 1 + φ exp −ϕ θ − φ

(5.117)

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263

where φ and ϕ are constants that depend on the specific environment and θ is the elevation angle. Letus denote the communication distance as d. Then θ is calculated  −1 H , where H is the hovering altitude of the UAV. Therefore, an by θ = 180 ×sin π d averaged path-loss model considering both the LoS and NLoS links having a Rician block-fading model is invoked for characterizing the channel between the UAV and the AP, where the Rician fading coefficient remains constant in each block, but changes randomly from one block to another. We assume that the block duration is the time needed to transmit a packet. Hence, the channel model is given by   ˜ h = ξ1 f LoS + ξ2 f NLoS d −α /2 h,

(5.118)

where ξ1 and ξ2 are path-loss coefficients in the LoS and NLoS cases, α denotes the path-loss exponent, h˜ represents the fast fading coefficient, and f NLoS = 1 − f LoS . We consider the effect of path loss and fast fading, while the effect of shadowing is neglected. Moreover, in this chapter, the fast fading coefficient h˜ is formulated as h˜ = X1 + j X2 ,

(5.119)

where X1 ∼ N (μ1 , σ 2 ) and X2 ∼ N (μ2 , σ 2 ) are Gaussian * * random variables. * * Therefore, the Rician probability density function (PDF) of *h˜ * is expressed as f** ˜ ** (z) *h*

< =  Az  1  2 σ2 2 exp − 2 z + A , = I0 z 2σ σ2

(5.120)

where A2 = μ21 + μ22 is the power of the LOS signal, while I0 is the 0-th order modified Bessel function of the first kind.

5.5.1.3 Cloud Computation Model In this subsubsection, the packets arriving from different FANETs are offloaded and processed in the clouds. Once data transmission from the gateways and the AP is finished, we assume that part of the tasks of FANET i, denoted as Ae,i (t), will be processed in the edge cloud, while Ar,i (t) packets of the tasks will be processed in the remote cloud. Here we have Ai (t) = Ae,i (t) + Ar,i (t).

5.5.1.4 Edge Cloud In the edge cloud, there are a total of I VMs exclusively used by I FANETs. When the packets reach the edge cloud, the corresponding VM allocates appropriate computational resources to carry out the processing task. The computational resources may be quantified in terms of the number of CPU cycles [76]. Naturally,

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5 Mobile Edge Computing in FANET

the number of CPU cycles per unit time duration is proportional to the CPU’s clockfrequency. In this subsubsection, we assume that FANET i has ni (t) CPU cycles in time slot t, while the total number of CPU cycles per unit time in the edge cloud is nmax . We express the number of packets that can be processed by the VM i in the edge cloud as μi (t) = Δtni (t)L−1 i ,

Δt > ni (t)L−1 i ,

(5.121)

where Δt denotes the duration of the time slot and Li is the minimum number of CPU cycles needed to process a single packet received from FANET i. Moreover, the power consumption of the computations in the edge cloud can be approximated by [76] Pe,i (t) = κn3i (t),

(5.122)

where κ is the capacitance proportionality factor. The newly arrived packets will be queued in the buffer of the edge cloud, when the corresponding VM is busy processing the earlier packets. Let Qi (t) denote the queue length in the i-th VM related to FANET i, where we have Qi (0) = 0 at the beginning. Then the evolution of the queue length can be expressed as Qi (t + 1) = max{Qi (t) − μi (t), 0} + Ae,i (t).

(5.123)

The computational delay of the edge cloud may simply arise from managing the queue. Relying on Little’s Law [77], the average queueing delay can be derived from the average queue length, which can be calculated from Eq. (5.123).

5.5.1.5 Remote Cloud By contrast, the power consumption in the remote cloud is closely related to the variation of the computational workload, which is formulated by Pr,i (t) = CeAr,i (t ),

(5.124)

where C is a proportionality coefficient. As for the execution delay in the remote cloud, given that it is equipped with a multi-core high-speed CPU, we assume that the packets arriving can be processed without any queueing delay. Hence, the time delay essentially depends on the Internet transmission process. Moreover, according to [78], the Internet’s transmission delay can only be characterized empirically. For simplicity, we assume that the Internet’s transmission process has a deterministic delay D.

5.5 Transmit-Energy and Computation-Delay Optimization

265

5.5.2 Energy-Efficient Gateway Selection If each UAV in a FANET establishes a communication link with the AP, this may lead to low spectral efficiency and high interferences at the AP. Hence, it is necessary to select superior UAVs to act as gateways so that the ordinary UAVs in the FANET can communicate with the AP via the relay of gateway. In this subsection, we design an energy-efficient gateway selection scheme considering both the energy and the time needed for data transmission. Given our stochastic channel, it may result in a probabilistic communication outage as well as stochastic energy consumption and time delay. Without loss of generality, in the following, we only consider FANET i as a simple example and study how to select the gateway drone.

5.5.2.1 The Communication Model Analysis In time slot t, let u denote the UAV selected as the gateway in FANET i, where u ∈ Gi . Then the signal received at the AP from u can be modeled as y=

   −α/2 Pu ξ1 fuLoS + ξ2 fuNLoS du h˜ u xu + nu ,

(5.125)

where Pu denotes the transmit power of drone u, while xu represents its transmitted data. Moreover, nu ∼ N (0, N0 ) is the additive white Gaussian noise (AWGN). Then, the signal-to-noise ratio (SNR) is given by

SNRu =

* *2  2 * * Pu ξ1 fuLoS + ξ2 fuNLoS du−α *h˜ u * N0

.

(5.126)

Let us now define the outage event. Proposition 9 The transmission between the gateway u and the AP fails, when the receiver’s SNRu is below a given threshold β, which is defined as an outage event. This event occurs with the probability fu , which can be expressed as ⎛

⎞ α N βd A 0 fu = 1 − Q ⎝ , ! " ⎠, σ Pu ξ1 f LoS + ξ2 f NLoS 2 u

(5.127)

u

where 

∞

Q(u, v) = v

is the Marcum Q function.

< = 1 x exp − (x 2 + u2 ) I0 (xu)dx 2

(5.128)

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5 Mobile Edge Computing in FANET

Proposition 9 indicates that the data transmission between the gateway UAV and the AP may fail because of the stochastic character of the channel. Hence, an effective retransmission scheme is needed for improving the reliability of the communication [79]. The automatic repeat request (ARQ) scheme allows the gateway UAV to retransmit the packet either until it is successfully received or a maximum number of retransmissions N is reached. The number of ARQ rounds required depends on the channel conditions.

5.5.2.2 Required Transmission Time and Energy Consumption The energy consumption and the time required for data transmission are the main parameters in selecting the gateway. Given that the energy consumption and the time required for transmitting a single packet depend on the number of ARQ attempts, only the average performance is considered in the following. We first calculate the average number N¯ utrans of packet retransmissions of the gateway u, which can be expressed as N¯ utrans = 1 · Pr(S 1 ) + 2 · Pr(F 1 , S 2 ) + · · · + (N − 1) · Pr(F 1 , F 2 , . . . , S N−1 ) + , + N · Pr(F 1 , F 2 , . . . , S N ) + Pr(F 1 , F 2 , . . . , F N )

(5.129)

= 1 · Pr(S 1 ) + 2 · Pr(F 1 , S 2 ) + · · · + (N − 1) · Pr(F 1 , F 2 , . . . , S N−1 ) + N · Pr(F 1 , F 2 , . . . , F N−1 ), where Pr(F 1 , F 2 , . . . , F m−1 , S m ) denotes the probability that the transmission fails at the 1st, . . . , (m − 1)-th rounds but succeeds at the m-th round. Since the channel state information (CSI) at each ARQ round is i.i.d., the failure and success probabilities of each time transmission are independent of each other, i.e., Pr(F 1 , F 2 , . . . , F m−1 , S m ) = Pr(F 1 )Pr(F 2 ) · · · Pr(F m−1 )Pr(S m ) = fum−1 (1 − fu ) = fum−1 − fum . Therefore, N¯ trans can be further expressed as N¯ utrans = (1 − fu ) + 2(fu − fu2 ) + · · · + (N − 1)(fuN−2 − fuN−1 ) + NfuN−1 = 1 + fu + · · · + fuN−1

1 − fuN = . 1 − fu

(5.130)

5.5 Transmit-Energy and Computation-Delay Optimization

267

Let Tuone be the average time required for transmitting a single packet, which is given by Tuone = N¯ utrans · T travel,

(5.131)

where T travel denotes the “flight-time” of a packet. Assuming that a packet contains K bits, T travel can be expressed as T travel =

K . Blog2 (1 + β)

(5.132)

If Ai (t) packets of a FANET have to be transmitted, the total transmission time is given by Tutotal = Ai (t) · Tuone = Ai (t) ·

1 − fuN K . · 1 − fu Blog2 (1 + β)

(5.133)

The energy consumption of the gateway UAV u includes both the hovering energy and the transmission energy, but naturally the hovering energy dominates the total energy consumption, which depends on the UAV type. We assume that the hovering power of the gateway UAV u is Puhover , and hence, the hovering energy consumption in each time slot can be calculated by Euhover = Puhover Δt.

(5.134)

By contrast, the energy consumption of transmitting Ai (t) packets is calculated by Eutrans = Ai (t) · Pu · Tuone = Ai (t) · Pu ·

1 − fuN K . · 1 − fu Blog2 (1 + β)

(5.135)

Therefore, the total energy consumption in each time slot can be expressed as Eutotal = Euhover + Eutrans = Puhover Δt + Ai (t) · Pu ·

1 − fuN K . · 1 − fu Blog2 (1 + β)

(5.136)

5.5.2.3 An Energy-Efficient Gateway Selection Scheme In this subsubsection, we design an energy-efficient gateway selection scheme. Our objective is to minimize the total energy consumption under specific energy and

268

5 Mobile Edge Computing in FANET Battery

transmission time constraints. Let Eu denote the residual battery energy of u, which should have sufficient energy for both hovering and data transmission, i.e., Battery > Eutotal . Moreover, the residual energy of the selected gateway u should Eu exceed a threshold E th for its operation in the next time slot. Additionally, the time required for transmission should not exceed a pre-defined threshold T th . Let ςu be a Boolean decision variable, which is defined as follows: ⎧ ⎨ 1 If u is selected as the gateway, ςu = (5.137) ⎩ 0 Otherwise. Then the gateway selection can be formulated as a linear integer problem given by P1 :

min ςu

s.t.



Eutotal · ςu

u∈Gi



Battery

(Eu

− Eutotal) · ςu ≥ E th ,

(5.138a)

u∈Gi

Tutotal ≤ T th ,  ςu = 1,

∀u ∈ Gi ,

(5.138b) (5.138c)

u∈Gi

ςu ∈ {0, 1},

∀u ∈ Gi .

(5.138d)

Specifically, Eq. (5.138a) ensures that the selected gateway has sufficient residual energy for continuing its operation, while Eq. (5.138b) guarantees that the transmission latency is lower than the threshold. Eq. (5.138c) requires that only one UAV can be selected as the gateway UAV in a FANET, and Eq. (5.138d) indicates that each UAV only has a binary selection space. Again, problem P1 is an integer programming problem, which can be solved by brute-force search. In fact, since the set Gi is given, the size of the search space is * * *Gi *, where | · | is the cardinality of a set. Therefore, the exhaustive search will have a complexity order of O(1), which is suitable for the computationally limited UAV network. Moreover, P1 can also be converted into a convex optimization problem. Since only a single of ςu has the value of one and the other ςu has a value of zero, we can relax the integer constraint of Eq. (5.138d) to a continuous convex constraint 0 ≤ ςu ≤ 1 without affecting the optimal outcome or increasing computational complexity. Hence, the optimal gateway can also be found by Algorithm 19.

5.5 Transmit-Energy and Computation-Delay Optimization

269

Algorithm 19 Energy-efficient gateway selection scheme 1: 2: 3: 4: 5:

At the beginning of the time slot t, obtain Ai (t). Observe the channel state of UAV u. Calculate fu according to Eq. (5.127). Calculate Tutotal and Eutotal according to Eq. (5.133) and Eq. (5.136), respectively. Calculate  Eutotal · ςu ςu = arg min u∈Gi

s.t. (5.138a), (5.138b), (5.138c), 0 ≤ ςu ≤ 1,

∀u ∈ Gi .

6: Select UAV u whose ςu = 1 as the gateway and set t = t + 1.

5.5.3 Task Scheduling and Resource Allocation Scheme As mentioned before, task scheduling is an important issue in heterogeneous cloud aided systems. Specifically, if all the packets are locally processed in the edge cloud, it is difficult to maintain the system’s stability because both the computational capability and the buffer capacity of the edge cloud are limited. On the other hand, if all the packets are offloaded and tackled by the remote cloud, the power consumption may become excessive. In this subsection, our goal is to find an optimal scheme to determine the percentage of packets processed in the edge cloud as well as the amount of computational resources allocated for different tasks considering both the average power consumption and the cloud execution delay.

5.5.3.1 Average Power Consumption and Cloud Execution Delay The power consumption of processing the packets arriving from FANET i in time slot t is composed of two parts, i.e., the power consumption in the edge cloud and the power consumption in the remote cloud. Let Pi (t) = Pe,i (t) + Pr,i (t) denote the total power consumption of fulfilling the task requested by UAV i in time slot t. Considering a total number of I FANETs, the system’s power consumption can be calculated as P (t) = Ii=1 Pi (t). Then, the time-averaged power consumption is given by ⎡ 1 P¯ = lim E ⎣ t →∞ t

t −1 

⎤ P (t)⎦ .

(5.139)

τ =0

Since the Internet’s transmission delay in the remote cloud is assumed to be constant, the average execution delay essentially hinges on the sojourn time in each edge cloud’s queue. Relying on Little’s Law [77], we use the time-averaged

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5 Mobile Edge Computing in FANET

queue length in the task buffer as a metric of the average execution delay, which is expressed as ⎤ ⎡ t −1  1 Qi (t)⎦ . Q¯ i = lim E ⎣ t →∞ t

(5.140)

τ =0

Definition 2 The queueing system of FANET i is strongly stable in the edge cloud, if [80] ⎡ lim

t →∞

1 ⎣ E t

t −1 

⎤ Qi (t)⎦ < ∞.

(5.141)

τ =0

Note that if all the queues are stable, the system’s average service rate is equal to the packet arrival rate, yielding t −1

t −1

1 1 ui (t) = lim Ae,i (t), t →∞ t t →∞ t lim

τ =0

(5.142)

τ =0

which guarantees that the arriving packets can be processed within a finite time delay. In this subsubsection, we aim for finding a task scheduling and resource allocation scheme for the sake of minimizing the time-averaged power consumption under the constraint that all the tasks can be executed within a finite time delay. / 0 A (t ) Let η(t) = η1 (t), η2 (t), . . . , ηI (t) , where ηi (t) = Ae,ii (t ) denotes the ratio of 0 / packets processed in the edge cloud, and n(t) = n1 (t), n2 (t), . . . , nI (t) . Hence, this scheduling and resource allocation problem can be formulated as P2 : s.t.

min

η(t ),n(t )

P¯

0 ≤ ηi (t) ≤ 1, I 

i = 1, 2, . . . , I, t ∈ T ,

ni (t) ≤ nmax ,

t ∈T,

(5.143a) (5.143b)

i=1

⎡ ⎤ t −1 1 ⎣ lim E Qi (t)⎦ < ∞, t →∞ t

i = 1, 2, . . . , I.

(5.143c)

τ =0

To elaborate, (5.143a) requires that the packets arriving from FANET i should be processed either by the edge cloud or by the remote cloud, while (5.143b) indicates that the sum of the number of CPU cycles does not exceed the total computational

5.5 Transmit-Energy and Computation-Delay Optimization

271

capacity. Moreover, (5.143c) indicates that the packets can be processed in the edge cloud within a finite delay.

5.5.3.2 Task Scheduling and Resource Allocation Scheme Based on Lyapunov Optimization Problem P2 is a stochastic optimization problem since both η(t) and n(t) are time-varying, and hence, the optimal strategy is temporally corrected. In this subsubsection, we design an online algorithm to determine the optimal task scheduling and resource allocation strategy of each time slot based on Lyapunov optimization. To elaborate, Lyapunov optimization is designed for the greedy minimization of the queue backlog in each time slot by solving a deterministic problem [81]. The detailed discussions and theorems of Lyapunov / 0 optimization can be found in [80]. First of all, we define the function L Q(t) as the sum of the squared number of packets in the queue: I / 0 1 L Q(t) = Q2i (t). 2

(5.144)

i=0

Then, the conditional Lyapunov drift in time slot t can be expressed by + 5 , / 0 6 5 6 Δ Q(t) = E L Q(t + 1) − L Q(t) |Q(t) .

(5.145)

/ 0 If we minimize Δ Q(t) in each time slot, this may stabilize the system. However, the average power consumption might be /unnecessarily high. Alternatively, we may 0 define a drift-plus-penalty function ΔV Q(t) to strike a trade-off between the power cost and queue backlog. The drift-plus-penalty function may be defined as / 0 / 0 / 0 ΔV Q(t) = Δ Q(t) + V · E P (t)|Q(t) ,

(5.146)

where V is the control weighting parameter that represents how much we emphasize the power consumption. A large value of V is beneficial of optimizing the average power consumption at the expense of high average delay. Thus, the drift-pluspenalty function provably strikes a balance between the power consumption and the execution delay in the cloud.

272

5 Mobile Edge Computing in FANET

/ 0 / 0 Lemma 2 For any / η(t) 0 and n(t) satisfying ηi (t) ∈ 0, 1 , ni (t) ∈ 0, nmax , i = 1, 2, . . . , I , ΔV Q(t) is upper bounded by /

0

ΔV Q(t) ≤

⎡ ⎤ I    1 E⎣ A2e,i (t) + μ2i (t) − 2Ae,i (t)μi (t) |Q(t)⎦ 2 i=1

⎡ −E⎣

I 

⎤ " Qi (t) μi (t) − Ae,i (t) |Q(t)⎦ !

/ 0 + V · E P (t)|Q(t) .

i=1

(5.147) For the sake of achieving a superior task scheduling and resource allocation, we conceived / 0Algorithm 2 aiming for the greedy minimization of the upper bound of ΔV Q(t) in each time slot, where we have I + , / 0 1 A2e,i (t) + μ2i (t) − 2Ae,i (t)μi (t) hc η(t), n(t) = 2 i=1

−

I + 

!

Qi (t) μi (t) − Ae,i (t)

",

(5.148) + V · P (t).

i=1

Note that in Algorithm 20, solving the stochastic optimization problem P2 is reduced to deal with a deterministic optimization problem P3 in each time slot. Since P3 is a convex optimization problem, Algorithm 20 is able to find the optimal solution in each time slot with a complexity order of O(I 2 ). By appropriately adjusting the value of V , we can strike a power-vs-delay trade-off. Moreover, the proposed algorithm is capable of minimizing the power consumption and of driving the queue backlog toward a low buffer content corresponding to a low delay. Algorithm 20 Task scheduling and resource allocation scheme 1: At the beginning of the time slot t, obtain {Qi (t)} and {Ai (t)}. 2: Calculate / 0 P3 : {η(t), n(t)} = arg min hc η(t), n(t) s.t. (5.143a), (5.143b). 3: Update {Qi (t)} according to Eq. (5.123) and set t = t + 1.

5.5 Transmit-Energy and Computation-Delay Optimization

273

5.5.3.3 A Low-Complexity Iterative Algorithm Problem P3 is a convex optimization problem and can be solved by interior point methods [82]. However, the generic convex problem solution algorithms suffer from high-computational cost. In this subsubsection, we conceive a low-complexity algorithm for solving P3 based on the structured nature of the problem. Since P2 is a joint task scheduling and resource allocation problem, its minimization can be achieved by searching through the solution space by exploiting the decreasing gradient direction of either of them. Hence, by fixing one of the two variables, we can obtain the optimal value of the other one. Substituting Eqs. (5.121), (5.122), and (5.124) into Eq. (5.148), we have / 0 hc η(t), n(t) = 1 2 −1 [ηi (t)A2i (t) + Δt 2 n2i (t)L−2 i −2ηi (t)Ai (t)Δtni (t)Li ] 2 I

i=1

I <  =  −1 − Qi (t) Δtni (t)Li − ηi (t)Ai (t)

(5.149)

i=1

+V

I + 

, κn3i (t) + Ce(1−ηi (t ))Ai (t ) .

i=1

nˆ i (t) =

−Δt 2 L−2 i

@ +

+ , " −1 ! ηi (t)Ai (t) + Qi (t) − λˆ Δt 4 L−4 i + 12V κ ΔtLi 6V κ

. (5.150)

Optimal Resource Allocation By fixing η(t), the optimization goal of P3 reduces to * / hc η(t), n(t)* η(t)] = , 1 + 2 2 −1 Δt ni (t)L−2 i − 2ηi (t)Ai (t)Δtni (t)Li 2 I

i=1

−

I  i=1

Qi (t)Δtni (t)L−1 i +V

I  i=1

κn3i (t).

(5.151)

274

5 Mobile Edge Computing in FANET

Hence, the resultant single-variable optimization problem can be formulated as P4 :

min n(t )

s.t.

I 

* / hc η(t), n(t)* η(t)] ni (t) ≤ nmax .

(5.152a)

i=1

Problem P4 can be solved using the Lagrangian dual method. The Lagrangian function of P4 can be written as ⎛ ⎞ I  * / / 0 ni (t) − nmax ⎠ , (5.153) L n(t), λ = hc η(t), n(t)* η(t)] + λ ⎝ i=1

where λ is the Lagrangian multiplier associated with the constraint Eq. (5.152a). Since P4 is a convex optimization problem, the optimal solution of the original ˆ should satisfy the Karush–Kuhn–Tucker and dual problems, i.e., of nˆ i (t) and λ, (KKT) conditions: ⎧ ⎪ λˆ ≥ 0, ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ I ⎪  ⎪ ⎪ ⎪ nˆ i (t) − nmax ≤ 0, ⎪ ⎪ ⎪ ⎪ i=1 ⎪ ⎪ ⎨ ⎞ ⎛ I (5.154)  ⎪ ⎪ λˆ ⎝ nˆ i (t) − nmax ⎠ = 0, ⎪ ⎪ ⎪ ⎪ i=1 ⎪ ⎪ ⎪ ⎪ ! "* ⎪ ⎪ ⎪ ∂hc η(t), n(t)|η(t) ** ⎪ ⎪ + λˆ = 0. * ⎪ ⎪ * ⎩ ∂ni (t) ni (t )=nˆ i (t )

Substituting Eq. (5.151) into Eq. (5.154), nˆ i (t) can be expressed as Eq. (5.150). I ˆ In Eq. (5.154), if λ = 0 and Hence, we only have to determine λ. ni (t) − nmax ≤ i=1

0, λˆ = 0 is the optimal solution. Otherwise, λˆ can be determined with the aid of the bisection search approach. The region of the search approach spans [λL , λU ], where I ni (t) − nmax ≤ 0. Thus, the available selection of λU is λL = 0 and λU satisfies i=1

given by 1 ! "2 λU = max ΔtL−1 η (t)A (t) + Q (t) . i i i i i

(5.155)

5.5 Transmit-Energy and Computation-Delay Optimization

The search for the optimal λˆ is terminated if * * * I * * i=1 ni (t) − nmax * nmax

≤ δ,

275

(5.156)

where δ is the search precision. Algorithm 21 An alternative iterative algorithm for solving P3 1: Initialize η(t), set k = 0, δ = 10−10 , ε = 10−6 . 2: Set hkc = 0. 3: repeat 4: Update k = k + 1. 5: Set λ = 0. 6: Calculate nki (t) according to Eq. (5.150). 7: if Ii=1 nki (t) − nmax ≤ 0 then 8: Update nˆ ki (t) = nki (t). 9: else 10: Set λL = 0. 11: Calculate λU according to Eq. (5.155). 12: repeat 13: Set λ = 12 (λL + λU ). 14: Calculate nki (t) according to Eq. (5.150). 15: Update nki (t) = max{nki (t), 0}. 16: if Ii=1 nki (t) − nmax ≤ 0 then 17: Update λU = λ. 18: else 19: Update λL = λ. 20: end * if * * *

* I i=1 ni (t)−nmax *

until ≤ δ. nmax Update nˆ ki (t) = nki (t). end if Update {ηˆ ik (t)} by solving Eq. (5.159). Update hkc according to Eq. (5.149). * * * * k k−1 26: until *hc − hc * ≤ ε.

21: 22: 23: 24: 25:

opt

opt

27: Obtain nˆ i (t) = nki (t), ηi (t) = ηˆ ik (t).

Optimal Task Scheduling By fixing n(t), the optimization objective reduces to * / hc η(t), n(t)* n(t)] = , 1 + 2 ηi (t)A2i (t) − 2ηi (t)Ai (t)Δtni (t)L−1 i 2 I

i=1

+

I  / i=1

M  0 Qi (t)ηi (t)Ai (t) + CV e(1−ηi (t ))Ai (t ). i=1

(5.157)

276

5 Mobile Edge Computing in FANET

Then, the optimization problem can be rewritten as P5 : s.t.

min η(t )

/ 0 hc η(t), n(t)|n(t)

0 ≤ ηi (t) ≤ 1,

i = 1, 2, . . . , I.

(5.158a)

Since ηi (t) s are i.i.d., the optimal solutions can be achieved by solving / 0 ∂hc η(t), n(t)|n(t) = ∂ηi (t)

Ai (t)CV e[1−ηi (t)]Ai (t) − ηi (t)A2i (t) + Ai (t)Δtni (t)L−1 i − Qi (t)Ai (t) = 0.

(5.159) Equation (5.159) is a transcendental equation, which can be readily solved by numerical methods such as Newton’s method or Secant method. The detailed procedure is omitted in this subsubsection. Let ηi∗ (t) be the solution of Eq. (5.159), * * 2 ∂ hc [η(t ),n(t )|n(t )] * ≥ 0. Hence, ηi∗ (t) is the global for which we have * ∂ηi2 (t ) ∗ / ηi (t )=η 0 i (t ) minimum point. Considering ηi (t) ∈ 0, 1 , the optimal solution is given by 1 5 62 ηˆ i (t) = max 0, min ηi∗ (t), 1 , i = 1, 2, . . . , I.

(5.160)

Note that although problems P4 and P5 are solved optimally, the solutions obtained in Eqs. (5.155) and (5.160) may not be the optimal ones to P3 for the existence of the coupling term. Therefore, we provide an iterative algorithm for finding the optimal solutions for P3. Our solution is detailed in Algorithm 21. Since both the subproblems, e.g., problems P4 and P5, are solved optimally, Algorithm 21 is guaranteed to converge to the optimal solutions to problem P3 with a complexity order of O(I L), where L is the number of iterations, which is usually far less than I .

5.5.4 Simulation Results In this subsection, we provide numerical results for characterizing the proposed algorithms. We assume that all the UAVs in I FANETs are randomly distributed in a circular area with a radius of R and hover at a height of H. We assume urban environment with φ = 11.95 and ϕ = 0.14 [74]. The path-loss coefficients are ξ1 = 7 × 10−5 , ξ2 = 3.5 × 10−5 , and the path-loss exponent is α = 2. The mean and variance of the Gaussian random signals are set to be μ1 = μ2 = 8 and σ 2 = 5, 2 2 2 respectively. Hence, the k-factor of the Rician fading channel is μ1 2σ+μ = 12.8. 2 The power of AWGN is N0 = Bn0 , where n0 = −174 dBm/Hz is the AWGN’s

5.5 Transmit-Energy and Computation-Delay Optimization

277

power spectral density and B = 10 MHz is the bandwidth allocated to each FANET. The SNR threshold is set to β = 5 dB. For each FANET, the length of one time slot is 30 ms, and we assume that Ai,min/ = 10, A 0 i,max = 100. Moreover, Ai (t) is uniformly distributed within the range of 10, 100 . The number of bits that a packet contains is K = 5000, and the maximum number of retransmission rounds of the ARQ scheme is N = 8. Additionally, let κ = 10−27, L = 3 × 106, nmax = 1010, and C = 10−20.

5.5.4.1 Performance of Gateway Selection Scheme Since the transmission energy and transmission time are related to the link quality, e.g., the outage probability, which further depends on the UAV’s transmit power and hovering altitude, we first explore the interaction between them. The corresponding results are shown in Fig. 5.25. It is observed from Fig. 5.25 that as expected, the

1 Pu = 0.1 W

0.8 0.6 Pu = 0.8 W 0.4 0.2 0

0

100

200

300

400

500

Outage probability fu

Outage probability fu

1

Pu = 0.1 W 0.8 0.6 Pu = 0.8 W 0.4 0.2 0

600

0

100

UAVs flying altitude (m)

(a) R = 50 m

300

400

500

600

(b) R = 100 m Pu = 0.1 W

1

Outage probability fu

200

UAVs flying altitude (m)

0.8 0.6 Pu = 0.8 W 0.4 0.2 0

0

100

200

300

400

500

600

UAVs flying altitude (m)

(c) R = 200 m Fig. 5.25 Outage probability (calculated by Eq. (5.127)) versus UAV’s hovering altitude parameterized by the UAV’s transmit power, where (a), (b), and (c) represent the cases that the horizontal distances between the UAV and the AP are 50 m, 100 m, and 200 m, respectively

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Electricity consumption (mAh)

40

38

36

Energy optimal scheme Time optimal scheme Greeedy scheme

34

32 5

10

15

20

25

30

35

40

Number of UAVs Fig. 5.26 Energy consumption (calculated by Eq. (5.136)) of different gateway selection schemes versus the number of UAVs

outage probability decreases with the transmit power. Moreover, it is also observed that the outage probability first decreases and then increases with the hovering altitude. This is plausible because when the hovering altitude increases from a low height, the probability of LoS links is increased. However, when the hovering altitude exceeds a certain height, the path-loss increase outweights the gains brought about by having more LoS links. This phenomenon indicates that the hovering altitudes of UAVs have to be carefully designed for maximizing the channel gain. We then evaluate the performance of the gateway selection scheme described in Algorithm 19. Without loss of generality, we highlight the performance of a single FANET in one time slot. We assume that the/ horizontal 0 distances between the AP and UAVs are randomly distributed/between 0150, 200 m and the hovering altitudes are randomly distributed between/ 200, 300 0m. The energies of the UAVs’ batteries are randomly distributed within 5000, 8000 mAh with an output voltage of 15 V. The energy threshold and time threshold are 4500 mAh and 30 ms, respectively. The hovering power / of the 0UAV is 40 W, while the transmit power is randomly distributed within 0.5, 0.8 W. The results are averaged over 500 simulations. The required transmission energy6 and transmission time performances are characterized in Figs. 5.26 and 5.27. The performances of our proposed energy-

6

The energy consumption is represented by the electricity consumption in our simulations, and they can be mutually transformed since the output voltage and the length of one time slot are known as given parameters.

5.5 Transmit-Energy and Computation-Delay Optimization

279

Transmission time (ms)

26

25.5 Energy optimal scheme Time optimal scheme Greeedy scheme

25

24.5

5

10

15

20

25

30

35

40

Number of UAVs Fig. 5.27 Required transmission time (calculated by Eq. (5.133)) of different gateway selection schemes versus the number of UAVs

optimal gateway selection scheme and of other schemes, i.e., of the time-optimal scheme and of the greedy scheme, are also compared at the same time. Specifically, the time-optimal scheme selects the specific UAV that needs the lowest transmission time as the gateway, while the greedy scheme randomly chooses a UAV that satisfies the energy and transmission time constraints considered. It is shown in Figs. 5.26 and 5.27 that our proposed energy-optimal scheme consumes the least energy, while the time-optimal scheme requires the least transmission time. Moreover, the performance of the greedy scheme falls somewhere in between. When jointly considering both the energy consumption and transmission time, our proposed energy-optimal scheme consumes nearly 10 mAh lower energy than that of the other two schemes at the cost of less than 2 ms higher transmission time than that of the time-optimal scheme. This is beneficial in the context of a battery-constrained environments. Therefore, our proposed scheme is superior to other two schemes.

5.5.4.2 Performance of Task Scheduling and Resource Allocation scheme This subsection analyzes the performance of the proposed task scheduling and resource allocation scheme described in Algorithm 20 and Algorithm 21. In Fig. 5.28, we first characterize the convergence of the bisection search process described in the inner loop of Algorithm 21. The convergence of the outer loop of Algorithm 21 is shown in Fig. 5.29, where we set the control parameter of the drift-plus-penalty function in Eq. (5.146) as V = 500. Figure 5.28 shows that the

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0.7 I=5 I = 10 I = 20

0.6

The relative error

0.5 0.4 0.3 0.2 0.1 0 0

5

10

15

Number of Iterations Fig. 5.28 The convergence of the bisection search process in Algorithm 21 parameterized by different numbers of FANETs

14000

The objective goal hc

12000 10000

M=5 M = 10 M = 20

8000 6000 4000 2000 0 -2000 1

5

10

15

20

Number of Iterations Fig. 5.29 The convergence of Algorithm 21 parameterized by different numbers of FANETs

5.5 Transmit-Energy and Computation-Delay Optimization

281

bisection based search finds the optimal solutions of P4 within 15 loops at a relative error below 10−10. It is much faster than solving P4 using other optimization algorithms considering the huge region of search. Additionally, it can be inferred from Fig. 5.29 that given a set of randomly generated η0 (t), Algorithm 21 is capable of achieving convergence in as few as 2 steps. Moreover, increasing the number of drones in the FANETs has almost no influence on the rate of convergence. Therefore, our algorithm achieves fast convergence at a lower computational cost compared to solving P3 using interior point methods. Figure 5.30 shows the time-averaged power consumption of task execution and the average queue length per user versus the control parameter, where we set I = 10. The results are averaged over 100 time slots. It can be observed that the timeaveraged power consumption decreases upon increasing V and converges to the minimum value, when V is sufficiently large. By contrast, the average queue length per user increases with V and also converges, when V is sufficiently large. It can be explained that when V is sufficiently large, the optimal ratio of packets processed in the edge cloud tends to be a constant, so do the time-averaged power consumption and time-averaged queue length. These results quantify the trade-off between the power consumption and execution delay, adjusted by the control parameter V . The time evolution of the ratio of packets processed in the edge cloud ηi (t) parameterized by the packets arrival rates is shown in Fig. 5.31, where we assume that there are I = 4 FANETs and the packet arrival in each / 0 /rates of the FANETs 0 time slot are fixed to A1 (t), A2 (t), A3 (t), A4 (t) = 20, 40, 60, 80 , and V is set

(b)

(a) 1000

50 40 30 20 0.4 0.2

10

8 0

0

2

4

× 104 6 8

Control parameter V

× 104

Time-averaged queue length per user

Time-averaged power consumption

60

900 800 700 600 500 400 300 200

0

2

4

6

Control parameter V

8 4

× 10

Fig. 5.30 Time-averaged power consumption (calculated by Eq. (5.139)) and queue length (calculated by Eq. (5.140)) versus the control parameter

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Ratio of packets processed in the edge cloud

0.5

0.4

0.3 Ai (t) = 20

0.2

A (t) = 40 i

A (t) = 60 i

A (t) = 80

0.1

0

i

2

4

6

8

10

12

14

16

18

20

Time slots Fig. 5.31 The time evolution of the ratio of packets processed in the edge cloud (calculated by Eq. (5.159)) parameterized by different packet arrival rates

to be 4000. It is observed that our scheme tends to offload more packets to the edge cloud for higher arrival rates. Specifically, all of the packets will be offloaded to the remote cloud when Ai (t) = 20. Moreover, less packets will be offloaded to the edge cloud, as time passes. The reason is that the queue length grows with the passage of time; thus, more packets will be sent to the remote cloud to strike a power-vs-delay trade-off. Figure 5.32 depicts the comparison of the average power consumption versus the queue length of systems between the scenarios operating both with and without the remote cloud. Here we set I = 10 and V ∈ {50, 100, 200, 300, 400, 500, 1000, 2000, 4000}. It is shown that in general, the average power consumption decreases with the average queue length for both systems. Therefore, it is necessary to carefully select a suitable V value to balance the power consumption vs. execution delay. Moreover, the decay rate of the power consumption operating without the remote cloud is more rapid than that of the system relying on the remote cloud, which indicates that the control parameter has more substantial influence on the system without the remote cloud. Additionally, more power is consumed by the system without the remote cloud while leading to longer delays. This is because the edge cloud cannot stabilize its task buffers, due to its limited computational capacity, if it is not assisted by the remote cloud. In this case, Fig. 5.32 confirms the superiority of the heterogenous cloud system advocated.

5.5 Transmit-Energy and Computation-Delay Optimization

283

Time-averaged power consumption

600 With Remote Cloud Without Remote Cloud

500 400 300

V = 50 200

V = 4000 100 0

0

500

1000

1500

2000

2500

Time-averaged queue length per user Fig. 5.32 The performance of average power consumption (calculated by Eq. (5.139)) and the system’s queue length (calculated by Eq. (5.140)) both with and without the assistance of the remote cloud

5.5.5 Conclusions In this section, we studied the QoS-based network association problem of heterogenous cloud aided multi-UAV systems. We proposed an energy-efficient gateway selection scheme for choosing the optimal UAV as the gateway in each time slot. Moreover, we jointly optimized the task scheduling and resource allocation in the heterogeneous cloud infrastructure. We formulated the problem as a power consumption minimization problem under specific system stability constraints. A power-vs-delay trade-off was struck as well as an optimal solution relying on Lyapunov optimization was designed. Our numerical results showed that our gateway selection scheme has a better energy consumption performance than other schemes. Furthermore, our proposed task scheduling and resource allocation scheme reaches the optimal solution within a few iterative rounds and yields an improved QoS performance. These results confirm that the heterogeneous cloud structure is beneficial for constructing high-performance multi-UAV systems.

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