Near-Earth Laser Communications [1 ed.] 082475381X, 9780824753818, 9781420015447

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Near-Earth Laser Communications Edited by

Hamid Hemmati

Boca Raton London New York

CRC Press is an imprint of the Taylor & Francis Group, an informa business

ß 2008 by Taylor & Francis Group, LLC.

OPTICAL SCIENCE AND ENGINEERING

Founding Editor Brian J. Thompson University of Rochester Rochester, New York

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CRC Press Taylor & Francis Group 6000 Broken Sound Parkway NW, Suite 300 Boca Raton, FL 33487-2742 © 2009 by Taylor & Francis Group, LLC CRC Press is an imprint of Taylor & Francis Group, an Informa business No claim to original U.S. Government works Printed in the United States of America on acid-free paper 10 9 8 7 6 5 4 3 2 1 International Standard Book Number-13: 978-0-8247-5381-8 (Hardcover) This book contains information obtained from authentic and highly regarded sources. Reasonable efforts have been made to publish reliable data and information, but the author and publisher cannot assume responsibility for the validity of all materials or the consequences of their use. The authors and publishers have attempted to trace the copyright holders of all material reproduced in this publication and apologize to copyright holders if permission to publish in this form has not been obtained. If any copyright material has not been acknowledged please write and let us know so we may rectify in any future reprint. Except as permitted under U.S. Copyright Law, no part of this book may be reprinted, reproduced, transmitted, or utilized in any form by any electronic, mechanical, or other means, now known or hereafter invented, including photocopying, microfilming, and recording, or in any information storage or retrieval system, without written permission from the publishers. For permission to photocopy or use material electronically from this work, please access www.copyright.com (http://www.copyright.com/) or contact the Copyright Clearance Center, Inc. (CCC), 222 Rosewood Drive, Danvers, MA 01923, 978-750-8400. CCC is a not-for-profit organization that provides licenses and registration for a variety of users. For organizations that have been granted a photocopy license by the CCC, a separate system of payment has been arranged. Trademark Notice: Product or corporate names may be trademarks or registered trademarks, and are used only for identification and explanation without intent to infringe. Library of Congress Cataloging-in-Publication Data Near-earth laser communications / editor, Hamid Hemmati. p. cm. -- (Optical science and engineering ; 142) Includes bibliographical references and index. ISBN 978-0-8247-5381-8 (hardback : alk. paper) 1. Laser communication systems. 2. Free space optical interconnects. I. Hemmati, Hamid, 1954- II. Title. III. Series. TK5103.6.N43 2009 621.382’7--dc22 Visit the Taylor & Francis Web site at http://www.taylorandfrancis.com and the CRC Press Web site at http://www.crcpress.com

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2008035719

Contents Preface Editor Contributors Chapter 1

Introduction Hamid Hemmati

Chapter 2

Systems Engineering and Design Drivers Morio Toyoshima

Chapter 3

Pointing, Acquisition, and Tracking Robert G. Marshalek

Chapter 4

Laser Transmitters: Coherent and Direct Detections Klaus Pribil and Hamid Hemmati

Chapter 5

Flight Optomechanical Assembly Hamid Hemmati

Chapter 6

Coding and Modulation for Free-Space Optical Communications Bruce Moision and Jon Hamkins

Chapter 7

Photodetectors and Receivers Walter R. Leeb and Peter J. Winzer

Chapter 8

Atmospheric Channel Sabino Piazzolla

Chapter 9

Optical Ground Station: Requirements and Design, Bidirectional Link Model and Performance Marcos Reyes García-Talavera, Zoran Sodnik, and Adolfo Comerón

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Chapter 10

Reliability and Flight Qualification Hamid Hemmati

Chapter 11

Optical Satellite Networking: The Concept of a Global Satellite Optical Transport Network Nikos Karafolas

Chapter 12

Future Directions Hamid Hemmati

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Preface The technology of free-space optical communications, also known as laser communications (lasercom), has finally matured sufficiently to meet the growing demand of operational multi-gigabit-per-second data rate systems communicating to and from aircrafts and satellites. Despite several potential advantages, lasercom has not yet been used widely in space due to the perceived risks that are associated with it. However, owing to a number of successful optical link demonstrations from the earth-orbit (during the last decade), this technology is likely to be used on a much larger scale than ever before in civilian, earth and space science, and military applications. The field deployment of lasercom is growing as it offers lower system size, mass, and power consumption, along with as much as two orders of magnitude higher bandwidth delivery when compared to its nearest competitors. Most of the advantages are brought about by a higher frequency, which results in a narrowing of the optical beam’s divergence. However, lasercom is nowhere near its technology peak, and much remains to be explored. A recent article suggests the potential for another 30 dB link improvement without any extraordinary efforts. This book is an amalgamation of the vast experiences of several authors. It is designed to acquaint the reader with the basics of laser satellite communications. The emphasis is on device technology, implementation techniques, and system trades. The theory behind laser communications has been covered in detail by several books published earlier. Chapter 1 is an introduction to near-earth laser communications technology. Justification for higher bandwidth and recent successful demonstrations are described here. Chapter 2 discusses design drivers, design trades, link budgets for acquisition, tracking and pointing, and communications links. Chapter 3 details approaches for laser beam pointing, acquisition, and tracking, with an emphasis on device technologies and implementation strategies. Chapter 4 elaborates on the flight laser transmitters for coherent and direct detection. Chapter 5 discusses the flight optomechanical assembly. Chapter 6 discusses the channel coding techniques describing applicable modulation for free-space optical communications. Chapter 7 describes the photodetectors and receivers as applicable to both the flight and ground transceivers. Chapter 8 discusses numerous implications of the atmospheric channel on laser beam propagation for both downlinks and uplinks. Chapter 9 describes the ground terminal and provides examples from recent successful flight links. Chapter 10 discusses methodologies for flight qualification of components and subsystems, including both optical and optoelectronic assemblies. Chapter 11 looks at approaches and configurations for cross-links and optical networking. Chapter 12 concludes the book with a brief summary of ongoing activities and those planned for the near future. I am indebted to all the contributing authors from the United States, Europe, and Japan for taking time off their busy schedules to share their knowledge. There are many others who have contributed directly or indirectly to the development of this book. They include members of the JPL’s Optical Communications Group,

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specifically Charles; Drs. Biswas, Ortiz, and Wright for critical review of certain chapters; and Weichman for a very thorough review of all chapters for consistency. I am also grateful to Farr, and Drs. Lesh, Wilson, Kovalik, Quirk, Roberts, Birnbaum, Chien Chen, Jimmy Chen, Sandusky, Schumaker, Rayman, Weber, Rafferty, Rush, Geldzahler, Deutsch, Townes, Pollara, Estabrook, Vilnrotter, Antsos, Davarian, Boroson, Yamakawa, Araki, and many others at JPL (and other research organizations) who have contributed greatly to the advancement of free-space laser communications technology. Finally, I would like to express my deepest gratitude to my wife Azita, and my children Elita and David for their continued and unfailing love and support. Hamid Hemmati Pasadena, California

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Editor Hamid Hemmati received a masters degree in physics from the University of Southern California, and a PhD in physics from Colorado University in 1981. Before joining the Jet Propulsion Laboratory (JPL) in 1986, he worked as a researcher at NASA’s Goddard Space Flight Center and at the National Institute of Standards and Technology, Boulder, Colorado. Currently, he is the supervisor of JPL’s Optical Communications Group developing laser communications technologies and systems for planetary and satellite communications. Dr. Hemmati has published over 150 journal and conference papers, holds 7 patents, has received 3 NASA Space Act Board Awards, and 34 NASA certificates of appreciation. He teaches optical communications courses at California State University, Los Angeles, and the UCLA Extension. He has edited and authored a book on Deep Space Optical Communications. Dr. Hemmati’s active areas of research include systems engineering for electrooptical systems, particularly for optical communications from space; solid-state lasers, particularly pulsed fiber lasers and microchip lasers, fl ight qualification of optical and electro-optical systems and components; low-cost multimeter diameter optical ground receiver telescopes; active and adaptive optics; novel deformable mirrors; free-space laser communication systems for short range to planetary distances; coherent optical communications; and laser beam acquisition, tracking, and pointing.

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Contributors Adolfo Comerón Department of Signal Theory and Communications Technical University of Catalonia Barcelona, Spain Jon Hamkins Jet Propulsion Laboratory National Aeronautics and Space Administration California Institute of Technology Pasadena, California Hamid Hemmati Jet Propulsion Laboratory National Aeronautics and Space Administration California Institute of Technology Pasadena, California

Bruce Moision Jet Propulsion Laboratory National Aeronautics and Space Administration California Institute of Technology Pasadena, California Sabino Piazzolla Jet Propulsion Laboratory National Aeronautics and Space Administration California Institute of Technology Pasadena, California Klaus Pribil NewComp Freienstein, Switzerland Marcos Reyes García-Talavera Technology Division Instituto de Astrofisica de Canarias Tenerife, Spain

Nikos Karafolas European Space Agency European Space Research and Technology Centre Noordwijk, The Netherlands

Zoran Sodnik European Space Agency European Space Research and Technology Centre Noordwijk, The Netherlands

Walter R. Leeb Institute of Communications and Radio-Frequency Engineering Vienna University of Technology Vienna, Austria

Morio Toyoshima Space Communication Group New Generation Wireless Communications Research Center National Institute of Information and Communications Technology Tokyo, Japan

Robert G. Marshalek Ball Aerospace and Technologies Corp. Boulder, Colorado

Peter J. Winzer Bell Labs Alcatel-Lucent Holmdel, New Jersey

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1 Introduction Hamid Hemmati CONTENTS 1.1 Introduction .......................................................................................................1 1.2 Lasercom Applications ...................................................................................... 3 1.2.1 Point-to-Point Links ...............................................................................4 1.2.1.1 Satellite-to-Satellite Links .......................................................4 1.2.1.2 Satellite-to-Air/Ground Links .................................................5 1.2.2 Point-to-Multipoint/Constellations/Networks .......................................7 1.2.2.1 Networks and Multiple Access Links......................................8 1.2.2.2 Protocols ..................................................................................8 1.2.2.3 Navigation and Ranging ..........................................................8 1.2.2.4 Multifunctional Transceivers ..................................................9 1.2.3 Planetary Links......................................................................................9 1.2.4 Retromodulator Links ............................................................................9 1.3 Subsystem Technologies ................................................................................. 10 1.3.1 Signal Detection ................................................................................... 10 1.3.1.1 Photon-Counting Detectors.................................................... 10 1.3.1.2 Modulation and Coding ......................................................... 13 1.3.2 Laser Transmitter ................................................................................. 14 1.3.3 Laser Beam Pointing and Stabilization ............................................... 15 1.3.4 Optomechanical Assembly for Flight Transceiver .............................. 17 1.3.5 Optomechanical Assembly for Ground Transceiver............................ 19 1.4 Technology Validations ................................................................................... 22 1.4.1 Recent Validations ............................................................................... 23 1.5 Conclusion ....................................................................................................... 23 References ................................................................................................................25

1.1 INTRODUCTION Airborne platforms equipped with multitude of earth-observing sensors and certain relay and earth-observing spacecraft are facing an exponential growth in data volumes that need to be transmitted to the Earth. Figure 1.1 shows data-rate trends as a function of time for unmanned aerial vehicles, and Figure 1.2 illustrates data-rate trends for earth-orbiting spacecraft [1,2].

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10 Tb/s 100 Gb/s 10 Gb/s

Potential RF limit due to frequency congestion NRO

AFRL

1 Gb/s

ABIT (CDL)

U2

Data rate

100 Mb/s 10 Mb/s 1 Mb/s Link 16

100 kb/s 10 kb/s 1 kb/s

Link 1

1955

Link 4 RF data link Optical data link 1960

1970

1980

1990

2000

2010

2020

FIGURE 1.1 Data-rate trends for unmanned aerial vehicles. (Adapted from the report: Unmanned Aerial Vehicle Roadmap 2000–2025, Ofice of the Secretary of Defense, p. 33, 2001.)

Because of their narrow transmit beamwidth and large carrier frequency, optical or laser communication (lasercom) technologies can meet the increased demand, and at the same time offer signiicant potential for improvement over conventional microwave radio frequency (RF) communications. Examples include frequency reuse (using the same wavelength for multiple links), improved channel security, reduced mass (∼1/2 of RF), reduced power consumption (∼1/2 of RF), reduced size 10,000

REF #2

9,000 8,000 Data rate (Mb/s)

7,000 6,000 5,000 4,000

SENTINEL

3,000 2,000 1,000

SPOT 2 LANDSAT 7 0 1995 2000 1985 1990

Worldview 1 TSAT 2005 2010 Launch year

FIGURE 1.2 Data-rate trends for earth-orbiting spacecrafts.

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2015

2020

2025

(∼1/10 the diameter of RF antenna), ability to track and communicate with the Sun within the ield of view, multifunctionality with other electro-optic instruments, and precision ranging [3]. Unlike RF communication systems where spectrum usage is restricted, optical links are not subject to frequency regulation—an attractive prospect for high bandwidth applications. Frequency reuse is an additional advantage made possible by the small divergence angle of the communications laser beam. Despite a multitude of advantageous features over RF communications, the perceived risk associated with lasercom has often been the primary impediment to its prevalent use in space. Even though most technological challenges have been resolved, there exists a potential to improve the link margin by more than three orders of magnitude relative to the present state of the art in lasercom technology [4]. In the oncoming decades, data rates exceeding 1 gigabits/second (Gb/s) are envisaged for the Mars missions, and tens of Gb/s for near-earth platforms. The technology of single-photon-sensitive detectors coupled with eficient laser transmitters and an array of low-cost large aperture receiving stations, offers the potential to signiicantly reduce the burden on space-borne telecommunication subsystem. Fine beam pointing from air or space, and strategies to mitigate cloud coverage still require the most attention from lasercom system developers. Beyond that, much of the iber-optic communication technologies may be employed in free-space optical communications (lasercom) systems wherein the iber waveguide is replaced with precision laser beam pointing from the transmitter side through air or space to the receiving target. This chapter provides a general high-level overview of the status of near-earth laser communications technology developments and future research opportunities. By near-earth we mean airborne platforms and earth-orbiting spacecrafts. The excellent performances of recent demonstrations and technology development efforts have been summarized in numerous publications [3–8]. In this book, we emphasize critical requirements and design drivers, the status of current subsystem technologies, and pathways to reach the immense potential of laser communications.

1.2

LASERCOM APPLICATIONS

Besides the standard links from low earth orbit (LEO), geostationary orbit (GEO), and deep-space spacecraft to ground, multigigabit links between LEO and GEO spacecraft, earth observation and communications spacecraft are also required. Figure 1.3 illustrates a partial range of application possibilities for point-to-point link, and networks of airborne or space-borne platforms communicating to the Earth or among each other. Lasercom allows the data to be sent at multiple Gb/s in a burst mode for a short contact time. Thereby, this technology can solve the current conlict between the requirement for space-borne observation spacecraft to be located at lower altitude orbits (for higher resolution imaging), and the telecommunications spacecraft requirements to be located at higher orbits (for greater link contact time).

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GEO sats Deep space probes

GEO

LEO sats

LEO

Airborne platforms

Mobile ground stations

FIGURE 1.3

1.2.1

Fixed ground stations

Concept of space optical communications network.

POINT-TO-POINT LINKS

Point-to-point optical communication links include satellite (or aircraft)-to-satellite (or aircraft), satellite (or aircraft)-to-airborne platforms (aircraft or balloon), and satellite (or aircraft)-to-ground-based stations. 1.2.1.1 Satellite-to-Satellite Links Both inter- (e.g., LEO–LEO) and intraorbit (e.g., LEO–GEO) links are of interest. A major advantage of satellite-to-satellite links is the lack of atmosphere between the two platforms. This enables iber-output to iber-input communications, where much of the already well-developed fiber-optic hardware and protocols may be utilized. A challenge (relative to spacecraft-to-ground links) is that both lasercom host platforms are moving and have dynamic characteristics. Distance between the two ends of the link, for example, between spacecrafts located in LEO, medium earth orbit (MEO) or GEO orbits, characterized by 10-X the optical beamwidth

Relative velocity implies a wellknown point-ahead angle of ~ 2-X–8-X the optical beamwidth

Local base disturbances are measured by the track sensor and corrected via a highbandwidth pointing element

FIGURE 3.2 PAT system overcomes several obstacles to establish and maintain a link between two moving platforms.

space-to-high-altitude aircraft, and other links to eficiently connect worldwide scientiic, military, and intelligence community users within a common data routing thread. A signiicant portion of this evolving communications architecture assumes the use of laser communications links between constituent platforms owing to the wide bandwidth, low probability of intercept, and antijam features mentioned above that result from the high optical carrier frequency. To realize the advantages of optical communications, an eficient means of pointing narrow optical beams must be realized. Figure 3.2 illustrates the general PAT problem encountered to establish and maintain an optical link between any two moving platforms within the architectural infrastructure described above. Two major PAT obstacles are overcome. The irst obstacle relates to the combination of initial pointing knowledge, local platform base motion, and point-ahead angle that greatly exceed the eventual optical beamwidth used to close the high data rate communications links. Beacon light is initially sent between the two terminals to convey their relative angular positions, thus greatly reducing the pointing error. The second obstacle is met once the link is established by completing the functional steps described below, when the terminal must provide precise pointing of the transmit beam and receive FOV, despite local disturbances that are often more than an order of magnitude larger than either parameter. This is accomplished by using the relayed narrow light beam as a stable reference, and eficiently measuring and attenuating the disturbances via an optical feedback control loop. Implementing an optical link involves an orderly process that reduces the initial pointing error and enables eficient use of the narrow beam. Figure 3.3 shows the top-level functional steps that establish and maintain the link between two platforms.

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Initial conditions

(1A) Acquisition scan and detect

(3A) Close link using narrow beam and NFOV track sensor

(1B) Respond to initial beacon detection (3B) Initialize communication and correct boresight

(2) Serial handoff steps

(3C) Transfer data

(4) Pointahead maintenance

(1A & 1B) Acquisition: Reduces pointing error from mrad to sub-urad levels (2) Handoff: Transfers LOS control from wide beam to narrow beam and from WFOV to NFOV optical sensors, to enable accurate pointing with the narrow transmit communications beam (3A, 3B, & 3C) Track: Uses high-bandwidth loop involving NFOV sensor and FSM to measure local base disturbances and point receive LOS back at the reference beam from the opposite platform (3A, 3B & 3C) Point ahead: Offsets the transmit LOS to accommodate relative velocity between linked platforms (3A, 3B & 3C) Gimbal offload: Supports wider field of regard by keeping the receive LOS close to the center of the FSM angular range of travel (4) Link maintenance: Periodically corrects alignment drifts between transmit and receive LOS to improve the long-term link efficiency

FIGURE 3.3 Functional low identiies critical PAT processes and interfaces.

Key elements include initial pointing information on each platform, completion of a beacon search routine, successful linking of the beacon beams between platforms, handoff to the narrow communication beam on each platform, communication data transfer, and periodic pointing error calibration to correct slow transmit–receive alignment drifts. Each functional step is further described below. Initial conditions: Each platform irst deines the angular location of the opposite platform as determined from the following elements at the determined time to begin the link establishment process: • Position knowledge typically provided by the host platform via global positioning system (GPS) inputs for each terminal, on order from ±100 to 250 m (3 sigma), imposing a signiicant impact only at close range • Orbital trajectory based on ephemeris data, also used to determine the relative velocity between the two platforms (v) and the corresponding pointahead angle given as 2v/c, where c is the speed of light • Establishment of local pointing coordinates axes relative to a ixed reference, i.e., local altitude knowledge, typically up to several milliradians per axis (3 sigma) at the attach point • Local terminal errors, including mechanical and optical alignments, such as telescope boresight alignment, gimbal mounting accuracy, and associated thermal drifts typically below 1 mrad. Thus, the third item usually dominates the combined uncertainty cone so derived for the opposite terminal, and the combined errors are typically on the order of several

ß 2008 by Taylor & Francis Group, LLC.

milliradians (i.e., tenths of a degree). By comparison, the optical beamwidth used to close the communications link, approximated by the ratio of the wavelength to the aperture diameter, is circa 10 µrad (i.e., several tenths of a millidegree). Furthermore, as available laser power is smaller than that required to lood this several-hundred optical beamwidth projected area and provide a detectable signal at maximum link range, a search routine is needed to begin the link establishment process. Acquisition scan and detect: In this step, each terminal uses a light beam to convey its angular position to the opposite terminal similar to a lighthouse at the seashore, or the rotating light atop a police car in your rear-view mirror. The beacon beam is often broadened relative to the narrow communications beam and methodically scanned over the uncertainty area, eventually illuminating the opposite aperture. The beacon is sensed by a position-sensitive detector located within the opposite terminal. The most common approach has each terminal staring over the initial error cone using a wide FOV (WFOV) sensor that covers all possible angles of arrival and uses the received beacon light to calculate the angle of arrival within the FOV. Since the transmit and receive functions are independent and performed simultaneously, many system designs implement a two-way acquisition sequence, whereby each terminal performs the scan and stare functions simultaneously to provide the shortest elapsed time before a beacon is detected by one of the terminals. To support this desire, an outward raster or spiral scan is commonly implemented that begins at the center of the initial uncertainty cone, as this is the most likely location of the opposite terminal. Finally, some approaches have considered using the narrow communications beam for acquisition to eliminate extra optics and switching between the two divergence modes, but this also implies that the initial scan process is more dependent on the platform base disturbances and the impact they place upon implementing a scan pattern that is free of intensity dropouts. Respond to initial beacon detection: Once the beacon is detected by one side of the link, the terminal stops its scan and uses the WFOV sensor to determine the angle of arrival within the initial error cone, despite no longer sensing a receive signal based on the continuing scan by the opposite terminal. A beam steering element, such as a fast steering mirror (FSM), then points a steady beacon beam along the calculated angular LOS often offset by the ixed point-ahead angle, to deliver the highest possible power density back to the opposite terminal. The opposite terminal receives the return beacon, stops its scan and returns a steady beacon beam back to the partner. This completes the irst portion of spatial acquisition process, but the power density relayed between the terminals is still well below the threshold for high data rate communications. Serial handoff steps: The terminals use the steady beacon to cooperatively increase the optical signal delivered between them, enabling an increase in the WFOV sensor readout rate and corresponding track loop bandwidth on each end that better attenuates local base disturbances to improve the pointing accuracy. As such, each terminal places a larger signal onto the counterpart, irst enabling a switch to the narrow communications beam and then eventually exceeding the threshold for handing LOS control off to the narrow FOV (NFOV) track sensor. The improved pointing accuracy allows each terminal to proceed closer to the peak intensity available from the narrow beam, eventually exceeding the power threshold for completing the handoff

ß 2008 by Taylor & Francis Group, LLC.

to ine track on each end, and enabling subsequent establishment of the communications link. An accurate point-ahead correction as described below, is a critical element in this portion of the process. Close link using narrow beam and NFOV track sensor: A steady narrow beam is relayed between the two terminals, providing a receive power density at each end that enables NFOV track sensor sampling rates typically ranging from 10 to 50 kHz. The high sampling rate allows effective rejection of platform jitter up through the 250–500 Hz range via commands to a FSM located in the common transmit–receive optical path that accurately points the FSM LOS directly back at the incoming reference beam. The 40-X to 100-X total oversampling ratio is consistent with standard control theory and represents the combination of two factors: • A 4-X ratio between the LOS control loop bandwidth and the disturbance rejection bandwidth • An optical feedback sensor readout rate in the range 10-X – 25-X higher than the LOS control loop bandwidth, for minimal phase margin and gain margin degradation Residual radial pointing jitters on the order of 10% of the communications beamwidth (3-sigma) provide a receive power versus time proi le that supports reliable communications with an adequate average bit error ratio (BER). This level of performance is also consistent with an acceptable tracking loss in the communications mode (∼1–2 dB) that couples with a suitably low number of random fades, or short-term BER increases, in a typical data relay mission. Initialize communication, correct boresight, and transfer data: Communications initialization is completed by relaying a predetermined bit pattern between platforms to synchronize the clocks prior to transferring the high-rate communications data. After establishment of frame synchronization, and periodically throughout a communication event, a cooperative end-to-end power-on-target algorithm corrects the alignment between the laser terminal transmit and receive paths to optimize the link eficiency. This normally consists of a predetermined pointing pattern, with far-ield receive power measurements versus pointing position provided by the link partner used via a “greatest-of” algorithm to correct the boresight. The end-to-end link maintenance process is completed without degrading the communications BER performance below the speciied requirement. Point-ahead/look-behind maintenance: One additional function is required to establish an effective relay between the two linked terminals that corrects the relative velocity between the platforms and the inite velocity of light. Based on the above ine track description, the system commands the FSM element to point back at the incoming LOS. However, relative motion, that is always present between the two platforms, must be corrected to properly point the outgoing beam. Figure 3.4 illustrates this effect. Light sent from the opposite terminal when it is located in position A, will be received by the local terminal when in position B and will receive the return beam when in position C. The transmit LOS must therefore be offset by the angle between positions A and C, to properly illuminate the far-ield target. As an aside, this description assumes that the transmit LOS is pointed ahead to correct this

ß 2008 by Taylor & Francis Group, LLC.

Platform #1

Platform #2

Time

Where they:

tk+1 rA B

Will be (position C)

tk

Point-ahead angle = 2 v/c

Are (position B)

rA B

k k−1

tk−1

FIGURE 3.4

Relative velocity = v

k k+1

Were (position A)

Point ahead corrects for relative LOS motion.

effect. Some implementations perform the ixed offset correction within the receive path in a look-behind implementation. Either approach accomplishes the same function. In either case, the process relies on accurate alignment between the transmit and receive LOS vectors versus time. To provide the most eficient relay between two terminals, the transmit-to-receive alignment is frequently corrected via the link maintenance power-on-target algorithm described previously.

3.3 GENERAL PAT REQUIREMENTS All PAT systems must meet a set of combined performance requirements in a lowrisk, cost-eficient manner. Figure 3.5 summarizes the key requirements that typically drive the optical PAT design, together with proven techniques that have been evaluated both analytically and demonstrated in risk-reduction hardware via several prior development efforts. In summary, the basic PAT requirements are • Acquire the link rapidly with a high probability of success: circa 1 to 2 min with at least 95% success is typical • Acquire close to the sun to increase acquisition opportunities: circa a degree or two from the receive optical boresight is typical • Track the opposite platform with submicroradian residual LOS jitter to reduce random link BER degradation (i.e., radial LOS jitter 1kHz bandwidth 2-deg steering range DIT position sensors support gimbal off-load loop

Heritage FSM mechanisms are flight proven Additional qualification and reliability development in process for specific mission applications

PAM

Transmit point ahead and beam scanning

Provides sub-µrad pointing accuracy in point-ahead mode Supports beam scan or dither for other operating modes Same basic mechanism as FSM

0.5 nm Δn > 130 GHz

1.0640 1.0635 1.0630

Tuning–rate 3.44 GHz/ ⬚C

1.0625 1.0620 1.0615 1.0610 −20

0

20

40 60 Crystal temperature (⬚C)

80

100

120

FIGURE 4.12 Free spectral range of a 300 µm microchip laser at 23 mW optical output power.

3.44 GHz/K. If optical output power is reduced, the free spectral range can be further extended, as shown in Figure 4.13. Thermal tuning offers a large tuning coeficient, but is still a rather slow mechanism to change the laser frequency. For a local oscillator using the microchip laser, additional fast tuning has to be implemented. Techniques proposed included 260

Single-frequency tuning range (GHz)

240 220 200 180 160 140 120 100 80 60 40 20 0 0

5

10

15

20

25

Single-frequency output power (mW)

FIGURE 4.13

Extension of free spectral range by reduction of output power.

ß 2008 by Taylor & Francis Group, LLC.

“Semimonolithic” Nd:YAG crystal

Actuator AR @ 1064 nm

808 nm pump

1064 nm output

Thruhole AR @ 1064 nm

PR @ 1064 nm

Output coupling mirror

Input coupling mirror (HR 1064 nm, HT 808 nm)

Tuning voltage input

FIGURE 4.14

Semimonolithic microchip laser with tuning element.

modulation of the pump light or the application of mechanical stress to the cavity e.g., by a piezo element. An alternative solution is the semimonolithic microchip laser in which one mirror is removed from the crystal and put onto a mechanical transducer, which allows one to modulate the mechanical length of the cavity. Actuators can be piezo or micromechanical elements [8]. The principle of such a laser is shown in Figure 4.14. In this design the output mirror is bonded onto a piezo foil which changes the length of the cavity according to the tuning voltage applied to it. A prototype of a semimonolithic microchip laser has been realized and integrated into a coherent communication system [9]. The performance of this laser is summarized in Table 4.2. Figure 4.15 shows a photo of the microchip laser with its proximity electronics, an external isolator, and a PPF pigtail.

TABLE 4.2 Performance of Microchip Laser Prototype Output power Output power (ex iber) Wavelength Linewidth Frequency drift Low tuning band

30 mW 5 mW 1064 nm Ppa. One can show [9] that, for ixed ns and nb, the capacity is monotonically decreasing in the PPM order. It follows that peak and average transmitter constraints impose an effective constraint on the optimum order of M ≤ Ppa. This can be seen as follows. If there is a signaling scheme with average photons per pulse ns and duty cycle 1/M that meets the peak and average power constraints, then ns ≤ min{M Pav, Ppk}. If M > Ppa (and Ppa is a power of 2), then, we can increase the capacity by reducing M to M = Ppa, without violating the power constraints. Hence, in the presence of peak and average power constraints, the PPM order should be set so that the average power is met with equality (or as close as possible), even if the peak constraint cannot be met with equality.

6.3.3

THE IMPACT OF DEAD-TIME

Certain lasers have a required dead-time after the transmission of a pulse during which another pulse cannot be transmitted. Suppose that this dead-time is an integer

ß 2008 by Taylor & Francis Group, LLC.

M= 64, nb = 1.0

Bits/slot

10−1

Cd, M = 64 10

−2

Cs, M = 64 10−3 −3 10

10−2 10−1 Pav (Signal photons/slot)

100

FIGURE 6.6 Achievable rates for M = 64, nb = 1, with and without dead-time.

d multiple of the slotwidth. To satisfy the dead-time constraint with PPM signaling, we can impose a period of d slots after each symbol during which a pulse cannot be transmitted. Dead-time may also be added to provide a tone to aid in synchronization, or to vary the duty cycle without changing the PPM order. How does this added dead-time impact the capacity of the channel? Suppose that we can close an optical link of PPM order M with average power Pav = ns/M. Adding a dead-time of d slots while retaining ns photons/pulse reduces the capacity by a factor of M/(M + d). However, the average power is also decreased by the same factor when keeping ns ixed. Hence, for each point (photons/slot, bits/ slot) = (Pav, Cs(M, Pav M, n b)) achievable with PPM there exists a family of points (photons/slot, bits/slot) = (Pav M/(M + d), Cs(M, Pav M, nb)M/(M + d)) achievable by adding dead-time. In a log–log domain plot of average power versus capacity, this is represented by extending each point on the Cs versus Pav curve down and to the left with a line of slope 1. Let

|

M ⎧ ⎫ Cd ( M , Pav , nb ) = max ⎨Cs ( M , ns , nb ) ns = Pav ( M + d )⎬ , d M+d ⎩ ⎭ the capacity maximized over dead-time d, illustrated in Figure 6.6 for M = 64. Cd is equal to Cs for Pav above the point where the tangent of Cs has slope one, and equal to that tangent below that point.

6.3.4

SUBOPTIMALITY OF PPM

At the high peak-to-average power ratios typical of many free-space optical links, PPM is an eficient modulation. However, as the available power increases such that the optimal PPM order approaches M = 4, PPM becomes less eficient. Here, we

ß 2008 by Taylor & Francis Group, LLC.

quantify the loss in eficiency, illustrating regions where non-PPM modulations should be pursued. Suppose that we are utilizing a slotted, binary modulation with duty cycle 1/M, but are not restricted to PPM. The capacity of a binary modulation with duty cycle 1/M on the Poisson channel is given by COOK ( M , ns , nb ) =

f (Y | 1) M − 1 f (Y | 0) 1 EY |1 log Y | X + EY |0 log Y | X M fY (Y ) M fY (Y )

where f Y|X(y|0), f Y|X(y|1) are given by Equations 6.1, 6.2, and fY ( y) =

1 M −1 fY | X ( y | 1) + fY | X ( y | 0) M M

is the probability mass function for a randomly chosen slot. Let h(p) be the binary entropy function, h(p) = p log2(1/p) + (1 − p) log2(1/(1 − p) ). COOK(M, ns, nb) has a horizontal asymptote at h(1/M), the limit imposed by restricting the input to duty cycle 1/M. Let COOK (ns , nb ) = max COOK ( M , ns , nb ), M

the capacity maximized over real-valued duty cycle 1/M, illustrated in Figure 6.7 for nb ∈ {0, 0.01, 0.1, 1, 10}.

100

COOK (M, ns, nb)

10−1

10−2

nb = 0

10−3

10−4 −4 10

0.01 0.1 1 10

10−3

10−2

10−1

100

101

Pav (Signal photons/slot)

FIGURE 6.7 Duty-cycle constrained capacity maximized over order, COOK(M, ns, nb), nb ∈ {0, 0.01, 0.1, 1, 10}.

ß 2008 by Taylor & Francis Group, LLC.

2 1.9

COOK (ns, nb)/Cs(ns, nb)

1.8 1.7 1.6

10

1.5

1 0.1

1.4 0.01

1.3 nb = 0

1.2 1.1 1 10−4

10−3

10−2 10−1 Pav (Signal photons/slot)

100

101

FIGURE 6.8 Relative loss due to using PPM, COOK(ns, nb)/Cs(ns, nb), nb ∈ {0, 0.01, 0.1, 1.0, 10}.

Figure 6.8 illustrates the ratio COOK(ns, nb)/Cs(ns, nb), relecting the potential gain in using an arbitrary duty cycle constraint relative to PPM. The gains are larger for high average power, corresponding to small PPM orders, and for smaller background noise levels. We can potentially double the capacity for moderate to high average power. This presumes, however, the existence of a modulation that eficiently implements an arbitrary duty cycle. There are systematic methods to design such codes [10], but we do not explore their use here.

6.4

FADING

A free-space optical communications link experiences fading due to time-varying changes in the atmospheric path from transmitter to receiver. Errors in the pointing and tracking loops may also introduce fading. In this section, we characterize losses due to fading, and illustrate methods to mitigate fading through the use of an interleaver in combination with an ECC. Let v(t) be the fading waveform, such that a fraction v(t)Pav(t) of the transmitted power Pav(t) is received at the aperture at time t. For most free-space optical channels, the slotwidth Ts is much smaller than the coherence time of the fading process, Tcoh, hence, we may assume that v(t) is constant over a slot duration. With ns, the mean signal photons per pulsed slot in the absence of fading and vk, a sample of the fading process in that slot, the mean signal photons in fading is taken to be nsvk. Let f V(v) be the probability density function (PDF) of a sample vk = v(tk) (v(t) is assumed stationary). Let l = log(v), and f L be the density of l. Atmospheric fading will be modeled by a lognormal distribution [11,12]

ß 2008 by Taylor & Francis Group, LLC.

⎛ −(log v + s l2 /2)2 ⎞ 1 exp ⎜ ⎟⎠ 2s l2 ⎝ 2 πs l2 v 1

fV (n ) = fL (l ) =

1 2 πs l2

(6.7)

⎛ −(l + s l2 /2)2 ⎞ exp ⎜ ⎟⎠ 2s 2 ⎝ l

In this model, the fading process vk has been normalized to have mean 1. We presume that static losses, the degradation in average received power, are accounted for separately. Here, we focus on dynamic losses. Numerical results in the remainder of the section will use the lognormal model. Figure 6.9 illustrates a sample of an observed fading time series over a 45 km free-space link [11]. The observed histogram of samples vk, and a best it to f V(v) (shown as both, a histogram of bin volumes corresponding to observations and a continuous function) given by Equation 6.7 is illustrated in Figure 6.10. We see that the lognormal model is a good it to observations. Other sources of fading may be characterized by replacing f V(v) with an appropriate model. For example, the fading waveform in the presence of pointing jitter may be modeled as Ref. [13] ⎛ wx2 + wy2 ⎞ v = exp ⎜ − ⎟ 2 ⎠ ⎝

(6.8)

where wx and wy are jointly Gaussian random variables. Certain atmospheric fading processes may also be modeled by Equation 6.8.

18 16 14

v (t)

12 10 8 6 4 2 0

FIGURE 6.9

0

5

Fading time series.

ß 2008 by Taylor & Francis Group, LLC.

10 t (s)

15

20

Data histogram

1

Best fit fv (v) Histogram induced by fv (v)

fv (v)

0.8 0.6 0.4 0.2 0

FIGURE 6.10

0

0.5

1

1.5

2 v

2.5

3

3.5

4 2

Histogram of fading samples and best it lognormal PDF f V (v): sˆ l = 0.98.

6.4.1 COHERENCE TIME, FADING DEPTH Samples of the fading process separated by a suficiently long interval will be uncorrelated. The coherence time, Tcoh, of the fading process is the duration such that samples separated by more than the coherence time are (approximately) uncorrelated. Tcoh is roughly the reciprocal of the bandwidth of the spectral density of the fading process. Let S(f) be the power spectral density of v(t) and deine the 100x % bandwidth as ⎧⎪ B W (x ) = min ⎨2 B | S ( f )df = x ∫− B ⎪⎩

⎫⎪ ⎬ S ( f ) df ∫ ⎪⎭ −∞ ∞

In our analysis, we put Tcoh =

1 W (0.90)

or the reciprocal of the 90% bandwidth of the process. Figure 6.11 illustrates the power spectral density of the sequence illustrated in Figure 6.9. The 90% bandwidth is 117 Hz, yielding a coherence time of 8.5 ms, typical of an atmospheric link.

6.4.2 LOSSES DUE TO FADING The fading process produces losses relative to a received signal in the absence of fading.* We follow the approach in Ref. [13] to quantify the losses. Let C(Pav) be the capacity of the channel with power Pav (in the absence of fading). The fading capacity of the channel is given by * We assume that timing recovery is not affected by the fading process.

ß 2008 by Taylor & Francis Group, LLC.

−20 −25 Tcoh =1/117 = 8.5 ms

−30

S(f)

−35 −40 −45 −50 −55 −60 0

200

400

600

800

1000

1200

f (Hz)

FIGURE 6.11

Power spectral density of sample fading time series with Tcoh = 8.5 ms.

∞

Cfad ( Pav ) = ∫ C (uPav ) fn (v) dv 0

The fading capacity is the limit on the achievable throughput, which may be achieved in the limit of ininitely long ECC blocklengths. The performance for a inite blocklength ECC is well predicted by the outage probability. For positive integer Nf, let C=

1 Nf

Nf

∑ C (v P

i av

)

i =1

the instantaneous capacity of the channel, where the vi are independent realizations of the process {vk}. For a code with rate R and blocklength chosen such that there are Nf independent fades observed per code word, the outage probability is given by R log 2 M ⎞ ⎛ Pout ( R, Pav ) = Pr ⎜ C < ⎝ M ⎟⎠

(6.9)

The losses due to fading may be divided into three components. The irst, the static loss is the reduction in average received power due to the fading process, and is nonrecoverable. In this section, we presume the fading process has been normalized so that the static loss is zero. The second, the capacity loss is the difference Pav /P¢av where Pav and P¢av are the average powers satisfying C(Pav) = Cfad(P¢av), and is also nonrecoverable. The third loss, the inite interleaver loss or dynamic loss is the difference between the fading capacity (Pav|Cfad(Pav) = (R log2 M)/M) and the power required to achieve a desired outage probability. Interleaving is used to increase Nf. Noting that

ß 2008 by Taylor & Francis Group, LLC.

B 2B (N − 1)B

FIGURE 6.12

A convolutional interleaver.

Cfad = lim C N f →∞

we see that the dynamic loss may be recovered by a suficiently long interleaver.

6.4.3 CHANNEL INTERLEAVING TO MITIGATE LOSSES Interleaving may be implemented via a convolutional interleaver, illustrated in Figure 6.12. A convolutional interleaver consists of N rows of delays (shift registers) of length 0, B, 2B, …, (N − 1)B. Each register contains the observations corresponding to one PPM symbol. The number of registers required to implement the interleaver or deinterleaver is N(N − 1)B/2. Letting Nf be the number of uncorrelated fades per code word, we have Nf ≈

N ( N − 1) B N coh

where Ncoh is the number of PPM symbols per coherence time. Assume that the receiver quantizes slot measurements to 4 bits. Each register, corresponding to one PPM symbol requires M/2 bytes, hence, the required de-interleaver memory to induce Nf fades/code word is MN ( N − 1) B bytes 4 MN f N coh ª bytes 4

Nb =

Figure 6.13 illustrates capacity and fading capacity thresholds at which C = Cfad = 1/4 and Pout for lognormal fading with s l = 0.8, M = 4, R = 1/2, and nb = 1.0 photons/ slot. There is a capacity loss (the gap between Pav|C(Pav) = (log2 M)/(2M) and Pav|Cfad(Pav) = (log2 M)/(2M) ) of 0.6 dB. The 12 dB loss that would be incurred due to fading in the absence of interleaving can be reduced to 1.1 dB with an interleaver that produces an Nf = 128. For a system with slotwidth Ts = 1 ns, coherence time Tcoh = 8.5 ms, M = 4 and 4 bits/slot, an interleaving depth of Nf = 128 could be implemented with a 272 Mbyte deinterleaver.

6.5

JITTER

Supporting low signal powers requires detectors that are capable of photon counting, that is, producing a pulse in response to a single incident photon. In any such detector,

ß 2008 by Taylor & Francis Group, LLC.

100

10

−1

Nf = 1 10

−2

2

10

C (Pav)

10−3

Cfad (Pav)

Pout

4 16 32 64 128

−4

−4

8

−2

0

2

4

6

8

10

12

14

Pav (Signal photons/slot)

FIGURE 6.13

Capacity and outage probabilities, s l = 0.8, M = 4, R = 1/2, nb = 1.

there is a random delay from the time a photon is incident on the detector to the time a pulse is produced in response to that photon. This delay, which we refer to as detector jitter, or simply jitter, causes some degradation in performance relative to a system with no jitter. The standard deviation of the jitter for current state-of-the-art photon detectors ranges between a few hundreths of a nanosecond up to a nanosecond. The degradation is negligible for systems where the slotwidth is much larger than the jitter standard deviation, but becomes signiicant as the slotwidth is narrowed to achieve higher data rates, and should be taken into account in an accurate link budget. In this section, we examine the impact of detector jitter on the capacity. Let {sj}j = 1,2,… be the collection of photon arrivals at the detector. Detector jitter is modeled by presuming that pulses are produced at the output of the detector at times tj = sj + d j, where the d j are assumed to be independent of one another as well as of the arrival times {sj} and identically distributed. Figure 6.14 illustrates measured jitter histograms (normalized to integrate to one) for an In-GaAsP photomultiplier tube, a niobium nitride superconducting single photon detector (NbN SSPD), and an InGaAsP Geiger-mode APD, respectively. The histograms were it to a weighted sum of Gaussians of the form [14] K

fd (d ) = ∑ g k k =1

1 2 πs k2

2

2

e − (d − mk ) /(2s k )

(6.10)

using the Levenberg–Marquardt algorithm [15], and normalized to have zero mean. The smallest value of K yielding a good it was used in each case. The itted models are overlaid on the histograms. Table 6.1 lists the parameters of the itted models, the standard deviation,

ß 2008 by Taylor & Francis Group, LLC.

InGaAsP PMT

0.8 0.6 0.4 0.2 0 −2

−1.5

−1

−0.5

0

0.5

1

1.5

InGaAsP GM−APD

3 2 1 0 −1

−0.8

−0.6

−0.4

−0.2

0

0.2

0.4

0.6

0.8

1

NbN SSPD

20 15 10 5 0

−0.1

−0.05

0 t (ns)

0.05

0.1

FIGURE 6.14 Detector jitter histograms and Gaussian its for InGaAsP PMT, NbN SSPD, and InGaAsP GM-APD.

TABLE 6.1 Parameters for Detector Jitter Models Detector InGaAsP PMT (s = 0.9154, b = 0.09)

NbN SSPD (s = 0.02591, b = 0.40) InGaAsP GM-APD (s = 0.2939, b = 0.45)

Units for s, sk , mk are ns.

ß 2008 by Taylor & Francis Group, LLC.

gk

mk

sk

0.7655 0.1940

−0.0930 0.8080

0.4401 0.4511

0.02723 0.01331

−4.0780 1.917

0.7241 0.2751

0.6550 0.3450

2.838e-3 −5.389e-3

0.01890 0.03498

0.4360 0.2731

6.041e-2 −0.1086

0.4200 0.06024

0.2909

1.141e-2

0.1172

K

s=

∑g

k

(s k2 + m k2 )

k =1

and the photon detection eficiency (b), the probability that an incident photon produces a pulse. This allows one to generate deviates modeling the jitter process by choosing k ∈ {1, 2, …, K} according to the weights {g k}, i.e., P(k = i) = g i, and generating a Gaussian deviate with mean and variance (mk, s k).

6.5.1

CAPACITY

On a channel with jitter, signal photons from a pulse in one symbol may extend beyond the symbol boundaries, creating not only interslot-interference but also intersymbol-interference. Suppose that in a single channel use we transmit n-PPM symbols, and there is no interference between channel uses. Let Cn denote the capacity of this channel with units of bits per second where one channel use requires nMTs seconds. The n-symbol capacity satisies C1 ≥ C2 ≥ … ≥ Cn, yielding a sequence of nondecreasing upper bounds on C¥ = lim n→¥ Cn. We will see that over a broad range, C1 is a good approximation to C¥, the true channel capacity, as noted in Ref. [16]. We represent the transmission of n-PPM symbols as the transmission of an inten −1 ger x ∈ {0, 1, …, Mn − 1}. Expanding each x as an l-vector over base M , x = ∑ l = 0 xl M l, we let xl select the lth PPM symbol, that is, the xlth slot of the lth PPM symbol is pulsed. Let N be the number of detected photons when X is transmitted and T = {t0, t1, …, tN−1} be the random N-vector of photon arrival times. The capacity of the n-symbol channel with equally likely transmitted PPM symbols is given by [17] Cn ( X ; T , N ) =

1 ET , N , X log2 nMTs

M n fT , N | X (T , N | X )

∑

Mn i =1

fT , N | X (T , N | X = i )

bits/s

(6.11)

where the expectation is over (T, N, X) and we have explicitly introduced the slotwidth to examine the degradation as the slotwidth is varied for ixed jitter statistics. Hence, the computation of the channel capacity requires a determination of the conditional channel likelihoods.

6.5.2

CHANNEL LIKELIHOODS

As described previously, the input is a pulse position modulated (PPM) signal and photon arrivals are modeled as a Poisson point process. Signal photons arrive at a rate of l s photons/s and noise or background photons arrive at a rate of lb photons/s. In the lth symbol period, one of M PPM symbols is transmitted by transmitting a pulse in the xlth slot of the M slot word, with slotwidths of Ts seconds. Let n −1

l x(t ) = M l sTs ∑ l = 0 p (t − ( x1 + Ml )Ts ) +l b be the incident photon intensity function when x is transmitted, where p(t) is a pulse with amplitude 1/Ts on [0, Ts] and zero elsewhere (a more accurate pulse shape may be substituted without loss of generality in the following analysis). The distribution of detected signal photons for a pulse transmitted in the irst slot is given by f(t) = (p * fd)(t). Substituting Equation 6.10 for fd yields ß 2008 by Taylor & Francis Group, LLC.

f (t ) =

1 2Ts

⎛ ⎛ t −T − m ⎞ ⎛ t − m ⎞⎞ k k s ⎜ − erfc erfc g ⎜ ⎟ ⎜ ⎟⎟ ∑ k 2 2 ⎟⎟ ⎜ ⎟ ⎜ ⎜ k =1 2s k ⎠ ⎝ ⎝ 2s k ⎠ ⎠ ⎝ K

The detected intensity (as opposed to the incident) when x is transmitted is given by n −1 ⎛ ⎞ λ ′x (t ) = b ⎜ l b + M lsTs ∑ f (t − ( xl + Ml )Ts )⎟ ⎝ ⎠ l=0

The probability density of the detected signal, conditioned on the transmitted signal, is given by [18] N

fT ,N |X ({t j }, N | x ) = e ∫Tlx ( t )dt ∏ l x′ ( t j ) ¢

(6.12)

j =1

where T is the interval over which there is a nonzero probability of detected signal photons, N is the number of detected photons over T, which is random with Poisson probability mass function. In practice, the accuracy of measuring the detection time is limited. Approximations to the likelihoods given by Equation 6.12 may be used, trading-off performance for complexity [19].

6.5.3

LOSSES DUE TO JITTER

In a typical system link design, the noise rate lb, the detector characteristics (fd and b), and certain system parameters, for example, an error-control-code rate R and PPM order M are ixed, and the designer determines the signal power required to support a desired throughput bits per second. That is the approach we take in this section. In numerical results, Equation 6.11 is estimated via a sample mean. The parameters M, lb, fd , and R are presumed ixed and the minimum signal power l s required to close the link, supporting a throughput of R log 2 M bits/s MTs is determined as a function of the slotwidth Ts. We presume the use of a rate R = 1/2 ECC, and consider various ixed PPM orders. Let ⎧ log 2 M ⎫ ls′ = ⎨ls | Cn = ⎬ 2 MTs ⎭ ⎩ the theoretical minimum required incident power to close the link with a rate 1/2 ECC. Deine the loss due to jitter, lossn as the ratio of l¢s in the presence of jitter to ~ = s / T , the normalized l¢s in the absence of jitter for the n-symbol channel and let s s jitter standard deviation. ß 2008 by Taylor & Francis Group, LLC.

10

4

9

3 2

8

n=1

3 2 n=1

Lossn (dB)

7 6 5 4 M=4

3 2

M=8

1 0 −1 10

100 s/Ts

FIGURE 6.15 Loss as a function of normalized jitter variance for n = 1, 2, 3, 4, M = 4, and M = 8. Gaussian jitter, s = 1.0 ns, l b = 1 photon/ns, R = 1/2 ECC, b = 1.0.

Figure 6.15 illustrates jitter loss for Gaussian jitter with s = 1.0 ns (the case K = 1, m1 = 0, s1 = 1.0). PPM orders M = 4 and M = 8 are illustrated for n-symbol capacities ~ with a “knee,” the point where of n ∈ {1, 2, 3, 4}. The loss is well it as quadratic in s, ~ ~ ~ C ≈C ≈C , the slope of loss versus s is one, around s ≈ 1.0. We see that for small s, 1 2 3 in agreement with Ref. [16], and that this approximation is tighter for larger M, since the impact of inter-PPM-symbol interference is less. This justiies using C1 and loss1 as proxies for C¥ and loss ¥.

0.4

r)

itte

0

,

β= al (

−5

β= N(

0.4

Nb

(β = AP

aA sP InG

5

aA sP

10

InG

ls (dB photons/ns)

15

D

PM T(

β=

20

5)

0.0

9)

)

25

1.0

j no

Ide

−10 −15 10−2

10−1

100

101

102

Throughput (Gb/s)

FIGURE 6.16 photon/ns.

Required power to achieve speciied throughput: M = 16, R = 1/2 ECC l b = 1

ß 2008 by Taylor & Francis Group, LLC.

Figure 6.16 illustrates the required signal power λs to achieve a speciied throughput for the three detectors characterized in Table 6.1 and an ideal detector (b = 1, no jitter) with M = 16, R = 1/2, and λb = 1 photon/ns. When normalized, we see a similar ~ for all (nonideal) detectors, with a knee occurring at s ~ ≈ 1. At loss as a function of s low throughputs, the detector performance is differentiated only by the photon detection eficiency, with, for example, the InGaAsP GM-APD demonstrating a 0.5 dB gain over the NbN SSPD. However, as the throughput is increased by narrowing the transmitted slotwidth, the jitter loss begins to dominate, so that the NbN SSPD, with less jitter, demonstrates large gains at high throughputs.

6.6 ERROR CORRECTION CODES An ECC adds redundant information to the message to be transmitted in a systematic manner so that errors in the data may be corrected on reception. An (n, k) binary ECC maps each k information bits to n coded bits, and we say the rate of the code is R = k/n. In return for this added redundancy, the ECC provides large gains over an uncoded system. Figure 6.17 illustrates the BER of an uncoded M = 16 PPM channel with nb = 1, as well as bounds on the the achievable BER for hard and soft decision rate 1/2 codes. Error rate bounds are determined as a function of the channel capacity and the code rate R (Ref. [7], Theorem 7.3.1). Figure 6.17 illustrates that, in theory, a rate 1/2 code provides gains up to 9 dB over an uncoded system (7.8 dB for hard decision), measured at a BER of 10 −6. We will see that practical ECCs can perform within 1 dB (2 dB for hard decision). Hence, at an error rate of 10 −6, a typical performance target, rate 1/2 soft and hard decision ECCs can provide approximately 8 and

100 10−1 10−2

BER

ed

d co

Un

10−3 10−4 Ch

Cs

10−5 10−6 10−7 −10

−8

−6

−4

−2

0

2

Pav (dB signal photons/slot)

FIGURE 6.17 nb = 1.0.

Channel BER and soft and hard capacity bounds for a rate 1/2 ECC, M = 16,

ß 2008 by Taylor & Francis Group, LLC.

5 dB gain, respectively, over an uncoded system. When normalized to a ixed bits/ slot to account for the code rate overhead, an ECC still provides 2–4 dB gain over an uncoded system. In this section, we illustrate performance for two types of ECCs: hard and soft decision. This distinction refers to the decoding algorithm used to decode the code rather than the structure of the code itself. However, the design of the codes is intimately tied to the decoding algorithms, hence, we use this common nomenclature to refer to the codes as well. Hard-decision codes accept symbol decisions and their performance is bounded by the hard-decision capacity. Similarly, soft-decision codes accept symbol likelihoods, or photon counts, and their performance is bounded by soft-decision capacity. We focus on the class of Reed-Solomon (RS) hard-decision codes and the class of serially concatenated PPM (SCPPM) soft-decision codes. These two classes represent the current state-of-the-art solutions for each case.

6.6.1

REED-SOLOMON CODES

An RS code is a linear block code over a Galois ield with q elements, denoted GF(q). The code maps blocks of k symbols to n symbols, each over GF(q), where n = q − 1. The ield order, q, is commonly taken to be a power of 2, in which case, the symbols have binary representations, and the code has an equivalent representation as a (n log2 q, k log2 q) binary code. The minimum number of symbol differences between two code words of an RS(n, k) code is dmin = n − k + 1. This is the largest achievable minimum distance of any (n, k) linear block code over GF(q), and RS codes are optimal in this sense. Note, however, that this optimality is speciic to the symbol distance. For example, the equivalent binary code may not necessarily provide the largest minimum distance over GF(2). A code with minimum distance d can correct any pattern of (dmin − 1)/2 errors. Hence, an RS(n, k) code can correct any pattern of (n − k)/2 symbol errors. The encoding and decoding operations may be carried out eficiently in hardware using shift registers [20]. The excellent distance properties and eficient encoding and decoding operations have led to the widespread use of RS codes in communications systems. In Ref. [21], an RS code was proposed for use on the noiseless, that is nb = 0, Poisson PPM channel. The noiseless Poisson PPM channel is a symbol erasure channel, and an (n, k) RS code may be tailored to it an M-ary PPM channel by choosing n = M − 1 and taking code symbols from the Galois ield with M elements. However, strictly following the convention of choosing n = M − 1 yields codes for small orders with short blocklengths, and codes for small n perform poorly and have less lexibility in choosing the rate (with M = 4, this convention would yield the small class of (3, k) RS codes). This can be generalized by grouping together i M-PPM symbols to form an element of GF(M i) [22]. The RS code is then taken to be an (n, k) = (M i − 1, k) code. The optimum choice of i will be a function of the target BER. We refer to the concatenation of an RS code with PPM formed in this manner as an RSPPM (n, k, M) code. Figure 6.18 shows the performance of rate ≈ 3/5 RSPPM with M = 64 for i ∈ {1, 2, 3, 4}, along with hard- and soft-decision capacities of rate 3/5 coded 64-PPM.

ß 2008 by Taylor & Francis Group, LLC.

100 10−1

BER

M PP 64

−10

=

−12

M

10−7 −14

d,

10−6

Ch

Cs

10−5

de co

10−4

Un

10−3

RS PPM (16777215, 10066329, 64) 64) 37, (63, PM RS PPM (262143, 157285, 64) RS P

10−2

RS PPM (4095, 2457, 64) −8

−6

−4

Pav (dB signal photons/slot)

FIGURE 6.18

Performance of rate ≈3/5 RSPPM, M = 64.

We would conventionally use the RSPPM (63, 37, 64) code, which matches 64-PPM, but the RSPPM(262143, 157285, 64) has better performance at a target BER of 10 −6. As the blocklength increases, the waterfall region is seen to move slightly to the right and get steeper, so that the optimal i is a function of the target BER. At a target BER of 10 −6, the RS(262143, 157285, 64) code is within 1.45 dB of hard-decision capacity and provides a gain of 5.23 over the uncoded system. However, the restriction to utilize hard-decisions limits the achievable performance. A soft-decision-based channel has a potential gain of 1.24 dB over this. In Section 6.6.2 we illustrate codes that close the gap to soft-decision capacity.

6.6.2

ITERATIVE SOFT-DECISION CODES

Convolutional codes (CCs) are linear codes whose code words may be produced with (typically short) shift registers, allowing an eficient representation of the code words as paths on a trellis. This trellis structure enables eficient decoding via the Viterbi algorithm, see, e.g., [20]. CCs were proposed for use on the noiseless PPM channel in [23], illustrating performance competitive with RS codes. However, the distinguishing characteristic of trellis codes is that the Viterbi algorithm accepts soft input information. Their use on the noisy PPM channel, accepting soft inputs, was explored in Ref. [24]. Turbo codes, introduced in Ref. [25], achieved a breakthrough in code performance by combining a pair of CCs in parallel to form one large code. In a turbo code, a block of data is irst encoded by one CC. The same data is interleaved, and encoded by a second CC. A maximum likelihood decoder of the subsequent, typically long, block code would be prohibitively complex to implement. A key feature of turbo codes was to use a suboptimal decoder, decoding each constituent code independently and passing information between them in an iterative manner. This

ß 2008 by Taylor & Francis Group, LLC.

100 10−1

BER

10−4

PPM

Cs

10−5

Rate = 1/2 SC

10−3

M (4085, 2047) RSPP

10−2

10−6 10−7 −16

−15

−14

−13

−12

−11

−10

Pav (dB signal photons/slot)

FIGURE 6.19

SCPPM and RSPPM performance, Poisson channel, M = 64, nb = 0.2.

decoding algorithm proves to have excellent performance in practice, achieving near capacity performance. Turbo codes were applied to the PPM channel in Refs. [26–28], demonstrating large gains over RSPPM. A variant on turbo codes utilizes a serial concatenation of the codes [29]. In this case, the output of the irst code, as opposed to the input, is interleaved and encoded by a second code. This approach was applied to coded PPM in Ref. [30], utilizing a convolutional code for the outer code and coded PPM as the inner code. In this approach, the modulation essentially becomes part of the ECC, providing large performance gains. These serially concatenated, convolutionally coded PPM (SCPPM) codes have the best performance of any known code to date on the Poisson PPM channel. Figure 6.19 illustrates performance of a rate 1/2 SCPPM code relative to (n, k) = (4085, 2047) RS coded PPM for M = 64 and nb = 0.2. The SCPPM code consists of a rate 1/2, memory 2 convolutional code, a permutation polynomial interleaver, and a recursive accumulator—described in more detail in Ref. [30]. The RS blocklength was chosen to yield the best performance over all RS codes with the same rate associating an integer number of PPM symbols with each code symbol [6]. The SCPPM code performs within 0.7 dB of soft-decision capacity and provides a 3 dB gain over the RS code.

6.6.3

COMPARISONS

Figure 6.20 illustrates achievable rates for nb = 1 populated by points for a collection of SCPPM codes, a collection of RSPPM codes, and the uncoded PPM channel. Also illustrated are the shells Cs(ns, nb) and COOK(ns, nb), illustrating gaps to capacity and the eficiency of using PPM. Points correspond to the average power at which the BER is 10 −5. The coded channels are evaluated at a inite number of rates, connected

ß 2008 by Taylor & Francis Group, LLC.

100 Cs(ns , 1) COOK(ns , 1)

Bits/slot

ed

cod

10−1

Un

SCPPM M = 64 RSPPM

10−2 −20

−15

−10

−5

0

5

Pav (dB signal photons/slot)

FIGURE 6.20 Sample operating points, nb = 1.

to illustrate typical performance for the class. Note that a ixed bits/slot takes into account the overhead of the coded systems. The point RSPPM corresponding to M = 64 shows a cluster of points corresponding to the codes illustrated in Figure 6.18. Other RSPPM points use the convention n = M − 1. The class of SCPPM codes lie approximately 0.5 dB from capacity, while the class of RSPPM codes lie approximately 2.75 dB from capacity, and uncoded performance is 4.7 dB from capacity. These gaps will vary with nb, but provide a good approximation over a range of expected background noise levels. For a conservative link budget calculation that does not require the design and evaluation of a speciic code, one could assess a loss of 0.75 dB relative to capacity for iterative codes, 3 dB for RS codes, and 5 dB for uncoded. For the purpose of constructing link budgets, we assess a conservative 1 dB loss for all operating points due to quantization and synchronization losses. A robust system design should also incorporate a margin above the minimum requirement, which we will take to be 3 dB. From these approximations, we may obtain achievable data rates as a function of average power and background noise, or the required average power for a speciied data rate. To a rough approximation, the achievable data rate versus average power curve (including receiver losses and margin) would be given by the capacity curve shifted by 4.75 dB for iterative codes, 7 dB for RS codes, and 9 dB for the uncoded case.

REFERENCES 1. S. Dolinar, D. Divsalar, J. Hamkins, and F. Pollara, Capacity of pulse-poisition modulation (PPM) on Gaussian and Webb channels, TMO Progess Report, vol. 42–142, pp. 1–31, Aug. 2000. http://tda.jpl.nasa.gov/progress_report/42-142/title.htm 2. A. Biswas and W. H. Farr, Laboratory characterization and modeling of a near-infrared enhanced photomultiplier tube, IPN Progress Report, vol. 42–152, pp. 1–14, Feb. 2003. http://tda.jpl.nasa.gov/progress_report/42-152/title.htm

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3. R. G. Lipes, Pulse-position-modulation coding as near-optimum utilization of photon counting channel with bandwidth and power constraints, DSN Progress Report, vol. 42, pp. 108–113, Apr. 1980. http://tda.jpl.nasa.gov/progress_report2/42-56/56title.htm 4. A. D. Wyner, Capacity and error exponent for the direct detection photon channel–Part I, IEEE Transactions on Information Theory, vol. 34, pp. 1449–1461, Nov. 1988. 5. B. Moision and J. Hamkins, Multipulse PPM on discrete memoryless channels, IPN Progress Report, vol. 42–160, Feb. 2005. http://tda.jpl.nasa.gov/progress_report/42160/title.htm 6. B. Moision and J. Hamkins, Deep-space optical communications downlink budget: Modulation and coding, IPN Progress Report, vol. 42–154, Aug. 2003. http://tda.jpl. nasa.gov/progress_report/42-154/title.htm 7. R. G. Gallager, Low-Density Parity-Check Codes. Cambridge, MA: MIT Press, 1963. 8. J. Hamkins, Accurate computation of the performance of M-ary orthogonal signaling on a discrete memoryless channel, IEEE Transactions on Communications, vol. 52, pp. 1844–1845, Nov. 2004. 9. J. Hamkins, M. Klimesh, R. McEliece, and B. Moision, Monotonicity of PPM capacity, Technical Report, JPL inter-ofice memorandum, Oct. 2003. 10. B. H. Marcus, P. H. Siegel, and J. K. Wolf, Finite-state modulation codes for data storage, IEEE Journal Selected Areas Communications, vol. 10, pp. 5–37, Jan. 1992. 11. A. Biswas and M. W. Wright, Mountain-top-to-mountain-top optical link demonstration: Part I, IPN Progress Report, vol. 42–149, pp. 1–27, May 2002. http://tda.jpl.nasa.gov/ progress_report/42-149/title.htm 12. G. R. Osche, Optical Detection Theory, Wiley Series in Pure and Applied Optics. Hoboken, NJ: Wiley, 2002. 13. R. J. Barron and D. M. Boroson, Analysis of capacity and probability of outage for freespace optical channels with fading due to pointing and tracking error, Proceedings of SPIE (G. S. Mecherle, Ed.), vol. 6105, Mar. 2006. 14. B. Moision and W. Farr, Communication limits due to photon detector jitter. Submitted to IEEE Photonics Technology Letters, December 2007. 15. W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in C, 2nd ed. New York: Cambridge University Press 2nd, 1992. 16. A. Kachelmyer and D. M. Boroson, Eficiency penalty of photon-counting with timing jitter, Proceedings of the SPIE. San Diego, CA, Aug. 2007. 17. T. M. Cover and J. A. Thomas, Elements of Information Theory. New York: Wiley, 1991. 18. D. L. Snyder, Random Point Processes. New York: Wiley, 1975. 19. B. Moision, Photon jitter mitigation for the optical channel, IPN Progress Report, vol. 42–171, Nov. 2007. 20. S. Lin and J. Daniel J. Costello, Error Control Coding: Fundamentals and Applications. NJ: Prentice-Hall, 1983. 21. R. J. McEliece, Practical codes for photon communication, IEEE Transactions on Information Theory, vol. IT-27, pp. 393–398, July 1981. 22. J. Hamkins and B. Moision, Performance of long blocklength Reed-Solomon codes with low-order pulse position modulation. Submitted to IEEE Transactions on Communications, Nov. 2005. 23. J. L. Massey, Capacity, cutoff rate, and coding for a direct-detection optical channel, IEEE Transactions on Communications, vol. COM-29, pp. 1615–1621, Nov. 1981. 24. E. Forestieri, R. Gangopadhyay, and G. Prati, Performance of convolutional codes in a direct-detection optical PPM channel, IEEE Transactions on Communications, vol. 37, pp. 1303–1317, Dec. 1989.

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25. C. Berrou, A. Glavieux, and P. Thitimajshima, Near shannon limit error-correcting coding and decoding: Turbo codes, Proceedings of IEEE International Conference on Communications, vol. 2 (Geneva), pp. 1064–1070, IEEE, May 1993. 26. J. Hamkins, Performance of binary turbo coded 256-PPM, TMO Progress Report, vol. 42, pp. 1–15, Aug. 1999. http://tda.jpl.nasa.gov/progress_report/42-138/title.htm 27. K. Kiasaleh, Turbo-coded optical PPM communication systems, Journal of Lightwave Technology, vol. 16, pp. 18–26, Jan. 1998. 28. M. Peleg and S. Shamai, Eficient communication over the discrete-time memoryless Rayleigh fading channel with turbo coding/decoding, European Transactions on Telecommunications, vol. 11, pp. 475–485, Sept. to Oct. 2000. 29. S. Benedetto, D. Divsalar, G. Montorsi, and F. Pollara, Serial concatenation of interleaved codes: Performance analysis, design, and iterative decoding, IEEE Transactions on Information Theory, May 1998. 30. B. Moision and J. Hamkins, Coded modulation for the deep space optical channel: Serially concatenated PPM, IPN Progress Report, vol. 42–161, 2005. http://tda.jpl. nasa.gov/progress_report/42-161/title.htm

ß 2008 by Taylor & Francis Group, LLC.

ß 2008 by Taylor & Francis Group, LLC.

7 Photodetectors and Receivers Walter R. Leeb and Peter J. Winzer CONTENTS 7.1 Requirements and Challenges ....................................................................... 189 7.2 Optoelectronic Detection Process ................................................................. 193 7.2.1 Square-Law Photodetection ............................................................... 193 7.2.2 Heterodyne Process ............................................................................ 194 7.2.3 Detection Noise .................................................................................. 195 7.3 Devices .......................................................................................................... 199 7.3.1 Photodiodes ........................................................................................ 199 7.3.2 Photon-Counting Detectors ................................................................207 7.3.3 Optical Filters .....................................................................................208 7.3.4 Optical Preampliiers .........................................................................209 7.3.5 Local Laser Oscillators ...................................................................... 211 7.4 Optical Receivers: Structures, Performance, and Optimization ................... 212 7.4.1 Optical Receiver Types: An Overview ............................................... 212 7.4.2 Optical Receiver Performance Measures ........................................... 212 7.4.3 Direct-Detection Receiver .................................................................. 215 7.4.4 APD Receiver ..................................................................................... 216 7.4.5 Coherent Receiver .............................................................................. 217 7.4.6 Optically Preampliied Receiver ........................................................ 222 7.4.7 Role of Modulation Formats .............................................................. 223 7.4.8 Coherent versus Optically Preampliied Direct Detection ................. 225 7.5 Background Radiation ................................................................................... 226 7.5.1 Determination of Background Power ................................................. 227 7.6 Summary and Outlook .................................................................................. 231 References .............................................................................................................. 232

7.1 REQUIREMENTS AND CHALLENGES As discussed in Chapter 1, the optoelectronic receiver constitutes an important subunit of an optical intersatellite terminal. Its position within the terminal and its interaction with other major subunits become clear from Figure 7.1. In the typical

ß 2008 by Taylor & Francis Group, LLC.

ATD CPA In ANT

FPA

DUP

RX

Electrical data out

Point ahead input

PAA

TX

Transmit data

Out

Optical beam or guided wave

Electrical connection

FIGURE 7.1 Basic block diagram of an optical transceiver for space-to-space laser links. Abbreviations: ANT, antenna; CPA, coarse pointing assembly; FPA, ine pointing assembly; DUP, optical duplexer; ATD, acquisition and tracking detector; PAA, point ahead assembly; TX, transmit laser, modulator and booster ampliier; RX, receiver.

terminal structure shown, the signal is generated in the optical transmitter (TX) unit and passes the point ahead assembly (PAA), which is required whenever the angular separation between transmit and receive beam due to fast terminal motion (e.g., on geostationary platforms), is larger than the associated beam divergence. The transmit signal then enters the input–output duplexer (DUP) unit. This unit assures suficient isolation between the powerful transmit signal (on the order of 30 dBm) and the weak receive signal (on the order of −40 dBm). Isolation is achieved through the use of orthogonal polarizations and/or through the use of different wavelengths for transmission and reception. After passing the ine pointing assembly (FPA), which is used for beam tracking purposes, the transmit beam is directed to the telescope, acting as an optical antenna (ANT). In order to save the terminal size and mass, transmit and receive paths typically share a single telescope, but different telescopes or different portions of one telescope for TX and RX may also be used to spatially increase TX/RX isolation. In the receiving path, incoming radiation received by the antenna passes the FPA and is directed by the duplexer into a receiver (RX). Typically, a small portion of the receive signal is diverted to the acquisition and tracking detector (ATD), which provides information for the FPA and the coarse pointing assembly (CPA) carrying the antenna. (In this section, we deal only with the detection of user data, i.e., with the block shaded in gray in Figure 7.1, but not with concepts and optical sensors required for acquiring and tracking the counter terminal. These are covered in Chapter 3 on acquisition, tracking, and pointing. As shown in Figure 7.1, the optical power collected by the terminal’s telescope is made available at the receiver input interface, either as a collimated optical beam or as an optical wave guided by a iber. The receiver has to convert data carried by the optical input signal into an electrical output signal. As the optical input power tends to be low, high receiver sensitivity is required. As discussed in Section 7.4, for digitally modulated input data, this sensitivity is expressed either by the number of photons per bit or by the optical power (at a given data rate) needed to achieve a certain

ß 2008 by Taylor & Francis Group, LLC.

Local laser oscillator Frequency control

Optical data and background radiation in

Electrical data out p(t)

Optical amplifier

Optical bandfilter

i(t)

Electical Baseband Sampling and Photoor RF detector preamplifier decision conditioning

FIGURE 7.2 Generic block diagram of a digital optical receiver.

bit error ratio (BER). Of course, optical receivers can also handle analog signals, typically characterized by their electrical signal-to-noise ratio (SNR). In this case, the linearity of the electronic circuits involved becomes a major issue, and not easy to cope with if the relative bandwidth is large. Figure 7.2 shows a generic block diagram of a receiver for digitally modulated data, i.e., the block RX accentuated in Figure 7.1. In its simplest form, the receiver comes without subunits dashed in Figure 7.2. The detection process is (in general) hampered by background radiation inadvertently received by the optical antenna. Hence, an optical band ilter centered at the carrier wavelength l is usually implemented to reduce background radiation. The data signal passes the filter and is converted into an electrical current i(t) using a photodetector. Baseband processing is followed by sampling and decision. This type of receiver, in which the information-bearing electrical signal current is linearly proportional to the optical signal power at the detector, is called a direct-detection receiver. As detailed in Section 7.4, by implementing a low-noise optical preampliier one may achieve a considerable improvement in receiver sensitivity. Alternatively, one may design a so-called coherent receiver, in which the single-frequency radiation of a local oscillator (LO) laser is mixed with the optical input signal upon detection (see Section 7.2). The photodetector then generates (among other terms) an electrical signal directly proportional to the optical ield* of the optical input signal. The electrical signal is centered at the frequency difference between the optical input signal and the local laser light. As discussed further in Section 7.4, compared to direct detection without optical preampliication, coherent receivers offer not only improved sensitivity, but also the possibility to readily detect signals that are modulated in phase or frequency. Being the heart of any optical receiver, the photodetector is usually implemented in the form of a semiconductor photodiode. One of its main characteristics is the responsivity S, deined as the current-to-optical-power ratio i/p, measured in amperes/watt. An upper limit for S is reached if each photon is converted into an * In optical sciences, the term “optical ield” is often used to denote either one of the four electromagnetic ield quantities observing the wave equation. It is usually expressed as a complex baseband quantity by eliminating the optical carrier frequency and is normalized such that its squared magnitude represents the optical power.

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electron. (The quantum eficiency h of the photodiode, introduced in Section 7.3, would then be 100%. This value can be approached within some 10%–20% in practice, leading to responsivities of typically S = 0.5 A/W at a wavelength of l = 0.8 µm.) Another important diode characteristic is the response time tr (closely related to the diode’s electrical bandwidth). In case of direct-detection and nonreturn-to-zero (NRZ) coding, the response time t r should obey the relationship t r ≤ 0.5/R where R is the data rate. The same applies for coherent detection if the LO laser and the received optical carrier have identical wavelengths, i.e., in the case of homodyne detection. If the wavelengths differ, it is a case of heterodyne detection and the bandwidth requirement of the photodiode is much higher. This last concept, however, lends itself well to applications with analog data modulation (see Section 7.4). For optical preampliication, devices offering considerable gain and a low noise igure are required. Up to now mostly erbium-doped iber ampliiers (EDFAs), not so much semiconductor optical ampliiers (SOAs), have been employed successfully in high-data-rate receivers approaching the sensitivity given by the quantum limit (QL) (see Section 7.4). Optical ampliiers typically ask for an optical single mode input in the form of the fundamental transverse mode. Background radiation originating from the Sun, Moon, planets, or from the sunlit Earth may be picked up by the receive antenna and directed to the photodetector, thus presenting optical noise to the receiver. If an optical preampliier is implemented, its ampliied spontaneous emission (ASE) constitutes an additional source of background radiation. Eficient iltering of background is achieved by bandpass iltering with bandwidths not exceeding a few times the data rate [1]. With the optical ilter technology and the ilter/laser wavelength stabilities available today, this makes optical iltering a technologically dificult task if data rates fall signiicantly short of 10 Gbit/s. The signal current generated by a pin-photodiode in a direct-detection receiver without optical preampliication is typically between 10−9 and 10 −5 A. Then, electrical low-noise ampliication is essential to achieve utmost receiver sensitivity. If an avalanche photodiode (APD) is used (or in the case of coherent receivers or preampliied receivers), this is not a problem. As discussed in Section 7.4, in these cases electronic noise will not be the dominating noise source. Of all the devices constituting the receiver, space qualiication may be an issue mostly for a iber ampliier EDFA. The iber of an EDFA is prone to darkening when subjected to hard radiation but this effect may be avoided by proper material composition [2,3]. Aging of the local laser oscillator cannot be used as an argument against coherent detection because this problem must already be addressed with the laser source in the transmitter. Before entering more detailed discussions on optical receivers in the following sections, we want to point out some basic differences between receivers for iberbased systems and those for free-space links: • In a free-space link, utmost receiver sensitivity i.e., close to quantumlimited performance is of prime importance for the following reasons: (a) there is no in-line ampliication available, (b) receiver sensitivity can be

ß 2008 by Taylor & Francis Group, LLC.

traded against antenna diameter, and (c) reduced antenna size allows to reduce onboard mass. • An optical intersatellite terminal will usually consist of both a transmitter (TX) and a receiver (RX). Cross talk of the high-power transmit signal into the receiver subunit has to be kept at a negligible level, which asks for high signal isolation between the transmit path and the receive path. • If there is a relative movement between the two terminals to be linked, the received signal will be Doppler shifted. This effect may amount to several gigahertz and thus may require fast frequency tuning of the optical ilter or of the local laser in the case of a coherent receiver. • Extreme speciications concerning device reliability usually found in space systems are even more stringent than for undersea iber-optic repeaters. As a result, subunits with critical reliability have to be devised redundantly. In the following sections we will irst describe fundamental aspects of the optoelectronic detection process (Section 7.2). We will then discuss important properties of state-of-the-art receiver hardware, that of pin photodiodes and APDs particularly, optical ilters, optical ampliiers, and local lasers (Section 7.3). In Section 7.4, we will study the performance of various types of digital optical receivers and derive their sensitivities. Finally, we will quantify the impact of background radiation for various types of receivers (Section 7.5). Section 7.6 points out critical aspects and recalls the choices which have to be made when designing a receiver for a free-space, high-data-rate link.

7.2 OPTOELECTRONIC DETECTION PROCESS 7.2.1

SQUARE-LAW PHOTODETECTION

Photodetectors linearly convert the incident optical power p(t), i.e., the squared mag nitude of the optical ield vector e (t ) , into an electric current. The factor of proportionality S (A/W) is called the detector’s responsivity. The photocurrent i(t) is given by  i(t ) = Sp(t ) ∗ h(t ) = S | e (t ) |2 ∗ h(t )

(7.1)

where “*” denotes a convolution. The impulse response h(t) represents the iltering action of the entire detection electronics, i.e., any ilter elements within the receiver (as well as the inherent band-limitation of the optoelectronic conversion process). The linear relation between optical power and electrical current holds for input powers below the detector’s saturation power (cf. Section 7.3), which sets an upper limit to the receiver’s dynamic range. Since photodetectors are typically polarization-independent square-law detectors (with respect to the optical ield), they are fundamentally insensitive to any phase  or polarization information contained in e (t ) . Thus, from a detection point of view, optical intensity modulation (IM) is the most straightforward way to establish an optical communication link. IM can be analog, e.g., with many radio frequency subcarriers sharing a common, intensity-modulated optical channel, or digital, with either two (on/off keying [OOK]) or more intensity levels, or even with information

ß 2008 by Taylor & Francis Group, LLC.

encoded on the arrival time of an optical pulse within the bit slot (pulse-position modulation [PPM]). More sophisticated modulation formats (e.g., [differential] phase shift keying ([D]PSK), frequency shift keying [FSK], or polarization shift keying [Pol-SK]), which also use the signal’s phase or polarization to encode information, have to employ special optical preprocessing in order to make the phase or polarization information accessible to square-law photodetection [4]. Such preprocessing (see Section 7.4) can be accomplished by means of a local laser source (coherent receiver), or by means of appropriate optical iltering (e.g., optical delay-line demodulation of DPSK). 7.2.2

Heterodyne Process   If two optical ields e1 (t ) and e2 (t ) are incident to a photodetector, it is the total power, i.e., the squared magnitude of their sum that generates the photosignal,

{

}

      i(t ) = S | e1 (t ) + e2 (t ) |2 ∗ h(t ) = S | e1 (t ) |2 + | e2 (t ) |2 + 2 Re{e1 (t ) ⋅ e2* (t )} ∗ h(t )

(7.2)

where Re{} denotes the real part “*” denotes the complex conjugation h(t) denotes the impulse response of the entire optoelectronic detection chain. The irst two terms within the curly braces in Equation 7.2 are the individual powers p1(t) and p2(t) of the two optical ields, as measured by the detector in the absence of the other ield. The third term, called interference term, beat term, or heterodyne term, relects the fundamental property of two optical ields to interact upon detection. The strength of the interference term depends on the inner product of the two beating optical ields: the strongest beating is observed if the two ields are copolarized, while no beating is found for orthogonally polarized ields. In Equation 7.2, we assume that the two beating ields share the same transversal mode structure. If this is not the case (which is particularly true for coherent receivers using free-space optics), we have to calculate the overlap integral of two ields over the detection area, resulting in a quantity called heterodyne eficiency µ [5,6]. With this deinition, we can rewrite Equation 7.2 in its common engineering notation i (t ) = S

{ p (t ) + p (t ) + 2 1

2

}

m p1 (t ) p2 (t ) cos (2 πΔf + j (t )) ∗ h(t ).

(7.3)

As will be further detailed in Section 7.4, it is the beat term that is exploited in coherent receivers, where p1(t) takes the role of a weak, information-bearing signal, and p2(t) = P2 represents an unmodulated LO laser of substantial power. Under these conditions, p1(t) can be neglected compared to P2, which itself represents a temporally constant offset. The remaining beat term, that is oscillating at the difference frequency Δf between the signal’s optical carrier and the LO, then contains full information of the signal ield’s amplitude, ampliied by P2 and of the signal’s phase j(t). Therefore, coherent detection offers a straightforward way of decoding amplitude- and phase-modulation formats.

ß 2008 by Taylor & Francis Group, LLC.

7.2.3

DETECTION NOISE

Detection of optical radiation is corrupted by various sources of uncertainties, which can be classiied by looking at their dynamic behavior. We ind uncertainties that are slowly varying compared to the bit duration (e.g., telescope vibrations, dynamic beam misalignment, or wavefront distortions due to atmospheric turbulence), as well as uncertainties that occur on the bit-scale (e.g., noise within the detection electronics). While the latter class of uncertainties determines the probability at which bit errors (BER) may occur, the slowly varying class of uncertainties collectively affect an extended string of information bits, and can therefore lead to complete system outage. Allocating suficient margins in the system’s link budget if upper bounds for the penalties exist can counteract such luctuations. However, sometimes there is only a small probability for the occurrence of exceedingly large penalties, which makes the allocation of excessive system margins impractical. In this case, one can use outage statistics* to describe the probability that these rare events will lead to system outage. As for detection noise, electronics, shot, and beat noise sources are the most relevant in optical communications. These three noise sources are independent in the sense that their variances can be added up to arrive at the total detection noise [8,9]. The term electronics noise comprises the sum of all noise sources generated within the optoelectronic detection circuitry that are independent of the optical radiation incident to the detector. Examples include thermal noise, transistor shot noise, 1/f-noise, or dark current shot noise. The design of the receiver front-end electronics signiicantly impacts its noise performance, and is detailed in numerous texts [10]. On a system level, electronics noise is often characterized by an equivalent noise current density in [A/ Hz ], which is related to the variance of the photocurrent by 2 s elec = in2 Be .

(7.4)

Here, Be denotes the noise equivalent bandwidth [11] of the entire detection chain. If the photocurrent is converted into an electrical voltage signal by means of some (trans) impedance RT, the voltage noise variance is obtained by multiplying the photocurrent noise variance by R2T; this conversion also holds for all other noise variances encountered in this chapter. If mostly thermal noise from the receiver’s front end makes up for electronics noise, in can be approximated by in2 ≈ kTCD Be ,

(7.5)

where k is the Boltzmann’s constant (1.38 × 10 −23 As/K) T is the front end’s temperature CD is the capacitance of the photodiode and the electrical preampliier. * The outage probability is deined as the probability that some slowly varying luctuation perturbs the system by such a high amount that the margin allocated in the link budget to cope with that luctuation is exceeded and communication errors occur. Outage statistics are widely used in iber-optic communications in connection with polarization-mode dispersion (PMD) [7].

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Note that the electronics noise current density increases with receiver bandwidth. In the several-Gbit/s regime in2 typically amounts to 10 pA/ Hz. Alternatively to i2n, the electronics noise performance of receivers is often speciied using the noise equivalent power (NEP) [W/ Hz], usually deined as the optical power per square root electrical receiver bandwidth that would be required at the photodiode to make the electrical signal power equal to the electronics noise variance 2 s elec = S 2 NEP 2 Be .

(7.6)

While electronics noise can (at least in principle) be engineered to an insigniicant level (by cooling and circuit optimization), shot noise cannot. This fundamentally present noise source has its origin in the discrete nature of the interaction process between light and matter. Governed by the rules of quantum mechanics, such light-matter interactions can take place only in discrete energy quanta (photons). For laser light, the photonic interaction statistics are Poissonian (Figure 7.3). Thus, a discrete, random number of charge carriers (electron–hole pairs in the case of semiconductor photodiodes) are generated in the detector whenever light impinges on it. As a consequence, the photocurrent is composed of individual elementary impulses, each carrying the elementary charge e ≈ 1.602 × 10 −19 C, as visualized in Figure 7.1. This ine structure of the electrical signal is perceived as shot noise [8,11,12], and leads to amplitude fluctuations around the average photosignal, Equation 7.1. It can be shown [11] that the shot noise variance reads 2 s shot (t ) = eS ( p ∗ h 2 )(t ) ≈ 2eSp(t ) Be .

(7.7)

Photonic interactions Elementary impulses, h(t)

Electrical signal

FIGURE 7.3 Photons arrive at random, dictated by quantum statistics. Each photonic interaction produces an elementary electronic impulse. The impulses add up to produce the overall electrical signal, whose luctuations are known as shot noise.

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Note that shot noise is a nonstationary noise process. Its statistical parameters (most notably its variance) change with time. As evident from Equation 7.7, the dynamics of shot noise are determined by convolving the optical power waveform incident on the detector with the square of the detection electronics’ impulse response h(t). If the optical power variations are much slower than the speed of the detection electronics, the expression for the shot noise variance simpliies to the frequently encountered right-hand side of Equation 7.7, with Be being the detection electronics’ noise equivalent bandwidth [11]. As discussed in Section 7.4, shot noise is usually dominated by electronics noise in direct-detection receivers, where optical signal power levels at the detector are low, and it is dominated by beat noise in optically preampliied receivers. Shot noise only plays an important role in coherent receivers, where it is generated by strong LO light, as well as in receivers that employ detectors with internal avalanche multiplication (e.g., APDs). As detailed in Section 7.3, APD-based detectors make use of an internal charge carrier multiplication to produce (on average) MAPD carriers for each primary carrier generated by a photonic interaction. Thus, MAPD is also called the avalanche gain. Random fluctuations in the multiplication process exacerbate the fundamental shot noise luctuations, and lead to multiplied shot noise [11]. This is quantitatively captured in the APD’s noise enhancement factor FAPD > 1 via the multiplied shot noise expression 2 2 2 s mult.shot (t ) = eSM APD FAPD ( p ∗ h 2 )(t ) ≈ 2eSM APD FAPD p(t ) Be ,

(7.8)

where the well-known approximation holds for optical power variations slow, compared to the detection electronics’ speed. In addition to the multiplied shot noise (whose variance is proportional to the optical power at the detector), an APD also generates multiplied dark current shot noise through avalanche multiplication of dark current charge carriers (cf. Equation 7.19). This noise term is stationary and independent of the optical power, and can thus be added to the 2 electronics noise variance selec . The third important noise source encountered in optical communications is called beat noise. It has to be considered whenever a substantial amount of incoherent background radiation (e.g., light from celestial bodies, stray light from the Earth’s atmosphere, or even ASE generated by optical ampliiers at the transmitter or at the receiver) impinges on the detector. Incoherent radiation is typically composed of a broadband and stationary random optical ield whose complex amplitude obeys circularly symmetric Gaussian statistics [8,12]. Most sources of background radiation are fully depolarized, i.e., the optical ields in any two polarizations are uncorrelated [13]. Physically, background radiation is turned into beat noise by the square-law photodetector. With reference to Equation 7.2, consider  a well-deined optical signal  ield e1 (t ) and a random optical background ield e2 (t ) . The irst term in the curly braces of Equation 7.2 then constitutes the electrical signal; the second term is the randomly fluctuating instantaneous power of background radiation; the third term represents a beating between signal and background radiation. Since    | e2 (t ) |2 = e2 (t ) ⋅ e2* (t ) , the second term can also be thought of as the beating of

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Optical spectrum

Signal-background beating

Background-background beating Electrical receiver bandwidth

Signal A Background

B

C

Frequency

FIGURE 7.4 Signal-background beat noise is produced by those frequency components of the signal and the background light whose difference frequency falls within the electrical receiver bandwidth (e.g., by frequency components A and B whose difference frequency is smaller than the electrical receiver bandwidth indicated by the double arrow). Background– background beat noise is generated by the beating of background radiation with itself (e.g., by B and C).

background light with itself. The convolution with h(t) in Equation 7.2 makes sure that only beat component whose beat frequencies fall within the bandwidth of the detection electronics reach the receiver output. All other beat frequencies are iltered out by the band-limited nature of the detection chain. The process of beat noise generation is visualized in Figure 7.4, which shows a typical optical signal spectrum together with the spectrum of background radiation after having passed through an optical bandpass ilter. Each frequency component of the signal may beat with each frequency component of the background radiation, as indicated by the circles denoted as A and B in Figure 7.4. The resulting beat frequency is given by the difference of two beating spectral components. All beat frequencies that are smaller than the receiver bandwidth (indicated by the double arrow in Figure 7.4) will show up at the detector output. Since the background ield is random in nature, the beating between each signal spectral component (with each background spectral component) will have a random amplitude and phase, thus the name signal-background beat noise. A similar process applies for the beating between any two spectral components of the background light (circles B and C in Figure 7.4), leading to background–background beat noise.* Using Equation 7.2 together with the statistics of background radiation, it can be shown [14] that the beat noise variances take the form

{∫ e ∞

2 (t ) = 2 S 2 N back Re s sig-back

sig

−∞

}

*  (t )esig (τ ) rback (t − τ)h(t − t )h(t − τ)dt dτ ,

(7.9)

* Beat noise has been extensively studied in the context of optical ampliiers, where ASE caused by the optical ampliication process is an unavoidable source of background radiation. Therefore, the terms signal-ASE beat noise and ASE–ASE beat noise are commonly used in the vast literature available on optical ampliier noise.

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and

∞

2 2 s back-back = S 2 M pol N back

∫ |r

back

(t ) |2 rh (t ) dt ,

(7.10)

−∞

where Nback is the background radiation’s peak power spectral density per (spatial and polarization) mode at the detector r back(t) is the background radiation’s autocorrelation function (i.e., the inverse Fourier transform of the background radiation’s power spectrum) Mpol is the number of spatial and polarization modes of the background light that actually reach the detector (discussed in more detail in Section 7.5) esig(t) is the signal ield at the detector r h(t) is the electrical circuitry’s autocorrelation function [14] In the limit of rectangular ilters and constant signal input power Psig at the detector, the above relations simplify to [15] 2 s sig-back ≈ 4 S 2 Psig N back Be ,

(7.11)

2 2 s back-back ≈ S 2 M pol N back (2 Bo − Be ) Be ,

(7.12)

and

where Bo denotes the optical ilter bandwidth. While these relations lend themselves to valuable intuitive explanations, they are often too crude for quantitatively accurate predictions of receiver performance [16], especially in the presence of optical ilters whose bandwidths are comparable to the optical signal bandwidth. From Equations 7.9 and 7.11, it is clear that the signal-background beat noise, like shot noise, is nonstationary and its variance grows linearly with signal power. It is independent of Bo as long as the optical ilter does not signiicantly inluence the signal spectrum. The latter fact becomes intuitively clear when one looks at Figure 7.4. Due to the limited spectral extent of the optical signal, increasing the spectral width of the background light does not produce more signal-background beat frequencies that can still fall within the limited electrical detection bandwidth. Equations 7.10 and 7.12, show that the background–background beat noise is stationary, and its variance grows linearly with both Bo and Mpol. Therefore, optical iltering (spectrally and spatially) reduces mostly the background–background beat noise rather than the signal-background beat noise.

7.3 7.3.1

DEVICES PHOTODIODES

For free-space laser communication receivers, photodiodes are considered the most appropriate devices* to convert incoming optical radiation into an electrical signal [17]. * Devices like photomultipliers, photoconductors, phototransistors, metal-semiconductor diodes and quantum-cascade detectors will not be treated here.

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These semiconductor elements provide high conversion eficiency, fast response (i.e., high bandwidths), and low inherent noise. They can be produced as small, rugged, and reliable elements in the form of either pin-diodes* or APDs, and are available for the visible and near-infrared wavelength regime. The devices discussed below are operated as reverse-biased diodes, where photons to be associated with the incident optical power p are absorbed to generate electron–hole pairs, leading to a current i in the electrical circuit connected to the diode’s electrodes. To this end, the energy of the photon, hf (h, Planck’s constant; f = c/l, optical frequency; c, velocity of light in vacuum; and l, wavelength in vacuum), has to exceed the bandgap energy Eg, separating the valence band and the conduction band of the semiconductor material. Therefore, the maximum wavelength that can be detected (also called the cutoff wavelength) is given by lg =

hc . Eg

(7.13)

The light-to-current conversion is characterized by the quantum eficiency h, deined as the ratio of the number of carrier pairs generated within the diode and the number of photons incident to the detector (both per time interval). Then the detector responsivity S, deined as the ratio of electrical current to optical power, reads S=

i he = , p hf

(7.14)

where e denotes the elementary charge. Figure 7.5 gives typical responsivities versus wavelength for three common diode materials (Si, Ge, and InGaAs) together with lines of constant quantum eficiency h (dashed). The igure mirrors the proportionality of S with l, expressed by Equation 7.14 for l ≤ l g. It also shows that the response at cutoff is not abrupt in a real-world device. This is a consequence of wavelength dependence of the number of absorbed photons through thermally broadened uncertainty of the bandgap energy at temperatures above 0 K. Table 7.1 gives the cutoff wavelengths and operating ranges for photodiodes made of various semiconductor materials. An exemplary cross section of a pin-diode is shown in Figure 7.6. An antirelection (AR) coating reduces the Fresnel loss of the incident radiation. Absorption takes place preferentially in the intrinsic layer, governed by an exponential decay of the optical power along the direction z. Under the inluence of the internal electric ield in the depletion zone, the resulting electrons and holes travel to the n+ and the p+ regions, thus creating a current i in the external circuit. To achieve a high quantum eficiency, most of the photons have to be absorbed before entering the n+ region. This calls for an i-zone with an extension of several photon absorption lengths.† A long i-zone advantageously reduces the capacitance of the diode and thus the RC time

* The letters “pin” indicate the basic sequence of layers in the semiconductor structure: p-doped, intrinsic, and n-doped. † The photon absorption length characterizes the degree of exponential decrease of optical power caused by the absorption process.

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1.2

h=1

0.9 0.7

1.0 0.5 InGaAs

S (A/W)

0.8 Si 0.6

0.3

Ge

0.4

0.2

0 0.7

FIGURE 7.5

0.9

1.1

1.3

1.5

1.7

l (µm)

Spectral sensitivity of pin-photodiodes made from Si, Ge, and InGaAs.

TABLE 7.1 Cutoff Wavelength and Operating Ranges of Some Photodiodes Material Si Ge InGaAs HgxCd1-xTe

Cutoff Wavelength (mm)

Typical Operating Range (mm)

1.1 1.85 1.65 Up to 18

0.5–0.9 1.0–1.7 1.0–1.6 4–11

Note: For HgCdTe diodes to operate in the mid-infrared, cooling to 77 K is usually employed.

constant of the external circuit. However, it increases the carrier transit time, which in turn results in reduced internal speed. Thus, a trade-off between overall bandwidth and quantum eficiency has to be accepted. Also note that a large bandwidth can be obtained only if the sensitive area is small to keep the diode capacitance low. Figures 7.7 and 7.8 show the current–voltage (i–u) characteristic and the equivalent circuit of a photodiode. For no illumination (p = 0), the i–u dependence is that of an ordinary semiconductor diode, with a dark current ID caused by thermal carrier excitation.

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p(t)

AR coating

Insulator

Electrodes R p+

− Bias U0

u(t)

Electric field strength in z-direction

i

+

n+ z i(t)

FIGURE 7.6 Cross section and bias supply of a pin-photodiode. Also shown is the electric ield causing the transport of the photo-generated carriers.

i

U0

di = GD du

ID

u

p=0 p>0

R

FIGURE 7.7 Current–voltage characteristic of a pin-photodiode.

RS

i = Sp

ID

GD

CD

FIGURE 7.8 Equivalent circuit of a pin-photodiode.

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CM

LM

For p > 0 the characteristic shifts and the operating point moves along the line given by the bias voltage U0 and the effective load resistance R. The equivalent circuit is modeled by the two current sources representing the photo-induced current i = Sp and the dark current ID, by the junction capacitance CD in parallel with a conductance GD and a series resistance RS. A diode mount may contribute a further capacitance CM and a series inductance L M. As in every diode and as explained along with Equation 7.7, the current through the pin-structure is associated with shot noise whose variance is given by 2 s shot = 2e( I D + pS ) Be ,

(7.15)

where Be is the effective (electrical) bandwidth. The dark current portion 2eIDBe of the shot noise variance is signal-independent and is therefore often considered part of the electronics noise (cf. Section 7.2). The dynamic range of the pin-diode is typically several orders of magnitude, extending from the noise level up to diode currents of a few milliamperes (optical input power of a few milliwatts). When entering saturation, two major effects are observed. First, the dependence between optical power and electrical current starts to become sublinear. Second (and often more importantly), the diode gets slower, which can severely impact digital reception quality. Table 7.2 presents typical parameters of pin-photodiodes developed for iberoptic communication systems at data rates of several Gbit/s.* As with most devices developed for iber-optic communications, these diodes are equally well suited for

TABLE 7.2 Typical Parameters of Pin-Photodiodes Made from Silicon and Indium-Gallium-Arsenide for Data Rates of Several Gbit/s Si Operating range (µm) Quantum eficiency h Rise time, fall time (ps) Capacitance (pF) Dark current ID (nA) at 290 K Bias voltage (V) Diameter of active area (µm)

0.5–1.1

InGaAs 1.0–1.6

0.8 at 900 nm

0.95 at 1550 nm

40 0.5 1

50 0.7 1

−5 80

−5 50

* Photodiodes based on InGaAs with bandwidths of several gigahertz for operation at 40 Gbit/s and beyond are also available today, but have not yet been widely discussed for space applications.

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optical free-space links. Note that the dark current ID strongly depends on temperature, rising by a factor of approximately 3 for a temperature increase of 10°C. As expected, capacitance and response time increase with increasing active area. In an APD, primary electrons and holes generated by photons experience internal ampliication by an effect known as impact ionization. By proper doping (and strong reverse-biasing), a zone with very high ield strength is established, and the primary carriers are accelerated to such high velocities that they can effectuate secondary electron–hole pairs. In turn, these will produce further pairs and an avalanche builds up in the gain region. Similar to the case of a pin-diode (Figure 7.3), a single photongenerated carrier pair results in an external current impulse. However, since m electrons are generated per photon in an APD, each impulse now carries a charge of m . e. Apart from the generation of primary carriers (which is a statistical process due to quantum mechanics) the avalanche multiplication process is also random. Hence, m is slightly different for each individual primary charge carrier. On an average, we observe a multiplication factor M APD = m =

i , iprim

(7.16)

where the overbar denotes averaging. The average avalanche multiplication is thus deined as the ratio of average multiplied photocurrent to average primary photocurrent where i is the average current provided by the APD to the external circuit and iprim would be the average current only due to the primary carriers. The photon-induced external current can thus be written as i = pM APD

he . hf

(7.17)

Cross section, internal electric ield, and external circuit of an APD are sketched in Figure 7.9. Similar to pin-diodes, the incident optical power is mostly absorbed in a zone with only light doping (p−). Each carrier that drifted into the high ield zone

p(t) Insulator

AR coating Electrodes

R _

p+ u(t)

Bias U0

Electric field strength in z-direction

p− p n+

+

i(t)

Gain region

z

FIGURE 7.9 Cross section and bias supply of an APD. Also shown is the electric ield causing the transport and multiplication of the photo-generated carriers.

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experiences multiplication by a random factor m (on average, MAPD). The statistical luctuations of m can be quantiied by the excess noise factor FAPD: FAPD =

s m2 m2 = 1 + . 2 2 M APD M APD

(7.18)

In case of deterministic ampliication (i.e., when no variance is associated with the multiplication process, sm2 = 0) one would have FAPD = 1. In practice, FAPD > 1 and an excess noise has to be associated with the avalanche ampliication. This turns up in the expression for the shot noise variance of the APD current. Equation 7.8 is repeated here in a more device-oriented form: 2 2 s shot = 2e( I DM + pS ) Be M APD FAPD + 2eI DO Be ,

(7.19)

where IDM is a dark current contribution, which experiences multiplication, and IDO is one that does not (e.g., because it lows along the surface of the device). Accordingly, the dark current of an APD may be written as I D = I DM M + I DO .

(7.20)

Some APD vendors characterize their devices by including dark current shot noise into a signal power independent NEP, or an equivalent electronics noise current density which leads to the multiplied shot noise formula (Equation 7.8) that represents only the signal power-dependent term of Equation 7.19. Equation 7.19 can be considered as an extension of the shot noise equation for the pin-diode, i.e., Equations 7.7 and 7.15, where the standard deviation of the primary noise current is now enlarged by the factor M APD FAPD and where there also exists a nonmultiplied dark current IDO. As with the pin-diode, the response time of the APD is inluenced by the carrier transit time in the absorption zone and by the external RC time constant, both making up for the impulse response h(t) of detection circuitry, which was introduced in Section 7.2. However, in many cases the response time is dominated by an effect speciic to the APD, namely the time it takes to develop the avalanche within the high ield zone. Thus, the overall APD rise time t becomes a function of the gain MAPD. (Moreover, a very simple model even predicts that when varying MAPD in a given device, the product MAPD.t is constant.) Short rise times are achieved if the probability of ionization by one carrier type (e.g., the holes) is much smaller than that by the other (e.g., the electrons). In this case of a small ionization ratio k ion, the avalanche buildup is completed faster, compared to the case that both carriers contribute equally (k ion = 1). A small value of k ion turns out to be also beneicial to achieve a low-noise factor FAPD. To give examples: for silicon we typically have k ion ≈ 0.03, while for InGaAs k ion ≈ 0.5, with the consequence that APDs made from Si are less noisy and allow for shorter rise times than those made from InGaAs. Simple modeling of the avalanche noise process leads to [11] ⎛ 1 ⎞ F = M APD kion + (1 − kion ) ⎜ 2 − ⎟. M ⎝ APD ⎠

ß 2008 by Taylor & Francis Group, LLC.

(7.21)

The dynamic range of the APD is (in general) smaller than that of a pin-diode. Because of the current multiplication and the rather large reverse voltage needed to achieve the avalanche effect, the maximum rating for the dissipated electric power may be reached at comparatively low optical input power. This effect has to be observed, especially in case of large background radiation, where background light may drive the diode into saturation and may eventually even damage it. On the other hand, the dependence of the gain MAPD on applied reverse voltage allows a rather easy implementation of an automatic gain control (AGC) within an optical receiver. Table 7.3 presents typical parameters of APDs. The dark current increases signiicantly with increasing reverse voltage. Further, dark current (IDO, IDM) and gain MAPD are strongly temperature dependent. The advantages of a pin-diode when compared with APD are • • • •

Low bias voltage Very fast response Simple driving circuit Large sensitive areas available (with reduced bandwidth Be)

while the APD has the following advantages • Internal ampliication, thus • Easy implementation of electronic AGC via variation of the APD bias voltage • Reduced low-noise requirements on a following electronic preampliier.

TABLE 7.3 Typical Parameters of APDs Made from Silicon and Indium-Gallium-Arsenide for Several Gbit/s Si

InGaAs

Operating range (µm)

0.4–1.06

0.9–1.6

Quantum eficiency h Rise time, fall time (ps) Capacitance (pF) Total dark current at room temperature (nA) Bias voltage (V) Ionization ratio kion Multiplication factor M Noise factor FAPD Overall responsivity SM (A/W)

0.85

0.65

40 0.5 3

40 0.5 100

160 0.02–0.04 100 5 40 at 850 nm 50

35 0.3–0.7 9 9 9 at 1550 nm 50

Diameter of active area (µm)

ß 2008 by Taylor & Francis Group, LLC.

One can also identify situations where an APD performs worse than a pinphotodiode. One example is the case when the background contribution dominates the overall SNR. Another is a well-designed receiver with optical preampliication (i.e., one where the signal-ASE beat noise dominates*). A third is a coherent receiver with dominating LO shot noise, which constitutes the desired operating condition. In general, an APD yields a better overall SNR only in cases where the noise of the electrical preampliier dominates the overall receiver noise. The very low currents delivered by a pin-diode (and also the low currents output by an APD) ask for an electronic preampliier to follow. This must be a broadband device with a low cutoff frequency at or near DC, and an upper cutoff frequency somewhere close to 0.7 times the data rate. To achieve a suficiently short rise time of the diode–ampliier combination, a low input impedance is asked for (i.e., a low input capacitance and a low input resistance [typically 50 Ω]). However, this concept suffers from large thermal noise. To overcome this problem, one often implements the transimpedance concept. Here, feedback of the ampliied signal to the ampliier input results in an enlarged input impedance without reducing the upper cutoff frequency. One useful characterization of the electronic noise (due to the preampliier) is done by specifying the equivalent noise current density in at the photodiode– ampliier interface (Equation 7.4). This number depends on parameters of the photodiode (like the junction capacitance), the input impedance of the ampliier, the noise generated within the transistors, and the stray capacitance and inductance between diode and ampliier. In general, lower values of in can be achieved for lower bandwidths Be, i.e., with receivers for low data rates R. Typical values are in = 30 fA/ Hz at Be = 50 kHz, in = 5 pA/ Hz at Be = 10 MHz, and in = 10 pA/ Hz at Be = 10 GHz.

7.3.2

PHOTON-COUNTING DETECTORS

For low data rate applications requiring extreme sensitivity (e.g., in optical links from deep-space probes), Geiger-mode APDs (GM-APDs) may be considered as detectors. GM-APDs operating at 1.06 and 1.55 µm are being developed with detection eficiencies greater than 50%, timing resolution less than 1 ns, and dark count rates less than 100 kHz [18]. One limitation of such devices is the relatively long reset time, which requires the detector to be quenched for a period of time before it can be reactivated after a detection event. GM-APDs operating at infrared wavelengths typically ask for reset times of tens of microseconds. Using conventional pulsed modulation formats, a single GM-APD detector with a 30 µs reset time would limit the achievable data rate to ~33 kbit/s. However, using higher order modulation formats (such as PPM) multiple bits can be received for each detection event. In a speciic experiment, a commercially available, iber-coupled GM-APD was biased at 47 V and operated at −40°C [19]. It showed a dark count rate of 428 kHz and a detection eficiency of 28%. In connection with 64-ary PPM and forward error correction (FEC), the scheme allowed to detect a signal at a source data rate of 100 kbit/s with a sensitivity as high as 1.5 photons/bit. * See Sections 7.2 and 7.4.

ß 2008 by Taylor & Francis Group, LLC.

7.3.3

OPTICAL FILTERS

As will be discussed in Section 7.4, in a free-space optical communication link, background radiation may severely reduce the sensitivity of a receiver. For reducing the detrimental effect of background radiation, one may place an optical bandpass i lter in front of the photodiode. For this device the system designer usually asks for • Narrow bandwidth • Low insertion loss • Wide blocking range with high rejection outside the ilter’s passband and, depending on the position of the ilter within the receiver • Wide ield of view. In the following we review several concepts of optical ilters and give their main characteristics. Thin ilm interference ilters rely on wavelength dependence of the transmission of a stack of thin ilms of different dielectric materials deposited on a transparent substrate. By proper choice of ilm materials and ilm thickness (e.g., alternating quarter wavelength and half wavelength), such ilters can be manufactured at any wavelength. For the smallest available bandwidths (around 1 nm), maximum transmission is often less than 60%, while greater than 90% throughput is possible for a bandwidth of 10 nm. Because these multilayer ilters are based on the interference effect (similar to a Fabry–Perot resonator), the center wavelength shifts with the angle of incidence. This shift may amount to 1 or 2 nm/deg, thus limiting the ilter’s ield of view. In some applications this effect may be counteracted by employing a curved substrate. A very compact realization of ilter action consists of directly applying the multilayer structure onto the photodiode’s surface instead of the AR coating shown in Figure 7.6. Fiber Bragg ilters have been developed primarily for iber systems. They rely on the distributed feedback action caused by periodic changes of the refractive index along the iber axis. A priori, they offer only a bandstop ilter characteristic, but the combination with a (iber) circulator yields the desired bandpass ilter (see Figure 7.10). Filter bandwidths below 0.1 nm may be achieved in connection with low insertion loss. On the other hand, such ilters intrinsically operate as single-mode devices, which means that their ield of view is restricted to the narrow cone to be associated with the fundamental (Gaussian-like) iber mode. Thus, their application in free-space systems will be restricted to those cases where the received radiation has already been coupled to a single-mode iber.* Absorption ilters may be considered in special cases when narrow bandwidth is not required, and where (by accident) a favorable closeness of the received wavelength l, the cutoff wavelength of the photodiode, and the band edge of a

* An example would be a receiver with an EDFA acting as optical preampliier.

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Fiber grating (bandstop)

Band-filtered optical output

Broadband optical input

Optical circulator

FIGURE 7.10 Optical bandpass ilter consisting of a iber grating and an optical circulator.

semiconductor material exists. Consider l = 980 nm and a silicon photodiode (cutoff near 1050 nm). If we arrange a window of undoped GaAs (cutoff at 920 nm, AR coated) in front of the photodiode, the setup would have a bandpass characteristic with a width of some 130 nm. While this bandwidth is very large, the ield of view is essentially unrestricted. Tunable Fabry–Perot ilters may be of interest for communication systems experiencing large Doppler shifts. Such ilters have been primarily developed for iber systems. In one implementation, two properly coated iber ends face each other and the gap in between can be varied piezoelectrically. The entire device usually comes with single-mode iber interfaces. The inherent periodicity of the transmission is a clear disadvantage for the purpose of background reduction. To achieve suficient off-band rejection across a wide bandwidth, this may require further iltering with a larger bandwidth. In the case that an optical free-space transmission system employs wavelength division multiplexing, the optical demultiplexer in the receiver could be implemented in the form of a waveguide grating router. * These planar optical devices not only serve as demultiplexer, but also provide narrow bandpass iltering for each of the optical channels [20].

7.3.4

OPTICAL PREAMPLIFIERS

As demonstrated widely in iber systems, optical preampliication may improve the sensitivity of optical receivers considerably. This is especially true for systems where APDs cannot provide enough bandwidth or enough internal low-noise ampliication (i.e., in high-data-rate receivers with pin-diodes where the noise is primarily due to

* These devices are also known under the name arrayed waveguide grating and PHASAR.

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the electronic ampliier). The prime speciications of an optical preampliier are its noise igure, F, and small-signal gain, G. The physical effect responsible for producing excess noise during ampliication is ampliied spontaneous emission (ASE). One can show that the noise power density NASE (measured in W/Hz) in a single mode at the output of an optical ampliier is [21,22] N ASE = (G − 1)hfnSP ,

(7.22)

where hf = hc/l is the energy of one photon nSP is the so-called inversion factor, which characterizes the degree of material inversion achieved through pumping electrons from lower to upper (excited) energy states. The noise is modeled to be white. In practice, it occupies the entire spectral region where optical ampliication is possible. For the perfect ampliier, the inversion would be complete, corresponding to the lowest possible value of n SP = 1. Values only slightly larger than n SP = 1 can be obtained with commercially available EDFAs. The optical noise power P N (in W) at the output of a single-mode ampliier then follows as PN = 2 N ASE BO ,

(7.23)

where BO is the optical bandwidth in Hz. The factor 2 in Equation 7.23 takes into account that even a single-mode device allows for two modes to propagate, which are degenerate with respect to their state of polarization. The factor 2 has to be omitted if a polarization ilter is implemented at the ampliier’s output. If we follow RF practices and deine the noise igure F as the quotient of SNR at the ampliier’s input to that at its output, one inds* 1⎞ ⎛ F = 2 ⎜ 1 − ⎟ nSP . ⎝ G⎠

(7.24)

In general, G >> 1. This implies that the lowest possible value of the noise igure of an optical ampliier, achievable for complete inversion (n SP = 1), is F = 2, corresponding to a noise igure of 3 dB. Figure 7.11 gives an equivalent circuit for an optical ampliier: a noiseless ampliication with gain G is followed by a summation of white noise with power density NASE per polarization. In an equivalent circuit with the noise source at the ampliier input, for G >> 1 and n SP = 1, this source would have the power density of hf per polarization. Combining Equations 7.22 and 7.24 yields an expression very useful for the design engineer, N ASE =

hfGF . 2

(7.25)

* A more exact analysis reveals an additional term 1/G in Equation 7.24 (see, e.g., Ref. [22]), but for the typical application in mind this is negligible.

ß 2008 by Taylor & Francis Group, LLC.

Pi

Po G

+

~ ~ 2NASE = 2(G −1) hfnsp

FIGURE 7.11 Equivalent circuit of an optical ampliier. Noise-less ampliication with gain G = PO/Pi is followed by the addition of white noise with power density NASE per polarization.

Up until today mostly single-transverse-mode optical ampliiers have been engineered. This means that the received radiation has to be coupled into a single-mode iber. The energy levels of erbium ions allow operation covering both the C-band (1530–1560 nm) and the L-band (1570–1600 nm). EDFAs operate close to the theoretical limit in that they offer a noise igure of less than 4 dB. A gain of G > 30 dB is easily achieved. Semiconductor optical ampliiers (SOAs) can be designed for any wavelength where suficient inversion can be achieved in the semiconductor material. They have been manufactured for wavelengths around 1300 and 1550 nm. A further advantage is their small mass and size. However, while their typical gain is only slightly lower than that of EDFAs, they fare considerably worse as far as the noise factor is concerned. Outside the laboratory, devices only with F > 9 dB have been reported. As a consequence, receivers with SOAs have demonstrated sensitivities of approximately 10 dB above the quantum limit (QL) (i.e., much worse than when using EDFA preampliication). Compared to EDFAs, SOAs have a relatively short relaxation time. This may lead to pattern-dependent ampliication and to cross talk in systems with wavelength multiplexing.

7.3.5

LOCAL LASER OSCILLATORS

Be it a heterodyne or a homodyne receiver, a coherent optical receiver requires a local laser oscillator. The most important requirements of such a device are • Transverse and longitudinal single-mode operation in order to achieve an intermediate frequency (IF) signal centered at a single carrier. • Narrow linewidth, i.e., little laser phase noise to avoid sensitivity degradation; the closer a receiver operates to the QL, the more pronounced is the inluence of nonzero linewidth. • Electronic frequency tunability to achieve constant IF despite variations in transmitter laser frequency and varying Doppler shift; in case of homodyne reception, tunability must be suficiently fast to control the optical phase between received carrier and local laser (LO) within a small fraction of 2p. • Suficient output power so that LO shot noise will dominate all other noise contributions.

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7.4 7.4.1

OPTICAL RECEIVERS: STRUCTURES, PERFORMANCE, AND OPTIMIZATION OPTICAL RECEIVER TYPES: AN OVERVIEW

The choice of receiver best suited for a particular free-space laser link depends on a variety of fundamental issues and hardware parameters, the most important of which are Receiver Sensitivity: For example, a 3 dB increase in receiver sensitivity can be traded for a 3 dB reduction in optical transmit power, a 41% increase in free-space communication distance, 16% smaller telescopes, or an increased tolerance to beam misalignment or beam proile distortions brought by atmospheric turbulence. Modulation Format: Not every reception technique is suited for every modulation format. For example, direct-detection receivers are insensitive to phase information and polarization information, unless this information is converted into IM by means of external optical components (e.g., delay demodulation of DPSK) [4]. On the other hand, coherent receivers detect the optical ield directly, and therefore allow for any modulation format without additional optical preprocessing. Hardware Availability, Reliability, Space Qualiication, and Cost: Different types of receivers require different hardware building blocks, which are not always available at reasonable cost or readily space-qualiied. For example, eficient and lownoise optical ampliication is predominantly available within the iber-telecom wavelength range around 1.55 µm. This is also where compact, low-cost, and high-speed optical transmitter modules are widely available. As another example, high-gain APDs are based on silicon technology, and therefore work only at wavelengths below 1.1 µm (see Section 7.2).

7.4.2

OPTICAL RECEIVER PERFORMANCE MEASURES

Before comparing different optical receiver concepts and discussing the most relevant receiver design trade-offs, we introduce some important receiver performance measures. The parameter of ultimate interest in any digital communication system is the BER, deined as the average ratio of wrong bit decisions to the total number of detected bits. The BER is an important measure for transmission quality. Different digital applications may ask for widely different BERs to operate properly. If a system cannot meet a certain BER target, the raw BER, i.e., the BER measured right after the receiver’s decision circuit, can be improved by means of FEC codes. However, the beneits of FEC come at the expense of a bit rate overhead of typically 7% for terrestrial multi-Gbit/s iber-optic systems, and up to 25% for stronger codes used in submarine applications. This overhead is required to generate redundancy, which is exploited for error correction within the receiver. When using FEC, the decoded BER (i.e., the BER measured after the FEC decoder) is signiicantly lower than the raw BER. Typical FEC chips working in the multi-Gbit/s range need an input BER between 10 −3 and 10 −5 to achieve an output BER of better than 10 −15. Apart from the BER, the temporal distribution of errors plays an important role in transmission quality. While occasional, randomly distributed bit errors may not ß 2008 by Taylor & Francis Group, LLC.

signiicantly affect a digital system, the occurrence of extended error bursts can lead to short periods of complete link failure, also called system outage. Since the BER is a long-term average quantity, the occurrence of error bursts is not captured by the BER. It may happen that the BER is within speciications, but that the occurrence of error bursts jeopardizes system performance. To counteract outage, bit scrambling can be employed to break up error bursts. Another important parameter for characterizing optical receiver performance is Personick’s Q-factor, deined as Q=

i1 − i0 , s1 + s 0

(7.26)

where i1 and i 0, respectively, represent the noise-free electrical signal current for a 1 bit and a 0 bit at the receiver’s decision gate s1 and s 0 are the noise standard deviations associated with these signal levels, as discussed in Section 7.2 Recall that some important noise sources encountered in optical communications are signal-dependent (i.e., their noise variance is a function of the optical signal power). This necessitates the distinction between 1 bit and 0 bit noise in Equation 7.26. The Q-factor relates to the BER via BER =

1 ⎧Q⎫ erfc ⎨ ⎬ , 2 ⎩ 2⎭

(7.27)

∞

2 where erfc{x} = (2 / π )∫x exp{−x }dx denotes the complementary error function. For purely signal-independent (thermal) noise, we ind s1 = s0 = s, and Equation 7.27 reduces to [23,24]

BER =

1 ⎧| i − i | ⎫ erfc ⎨ 1 0 ⎬ . 2 ⎩ 2 2s ⎭

(7.28)

Equation 7.26 is a powerful tool that allows for intuitive interpretations of receiver performance, and can give deep insight in certain receiver design trade-offs. However, any receiver analysis based on the Q-factor automatically comprises several important assumptions, which may not be met in reality.* Thus, care has to be taken whenever quantitative predictions based on the Q-factor are made. The Q-factor is also used as a convenient substitute for the BER, following Equation 7.27. A BER

* The most important assumptions for the validity of any Q-factor-based analysis are the following [25]: (a) The statistics of the electrical decision variable are Gaussian, which is not the case for beat noise or APD shot noise. However, it turns out that analyses based on Gaussian statistics work well for OOK, while they fail for balanced detection of DPSK. (b) Receiver performance is dominated by noise rather than by intersymbol interference (ISI), since the Q-factor uses only the two discrete signal levels i1 and i0; in the case of severe ISI, there are many different 1 bit and 0 bit amplitudes, which requires further averaging. (c) The receiver’s decision threshold is dynamically optimized, which is an inherent and important assumption for Gaussian detection statistics to work, but is not always done in practical receivers.

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of 10 −9, which is frequently taken as a baseline for specifying receiver performance, corresponds to Q ≈ 6 or 15.6 dB. This use of the Q-factor is a pure renormalization of the BER and, as such, is free of any assumptions. While the BER speciies an external requirement that makes an optical receiver useful for a given digital transmission task, the receiver sensitivity speciies the average optical signal power Pav that is required at the receiver input to achieve a target BER.* Obtaining the highest possible receiver sensitivity (i.e., meeting the target BER with the lowest possible input signal power) is one of the top priorities in free-space optical receiver design. The receiver sensitivity is often given in terms of the average number of photons per bit, nav =

Pav , hfR

(7.29)

where hf denotes the photon energy at the transmit wavelength R denotes the bit rate This speciication eliminates the wavelength dependence and data rate dependence of Pav, and therefore allows for an easier performance comparison of different receivers as well as for straightforward benchmarking to a receiver’s ultimate performance limit the QL. The QL represents a strict lower bound on the performance of any receiver in optical communications. It is usually speciied in terms of nav, and depends on the target BER, modulation format, and receiver type. It is calculated by assuming an ideal transmitter (perfect extinction, no ISI, etc.) and an ideal receiver. Obviously, the QL can only be approached by careful engineering, but it can never be reached in practice. Speaking about receiver sensitivities, we want to make an important remark related to coded systems: since FEC always introduces some amount of bit rate overhead, a certain portion of the optical power at the receiver input is not used for information transport, but rather for redundancy. For a fair comparison, receiver performance for coded systems therefore has to be given in terms of the average number of photons per information bit at the target BER after decoding. This number is always larger than the number of photons per bit on the channel, which inherently reduces the FECs coding gain, and leads to the notion of a net coding gain [26]. Another important performance measure of digital optical receivers is the optical signal-to-noise ratio (OSNR) required to achieve a certain BER. This quantity is predominantly used to characterize receivers for iber-optic communication systems, but is uniquely related to receiver sensitivity for the class of beat-noise limited receivers (e.g., the optically preampliied receiver discussed below). We briely * Note that the receiver sensitivity not only characterizes the receiver itself, but also to some extent the properties of the transmitter and its interplay with the receiver, such as extinction ratio or intersymbol interference (ISI) generated by transmitter optoelectronics. Thus, knowledge of the receiver sensitivity alone does not allow trustworthy predictions on how the receiver will perform with different transmitters or with other modulation formats.

ß 2008 by Taylor & Francis Group, LLC.

introduce this parameter in order to allow the reader to leverage from the vast literature base on iber-optic communications. The required OSNR speciies the ratio of average optical signal power to the power of all background radiation sources (including an optical preampliier) that is needed to guarantee a target BER. The power of the background radiation is typically assumed unpolarized and within an optical reference bandwidth of 12.5 GHz. (Note that the required OSNR is dei ned directly at the photodetector, in contrast to the receiver sensitivity, which is deined at the receiver input.*)

7.4.3

DIRECT-DETECTION RECEIVER

The pin-receiver depicted in Figure 7.12 is the simplest optical receiver structure. It consists of a pin-photodiode (see Section 7.3), an electronic ampliication, an inherent an or intentionally introduced postdetection electrical iltering, and a samplingand-decision device that restores the digital data. As discussed along with Equation 7.1 the photocurrent i(t) is linearly proportional to the incident optical power. The relevant noise terms in a pin-receiver are electronics noise, shot noise, and beat noise, the latter only in the presence of background radiation (either due to celestial bodies or due to optical ampliiers). Although electronics noise usually dominates shot noise, it could be engineered to insignificance by cooling the receiver. While this is usually not an option for terrestrial applications, it is worth considering for space-borne hardware. On the other hand, shot noise is fundamentally present. The limit when shot noise dominates all other noise terms is referred to as the shot noise limit. (Note that the shot noise limit is a condition rather than a quantity.) A shot-noise limited pin-receiver approaches quantum-limited performance if all other engineering optimization measures are fully exhausted (photon-counting operation, elimination of ISI, etc.). The QL for the pin-receiver using OOK is obtained by ignoring electronics noise, assuming a perfect photodiode (quantum eficiency h = 1), and by evaluating the BER for Poissonian photon statistics of perfect laser light [11]. Leaving the derivation to more detailed texts on optical receivers [27,28], we merely cite the result:

i(t)

h(t), Be

FIGURE 7.12 Setup of a direct-detection pin-receiver. * The reason for specifying the OSNR at the detector is the huge amount of ASE generated by in-line optical ampliication in iber-optic systems. This source of background radiation is much stronger than that is added by the optical preampliier within the receiver, so that the OSNR is essentially left unchanged upon optical preampliication. If the optical preampliier contributes a signiicant amount of noise, though, the OSNR is only a reasonable quantity when deined at the detector.

ß 2008 by Taylor & Francis Group, LLC.

BER = 0.5 exp(− 2 nav).

(7.30)

For BER = 10−9, the quantum-limited receiver sensitivity of the pin-receiver is nav ≈ 10 photons/bit. However, this intriguingly low receiver sensitivity does not apply to receivers that can be implemented in practice, since in reality, electronics noise dominates shot noise. As a consequence, receiver sensitivities achieved by pin-receivers are typically 15–30 dB off the QL (depending on the data rate). Assuming an equivalent noise current density of 10 pA/ÖHz and a 10 Gbit/s receiver with some 7 GHz electrical bandwidth operating at a wavelength of 1550 nm, the electronics noise variance amounts to 7 × 10 −13 A2 (cf. Equation 7.4), while the 1 bit shot noise variance going with the detection of 10 photons/bit comes to about 4 × 10 −17 A2 (cf. Equation 7.7), four orders of magnitude below the electronics noise. For a realistic BER, the Q-factor is thus entirely dominated by electronics noise, and for Q = 6 we arrive at a receiver sensitivity of some nav ≈ 5000 photons/bit, 27 dB above the QL. To achieve higher receiver performance, more advanced receiver types have to be employed. There are basically three ways to proceed: avalanche photodetection, coherent detection, and optically preampliied detection. These rather diverse techniques have one common attribute. They all amplify the received signal before or at the stage of photodetection, while at the same time unavoidably introducing additional noise. As soon as the newly introduced noise terms dominate electronics noise, any further increase of the employed gain mechanism does not affect receiver performance any more. In contrast to pin-receivers, the QLs can be closely approached with these receiver types in experimental reality.

7.4.4 APD RECEIVER As discussed in Section 7.3, an APD multiplies the generated primary photoelectrons (on average) by its avalanche gain MAPD. This multiplication comes at the expense of enhanced shot noise, captured in the APD’s excess noise factor FAPD (see Equation 7.8). In the desired limit when multiplied shot noise dominates 2 electronics noise (s 2elec eps(t)], so that the irst term in Equation 7.32 can be neglected compared to the second and third one. Filtering out the temporally constant second term, we are left with the beat term, revealing an exact replica of the received optical ield’s amplitude √ps(t) and phase j(t). In contrast to direct-detection receivers, since both amplitude and phase of the optical ield are translated into an electrical signal, any amplitude or phase modulation scheme can be directly used in combination with coherent receivers. Note that the beat term (in general) oscillates at the frequency difference between LO and signal light Δf, also called the IF. If the

Signal LO

FIGURE 7.13 Setup of a coherent receiver. Signal and LO are optically combined and detected by a pin-photodiode. Before making bit decisions, the IF signal is electronically postprocessed, including iltering and mixing to baseband. ß 2008 by Taylor & Francis Group, LLC.

frequency of LO differs from signal frequency, we speak of a heterodyne receiver. In this case, Δf is typically chosen to be at least 2–3 times the data rate. In a heterodyne receiver, the IF signal is transposed to baseband after photodetection using standard microwave techniques. If LO and signal have the same frequency (such that Δf = 0), we speak of a homodyne receiver. Homodyne detection requires strict optical phase locking between LO and signal optical ields in addition to keeping the IF zero. Since the stable operation of an optical phase-locked loop implies signiicant technological effort [31], only homodyning is taken into consideration if maximum receiver sensitivities are desired. As an alternative to strict homodyne detection, a phase-diversity [32] or, more recently, an intradyne receiver [33–35] can be constructed by detecting both quadratures of the IF signal, oscillating at Δf ≈ 0. This approach offers the advantage of reduced bandwidth requirements for the detection of optoelectronics. Only when using intensity modulation (IM) or differential phase modulation (as opposed to phase-locked PSK), these quasihomodyne receiver structures do not require phase locking [32]. Alternatively, phase locking can be done in the digital domain, if suficiently fast digital signal processing electronics are available. Using this technique, homodyne detection with a free-running LO laser has been demonstrated up to 40 Gbit/s at a symbol rate of 10 Gbaud [36]. In the single-ended setup of coherent receivers (shown in Figure 7.13), the transmission factor e of the optical beam combiner has to be chosen as high as possible such as not to waste too much signal power, and as low as acceptable to let suficient LO power reach the detector in order to achieve shot-noise limited performance, as discussed below. The heterodyne eficiency m accounts for the degree of spatial overlap as well as for any polarization mismatch between the LO ield and the signal ield. When using free-space beam combination, m directly relects a mismatch in the transversal mode structure of two interfering beams. Such a mismatch becomes particularly important if the signal beam has acquired random phase distortions, as is the case in the presence of atmospheric turbulence. If both the signal and LO are provided copolarized in single-mode optical ibers, the mode structure of signal and LO are inherently equal at the point of beam combination. However, coupling the free-space signal beam into a single-mode iber is associated with a certain, mode-dependent coupling eficiency that equals m, and then takes the role of the heterodyne eficiency [37]. Due to high LO power reaching the detector, the main noise contribution in a coherent receiver (in the absence of background radiation) is shot noise produced by the LO (cf. Equation 7.7). s 2LO,shot = 2eS (1 − e ) PLO Be .

(7.33)

2 If this noise term dominates electronics noise (s2LO,shot >> s elec ), the Q-factor becomes independent of electronics noise. The limit of dominating LO shot noise is known as the shot noise limit in the context of coherent receivers. In the shot noise limit, receiver performance is independent of the LO power, since both the informationbearing beat term in Equation 7.32 and the noise standard deviation (i.e., the square root of Equation 7.33) scale with ÖP LO, which lets the LO power cancel in the Q-factor. This independence of receiver performance on the ampliication mechanism is common to all types of high-performance receivers. In the case of the APD

ß 2008 by Taylor & Francis Group, LLC.

receiver, increasing the multiplication factor does not help once multiplied shot noise dominates electronics noise, and in the case of the optically preampliied receiver discussed below it is of no use to increase the ampliier gain beyond its value necessary to let beat noise dominate all other noise terms. Unlike direct-detection pin-receivers (where thermal noise can typically not be engineered away), a coherent receiver can be made shot-noise limited, and by careful design closely approach quantum-limited performance. The highest receiver sensitivity with the potential of practical implementation, that is known today, can be achieved using homodyne detection of PSK, where the data bits are directly mapped onto the phase of the optical signal {0, 1} → {0, p}. To derive this important QL, we use the deinition of the Q-factor (Equation 7.26), and insert the beat term of Equation 7.32 for i1 and i0, setting Δf = 0 (homodyning), and ps(t) = Pav, j 0 = 0 and j1 = p (PSK). We also make use of the shot noise expression (Equation 7.33), as well as the fact that LO shot noise affects both the detection of a 1 bit and 0 bit, i.e., s1 + s 0 = 2s LO,shot. Assuming ISI-free detection with a matched electrical ilter* of noise bandwidth Be = R/2, we arrive at Q = 2 hme nav .

(7.34)

We see that both a reduced heterodyne eficiency m and a reduced quantum eficiency h of the photodetector linearly affect receiver sensitivity. Assuming an ideal receiver (m = 1, e → 1, h = 1), we immediately arrive at the quantum-limited Q-factor for homodyne PSK, Q = 2 nav .

(7.35)

For BER = 10 −9 (Q ≈ 6), we thus require nav ≈ 9 photons/bit at the receiver input. Note that this number is almost identical to the QL of a direct-detection pin-receiver (Equation 7.30) with the big difference that the QL can be closely approached in a coherent receiver in practice, while in a pin-receiver it cannot. The best reported receiver sensitivity for homodyne PSK to date is 20 photons/bit at 565 Mbit/s [39]. Using OOK instead of PSK, the sensitivity degrades by 3 dB. Going to heterodyne detection results in an additional sensitivity loss of 3 dB. Table 7.4 summarizes the QL of a selection of modulation formats in combination with various receivers, together with some experimentally achieved results. A detailed discussion on the derivation of various QLs can be found in Ref. [27]. It became evident during our above analysis of coherent receivers that the singledetector receiver structure of Figure 7.13 has the fundamental drawback of wasting some available signal and LO power, with the receiver sensitivity depending linearly on the beam combiner’s splitting ratio e (cf. Equation 7.34). A frequently employed alternative implementation of coherent receivers that overcomes this problem is shown in Figure 7.14. It makes use of balanced detection with e ≈ 1/2. In this case,

* A matched ilter is the theoretically optimum ilter for the detection of a pulse in white Gaussian noise, provided that no ISI is present [38]. The matched ilter’s impulse response equals the temporally inverted, complex conjugated pulse shape to be detected.

ß 2008 by Taylor & Francis Group, LLC.

ß 2008 by Taylor & Francis Group, LLC.

TABLE 7.4 Overview of Detection Techniques and Their Sensitivities for Various Modulation formats at BER = 10−9 Coherent Homodyne QL (ppb) Off by (dB) PSK

9

3.5 9.0 10.5

Heterodyne

R

Ref.

565 Mbit/s 4 Gbit/s 10 Gbit/s

[39] [40] [41]

QL (ppb) Off by (dB)

Refs.

QL (ppb) Off by (dB) R (Gbit/s)

Ref.

18

DPSK

10

20

OOK

18

36

FSK

R

Optically Preamplified

40

8.2 10.2 13 6.9 12 2.1 2.2 6.8

565 Mbit/s 4 Gbit/s 10 Gbit/s 4 Gbit/s 10 Gbit/s 1 Gbit/s 2.5 Gbit/s 4 Gbit/s

[42] [43] [44] [43] [44] [45] [46,47] [43]

20

1.8 2.8

10 42.7

[48] [49]

38

0.5 1.4 3.1

5 10 40

[50] [51] [52]

40

Note: Not all combinations of modulation formats and detection techniques have been actively pursued. (QL, quantum limit; ppb, photons per bit; R, data rate).

A − Signal B LO

FIGURE 7.14

Setup of a balanced coherent receiver.

both output ports of the beam combiner (which are inherently out of phase by 180° [11]) are detected individually, yielding

{

}

{

}

iA (t ) = SA (1 − e ) ps (t ) + e PLO − 2 m e (1 − e ) ps (t )PLO cos [2 πΔf + j (t )] , (7.36) and iB (t ) = SB e ps (t ) + (1 − e )PLO + 2 m e (1 − e ) ps (t )PLO cos [2 πΔf + j (t )] . (7.37) The difference between the two photocurrents then reads i(t ) = iA (t ) − iB (t ) = {(1 − e )SA − eSB }ps (t ) + {e SA − (1 − e )SB }PLO − 2(SA + SB ) m e (1 − e ) ps (t )PLO cos (2 πΔf + j (t )),

(7.38)

where SA and SB denote the responsivities of the two photodetectors. Ideally (SA = SB, e = 1/2), the irst two terms vanish, and we are left with the desired beat term only. Note that a balanced coherent receiver has exactly the same quantum-limited sensitivity as its single-detector equivalent. This is easily veriied by evaluating the Q-factor and taking note of the fact that shot noise variances of both detectors have to be added to obtain the noise variance of the difference signal, as the two shot noise processes are statistically independent. Apart from making more eficient use of signal and LO power, a balanced receiver is more robust to relative intensity noise (RIN) of the LO, i.e., to random luctuations of the LO power PLO. Depending on the type of LO laser and the IF of the system, the RIN spectrum of the strong LO power may extend into the signal band, where it acts as an additional noise source. By carefully balancing the receiver, the second term in Equation 7.38, which includes possible LO power luctuations translating to the difference signal, can be greatly suppressed. It is evident that the manufacturing of equal detectors (SA = SB) is a critical point in building balanced coherent receivers. In practice, equality can be well obtained by integrating both detectors (together with the subtracting circuitry) on a single chip. Fully integrated balanced InGaAs detectors with bandwidths of several gigahertz are available today [53,54]. Another important effect with the potential of seriously affecting coherent receiver performance is laser phase noise [31]. In coherent receivers (which always operate on the beating of two optical ields) it is the sum of the LO’s linewidth and

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transmit laser’s linewidth that are responsible for sensitivity penalties. Therefore, both lasers have to meet high spectral requirements. Note, however, that while this hardware requirement is particularly stringent at low data rates, it becomes less important for data rates exceeding 10 Gbit/s. Homodyne PSK, the most sensitive modulation format with respect to phase noise, needs a laser linewidth-to-data rate ratio of ≤5 × 10 −4, which translates to the technologically realizable value of ≤5 MHz at 10 Gbit/s.

7.4.6

OPTICALLY PREAMPLIFIED RECEIVER

Historically, the youngest class of highly sensitive optical receivers use optical preampliication to boost the weak received signal to appreciable optical power levels prior to detection, as shown in Figure 7.15. At the same time (and fundamentally unavoidable), ASE is introduced by the ampliication process. The intriguing performance characteristics of EDFAs have made optically preampliied receivers an attractive detection technique. Since the gain spectrum (and thus also the ASE spectrum) is much broader than the signal spectrum (typically 30 nm in the 1550 nm wavelength band), an optical bandpass ilter is employed to suppress out-of-band ASE. ASE enters the detection process in complete analogy to any other (external) source of incoherent background radiation, leading to signal-ASE beat noise and to ASE–ASE beat noise. If the beat noise variance, given by Equations 7.9 to 7.12, dominates all other noise sources in the system (speciically electronics noise), we speak of beat-noise limited detection. Since both the photocurrent (i1 and i0) and the beat noise standard deviations (s1 and s2) scale linearly with the ampliier gain G, the Q-factor becomes independent of the ampliier gain in the beat noise limit, and any further increase of G does not improve the receiver’s performance (cf. Equation 7.39 below). Using the deinition of the Q-factor, Equation 7.26, and the simpliied signal-background beat noise expression, Equation 7.11, and assuming (a) no background radiation at the receiver input (such that the entire background radiation at the detector is given by the optical preampliier’s ASE), (b) reasonably narrow-band optical iltering such that s back-back ΩS.

ß 2008 by Taylor & Francis Group, LLC.

We now employ the antenna theorem [68] Ω DL = l 2 /ARX ,

(7.42)

which relates ΩDL, the diffraction-limited value of the antenna’s ield of view at wavelength l = c/f, with the antenna area ARX. Combining Equations 7.41 and 7.42 yields N RX = 2 N f l 2 ΩFV /Ω DL.

(7.43)

In Equation 7.43, the factor 2 ΩFV/ΩDL can be interpreted as the number of spatial and polarization modes, Mpol, of the background light that actually reach the detector, i.e., M pol = 2Ω FV / Ω DL (if ΩFV < Ω S ).

(7.44)

This relationship can also be deduced from Figure 7.18a, following purely geometric considerations. The factor 2 in Equation 7.44 takes into account that background radiation is depolarized. In case of a polarizer placed before the photodetector, one has Mpol = ΩFV/ΩDL. The total received background power would be obtained by multiplying NRX with the bandwidth BO of the optical ilter. The spectral density per mode, Nback, follows as N back = N f l 2 .

(7.45)

If the receiver’s ield of view, ΩFV, is larger than ΩS (see Figure 7.18b), we now ind N RX = N f ARX Ω S,

(7.46)

M pol = 2 Ω S / Ω DL (if Ω FV > Ω S ).

(7.47)

and

However, combining Equations 7.42, 7.46, and 7.47 we arrive again at Nback = Nfl2. Thus while the number of spatial and polarization modes received is different for the cases ΩFV < ΩS and ΩFV > ΩS, Equation 7.45 giving the spectral density per mode, Nback, applies equally, as expected. Next we show how to ind the spectral radiance function Nf. In case of dominating self-emission, a background radiator may well suficiently be modeled by a blackbody radiator, characterized by its absolute temperature TB. The spectral radiance Nf of a blackbody is given by Planck’s law, Nf =

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hf 3 ⎡ ⎛ hf ⎞ ⎤ − 1⎥ c 2 ⎢ exp ⎜ ⎝ kTB ⎟⎠ ⎦ ⎣

.

(7.48)

Using Equation 7.45 we obtain, for the power spectral density per mode N back =

hf ⎡ ⎛ hf ⎞ ⎤ − 1⎥ ⎢exp ⎜ ⎝ kTB ⎟⎠ ⎦ ⎣

(7.49)

.

This result was also to be expected and is identical to the expression for the average energy per mode of a blackbody in thermal equilibrium. Equation 7.49 is quite well suited to estimate the radiation from the Sun (with TB = 5700 K). For sunilluminated bodies like the Moon (TB = 400 K), the Earth (TB = 300 K), or the Venus (with TB = 330 K), Equation 7.49 yields good results only for the infrared region above 3 µm. At smaller wavelengths, the Sun relectance has to be taken into account and in fact is the dominating contribution if l < 2 µm [69]. To determine Nback in these instances, one may resort to the values of spectral irradiance Hl . This quantity gives the wavelength-dependent radiant power incident on a surface (e.g., the receiver) per unit area and unit wavelength increment (dimension [W/m3]). The relation to Nback is [69] N back =

Hl l 4 , cΩ S

(7.50)

with c being the vacuum velocity of light. For radiation caused by relected sunlight, the spectral irradiance Hl also follows Planck’s l-dependence but its maximum is not given by the body’s temperature. In such cases Hl is determined by an effective temperature and a case-specific maximum value of H l . More details and numerical values can be found in the Refs. [69–71]. Table 7.5 cites a few examples. If an optical preampliier is employed in the receiver, its ASE will also act as background radiation. The spectral density per mode caused by this process is then given by Equation 7.25 N back,ASE = hf

FRX GRX , 2

(7.51)

TABLE 7.5 Power Spectral Density per Mode, Nback (in W/Hz), produced by Various Celestial Bodies at Selected Wavelengths Nback (W/Hz) l (µm) Sun Moon Venus Earth

ß 2008 by Taylor & Francis Group, LLC.

0.85

1.06

1.55

1.3 × 10−20 1.8 × 10−26 2.1 × 10−25 2.6 × 10−26

1.9 × 10−20 3.6 × 10−26 3.1 × 10−25 7.0 × 10−26

7.1 × 10−20 8.6 × 10−26 3.5 × 10−26 7.6 × 10−25

where FRX and GRX are the preampliier’s noise factor and gain, respectively. Note that for typical parameters of an erbium-doped iber preampliier (l = 1.55 µm, GRX = 40 dB, FTX = 4 dB), the ASE-induced background radiation at the detector amounts to about 1.6 × 10−15 W/Hz, while the corresponding background radiation per mode at the detector for a receiver looking directly into the Sun is in the order of GRX 4 × 10−20 W/Hz ~ 4 × 10−16 W/Hz. Hence, in this example, the preampliier ASE contributes about four times as much noise as the Sun. If an optical booster ampliier is implemented at the transmitter site, its ASE may also contribute to the background radiation received [72]. The booster ampliier will (in general) constitute a wide-band, point-like (i.e., spatially coherent) background source. It is easy to show that the associated power spectral density per mode at the receiver is N back,ASE,booster =

hfGTX FTX l2 gTX gRX , 2 (4πL )2

(7.52)

where G TX and FTX are the booster ampliier’s gain and noise igure, respectively gTX and gRX are the transmit antenna gain and the receive antenna gain, respectively L is the link distance As is clear from the irst factor on the right-hand side of Equation 7.52, a single-mode booster ampliier (e.g., a single-mode EDFA) has been assumed. For a high-gain booster EDFA (l = 1.55 µm, and, e.g., G TX = 35 dB, FTX = 6 dB), Nback,ASE,booster may take on disturbingly high values if the link distance L is small. Then, the beating between the signal and the transmit booster ASE may dominate all other noise terms, leading to a SNR independent of the link distance L [72]. Finally, we wish to mention yet another source of degradation similar to background radiation. In a transceiver, nonnegligible optical cross talk may occur from the transmitter part into the (sensitive) receiver. The causes for such cross talk are relections and stray light, especially if one and the same antenna is employed for outgoing and received signals. Its inluence on receiver performance can be treated the same way that multipath interference is treated in iber-optic wavelength division multiplexed systems [73]. The inluence of background radiation caused by celestial bodies may be reduced by spectral, spatial, and polarization iltering, that of (single mode) optical ampliiers only by spectral and polarization iltering. The eficiency with which this iltering can be implemented strongly depends on the system design of the free-space link, as exempliied by the following three cases: • Transmission system operating at a low data rate with direct detection and no optical preampliication (e.g., SILEX [74], data rate R = 50 Mbit/s): Because optical ilters as narrow as the signal spectrum are not available (see also Section 7.3), spectral iltering cannot be effective. If it is the (nonnegligible) transmitter laser carrier linewidth, which determines the signals’ spectral width, then the optical ilter would have to be designed according to this (large) linewidth, but not according to the data bandwidth (again leading to poor spectral iltering of the background). Spatial iltering is governed by the instantaneous ield of view of the receive telescope, ΩFV, and the extension

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of the background, ΩS. If, for example, the Sun or the Earth constitutes the background source, the number of received background modes will be quite high, assuming the receive telescope is not diffraction limited. • Coherent reception: Spectral iltering can be obtained in the receiver’s IF section. Spatial iltering is done automatically by the mixing process of the input radiation and the local laser’s radiation, and is related to the fact that the heterodyne eficiency for all other modes than that of the signal is ideally zero (cf. Equation 7.3). In any practical case, the LO will operate in a single-transverse-mode and in a single polarization. Hence, only a single spatial background mode in a single polarization will be detected. • Transmission system operating at high data rate (e.g., R = 10 Gbit/s), with optical preampliication by a single-mode device, e.g., by an EDFA: Optical ilters with a bandwidth as narrow as 10 GHz are available today (in the form of iber Bragg gratings). Hence, spectral iltering can be very effective. Optimal spatial iltering down to a single mode is obtained by the coupling of the receive signal into the single-mode waveguide (e.g., a single-mode iber) preceding the EDFA. A general remark in this context is that poor spatial and spectral iltering of background radiation will cause a larger degradation in receiver sensitivity the closer to the QL the receiver operates.

7.6

SUMMARY AND OUTLOOK

Preceding sections discuss optical receivers from the perspective of their application in free-space systems. The sections describe the process of photodetection and review the properties of the main building blocks (photodiodes, optical ilters, optical preampliiers, etc.). These sections also account for sources of background radiation, explain the various receiver concepts (direct detection with and without optical preampliication, coherent detection), and develop expressions for these receivers’ sensitivities. Today, reception of high-data rate optical signals is well understood, concerning both the physical limits as well as the method of designing devices with speciied properties. Many aspects of optical receiver technology have reached high maturity and suficient reliability. This is partly due to the worldwide activities in the ield of laser space communication systems, but mostly a result of the huge efforts expended for the development of iber-optic transmission systems. Despite the existence of many communalities among receivers requirements for iber systems on the one hand, and those for space systems on the other, a number of differences exist which may be the cause for different implementation—also for differing status of maturity. In this respect, one has to point out that the free-space receiver • Will not have to cope with pulse envelopes distorted by dispersion along the channel; thus the received signal is just a replica of the transmitted one, with known shape. • Will have to face wave front distortion when the beam passes the Earth’s atmosphere—with associated signal reduction, both in case of coherent

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reception and in case of coupling to a single-mode optically preampliied receiver. • Will usually strive for utmost sensitivity because no in-line ampliication is available in space and because transmit power is extremely valuable. • Will have to work under considerable input power luctuations caused by antenna vibrations not completely compensated for by an automatic tracking system. • Will have to cope with Doppler shift of the received signal. These effects require additional effort in the receiver development. Unfortunately, coherent receivers are only recently becoming of interest for iber systems. In the case of homodyne PSK, they are attractive for space systems mainly because of their 3 dB better theoretical sensitivity limit. In general, coherent receivers cannot look back to a long history of successful application, with the consequence that the local laser oscillator required for this concept needs further development (mainly with regard to reliable and fast electronic tunability) and, depending on the data rate and on the speciic laser system, with regard to low phase noise. Another problem speciic to coherent receivers is the implementation of frequency acquisition to a (faint) incoming signal. A task still awaiting optimization and simpliication is found at the receiver’s input interface, if signal routing inside the receiver is done by single-mode ibers. The reason for such a design may be to achieve a lexible, low-weight setup, or the implementation of optical preampliication by an EDFA. Then, the beam delivered by the antenna has to be coupled into a iber, which is not easy to obtain if high coupling eficiency must be guaranteed over a long time and under varying environmental conditions. Last but not the least, the application in space asks for space qualiication of all devices and functionalities. With iber optics, somewhat similar requirements exist for undersea communication links. However, it is still space which poses the biggest demands in this respect, and despite the excellent status of development of optical receivers for terrestrial applications, time and cost of space qualifying a receiver must not be underestimated.

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8 Atmospheric Channel Sabino Piazzolla

CONTENTS 8.1

Introduction ................................................................................................... 237 8.1.1 Statistical Description of Atmospheric Turbulence .......................... 238 8.1.2 Modeling of the Refractive Index Structure Parameter ....................240 8.1.3 Propagation in Turbulent Atmosphere ..............................................244 8.1.4 Scintillation Index ............................................................................. 245 8.1.5 Scintillation Statistics ........................................................................246 8.1.6 Aperture Averaging Factor ................................................................248 8.1.7 Modeling of Scintillations in Strong Turbulence .............................. 249 8.1.8 Phase Statistics .................................................................................. 251 8.1.9 Beam Effects ..................................................................................... 256 8.2 Atmospheric Transmission Loss and Sky Background Noise ......................260 8.2.1 Absorption and Scattering.................................................................260 8.2.2 Background Radiation and Sky Radiance......................................... 265 8.3 Conclusions ................................................................................................... 268 References .............................................................................................................. 269

8.1

INTRODUCTION

When an optical beam propagates in the atmosphere, it can experience attenuation loss of its irradiance and random degradation of the beam quality itself. The irst effect is caused by absorption and scattering, operated by molecular constituents and particulates present in the atmosphere. The second effect is related to clear air turbulence that induces (among other things) phase luctuations of the laser signal, focusing or defocusing effects, local deviations in the direction of electromagnetic propagation, and signal intensity luctuations at the receiver (also known as signal scintillation). The purpose of this chapter therefore, is to introduce a theoretical basis of the beam propagation characteristics concerning atmospheric absorption loss and clear air turbulence. Particularly, we irst introduce a description of the cause of clear air turbulence, a description of scintillation of the optical signal, deterioration of the

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receiver performance resulting from phase degradation of the signal (due to turbulence), and other beam effects. Finally, we describe the mechanisms that induce atmospheric loss and sky background noise radiance.

8.1.1

STATISTICAL DESCRIPTION OF ATMOSPHERIC TURBULENCE

Clear air turbulence phenomena affect the propagation of an optical beam because the refractive index randomly varies in space and time. Mainly, random variation of the refractive index of air depends on the air mixing due to temperature variation in the atmosphere. Infact, sunlight incident upon the earth’s surface causes heating of the earth’s surface and the air in its proximity. This sheet of warmed air becomes less dense and rises to combine with the cooler air of the above layers, which causes air temperature to vary randomly (from point to point). Because the atmospheric refractive index depends on air temperature and density, it varies in a random fashion in space and time, and this variation is the origin of clear air turbulence. To describe clear air turbulence, one should consider the atmosphere as a luid that is in continuous low. A luid low at small velocity is irst characterized by a smooth laminar phase. In luid dynamics, a igure of merit of the luid low is the Reynolds number (Re), which is the ratio between luid inertial forces and viscous forces [1]: Re = Vc l /n k ,

(8.1)

where Vc and l are the characteristic velocity scale and length given in m/s and m, respectively nk is the kinematics viscosity given in m2/s The laminar low of the luid is stable only when the Reynolds number does not exceed a certain critical value (Re ~ 2300). When the Reynolds number exceeds the critical value (e.g., by increasing low velocity), motion becomes unstable and the low changes from laminar to a more chaotic, turbulent state. To describe this turbulent state, Kolmogorov developed a theory based on the hypothesis that kinetic energy associated with larger eddies is redistributed without loss to eddies of decreasing size, until they are inally dissipated by viscosity [1]. The structure of the turbulence according to this theory is depicted in Figure 8.1. The scale of the turbulence can be divided into three ranges: input range, dissipation range, and inertial subrange. The input range, where the energy is injected in the turbulence, is characterized by eddies of size greater than the outer scale of turbulence (L 0). Since the turbulence in this range greatly depends on local conditions, there is no mathematical approach capable to describe it. The dissipation range is characterized by eddies of size smaller than the inner scale of turbulence (l0