Securing Unmanned Aerial Vehicle Networks: Models and Algorithms (SpringerBriefs in Computer Science) [1st ed. 2024] 3031456041, 9783031456046

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Bin Duo • Xiaojun Yuan • Yifan Liu

Securing Unmanned Aerial Vehicle Networks Models and Algorithms

Bin Duo Chengdu, China

Xiaojun Yuan Chengdu, China

Yifan Liu Chengdu, China

ISSN 2191-5768 ISSN 2191-5776 (electronic) SpringerBriefs in Computer Science ISBN 978-3-031-45604-6 ISBN 978-3-031-45605-3 (eBook) https://doi.org/10.1007/978-3-031-45605-3 © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2024 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 Switzerland AG The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland Paper in this product is recyclable.

Preface

The fifth generation (5G) mobile communication network has been widely used in various typical scenarios, providing people with high data rate, high bandwidth, low latency, high coverage, and high reliability of quality of service (QoS). Numerous emerging applications, including autonomous driving, remote surgery, virtual and augmented reality (VAR), e-commerce, online education, telecommuting, contactless payments, intelligent transportation systems and machine-to-machine communication, have brought great convenience to people’s lives, all of which demonstrate the great potential of 5G technologies. However, the need for communication services remains unmet and challenging in remote areas that are not accessible to existing communication infrastructure (e.g., on the ocean or in deserts), or in unexpected or emergency situations, such as congestion or infrastructure disruption due to large-scale access to communications or terrestrial communication failures caused by natural disasters. Besides the improvement of conventional communication performance metrics, the sixth generation (6G) wireless networks will be more about real-time information sharing between all things, narrowing the digital divide, and realizing the real “Interconnection of Everything (IoE)”. According to experts’ predictions, after 2030, 6G will be a closed-loop autonomous network with characteristics such as highly intelligent, dynamic, and heterogeneous, and will become a key driver of information interaction and social life. 6G will not only enable universally intelligent, reliable, scalable, and secure terrestrial wireless networks, but also incorporate space, air, and sea to form a ubiquitous wireless network to meet the unlimited connection needs of “human-cyber-physical universe” anytime and anywhere with safety and reliability. The interconnection of the future 6G network means that a large number of Internet of Thing (IoT) devices that can connect to the network and intelligently collect real-world images and sensing information will be required. Unmanned aerial vehicles (UAVs), as typical aerial IoT devices in 6G network, with the advantages of high mobility, rapid deployment on demand, line-of-sight (LoS) transmission, and large service coverage, have attracted interest from academia and industry for UAV applications, and the global commercial UAV market is expected to surge to .45.8 billion by 2025. UAVs will play an important role in v

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Preface

expanding the coverage of 6G wireless networks as aerial mobile base stations, providing ubiquitous access from the air to user equipments in specific areas and situations (such as hotspots, large public places, and remote areas without network coverage). By combining UAVs with key technologies related to satellite, terrestrial, and maritime communications, 6G-integrated space-air-ground-sea networks can be leveraged to achieve global coverage. Despite the above advantages, when the UAVs are applied to 6G wireless networks, they need the support of control link and data link to complete their missions, which faces critical security threats owing to the broadcast nature of wireless channels. Specially, UAVs are vulnerable to severe interference from ground jammers (GJs) due to strong air-to-ground (AG) links (for example, unintentional interference from adjacent base stations or malicious interference from potential adversaries). If the GJs transmit with higher interference power, the communication quality between the ground nodes and UAVs may be degraded or even interrupted, which will lead to the failure of the UAV mission. Therefore, designing effective methods to protect UAV networks from interference is a challenging problem. Besides, the UAV networks are also vulnerable to eavesdropping by illegal ground nodes, which cause to the risk of leakage of some key confidential information, such as personal information, account passwords, etc. In particular, when UAV networks are deployed in different environments, such as rural, urban, and dense urban areas, the degree of security threats to which their networks are exposed and the corresponding analysis methods are also different. Therefore, how to adopt the proper channel models for accurately capturing the practical characteristics of different environments to improve the security of UAV networks is a new and challenging problem that needs to be solved in the current 5G and future 6Gintegrated UAV networks. Traditionally, the security of UAV networks can be protected from malicious interference by anti-jamming technologies such as channel access optimization, channel hopping, and ambient backscatter communication. For the problem of illegal eavesdropping, encryption methods can be used at higher communication protocol layers. However, a common disadvantage of channel access optimization and cryptography is that they require high computational complexity. In contrast, physical layer security technology, as an important supplement to upper-layer security, can take advantage of the inherent randomness of wireless channels, relying on signal processing, artificial noise, and other physical layer means to establish more favorable legal channel conditions without the need of secret keys and complex algorithms. Due to the advantage of flexible maneuverability, the flight trajectory of UAVs has a considerable impact on the performance of UAV networks, such as communication throughput, energy efficiency, and secrecy rate. Combined with physical layer security technique and UAV trajectory design, the UAV can be used as an air mobile base station, flying near legitimate ground nodes to send confidential information and staying away from malicious nodes’ attacks. It can also be used as an airborne mobile jammer, flying near the ground eavesdroppers to send jamming signals for confusion. Meanwhile, it keeps away from legitimate users to avoid unnecessary interference, thereby strengthening the legitimate link

Preface

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and weakening the eavesdropping link. Therefore, the joint design of UAV trajectory and physical layer security has become a promising solution to improve the secrecy performance of UAV networks. The book provides a systematic view on models and algorithms towards securing UAV networks. In addition, it presents appropriate channel models for various environments that UAV networks are exposed, possible technologies, and classic studies for UAV networks with physical layer security requirements. The book also outlines the future challenges and research directions to facilitate further studies on secure UAV networks. It covers the following topics: • • • •

UAV Air-to-Ground Propagation Scenarios and Models Energy-Efficient and Secure UAV Networks Elevation Angle-Distance Trade-Off for Securing UAV Networks Securing UAV Networks with the Aid of Reconfigurable Intelligent Surfaces

We wish that the book can help researchers with understanding how to select a proper channel model according to different propagation scenarios, and the mechanism by which the efficient optimization algorithms operate for safeguarding UAV networks. Chengdu, China

Bin Duo Xiaojun Yuan Yifan Liu

Acknowledgements

This work was supported by the Sichuan Science and Technology Program of China under Grants 2022YFQ0017 and 2023YFH0092, and in part by National Natural Science Foundation of China under Grant 62172060.

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Contents

1

Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.1 UAV Definitions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.2 UAV Networks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.3 Secure UAV Networks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.4 Physical Layer Security for UAV Networks . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.4.1 Trajectory Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.4.2 Cooperative Jamming. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.4.3 Passive Beamforming Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.5 The Importance of Channel Modeling on Securing UAV Networks . 1.6 Main Organization of the Book . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1 1 2 5 6 6 7 7 8 9

2

Air-to-Ground Channel Modeling and Generalized Algorithms . . . . . . . 2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2 UAV AG Propagation Scenarios . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2.1 Rural Environments. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2.2 Urban Environments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2.3 Dense Urban Environments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3 AG Propagation Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3.1 LoS Channel Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3.2 Probabilistic LoS Channel Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3.3 Rician Channel Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3.4 Comparioson of Different AG Channel Models. . . . . . . . . . . . . . . 2.4 General Problem Formulation for Securing UAV Networks . . . . . . . . . . 2.5 Time Discretization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.6 Block Coordinate Descent Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.7 Successive Convex Approximation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.8 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

11 11 12 12 12 13 13 13 14 16 17 18 19 19 20 21

3

Securing UAV Networks for Rural Areas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2 Security Threats in UAV Networks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2.1 Jamming Attacks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

23 23 24 25 xi

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3.2.2 Interception Attacks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2.3 Spoofing Attacks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2.4 DoS Attacks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2.5 Physical Attacks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3 Case Studies: Energy-Efficient UAV Secure Communication . . . . . . . . 3.3.1 System Model With Eavesdropping . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3.2 System Model With Jamming . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

25 26 26 26 27 27 37 48

4

Securing UAV Networks for Urban Areas. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2 Elevation Angle-Distance Trade-Off . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.3 Case Studies: 3D Trajectory Design for Securing UAV Networks . . . 4.3.1 System Model with Eavesdropping . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.3.2 System Model with Jamming . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.3.3 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

51 51 52 53 53 73 85

5

Securing UAV Networks for Dense Urban Areas . . . . . . . . . . . . . . . . . . . . . . . . . 5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.1.1 System Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.1.2 Transmission Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.1.3 CSI Assumption . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.1.4 Secrecy Rate Maximization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.2 Proposed Algorithm for Joint Uplink/Downlink Optimization . . . . . . . 5.2.1 Robust Solution to Transmit Powers . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.2.2 Robust Solution to Phase Shifts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.2.3 Robust Solution to UAV Trajectory . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.2.4 Overall Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.3 Numerical Results. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

87 87 88 89 92 93 94 95 99 102 106 107 113

6

Conclusions and Open Issues . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115

Reference . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119

Acronyms

3GPP 5G 6G AG AI AN AO AP AWGN BCD BR BS BVLoS CSCG CSI DDoS DoF DoS EE FAA FD GCS GE GJ GPS GS IoT IoE ITU KKT LAP

Third-Generation Partnership Project fifth generation sixth generation air-to-ground artificial intelligence artificial noise alternating optimization access point additive white Gaussian noise block coordinate descent best response base station beyond visual line of sight circularly symmetric complex Gaussian channel state information distributed denial of service degree of freedom denial of service energy efficiency Federal Aviation Administration full duplex ground control station ground eavesdropper ground jammer global positioning system ground source/sensor Internet of Things Interconnection of Everything International Telecommunication Union Karush-Kuhn-Tucker Low Altitude Platform xiii

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LIL LoS LoSC ML MM NLoS PLS PrLoSC QoS RF RIS RSI SCA S-curve SDR SINR TDMA UAV URA VAR WSN

Acronyms

loop interference level line of sight LoS channel machine learning majorization minimization non-line of sight physical layer security probabilistic LoS channel quality of service radio frequency reconfigurable intelligent surface residual self-interference successive convex approximation Sigmoid function semidefinite relaxation signal-to-interference-plus-noise ratio time division multiple access unmanned aerial vehicle uniform rectangular array virtual and augmented reality wireless sensor network

Chapter 1

Overview

1.1 UAV Definitions Aircrafts capable of operating without any human pilot onboard are known as drones or unmanned aerial vehicles (UAVs). UAVs can be controlled remotely by a human operator, or they can operate autonomously using pre-programmed flight plans [1]. UAVs are classified into different categories based on their weight, range, endurance, and capabilities. In the United States, the Federal Aviation Administration (FAA) has defined five categories for UAVs (more UAV classificaitons are shown in Fig 1.1) [2]: Micro UAVs—weigh less than 20 pounds; Small UAVs—weigh between 21 pounds and 55 pounds; Medium UAVs—weigh between 55 pounds and 1320 pounds; Large UAVs—weigh more than 1320 pounds; Experimental UAVs—used for research and development purposes. UAVs are becoming an increasingly important tool for many industries due to their versatility and cost-effectiveness. In agriculture, for example, UAVs can be used to monitor crops, assess soil conditions, and apply pesticides more efficiently [3]. In forestry, UAVs can be used to track changes in forest cover and assess the health of trees. In mining and construction, UAVs can be used for surveying and mapping, as well as for monitoring construction sites and tracking progress. UAVs offer advantages such as longer flight times and lower costs compared to traditional manned aircraft, as well as reduced risks to human pilots [4]. In addition, UAVs can be used for missions that would be too dangerous or difficult for human pilots, such as reconnaissance and search/rescue operations. Commercial use of UAVs has been on the rise in recent years. For instance, aerial photography and videography can provide stunning perspectives that are difficult or impossible to achieve with traditional cameras [5]. UAVs can also be used for building inspections, infrastructure monitoring, and even delivery services. As UAV technology continues © The Author(s), under exclusive license to Springer Nature Switzerland AG 2024 B. Duo et al., Securing Unmanned Aerial Vehicle Networks, SpringerBriefs in Computer Science, https://doi.org/10.1007/978-3-031-45605-3_1

1

2

1 Overview

Fig. 1.1 UAV classification

to advance, there is growing interest in developing UAVs that can operate beyond visual line-of-sight (BVLoS) [6]. BVLoS capabilities would enable UAVs to travel longer distances and perform more complex tasks, such as pipeline inspections and emergency response missions. However, BVLoS operations also pose new challenges and safety concerns, such as collision risk, airspace management, communication and control reliability, emergency response, and regulatory compliance, etc. Overall, the UAV market is expected to continue to grow in the coming years as more industries adopt this technology and new application cases are developed. With continued advancements in the state-of-the-art technologies and a focus on safety and responsible use, UAVs have the potential to transform many industries and offer new solutions to complex problems.

1.2 UAV Networks UAVs are becoming increasingly important for a wide range of applications, including military operations, commercial and industrial uses, and scientific research [7, 8]. One key aspect of UAVs is their ability to communicate with ground control stations (GCSs) and other aircrafts, enabling them to transmit data, receive instructions, and coordinate with other UAVs or manned aircraft. In this section, we will examine some of the key considerations related to UAV networks, including the technologies used, the challenges faced, and the latest trends and developments in this field. Broadly, the communication of UAV networks could be seperated into two different categories: command and control, and data communication. Command and control refers to the communication between the GCS and the UAV that allows operators to control the UAV’s movements, receive telemetry data, and monitor its status. Data communication refers to the transmission of information from the UAV to the GCS or other devices, such as cameras or sensors. There are several technologies that can be used for communications in UAV networks, including radio frequency (RF), satellite, and cellular networks. RF is the most common method used for UAVs operating within line-of-sight (LoS) ranges, as

1.2 UAV Networks

3

it is relatively low-cost and has low latency [9]. However, the UAV networks can be limited by the LoS requirement, which means that UAVs flying behind buildings or mountains may lose communication with the GCS. For BVLoS operations, satellite or cellular networks can be used to provide longer-range communication capabilities. However, these technologies have higher latency and can be more expensive. UAV networks also face several challenges related to security, bandwidth limitations, and interference. One major concern is the risk of signal interference or jamming, which can disrupt or disable UAV communication and potentially lead to accidents or loss of control [10]. UAVs can also be vulnerable to cyberattacks, wretapping or hacking, which can compromise the security and integrity of their communication systems. Additionally, as UAVs are capable of generating large amounts of data, there is a need for efficient and reliable data transmission and storage solutions that can handle the bandwidth requirements of high-resolution cameras and sensors. Despite these challenges, the use of UAVs for various applications is growing rapidly, and the demand for reliable and secure communication systems is driving significant innovation in this field. One emerging trend in UAV communication is the use of artificial intelligence (AI) and machine learning (ML) to improve communication capabilities and enable more advanced autonomous operations [11, 12]. For example, AI algorithms can be used to optimize the communication protocol, minimize latency, and reduce the risk of signal interference or jamming. Other trends include the development of lightweight and low-power communication hardwares, the integration of multiple communication technologies into a single system, and the adoption of open standards and protocols to facilitate interoperability between different UAVs and GCSs. To further elaborate on the topic of UAV networks, it is worth exploring some of the specific applications that are driving their development. In military, UAVs are used for reconnaissance, surveillance, and target acquisition, as well as for conducting airstrikes or delivering payloads. In these scenarios, the communication network is essential for ensuring that the UAVs can operate safely and effectively, while minimizing the risk of collateral damage or friendly fire. In commerce and industry, UAVs are increasingly being used for tasks such as aerial mapping, inspection of infrastructure and buildings, and delivery of goods. In these applications, UAV communication is critical for ensuring that the UAV can safely navigate around obstacles, collect and transmit accurate data, and perform tasks with minimal human intervention [13]. For example, in the oil and gas industry, UAVs are used to inspect pipelines, oil rigs, and other critical infrastructure, where the communication is essential for identifying potential problems and ensuring that maintenance or repairs can be carried out as quickly and efficiently as possible. Another area where UAV network is of growing importance is in the field of scientific research. UAVs are increasingly being used to collect data on the environment, including temperature, humidity, atmospheric conditions, and other factors [14]. These data are used to support research on topics such as climate

4

1 Overview

Fig. 1.2 Application scenarios of UAV communication networks

change, ecology, and biodiversity, and can help scientists to better understand the complex interactions between different natural systems. In these scenarios, communication is essential for ensuring that the data collected by the UAV is transmitted and processed in real-time, allowing scientists to make timely and informed decisions based on the latest information [15]. As the field of UAV networks continues to evolve, there are several key areas of research and development that are likely to be of particular importance. One of these is the development of advanced communication protocols and standards that can enable different UAVs and GCSs to communicate with each other seamlessly, even when using different technologies or operating in different environments. Another area of focus is the development of more efficient and robust data transmission and storage solutions, which can help to minimize latency and improve the reliability of UAV networks. Overall, UAV network is a rapidly evolving field that is essential for the safe and effective operation of UAVs in a wide range of applications. With ongoing research and development, we can expect to see significant advances in this field, enabling more advanced and sophisticated employment of UAVs in the years to come. Figure 1.2 represents more application scenarios of UAV networks.

1.3 Secure UAV Networks

5

1.3 Secure UAV Networks The burgeoning UAV market holds considerable promise for the growth of fifthgeneration (5G) cellular network [16]. For ensuring the reliability of communication for the UAVs deployed widely in the future, a feasible option could be the application of the integrated UAVs served by the terrestrial base stations (BSs), in the form of new aerial customers [17]. The current cellular network has been known to support the needs of basic communication of the UAVs, as demonstrated by the recent research conducted by the Third Generation Partnership Project (3GPP) [18]. However, due to the decreasing size of BSs and relays, to enhance the communication services to the terrestrial customers, it would be practically more efficient to establish supplementary aerial communication platforms under the 5G cellular networks or to mount them on UAVs. Nevertheless, certain new challenges that arise in the integration of the 5G networks with UAVs need to be addressed. As against the terrestrial wireless channels being riddled with the problems of multi-path fading, shadowing, and significant path loss, the high-altitude deployment of the UAVs provides stronger LoS channels (LoSCs) with ground nodes. Therefore, for applications of UAVs in the wireless networks in the future, additional concerns of security will be raised against the unique LoS-dominant air-to-ground (AG) channel. Specifically, Fig. 1.3 demonstrates the transmission or forwarding of confidential messages to a trusted node on the ground from the UAV in the form of an aerial GCS or an aerial relay, as illustrated in Fig. 1.3a, b, respectively. Nevertheless, the ability

Fig. 1.3 Adversarial activities targeting legitimate UAV communications in 5G wireless networks, including eavesdropping and jamming attacks

6

1 Overview

of the eavesdropper in receiving the signals on the ground can also be enhanced by the robust links. As a consequence, the LoS link between the UAV and the ground node can allow a distant eavesdropper to clearly intercept AG transmissions. Moreover, in Fig. 1.3c, d, the UAV operates as a mobile hub in the collection of private data from Internet of Things (IoT) devices on the ground such as various sensors, or as an aerial user in the receiving of control signals from its serving GCS. Under such circumstances, there can be a complete failure of AG transmission or severe degradation of the reception quality owing to powerful jamming attacks lanched by ground jammers (GJs) via the AG LoS links. Hence, compared to the terrestrial communications, the AG trasnmission links tend to be more susceptible to terrestrial jamming and eavesdropping. Thus, ensuring the secure communication of UAVs in future wireless networks presents a novel and challenging problem that needs to be addressed urgently. It is noted that to counter jamming or eavesdropping attacks in terrestrial wireless networks, physical layer security (PLS) has been studied thoroughly in the literature. Some typical techniques against eavesdropping are transmit beamforming, cooperative jamming, and artificial noise (AN). In contrast, at the physical layer, two most widely used approaches for anti-jamming are the direct sequence spread spectrum and the frequency hopping spread spectrum. Nevertheless, for the security of UAV networks, these solutions may be unsuccessful in coping with the more difficult and new challenges due to the LoS-induced security issues. In the following section, we review the established pysical layer security techniques for securing UAV networks.

1.4 Physical Layer Security for UAV Networks The physical layer of a wireless system is the lowest layer in the communication protocol stack, and it deals with the transmission and reception of the wireless signals between the transmitter and receiver. PLS techniques use the physical properties of the wireless signals to provide security against eavesdropping, interference, and other attacks. In UAV networks, PLS techniques can be used to secure the communication links between the UAVs and the GCSs or other UAVs. One of the primary challenges in securing UAV networks is the broadcast nature of the wireless medium. The signals transmitted by the UAVs can be intercepted by eavesdroppers or interfered by malicious jammers, which can lead to the compromise of sensitive information or the disruption of the network operation. We will then discuss some interesting PLS technologies.

1.4.1 Trajectory Design Trajectory design in UAV networks is an important problem that involves determining the optimal path or paths for a group of UAVs to traverse in order to

1.4 Physical Layer Security for UAV Networks

7

achieve a specific objective. This problem is important in various fields, including surveillance, search and rescue, and package delivery, where multiple UAVs may work together to cover a large area or deliver packages to multiple locations efficiently. In order to design the best trajectory for a UAV network, various optimisation techniques can be used, such as convex optimisation methods [19], reinforcement learning [20, 21], etc. These optimisation techniques can help find the best route for a UAV to achieve its mission objectives (e.g., maximizing secrecy rates), taking into account various constraints and factors (such as signal to interference plus noise ratio (SINR) constraints).

1.4.2 Cooperative Jamming Cooperative jamming in UAV networks is a technique used to enhance the security and reliability of communication links between UAVs and their GCSs. It involves the use of multiple UAVs working together to create a cooperative jamming system, which can improve the effectiveness of jamming and reduce the likelihood of signal interference. As discussed in [22], since unscheduled users may be potential eavesdroppers, a cooperative jammer UAV can be used to support the transmission of confidential data to a scheduled user by sending jamming signals. Furthermore, as proposed in [23], the cooperative jammer UAV can be a useful solution to enhance secrecy performance when UAV relays are deployed to forward information between source and destination nodes. However, it is important to note that cooperative jamming can also have negative consequences if used improperly. For example, if the jamming system is not properly coordinated, it may cause interference with other communication systems in the surrounding area, leading to safety hazards and potential legal issues. Therefore, it is important to ensure that the cooperative jamming system is designed and implemented in a safe and responsible manner.

1.4.3 Passive Beamforming Design Reconfigurable intelligence surface (RIS) is a new technology that has the potential to revolutionize wireless communication networks, including UAV networks[24, 25]. RIS is a surface composed of a large number of small reflecting elements, which can be individually controlled to manipulate the phase and amplitude of the reflected signal. This allows for the creation of a reconfigurable reflecting surface that can enhance the signal quality and coverage area of wireless communication links. In UAV networks, RIS can be used to improve the communication links between UAVs and GCSs. The reflecting elements can be designed to reflect the signal towards the desired direction. This results in increased signal strength and reduced

8

1 Overview

interference or information leakage leading to a more reliable communication link. Therefore, RIS design in UAV networks has the potential to significantly improve the performance of wireless communication links, particularly in challenging environments where the signal strength is weak or subject to interference or eavesdropping.

1.5 The Importance of Channel Modeling on Securing UAV Networks Accurate channel modeling for different AG propagation environments has an important impact on the secure communication in UAV networks, since it can provide an accurate description of channel behavior, so as to better understand and respond to various transmission characteristics under jamming and eavesdropping attacks. Therefore, to improve the security of UAV networks, it is imperative to adopt proper channel models for different AG propagation environments, due to the following reasons: Communication Performance Prediction Accurate channel modeling can simulate and analyze factors such as fading, multipath effects, and interference in AG wireless channels to better evaluate and predict metrics such as reliability, secrecy rate, throughput, and transmission delay of communication links, which helps design and optimize communication systems to meet the requirements of secure communications in UAV networks. Security Assessment Accurate channel modeling can help assess the security of UAV networks. By adopting an accurate model of AG wireless channels, it is possible to analyze and predict potential threats and attacks in the channel, such as interference or eavesdropping. This helps to design and implement appropriate security mechanisms and defense strategies to protect the confidentiality and integrity of UAV communications. Performance Optimization Accurate channel modeling can help optimize the performance of UAV communication systems. By understanding the characteristics and trends of channels, appropriate UAV trajectories, scheduling algorithms, power control strategies, and resource allocation methods can be designed to maximize the throughput, secrecy rate and energy efficiency (EE) of communication systems. In addition, it can also be used to optimize active and passive beamforming design for significantly improving the signal-to-noise ratio (SNR) and gain of signal reception, thereby enhancing the transmission distance and coverage of UAV secure communication. Communication Link Planning Accurate channel modeling is critical to the planning and design of UAV communication links. By establishing an accurate channel model, parameters such as the coverage, transmission distance and capacity of the

1.6 Main Organization of the Book

9

channel can be predicted to guide the deployment and planning of the UAV network. This helps ensure the reliability, security, and stability of the communication links, reducing the risk of communication interruptions, leaks, and information transmission errors. It is noted that the UAV AG wireless channels are always dynamic and timevariant, and are affected by the environment and conditions. Therefore, channel modeling needs to be updated and adjusted as environmental conditions change. Only on the basis of accurate modeling and analysis of AG wireless channels can the secrecy performance of UAV networks be better optimized.

1.6 Main Organization of the Book The book discusses various algorithms for securing UAV networks based on different channel models. It contains a total of 5 chapters. The current chapter (Chap. 1) gives an overview of secure threats in UAV networks at the physical layer and discusses the impact of accurate channel modeling on secure communication of UAVs. Chapter 2 provides a thorough analysis of various channel models related to different environments for AG communications, and a general problem for secure UAV-enabled networks is formulated and several useful techniques for solving the problem are introduced. Chapter 3 mainly focuses on securing UAV networks for rural areas, and two cases of energy-efficient UAV secure communications are investigated by considering the limited on-board energy of UAVs. In Chap. 4, elevation angle-distance trade-off is discussed for securing UAV networks in urban areas, and the main techniques for joint 3D UAV trajectory and communication resource design are studied. Chapter 5 discusses reconfigurable intelligent surface technique as an efficient solution for enabling security for UAV networks in dense urban areas.

Chapter 2

Air-to-Ground Channel Modeling and Generalized Algorithms

2.1 Introduction As technological advancements continue to progress in the field of UAVs, their potential applications are vast and diverse, ranging from surveillance and aerial photography to agriculture and emergency rescue. This growth is anticipated to be significant, with the FAA predicting a tripling of the UAV market by the end of 2023 [26]. In particular, UAVs can play a crucial role in improving the quality of service (QoS) requirements of various users in smart cities by taking advantage of fog and mobile edge computing techniques, providing higher data rates and reduced latency. However, the open nature of wireless channels and the dominance of LoS links make UAV networks highly vulnerable to eavesdropping or jamming by unauthorized GCSs. Therefore, to enable the widespread deployment of UAVs in 5G and beyond networks, it is imperative to investigate AG propagation models for effectively improving the secrecy performance of UAV networks [27]. AG communication channels possess distinctive characteristics compared to terrestrial ones. The employment of UAVs in various environments such as rural, urban, or dense urban areas results in unique security concerns. For instance, the LoSC model is suitable for communication-oriented UAV trajectory design in rural environments or at high altitudes due to its simplicity and accuracy [28]. On the other hand, the Rician fading channel and probabilistic LoS channel (PrLoSC) models are more appropriate for urban settings. In dense urban areas where shadowing effect tends to be dominated by small-scale attenuation and as the UAVs fly at high altitudes, Rician fading channels are used more frequently. For coverage optimization, UAV placement, or the theoretical analysis of the UAV networks, LoS probability-based models are usually adopted [29]. Nonetheless, since they provide different trade-offs between the modeling accuracy and analytical tractability, the communication scenarios form the base for the selection of the most appropriate channel models for secure UAV communications. Thus, safeguarding legitimate

© The Author(s), under exclusive license to Springer Nature Switzerland AG 2024 B. Duo et al., Securing Unmanned Aerial Vehicle Networks, SpringerBriefs in Computer Science, https://doi.org/10.1007/978-3-031-45605-3_2

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2 Air-to-Ground Channel Modeling and Generalized Algorithms

UAV networks in diverse environments presents a novel and complex problem that requires careful consideration. Motivated by the above concerns, in this chapter, we conduct an extensive study on different channel models related to AG propagation scenarios.

2.2 UAV AG Propagation Scenarios Rural (suburban), urban, and dense urban are terms used to describe different types of human settlements or communities based on their physical characteristics, population density, and socio-economic factors.

2.2.1 Rural Environments Rural areas are typically located on the outskirts of urban centers, and are characterized by lower population densities, larger residential lots, and a more dispersed layout. Rural areas often have more single-family homes, lower-rise apartment buildings, and more open spaces than urban areas, and are often associated with a more relaxed, family-friendly lifestyle. LoSCs are more suitable for rural environments because they typically have fewer obstacles, such as buildings and trees, which can obstruct the AG signal propagation [30]. For a LoSC model, the signal propagates directly from the UAV to the GCS without encountering significant obstacles. This means that the signal attenuation and SNR are typically better in LoSCs, which can lead to higher quality and more reliable communication. In rural environments, the terrain is often flat, and there are fewer man-made structures that can block the signal. This makes it easier for the UAV and the GCS to maintain a clear LoS transmission, even over long distances. In addition, rural areas often have lower levels of electromagnetic interference, which can further improve the quality of the communication in LoSCs [31]. In contrast, in urban environments, the presence of buildings and other obstacles can make it difficult to maintain a clear AG transmission link. The signal can be blocked or reflected by buildings, causing signal attenuation and interference. This can lead to a higher error rate and lower signal quality in non-LoS (NLoS) channels. LoSC model cannot effectively capture the non-LoS states in urban areas. The corresponding methods for securing UAV networks in urban areas based on LoSC may lead to significant secrecy performance loss.

2.2.2 Urban Environments Urban areas are typically more densely populated than rural areas, with a higher concentration of people living and working within a smaller geographic area. Urban

2.3 AG Propagation Models

13

areas are characterized by a mix of residential, commercial, and industrial land uses, and a more compact and centralized layout. Urban areas often have taller buildings, more public transportation options, and a greater diversity of people and cultures than suburban areas. Probabilistic LoS (PrLoS) channels are more suitable for urban environments because they can take into account the complex and unpredictable nature of signal propagation in highly built-up areas. In urban environments, the presence of buildings, trees, and other obstacles can obstruct the LoS transmission between the UAV and the GCS, resulting in more NLoS paths. PrLoSCs consider the LoS probability that can vary depending on the environment and other factors. In urban areas, where NLoS paths are more common, PrLoSCs can provide a more accurate representation of the signal propagation and shadowing effect between the UAV and the GCS. Furthermore, PrLoSCs can be used to optimize the UAV’s threedimensional (3D) trajectory to maximize the LoS probability with the GCS. For example, the UAV can be programmed to fly at a certain altitude or to avoid flying in areas with a high probability of NLoS paths.

2.2.3 Dense Urban Environments Dense urban areas are a subset of urban areas that are even more densely populated, with a higher concentration of people and buildings within a smaller geographic area. Dense urban areas are often associated with high-rise apartment buildings, crowded streets and public spaces, and a greater diversity of land uses and cultures. Rician channels are more suitable for dense urban environments compared to other wireless channel models because they can accurately model the complex signal propagation effects, including reflections, diffraction, and scattering caused by the high density of buildings and other obstacles. Due to these negative effects, the signal from the UAV to the GCS can experience significant interference and attenuation. Rician channel model is particularly useful in these scenarios because it takes into account the LoS path as well as the scattered signal paths, allowing for an accurate representation of the signal strength and the distribution of the scattered signals.

2.3 AG Propagation Models 2.3.1 LoS Channel Model With out consideration of small-scale fading and shadowing effects, the LoSC model, as the most appropriate one in the absence of signal reflection or obstruction, can represent an ideal rural scenarios. Thus, for the free space loss model, the channel power gain could be determined simply as

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2 Air-to-Ground Channel Modeling and Generalized Algorithms

Fig. 2.1 UAV communication network in urban environments

β(d) = β˜0 d −2 ,

.

(2.1)

where .β˜0 is the channel power at the reference distance of .1 m and d is the distance between the UAV and the GCS. UAV networks in earlier works involve the optimization of the offline UAV trajectory. The LoSC model has been extensively used, as it provides a simple and accurate representation of the channel power gain based on the transmitter-receiver distance [28]. It is a reasonable approximation in rural areas with minimal blockage or scattering, or when the UAV operates at a high altitude where a clear LoS link can be established with the ground node. However, as shown in Fig. 2.1, the LoSC model falls short in urban environments where the UAV’s flying altitude is low compared to that of buildings, leading to significant reflection and scattering that may interfere with the signal. To address this issue, more sophisticated channel models are required to accurately account for the changing propagation environment as the UAV’s altitude varies. Two commonly used approaches are to adjust channel modeling parameters based on UAV altitude or elevation angle, or to adopt a PrLoSC model that randomly represents LoS and NLoS states with a specific probability distribution. These details will be discussed in the following sections.

2.3.2 Probabilistic LoS Channel Model The AG propagation environment is commonly classified based on the type of urban areas. The International Telecommunication Union (ITU) offers the most widely

2.3 AG Propagation Models

15

accepted classification for urban areas. In its recommendation document [32], the ITU proposes a standardized model for urban areas based on three straightforward parameters: .α, .β, and .γ . These parameters provide a reasonable representation of the general geometrical statistics of a given urban area in which RF signals propagate. The parameters are defined as follows: • .α denotes the dimensionless ratio of built-up land area to the total land area; • .β represents the average number of buildings per unit area in terms of buildings per square kilometer (.km2 ); • .γ is a scale parameter that characterizes the distribution of building heights, following a Rayleigh probability density function  2 −h h , exp .P (h) = 2 γ 2γ 2

(2.2)

where h is the building height in meters (m). Following the mathematical steps in [32], we can write the resulting LoS probability in a single equation as: ⎡

⎛ 

⎜ ⎢ hTX − m ⎢ ⎜  ⎜ ⎢ .P(LoS) = ⎢1 − exp ⎜− ⎜ ⎢ n=0 ⎣ ⎝



2 ⎞⎤

n+ 21 (hTX −hRX ) m+1

2γ 2

⎟⎥ ⎟⎥ ⎟⎥ ⎟⎥ , ⎟⎥ ⎠⎦

(2.3)

  √ where .m = (r αβ − 1) , r is the ground distance between the transmitter and the receiver, and n is the product index. Equation (2.3) is a generic formula that can be applied to any transmitter and receiver heights .hTX and .hRX . A similar geometric approach for estimating the LoS probability in built-up areas was employed in [9], but without using the ITU parameters. For a Low Altitude Platform (LAP), .hRX can be disregarded since it is significantly lower than both of the LAP altitude and the average building height. In this case, the ground distance can be computed as .r = hLAP / tan(θ ), where .hLAP is the LAP altitude. It is important to note that for large .hLAP , the LoS probability .P(LoS) can be considered as a continuous function of elevation angle .θ and the environmental parameters. The LoS probability was plotted in Fig. 2.2 for four selected urban environments: Suburban .(0.1, 750, 8), Urban .(0.3, 500, 15), Dense Urban .(0.5, 300, 20), and Highrise Urban .(0.5, 300, 50) for .α, β, and .γ , respectively. It can be observed that the LoS probability can be approximated closely to a modified Sigmoid function (S-curve), which can be expressed as follows: P(LoS, θ ) =

.

1 , 1 + a exp(−b[θ − a])

(2.4)

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2 Air-to-Ground Channel Modeling and Generalized Algorithms

Fig. 2.2 LoS probability with respect to elevation angle

where a and b are called here the S-curve parameters. According to Eq. (2.4), this model is based on the elevation angle rather than the horizontal distance and height of the UAV, which is different from the model proposed by ITU. To clarify this, we assume .a = 11.95 and .b = 0.14, which corresponds to the urban environment. As shown in Fig. 2.3, the approximation errors between the LoS probabilities proposed in [9] and in [32] are extremely small and thus can be ignored. In fact, from Fig. 2.3, it is also observed that the PrLoSC model proposed in [32] suffers from errors for approximating the dense urban/high-rise urban environment, which may cause certain performance loss.

2.3.3 Rician Channel Model Practically, the AG transmissions are impacted not only by large-scale path loss, but also by the small-scale fading. Therefore, it is necessary to consider both of the fading for a more precise performance evaluation. To this end, the Rician model has been widely used, which both the LoS and scattered components that provide a more realistic representation of real-world wireless channels. The channel gain of the Rician channel can be mathematically expressed as:

2.3 AG Propagation Models

17

Fig. 2.3 Comparison of the ITU-R model and elevation model in different urban environments

 g=

.

K˜ K˜ + 1

 g(d) +

1 g, ˜ ˜ K +1

(2.5)

where .g(d) denotes the deterministic LoSC component with .|g| = 1, g˜ represents the random scattered component which is a zero-mean unit-variance circularly symmetric complex Gaussian (CSCG) random variable, and .K˜ denotes the Rician factor of the channel.

2.3.4 Comparioson of Different AG Channel Models Rician channel, PrLoSC, and LoSC models are all suitable for UAV communication network in different types of AG propagation scenarios, depending on the specific characteristics of the environment and the requirements of the communication network. In situation of clear LoS link between the GCS and the UAV, the LoSC seems to be the most appropriate for the UAV communication network with low levels of

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2 Air-to-Ground Channel Modeling and Generalized Algorithms

obstruction in urban scenarios. Providing an unobstructed and direct path between the GCS and the UAV, and in situations where low latency and high data rates are required, this type of channel has been found to be most suitable for UAV networks. In case of the probability of establishing a clear LoS link between the GCS and the UAV being significant, and with moderate-to-high levels of obstruction in the urban areas, the PrLoSC has been found to be an appropriate alternative. Adapting to the LoS or NLoS states of the changing environment, this type of channel could be applied for analyzing the elevation-distance trade-off for enhancing the performance of UAV networks. Rician channel is well-suited for UAV communication network in urban environments with tall buildings, narrow streets, and other obstacles that can cause reflections and multipath effects. Under the NLoS communication environments, this type of channel has been found to be suitable in designing UAV networks that are robust against interference caused by reflections and fading.

2.4 General Problem Formulation for Securing UAV Networks Unlike traditional terrestrial communication infrastructure, which includes GCSs, access points (APs), and relays, the UAV-equipped communication platform can move dynamically to meet communication demand. This provides a new design degree of freedom (DoF), i.e., UAV trajectory optimization, which can enhance the legitimate channel and limits the unlawful eavesdropping or jamming channel, thus improving the security. In this section, for securing the UAV networks, the main techniques utilising the fully controllable UAV mobility will be discussed. Consider a UAV-enabled downlink communication network in which the legitimate communication between a UAV and a ground node is intercepted/interfered by K eavesdroppers/jammers on the ground. The trajectory of the UAV is denoted by .q(t), which captures its time-varying locations. The relevant communication resource allocations, including transmit power, bandwidth, channel allocation, and so on, are represented by .r(t). To optimize both the UAV trajectory and communication resources, we formulate the following mathematical problem: .

max

U ({q(t)}, {r(t)}).

(2.6)

{q(t)},{r(t)}

s.t. fi ({q(t)}) ≥ 0,

i = 1, . . . , I1 , .

(2.7)

gi ({r(t)}) ≥ 0,

i = 1, . . . , I2 , .

(2.8)

hi ({q(t)}, {r(t)}) ≥ 0,

i = 1, . . . , I3 ,

(2.9)

where .U (·, ·) is the utility function for evaluating the secure performance, .fi (·) represent the UAV mobility constraints, some of which are discussed in the

2.6 Block Coordinate Descent Algorithm

19

following, .gi (·) denote the communication resource constraints, and .hi (·) specify the coupled constraints involving both the UAV trajectories and communication resource allocation.

2.5 Time Discretization To optimize the UAV trajectory, we can divide the given time horizon .[0, T ] into N equal time slots with suitably short length .δt , where .T = N δt . The maximum speed of the UAV is indicated by .Vmax . To guarantee that the length of each segment does not exceed .Δmax, even at the fastest flying speed, .δt should be chosen as .δt ≤ Δmax /Vmax . This means that the necessary minimum number of segments for time discretization is N . As a consequence, the continuous UAV trajectory .q(t) can be approximated as a sequence of N segments, denoted as .{q[n]}N n=1 , where the sequence must satisfy the UAV’s maximum speed and acceleration. It should be noted that a larger N will lead to greater complexity, but we can always satisfy better performance as well as any necessary accuracy of the adopted discrete-time approximation by selecting a minimum N , i.e., .N ≥ Vmax T /H max , which .max is a given threshold, and H is the flying altitude of the UAV. Thanks to time discretization, it is straightforward to integrate the UAV’s mobility constraints, such as its position, speed, and acceleration, into the optimization problem (2.6).

2.6 Block Coordinate Descent Algorithm By applying the time discretization technique mentioned above, problem (2.6) can be rewritten as .

max

U ({q[n]}, {r[n]}).

(2.10)

{q[n]},{r[n]}

s.t. fi ({q[n]}) ≥ 0,

i = 1, . . . , I1 , .

(2.11)

gi ({r[n]}) ≥ 0,

i = 1, . . . , I2 , .

(2.12)

hi ({q[n]}, {r[n]}) ≥ 0,

i = 1, . . . , I3 ,

(2.13)

In general, problem (2.10) happens to be a non-convex problem. However, the block coordinate descent (BCD) approach is an efficient strategy for getting a locally optimum solution to the non-convex problem by updating one block of variables alternately while keeping other blocks constant [33, 34].   At the lth iteration, the current UAV trajectory is denoted as . q (l) [n] . We solve  (l)  the subproblem of problem (2.10) by fixing .q[n] to . q [n] to obtain optimized   resource allocation, denoted by . r (l+1) [n] . Then, with .r[n] in problem (2.10) being

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2 Air-to-Ground Channel Modeling and Generalized Algorithms

    fixed to . r (l+1) [n] , we optimize the UAV trajectory to obtain . q (l+1) [n] . The process of iteration continues until convergence. Note that the resulting communication resource optimization problem for any fixed UAV trajectory has been extensively studied in traditional terrestrial communication systems, and the developed approaches may be used directly. The UAV trajectory optimization problem is relatively new and typically non-convex due to the non-concave objective functions and non-concave constraints associated with UAV trajectory .q[n] in any fixed communication resource allocation. In the next section, we examine the successive convex approximation (SCA) method as an efficient technique for solving non-convex UAV trajectory optimization problems.

2.7 Successive Convex Approximation For any fixed communication resource allocation in problem (2.10), the resulting UAV trajectory optimization subproblem can be expressed concisely as follows: .

max f0 ({q[n]}).

(2.14)

{q[n]}

s.t. fi ({q[n]}) ≥ 0,

i = 1, . . . , I,

(2.15)

where .f0 (·) is the utility to be maximized and .fi (·) are the equivalent constraints in Eqs. (2.11) and (2.13) for the UAV trajectory with .I = I1 + I3 . If at least one of the functions .fi (·) is non-concave with respect to .q[n], i = 0, 1, . . . , I , then the problem is non-convex. Due to the fact that the majority of utility and constraint functions are non-concave over .q[n], traditional convex optimization techniques cannot be used directly. Ensuring a monotonic convergence to a Karush-KuhnTucker (KKT) solution, the SCA as a valuable technique can convert a non-convex optimization problem into a series of convex optimization problems [35]. SCA is an iterative optimization technique. Specifically, for iteration l, define   the presently acquired UAV trajectory as . q (l) [n] , based on which we need to first establish a global convex lower bound for those non-concave functions .fi ({q[n]}) in (2.14)–(2.15), such that (l)

fi ({q[n]}) ≥ fi,lb ({q[n]}).

.

(2.16)

Then, by replacing those non-concave functions .fi ({q[n]}) in (2.14)–(2.15) with we have the following optimization problem:

(l) .f i,1 b ({q[n]}),

.

(l) max f ({q[n]}), . {q[n]} 0,lb (l) s.t. fi,lb ({q[n]}) ≥ 0,

(2.17) i = 1, . . . , I.

(2.18)

2.8 Summary

21

By using the readily available software tool like CVX [36] and through standard convex optimization techniques, the convexity of the above problem has been established as   all the functions in (2.17) and (2.18) have been concave functions. Let . q (l) [n] denote the optimal solution to problem (2.17). Owing to the global   lower bound established by (2.16), it can be readily observed that . q (l) [n] is a feasible solution for the non-convex problem (2.14) and the obtained optimal value serves as a lower bound for problem (2.14). Moreover,  assuming  that at the lth iteration, the lower bound (2.16) is tight at the local point . q (l−1) [n] , i.e., (l)

fi,lb

.

    q (l−1) [n] = fi q (l−1) [n] ,

(2.19)

  the sequence .f0 q (l) [n] exhibits monotonic growth and converges to a finite limit. Assuming an additional requirement for a tight gradient at the local point, i.e., (l)

∇fi,lb

.

    q (l−1) [n] = ∇fi q (l−1) [n] ,

(2.20)

  under some mild constraint qualifications, . q (l) [n] converges to a solution fulfilling the KKT conditions of problem (2.14). Consequently, a KKT solution to the non-convex trajectory optimization   problem (2.14) can be achieved by iteratively changing the local point . q (l) [n] and successfully resolving a series of convex optimization problems.

2.8 Summary In this chapter, we have presented a survey and analysis for typical AG propagation environments of UAV networks. The corresponding channel models to simulate these environments were also discussed. For securing UAV networks, the general problem formulation was provided and the algorithms for such problem was described, which lays a solid theoretical foundation for the following design of optimization algorithm and performance analysis.

Chapter 3

Securing UAV Networks for Rural Areas

3.1 Introduction UAVs have been widely used in wireless communication networks due to their manoeuvrability, low cost and LoS AG links [37]. Despite the rapid development of UAV networks, there are still new challenges when UAVs implement their missions in rural areas. Due to the dominant LoS links, legitimate UAV communications are more susceptible to wiretapping or interference caused by ground eavesdroppers (GEs) or jammers [38], which may lead to the failure of UAV missions. Fortunately, we can take the advantage of the high mobility of UAVs by designing appropriate trajectories and incorporating PLS techniques to improve the security of UAV communications. For example, the authors in [39] studied the secure UAV network and improved the average secrecy rate by jointly optimising the resource allocation as well as the UAV trajectories in a given time duration. A dual UAV network was studied in [40] and [41], in which one UAV communicates with legitimate ground users while the other UAV sends jamming signals to GEs to safeguard the secrecy of the network. Recently, various anti-interference strategies have been investigated through all sorts of cutting-edge techniques in UAV-enabled wireless communication networks. For instance, to counter sophisticated jamming effects in UAV networks, an iterative Bayesian Stackelberg algorithm based on subgradients was proposed in [42]. For the UAV-aided cellular network in [43], the authors used deep reinforcement learning and transfer learning to maximize the UAV transmit power against jamming. The effectiveness of UAV networks in the presence of jammers was explored in [44] by using an enhanced Q-learning algorithm. The research in [45] investigated a deep Q-network-based power allocation technique to strengthen UAV communication network against intelligent jamming attacks. UAV trajectory design is another key technique that can effectively avoid interference caused by malicious jammers. The authors in [46] proposed a best response (BR) based algorithm to obtain Stackelberg equilibrium by optimising © The Author(s), under exclusive license to Springer Nature Switzerland AG 2024 B. Duo et al., Securing Unmanned Aerial Vehicle Networks, SpringerBriefs in Computer Science, https://doi.org/10.1007/978-3-031-45605-3_3

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3 Securing UAV Networks for Rural Areas

the trajectory of the UAV, which effectively resist jamming attacks. The authors in [47] optimised the trajectory of the UAV to maximise the SINR in a UAV relay network in the presence of interference. The authors in [48–50] investigated trajectory planning algorithms to improve the quality of communication services in UAV wireless networks affected by intentional interference. Due to the limited on-board energy of UAVs, it is necessary to study energyefficient UAV trajectory optimisation methods to extend the operating time of UAVs. The authors in [51, 52] derived theoretical energy consumption models for rotarywing UAVs and fixed-wing UAVs, respectively. The authors in [53] maximised the secrecy EE of a full-duplex UAV network by jointly optimising the transmit power and the trajectory of the UAV. The problem of energy-efficient cooperative secure transmission in multi-UAV wireless networks was considered in [54], and the EE is effectively improved by optimising the UAV trajectory. In this chapter, we examine how the security of UAV networks in rural areas can be enhanced. To this end, we first provide a brief overview of possible security attacks on UAV-supported wireless networks. Then, we discuss two case studies of energy-efficient secure UAV networks in terms of eavesdropping and jamming, respectively.

3.2 Security Threats in UAV Networks UAV networks are vulnerable to security attacks, firstly because UAVs use wireless communication channels to interact with GCSs, which can be intercepted or compromised by attackers using a variety of techniques. This makes UAV networks vulnerable to attacks such as jamming and interception. Secondly, because UAVs have limited processing power, this makes them vulnerable to attacks that can overwhelm their processing power. For example, a Denial of Service (DoS) attack can flood a UAV with requests or packets, causing it to crash or lose connectivity. Finally, because UAVs are commonly used for sensitive tasks such as surveillance, data collection and the delivery of critical payloads. An attacker could target these payloads or data collected by the UAV, leaving it open to interception and theft. Overall, the wireless and remotely manipulated nature of UAV networks, combined with their limited processing power and mission sensitivity, make them an attractive target for attackers. The security of UAV networks refers to the protection of the communication systems, data, and devices used in the operation of UAVs from unauthorized access, modification, theft, or destruction. This involves implementing security measures such as encryption, access controls, intrusion detection, and threat monitoring to ensure the integrity, confidentiality, and availability of UAV networks. It also involves establishing protocols and guidelines for securing UAV networks, and mitigating potential cyber threats that may impact the reliability and security of the network.

3.2 Security Threats in UAV Networks

25

Security threats to UAV networks are usually divided into active and passive attacks [55]. Active attacks mainly attempt to alter network data and thus affect the exchange of information in UAV networks, while passive attacks do not affect network operations and their main purpose is to steal information from the network. In the following we will describe some of the traditional security attacks in UAV networks.

3.2.1 Jamming Attacks Jamming attacks on UAV networks are a type of security attack where an attacker transmits a high-power signal on the same frequency used by the UAV networks, disrupting the communication link between the UAV and its control station. As a result, the UAV may lose its navigation capability and may not be able to receive or execute further commands. Specifically, jamming attacks can affect different parts of the UAV networks, including the control link, telemetry link, and global positioning system (GPS) signals. If the control link is jammed, the UAV may lose its ability to communicate with its operator, making it uncontrollable. If the telemetry link is jammed, the operator may not receive the UAV’s flight status or sensor data, making it difficult to monitor the UAV’s behavior. Jamming of GPS signals can cause the UAV to lose its positioning and navigation capabilities, which can result in the UAV drifting off course or even crashing.

3.2.2 Interception Attacks In interception attacks on UAV networks, the attacker intercepts and eavesdrops on the communication between the UAV and the GCS. The goal of an interception attack is to gain unauthorized access to sensitive information, such as sensor data, video feed, or command and control data, which can be used for malicious purposes. Interception attacks can be conducted using various techniques, such as RF scanning, signal interception, or packet sniffing. RF scanning involves scanning the RF spectrum to identify the frequencies used by the UAV networks. Once the frequencies are identified, an attacker can use specialized equipment to intercept the communication and capture the sensitive information. Signal interception involves using a directional antenna to capture the signals transmitted by the UAV, which can then be decoded and analyzed. Packet sniffing involves capturing and analyzing the data packets transmitted between the UAV and the GCS to extract sensitive information.

26

3 Securing UAV Networks for Rural Areas

3.2.3 Spoofing Attacks In a spoofing attack on UAV networks, an attacker impersonates a legitimate GCS and sends false commands to the UAV to cause it to perform unintended actions. A spoofing attack occurs when an attacker gains access to the communication channel between the GCS and the UAV, or when the attacker creates a fake GCS that the UAV mistakenly believes to be legitimate. In a spoofing attack, an attacker can send commands that force the UAV to change its flight path, speed, altitude, or drop its payload to the wrong location. For example, an attacker could spoof the GPS signal to trick the UAV into believing it in a different location, causing it to fly off course or even crash. Similarly, an attacker can modify telemetry data and sensor readings, causing the operator to misinterpret the UAV’s behaviour.

3.2.4 DoS Attacks In a DoS attack on UAV networks, an attacker disrupts the normal function of the UAV network by flooding it with traffic or causing it to crash. The goal of a DoS attack is to prevent legitimate users from accessing the UAV network, causing disruption and damage. DoS attacks can be conducted using various techniques, such as flooding the network with a large number of requests, overwhelming the communication channel, or sending malformed or invalid packets that cause the UAV to crash or malfunction. For example, an attacker can flood the UAV’s communication network with a large number of data packets, causing the networks to become congested and unresponsive. Alternatively, an attacker can use a Distributed Denial of Service (DDoS) attack, which involves using a network of compromised devices to simultaneously flood the UAV network with traffic from multiple sources, making it difficult to filter out the malicious traffic.

3.2.5 Physical Attacks A physical attack on a UAV network involves the physical destruction or damage of a UAV, its components or its communication systems. Shooting is a common physical attack technique against UAVs, particularly in military applications. Attackers can use guns, missiles or other types of projectiles to shoot down UAVs. In addition, attackers can use hacking techniques to gain control of UAV networks, which involves exploiting vulnerabilities in the UAV’s software or hardware, causing them to crash or malfunction. For example, an attacker could hack into a UAV’s control system and send commands to cause it to perform unintended actions, such as altering its flight path or dropping its payload into the wrong location.

3.3 Case Studies: Energy-Efficient UAV Secure Communication

27

3.3 Case Studies: Energy-Efficient UAV Secure Communication Despite these security threats in UAV networks, this book mainly focus on PLS, i.e., the consideration of tackling jamming and eavesdropping attacks. Therefore, in this section, we provide two interesting case studies of energy-efficient secure UAV communications in terms of eavesdropping and jamming, respectively. Specifically, in the UAV network with eavesdropping, the UAV needs to receive confidential information from a ground source/sensor (GS) and at the same time transmit a jamming signal to prevent GEs from listening to the signal. In the UAV network with jamming, multiple ground jammers (GJs) are deployed and the UAV has to maximize the data collection rate from multiple GSs in the presence of jamming. Next, we describe each of the two cases in detail.

3.3.1 System Model With Eavesdropping As shown in Fig. 3.1, we examine a UAV-enabled wireless network in rural areas in which a GS sends confidential information to a rotary-wing UAV, while a GE attempts to steal that confidential information during a given UAV flight time .T > 0. Taking the 3D Cartesian coordinate system into consideration, we denote T  T .wGS = [0, 0, 0] and .wGE = xGE , yGE,0 as the 3D coordinates of GS and GE, respectively. For ease of use, T is split into N equal-sized time slots, i.e., .T = δt N,

Fig. 3.1 A full-duplex UAV secrecy communication network

28

3 Securing UAV Networks for Rural Areas

where .δt denotes the size of each time slot, which is small enough in the actual setting. Therefore, the horizontal trajectory of the UAV over  T can be approximated  by a sequence of positions as .q = q[n]  [x[n], y[n]]T , n = 0, . . . , N − 1. The UAV is considered to fly at a fixed height H , and its beginning location and final position are indicated by .qo = [xo , yo ]T and .ql = [xl , yl ]T , respectively. We use .Vmax to denote the maximum speed of the UAV and thus the maximum horizontal distance the UAV can fly in each time slot is .Ω = Vmax δt . Based on the above assumptions, the trajectory of the UAV must adhere to the following restrictions: ‖q[n + 1] − q[n]‖2 ≤ Ω2 , n = 0, . . . , N − 1,

(3.1)

q[0] = qo , q[N ] = ql .

(3.2)

.

.

In our system, in order to safeguard the AG communication, we suppose that the UAV works in full duplex (FD) mode, where it can transmit jamming signals to disrupt the GE while simultaneously collecting sensitive data from the GS. We assume that the position of the GS and the UAV are known to a central controller. Offline optimization are used by the controller to determine the trajectory, jamming power, and source transmit power of the UAV. In contrast to the UAV, which has two antennas—one for receiving and the other for transmitting, we assume that the GS and the GE have a single sending antenna and a single receiving antenna, respectively.

3.3.1.1

LoS Channel Model

The field tests in [6, 56, 57] have shown that the LoS propagation primarily dominates communication channels between GSs and UAVs that are at a medium height. For example, the LoS probability of the AG channel exceeds 95% when the UAV is flying at an altitude of 80 meters or more with a horizontal distance of 2 kilometers in a rural environment. Therefore, we assume that the corresponding channel gain follows the free-space path loss model in rural areas, i.e., the channel gain in time slot n depends mainly on the distance from the UAV to the ground ρ0 node, given by .hsu [n] = H 2 +‖‖ρ0q[n]‖2 and .hue [n] = 2 , where .ρ0 H +‖q[n]−wGE ‖2 [ is the power gain of the channel with respect to the reference distance .d0 = 1 m. For the terrestrial link between GS and GE, we assume that it obeys Rayleigh fading and the channel gain can be expressed as .hse = ρ0 ‖wE ‖−κ ζ , where .ζ is an exponentially distributed random variable with unit mean accounting for small-scale Rayleigh fading and .κ ≥ 2 is the path-loss exponent. As it is difficult to completely remove residual self-interference (RSI) at the UAV using FD radios in practice, we take into account its impact on the secrecy performance of the UAV networks. The RSI caused by incomplete loop interference cancellation from the UAV’s sending antenna to its receiving antenna is represented by the channel gain .hUAV . The RSI channel .hUAV is commonly dominated by Rayleigh fading that is independently

3.3 Case Studies: Energy-Efficient UAV Secure Communication

29

  2 , where .σ 2 is regarded as the average loop interference drawn from .CN 0, σRSI RSI   2 . level (LIL) with .E |hUAV |2 = σRSI Denote by .Ps [n] and .Pu [n] the transmit power of the GS and the jamming power of the UAV in time slot n, respectively, satisfying both the peak and average power constraints given as below 0 ≤ pi [n] ≤ Pimax ,

.

N 1  pi [n] ≤ P¯i , N

(3.3)

n=1

where .i ∈ {s, u}, .Pimax ≥ P¯i . Then, the achievable rates of the UAV and the eavesdropper in time slot n can be expressed respectively as

RU [n] = E1 log2 1 +

 Ps [n]hsu [n] Pu [n] |hUAV |2 + σ 2

 (a) Ps [n]hsu [n] ≥ log2 1 +  Rˇ U [n], 2 + σ2 Pu [n]σRSI

(3.4)



 Ps [n]ρ0 ‖wE ‖−κ ζ RE [n] = E2 log2 1 + Pu [n]hue [n] + σ 2 .

 (b) Ps [n]ρ0 ‖wE ‖−κ  Rˆ E [n], ≤ log2 1 + Pu [n]hue [n] + σ 2

(3.5)

.

where the power of the additive white Gaussian noise (AWGN) at the associated receiver is denoted by .σ 2 . .E1 [.] and .E2 [.] are the expectation operators on 2 .|hUAV | and .ζ , respectively. (a) in (3.4) and (b) in (3.5) hold based on Jensen’s inequality. Note that since logarithmic functions are concave with respect  to Ps [n]hsu [n] and their positive variables [58], we can infer that .log2 1 + Pu [n]|hUAV |2 +σ 2    Ps [n]ρ0 ‖wE ‖−κ . log2 1 + ζ are also convex (concave) with respect to their variPu [n]hue [n]+σ 2 ables. Therefore, we can obtain that the achievable secrecy rate in each time slot should satisfy the following constraints [59, 60]: Rasr [n] = max(0, Rˇ U [n] − Rˆ E [n]).

.

3.3.1.2

(3.6)

Rotary-Wing UAV Energy Model

The energy consumption of the UAV in the network we consider consists of two main components, one is the communication-related energy consumption and the other is the propulsion energy consumption. It is worth noting that we ignore the communication energy consumption of the UAV, because in practice the communication-related energy consumption of the UAV is much smaller than that

30

3 Securing UAV Networks for Rural Areas

generated by propulsion. Based on [51], the propulsion energy consumption of the UAV in time slot n can be expressed as

 1 Ep [n] = δt P0 φ[n] + P1 ϕ 1/2 [n] + d ' ρs ' Av 3 [n] , 2

(3.7)

.

where .P0 and .P1 are both constants denoting the lobe power, induced power of the 1/2

4 2 2 UAV when hovering, respectively. .φ[n] = 1+ 3v 2[n] , ϕ[n] = 1 + v [n] − v [n] 4 2 , Utip

4v0

2v0

and .v[n] = δ1t ‖q[n + 1] − q[n]‖ is the UAV horizontal flying speed, where .v0 is the average rotor-induced speed while the UAV is hovering. .s ' , .d ' , A, .ρ and .Utip denote the rotor solidity, the fuselage drag ratio, the rotor disc area, the air density and the tip speed of the UAV’s rotor blade, respectively.

3.3.1.3

Secrecy Energy Efficiency Maximization

In this case, our goal is to maximize the secrecy EE of the UAV network over T by jointly optimizing the transmit power of the GS .Ps  {Ps [n]}N n=1 , the jamming power of the UAV .Pu  {Pu [n]}N , and the trajectory of the UAV .q. It is possible n=1 to frame this optimization problem as max

.

Ps ,Pu ,q

B

N

n=1 Rasr [n]

N

n=1 Ep [n]

(3.8)

s.t. (3.1) − (3.3), where B is the bandwidth of the system. Since problem (3.8) is a highly nonlinear fractional programming problem and its objective function is not concave with respect to the optimization variables, it is challenging to solve it optimally with a practical complexity in general.

3.3.1.4

Proposed Algorithm

In this section, to obtain a high-quality suboptimal solution to problem (3.8), we offer a low-complexity iterative algorithm that relies on BCD and SCA techniques. With regard to problem (3.8), three subproblems for obtaining the optimization variables .Ps , .Pu , and .q are alternately solved, while holding the other two constant. The algorithm keeps iterating until it reaches a designated threshold, .ϵ > 0. (1) Optimization of the transmit power of the GS: Given the jamming power .Pu and the trajectory .q of the UAV, problem (3.8) can be simplified as

3.3 Case Studies: Energy-Efficient UAV Secure Communication

max .

Ps

31

N    log2 (1 + αn Ps [n]) − log2 (1 + βn Ps [n])

(3.9)

n=1

s.t. (3.3) for i = S, where .αn =

γ0 , βn (Pu [n]β0 +1)(H 2 +‖q[n]‖2 )

=

γ0 ‖wE ‖−κ

γ0 Pu [n] 1+ ‖q[n]−wE ‖2 +H 2

, .β0 =

2 σRSI σ2

is

defined as the LIL-to-noise ratio, and .γ0 = σρ02 is the reference SNR. According to (3.3), it is possible to express the optimal solution as  ∗ .Ps [n]

where .ηn =



=

1 2βn

−

  min [ηn ]+ , Psmax , if αn > βn ;

(3.10)

0, otherwise. 1 2αn

2

+

1 μ ln 2

N



1 βn

−

1 αn

 12

−

1 2αn

−

1 2βn .

Notice that

μ ≥ 0 is a constant and satisfies . n=1 Ps∗ [n] ≤ N P¯S , and the bisection method can be used to obtain it efficiently. (2) Optimization of the UAV jamming power: In this case, for any given .Ps and .q, we observe that every term in .Rasr [n] can be expressed as the difference of two concave functions with respect to .Pu , i.e., .

.

Rasr [n] = log2

(β0 Pu [n] + 1 + τn ) (β0 Pu [n] + 1)



 + log2

 (δn Pu [n] + 1) , (δn Pu [n] + 1 + υn ) (3.11)

s [n]γ0 where .υn = Ps [n]γ0 ‖wE ‖−κ , .δn = 2 γ0 and .τn = H 2P+‖q[n]‖ 2. H +‖q[n]−wE ‖2 Even though (3.11) is nonconvex, we can use the SCA technique to find the  N approximate solution. We define .Pku = Puk [n] n=1 as the jamming power of the UAV in the k-th iteration, and their respective global upper bounds can be obtained by applying a first-order Taylor expansion on .Pku , i.e.,

.

  log2 (1 + δn Pu [n] + υn ) ≤ log2 1 + δn Puk [n] + υn + B k [n],

(3.12)

  log2 (1 + β0 Pu [n]) ≤ log2 1 + β0 Puk [n] + Ak [n],

(3.13)

.

where . Ak [n] =

  β0 Pu [n]−Puk [n] ln 2(1+β0 Puk [n])

and . B k [n] =

  δn Pu [n]−Puk [n]   k [n]+υ . ln 2 δn P1+u n

(3.12) and (3.13), we can redescribe problem (3.8) as

Based on

32

3 Securing UAV Networks for Rural Areas

max pU

.

N    log2 (1 + β0 Pu [n] + τn ) + log2 (1 + δn Pu [n]) − Ak [n] − B k [n] n=1

s.t. (3.3) for i = U. (3.14) Noting that subproblem (3.14) is now convex, CVX solver can then handle it with ease. (3) Optimization of the UAV Trajectory: Even given .Ps and .Pu , obtaining the optimal solution to problem (3.8) is challenging because the objective function with respect to .q is non-convex. We first introduce relaxation variables .u = N {u[n]}N n=1 and .z = {z[n]}n=1 to solve the non-convexity of .Rasr [n] in (3.8), 2 where .u[n] ≥ H + ‖q[n]‖2 and .z[n] ≥ H 2 + ‖q[n] − wE ‖2 . Thus, .Rasr [n] can be written as Rasr [n] =

.



  N  fn υn z[n] log2 1 + − log2 1 + , u[n] γ0 Pu [n] + z[n]

(3.15)

n=1

s [n] . To solve problem (3.8) optimally, The equalities must where .fn = β0γP0 uP[n]+1 be satisfied for both .u and .z constraints; otherwise, the objective value may be reduced by increasing .u[n] and .z[n]. Similarly, in the k-th iteration, at N  N  given local points denoted by .uk = . uk [n] n=1 and .zk = zk [n] n=1 , the convex lower and concave upper bounds can be used to replace the first and second terms in (3.15) by using the first-order Taylor expansion, respectively. Specifically, we have

.



  fn υn z[n] lb ub ≥ Rasr ≤ Rasr log2 1 + [n], log2 1 + [n] u[n] γ0 Pu [n] + z[n] (3.16)

where  

 fn u[n] − uk [n] fn   − = log2 1 + k , u [n] ln 2 uk [n] + fn g k [n]   ub [n] = C k [n] z[n] − zk [n] + D k [n], Rasr

lb Rsec [n]

.

υn γ0 Pu [n]   , ln 2 γ0 Pu [n] + zk [n] γ0 Pu [n] + (υn + 1) zk [n] 

υn zk [n] k . D [n] = log2 1 + γ0 Pu [n] + zk [n] C k [n] =

3.3 Case Studies: Energy-Efficient UAV Secure Communication

33

We further introduce the relaxation variable .r = {r[n]}N n=1 such that .r[n] ≥ 1  1  2 2 4 v 2 [n] − to solve the non-convexity of .Ep [n] in (3.8), which is [(1 + v [n] 4 2 4v0

2v0

equivalent to .

1 v 2 [n] ‖q[n + 1] − q[n]‖2 2 2 ≤ r [n] + = r [n] + . r 2 [n] v02 v02 δt2

(3.17)

Noting that .r[n] might be raised to lower the objective value of the problem, and constraint (3.17) should hold with equality in order to find the optimal solution (3.8). Next, we focus on addressing the nonconvex constraint (3.17). Since .‖q[n + 1] − q[n]‖2 and .r 2 [n] are convex with respect to .q[n] and .r[n],  N  N respectively, for any given points .rk = r k [n] n=1 and .qk = qk [n] n=1 in the k-th iteration, we can use the first-order Taylor expansion on the right hand side (RHS) of (3.17) to get the following lower bound, i.e., r 2 [n] +

 2 ≥ r k [n] +

‖q[n+1]−q[n]‖2 v02 δt2

.

−

   k 2 ψ [n] v02 δt2

2 v02 δt2

 k T ψ [n] (q[n + 1] − q[n])

  + 2r k [n] r[n] − r k [n]  F k [n] (3.18)

where .ψ k [n] = qk [n + 1] − qk [n]. With (3.16)–(3.18), the optimization problem that we have is as follows. N .

max

q,u,z,r

N n=1

s.t.

n=1

 lb  ub [n] Rasr [n] − Rasr

 . P0 φ[n] + P1 r[n] + 12 d ' ρs ' Av 3 [n]

(3.19)

1 ≤ F k [n], . r 2 [n]

(3.20)

u[n] ≥ H 2 + ‖q[n]‖2 , .

(3.21)

z[n] ≥ H 2 + ‖q[n] − wE ‖2 , .

(3.22)

r[n] > 0,

(3.23)

(3.1)–(3.2). Problem (3.19) is shown to be a quasi-convex optimization problem since all constraints are convex and the objective function has a linear numerator and a convex denominator. As a result, it can be solved using fractional programming techniques, such as the Dinkelbach’s algorithm, in an optimal and effective manner.

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3 Securing UAV Networks for Rural Areas

(4) Overall Algorithm and Computational Complexity: Drawing from the outcomes of the three subproblems mentioned earlier, we provide Algorithm 3.1 for addressing problem (3.8) by alternately optimizing the variables .Ps , .Pu and .q. According to the constraints in (3.12), (3.13), (3.16), and (3.18), resolving problems (3.14) and (3.19) should provide their respective lower bounds for the optimal objective value of problem (3.8), which may ensure convergence as described in [39]. The derived solution to problem (3.8) is often suboptimal, however, numerical results show that the proposed algorithm is beneficial in improving the EE of the UAV when compared to previous benchmarks. Additionally, Algorithm 3.1’s computational cost is .O(N 3.5 log3 (1/ϵ)), meaning that the suboptimal solution can be calculated in polynomial time and is thus effectively applied in real-world UAV networks.

Algorithm 3.1 Proposed Algorithm for Solving Problem (3.8) 1: Set iteration index .k = 0 and initial .P0u and .q0 . 2: repeat 3: Using given .Pku and .qk to solve problem (3.9), and we can obtain the corresponding optimal solution denoted by .Pk+1 s . k 4: Using given .Pk+1 and .q to solve problem (3.14), and we can obtain the corresponding s optimal solution denoted by .Pk+1 u . k+1 k 5: Using given .Pk+1 s , Pu , and .q to solve problem (3.19), and we can obtain the corresponding optimal solution denoted by .qk+1 . 6: until the caculated objective value of problem (3.8) converges within a pre-specified precision .ϵ > 0.

3.3.1.5

Numerical Results

We compare the proposed power control and trajectory co-design algorithm (abbreviated as PTD) with the following benchmark algorithms in this section: (1) Designing the trajectory of the UAV without regulating power usage (denoted as NPTD); (2) Best-effort trajectory with power control (denoted as PBTD) and (3) Optimization of the trajectory for the UAV in the absence of jamming (denoted as NJPTD). Specifically, in NPTD, the powers of the GS and the UAV are set to be .Ps [n] = P¯S and .Pu [n] = P¯U ∀n, respectively. For the PBTD, the UAV first travels in a straight line at speed .Vmax towards the spot directly above the GS. Then, if time allows, it remains stable for as long as feasible before flying at speed .Vmax to its ultimate destination by the end of T . The simulation settings are as follows: T T T .H = 100 m, qo = [50, −800] m, ql = [50, 800] .m, wGE = [200, 0] m, δt = 0.5 s, ρ0 = .−60 dB, Vmax = 40 m/s, Psmax = 26 dBm, P¯S = 20 dBm, PUmax = 2 = −110 dBm, B = 1 MHz, and .ϵ = 10−4 . All .16 dBm, P¯U = 10 dBm, σ necessary parameter values in (3.7) are set in accordance with the example provided in [51].

3.3 Case Studies: Energy-Efficient UAV Secure Communication

35

Fig. 3.2 Optimized UAV trajectories for T = 160 s by different algorithms. All trajectories are sampled every 2.5 s

The different UAV trajectories generated by various algorithms are shown in 2 = 80 dBm. For the proposed PTD algorithm, it has Fig. 3.2 with T = 160 s and .σRSI been observed that the UAV first flies towards GS, then circles between locations A and B, and finally reaches .ql by the end of T . Compared to other algorithms, the UAV can achieve a higher EE for the secrecy communication along this optimized trajectory (including the path and UAV speed) while using less propulsion energy. This is because the algorithm more effectively balances information reception from the GS against jamming signal transmission to the GE via the optimal power control. Since jamming is not possible in NJPTD, the UAV mostly hovers around the GS to balance the consumption of energy for propulsion and the secrecy, leaving only the necessary amount of time for travel. In the case of the NPTD algorithm, we see that the UAV first arrives at a point near to the GS and then stays there as long as possible. Due to the fixed source transmit power and UAV jamming power, the

36

3 Securing UAV Networks for Rural Areas

Fig. 3.3 EE of the UAV for secrecy communication by different algorithms. (a) EE of the UAV versus T . (b) EE of the UAV versus LIL

UAV must make a compromise to acquire the greater secrecy rate despite the high propulsion energy consumption for keeping stationary. The secrecy EE for the UAV network is shown in Fig. 3.3 for T = 160 s, respectively. The EE attained by all schemes greatly rises with T , as can be shown in Fig. 3.3a. This is due to the fact that for sufficiently large T , higher secrecy rates are obtained at nearby locations (for PTD and NJPTD algorithms) and stationary

3.3 Case Studies: Energy-Efficient UAV Secure Communication

37

locations (for NPTD and PBTD algorithms) at the expense of lower propulsion energy consumption, and larger T implies the UAV to remain at such locations for a longer period of time, resulting in higher EE. Due to its joint optimization of the trajectory and powers, the proposed PTD algorithm consistently outperforms other benchmark algorithms when the value of LIL is less than 75 dBm. However, as shown in Fig. 3.3b, the PTD algorithm’s EE decreases to that of the NJPTD algorithm and the PBTD value decreases to a particular steady value as the LIL value  2 ≥ −75 dBm . This is because jamming signals are useless increases (e.g., . σRSI when the UAV’s ability to cancel loop interference is significantly reduced. In this case, the optimal solution to .Pu [n] is 0 for larger LIL, which restuls in a constant EE. Therefore, the NJPTD algorithm offers a performance lower bound for the proposed PTD algorithm, and whether or not the UAV sends jamming signals in PTD depends mostly on the amount of RSI. Due to the fixed jamming power that drastically interferes with the UAV itself when it experiences the increased RSI, the EE for NPTD dramatically decreases as the LIL rises.

3.3.2 System Model With Jamming This case examines a UAV-assisted wireless sensor network (WSN) in a rural region. As illustrated in Fig. 3.4, a rotary-wing UAV is used as a mobile data collector in the air to fly over GSs and gather sensory data from them during a specific period of time

Fig. 3.4 UAV-enabled WSN in the presence of GJs in a rural area

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3 Securing UAV Networks for Rural Areas

T . The GJs, however, deliberately emit jamming signals to impede the proper GSto-UAV associations. We assume that the positions of GSs and GJs are represented by a 3D Cartesian coordinate system and are indexed by the sets .S = {1, 2, . . . , S} and .J = {1, 2, . . . , J }, respectively. Define .ws = [xs , ys ]T ∈ R2×1 , s ∈ S and T  .wj = xj , yj ∈ R2×1 , j ∈ J to denote the horizontal coordinates of GS s and GJ j , respectively. Practically, localization methods like the global navigation satellites systems (GNSS) in [61] may be used to approximately estimate the positions of GJs, although the localization may include mistakes. Due to this, we describe the correlation between the actual and predicted locations of GJs as follows xj = xej + Δxj , yj = yej + Δyj ,

(3.24)

.

T  where .wej = xej , yej is the predicted position of GJs, .Δxj and .Δyj are the associated estimation errors, i.e.,      . Δxj , Δyj ∈ εj  Δxj , Δyj | Δxj2 + Δyj2 ≤ Cj2 , (3.25) and .εj represents the possible error set. It indicates that GJs locate in a circular  T and radius .Cj . By using the time discretization region with center . xej , yej approach, T is divided into N time slots of equal length, where .δt = T /N. As such, given a constant flying altitude of H , the sequence .q[n] = .[x[n], y[n]]T ∈ R2×1 , n ∈ N  {0, 1, . . . , N } may roughly represent the horizontal trajectory of the UAV. For suburban terrain, we assume that the AG propagation adhere to the freespace path loss model. As a result, the power gain of the channel from ground node .i ∈ {s, j } to the UAV in time slot n is represented by hi [n] =

.

ρ0 H 2 + ‖q[n] − wi ‖2

(3.26)

,

where .ρ0 denotes the power gain of the channel at the reference distance .d0 = 1 m. To be fair, we assume that the UAV uses periodic time division multiple access (TDMA) throughout each period of T to deliver communication services to each GS. The binary scheduling variable for GS s in time slot n is therefore indicated by .αs [n] ∈ {0, 1}. When .αs [n] = 1, GS s transmits; otherwise, it remains quiet. For offline UAV trajectory planning, .Pj stands for the maximum transmit power of GJ j across N , which is assumed to be known to the ground central controller. Therefore, at each time slot, the achievable rate in bits/second/Hertz (bps/Hz) from GS s to the UAV is provided by

Rs [n] = αs [n] log2 1 + J

.



Ps hs [n]

j =1 Pj hj [n] + σ

2

,

(3.27)

3.3 Case Studies: Energy-Efficient UAV Secure Communication

39

 where . Jj=1 Pj hj [n] is the interference that the UAV experiences from intentional GJs in time slot n, .σ 2 is the power of the AWGN at the UAV receiver, and .Ps signifies the fixed transmit power of GS s in its planned transmission slots. It is important to note that we take into account the worst-case rate performance by assuming that the GJs send jamming signals with their maximum transmit powers throughout the entire T , so that the implementation of TDMA under the presence of malicious jammers has no effect on the design of the UAV’s trajectory and resource allocation.

3.3.2.1

Energy Effciency Maxmization

For the rotary-wing UAV, we also adopt the propulsion energy consumption model (their energy for communications is negligible compared to that for movement) [51]. Thus, the propulsion energy consumption in Joule (J) of the UAV in time slot n is given by

   1 2 2 E[n] = δt P0 1 + β1 c [n] + Pi 1 + β22 c4 [n] .

−β2 c [n] 2

1 2



(3.28)

+ β3 c [n] , 3

where .c[n] = ‖q[n + 1] − q[n]‖/δt are the horizontal flying speed of the UAV in 2 , β = 1 , β = 1 d ' ρs ' A. each time slot n and .β1 = 3/Utip 3 2 2 2 2v0

With (3.27) and (3.28), for the UAV-enabled WSN, the EE of the UAV may be written as the following: Rmin , η = N n=1 E[n]

.

(3.29)

 where B stands for the system bandwidth and .Rmin = δt B mins∈S N n=1 Rs [n] is the minimal throughput across N . Our goal is to maximise the EE .η by jointly optimising transmission scheduling .A = {αs [n], ∀s, n} and the trajectory of the UAV .Q = {q[n], ∀n}. The EE maximization problem may be expressed mathematically as follows: .

max

A,Q,η,Rmin

s.t.

(3.30)

η.

min

(Δxj ,Δyj )∈εj

δt B

αs [n] ∈ {0, 1}, .

N 

Rs [n] ≥ Rmin , .

(3.31)

n=1

(3.32)

40

3 Securing UAV Networks for Rural Areas S 

αs [n] ≤ 1, .

(3.33)

s=1

q[1] = q[N ], .

(3.34)

‖q[n + 1] − q[n]‖2 ≤ Ω2 , n = 0, . . . , N − 1,

(3.35)

where constraint (3.31) indicates that each GS satisfies the minimum throughput requirement, constraint (3.32) denotes the scheduling state of each GS, constraint (3.33) specifies that the UAV establishes a communication link with no more than one GS during each time slot, constraint (3.34) means that the UAV’s initial and final locations are the same, and constraint (3.35) specifies that the maximum flying distance of the UAV during each time slot is given by .Ω  .δt Vmax . It is challenging to find the best solution to problem (3.30) for the following reasons: (1) It has nonconvex constraint (3.31) with regard to .Q and binary variables for GS scheduling; (2) In relation to the UAV speed variables .c[n], .E[n] is non-convex; and (3) The received SINR of the UAV has a strong correlation with the variables .Q. Therefore, problem (3.30) is a mixed-integer nonlinear fractional programming problem for which it is often impossible to find an optimum solution. Taking into account the worst-case situation, where each GS may transmit with its minimum rate, we construct UAV trajectories  to address the infinitely potential locations of GJs induced by . Δxj , Δyj . First, we approximate .min Δx ,Δy ∈ε Rs [n] in the objective function as an explicit function to speed ( j j) j up the derivation. Assume that .Pj represents the best power gain of the channel to the GJs, .Rswc [n] represents the worst-case achievable rate for from the UAV  . Δxj , Δyj ∈ Cj , and .w ˇ j [n] is the position of GJ j closest to the UAV. Thus, we have

 h [n] P s s wc .Rs [n] = αs [n] log2 (3.36) 1 + J , 2 ˆ j =1 Pj hj [n] + σ ˇ j [n] = wej + where .w

q[n]−wej ˆ j [n]   Cj , .h   q[n]−wej 

=

ρ0   2 .   H 2 + q[n]−wej [n]−Cj

As a result, we reformulate problem (3.30) as the following problem:

.

max

A,Q,η,Rmin

(3.37)

η.

s.t. δt B

N 

Rswc [n] ≥ Rmin ,

n=1

(3.32)–(3.35).

(3.38)

3.3 Case Studies: Energy-Efficient UAV Secure Communication

41

Problem (3.37) is still non-convex even if we have overcome the challenge of the infinitely conceivable sites of GJs. It remains difficult to find the optimal solution to it using currently available optimization methods with manageable computing complexity. In the following section, we provide an efficient iterative approach to solve problem (3.37).

3.3.2.2

Proposed Algorithm

In this section, by using BCD, SCA and fractional programming techniques, we propose an optimization algorithm to resolve problem (3.37) iteratively. (1) GS Scheduling Optimization: The following problem results from the relaxation of the binary variable .αs [n] ∈ {0, 1} to a continuous variable .0 ≤ αs [n] ≤ 1 for any specified .Q. .

max η.

(3.39)

A,η,Rmin

s.t. δt B

N 

αs [n] log2

n=1

Ps hs [n] 1 + J 2 ˆ j =1 Pj hj [n] + σ

 ≥ Rmin , .

0 ≤ αs [n] ≤ 1,

(3.40) (3.41)

(3.33). Due to the fact that problem (3.39) is a classic linear programming problem, it can be effectively addressed by using known solutions (e.g., CVX). After solving problem (3.39), the GS scheduling variables .A are used as the supplied inputs in the following subproblem to optimize the anti-jamming UAV trajectory. (2) UAV Trajectory Optimization: Due to its non-convexity, the UAV trajectory optimization subproblem is challenging to solve even with any known value of .A. We thereforefirst introduce the slack variables .u = {us [n], n ∈ N} and wc .v = vj [n], n ∈ N . To this end, .Rs [n] can be transformed as below, ⎛ Rswc [n] = αs [n] log2 ⎝1 + .

Ps γ0 us [n] J Pj γ0 j =1 vj [n]

⎞ +1

⎠ (3.42)

= αs [n] [θs [n] − δ[n]] 2 where received SNR, .δ[n]  = .γ0 = ρ0 /σ  denotes the reference  J Pj γ0 P γ Ps γ0 J j 0 log2 and .θs [n] = log2 j =1 vj [n] + 1 j =1 vj [n] + us [n] + 1 . Consequently, the subproblem of the anti-jamming UAV trajectory may be rewritten as the following problem:

42

3 Securing UAV Networks for Rural Areas

.

max η.

(3.43)

s.t. us [n] ≥ H 2 + ‖q[n] − ws ‖2 , .  2  vj [n] ≤ H 2 + q[n] − wej  − Cj ,

(3.44)

Q,u,v,η

(3.45)

(3.34), (3.35), (3.38). Note that we must ensure that constraints (3.44) and (3.45) hold,  since  otherwise .Rswc [n] can be decreased by increasing (decreasing) .us [n] vj [n] . Problem (3.43) is still non-convex with regard to the variables .vj [n] and .us [n] notwithstanding transformation. We break down this challenging problem into the following three phases to solve it: (1) Resolve the non-convexity of the objective function .Rswc [n]; (2) Address the non-convexity of constraint (3.45) in relation to .q[n]. (3) Find the solution to the non-convexity of .E[n] with regard to .q[n]. Since it is known  that given with  .K1 > 0 and .K2 > 0, the function J K1 K2 .f (x, y) = log2 + + 1 is convex with respect to .x > 0 and .y > j =1 xj y 0, where .x = .(x1 , x2 , . . . , xJ ), the term .θs [n] in (3.42) is shown to be jointly convex with regard to its optimization variables. Although the constraint (3.45)   2 is still non-convex, it is noted that . q[n] − wej  − Cj is convex in relation to .q[n]. Then, we use the fact that the globally lower bound of any convex   2 function is the first-order Taylor expansion, . q[n] − wej  − Cj and .θs [n] can be replaced by their respective convex lower bounds at  given localpoints. Using the specified local points in the k-th iteration .uks = uks [n], ∀n, s , vkj =     vjk [n], ∀n, j and .Qk = qk [n], ∀n , we can get the lower bounds shown below,   γ0 B k [n] + C k [n] s k k  θs,lb .θs [n] ≥ log2 As [n] − [n] Aks [n] ln 2

(3.46)

 2      q[n] − we  − Cj 2 ≥  qk [n] − wej  − Cj j .

qk [n] − wej

C + 2 q [n] − wej −  k q [n] − we  j k

T

  q[n] − qk [n]  D k [n],

j

(3.47)  −2   P γ γ0 where .Aks [n] = Jj=1 kj 0 + uPks[n] + 1, .B k [n] = Jj=1 Pj vjk [n] vj [n] s    −2   k k vj [n] − vj [n] and .Cs [n] = Ps uks [n] us [n] − uks [n] .

3.3 Case Studies: Energy-Efficient UAV Secure Communication

43

We solve the non-convexity of .E[n] by introducing a relaxation variable .Ф =  1/2 1/2 {ϕ[n] = 1 + β22 c4 [n] − β2 c2 [n] , ∀n}, which equivalently satisfy .

1 ≤ ϕ 2 [n] + 2β2 c2 [n], ϕ 2 [n]

(3.48)

where the equality should hold, since otherwise .φ[n] can be increased to decrease the objective value of problem (3.43). Due to .ϕ 2 [n] and .c2 [n] being convex with respect to .ϕ[n] and .c[n], respectively, the first-order Taylor expansion to them in a similar manner at any given points  k may be  applied k k k .Ф = ϕ [n], ∀n and .Q = q [n], ∀n , i.e.,  2   ϕ 2 [n] + 2β2 c2 [n] ≥ ϕ k [n] + 2ϕ k [n] ϕ[n] − ϕ k [n]

2  T 2β2    . − 2 qk [n + 1]−qk [n] − 2 qk [n + 1] − qk [n] δt × (q[n + 1] − q[n]))  F k [n]. (3.49) With (3.46)–(3.48), problem (3.43) is approximated to the following problem, .

max

k Rk Q,u,v,Ф,ηlb min,lb

k ηlb .

s.t. δt B

(3.50) N 

  k k αs [n] θs,lb [n] − δ[n] ≥ Rmin,lb ,.

(3.51)

n=1

vj [n] ≤ H 2 + D k [n], . 1 ϕ 2 [n]

≤ F k [n], .

ϕ[n] ≥ 0,

(3.52) (3.53) (3.54)

(3.34), (3.35), (3.44). k     k = Rmin,lb and .E k = N 2 3 where .ηlb n=1 P0 1 + β1 c [n] + Pi ϕ[n] + β3 c [n] . Ek Problem (3.50) is a fractional programming problem, so we can solve it efficiently by updating .Q in each iteration using Dinkelbach’s algorithm. It is worth noting that the feasible set of problem (3.50) is always a subset of problem (3.43), as indicated by the lower bounds in (3.46), (3.47) and (3.49). Therefore, the objective value of problem (3.50) is a lower bound on the objective value of problem (3.43). The UAV trajectory variable .Q obtained

44

3 Securing UAV Networks for Rural Areas

after solving problem (3.50) can be used as input for the next iteration of GS scheduling optimisation.

Algorithm 3.2 Proposed Algorithm for Solving Problem (3.37). Input: Set .k = 0, initial .A, Q, u, v, Ф, ηlb 1: repeat 2: (outer loop) 3: .Set .k = k + 1. k+1 4: Solve problem (3.39) for given .Qk , and denote the optimal solution as .Ak+1 , ηlb . 5: repeat 6: (inner loop) k+1 7: Solve problem (3.50) for given .Ak+1 , ηlb and denote the optimal solution as k+1 k+1 k+1 k+1 k+1 k+1 .Q , Rmin,lb , .E , u , v , Ф k+1 k+1 k+1 8: if .Rmin,lb − ηlb E ≤ ϵ then 9: Convergence  = .true.  k+1 , Qk+1 , uk+1 , vk+1 , ϕk+1 , ηk+1 , R k+1 , E k+1 10: .Output . A lb min,lb 11: else R k+1

k+1 12: .Set .ηlb = Emin,lb k+1 . 13: Convergence = .false. 14: end if 15: until Convergence = .true. 16: until The increase of the objective value is smaller than a threshold .ϵ.

(3) Overall Algorithm: In conclusion, the suboptimal solution to problem (3.37) may be found by resolving the two subproblems (3.39) and (3.50) alternately until the algorithm converges to the predetermined accuracy .ϵ > 0. Algorithm 3.2 summarizes the specific steps for resolving problem (3.37) in detail. Additionally, it is important to note that the circular initialization approach as suggested in [62] is used to determine the initial UAV trajectory. Based on [63], the proposed algorithm’s convergence over iterations can be easily shown,   and its overall computational complexity is about .O (N + SN )3.5 log2 (1/ϵ) , making it appropriate for UAV-assisted WSNs in the presence of jammers.

3.3.2.3

Numerical Results

This section compares the proposed energy-efficient anti-jamming trajectory optimization algorithm (abbreviated as EE-AJT) with the following benchmark schemes and demonstrate its effectiveness: (1) optimization of the trajectory without using an anti-jamming design (denoted by EE-NAJT), e.g., the UAV is unaware that the jamming caused by the GJs exists; and (2) anti-jamming trajectory optimization without energy-efficient design (denoted by NEE-AJT). To be more precise, for EENAJT, the UAV trajectory is produced by setting all GJs’ powers to be zero in the EE-AJT scheme. In NEE-AJT, the minimum throughput .Rmin among all GSs is

3.3 Case Studies: Energy-Efficient UAV Secure Communication

45

maximized in order to optimize the UAV trajectory, and the resultant trajectory is used to determine the UAV’s energy consumption. The simulation parameters are established as follows: .H = 100 m, S = 5, J = 2, Vmax = 40 m/s, ρ0 = −60 dB, −4 , C = C = 20 m, .σ 2 = −110 dBm, P = 10−1 W, P = .B = 1 MHz, ϵ = 10 1 2 s 1 −1 P2 = 10 W, .we1 = [−50, 800]T m, we2 = [350, 700]T m and the parameters pertaining to rotary-wing UAVs’ energy consumption are taken from [51]. Figure 3.5 displays several UAV trajectories generated by various algorithms. It is observed in Fig. 3.5 that the UAV trajectories exhibit noticeable changes as T increases, particularly for sufficiently high T , such as T = 240 s. In order to prevent jamming of different intensities produced by the GJs, the UAV in NEEAJT properly flies towards each GS sequentially at its maximum speed and varies its flight path by different degrees of curve. Furthermore, the UAV cannot use the optimal communication channels when flying directly above each GS because of the presence of jamming. As a result, as shown in Fig. 3.5, the UAV hovers at a certain horizontal position near each GS while avoiding the GJs. As the jamming strength is decreased, there is a shorter horizontal distance between each GS and the corresponding UAV hovering location. At its hovering positions, the UAV is able to balance a trade-off between greater data gathering from the GSs and less jamming impact brought on by the GJs. After gathering enough data from each GS at the end of T , the UAV eventually returns to the starting point. However, there are two key distinctions between the EE-AJT and NEE-AJT’s UAV trajectories: (1) the UAV no longer hovers with a zero speed above certain locations close to GSs but surrounding these locations; and (2) the UAV’s flight route is more adaptable and energy-efficient since it must maintain low energy consumption in EE-AJT (as shown in Fig. 3.7). In addition, the UAV feels that circling over each GS may gather more data with less energy usage across a better AG link since jamming is not taken into account in EE-NAJT. Figure 3.6 shows a comparison of the UAV trajectories for various jamming powers when T = 240 s. As the jamming powers rise, it is seen that the UAV trajectories exhibit noteworthy differences. When .P1 = P2 = 10−1 W, the UAV surrounds close to each GS and avoids the GJs as much as possible. This is because the UAV can strike the ideal balance between increasing the achievable rate and mitigating the GJs’ interference. However, as the jamming powers decreases, especially when .P1 = P2 = 0 W, the trajectory of the UAV tends to gradually approach each GS. In this scenario, the UAV can both achieve its maximum data collection rate and maintain minimal energy consumption by circling around each GS overhead at a speed of around 20 m/s. Figures 3.7 and 3.8 show the UAV energy consumption and speed over time for T = 240 s, respectively. It is demonstrated that the UAV in EE-AJT uses the least propulsion energy. This is due to the UAV’s ability to more effectively control its speed along its optimal trajectory, preventing it from flying at excessively high or low speeds (as shown in Fig. 3.8). In contrast, among all the algorithms, the NEEAJT’s energy consumption is the highest. Since it hovers at zero speed for its best effort trajectory while flying at maximum speed. This proves that hovering is not an energy-saving maneuver for rotary-wing UAVs. Then, by contrasting Figs. 3.7

46

3 Securing UAV Networks for Rural Areas

Fig. 3.5 UAV trajectories by different algorithms. The horizontal locations of the GSs and GJs are marked with open square and open triangle, respectively

Fig. 3.6 UAV trajectories by EE-AJT for different jamming powers

and 3.8, it can be shown that the most energy-efficient UAV flying speed is about 20 m/s as opposed to excessively high and low speeds (such as 40 m/s or 0 m/s) in NEE-AJT.

3.3 Case Studies: Energy-Efficient UAV Secure Communication

47

Fig. 3.7 Energy consumption of the UAV versus t

Fig. 3.8 Speed of the UAV versus t

Figure 3.9 shows, for .P1 = P2 = 10−1 W and .P1 = P2 = 10−4 W, respectively, the EE of the UAV using various schemes across different T . It is evident that the proposed EE-AJT algorithm has superior EE compared to other benchmarks. This suggests that the challenge of improving the EE for the UAV can be solved

48

3 Securing UAV Networks for Rural Areas

by finding the optimal balance between maximising minimum throughput and minimizing energy consumption. In particular, it is shown that the anti-jamming trajectory is more successful in enhancing the EE than EE-NAJT when the UAV is exposed to severe jamming, such as .P1 = P2 = 10−1 W. Then, when .P1 = P2 = 10−4 W, the EE of the NEE-AJT scheme is noticeably lower than that of the other schemes. Additionally, it is anticipated that the EE of EE-NAJT will converge to that of EE-AJT when the jamming power lowers. The explanation is because there isn’t much of a difference in the UAV trajectory between EE-AJT and EENAJT as the jammer strengths steadily decrease. The energy-efficient design is especially important in this situation since it greatly improves the EE for lower jamming powers. Finally, the EE of all schemes grows with T , and when T is large enough, it is anticipated to achieve saturation. This is due to the fact that as flight duration grows, the UAV has more opportunity to encircle or remain at the appropriate hovering point to feed each GS, enhancing the EE. In particular, the flight time to GSs is insignificant when T is large enough. In this instance, the upper bound of the system EE may be determined by ⎛ ηub =

.

1  S2E

S

⎜ log2 ⎜ ⎝1 +

Ps γ0  op 2 H 2 +qs −ws  J γ0  2 j =1 Pj 2   opt  H + qs −wej −Cj

⎞ ⎟ ⎟, + 1⎠

(3.55)

opt

where .qs represents the optimal UAV hovering location for GS s in the presence of multiple GJs by maximizing the data collection rate .Rs from GS s to the UAV, and E is given in (3.28). We also set the UAV flying speed to be c = 20 m/s, which has been shown in Fig. 3.9 to be energy-efficient for rotary-wing UAVs. Notably, .ηub in (3.55) is an ideal upper bound, since UAV cannot stay static at its hovering location with the least energy consumption in practice. As a result, we have .ηub = 0.8081 Kbits/J if .Pj = 10−1 .W; and .ηub = 1.9537Kbits/J if .Pj = 10−4 W. Figure 3.9 illustrates the asymptotic optimum of the proposed EE-AJT algorithm as T rises for different jamming powers.

3.4 Summary UAV-enabled WSNs are vulnerable to malicious security attacks, mainly due to the LoS AG link and the highly controllable manoeuvrability. In this chapter, we first discuss possible security attacks in UAV networks. Then, PLS techniques for securing UAV networks was investigated in terms of eavesdropping and jamming through two case studies. In case 1, we investigated a new energy-efficient FD scheme for UAV secrecy communication network, and proposed an efficient iterative algorithm to solve the non-convex fractional problem of maximising EE within a given flight cycle by

3.4 Summary

49

Fig. 3.9 EE of the UAV by different algorithms versus T

jointly designing the GS transmit power and the UAV jamming power, as well as the UAV trajectory. Simulation results show that the improvement on the secrecy EE on the UAV network depends heavily on the UAV’s self-interference cancellation capability. Specifically, there is no need to optimise the UAV interference power when the RSI drops significantly. Otherwise, the EE performance can be significantly improved by additionally optimising the UAV’s interference power. In case 2, to maximize the EE of the UAV by concurrently optimizing the GS scheduling and UAV trajectory, an EE-aware anti-jamming trajectory design for the UAV-assisted WSN exposed to jamming was examined. An iterative approach based on BCD, SCA and fractional programming techniques was suggested to find the suboptimal solution in order to successfully address the formulated problem. According to numerical results, the proposed algorithm can both withstand jamming and lower UAV energy consumption when compared to existing benchmarks. Significant EE benefits also show the need of designing an energy-efficient antijamming trajectory in UAV-enabled WSNs with GJs from a practical standpoint.

Chapter 4

Securing UAV Networks for Urban Areas

4.1 Introduction Cooperative jamming, a well-known technique used in current ground communication networks, has been found to be effective in UAV communication networks as well. In [64–66], the authors suggested the use of UAVs as collaborative mobile jammers to enhance the secrecy performance of the ground eavesdropping channel. Furthermore, several studies [40, 67–70] have designed a dual-UAV downlink communication network, which involves one UAV establishing a communication link with a legitimate ground node, while the other UAV helps to disrupt potential eavesdroppers. This scheme has been shown to increase the system’s secrecy rate, as compared to using a single UAV. In [54], multiple UAVs were employed for secure cooperative transmission to enhance the system’s EE. The article [71] presented a new concept of a mobile relay system that employs a swarm of UAVs to facilitate multi-hop data transmission between ground users. The system utilizes specific UAVs as multi-hop relays while the others serve as friendly jammers to collectively obscure GEs, which effectively facilitates maximizing the minimum EE of the system. In addition, for another type of security threats, i.e., malicious jamming, anti-jamming UAV trajectory design as an effective means has been proposed to impede GJs from obstructing authorized communication in UAV networks by leveraging the flexibility and mobility of UAVs [49, 72]. The majority studies on AG transmission with UAVs assume a simple LoSC model in the countrysides, in which UAVs maintain a fixed altitude. However, this assumption may not be valid when UAVs operate in the cities with a dense concentration of buildings or other obstructions. This is because the simplified LoSC model fails to capture the significant shadowing effects of signal propagation between the ground terminals and UAVs [37]. By still considering the LoSC model in urban areas, the anti-eavsdropping/anti-jamming UAV trajectory design usually results in noticeably degraded performance. Furthermore, some studies [53, 65, 69] made the assumption that the eavesdropper’s precise location was known beforehand. © The Author(s), under exclusive license to Springer Nature Switzerland AG 2024 B. Duo et al., Securing Unmanned Aerial Vehicle Networks, SpringerBriefs in Computer Science, https://doi.org/10.1007/978-3-031-45605-3_4

51

52

4 Securing UAV Networks for Urban Areas

However, in a practical urban environments, although UAVs can utilize GNSSbased positioning to measure the possible eavesdroppers’ positions, the positioning can be incorrect due to multipath and NLoS signal reception [61]. Additionally, while [65, 73] have considered single user and eavesdropper scenarios, these do not accurately represent the complicated communication networks involving multiple ground users and eavesdroppers. Hence, there is a requirement for secure UAV networks under a channel model that is applicable to complex urban environments.

4.2 Elevation Angle-Distance Trade-Off In practical urban environments, simplified LoS dominant channel models may not be accurate. This is because they fail to consider the significant effects of multipath fading and shadowing that can arise due to the UAV’s changing locations. Specifically, the shadowing effect becomes less prominent as the UAV flies higher above the ground, the primary channel randomness arises from multi-path reflection, scattering, and bypassing of obstacles on the ground. To capture this feature, [74] considered the Rician factor’s elevation angle between the UAV and the ground node it serves, and it was then used to design a 3D UAV trajectory in [63] to maximize the data collection throughput of the UAV-enabled WSNs. The PrLoSC model proposed in [9] is useful in avoiding over-measurement when obtaining complete information about the LoS/NLoS channel over a large area. This model uses a heuristic function of the elevation angle between the UAV and the ground node to statistically characterize the occurrence probabilities of the LoS/NLoS states. When the elevation angle increases, the LoS probability also increases, which can be attained by either horizontally bringing the UAV closer to the ground node or by ascending it to a higher altitude above the ground. However, in the latter scenario, the channel path loss also enhances with distance, resulting in a compromise between the AG channel gain and its height that necessitates additional investigation. The model is particularly helpful when the UAV is flying close to the ground in a manner of 3D movement. In this case, the shadow effect is most noticeable and the communication between the UAV and the ground node may be obstructed by nearby buildings. The extent of signal interference is influenced by the positioning of the UAV in relation to the ground node and the distribution of building height and density in the surrounding region. To show more insights on the elevation angle-distance trade-off, in the following section, we present two case studies on 3D trajectory design for securing UAV networks in urban areas.

4.3 Case Studies: 3D Trajectory Design for Securing UAV Networks

53

4.3 Case Studies: 3D Trajectory Design for Securing UAV Networks 4.3.1 System Model with Eavesdropping This section aims to explore the significance of incorporating 3D UAV trajectory design in a more precise PrLoSC model to enhance secrecy rates in urban areas. As seen in Fig. 4.1, a ground wiretap communication network in a city is considered. For a flight mission period T , a source node S attempts to secretly communicate with several legitimate destination nodes .{Dj , j ∈ J  {1, . . . J }}. But in the same frequency band, the transmitted messages will be leaked to terrestrial eavesdroppers .{Ek , k ∈ K  {1, . . . K}}, because of the broadcast nature of radio signals. Therefore, to enhance the confidentiality of the terrestrial communication network, we integrate a legitimate collaborative UAV jammer in the network which transmits jamming signals to perplex potential eavesdroppers. In this system, S acts as a BS for .Dj and can adjust its transmission power to optimize the legitimate rate and

Fig. 4.1 UAV-Enabled cooperative jamming network in PrLoSC

54

4 Securing UAV Networks for Urban Areas

minimize the eavesdropping rate. By moving closer to .Ek and farther away from .Dj , the UAV can appropriately control the jamming power to balance the interference with .Ek and .Dj . Assuming S, .Dj , and .Ek locate at .wS = [0, 0]T , .wDj = [xDj , yDj ]T , and T .wEk = [xEk , yEk ] , respectively. In practical scenarios, the position of .Ek can be approximately estimated using a camera or synthetic aperture radar [39], however, errors in position estimation may arise since the eavesdroppers may intentionally conceal their locations to avoid detection. Therefore, this chapter examines the correlation between the true position and the estimated position of .Ek in the .x − y coordinate system as follows: xEk = xek + ΔxEk , yEk = yek + ΔyEk ,

.

(4.1)

where the estimated location of .Ek is denoted as .wek = [xek , yek ]T , the actual location of .Ek is .wEk = [xEk , yEk ]T , and the estimation errors of .xEk and .yEk are .ΔxEk and .ΔyEk , respectively. We consider that .Ek locates in a circular region with center .[xek , yek ]T and radius .CEk , and let .εEk represent the possible error set. Therefore, we can obtain Δ

(ΔxEk , ΔyEk ) ∈ εEk = {(ΔxEk , ΔyEk )|ΔxE2 k + ΔyE2 k ≤ CE2 k }.

.

4.3.1.1

(4.2)

UAV 3D Trajectory Model

Suppose that the UAV flies from .[q0 T , z0 ] to a final location .[qF T , zF ], where .q0 is the initial horizontal coordinate, .qF is the final horizontal coordinate, .z0 is the initial altitude, and .zF is the final altitude, respectively. In order to resolve the difficulty in solving the UAV trajectory, this chapter also divides the flight time T of the UAV into N time slots of equal length, i.e., .δt = T /N. Using a sequence of waypoints .{qT [n], z[n]}, we can roughly represent the UAV’s horizontal and vertical trajectories over T , for .n ∈ N  {1, ..., N }, where the horizontal and altitude coordinates are expressed by .q[n] = [x[n], y[n]]T and .z[n], respectively. In practice, the UAV is subject to the following movement restrictions ‖q[n + 1] − q[n]‖2 ≤ (Vxy δt )2 , n = 1, ..., N − 1,

(4.3)

q0 = q[0], qF = q[N ],

(4.4)

z0 = z[0], zF = z[N ],

(4.5)

|z[n + 1] − z[n]|2 ≤ (Vz δt )2 , n = 1, ..., N − 1,

(4.6)

Hmin ≤ z[n] ≤ Hmax , ∀n ∈ N,

(4.7)

.

.

.

.

.

4.3 Case Studies: 3D Trajectory Design for Securing UAV Networks

55

where the UAV’s maximum horizontal and vertical speeds are expressed by .Vxy and Vz , the lowest and highest altitudes are expressed as .Hmin and .Hmax , respectively.

.

4.3.1.2

Propagation Channel Models

The simplified LoSC model cannot provide an accurate representation of signal transmission between the UAV and the ground node in urban areas, because of the shadow fading and the path loss. Therefore, we use the PrLoSC model to depict the AG channel, and the LoS probability is denoted by PiL [n] =

.

1 1+ae−b(θi [n]−a)

, i ∈ {Dj , Ek }, ∀n ∈ N,

(4.8)

z[n] −1 In time slot n, .θi [n] = 180 π tan ( ‖q[n]−wi [n]‖ ) represents the elevation angle between the UAV and .Dj or .Ek , while a and b denote the parameters of the S-curve that are measured by city areas [9]. Furthermore, the NLoS probability is expressed as .PiN [n] = 1 − PiL [n]= 1 b(θ1 i [n]−a) . In addition, in the LoS or 1+ a e

NLoS state, the channel gain between the UAV and the ground node is denoted by −αN −αL N L .hUi [n] = h [n] = ρ0 d Ui Ui [n] or .hUi [n] = hUi [n] = μρ0 dUi [n], the average path loss exponents can be represented by .αL or .αN , the distance between the UAV and  the corresponding ground nodes is denoted as .dUi [n] = ||q[n] − wi [n]||2 + z2 [n]. Assuming that the ground channels satisfy independent Rayleigh fading, the channel −φ power gain is given by .gSi = ρ0 dSi ζi , at a reference distance of .d0 = 1 m. In time slot n, .ρ0 is the average channel power gain, and the distance between S and the corresponding ground nodes can be expressed as .dSi [n] = ||wS [n] − wi [n]||.

4.3.1.3

Secrecy Rate Model

In time slot n, the transmit power of the source and the jamming power of the UAV are denoted by .PS [n] and .PU [n]. The relevant restrictions are shown below

.

N 1  PS [n] ≤ P¯S , 0 ≤ PS [n] ≤ PS max , N

∀n ∈ N,

(4.9)

n=1

N 1  . PU [n] ≤ P¯U , 0 ≤ PU [n] ≤ PU max , N

∀n ∈ N,

(4.10)

n=1

where .P¯S ≤ PS max , .P¯U ≤ PU max . In addition, when it comes to ground-to-ground communication, we take into account the utilization of TDMA for multiple destination nodes. The variable .sj [n] is utilized to indicate the binary communication scheduling for .Dj . In case .sj [n]

56

4 Securing UAV Networks for Urban Areas

equals 1, S communicates with .Dj , otherwise .sj [n] is set to 0. Consequently, the scheduling constraints are given as below.  .

sj [n] ≤ 1, ∀n,

(4.11)

j ∈J

sj [n] ∈ {0, 1}, ∀j, n.

(4.12)

.

The achievable rate at .Dj or .Ek is denoted by Ri [n] = log2 (1 +

.

PS [n]gSi ), PU [n]hUi [n] + σ 2

(4.13)

where .σ 2 refers to the power of AWGN at the receiver, while the NLoS states are represented by an attenuation factor .μ < 1 that causes an extra signal attenuation. The expected achievable rate at .Dj is obtained [75], L N E[RDj [n]] = PDLj [n]RD [n] + PDNj [n]RD [n], j j

(4.14)

.

where  L .RD [n] j

= E(ζDj ) log2 1 + 

N RD [n] j





= E(ζDj ) log2 1 +

PS [n]gSDj PU [n]hLU Dj [n] + σ 2 PS [n]gSDj

 , 

2 PU [n]hN U Dj [n] + σ

.

L [n] and .R N [n] in (4.14) are denoted as follow The lower bound of .RD Dj j

⎛

−φ

L RD [n] ≥ log2 ⎝1 + j

.

⎛

e−ι ρ0 dSDj PS [n] PU [n]hLU Dj [n] + σ 2 −φ

N RD [n] ≥ log2 ⎝1 + j

.

e−ι ρ0 dSDj PS [n] 2 PU [n]hN U Dj [n] + σ

⎞ Δ L,lb ⎠= R [n], Dj

(4.15)

⎞ Δ N,lb ⎠= R [n], Dj

(4.16)

The Euler constant is denoted by .ι = 0.58 [76]. Therefore, the lower bound of E[RDj [n]] is expressed as

.

Δ

L,lb N,lb lb RD [n] = PDLj [n]RD [n]+PDNj [n]RD [n]. j j j

.

(4.17)

4.3 Case Studies: 3D Trajectory Design for Securing UAV Networks

57

Thus, the expected achievable rate at .Ek is denoted as L N E[REk [n]] = PELk [n]RE [n] + PENk [n]RE [n], k k

(4.18)

.

where  L .RE [n] k



= E(ζEk ) log2 



PS [n]gSEk 1+ PU [n]hLU Ek [n] + σ 2

N RE [n] = E(ζEk ) log2 1 + k

PS [n]gSEk

 , 

2 PU [n]hN U Ek [n] + σ

.

L [n] and .R N [n] in (4.18) can be respectively indicated as The upper bound of .RE Ek k below respectively, according to Jensen’s inequality



−φ

L RE [n] ≤ log2 1 + k

.

ρ0 dSEk PS [n]

−φ

N RE [n] ≤ log2 1 + k

Δ

L,ub = RE [n], k

PU [n]hLU Ek [n] + σ 2

 .



ρ0 dSEk PS [n] 2 PU [n]hN U Ek [n] + σ

(4.19)

 Δ

N,ub = RE [n]. k

(4.20)

Thus, .E[REk [n]] is expressed as Δ

L,ub N,ub ub RE [n] = PELk [n]RE [n] + PENk [n]RE [n]. k k k

.

(4.21)

With (4.17) and (4.21), over N time slots, the minimum average (expected) achievable secrecy rate is lower bounded by Gopala et al. [60] RSEC =

.

N

+ 1  lb ub ˜E min sj [n] RD [n] − R [n] , j k j ∈J N

(4.22)

n=1

Δ ub [n]= where .R˜ E max k

max

k∈K (ΔxEk ,ΔyEk )∈εEk

4.3.1.4

Δ

ub [n], and . + = max(·, 0). RE [·] k

Secrecy Rate Maximization

By jointly optimizing the user scheduling .S  {sj [n]}, the source’s transmit power .PS  {PS [n]}, the jamming power of UAV .PU  {PU [n]}, the horizontal trajectory .Q  {q[n]}, and the vertical trajectory .Z  {z[n]}, where .n ∈ N, j ∈ J. The optimization problem is expressed as

58

4 Securing UAV Networks for Urban Areas

.

max

min

S,Q,Z,Ps ,PU j ∈J

N 

lb ub sj [n](RD [n] − R˜ E [n]) j k

(4.23)

n=1

s.t. (4.3)–(4.7), (4.9)–(4.12), As a result of the power constraints in (4.9) and (4.10), each term in the summation of (4.22) must be non-negative in the optimal solution. Therefore, the .[·]+ operator can be omitted. In order to address the enormous possible positions of the eavesdroppers caused by .(ΔxEk , ΔyEk ), by contemplating the most unfavorable eavesdropping situation, we consider that each eavesdropper can attain its maximum eavesdropping rate. wc [n] express the worst-case achievable rate for .(Δx , Δy ) ∈ C , the Let .RE Ek Ek Ek k N L L ˆ maximum probabilities of .PEk [n] and .PEk [n] are denoted by .PEk [n] and .PˆENk [n], respectively. The minimum and maximum distances of .dSEk and .dU Ek [n] are and .dˆ [n]. The maximum and minimum elevation angles of indicated by .dˇ SEk

U Ek

θEk [n] are expressed as .θˆEk [n] and .θˇEk [n], respectively. The farthest and nearest ˆ ek [n] and .w ˇ ek [n], respectively. locations of .Ek from the UAV is represented by .w Therefore, we can get

.

wc RE [n] . k

 L ˆ = PEk [n]log2 1 +  + PˆENk [n]log2



−φ ρ0 dˇSEk PS [n]

ρ0 PU [n]dˆU−αELk [n] + σ 2 −φ

1+

ρ0 dˇSEk PS [n]

μρ0 PU [n]dˆU−αENk [n] + σ 2

where dˇSEk = ||wS − wek || − CEk ,

.

PˆELk [n] = θˆEk [n] =

1 1 + a exp(−b(θˆEk [n] − a))

z[n] 180 −1 tan ( ), ˇ ek [n]|| π ||q[n] − w

ˇ [n] = wek + w ek

PˆENk [n] = θˇEk [n] =

,

1+

q[n] − wek CE , ||q[n] − wek || k 1 a

1 , exp(b(θˇEk [n] − a))

180 −1 z[n] tan ( ), ˆ ek [n]|| π ||q[n] − w

 ,

(4.24)

4.3 Case Studies: 3D Trajectory Design for Securing UAV Networks

ˆ ek [n] = wek − w 

dˆU Ek [n] =

59

q[n] − wek CE , ||q[n] − wek || k

(||q[n] − wek || + CEk )2 + z2 [n].

With (4.24), problem (4.23) can be reformulated as the following problem:

.

max

min

S,Q,Z,Ps ,PU j ∈J

N 

lb wc sj [n](RD [n] − RE [n]) j

(4.25)

n=1

s.t. (4.3)–(4.7), (4.9)–(4.12), wc [n]  R wc [n], and therefore, in time slot n, .R wc [n] is the maximum where .max RE E E k k∈K

achievable rate among multiple eavesdroppers. Although addressing the difficulty of solving the problem due to the infinite number of the eavesdropper’s possible locations, problem (4.25) is still non-convex, making it difficult to apply existing optimization techniques to get its optimal solution with low computational complexity. Thus, we design an efficient iterative algorithm to approximate the solution to problem (4.25) in the next section. 4.3.1.5

Proposed Algorithm

The joint optimization algorithm proposed in this section aims to solve problem (4.25) based on SCA and BCD techniques. To achieve this, the problem is split into five sub-problems, each of which optimizes specific variables, including the user’s communication scheduling .S, the transmit power of the source .PS , the jamming power of UAV .PU , the UAV horizontal trajectory .Q, and the UAV vertical trajectory .Z. These sub-problems are alternately optimized in an iterative manner until the convergence criterion is met. Finally, the proposed algorithm is summarized, and its computational complexity is analyzed. (1) Optimization of the User scheduling Given any feasible .PS , .PU , .Q, and .Z, the subproblem can be reduced to a typical integer programming problem. Thus, by converting the binary communication scheduling constraints in (4.12) to continuous variables, the subproblem is transformed to .

max η.

(4.26)

S,η

s.t.

N 

lb wc sj [n][RD [n] − RE [n]] ≥ η, . j

(4.27)

n=1

0 ≤ sj [n] ≤ 1, ∀j, (4.11).

(4.28)

60

4 Securing UAV Networks for Urban Areas

Problem (4.26) is a standard linear program, so by commonly used solvers such as CVX [77], it can be simply determined. It should be noted that although the solution to problem (4.26) yields a continuous communication scheduling variable, it can be reconstructed to a binary communication scheduling variable after the algorithm terminates without affecting its optimality [62]. (2) Optimization of the transmit power of the source Given any .Q, .Z, .S and .PU , problem (4.25) can be rewritten as

.

max min PS j ∈J

N 

sj [n][PDLj [n]log2 (1 + ajL [n]PS [n])

n=1

+ PDNj [n]log2 (1 + ajN [n]PS [n]) − PˆEL [n]log2 (1 + bL [n]PS [n]) − PˆEN [n]log2 (1 + bN [n]PS [n])]

(4.29)

s.t. (4.9). −φ j N . −αL j ρ0 PU [n]dU D +σ 2 j −φ ρ0 dˇSE −α μρ0 PU [n]dˆU EN +σ 2

e−ι ρ0 dSD

where .ajL [n] = −φ

ρ0 dˇSE , .bN [n] −α ρ0 PU [n]dˆ L +σ 2 UE

, a [n] =

=

−φ j −αN μρ0 PU [n]dU D +σ 2 j

e−ι ρ0 dSD

, .bL [n] =

.

Because of the concavity of .log2 (1 + bL [n]PS [n]) and .log2 (1 + bN [n]PS [n]) in (4.29), by applying the first-order Taylor expansion at the given local point, their respective global upper bounds can be obtained, i.e., (κ)

log2 (1 + bL [n]PS [n]) ≤ log2 (1 + bL [n]PS [n])

.

(κ)

(κ)

+ AL [n](PS [n] − PS [n]), .

(4.30)

log2 (1 + bN [n]PS [n]) ≤ log2 (1 + bN [n]PS(κ) [n]) (κ)

(κ)

+ AN [n](PS [n] − PS [n]), (κ)

where .AL [n] =

(κ) bL [n] , .AN [n] (κ) ln 2(1+bL [n]PS [n])

=

(4.31)

bN [n] . (κ) ln 2(1+bN [n]PS [n])

Therefore, problem (4.29) can be reformulated to .

max η.

(4.32)

PS ,η

s.t.

N 

sj [n][PDLj [n]log2 (1 + ajL [n]PS [n])

n=1

+ PDNj [n]log2 (1 + ajN [n]PS [n])

4.3 Case Studies: 3D Trajectory Design for Securing UAV Networks

61

(κ) − PˆEL [n]AL [n]PS [n] (κ) − PˆEN [n]AN [n]PS [n])] ≥ η,

(4.33)

(4.9), which can be solved efficiently by the CVX solver. (3) Optimization of the UAV’s jamming power Given any .S, .PS , .Q, and .Z, problem (4.25) can be denoted as

.

max min PU

j ∈J

N  sj [n][PDLj [n]log2 (1 + n=1

+ PDNj [n]log2 (1 + − PˆEL [n]log2 (1 + − PˆEN [n]log2 (1 +

cj [n] 1 + djL [n]PU [n] cj [n]

1 + djN [n]PU [n]

)

)

e[n] ) 1 + f L [n]PU [n] e[n] 1 + f N [n]PU [n]

(4.34)

)]

s.t. (4.10). −φ

where .cj [n] = γ0 dSDj [n]e−ι PS [n], .djL [n] = γ0 dU−αDLj [n], .djN [n] = γ0 dU−αDNj [n], −φ .e[n] = γ0 dˇ [n]PS [n], .f L [n] = γ0 dˆ −αL [n], .f N [n] = μγ0 dˆ −αN [n], .γ0 = ρ02 . UE

SE

Due to the convexity of .log2 (1 +

cj [n] ) 1+djL [n]PU [n]

UE

and .log2 (1 +

σ cj [n] ) 1+djN [n]PU [n]

in (4.34), similarly, we can apply the first-order Taylor expansion at the given local point to obtain their globally lower bounds, i.e., log2 (1 +

.

cj [n] 1 + djL [n]PU [n]

) ≥ log2 (1 +

cj [n] ) (κ) L 1 + dj [n]PU [n]

(κ)

(κ)

+ Bj,L [n](PU [n] − PU [n]), . log2 (1 +

cj [n] 1 + djN [n]PU [n]

) ≥ log2 (1 +

(4.35)

cj [n] ) (κ) N 1 + dj [n]PU [n]

(κ)

(κ)

+ Bj,N [n](PU [n] − PU [n]),

(4.36)

where −cj [n]djL [n]

(κ)

Bj,L [n] =

.

(κ)

(κ)

(1 + djL [n]PU [n])(1 + djL [n]PU [n] + cj [n]) ln 2

,

62

4 Securing UAV Networks for Urban Areas

−cj [n]djN [n]

(κ)

Bj,N [n] =

(κ)

(κ)

(1 + djN [n]PU [n])(1 + djN [n]PU [n] + cj [n]) ln 2

.

Problem (4.34) can be rewritten as the following problem based on (4.35) and (4.36): .

max η.

(4.37)

PU ,η

s.t.

N 

(κ) sj [n][PDLj [n]Bj,L [n]PU [n]

n=1 (κ)

+ PDNj [n]Bj,N [n]PU [n] − PˆEL [n]log2 (1 + − PˆEN [n]log2 (1 +

e[n] 1 + f L [n]PU [n]

)

e[n] )] ≥ η, 1 + f N [n]PU [n]

(4.38)

(4.10). The subproblem (4.37) is solved effectively by CVX, because it is concave with respect to .PU [n]. (4) Optimization of the UAV’s horizontal trajectory −φ Given any .S, .PS , .PU , and .Z, let .o[n] = γ0 dˇSE [n]PS [n] and .P [n] = γ0 PU [n]. By introducing slack variables .v  {vj [n]}, .g  {gj [n]}, .l  {l[n]}, Δ

t  {t[n]}, .m = {m[n]}, .u  {uj [n]}, where .n ∈ N, problem (4.25) is rewritten as

.

.

max

Q,v,g,l,t, u,m,ΘD ,ΘE j

s.t.

.

N  cj [n] 1 sj [n][ ) log2 (1 + α /2 j ∈J vj [n] 1 + P [n]uj L [n] n=1

min

+

cj [n] 1 log (1 + ) α /2 gj [n] 2 1 + μP [n]uj N [n]

−

o[n] 1 log2 (1 + ) l[n] 1 + P [n]mαL /2 [n]

−

1 o[n] log (1 + )] t[n] 2 1 + μP [n]mαN /2 [n]

1 − ||q[n] − wDj ||2 − z2 [n] ≤ 0, . uj [n]

(4.39)

(4.40)

4.3 Case Studies: 3D Trajectory Design for Securing UAV Networks

1 − (||q[n] − we || + CE )2 − z2 [n] ≥ 0, . m[n] vj [n] ≥ 1 + aeab e gj [n] ≥ 1 +

−bθˇDj [n]

63

(4.41)

,.

(4.42)

1 −ab bθˆDj [n] e e ,. a

(4.43)

ˆ

l[n] ≤ 1 + aeab e−bθE [n] , .

(4.44)

1 ˇ t[n] ≤ 1 + e−ab ebθE [n] , . a 180 −1 z[n] θˇDj [n] ≤ tan ( ), . π ||q[n] − wDj ||

(4.45) (4.46)

θˆDj [n] ≥

z[n] 180 −1 tan ( ), . π ||q[n] − wDj ||

(4.47)

θˇE [n] ≤

180 −1 z[n] tan ( ), . ˆ e [n]|| π ||q[n] − w

(4.48)

θˆE [n] ≥

180 −1 z[n] tan ( ), ˇ e [n]|| π ||q[n] − w

(4.49)

(4.3), (4.4), where .ΘDj [n]  {θˆDj [n], θˇDj [n]} and .ΘE [n]  {θˆE [n], θˇE [n]}. In problem (4.39), all constraints must satisfy the equality condition, or the objective value of the problem will be reduced. Despite the introduction of slack variables to simplify the original problem, problem (4.39) remains intractable due to the objective function and constraints (4.40), (4.41), (4.44), (4.45), (4.46) and (4.48) are still non-convex. Proposition 1 Problem (4.39) can be transformed into the following problem (4.50) with a convex form. .

max

Q,v,g,l,t,𝛀,τ ,Λ

(4.50)

η.

u,m,ΘD ,ΘE ,𝚪,η j

s.t.

N 

(κ)

(κ)

sj [n][Bj,1 [n]uj [n] + Cj,1 [n]vj [n]

n=1 (κ)

(κ)

+ Bj,2 [n]uj [n] + Cj,2 [n]gj [n] − 𝛀[n] − τ [n]] ≥ η, .

(4.51)

(κ)

(4.52)

(κ)

(4.53)

ln 𝛀[n] ≥ G1 [n] − ln l[n], . ln τ [n] ≥ G2 [n] − ln t[n], .

64

4 Securing UAV Networks for Urban Areas

1 + P [n]G3 [n] ≥ o[n]e−𝚪1 [n] , .

(4.54)

1 + μP [n]G4 [n] ≥ o[n]e−𝚪2 [n] ,

(4.55)

(κ)

(κ)

(4.3), (4.4), (4.42), (4.43), (4.47), (4.49), (4.67), (4.68), (4.71)–(4.76). Proof To prove Proposition 1, we note that . vj1[n] log2 (1 + convex with respect to .vj [n] and .uj [n],

.

1 gj [n] log2 (1

+

cj [n] α /2

1+P [n]uj L [n] cj [n] α /2

) is jointly

) is jointly

1+μP [n]uj N [n] −bθˆE [n] , and .ebθˇE [n] .e

1 convex with respect to .gj [n] and .uj [n], . m[n] , are conz[n] −1 ˆ ˇ vex with respect to .m[n], .θE [n], and .θE [n], respectively, .tan ( ||q[n]−wD || ) and j

z[n] tan−1 ( ||q[n]− ) are both convex with respect to .q[n], and .−||q[n] − wDj ||2 is ˇ e [n]|| w concave with respect to .q[n]. Hence, by utilizing the first-order Taylor expansion at the given local points, their corresponding convex lower or concave upper bound can be substituted. In the .κ-th iteration, given .Q(κ) [n]  {q(κ) [n]} as the obtained trajectory, we can get

.

.

cj [n] 1 (κ) (κ) log (1 + ) ≥ Aj,1 [n] + Bj,1 [n](uj [n] αL /2 vj [n] 2 1 + P [n]uj [n] (κ) (κ) − u(κ) j [n]) + Cj,1 [n](vj [n] − vj [n]), . (4.56)

cj [n] 1 (κ) (κ) log2 (1 + ) ≥ Aj,2 [n] + Bj,2 [n](uj [n] αN /2 gj [n] 1 + μP [n]uj [n] (κ)

(κ)

(κ)

− uj [n]) + Cj,2 [n](gj [n] − gj [n]), . (4.57) (κ) −||q[n] − wDj ||2 ≤ Fj,1 [n], .

(4.58)

1 (κ) ≥ F2 [n], . m[n]

(4.59)

ˆ

(κ)

ˇ

(κ)

e−bθE [n] ≥ F3 [n], . ebθE [n] ≥ F4 [n], .

(4.61)

z[n] (κ) ) ≥ Fj,5 [n], . ||q[n] − wDj ||

(4.62)

z[n] (κ) ) ≥ F6 [n], ˆ e [n]|| ||q[n] − w

(4.63)

tan−1 ( tan−1 (

(4.60)

4.3 Case Studies: 3D Trajectory Design for Securing UAV Networks

65

where (κ)

Aj,1 [n] =

.

cj [n] 1 log2 (1 + αL /2 ), (κ) (κ) vj [n] 1+P [n](uj [n])

(κ) Bj,1 [n] = −

.

(κ)

Aj,2 [n] =

.

2

(κ)

)(1+P [n](uj [n])

cj [n]

log2 (1 +

1 (κ)

(vj [n])

(κ)

1+P [n](uj [n])

αL /2

(κ)

log2 (e)αN cj [n]μP [n](uj [n])

(κ)

(κ)

(κ)

2gj [n](1+μP [n](uj [n])

(κ)

Cj,2 [n] = −

.

(κ)

αL /2−1 αL /2

+cj [n])

,

),

cj [n] 1 log2 (1 + αN /2 ), (κ) (κ) gj [n] 1+μP [n](uj [n])

Bj,2 [n] = −

.

(κ)

αL /2

2 ln(2)vj [n](1+P [n](uj [n])

(κ)

Cj,1 [n] = −

.

(κ)

αL cj [n]P [n](uj [n])

(κ)

)(1+μP [n](uj [n])

cj [n]

log2 (1 +

1 2 (κ) (gj [n])

αN /2

αN /2−1

(κ)

1+μP [n](uj [n])

αN /2

αN /2

+cj [n])

,

),

(κ)

Fj,1 [n] = ||q(κ) [n]||2 − 2[q(κ) [n] − wDj ]T q[n] − ||wDj ||2 ,

.

(κ)

F2 [n] =

.

1 m(κ) [n]

−

ˆ

F3(κ) [n] = e−b(θE [n])

.

ˇ

(κ)

(κ)

(κ)

F4 [n] = eb(θE [n])

.

1 (κ) [n]), 2 (m[n] − m (m(κ) [n]) (κ)

ˆ − be−b(θE [n]) (θˆE [n] − (θˆE [n])(κ) ), (κ)

ˇ + beb(θE [n]) (θˇE [n] − (θˇE [n])(κ) ),

z[n] Fj,5 [n] = tan−1 ( ||q(κ) [n]−w

.

(κ)

Dj ||

) −

2 z[n] ||q(κ) [n]−wDj ||

+ H 2 (||q[n] − wDj || −

||q(κ) [n] − wDj ||), z[n] F6 [n] = tan−1 ( ||q(κ) [n]− ˆ w

.

(κ)

ˆ e [n]||). ||q(κ) [n] − w

e [n]||

)−

z[n] 2 ˆ e [n]||) (||q(κ) [n]−w

ˆ e [n]|| − + z2 [n](||q[n] − w

Despite obtaining a lower bound for problem (4.39), the direct solution to the right-hand side of the objective function remains difficult. Given slack variables .τ  {τ [n]}, .𝛀  {𝛀[n]}, .𝚪  {𝚪1 [n], 𝚪2 [n]}, and .Λ  {Λ1 [n], Λ2 [n]}, where .n ∈ N, we then have the following optimizaiton problem

66

4 Securing UAV Networks for Urban Areas

.

max

min

Q,v,g,l,t,𝛀,τ ,Λ j ∈J u,m,ΘD ,ΘE ,𝚪 j

N 

(κ)

(κ)

sj [n][Bj,1 [n]uj [n] + Cj,1 [n]vj [n]

n=1

(κ) (κ) + Bj,2 [n]uj [n] + Cj,2 [n]gj [n] − 𝛀[n] − τ [n]]

s.t.

.

(4.64)

ln 𝛀[n] ≥ ln Λ1 [n] − ln l[n], .

(4.65)

ln τ [n] ≥ ln Λ2 [n] − ln t[n], .

(4.66)

Λ1 [n] ≥ log2 (1 + e𝚪1 [n] ), .

(4.67)

Λ2 [n] ≥ log2 (1 + e𝚪2 [n] ), .

(4.68)

1 + P [n]mαL /2 [n] ≥ o[n]e−𝚪1 [n] , .

(4.69)

1 + μP [n]mαN /2 [n] ≥ o[n]e−𝚪2 [n] , .

(4.70)

1 (κ) + Fj,1 [n] − z2 [n] ≤ 0, . uj [n]

(4.71)

(κ)

F2 [n] − (‖q[n] − we ‖ + CE )2 − z2 [n] ≥ 0, . (κ)

l[n] ≤ 1 + aeab F3 [n], . t[n] ≤ 1 +

θˇDj [n] ≤

θˇE [n] ≤

1 −ab (κ) e F4 [n], . a

180 (κ) F [n], . π j,5 180 (κ) F [n], π 6

(4.3), (4.4), (4.42), (4.43), (4.47), (4.49).

(4.72)

(4.73)

(4.74)

(4.75)

(4.76)

4.3 Case Studies: 3D Trajectory Design for Securing UAV Networks

67

In order to solve the non-convex constraints (4.65), (4.66), (4.69) and (4.70), we use the first-order Taylor expansion at the given local point, i.e. .

(κ)

(κ)

ln Λ1 [n] ≤ G1 [n], ln Λ2 [n] ≤ G2 [n], . (κ)

(κ)

mαL /2 [n] ≥ G3 [n], mαN /2 [n] ≥ G4 [n],

(4.77) (4.78)

where (κ)

1

(κ)

G1 [n] = ln Λ1 [n] +

.

(κ)

1

(κ)

G2 [n] = ln Λ2 [n] +

(κ)

(κ) Λ1 [n]

(Λ1 [n] − Λ1 [n]), (κ)

(κ) Λ2 [n]

(Λ2 [n] − Λ2 [n]),

αL (κ) (m [n])αL /2−1 (m[n] − m(κ) [n]), 2 αN (κ) (κ) (m [n])αN /2−1 (m[n] − m(κ) [n]). G4 [n] = (m(κ) [n])αN /2 + 2 (κ) αL /2 G(κ) + 3 [n] = (m [n])

Finally, by replacing Eqs. (4.65), (4.66), (4.69) and (4.70) with (4.77) and (4.78), problem (4.64) is transformed into problem (4.50). Problem (4.50) is convex with all convex constraints, which concludes the proof. ⨆ ⨅ (5) Optimization of UAV’s vertical trajectory Given any .S, .PS , .PU , and .Q, problem (4.25) can be rewritten as

.

max min Z

j ∈J

N 

lb wc sj [n](RD [n] − RE [n]) j

(4.79)

n=1

s.t. (4.5)–(4.7). Using the similar approach for solving the UAV horizontal trajectory optimization problem (4.79) is reformulated as .

max

Z,v,g,l,t,𝛀,τ ,Λ

(4.80)

η.

u,m,ΘD ,ΘE ,𝚪,η j

s.t.

N 

(κ)

(κ)

sj [n][Bj,1 [n]uj [n] + Cj,1 [n]vj [n]

n=1 (κ) (κ) + Bj,2 [n]uj [n] + Cj,2 [n]gj [n]

− 𝛀[n] − τ [n]] ≥ η, (4.5)–(4.7), (4.40), (4.42), (4.43), (4.46)–(4.49),

(4.81)

68

4 Securing UAV Networks for Urban Areas

(4.52)–(4.55), (4.67), (4.68), (4.72)–(4.74). It can be seen that the constraints (4.40), (4.47) and (4.49) are all non-convex. We can obtain .

(κ)

− z2 [n] ≤ F7 [n], .

(4.82)

tan−1 (

z[n] (κ) ) ≤ Fj,8 [n], . ||q[n] − wDj ||

(4.83)

tan−1 (

z[n] ) ≤ F9(κ) [n], ˇ e [n]|| ||q[n] − w

(4.84)

where (κ)

F7 [n] = (z(κ) [n])2 − 2z(κ) [n]z[n],

.

Fj,8 [n] = tan−1 ( (κ)

+

||q[n] − wDj || ||q[n] − wDj ||2 + (z(κ) [n])

F9 [n] = tan−1 ( (κ)

+

z(κ) [n] ) ||q[n] − wDj || 2

(z[n] − z(κ) [n]),

z(κ) [n] ) ˇ e [n]|| ||q[n] − w ˇ e [n]|| ||q[n] − w 2

ˇ e [n]||)2 + (z(κ) [n]) (||q[n] − w

(z[n] − z(κ) [n]).

Therefore, problem (4.80) is coverted into the following convex problem max

.

Z,v,g,l,t,𝛀,τ ,Λ

(4.85)

η.

u,m,ΘD ,ΘE ,𝚪,η j

s.t.

N 

(κ)

(κ)

sj [n][Bj,1 [n]uj [n] + Cj,1 [n]vj [n]

n=1 (κ)

(κ)

+ Bj,2 [n]uj [n] + Cj,2 [n]gj [n] − 𝛀[n] − τ [n]] ≥ η, .

(4.86)

1 (κ) − ||q[n] − wDj ||2 + F7 [n] ≤ 0, . uj [n]

(4.87)

(κ) θˆDj [n] ≥ Fj,8 [n], .

(4.88)

4.3 Case Studies: 3D Trajectory Design for Securing UAV Networks (κ) θˆE [n] ≥ F9 [n],

69

(4.89)

(4.5)–(4.7), (4.42), (4.43), (4.46), (4.48), (4.52)–(4.55), (4.67)(4.68), (4.72)–(4.74). Problem (4.85) is a standard convex optimization problem, and then by CVX, it can be efficiently solved.

Algorithm 4.1 Proposed Algorithm for Problem (4.25) (0) (0) and Z(0) . Set κ = 0. 1: Initial S(0) , P(0) S ,PU , Q 2: repeat (κ) (κ) 3: GivenPS , PU , Q(κ) , Z(κ) , solve problem (4.26), get S(κ+1) . (κ) (κ+1) (κ+1) 4: Given S , PU , Q(κ) , Z(κ) , solve problem (4.33), get PS ; (κ+1) (κ+1) (κ) (κ) 5: Given S , PS , Q , Z , solve problem (4.37), get P(κ+1) ; U (κ+1) (κ+1) 6: Given S(κ+1) , PS , PU ,Z(κ) , solve problem (4.50), get Q(κ+1) ; (κ+1) (κ+1) 7: Given S(κ+1) , PS , PU ,Q(κ+1) , solve problem (4.85), get Z(κ+1) ; 8: Update κ = κ + 1; 9: until The fractional increase of the objective value is below a threshold ϵ > 0.

In summary, a suboptimal solution to problem (4.25) can be obtained by solving five subproblems (4.26), (4.33), (4.37), (4.50) and (4.85) alternately until the algorithm converges to a accuracy .ϵ. In Algorithm 4.2, the overall algorithm used for obtaining the suboptimal solutions is summarized.

4.3.1.6

Numerical Results

Numerical results are presented to verify the superior performance of the proposed joint 3D UAV trajectory and power control design under PrLoSC (JTPD) and to compare it with the following benchmark algorithms. ● LoSC model-based UAV trajectory design (LBD), which jointly optimizes the user scheduling, the 3D UAV trajectory, the transmit power, and the UAV jamming power under the simplified LoSC model; ● PrLoSC model-based UAV horizontal trajectory design at the lowest flight altitude (HTD-LA); ● PrLoSC model-based 3D UAV trajectory design without power control(TD/NP). By solving problems (4.50) and (4.85), the optimized 3D UAV trajectory can be obtained; ● Non-robust design (NRD), which by assuming .CEk = 0 m, the 3D trajectory of the UAV, power control, and the user scheduling are jointly optimized. The simulation parameters are set as: .Hmin = 50 m, .Hmax = 300 m, .Vxy = 10 m/s, .Vz = 5 m/s, .αL = 2.2, .αN = 3.2, .p¯ S = 20 dBm, .PS max = 26 dBm,

70

2.25

Average secrecy rate (bps/Hz)

Fig. 4.2 Convergence performance of JTPD under different T

4 Securing UAV Networks for Urban Areas

2 1.75 1.5 1.25 1 T = 80 s T = 120 s T = 160 s

0.75 0.5

1

5

10

15

20

25

Number of iterations

p¯ U = 10 dBm, .PU max = 16 dBm, .a = 11.95, 9.61, 7.21, .b = 0.14, 0.16, 0.19, δt = 1s ,.ρ0 = −50 dB, .σ 2 = −110 dBm, .μ = −20 dB, .ϵ = 10−4 . Moreover, the UAV’s initialized trajectory is set at a fixed altitude .H = 50 m, i.e., the UAV flies at the maximum speed towards the centre of the multiple eavesdroppers, and hovers for a period of time, then flies at the maximum speed towards the final position by the end of T . As depicted in Fig. 4.2, we examine the convergence performance of JTPD for different T . Specifically, the analysis focuses on two users (.D1 and .D2 , which locate at .wD1 = (150, 100) m, .wD2 = (200, −100) m) and two eavesdroppers (.E1 and .E2 , which locate at .wE1 = (400, 150) m, .wE2 = (300, 0) m). The results indicate that the average secrecy rates achieve their maximum and stabilize after about ten iterations. Additionally, as the value of T increases, the secrecy rate experiences a notable improvement. This can be attributed to the UAV having more time to remain stationary and disrupt the eavesdroppers, resulting in a greater secrecy rate. Furthermore, to show the effectiveness of JTPD, a comparison is drawn between the trajectories and secrecy rates of various algorithms for the multi-user and multieavesdropper scenario in the following. In Fig. 4.3a, it can be seen that the UAV’s hovering places typically lie nearer to .E2 for all the algorithms. This is due to the fact that compared to .E1 , .E2 has a stronger channel gain from S. By getting closer to .E2 , the UAV can generate more jamming and provide effective interference to both eavesdroppers, thus increasing the secrecy rate. For the LBD algorithm, the UAV follows the outermost trajectory while flying toward .E2 . Because under the LoSC model, the UAV only can set its distance from .D1 and .D2 to interfere with .E2 effectively while reducing the impact of interference on the destinations. Moreover, the UAV flies closer to .E2 for the TD/NP algorithm, as compared to the LBD algorithm’s trajectory. Because the UAV can tune its elevation angle towards both .E1 and .E2 to cause more interference, while moving away from both users to avoid unintentional interference. . .

4.3 Case Studies: 3D Trajectory Design for Securing UAV Networks

71

Fig. 4.3 UAV trajectories for different schemes for .T = 140 s and .CE1 = CE2 = 5 m. (a) UAV horizontal trajectories. (b) UAV 3D trajectories

For JTPD, the UAV flies closer to .E2 . By doing so, in order to obtain a higher probability of the LoS, it raise the elevation angle with .E2 , resulting in an improved secrecy rate. In the case of the HTD-LA algorithm, the UAV cannot optimize its altitude, which limits its ability to raise the elevation angle with .E2 . Instead, it has to strike a balance between minimizing information leakage and maximizing information transmission by decreasing the horizontal distance from .E2 . As the UAV flies towards the final location in JTPD, it moves as far away as possible from .D1 and .D2 . Because in order to jam the two eavesdroppers better than the HTDLA algorithm, and to get a higher LoS probability, the UAV in JTPD must raises its altitude by a certain amount. As a result, the elevation angle between the UAV and the two destinations raises, and the UAV must reduce the elevation angle while also adjusting its distance with the destinations to ensure less interference with the destinations. This fully demonstrates the UAV elevation angle-distance trade-off. Figure 4.3b displays the UAV’s 3D trajectory. The UAV ascends gradually towards .E2 to enhance its elevation angle and achieve a higher LoS probability. As the UAV approaches .E2 , it descends to a lower altitude to minimize path loss while maintaining a larger LoS probability, thus enabling maximum interference with .E2 . The TD/NP algorithm results in the UAV flying higher than JTPD due to the lack of power control, as it can only mitigate unintentional interference by raising the distance from the destinations. However, the LBD algorithm fails to demonstrate the elevation angle-distance trade-off in this multi-user and multieavesdropper scenario. Figure 4.4 depict the average secrecy rate versus T for various algorithms for .CE1 = CE2 = 5 m. Firstly, it can be seen that compared to the other algorithms, the LBD algorithm still produces the worst secrecy rate, thereby highlighting the significance of utilizing a more precise channel model to enhance the secrecy rate in the UAV network. Furthermore, compared to the TD/NP and NRD algorithms, the HTD-LA algorithm performs worse, indicating that the UAV altitude planning

72

2.4

Average secrecy rate (bps/Hz)

Fig. 4.4 Secrecy rate versus T for different schemes with .CE1 = CE2 = 5 m

4 Securing UAV Networks for Urban Areas

2

JTPD TD/NP HTD-LA NRD LBD

1.6 1.2 0.8 0.4 80

100

120

140

160

T (s) Fig. 4.5 UAV trajectories under different environment with .T = 140 s

can yield substantial performance gains for scenarios with multiple destinations and eavesdroppers. Figure 4.5 depicts that in a densely populated urban area with taller buildings, the UAV will fly higher as it approaches eavesdroppers to raise its LoS probability, which results in more interference for the eavesdroppers. Figure 4.6 presents the variation in the secrecy rate of JTPD across different environments, indicating a decrease in the secrecy rate as the environment complexity raises. This highlights the significance of designing the power allocation and 3D trajectory jointly to enhance the secrecy rate, particularly in a densely populated urban setting. In Fig. 4.7, the average secrecy rate of different algorithms is plotted against the number of destination nodes. The graph indicates that as the number of destination nodes increases, the average secrecy rate decreases for all the algorithms. This is due

4.3 Case Studies: 3D Trajectory Design for Securing UAV Networks

2.5

Average secrecy rate (bps/Hz)

Fig. 4.6 Secrecy rates versus T under various environments

73

Algorithm 1 dense urban Algorithm 1 urban Algorithm 1 suburban

2.25 2 1.75 1.5 1.25 1 80

100

120

140

160

T (s) 4.5

Average secrecy rate (bps/Hz)

Fig. 4.7 Average secrecy rate versus number of destination nodes when .T = 140 s

JTPD TD/NP HTD-LA LBD

4 3.5 3 2.5 2 1.5 1 0.5 0

1

2

3

4

5

Number of destination nodes

to the sharing of communication resources among more destination nodes, resulting in lower achievable rates for the worst-case destination node. Additionally, the TD/NP algorithm performs almost as well as the proposed JTPD, as their trajectories are nearly identical, and the power control provides only a marginal rate gain, as confirmed in [39]. These findings highlight that the trajectory optimization yields a more significant rate gain for secrecy than power control in scenarios involving multiple ground nodes.

4.3.2 System Model with Jamming For UAV-enabled WSNs in urban areas, under the practical elevation angledependent PrLoSC model, we address the challenge of designing anti-jamming 3D

74

4 Securing UAV Networks for Urban Areas

UAV trajectories to defend against malicious jamming in this case study. Our goal is to optimize the data collection rate from a set of GSs while mitigating the impact of a GJ, by dispatching a UAV to collect data sequentially from each GS. Specifically, through the joint optimization of GS transmission scheduling, UAV horizontal and vertical trajectories over a finite number of flight cycles, our goal is maximize the minimum (average) data collection rate for all GSs.

4.3.2.1

Probabilistic LoS Channel Modeling

In this UAV-enabled WSN, a UAV serves as an aerial data collector that hovers over the GSs. However, the legitimate communications between the UAV and the GSs are targeted by a malicious GJ that transmits jamming signals to disrupt the communication. Let .S = {1, 2, ..., S} denote the set of the GSs, where .|S| = S. Let .ws = [xs , ys ]T ∈ R2×1 , .∀s ∈ S and .wj = [xi , yj ]T ∈ R2×1 denote GS s’s and GJ j ’s horizontal locations, respectively. We apply time discretization to partition T into I equal-time slots, where .σ = T /I . Therefore, a length-I 3D sequence .{(qT [i], h[i])}Ii=1 expresses the UAV trajectory approximately, where T ∈ R2×1 and .h[i] express the horizontal and vertical coordinates. .q[i] = [xi , yj ] Assuming the need for periodic service to the GSs, the UAV is required to return to its initial position by T . We also consider the constraints that limit the UAV’s maximum horizontal and vertical flight speeds, and its flight altitude, which are given by: .

.

ˆ ‖ q[i + 1] − q[i] ‖≤ Δ,

(4.90)

˜ Hmin ≤ h[i] ≤ Hmax , ∀i ∈ I | h[i + 1] − h[i] |≤ Δ,

(4.91)

ˆ = σ Vˆ and .Δ ˜ = σ V˜ are the where within each time slot .i ∈ I  {1, ..., I }, .Δ maximum distances that the UAV flies horizontally and vertically, respectively, and the minimum and maximum altitudes that the UAV can reach are denoted by .Hmin and .Hmax . Assume that the central controller performs offline implementation of the antijamming 3D trajectory design and has knowledge of the GJ’s location. For AG communication links, we use the practical PrLoSC model. Specifically, in time slot i, the LoS probability for ground node .m ∈ {s, j }, .s ∈ S, is denoted by: PmL [i] =

.

1 1 + ae(−b[θm [i]−a])

.

(4.92)

The practical environment specifies the constants .a > 0 and .b > 0, and .PmN [i] = 1 − PmL [i] denotes the corresponding NLoS probability. Moreover, the elevation angle from the ground node m to the UAV is expressed as:

4.3 Case Studies: 3D Trajectory Design for Securing UAV Networks

  h[i] 180 arctan .θm [i] = . ‖q[i] − wm ‖ π

75

(4.93)

It is assumed that each GS can transmit messages at a fixed power .ps only when it is woken up by the UAV to send messages. Therefore, a binary variable .αs [i] ∈ {0, 1} is defined to indicate whether GS s transmits messages to the UAV, i.e., GS s transmits data when .αs [i] = 0 and remains silent otherwise. Assuming that each time slot only allows one GS to send messages to the UAV, the following scheduling constraint is obtained: S  .

αs [i] ≤ 1, ∀i ∈ I.

(4.94)

s=1

αs [i] ∈ {0, 1}, ∀s, i.

(4.95)

.

The data collection rate from the scheduled GS to the UAV can be expressed as below according to the PrLoSC model:  Rs [i] = log2 1 +

.

gsl [i]ps σ 2 + gjl [i]pj

 ,

(4.96)

where the AWGN power is denoted as .σ 2 , and the GJ’s maximum transmit power is represented by .pj . We capture the effect of dominant path loss and shadowing l [i], as effects on the achievable rate, by modeling the channel power gain .gm −αL L conditioned on the LoS or NLoS state in each time slot i, where .gm [i] = β0 dm [i], −α N N and .gm [i] = μβ0 dm [i], .l ∈ {L, N}, .m ∈ {s, j }, the power gain of the channel with respect to the reference distance .d0 = 1 m is denoted by .β0 , and .μ < 1 represents the additional signal decay due to the NLoS propagation, the distance between 

ground node m and the UAV is denoted by .dm [i] = (‖q[i] − wm ‖2 + h2 [i]), the average path loss exponents regarding the LoS and NLoS propagation is represented by .αL and .αN , respectively.

4.3.2.2

Rate Approximation

The expected rate from GS s to the UAV under the PrLoSC model in a statistical sense in time slot i, is denoted as E[Rs [i]] =PsL [i]PjL [i]RsLL [i] + PsL [i]PjN [i]RsLN [i]

.

+ PsN [i]PjL [i]RsNL [i] + PsN [i]PjN [i]RsNN [i]. where

(4.97)

76

4 Securing UAV Networks for Urban Areas

 LL .Rs [i]

= log2 1 + 

RsLN [i]

= log2 1 + 

RsNL [i]

= log2 1 + 

RsNN [i] = log2 1 +



γs ds−αL [i]

1 + γj dj−αL [i] γs ds−αL [i]

1 + γj μdj−αN [i]  γs μds−αN [i] 1 + γj dj−αL [i] γs μds−αN [i]

1 + γj μdj−αN [i]

(4.98)

,. 

(4.99)

,.

(4.100)

,. 

(4.101)

,

indicate the achievable rates of the UAV in the LoS and NLoS propagation of the AG channel, respectively, and .γm = β0σp2m . Therefore, in (4.97), the expected rate is denoted by E[Rs [i]] ≥PsL [i]PjL [i]RsLL [i] + PsL [i]PjN [i]RsLN [i]

.

+ PsN [i]PjN [i]RsNN [i]  R¯ s [i].

(4.102)

4.4 4 3.6 3.2 2.8 2.4 2 1.6 1.2 0.8 0.4 0 100

Achievable rate (bps/Hz)

Achievable rate (bps/Hz)

As shown in Fig. 4.8, we provide an illustrative example to indicate the accuracy and achievability of .R¯ s [i]. The simulation parameters are defined below: .αL = 2.2, 2 = −110 dBm, .p = 0.1 W, .p = 0.1 W, and .μ = .αN = 3.2, .β0 = −60 dB, .σ s j −20 dB. And the approximate lower bound in (4.102) is the same as the expected rate in (4.97), so that in time slot i, a LoS probability is achievable, e.g., .PsL [i] = 0.5 and .PjL [i] = 0.5.

150

200

ds (m)

(a)

250

300

4.4 4 3.6 3.2 2.8 2.4 2 1.6 1.2 0.8 0.4 0 100

150

200

250

300

dj (m)

(b)

Fig. 4.8 An illustrative example for the achievability of .R¯ s [i]. (a) Achievable rate versus .ds . (b) Achievable rate versus .dj

4.3 Case Studies: 3D Trajectory Design for Securing UAV Networks

4.3.2.3

77

Rate Maximization

The optimization problem to maximize the minimum average data collection rate for all GSs over .I can be expressed as: (P0 ) :

.

max

A,Q,H,Θm ,η

s.t.

η I 1 αs [i]R¯ s [i] ≥ η, ∀s, . I

(4.103)

(qT [1], h[1]) = (qT [I ], h[I ]),

(4.104)

i=1

(4.90), (4.91), (4.93), (4.94), (4.95). where .Θm = {θm [i], ∀i, m ∈ {s, j }}Ii=1 , .H = {h[i], ∀i}Ii=1 , .Q = {q[i], ∀i}Ii=1 , I .A = {αs [i], ∀s, i} i=1 . Finding an optimal solution to problem (P.0 ) is challenging for several reasons. First, the LoS probability of the AG link, as shown in (4.92), is non-concave, and the achievable rates presented in (4.98), (4.99), and (4.101) are also non-concave. This results in .R¯ s [i] in (4.102) being non-concave with respect to the UAV 3D trajectory variable. Second, the constraints in (4.103) are non-convex, and the GS scheduling and the 3D trajectory variables are interdependent. Third, the problem features non-convex binary constraints in (4.95) for the GS transmission scheduling and non-affine constraints in (4.93) that arise due to the elevation angle.

4.3.2.4

Proposed Algorithm

To solve problem (P.0 ), we devise an efficient iterative algorithm utilizing the BCD and SCA techniques. In each iteration, we alternately optimize the variables of the GS transmission scheduling and UAV horizontal and vertical trajectory until the algorithm converges. (1) Optimization of GS Transmission Scheduling By relaxing .αs [n] ∈ {0, 1} to a continuous variables .0 ≤ αs [n] ≤ 1, the relaxed problem can be obtained for any given feasible UAV 3D trajectory .{Q, H} (P1 ) : max

.

A,η

η

s.t. 0 ≤ αs [1] ≤ 1, ∀s, i, (4.94), (4.103). This standard linear programming problem can be solved via CVX.

(4.105)

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4 Securing UAV Networks for Urban Areas

(2) Optimization of Anti-jamming Horizontal Trajectory We obtain the following optimization problem for the UAV horizontal trajectory given any feasible GS scheduling .A and UAV vertical trajectory .H. (P2 ) : max

.

Q,Θm ,η

η

s.t. (4.90), (4.93), (4.103), (4.104). By introducing the slack variables into (4.102), the complicated non-convex constraints (4.103) can be tackled. Therefore, .R¯ s [i] is reformulated as   −1 γs ys, [i] 1 L ¯ s [i] = log2 1 + .R −1 xs [i]xj [i] 1 + γj yj, L [i]   −1 γs ys, 1 L [i] log2 1 + + −1 xs [i]zj [i] 1 + γj μyj, N [i]   −1 γs μys, 1 N [i] log2 1 + + −1 zs [i]zj [i] 1 + γj μyj, N [i]

(4.106)

with the following additional constraints: xm [i] ≥ 1 + ae(−b[θm [i]−a]) , .

(4.107)

1 (b[φm [i]−a]) e ,. a

(4.108)

.

zm [i] ≥ 1 +

 αl /2 ys,l [i] ≥ ‖q[i] − ws ‖2 + h2 [i] ,.

(4.109)

 αl /2 2 yj,l [i] ≤ q[i] − wj  + h2 [i] ,

(4.110)

where   h[i] 180 ,. arctan .θm [i] ≤ ‖q[i] − wm ‖ π   h[i] 180 , arctan φm [i] ≥ ‖q[i] − wm ‖ π

(4.111) (4.112)

are the constraints (4.93) relaxed to handle the non-affine constraints. For the non-decreasing utility value of (P.2 ), it is necessary to satisfy the equality of constraints (4.107)–(4.112), and also ensure that .φm [i] is equal to .θm [i]. This can be proven through contradiction. Although we introduce relaxation variables and relax the non-affine constraints in problem (P.2 ), obtaining the optimal solution is still difficult due to its

4.3 Case Studies: 3D Trajectory Design for Securing UAV Networks

79

non-convexity. Therefore .R¯ s [i] is modified as below to address this issue, R¯ s [i] = R¯ s+ [i] − R¯ s− [i],

.

(4.113)

where R¯ s+ [i] =

.

  γj γs 1 log2 1 + + xs [i]xj [i] ys,L [i] yj,L [[i]   γj μ γs 1 log2 1 + + + xs [i]zj [i] ys,L [i] yj,N [i]   γj μ γs μ 1 log2 1 + + + zs [i]zj [i] ys,N [i] yj,N [i]

(4.114)

and R¯ s− [i] =

.

  γj 1 log2 1 + xs [i]xj [i] yj,L [i]   γj μ 1 log2 1 + + xs [i]zj [i] yj,N [i]   γj μ 1 log2 1 + . + zs [i]zj [i] yj,N [i]

(4.115)

¯ + [i] exhibit convexity w.r.t their It is possible to prove that all terms in .Rs respective variables. Consequently, the first-order Taylor expansion can be employed at any point to approximate .R¯ s+ [i] within its global lower bound. Proposition 2 During the k-th iteration of a specific UAV horizontal trajectory, denoted as .Qk = qk [i], ∀i, the lower bound of .R¯ s+ [i], as given in (4.114), is:   k k k + f R¯ s+ [i] ≥f1k + f2k + f3k + f1,x 2,xs [i] Xs [i] + f1,xj [i] Xj [i] s [i]   k k k k + f3,z Zj [i] + f3,y Z [i] + f2,z + f3,z Y [i] s [i] s j [i] j [i] s,N [i] s,N   k k k + f1,y Ys,L [i] + f1,y + f Y [i] 2,y [i] [i] s,L s,L j,L [i] j,L   k k + f2,y Yj,N [i]  R¯ s+,lb [i], + f3,y (4.116) j,N [i] j,N [i]

.

k [i], .Z [i] = z [i] − zk [i], .Y where .Xm [i] = xm [i] − xm m m m,l [i] = ym,l [i] − m k ym,l [i], m ∈ {s, j }, l ∈ {L, N}.   Proof Because .f (x1 , x2 , y1 , y2 ) = x11x2 log2 1 + yA1 + yB2 is jointly convex with respect to their positive variables, based on the first-order Taylor expansion at any

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4 Securing UAV Networks for Urban Areas

given points .x1k , .x2k , .y1k and .y2k in the k-th interaction, we have f ≥ f k + fxk1 X1 + fxk2 X2 + fyk1 Y1 + fyk2 Y2 ,

(4.117)

.

where k .fx 1

fxk2

fk =

.

 log2 1 +

  log2 C k A log2 e , fyk1 = − , = −  2  2 x1k x2k x1k x2k y1k C k   log2 C k B log2 e , fyk2 = − , =−    2 2 x1k x2k x1k x2k y2k C k 

k .Xm = xm − xm and .Ym =   γj γs 1 k , m ∈ {1, 2}. Denote by .f = 1 + ym − ym log + , .f2 = 1 2 xs [i]xj [i]   ys,L [i] yj,L [i]  γ μ γj μ γ γ μ j 1 1 s s 1 + 1 + log + and .f3 = log + 2 2 xs [i]zj [i] ys,L [i] yj, N [i] zs [i]zj [i] ys,N [i] yj,N [i] . + ¯ Due to the similar forms for each term in .Rs [i] of (4.114), we can complete the proof of proposition 2 by applying (4.117). To further deal with the complex terms in .R¯ s− [i], .R¯ s [i] is indicated as 1 x1k x2k

A y1k

+

B y2k

, Ck = 1 +

A y1k

+

B , y2k

R¯ s [i] = R¯ s+,lb [i] − 𝛀1,s [i] − 𝛀2,s [i] − 𝛀3,s [i],

(4.118)

.

with additional constraints ⎧  1 ⎪ 𝛀 Λ [i], Λ [i] ≥ log [i] ≥ ⎪ 1 2 1+ ⎪ xs [i]xj [i] 1 ⎨ 1,s  1 . 𝛀2,s [i] ≥ xs [i]z 1+ Λ [i], Λ [i] ≥ log 2 2 2 j [i] ⎪ ⎪ ⎪ 1 ⎩ 𝛀3,s [i] ≥ zs [i]zj [i] Λ2 [i],



γj yj ,L[i] , γj μ yj,N [i] ,

(4.119)

If the equality is not guaranteed, .R¯ s [i] will decrease. Thus, during the k-th iteration, the first-order Taylor expansion can be applied at local points .Λk = I {Λk1 [i], Λk2 [i]}i=1 to ensure the equality is satisfied. The above constraint can be reformulated as the following inequality for all positive variables in (4.119), ⎧     ⎪ log2 (xs [i]) + log2 xj [i] + log2 𝛀1,s [i] ⎪ ⎪ ⎪    k  Λ1 [i]−Λk1 [i] ⎪ ⎪ v1 [i] , ⎪ 1 + e , Λ [i] ≥ log Λ [i] + ≥ log 1 ⎪ k 2 2 1 ⎪ Λ [i] ln 2 ⎪ ⎪  1    ⎪ ⎨log2 (xs [i]) + log2 zj [i] + log2 𝛀2,s [i]  k  Λ2 [i]−Λk2 [i]   . v2 [i] , ⎪ [i] + , Λ [i] ≥ log Λ 1 + e ≥ log 2 ⎪ k 2 2 2 ⎪ Λ [i] ln 2 ⎪ ⎪  2    ⎪ ⎪log2 (zs [i]) + log2 zj [i] + log2 𝛀3,s [i] ⎪ ⎪ ⎪ k   ⎪ ⎪ ⎩≥ log Λk [i] + Λ2 [i]−Λ2 [i] , 2

2

Λk2 [i] ln 2

(4.120)

4.3 Case Studies: 3D Trajectory Design for Securing UAV Networks

81

where ys,L [i] ≥ γj e−v1 [i] , yj,N [i] ≥ γj μe−v2 [i] ,

.

(4.121)

and the constraints (4.120) and (4.121) are now convex. The constraints (4.110) and (4.111) are non-convex, but the functions on the right-hand side of (4.110) and (4.111) are convex with respect to .q[i] and .‖q[i] − wm ‖. Therefore, using the first-order Taylor expansion at any local point .Qk , we have  T   αl αl −2   qk [i] − wj q[i] − qk [i] , . yj,l [i] ≤ djk [i] + αl djk [i] (4.122)   h[i] 180 arctan θm [i] ≤ ‖q[i] − wm ‖ π     180   Fmk [i] − Gkm [i] ‖q[i] − wm ‖ − qk [i] − wm  , = (4.123) π       h[i] k qk [i] − wj 2 + h2 [i] , .F k [i] = arctan where .dj [i] = k m ‖q [i]−wm ‖ , and h[i] k .Gm [i] = . ‖qk [i]−wm ‖2 +h2 [i] With (4.120)–(4.123), (P.2 ) are rewritten into the convex optimization problem as below, .

(P3 ) :

.

s.t.

max

Q,Θm ,Фm ,Λ,𝛀, xm ,zm ,ys,l ,yj,l ,v,η

η

I   1 αs [n] R¯ s+,lb [i] − 𝛀1,s [i] − 𝛀2,s [i] − 𝛀3,s [i] ≥ η, ∀s, I

(4.124)

i=1

(4.90), (4.104), (4.107)–(4.109), (4.112), (4.120)–(4.123).  I where .𝛀 = 𝛀1,s [i], 𝛀2,s [i], 𝛀3,s , [i], ∀s i=1 , .Фm = {φm [i]}Ii=1 , .Λ = {Λ1 [i], Λ2 [i]}Ii=1 , and .v = {v1 [i], v2 [i]}Ii=1 . Thus, using CVX, (P.3 ) is solved. Because of the SCA in each iteration of (4.120), (4.122) and (4.123), solving (P.3 ) can provide a lower bound for the optimal objective value of (P.2 ). ⨆ ⨅ (3) Optimization of Anti-jamming Vertical Trajectory Finally, (P.0 ) can be rewritten by the following problem based on the GS scheduling .A and the UAV horizontal trajectory .Q. (P4 ) : max

.

H,Θm ,η

s.t.

η (4.91), (4.93), (4.103), (4.104).

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4 Securing UAV Networks for Urban Areas

Since problem (P.4 ) has similar characteristics as problem (P.2 ) but differs only in the optimization variables .H, we adopt a similar approach to solve (P.2 ) by using the slack variables and SCA techniques. To handle the non-convex constraint, an approximation method is used to derive a lower bound on the objective value of (P.4 ). In conclusion, the three subproblems are solved alternately until the fractional increase of the objective value converges to a predetermined accuracy .ϵ > 0, and we get a suboptimal solution. For the continuous GS transmission scheduling, we can use the proposed method in [62], and then the binary solution is accurately reconstructed.

4.3.2.5

Numerical Results

The superiority of the optimized anti-jamming 3D trajectory under the PrLoSC model is verified by simulation results (AJT-PrLoSC). In addition, we compare the following benchmarks: ● Under the PrLoSC model, an anti-jamming horizontal trajectory is designed with a lowest altitude of .h[i] = Hmin , ∀i (denoted by AJT-PrLoSC-LA); ● Under the simplified LoSC model, an anti-jamming 3D trajectory is designed with the LoS probability of the AG channel in (4.92) being set to .PmL [i] = 1, ∀i, m ∈ {s, j } (denoted by AJT-LoSC);  S

w

s and a corresponding ● A heuristic circular trajectory with a center of .c = s=1 S   Vˆ N maxs∈S ‖ws −c‖ radius of .rtrj = min 2π , [62] is designed with the UAV altitude 2 and the GS scheduling being alternately optimized until convergence (denoted by HCT).

The simulation parameters are set as: .a = 11.95, .b = 0.14, .S = 4, .ps = 0.1 W, pj = 0.1 W, .δ = 0.2 s, .αL = 2.2, .αN = 3.2, .Vˆ = 40 m/s, .V˜ = 20 m/s, .μ = −20 dB, .β0 = −60 dB, .σ 2 = −110 dBm, and .ϵ = 10−4 . Figure 4.9 displays the UAV trajectories for different strategies with a time period of .T = 40 s. In Fig. 4.9a, in contrast to the AJT-LoSC scheme, the UAV’s horizontal trajectory in AJT-PrLoSC is like to that in AJT-PrLoSC-LA. However, the UAV hovers at a greater distance from GS 2 and 3 but closer to GS 1 and 4. This can be attributed to the fact that when the UAV obtains messages from GS 2 and 3, the elevation angle between the UAV and these two GSs, as well as the GJ, is relatively large. Therefore, in order to lower the LoS probability of the GJ-to-UAV channel, the UAV trajectory is adjusted without causing a significant rate loss. This adjustment involves reducing the elevation angle between the UAV and the GJ. On the other hand, GSs 1 and 4 are located further away from the GJ, resulting in a smaller elevation angle between the UAV and the GJ when receiving messages from them. To further improve the UAV’s data rate, the UAV trajectory is adjusted to increase the elevation angle between the UAV and GS 1 and GS 4. It is important to note that this trade-off between elevation angles and distances is not observed in the AJT-

.

4.3 Case Studies: 3D Trajectory Design for Securing UAV Networks

83

Fig. 4.9 UAV trajectories for different strategies. (a) UAV horizontal trajectories. (b) 3D UAV trajectories

Fig. 4.10 UAV trajectories with various .pj . (a) UAV horizontal trajectories. (b) 3D UAV trajectories

LoSC strategy. In Fig. 4.9b, the AJT-PrLoSC strategy can adjust the UAV’s elevation angle adaptively based on the positions of the scheduled GS. This additional design of the UAV’s vertical trajectory enables the AJT-PrLoSC scheme to achieve a more efficient angle-distance trade-off compared to AJT-PrLoSC-LA. In Fig. 4.10, the trajectories of the UAV under the AJT-PrLoSC scheme are compared for different values of .pj when .T = 40 s. Firstly, in Fig. 4.10a, the UAV can hover closer to each GS, allowing it to achieve a greater elevation angle and suffer less path loss when the jamming power .pj is lower, resulting in a higher transmission rate. Secondly, the UAV hovers at the lowest altitude close to each GS for a certain period of time because it provides the best balance between a larger elevation angle and less path loss, leading to a higher rate. As .pj increases, the UAV reduces its altitude when flying between GSs to reduce its elevation angle to the GJ, which lowers the probability of interference and improves the overall performance.

4 Securing UAV Networks for Urban Areas 2.4 2 1.6 AJT-PrLoSC, p = 0.1W j

1.2

AJT-PrLoSC-LA, pj = 0.1W AJT-LoSC pj = 0.1W

0.8

HCT, p = 0.1W j

AJT-PrLoSC, p = 0.01W j

AJT-PrLoSC-LA, p = 0.01W

0.4

j

AJT-LoSC pj = 0.01W HCT, p = 0.01W

0 15

j

20

25

30

35 T (s)

(a)

40

45

50

Average max-min data collection rate (bps/Hz)

Average max-min data collection rate (bps/Hz)

84

2

AJT-PrLoSC AJT-PrLoSC-LA AJT-LoSC HCT

1.6 1.2 0.8 0.4 0

4

5

6

7

8

9

10

Number of GSs

(b)

Fig. 4.11 Average max-min rate by different trajectory designs. (a) Max-min rate versus T . (b) Max-min rate versus number of GSs

Figure 4.11a compares the average max-min data rate for various UAV trajectory designs with different .pj under varying T conditions. Firstly, when the UAV is subjected to strong interference, the HCT scheme performs better than the AJTLoSC scheme, even without any anti-jamming trajectory design. This is attributed to the HCT scheme utilizing a more precise PrLoSC model. Moreover, the AJTPrLoSC-LA scheme effectively utilizes the horizontal trajectory of the UAV to avoid severe interference and achieve higher rates than the HCT scheme. The AJTPrLoSC design surpasses the AJT-PrLoSC-LA scheme due to its vertical trajectory design, highlighting the significance of anti-jamming 3D trajectory design in UAVenabled WSNs with malicious jammers. Additionally, while increased interference power decreases the max-min rate for all strategies, the performance gap between AJT-PrLoSC and AJT-LoSC and HCT widens, emphasizing the importance of antijamming 3D trajectory design, particularly with the more precise PrLoSC, when the interference is severe. Furthermore, for large T , since there is little difference between the trajectories of AJT-LoSC and AJT-PrLoSC-LA, the rate of the AJTLoSC scheme increases notably as .pj decreases. In contrast, the rate disparity between AJT-PrLoSC-LA and AJT-PrLoSC increases progressively because adjusting UAV altitude is a viable approach for enhancing the rate performance of AJT-PrLoSC when jamming power is low. Figure 4.11b depicts the impact of the number of GSs on the expected max-min rate achieved, where the GSs are placed within a 350 .× 350 .m2 area. The results indicate that, as anticipated, the rate decreases for all strategies as the number of GSs increases. This is due to the shared communication resources among more GSs, causing the UAV’s average max-min rate to depend on the worst-case GS with the lowest average rate.

4.3 Case Studies: 3D Trajectory Design for Securing UAV Networks

85

4.3.3 Summary The security of UAV networks in urban environments was considered in this chapter. Compared with the traditional LoSC model, the PrLoSC model can better represent the communication states. Especially in the face of security threats such as eavesdropping and jamming, this more accurate model can significantly improve the security and reliability of UAV networks. Therefore, this chapter discussed two cases. Firstly, we considered a robust PrLoSSC-based 3D trajectory and power design against multiple eavesdropper nodes. In this scenario, the source node sends classified data to the destination nodes with partial location information of the eavesdroppers, while a UAV acts as a mobile jammer to resist eavesdropping on the ground and enhance the PLS of the network. Because of the non-convexity of the optimization problem, an optimal solution is challenging obtain, and then an efficient iterative algorithm using BCD and SCA techniques was proposed to get a suboptimal solution. The simulation results indicate that our proposed algorithm is superior in achieving significant secrecy rate improvement compared to baseline algorithms. Secondly, we concentrated on the UAV-enabled WSNs in urban areas when malicious jamming is present. To maximize the minimum achievable rate of the GSs, we seeked to optimize the 3D trajectory of the UAV and the transmission scheduling of the GSs based on the more accurate PrLoSC model. We proposed an effective iterative algorithm that leverages BCD and SCA techniques to get a suboptimal solution. This approach significantly promotes the data collection rate improvement for the UAV-enabled WSNs.

Chapter 5

Securing UAV Networks for Dense Urban Areas

5.1 Introduction In the typical application scenarios of 6G networks, UAVs can make full use of their flexible maneuverability in the air to expand the coverage of the network, while avoiding environmental obstacles, reducing the path loss of signal transmission, improving communication quality, and reducing system latency. UAVs can also meet the increasing demand for wireless network by providing seamless connectivity and reliable communication for a large number of users through on-demand deployment, especially in emergency communication and short-term communication scenarios. Although UAV-assisted communication has many advantages, in typical application scenarios of UAV network in dense urban areas, such as cargo transportation and traffic monitoring, UAV communication links are often blocked by high-rise buildings and scatterers, resulting in serious degradation of channel quality. In addition, the illegal eavesdroppers are more hidden and their security attacks are more complex. Therefore, how to improve the secrecy performance of UAV communication networks in complex urban environments has become a very challenging problem. Fortunately, owing to low power consumption, light weight, and being easily installed in appropriate locations, RIS has the advantages of reconfiguring the propagation environment of wireless links, and have been studied to realize the intelligent radio environments [78–81]. An RIS consists of energy-saving reconfigurable passive elements that reflect the signal and alter its phase shift via an intelligent controller. Therefore, the RIS can enable coherent addition of signals at the receiver to enhance the signal or destructive addition to prevent eavesdropping, which brings great interest in the RIS-assisted secure communication networks [82–86]. In [82], an eavesdropper wiretaps the private messages, while an RIS assists the secure communication. To obtain the maximum achievable secrecy rate, semidefinite relaxation (SDR) and Gaussian randomization methods were used to optimize passive and transmit beamforming with AN. The shortcoming of the © The Author(s), under exclusive license to Springer Nature Switzerland AG 2024 B. Duo et al., Securing Unmanned Aerial Vehicle Networks, SpringerBriefs in Computer Science, https://doi.org/10.1007/978-3-031-45605-3_5

87

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5 Securing UAV Networks for Dense Urban Areas

SDR methods is that they cannot get rank-one solution, which can be solved by majorization minimization (MM) technique [83] and manifold optimization theory [84]. In [85] and [86], the robust and secure RIS-assisted communication networks have been investigated. In [85], the authors jointly and robustly optimized active beamforming and passive beamforming to obtain the maximum worst-case secrecy rate in the case of collusive and non-collusive eavesdropping. In [86], the base station was considered to be not fully aware of the channel state information (CSI) of the wiretap channel. Limited by the given information leakage threshold, the authors presented a robust scheme via jointly optimizing the AN covariance matrix, and active and passive beamforming. Since UAVs can communicate with ground nodes through LoS-dominated links due to their high mobility, while RISs are able to perform passive beamforming via a controller, the combination of RISs and UAVs can obtain expected performance enhancement and has been paid much attention recently [87–89]. The authors in [87] considered rate-splitting multiple access scheme for a UAV-based RIS-assisted vehicular communication network, by considering the interference from multiple vehicles operating in the same spectrum. By designing the downlink power transfer and uplink information transmission protocol, the authors in [88] investigated an RIS-assisted UAV communications in which they proposed a deep learning algorithm to maximize the system throughput. The IoT data collection performance of a UAV-mounted RIS system was studied in [89], where the RISs installed on the UAV can help reduce the hardware requirements and signal processing complexity, while improving the EE and the coverage of the network. In this chapter, we tackle the secure downlink and uplink transmission problem of UAV networks in dense urban areas. To better describe the practical environment, we adopt the Rician channel model and consider the uncertainty CSI of the illegal eavesdroppers. By robustly co-design the passive beamforming of RIS and the UAV trajectory, we maximize the secrecy rate of the RIS-aided UAV networks. The objective function of the non-convex optimization problem is non-smooth, which is often challenging. We first convert the problem to an equivalent one according to the results in [39]. Then, an efficient algorithm using the BCD technique is proposed to tackle the tightly coupled optimization variables, that is, we divide the reformulated problem into sub-problems and solve them based on the SCA technique. Simulation results show that our algorithm can obviously enhance the average worst-case secrecy rate.

5.1.1 System Model The system in which a UAV and a ground user communicate with each other in the presence of an eavesdropper is considered in Fig. 5.1. The limited capability of the UAV results in potentially low performance for such secure communications. Therefore, an RIS installed on building can be used to facilitate confidential data transmission. For generality, all nodes are assumed to be placed in a 3D Cartesian coordinate system, where .qG = [XG , YG ]T and .qE = [XE , YE ]T represent the

5.1 Introduction

89

Fig. 5.1 An RIS-assisted UAV secure communication system

horizontal coordinates of the ground user and eavesdropper, respectively. The UAV height is .ZU within a given flight cycle T . For ease of operation, T is discretized into I time slots, i.e., .T = I δt , where .δt is the time slot length. Hence, the horizontal trajectory of the UAV is expressed as .w[i] = [X[i], Y[i]]T , i ∈ I  {1, · · · , I }, meeting the maneuverability constraints: .

2 ‖ w[i + 1] − w[i] ‖2 ≤ Dmax , i = 1, . . . , I − 1, . 2 ‖ w[I ] − wF ‖2 ≤ Dmax , w[1] = w0 ,

(5.1a) (5.1b)

where .w0 and .wF denote the preset starting and ending horizontal positions, respectively, .Dmax = vmax δt and .vmax is the maximum flying speed. Assume that all the nodes are provided with a single-antenna. The RIS is provided with a uniform rectangular array (URA) consisting .Mx × Mz reflecting elements, and the phase of each reflective element can be smartly adjusted by the controller. The altitude and horizontal coordinates of the RIS placed in the x-z plane are represented by .ZR and .qR = [XR , YR ]T , respectively. The mth reflecting element is .ψm [i] ∈ [0, 2π matrix of the RIS  ), m ∈ M  {1, · · · , M} and the phase-shift  is .Ф[i] = diag ej ψ1 [i] , ej ψ2 [i] , · · · , ej ψm [i] · · · , ej ψM [i] where diag.(x) denotes a diagonal matrix in which each diagonal element is the corresponding element in .x. TDMA protocol is assumed to be adopted. Especially, let .χ ∈ [0, 1] be the weighting factor, then .χ δt is time duration for downlink transmission of the UAV serving ground users in one time slot, while .(1 − χ )δt is that for uplink transmission of the ground users uploading the data intended to be collected by the UAV.

5.1.2 Transmission Model (1) Downlink Transmission: Let l[i] denote the UAV’s transmit power in time slot i. In practice, l[i] is typically limited by L¯ and Lpeak .

90

5 Securing UAV Networks for Dense Urban Areas I 1 ¯ . l[i] ≤ L, I

(5.2a)

0 ≤ l[i] ≤ Lpeak , ∀i.

(5.2b)

.

i=1

Assume that all communication links adopt the Rician fading channel model. Let GU R [i] ∈ CM×1 represent the small-scale fading component of the link from the UAV to the RIS (UAV-RIS link), which can be written as  GU R [i] =

.

 κU R GLoS [i] + 1 + κU R U R

 1 N LoS G , 1 + κU R U R

(5.3)

where κU R is the Rician factor the UAV-RIS link, let GNLoS U R represent the NLoS component and obeys CSCG distribution whose mean and variance is zero and unit, respectively, and GLoS U R [i] can be given by [90, 91] GLoS U R [i] = Ay [i] ⊗ Ax [i],

.

(5.4)

where

T 2π 2π Ax [i] = 1, e−j λ d cos φU R [i] sin ϕU R [i] , . . . , e−j λ (Mx −1)d cos φU R [i] sin ϕU R [i] ,

.

T 2π 2π Ay [i] = 1, e−j λ d sin φU R [i] sin ϕU R [i] , . . . , e−j λ (Mz −1)d sin φU R [i] sin ϕU R [i] ,

.

.

cos φU R [i] sin ϕU R [i] =

ZR − X[i] , DU R [i]

sin φU R [i] sin ϕU R [i] =

ZU − ZR , DU R [i]

.

 DU R [i] = (ZU − ZR )2 + ‖w[i] − qR ‖2 is the distance of the UAV-RIS link, φU R [i] and ϕU R [i] denote the azimuth and elevation angles of the LoS component in the ith time slot, respectively, d and λ denote the antenna separation and the carrier 1×M wavelength, respectively. Let the small-scale fading components GH , RG ∈ C H 1×M GRE ∈ C , GU G ∈ C, and GU E ∈ C belong to the link from the RIS to the Ground (RIS-Ground link), the link from the RIS to the Eav (RIS-Eav link), the link from the UAV to the Ground (UAV-Ground link), and the link from the UAV to the Eav (UAV-Eav link), respectively. The link from the UAV to the Ground via the RIS (UAV-RIS-Ground link) and the link from the UAV to the Eav via the RIS (UAV-RIS-Eav link) can be given by

5.1 Introduction

91

 ρ (DU R [i]DRG )−β , .LU RG [i] =

(5.5)

 ρ (DU R [i]DRE )−β ,

(5.6)

LU RE [i] =

.

where DRG =

.

DRE =

.



Z2R + ‖qR − qG ‖2 ,



Z2R + ‖qR − qE ‖2 .

ρ and β are the path loss at the reference distance D0 = 1 m and the path loss exponent for the UAV-RIS-Ground and the UAV-RIS-Eav links, respectively. The UAV-Ground link and the UAV-Eav link are written as 

− α 2 , (5.7) .LU G [i] = ρ Z2U + ‖w[i] − qG ‖2  LU E [i] =

.

− α 2 , ρ Z2U + ‖w[i] − qE ‖2

(5.8)

where α denotes the path loss exponent of the UAV-Ground and the UAV-Eav links. The received SNRs of the ground user and eavesdropper are given by 2   l[i] LU G [i]GU G + LU RG [i]GH RG Фd [i]GU R [i] , .CU G [i] = σ2

(5.9)

2   l[i] LU E [i]GU E + LU RE [i]GH RE Фd [i]GU R [n] , (5.10) .CU E [i] = σ2

d d d where Фd [i] = diag ej ψ1 [i] , ej ψ2 [i] , · · · , ej ψM [i] and σ 2 are the phase-shift matrix of the downlink transmission and the noise variance, respectively. Therefore, the achievable rates can be obtained as below .

RU G [i] = log2 (1 + CU G [i]) , .

(5.11a)

RU E [i] = log2 (1 + CU E [i]) .

(5.11b)

(2) Uplink Transmission: Let p[i] denote the UAV’s transmit power in time slot i. In practice, p[i] is typically bounded by P¯ and Ppeak .

92

5 Securing UAV Networks for Dense Urban Areas I 1 p[i] ≤ P¯ , . I

(5.12a)

0 ≤ p[i] ≤ Ppeak , ∀i.

(5.12b)

.

i=1

The distance-dependent path loss of the link from the ground user to the eavesdropper (Ground-Eav link) is written as  LGE =

.

− ς  ρ ‖qG − qE ‖2 2 ,

(5.13)

where the path loss exponent ς belongs to the Ground-Eav link. We assume that the Ground-Eav link is modeled as a Rayleigh fading channel. The small-scale fading component GGE of the Ground-Eav link is a zero-mean and unit-variance CSCG random variable. Similar to the downlink transmission, we assume the Rician fading channel model for the other links in the uplink transmission. The small-scale fading 1×M components GH , GGR ∈ CM×1 , GGU ∈ C corresponds to the RISRU [i] ∈ C UAV link, the Ground-RIS link, and the Ground-UAV link, respectively. LU RG [i] and LU G [i] represent the distance-dependent path loss models of the Ground-RISUAV link and Ground-UAV link, respectively. Hence, the corresponding SNRs are  2  p[i] LU G [i]GGU + LU RG [i]GH RU [i]Θu [i]GGR .CGU [i] = , σ2

(5.14)

2   p[i] LGE GGE + LGRE GH RE Θu [i]GGR , (5.15) .CGE [i] = σ2 



− β 2 denotes where LGRE = ρ Z2R + ‖qR − qG ‖2 Z2R + ‖qR − qE ‖2 the large-scale fading component of the Ground-RIS-Eav link, and Фu [i] = u u u diag ej ψ1 [i] , ej ψ2 [i] , · · · , ej ψM [i] is the phase-shift matrix of the uplink transmission. Therefore, the achievable rates of the UAV and the eavesdropper are respectively written as .

RGU [i] = log2 (1 + CGU [i]) , .

(5.16a)

RGE [i] = log2 (1 + CGE [i]) .

(5.16b)

5.1.3 CSI Assumption The legitimate transmitter can improve the CSI of the legitimate receiver periodically according to the uplink pilot in the presence of RISs using CSI acquisition

5.1 Introduction

93

techniques [92–94]. However, due to the eavesdropping, the estimated CSI of the wiretap channel is usually inaccurate, and .CU E [i] and .CGE [i] can be expressed as CU E [i] =

.

2 l[i]    H d I [i]s [n]  , G E 1 E1 σ2

(5.17)

2 p[i]    H GE2 IE2 s u [i] , 2 σ

(5.18)

CGE [i] =

.

where  IE1 [i] = diag

.

 IE2 [i] = diag

.

LU RE [i]GU R [i]] LU E [i] LGRE [i]GGR [i]] LGE [n]

 ,  ,

H H d     d [i], 1 T , GE1 = GH , .GE2 = GH , .s [i]= s1d [i], s2d [i], · · · , sM RE , GU E RE , GGE

.

and .sid [i] = ej ψi [i] . The structure of .s u [i] is similar to .s d [i]. In particular, the CSI uncertainty of .GE1 and .GE2 is characterized by a deterministic model. The uncertainties of the downlink and uplink transmissions are respectively denoted as d

¯ E + ΔGE [i], GE1 [i] = G 1 1     Ω1  ΔGE1 [i] ∈ CM+1 : ΔGE1 [i] ≤ ϵ1 , ∀i , .

(5.19a)

¯ E + ΔGE [i], GE2 [i] = G 2 2     Ω2  ΔGE2 [i] ∈ CM+1 : ΔGE2 [i] ≤ ϵ2 , ∀i ,

(5.19b)

.

H

H ¯E = G ¯E = G ¯H ¯ ¯H ¯ where .G and .G are the estimated CSI, RE , GU E RE , GGE 1 2 ¯ E and .G ¯ E , respectively. All and .ΔGE1 and .ΔGE2 denote the estimated errors for .G 1 2 possible CSI uncertainties are contained in the continuous sets .Ω1 and .Ω2 whose norms are limited by the uncertainty radii .ϵ1 and .ϵ2 , respectively.

5.1.4 Secrecy Rate Maximization According to (5.11) and (5.16), the worst-case secrecy rates of the downlink and uplink transmissions in time slot i can be respectively written as

94

5 Securing UAV Networks for Dense Urban Areas

 down .Rsec [i]

+

= RU G [i] −

max

ΔGE1 [i]∈Ω1

RU E [i]

 up Rsec [i]

,.

(5.20a)

,

(5.20b)

+

= RGU [i] −

max

ΔGE2 [i]∈Ω2

RGE [i]

where .[x]+  max(x, 0). The average worst-case secrecy rate of the joint uplink/downlink is written as Rsec =

.

I  1   down up χ Rsec [i] + (1 − χ ) Rsec [i] . I

(5.21)

i=1

The objective is to jointly optimize .W  {w[i], i ∈ I}, .Ψ d  {Фd [i], i ∈ I} and Ψ u  {Фu [i], i ∈ I}, .l  {l[i], i ∈ I}, and .p  {p[i], i ∈ I} to maximize .Rsec .

.

.

max

W,Ψ d ,Ψ u l,p

Rsec.

(5.22a)

d s.t. 0 ≤ ψm [i] ≤ 2π, ∀i, m, .

0≤

u ψm [i]

≤ 2π, ∀i, m,

(5.22b) (5.22c)

(5.1), (5.2), (5.12). Problem (5.22) is challenge because its non-concave objective function. In the next section, an efficient algorithm is developed to obtain its suboptimal solution.

5.2 Proposed Algorithm for Joint Uplink/Downlink Optimization The transmission power control design can guarantee .RU G [i] − maxΔGE1 ∈Ω1 RU E [i] ≥ 0 and .RGU [i] − maxΔGE2 ∈Ω2 RGE [i] ≥ 0. Therefore, problem (5.22) is rewritten as

.

max

W,Ψ d ,Ψ u l,p .

where

I  1   ˜ down ˜ up χ Rsec [i] + (1 − χ ) R [i] sec I i=1

s.t. (5.1), (5.2), (5.12), (5.22b), (5.22c),

(5.23)

5.2 Proposed Algorithm for Joint Uplink/Downlink Optimization

95

 ˜ down .R sec [i]



= RU G [i] −

max

ΔGE1 [i]∈Ω1

RU E [n]

and  ˜ up .R sec



[i] = RGU [i] −

max

ΔGE2 [i]∈Ω2

RGE [i] .

However, the existence of the coupled optimization variables .W, .Ψ d , .Ψ u , .l, and .p in the objective function makes problem (5.23) still challenging to solve. Therefore, an efficient algorithm is proposed by using BCD technique, which divides problem (5.23) into three sub-problems: (1) Given .W, .Ψ d and .Ψ u , optimize .l and .p; (2) Given .W, .l and .p, optimize .Ψ d and .Ψ u ; (3) Given .Ψ d , .Ψ u , .l and .p, optimize .W.

5.2.1 Robust Solution to Transmit Powers Given .W, .Ψ d and .Ψ u , we have d H GH G1 IG1 [i]s [i] = LU G [i]GU G + LU RG [i]GRG Фd [i]GU R [i],

.

u H GH G2 [n]IG2 [i]s [i] = LU G [i]GGU + LU RG [i]GRU Фd [i]GGR [i],

.

where  IG1 [i] = diag

.

 IG2 [i] = diag

.

LU RG [i]GU R [i]] LU G [i] LU RG [i]GGR [i]] LU G [i]

 ,  ,

    H GG1 = GH RG , GU G , and .GG2 [i] = GRU , GGU . The first sub-problem can be given as

.

max .

l,p

I  1   power power χ Rdown [i] + (1 − χ ) Rup [i] I i=1

s.t. (5.2), (5.12), where

(5.24)

96

5 Securing UAV Networks for Dense Urban Areas

power .R down [i]

 2  l[i]   H  d = log2 1 + 2 GG1 IG1 [i]s [i] σ   2 l[i]    H d − log2 1 + max GE1 [i]IE1 [i]s [i] ΔGE1 [i]∈Ω1 σ 2

and  power .Rup [i]

= log2 

2  p[i]   H  u 1 + 2 GG2 IG2 [i]s [n] σ

− log2 1 +

max

ΔGE2 [i]∈Ω2

 2 p[i]   H u  GE2 [i]IE2 [i]s [i] . σ2

      H  d u  The special structure of .GH E1 [i]IE1 [i]s [i] and .GE2 [i]IE2 [i]s [i] can be used to solve problem (5.24) in which .Ω1 and .Ω2 contain an infinite number of possible CSI uncertainties. The phase angle vector of .x is denoted as .arg(x). Then, the following inequality holds: .

       H  ¯H    d H d GE1 [i]IE1 [i]s d [i] ≤ G E1 IE1 [i]s [i] + ΔGE1 [i]IE1 [i]s [i] ,

where the equality holds if and only if .





d H d ¯H arg G E1 IE1 [i]s [i] = arg ΔGE1 [i]IE1 [i]s [i] .

 2  d [i] /σ 2 can then be converted to maxΔGE1 [i]∈Ω1 l[i] GH [i]I [i]s  E 1 E1

.

.

max

ΔGE1 [i]

s.t.

 2   d [i]I [i]s [i] ΔGH  . E1 E1   ΔGE [i] ≤ ϵ1 , . 1



d H d ¯H arg G E1 IE1 [i]s [i] = arg ΔGE1 [i]IE1 [i]s [i] .

(5.25a) (5.25b) (5.25c)

For the convenience of subsequent derivation, .ΔGE1 [i] can be written as ΔGE1 [i]

      = ΔGE1 ,1 [i] ej τ1 [i] , ΔGE1 ,2 [i] ej τ2 [i] , · · · ΔGE1 ,M+1 [i] ej τM+1 [i] ,

.

(5.26)

5.2 Proposed Algorithm for Joint Uplink/Downlink Optimization

97

Because .γ [i] = IE1 [i]v d [i], .γ [i] can be similarly written as

γ [i] = ‖γ1 [i]‖ ej ι1 [i] , ‖γ2 [i]‖ ej ι2 [i] , · · · , ‖γM+1 [i]‖ ej ιM+1 [i] ,

.

(5.27)

d Hence, .GH E1 [i]IE1 [i]s [i] can be given by d H ΔGH E1 [i]IE1 [i]s [i] =ΔGE1 [i]γ [i]   = ΔGE1 ,1 [i]‖γ1 [i] ej (ι1 [i]−τ1 [i]) + · · ·   + ΔGE1 ,M+1 [i] ‖γM+1 [i]‖ ej (ιM+1 [i]−τM+1 [i]) .

.

(5.28)

Add all the terms in the last step of (5.28) coherently, that is,.ι1 [i]−τ1 [i] = ι2 [i]−    d τ2 [i] = . . . = ιM+1 [i] − τM+1 [i], to obtain the maximum of .GH E1 [i]IE1 [i]s [i]. op

According to the constraints in (5.25c), the optimal .τk [i] is written as

op d ¯H τk [i] = ιk [i] − arg G E1 IE1 [i]s [i] .

.

(5.29)

As such, problem (5.25) can be converted to .

max

m1 [i]

s.t.

 2  T  m1 [i]m2 [i] .

(5.30a)

‖m1 [i]‖ ≤ ϵ1 ,

(5.30b)

where     T  m1 [i] = ΔGE1 ,1 [i] , ΔGE1 ,2 [i] , · · · , ΔGE1 ,M+1 [i]

.

and m2 [i] = [‖γ1 [i]‖ , |γ2 [i]| , · · · , ‖γM+1 [i]‖] .

.

op

The optimal .m1 [i], represented as .m1 [i], is given by op

m1 [i] =

.

ϵ1 m2 [i]. ‖m2 [i]‖

(5.31) op

Therefore, the optimal .ΔGE1 [i], represented as .ΔGE1 [i], is op

ΔGE1 [i] = diag

.

op op op op ej τ1 [i] , ej τ2 [i] , · · · , ej τM+1 [i] m1 [i].

(5.32)

98

5 Securing UAV Networks for Dense Urban Areas op

op

op

ΔGE2 [i] can also be obtained similarly. With .ΔGE1 [i] and .ΔGE2 [i], problem (5.24) can be represented as

.

I

1  ˜ power ˜ power χ Rdown [i] + (1 − χ )R [i] up I

max .

l,p

i=1

(5.33)

s.t. (5.2), (5.12), where ˜ power R down [i] = log2 (1 + l[i]a1 [i]) − log2 (1 + l[i]b1 [i]) ,

.

˜ power R [i] = log2 (1 + p[i]a1 [i]) − log2 (1 + p[i]b2 [i]) , up

.

a1 [i] =

.

b1 [i] =

σ2

,

 2  op H   G [i] IE [i]s d [i] 1  E1 

.

a2 [i] =

.

b2 [i] =

.

 2  H  GG1 IG1 [n]s d [n]

σ2  2  H  GG2 [i]IG2 [i]s u [i] σ2

,

,

 2  op H   G [i] IE s u [i] 2  E2  σ2

op ¯ E + ΔGop [i] and .Gop [i] = G ¯ E + ΔGop [i]. According to [39], the GE1 [i] = G E1 E2 E2 1 2 optimal solution to problem (5.33) is written as

.

⎧

⎨min [l[i]] ˜ + , Lpeak , a1 [i] > b1 [i] op .l [i] = ,. ⎩0, a1 [i] ≤ b1 [i]  p [i] = op

where

  min [p[i]] ˜ + , Hpeak , a2 [i] > b2 [i] 0,

a2 [i] ≤ b2 [i]

,

(5.34a)

(5.34b)

5.2 Proposed Algorithm for Joint Uplink/Downlink Optimization

 ˜ = l[i]



.





p[i] ˜ =

1 1 − 2b1 [i] 2a1 [i]

1 1 − 2b2 [i] 2a2 [i]

2 + 2

1 1 μ1 ln 2

1 1 + μ2 ln 2





1 1 − b1 [i] a1 [i]

1 1 − b2 [i] a2 [i]

99

 −

1 1 − ,. 2b1 [i] 2a1 [i] (5.35a)

−

1 1 − . 2b2 [i] 2a2 [i] (5.35b)



Note that by a one-dimensional bisection search, .μ1 ≥ 0 and .μ2 ≥ 0 in (5.35) can be obtained.

5.2.2 Robust Solution to Phase Shifts Given .l, p, and .W, by introducing the slack variables .ξ 1 = {ξ1 [i]}Ii=1 and .ξ 2 = {ξ2 [i]}Ii=1 , sub-problem 2 is given by max

.

s d [i],s u [i], ξ1 [i],ξ2 [i]

s.t.

I

1  phi phi χ Rdown [i] + (1 − χ )Rup [i] . I

(5.36a)

i=1

2 l[i]   H  d [i]I [i]s [i] G  ≤ ξ1 [i], ∀i, . E1 E1 ΔGE1 [i]∈Ω1 σ 2 2 p[i]   H u  [i]I s [i] max  ≤ ξ2 [i], ∀i, . G E2 E2 ΔGE2 [i]∈Ω2 σ 2     d   si [i] , siu [i] = 1, ∀i, m, max

(5.36b) (5.36c) (5.36d)

where  2  l[i]    phi d Rdown [i] = log2 1 + 2 GH I [i]s [i]  − log2 (1 + ξ1 [i]) G 1 G1 σ

.

and  2  p[i]   phi u  Rup [i] = log2 1 + 2 GH I [i]s [i]  − log2 (1 + ξ2 [i]) . G2 G2 σ

.

Constraints (5.36b) and (5.36c) contain an infinite number of inequality constraints, which makes solving problem (5.36) difficult. Firstly, (5.19a) and (5.19b) are respectively substitute into (5.36b) and (5.36c), and we have

100

5 Securing UAV Networks for Dense Urban Areas

.

2 ΔGH E1 [i]ΔGE1 [i] − ϵ1 ≤ 0, ∀i, .

(5.37a)

2 ΔGH E2 [i]ΔGE2 [i] − ϵ2 ≤ 0, ∀i, .

(5.37b)

l[i] H G [i]IE1 [i]S d [i]IH E1 [i]GE1 [i] − ξ1 [i] ≤ 0, ∀i, . σ 2 E1 p[i] H G [i]IE2 S u [i]IH E2 GE2 [i] − ξ2 [i] ≤ 0, ∀i, σ 2 E2

(5.37c) (5.37d)

where .S d [i] = s d [i]s d [i]H and .S u [i] = s u [i]s u [i]H . .S d [i] and .S u [n] are rank-one. Lemma 1 (.S-Procedure [95]) Define a function .fn (x), .n ∈ {1, 2}, .x ∈ CI ×1 as   fn (x) = x H Bn x + 2 Re bH x + bn , n

(5.38)

.

where .B ∈ HI , .bn ∈ CI ×1 , and .bn ∈ R1×1 . The implication .f1 (x) ≤ 0 ⇒ f2 (x) ≤ 0 is valid if and only if there exist a .δ ≥ 0 such that    B2 b2 B1 b1 − H 0, .δ bH b2 b2 1 b1 

(5.39)

˘ ≤ 0. provided that there exists a point .x˘ such that .fn (x) According to Lemma 1, the following implications can be obtained: (5.37a) ⇒ (5.37c) and .(5.37b) ⇒ (5.37d) holds if and only if there exist .η1 [i] ≥ 0 and .η2 [i] ≥ 0 such that .

.

U 1 [i] − U 2 [i] 0, .

(5.40a)

U 3 [i] − U 4 [i] 0,

(5.40b)

where  .

U 1 [i] =

.

U 3 [i] =



l[i] .U 2 [i] = σ2



 0 η1 [i]IM+1 , 0 −η1 [i]ϵ12 + ξ1 [i]

(5.41)

 0 η2 [i]IM+1 , 0 −η2 [i]ϵ22 + ξ2 [i]

(5.42)

¯ IE1 [i]S d [i]IH E1 [i]GE1 H H H H d d ¯ E IE [i]S [i]I [i] G ¯ E IE [i]S [i]I [i]G ¯E G 1 1 E1 E1 1 1 1 IE1 [i]S d [i]IH E1 [i]

p[i] .U 4 [i] = σ2



IE2 S u [i]IH E2

H u ¯H G E2 IE2 S [i]IE2

¯ HE2 S u [i]IH E2 G E2 H H ¯ u ¯ GE IE S [i]I GE 2

2

E2

 ,

(5.43)

 , 2

(5.44)

5.2 Proposed Algorithm for Joint Uplink/Downlink Optimization

101

IM+1 represents the .(M + 1) × (M + 1) identity matrix. We use the SDR method to relax the non-convex unit-modulus constraints and have

.

.

.

 2

 H  d H d GG1 IG1 [i]s d [i] = GH G1 IG1 [i]S [i]IG1 [i]GG1 = Tr S [i]A1 [i] ,

 2  u   H  u H GG2 [i]IG2 [i]s u [i] = GH G2 [i]IG2 [i]s [i]IG2 [i]GG2 [i] = Tr S [i]A2 [i] ,

where H A1 [i] = IH G1 [i]GG1 GG1 IG1 [i],

.

H A2 [i] = HH G2 [i]GG2 [i]GG2 [i]IG2 [i],

.

and .Tr(X) represents the trace of .X. Therefore, problem (5.36) can be rewritten as max

.

S d [i],S u [i],ξ1 [i], ξ2 [i],η1 [i],η2 [i]

I

1  ˜ phi ˜ phi χ Rdown [i] + (1 − χ )R up [i] . I

(5.45a)

i=1

s.t. η1 [i], η2 [i] ≥ 0, ∀i, .

(5.45b)

S d [i], S u [i] 0, ∀i, .

(5.45c)

S dr,r [i], S ur,r [i] = 1, r = 1, · · · , M + 1, ∀i,

(5.45d)

(5.40), where 

 l[i] d ˜ phi 1 + R [i] = log Tr S [i]A [i] − log2 (1 + ξ1 [i]) , 1 2 down σ2    h[i]  u ˜ phi R 1 + Tr S [i]A [i] − log2 (1 + ξ2 [i]) , [i] = log 2 2 up σ2

.

the .(r, r)th element of .S d [i] and .S u [i] are denoted by .S dr,r [i] and .S ur,r [i], respectively. Since .− log2 (1 + ξ1 [i]) and .− log2 (1 + ξ2 [i]) are not concave in regard to .ξ1 [i] and .ξ2 [i], respectively, it is challenging to obtain the optimal solution to problem (5.45). However, the first-order Taylor expansions of concave and convex functions are known to be global upper and global lower estimates, respectively. Using the SCA method to solve problem (5.45), the first-order Taylor expansion  I of .log2 (1 + ξ1 [i]) and .log2 (1 + ξ1 [i]) at given points .ξ 1,0 = ξ1,0 [i] i=1 and  I .ξ 1,0 = ξ1,0 [i] can be respectively given by i=1

102

5 Securing UAV Networks for Dense Urban Areas

    1 1   η1 [i] − ξ1,0 [i] , log2 (1 + ξ1 [i]) ≤ log2 1 + ξ1,0 [i] + ln 2 1 + ξ1,0 [i] (5.46)     1 1   ξ2 [i] − ξ2,0 [i] , . log2 (1 + ξ2 [i]) ≤ log2 1 + ξ2,0 [i] + ln 2 1 + ξ2,0 [i] (5.47)

.

Problem (5.45) can be transformed into max

.

S d [i],S u [i],ξ1 [i], ξ2 [i],η1 [i],η2 [i]

I

1  ˜ phi ˜ phi χ Rdown [i] + (1 − χ )R up [i] I i=1

(5.48)

s.t. (5.40), (5.45b), (5.45c), (5.45d), where 

 l[i] d ξ1 [i] 1 phi ˆ  , Tr S [i]A1 [i] − .Rdown [i] = log2 1 + ln 2 1 + ξ1,0 [i] σ2 and    p[i]  u ξ2 [i] 1 ˆ phi  . 1 + R Tr S [i]A [i] − [i] = log 2 2 up 2 ln 2 1 + ξ2,0 [i] σ

.

Convex optimization problem (5.48) can be solved effectively by CVX, but cannot obtain a rank-one solution. Therefore, the Gaussian randomization method is used to restore .s d [i] and .s u [i] from .S d [i] and .s u [i], respectively.

5.2.3 Robust Solution to UAV Trajectory Given .Ψ d , .Ψ u , .l, and .p, we can express sub-problem 3 as

W

  I  2  p[i]  1  traj u  (1 − χ ) log2 1 + 2 GH + χ R [i]I [i]s [i] [i]  G2 G2 down I σ

s.t.

(5.1),

max .

i=1

(5.49) where  2  l[i]    traj d Rdown [i] = log2 1 + 2 GH I [i]s [i]  G1 G1 σ

.

5.2 Proposed Algorithm for Joint Uplink/Downlink Optimization

 − log2 1 +

max

ΔGE1 ∈Ω1

103

 2 l[i]   H  d GE1 IE1 [i]s [i] . σ2

We omit .RGE [i] which has nothing to do with the UAV trajectory in problem (5.49). Therefore, we use the trajectory of the .(j − 1)th iteration to figure op out the worst case setting for eavesdropping channels .GE1 [i] in the j th iteration. In addition, it can be seen from (5.4)–(5.8) that in addition to .LU G [i], .LU E [i], LoS .LU RG [i], and .LU RE [i], .G U R [i] is also related to the UAV trajectory. However, LoS since .GU R [i] is a complex nonlinear function of the UAV trajectory variables, the UAV trajectory design becomes very tricky. In order to solve it, we use the UAV trajectory of the .(j − 1)th iteration to obtain an approximate .GLoS U R [i] in the j th iteration. Then, problem (5.49) can be reformulated as

W

I

1  ˙ traj (1 − χ ) log2 1 + ρC1 [i]GTue [i]IGW [i]Gue [i] + χ R [i] down I

s.t.

(5.1),

max .

i=1

(5.50) where

T ˙ traj R down [i] = log2 1 + ρC0 [i]Gue [i]IW G [i]Gue [i] .

− log2 1 + ρC0 [i]GTst [i]IW E [i]Gst [i] , Gue [i] =



.

Gst [i] =

.



(DU G [i])

−α

−α

(DU E [i])



−β

T

, (DU R [i]) 

−β

(5.51)

,

(5.52)

,

(5.53)

T

, (DU R [i])

H  

H (j −1) H −β G IW G [i] = GH , [i] Ф [i]G (d ) RG RG d UG UR

.

  

H (j −1) H −β G × GH , [i] Ф [i]G (d ) RG RG , UG d UR  H  (j −1) H H −β H .IGW [i] = GGU , (dRG ) GGR Фu [i]GRU [i]

(5.54)

104

5 Securing UAV Networks for Dense Urban Areas

 ×

 GH GU ,

(dRG )

−β

(j −1) H GH GR Фu [i]GRU [i]

 ,

(5.55)



 op G [i]   op U EH .IW E [i] = (j −1) (dRE )−β GRE [i] Фd [i]GU R [i]  H op G [i] U E  op H , ×  (j −1) (dRE )−β GRE [i] Фd [i]GU R [i] (j −1)

(5.56)

(j −1)

C0 = p[i]/σ 2 , .C1 = g[i]/σ 2 , and .GU R [i] and .GRU [i] are .GU R [i] and .GRU [i] obtained by the trajectory of the .(j − 1)th iteration, respectively. The objective function in problem (5.50) is a non-concave function of the UAV trajectory. After introducing the slack variables .u = {u[i]}Ii=1 , .e = {e[i]}Ii=1 , .s = {s[i]}Ii=1 , .t = {t[i]}Ii=1 , .ζ = {ζ [i]}Ii=1 , .rd = {rd [i]}Ii=1 , and .ru = {ru [i]}Ii=1 , problem (5.50) is transformed into

.

.

max

W,u,e,s t,ζ ,rd ,ru

s.t.

.

I

1  ˜ traj χ Rdown [i] + (1 − χ ) log2 (1 + ργ1 [i]ru [i]) . I

(5.57a)

i=1

 (DU G [i])−α  (DU R [i])−β  (DU E [i])−α  (DU R [i])−β

≥ u[i], ∀i, .

(5.57b)

≥ e[i], ∀i, .

(5.57c)

≤ s[i], ∀i, .

(5.57d)

≤ t[i], ∀i, .

(5.57e)

˜ Tst [i]IW E [i]G ˜ st [i] ≤ ζ [i], ∀i, . ρC0 [i]G

(5.57f)

˜ Tue [i]IW G [i]G ˜ ue [i] ≥ rd [i], ∀i, . G

(5.57g)

˜ Tue [i]IGW [i]G ˜ ue [i] ≥ ru [i], ∀i, G

(5.57h)

ϱ[i] ≤



(ZU − ZE )−α , υ[i] ≤



(ZU − ZR )−β , ∀i,

(5.57i)

(5.1), T¯ ˜ traj ˜ where .R down [i] = log2 (1 + ργ0 [i]rd [i]) − log2 (1 + ζ [i]), .Gue [i] = [u[i], e[i]] , ˜ st [i] = [s[i], t[i]]T . For the sake of the subsequent derivations, we perform and .G the first-order Taylor expansions of (5.57b)–(5.57e) as follows,

5.2 Proposed Algorithm for Joint Uplink/Downlink Optimization

105 4

X2 [i] + X2G + Y2 [i] + Y2G − 2XG X[i] − 2YG Y[i] + Z2U − (u[i])− α ≤ 0, ∀i, . (5.58a)

.

X2 [i] + X2R + Y2 [i] + Y2R − 2XR X[i] − 2YR Y[i] + (ZU − ZR )2 − (e[i])

≤ 0, ∀i, .

(5.58b)

− α4

− X2 [i] − X2E − Y2 [i] − Y2E + 2XE X[i] + 2YE Y[i] − Z2U ≤ 0, ∀i, . (5.58c)

− β4

− X2 [i] − X2R − Y2 [i] − Y2R + 2XR X[i]

(s[i])

(t[i])

− β4

+ 2YR Y[i] − (ZU − ZR )2 ≤ 0, ∀i.

(5.58d) 4

−4

The first-order Taylor expansions of .−X2 [i], .−Y2 [i], .(u[i])− α , .(e[i]) β , ˜ Tue [i]IW G [i]G ˜ Tue [i]IGW [i]G ˜ ue [i], and .G ˜ ue [i] at the given feasible .log2 (1 + ζ [i]), .G I I points .X0 = {X0 [i]}i=1 , .Y0 = {Y0 [i]}i=1 , .u0 = {ϑ0 [i]}Ii=1 , .e0 = {ν0 [i]}Ii=1 ,  I I ˜ ue,0 [i] .ζ 0 = {ζ0 [i]} , and .Iϑν,0 = G are given by i=1 i=1

T

˜ Tue [i]IQG [i]G ˜ ue [i] ≥−G ˜ Tue,0 [i]IQG [i]G ˜ ue,0 [i]+2 G ˜ ue [i] , . ˜ ue,0 [i]IQG [i]G G

.

(5.59a)

˜ Tue [i]IGW [i]G ˜ ue [i] ≥−G ˜ Tue,0 [i]IGW [i]G ˜ ue,0 [i]+2 G ˜ Tue,0 [i]IGW [i]G ˜ ue [i] , . G

(5.59b) log2 (1 + ζ [i]) ≤ log2 (1 + ζ0 [i]) + 4

4

1 (ζ [i] − ζ0 [i]) , . ln 2 (1 + ζ0 [i])

4 4 (u0 [i])− α −1 (u[i] − u0 [i]) , . α 4 − 4 −1 − (e0 [i]) β (e[i] − e0 [i]) , . β

(u[i])− α ≥ (u0 [i])− α − (e[i])

− β4

− β4

≥ (e0 [i])

(5.59c) (5.59d) (5.59e)

− X2 [i] ≤ X20 [i] − 2X0 [i]X[i], .

(5.59f)

− Y2 [i] ≤ Y20 [i] − 2Y0 [i]Y[i].

(5.59g)

Problem (5.57) can be approximated as

.

max

W,u,e,s, t,ζ ,rd ,ru

I 1  ˆ traj χ Rdown [i] + (1 − χ ) log2 (1 + ργ1 [n]ru [n]] I i=1

(5.60a)

106

5 Securing UAV Networks for Dense Urban Areas

X2 [i] + X2G + Y2 [i] + Y2G − 2XG X[i] − 2YG Y[i] + Z2U   4 4 4 4 − 1+ (u0 [i])− α + (u0 [i])− α −1 u[i] ≤ 0, ∀i, α α

s.t. .

X

2

[i] + X2R

2

+Y

[i] + Y2R

  4 −4 − 2XR X[i] − 1 + (e0 [i]) β β

.

− 2YR X[i] + (ZU − ZR )2 +

4 − 4 −1 (e0 [i]) β e[i] ≤ 0, ∀i, β

(5.60b)

(5.60c)

4

(s[i])− α + X20 [i] − 2X0 [i]X[i] − X2E + Y20 [i] − 2Y0 [i]Y[i] .

− Y2E + 2XE X[i] + 2YE Y[i] − Z2U ≤ 0, ∀i,

(t[i]) .

− β4

+ X20 [i] − 2X0 [i]X[i] − X2R + Y20 [i] − 2Y0 [i]Y[i]

(5.60d)

(5.60e)

− Y2R + 2XR X[i] + 2YR Y[i] − (ZU − ZR )2 ≤ 0, ∀i,

.

T

˜ ue,0 [i]IW G [i]G ˜ Tue,0 [i]IW G [i]G ˜ ue,0 [i] − 2 G ˜ ue [i] ≤ 0, ∀i, rd [i] + G (5.60f)

.

T

˜ Tue,0 [i]IGW [i]G ˜ ue,0 [i] − 2 G ˜ ue,0 [i]IGW [i]G ˜ ue [i] ≤ 0, ∀i, ru [i] + G (5.60g)

(5.1), (5.57f), (5.57i),

.

traj

ζ [i] ˆ down [i] = log2 (1 + ργ0 [n]rd [i]) − where .R ln 2(1+ζ0 [i]) . Problem (5.60) is a convex optimization problem that can be solved using CVX solver.

5.2.4 Overall Algorithm Algorithm 5.1 summarizes three sub-problems of problem (5.22), where .ϵc is the convergence accuracy and .jmax represents the maximum number of iterations. According to [86] and [29], the computational complexity  √  of solving sub-problem 2 and sub-problem 3 are .Osub2 2 M + 1 log (1/ϵc ) 2I (M + 1)3

5.3 Numerical Results

107

Algorithm 5.1 Proposed algorithm for solving problem (5.22)

  (0) (0) initializel: Set the initial feasible points 0 = W(0) , Ψ d , Ψ u , l(0) , p(0) , ϑ 0 , ν 0 , ξ 1,0 , ξ 2,0 , ζ 0 . (0)

Set iteration index j = 0 and Rsec . repeat Set j ← j + 1; (j −1) (j −1) , Ψu , ϑ 0 , ν 0 , and ζ 0 , With given W(j −1) , l(j −1) , p(j −1) , Ψ d (j ) (j ) (j ) (j ) update W , ϑ , ν and ζ by solving problem (5.60); Set ϑ 0 = ϑ (j ) , ν 0 = ν (j ) , and ζ 0 = ζ (j ) ; With given W(j ) , l(j −1) , p(j −1) , ξ 1,0 , and ξ 2,0 , (j )

(j )

(j )

update Ψ d , Ψ u , ξ , and ξ 2 by solving problem (5.48); (j ) (j ) Set ξ 1,0 = ξ 1 and ξ 2,0 = ξ 2 ; (j )

(j )

With given W(j ) , Ψ d , and Ψ u update l(j ) and p(j ) by using (5.34); (j ) (j ) (j ) With given W(j ) , Ψ d , Ψ u , l(j ) , and p(j ) , compute Rsec ; (j )

(j −1)

until Rsec − Rsec

≤ ϵc or j > jmax ;

   +4I 2 (M + 1)2 + 8I 3 and .Osub3 (8I )3.5 log (1/ϵc ) , respectively. Therefore, the overall complexity of solving problem (5.22) is .Osub2 + Osub3 .

5.3 Numerical Results Numerical results are given to verify the effectiveness of our proposed joint uplink/downlink optimization algorithm (denoted as PA). The benchmark algorithms used for comparison are as follows: .(1) Proposed algorithm without passive beamforming design (denoted as PA/PBD); .(2) Proposed algorithm without trajectory design (denoted as PA/TD); .(3) Proposed algorithm without robust design (denoted as PA/RD). In PA/TD, the UAV flies in a straight line from the starting point to the user, hovers above it, and then flies in a straight line to the end point. According to the definition of uncertainty radii .ϵ1 and .ϵ2 in [86], we definethe maximum normalized  ¯ Ep , where .p ∈ {1, 2}. estimation error of the eavesdropping links as .δp = ϵp / G Considering that the flight height of the UAV in downlink transmission is usually higher than others, the Rician factors of UAV-Ground and UAV-Eav links are set as .βU G = βU E = 10 dB and those of RIS-Ground, RIS-Eav, and UAV-RIS links are set as .βU R = βRG = βRE = 3 dB. Similarly, the corresponding Rician factors in uplink transmission are .βGU = 10 dB and .βRU = βGR = βGE = 3 dB. The PA/TD algorithm gives the initial feasible solution of the proposed PA algorithm. Other set parameters are as follows: .w0 = [−250, 20]T m, .wF = [250, 20]T m, qG = [0, 60]T m, qE = [100, 75]T m, .qR = [0, 0]T m, ZU = 100 m, ZR = 40 m, vmax = 30 m/s, .δt = 0.4 s, M = Mx × My = 6 × 5, σ 2 = −80 dBm, .d = λ2 , α = 2.2, κ = 3.3, ς = 3.4, ρ = −30 dB, ϵc = 10−3 ,

5 Securing UAV Networks for Dense Urban Areas

Average worst-case secrecy rate(bps/Hz)

108

1.6 1.4 1.2 1 0.8 0.6 0.4

T=32s T=62s T=92s

0.2 0 0

5

10

15

20

Iteration Number

Fig. 5.2 Average worst-case secrecy rate versus iteration number

¯ and .Ppeak = 4P¯ . Assume that all the normalized jmax = 40, Lpeak = 4L, estimation error variances share the same maximum, namely, .δ1 = δ2 = δa . It can be seen from Fig. 5.2 that the average worst-case secrecy rate of the PA algorithm changes with the number of iterations under different T with .λ = 0.5, 2 .δa = 0.5. The algorithm can converge rapidly, and the rate enhances with the increase of T . Figure 5.3 shows the UAV trajectories, which are obtained when .T = 62 s, .δa2 = 0.5, .L¯ = P¯ = 20 dBm and .λ = 0.5, while Fig. 5.4 presents the corresponding velocities of the UAV for different algorithms. The two figures show that the UAV first flies to a position at a speed of .Vmax , then remains stationary, and flies to the final position at a speed of .Vmax . For the PA/PBD algorithm, however, the UAV first flies in a straight line to a location, then hovers as close as possible to the user and away from the eavesdropper for long enough, and finally flies in a straight line to the destination to avoid wiretapping. In contrast, the PA and PA/RD algorithms indicate that the UAV tries to fly along an arc to a location between the user and RIS, then hover, and ultimately fly to the end point. This is because the PA and PA/RD algorithms trade off the channel gain between the direct links (i.e., the UAVGround, UAV-Eav, Ground-UAV, and Ground-Eav links) and the reflecting links (i.e., the UAV-RIS-Ground, UAV-RIS-Eav, Ground-RIS-UAV, and Ground-RIS-Eav links) in each time slot to choose a trajectory for optimal communication quality. In addition, because the PA algorithm considers the imperfect CSI, its UAV trajectories are more dispersed than those of the PA/RD algorithm. Figure 5.5 shows the average worst-case secrecy rates versus T for different algorithms with .λ = 0.5, .δa2 = 0.5, and .L¯ = P¯ = 20 dBm. In the hovering position, the UAV achieves a trade-off between improving the quality of the legitimate user’s signal and weakening that of the eavesdropper’s signal. Therefore, the maximum average worst-case secrecy rate is obtained. Specifically, the PA .

5.3 Numerical Results 90 80

Eavesdropper

70 Ground User

Y(m)

60 50 40 30 20 10

q0

qF RIS

0 -300

-200

-100

0

100

200

300

X(m)

(a) 90

Eavesdropper

80 70

Ground User

Y(m)

60 50 40 30 20 10

qF

q0 RIS

0 -300

-200

-100

0

100

200

300

X(m)

(b) 90

Eavesdropper

80 70

Ground User 60

Y(m)

Fig. 5.3 UAV trajectories by using different algorithms with .T = 62 s, .δa2 = 0.5, ¯ = P¯ = 20 dBm and .L .λ = 0.5. (a) The UAV trajectory of the PA algorithm. (b) The UAV trajectory of the PA/PBD algorithm. (c) The UAV trajectory of the PA/RD algorithm

109

50 40 30 20 10 0 -300

q0

qF

RIS -200

-100

0

X(m)

(c)

100

200

300

110

5 Securing UAV Networks for Dense Urban Areas

Speed(m/s)

40 (270,30)

(41,30)

20

(269,2.11)

(42,12.13)

0

(268,0)

(43,0)

0

50

100

150

200

250

300

N

Speed(m/s)

40 (270,30)

(41,30)

(269,21.76)

(42,22)

20

(268,0)

(43,0)

0

0

50

100

150

200

250

300

N

Speed(m/s)

40 (269,30)

(42,30)

(268,27.44)

20

(43,1.45) (267,0)

(44,0)

0

0

50

100

150

200

250

300

N Fig. 5.4 Upper figure: UAV speed (m/s) versus N for the PA algorithm; middle figure: UAV speed (m/s) versus N for the PA/RD algorithm; lower figure: UAV speed (m/s) versus N for PA/PBD algorithm. The system parameters are set as .T = 62 s, .δa2 = 0.5, .L¯ = P¯ = 20 dBm and .λ = 0.5

algorithm outperforms all benchmark schemes. This shows that the secrecy rate performance can be effectively improved with the help of the proposed robust joint design. In addition, the performance of PA/RD algorithm is superior to other benchmark algorithms, indicating that even without considering CSI uncertainty of the wiretap channel, the joint design can obtain considerable benefits compared with other benchmark schemes. Figure 5.6 shows the average worst-case secrecy rates versus .δa2 for the different algorithms with .λ = 0.5, .T = 62 s, and .L¯ = P¯ = 20 dBm. The secrecy rates of all algorithms decrease with the increase of CSI uncertainty of the wiretap channel, because when the CSI uncertainty is large, it is more challenge to implement a robust design. However, the PA algorithm uses the proposed robust co-design to obtain better performance than other algorithms. In addition, the secrecy rate of the PA/RD algorithm without considering the CSI estimation errors is higher than other algorithms. This verifies the joint design has achieved significant gains. When 2 2 .δa is large enough (e.g., .δa = 0.5), excessive CSI uncertainty will lead to passive beamforming failure of RIS or even have the opposite effect. In this case, the secrecy of the PA/PBD algorithm can approach that of the PA/TD algorithm. In contrast,

5.3 Numerical Results

111

Average worst-case secrecy rate(bps/Hz)

1.8 1.6 1.4 1.2 1 0.8 0.6

PA PA/TD PA/RD PA/PBD

0.4 0.2 0 17

32

47

62

77

92

T(s)

Average worst-case secrecy rate(bps/Hz)

Fig. 5.5 Average worst-case secrecy rate performance by different algorithms 3

PA PA/TD PA/RD PA/PBD

2.5

2

1.5

1

0.5 0.1

0.2

0.3

0.4

0.5

2 a

Fig. 5.6 Average worst-case secrecy rate versus the maximum normalized channel estimation error variance

large CSI uncertainty has almost no impact on the trajectory or transmit power optimization, as shown by the smoothed curves of the PA/PBD algorithm. In Fig. 5.7, the UAV trajectories of the proposed algorithm are shown for different, .λ, with .T = 62 s, .δa2 = 0.5, and .L¯ = P¯ = 20 dBm. Specifically,

90

Eavesdropper

80 70

Ground User

Y(m)

60 50 40 30 20 10

q0

0 -300

qF

RIS

-200

-100

0

100

200

300

X(m)

90

Eavesdropper

80 70

Ground User

Y(m)

60 50 40 30 20 10

q0

0 -300

qF

RIS

-200

-100

0

100

200

300

X(m)

90

Eavesdropper

80 70

Ground User 60

Y(m)

Fig. 5.7 UAV trajectories of the PA algorithm by different 2 .λ with .T = 62 s, .δa = 0.5, ¯ = P¯ = 20 dBm. (a) .L .λ = 0.1. (b) .λ = 0.3. (c) .λ = 0.7. (d) .λ = 0.9

5 Securing UAV Networks for Dense Urban Areas

50 40 30 20 10

q0

0 -300

qF

RIS -200

-100

0

100

200

300

X(m)

90

Eavesdropper

80 70

Ground User 60

Y(m)

112

50 40 30 20 10 0 -300

q0

qF

RIS -200

-100

0

X(m)

100

200

300

5.4 Summary

113

λ = 0.1 means a greater focus on uplink transmission, while .λ = 0.9 means a greater focus on downlink transmission. In uplink transmissions, since .RGE [i] is not a function of the trajectory, it is only necessary to maximize .RGU [i] to solve the UAV trajectory. Therefore, when .λ = 0.1, uplink transmission dominates, and the PA algorithm almost realizes the trade-off between the channel gains of the GroundUAV link and the Ground-RIS-UAV link to select a trajectory, thus obtaining the best communication quality. As .λ increases, it becomes more and more evident that downlink transmission dominates, and how to trade-off the channel gain between the UAV-Ground link and UAV-RIS-Ground link, and UAV-Eav link and UAV-RISEav link is crucial for the trajectory design. Therefore, it is clear that the first half paths are more dispersed when .λ = 0.9 than that when .λ = 0.1. This is because the PA algorithm considers how to improve the legitimate rate, and also how to reduce the eavesdropping rate. In addition, when .λ is large enough (e.g., .λ = 0.9), the UAV tends to fly in a straight line to the ending point, thus improving the secrecy rate, because the UAV is closer to the eavesdropper in the latter half paths than the first half path.

.

5.4 Summary In this chapter, an RIS-assisted UAV network in dense urban areas was studied. The RIS is deployed to assist the secure communication between the UAV and user on the ground, whose confidential information is susceptible to interception by an eavesdropper. We considered that the TDMA protocol is used for both downlink and uplink communications and assumed that the CSI of the wiretap channels is imperfect. Our goal was to maximize the average worst-case secrecy rate through robustly co-designing the UAV trajectory, the passive beamforming of the RIS, and the transmit power of the legitimate transmitter. An efficient algorithm is proposed based on the BCD technique to deal with the non-convex joint uplink/downlink optimization problem. The problem is divided into three subproblems, and the SCA, S-Procedure and SDR techniques are adopted to deal with them. Simulation results show that the average secrecy rate of our algorithm is significantly higher than that of the benchmark algorithms, which verifies the robustness of the proposed algorithm.

Chapter 6

Conclusions and Open Issues

With the large-scale commercialization of 5G, the research on next-generation wireless communication networks is on the rise in both academia and industry. It is believed that these networks can achieve intelligent, secure, reliable and ubiquitous connectivity in the future. Space-air-ground-sea integration will provide key technical support for the unlimited connection of next-generation wireless networks. UAVs can provide greater coverage and stronger communication capabilities for communication networks due to their rapid deployment on demand, high mobility and strong LoS link characteristics. UAV networks are increasingly widely used in practical scenarios and are considered to be the key platform for realizing spaceair-ground-sea integrated networks. However, due to the strong LoS link and the openness of wireless channels of the UAV networks, the communication security of UAVs is difficult to be guaranteed, and UAV networks are highly vulnerable to malicious interference or eavesdropping attacks. Physical layer security is one of the technologies to improve the secrecy performance of communication systems, and the characteristics of UAV networks, such as high maneuverability, limited onboard energy and different propagation scenarios, bring new design dimensions and challenges by applying PLS technology. The book has covered the models and algorithms for securing UAV networks, mainly includes UAV AG propagation scenarios (i.e., rural areas, urban areas, dense urban areas) and the corresponding channel models (i.e., LoSC, PrLoSC and Rician channel) appropriate for these scenarios, the techniques (e.g., RIS, cooperative jamming and robust optimization) and algorithms (e.g., joint design of UAV trajectory and communication resources) for enhancing secrecy performance of UAV networks. At present, there are still open issues and challenges in the research of the PLS for UAV networks, which has not been covered in this book and also needs future study. First, most of the current research focus on non-dynamic scenarios, i.e., the locations of ground nodes are fixed. In fact, since ground jammers or eavesdroppers © The Author(s), under exclusive license to Springer Nature Switzerland AG 2024 B. Duo et al., Securing Unmanned Aerial Vehicle Networks, SpringerBriefs in Computer Science, https://doi.org/10.1007/978-3-031-45605-3_6

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may be mobile, communication UAVs or friendly jamming UAVs need to adaptively adjust their trajectories and transmit powers to better avoid/disrupt ground jammers/eavesdroppers. To secure dynamic UAV networks, the state prediction of the ground attackers is of great significance. ML is a good option to solve such problems. The rapidly advancing technology of ML offers promising and powerful tools for solving tricky scenarios. ML has the advantages of low complexity and high efficiency to achieve reliable prediction of channel states between UAVs and ground nodes for improving system performance. For example, reinforcement learning can facilitate UAV trajectory design. However, using ML methods may introduce new security issues, such as data collection or parameter updating. Second, in practical applications, the secrecy rate will increase with the increase of the number of friendly jamming UAVs. However, the increased number of friendly jammers will also bring higher costs and harder management, so there is a trade-off in the secrecy rate and the complexity of UAV networks. In the future, the general system model with multi-UAV and multiple ground nodes, i.e., UAVswarm enabled networks can be studied. Multiple UAVs can efficiently cooperate with each other to locate and trace the malicious mobile jammers for flying away from them promptly or confuse the eavesdroppers via collaborative beamforming for further improving the network secrecy performance. Last but not least, RIS-assisted UAV network is an emerging field of research, and addressing the attendant security challenges is key to realize its full potential. Several problems and challenges to be solved for future development and work are listed as below. • Physical layer security techniques against the attacks of malicious RIS-enhanced UAVs. Malicious RIS-enhanced UAV attacks refer to the attacks that a UAV, equipped with an RIS, is used to intercept or manipulate wireless signals. Noteworthily, this security issue has not been well studied from the perspective of UAV communication networks. Therefore, it is best to explore advanced methods in PLS to protect against this kind of challenging attacks. • Cooperative jamming in RIS-enhanced UAV networks. In this technique, multiple UAVs can work cooperatively to jam the received signals of the potential eavesdroppers, while simultaneously mitigate the unintentional interference with the legitimate receivers by properly designing the RISs. The goal of cooperative jamming is to create a secure communication channels for UAVs. By using cooperative jamming, UAVs can increase the security of their communications, making it harder for attackers to intercept their signals. Overall, cooperative jamming is a promising technique that can help ensure that UAVs can operate efficiently and securely in a range of different applications. • Artificial Intelligence approaches in RIS-enhanced UAV networks. Optimizing large-scale RIS to enhance the secrecy of UAV networks is challenging, especially when the UAVs is deployed in partially unknown environments and the network is highly dynamic. There are several AI approaches, such as, deep reinforcement learning, transfer learning, and evolutionary algorithms, can be used as effective solution tools for improving secrecy between RIS-enhanced

6 Conclusions and Open Issues

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UAVs and ground nodes or other UAVs in the presence of malicious jammers and eavesdroppers. The choice of the AI approach depends on the specific requirements of the UAV networks. With ubiquitous learning and explainable AI techniques, it is believed that the security guarantees will be achieved for long-term evolution of intelligence in future 6G integrated UAV networks.

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