Advanced Spatial Modulation Systems [1st ed.] 9789811599590, 9789811599606

Table of contents :
Front Matter ....Pages i-xxii
Introduction (Anirban Bhowal, Rakhesh Singh Kshetrimayum)....Pages 1-23
Channel Model (Anirban Bhowal, Rakhesh Singh Kshetrimayum)....Pages 25-42
Advanced Spatial Modulation for Body Area Network Based Communication (Anirban Bhowal, Rakhesh Singh Kshetrimayum)....Pages 43-85
Advanced Spatial Modulation for FSO Communication (Anirban Bhowal, Rakhesh Singh Kshetrimayum)....Pages 87-140
Advanced Spatial Modulation for Underwater Optical Wireless Communication (Anirban Bhowal, Rakhesh Singh Kshetrimayum)....Pages 141-190
Advanced Spatial Modulation for Hybrid FSO/RF Communication (Anirban Bhowal, Rakhesh Singh Kshetrimayum)....Pages 191-216
Future Research Scopes (Anirban Bhowal, Rakhesh Singh Kshetrimayum)....Pages 217-226
Back Matter ....Pages 227-229

Citation preview

Signals and Communication Technology

Anirban Bhowal Rakhesh Singh Kshetrimayum

Advanced Spatial Modulation Systems

Signals and Communication Technology Series Editors Emre Celebi, Department of Computer Science, University of Central Arkansas, Conway, AR, USA Jingdong Chen, Northwestern Polytechnical University, Xi’an, China E. S. Gopi, Department of Electronics and Communication Engineering, National Institute of Technology, Tiruchirappalli, Tamil Nadu, India Amy Neustein, Linguistic Technology Systems, Fort Lee, NJ, USA H. Vincent Poor, Department of Electrical Engineering, Princeton University, Princeton, NJ, USA

This series is devoted to fundamentals and applications of modern methods of signal processing and cutting-edge communication technologies. The main topics are information and signal theory, acoustical signal processing, image processing and multimedia systems, mobile and wireless communications, and computer and communication networks. Volumes in the series address researchers in academia and industrial R&D departments. The series is application-oriented. The level of presentation of each individual volume, however, depends on the subject and can range from practical to scientific. **Indexing: All books in “Signals and Communication Technology” are indexed by Scopus and zbMATH** For general information about this book series, comments or suggestions, please contact Mary James at [email protected] or Ramesh Nath Premnath at [email protected].

More information about this series at http://www.springer.com/series/4748

Anirban Bhowal Rakhesh Singh Kshetrimayum •

Advanced Spatial Modulation Systems

123

Anirban Bhowal Department of Electronics and Electrical Engineering Indian Institute of Technology Guwahati Guwahati, Assam, India

Rakhesh Singh Kshetrimayum Department of Electronics and Electrical Engineering Indian Institute of Technology Guwahati Guwahati, Assam, India

ISSN 1860-4862 ISSN 1860-4870 (electronic) Signals and Communication Technology ISBN 978-981-15-9959-0 ISBN 978-981-15-9960-6 (eBook) https://doi.org/10.1007/978-981-15-9960-6 © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021 This work is subject to copyright. All rights are solely and exclusively licensed by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, expressed or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. This Springer imprint is published by the registered company Springer Nature Singapore Pte Ltd. The registered company address is: 152 Beach Road, #21-01/04 Gateway East, Singapore 189721, Singapore

Anirban Bhowal would like to dedicate this book to his parents for their love, affection and support. Rakhesh Singh Kshetrimayum would like to dedicate this book to his daughter, son and wife for making this life more meaningful.

Preface

This book aims to investigate advanced spatial modulation schemes for various applications using different media of transmission. The motivation of this work is to remove the inter-optical interference prevalent in MIMO systems and also to achieve higher spectral efficiencies than conventional SM/OSM at lower cost and power consumption. The investigation of performance and complexity analysis in terms of ASEP, BER, outage probability, cost and power consumption has been performed for various ASM techniques in this book. • In Chap. 1, a brief introduction of the various technologies like BAN, FSO, UOWC and hybrid FSO/RF systems has been provided. The concept of PLNC, SM and other performance metrics has also been described for the convenience of the readers. The benefits of using SM and ASM techniques for various applications have been highlighted. • In Chap. 2, the various channel models required for various applications have been justified. The statistics of the channel models have also been derived. Channel models like LN-4 distribution, MG distribution, G-G model, lognormal model and Rayleigh model have been utilized for various applications throughout the book. • Chapter 3 highlights the application of SM techniques for BAN communication. Initially, performance analysis of SISO BAN communication has been investigated in terms of BER for running and cycling activities across diverse BMI categories and two different scenarios. BER closed-form expressions have been achieved by approximating intractable lognormal distribution with the 5-MG distribution. To enhance the performance, MIMO BAN communication has been explored by utilizing SM, ESM and SMBM for running and cycling activities under different scenarios and diverse BMI categories. From the results, it is conclusive that SMBM performs the best for a particular spectral efficiency and activity because it uses a single RF chain and mutliple RF mirrors to create distinct channel perturbations and achieve high spectral efficiency using a lower modulation scheme. Cycling also performs better than running because of the fact that cycling involves movement of only the lower body portion keeping the

vii

viii

Preface

hands outstretched. Meanwhile in case of running, the entire body is in an oscillatory motion. This results in a more body shadowing effect in running than cycling, thereby affecting the data transmission more in running. • Chapter 4 highlights the performance analysis of various ASM techniques in FSO communication. Initially, OSM along with PLNC has been discussed for bidirectional FSO cooperative communication which helps the entire data transfer to take place in only two time slots. The effect of turbulence factors and the distance of separation between the nodes have also been highlighted. The limitations of OSM are resolved by the introduction of TLS and hybrid TLS schemes. The technique of laser selection, based on feedback through which TLI is sent for the maximum received SNR, has been discussed for FSO cooperative communication. Closed-form outage probability and BER expressions have been derived for such ASM schemes. More ASM schemes like OESM, OGSM and OIQSM have been introduced for FSO communication to enhance the spectral efficiency of OSM based schemes. Cost and power consumption analysis have been provided for all the introduced schemes. It has been inferred that advanced OSM schemes give improved BER performance than OSM because of the use of a lower modulation scheme to achieve the same spectral efficiency. • Chapter 5 extends the application of ASM techniques to UOWC communication. First, SISO UOWC cooperative communication for one-way and two-way relays has been explored. The intractable lognormal distribution has been approximated by 5-MG distribution to derive closed-form BER expressions for SISO UOWC cooperative communication. Next, the chapter highlights MIMO UOWC communication, where the OIQSM technique is analyzed in terms of closed-form BER expressions for UOWC cooperative communication. TLS and TLS-OSM techniques have been analyzed in terms of outage probability for UOWC cooperative communication. These techniques offer the promise to remove the limitations of OSM by selecting the transmit laser based on the channel condition. The cost and power consumption of all the introduced methods have been analyzed in detail. It is evident from the results that OIQSM can perform better than OSM and SISO UOWC techniques because of the ability of OIQSM to achieve high spectral efficiency using the lower modulation scheme and two sets of laser sources. TLS and TLS-OSM also perform better than OSM because these methods can select the laser depending on the channel conditions. • The applications of the ASM techniques in both RF and FSO domains have been combined to study hybrid SM techniques in hybrid FSO/RF cooperative systems in Chap. 6. HSM, TSS and TSS-HSM have been analyzed in terms of outage probability for cellular communication based hybrid FSO/RF systems. The techniques have been introduced for a DF based relay. However, the results have also been compared with an AF relay system and the challenges involved in deriving the exact outage probability expressions for the AF system have been highlighted. Cost and power consumption analysis of the introduced methods has been performed. From the outage probability analysis, it is evident

Preface

ix

that TSS-HSM gives superior results because of the availability in diversity while choosing the transmit source. • In Chap. 7, future applications of such ASM techniques are highlighted. ASM techniques can also be incorporated in quantum communication, reconfigurable intelligent surfaces and ambient backscattering communication which are part of future 6G communication. A brief idea of such advanced technologies and the implementation of ASM techniques have been presented which gives a new research direction to the readers. Thus, the overall book highlights the performance analysis of various ASM techniques for various applications. Such a study can be beneficial for deployment in future cellular communication networks or device-to-device communication in a closed environment in IoT networks. The applications of ASM techniques in FSO and UOWC technologies can be useful in effective data transfer for larger distances in harsh environments where turbulence and aquatic environment severely hamper optical signal propagation. Guwahati, India August 2020

Anirban Bhowal Rakhesh Singh Kshetrimayum

Acknowledgements

Both Anirban Bhowal and Rakhesh Singh Kshetrimayum are grateful to Swati Meherishi, Ms. Kamiya Khatter, Ms. Jayarani Premkumar and Mr. Vishnu Muthuswamy for helping us in making the book project successful. Anirban Bhowal would like to thank all his friends, seniors, juniors, faculty and staff members at IIT Guwahati for helping him in this journey and providing valuable knowledge. He wants to specially acknowledge Ms. Aditi Sapre and Mr. Ronak Lalani for their partial contribution in Chap. 3 of this book. He is also grateful to his friends at IIIT Allahabad and Heritage Institute of Technology and school friends. He is indebted to his family members for their upbringing and continuous support. Last but not least, he would like to extend his thanks to his Ph.D. supervisor Prof. Rakhesh Singh Kshetrimayum for helping him in this book project and continuously guiding him throughout his Ph.D. journey. First and foremost, Rakhesh Singh Kshetrimayum shows his gratitude to his supervisor at NTU Singapore (Prof. L. Zhu, presently with University of Macao) and his postdoctoral mentor at IISc Bangalore (Prof. K. J. Vinoy) and Pennsylvania State University (Prof. R. Mittra, retired now). Secondly, he is also thankful to Prof. G. Kumar (IIT Bombay), Prof. S. K. Koul (IIT Delhi), Prof. R. K. Shevgaonkar (IIT Bombay), Prof. G. Biswas (IIT Kanpur), Prof. T. Punniyamurthy (IIT Guwahati), Prof. Y. Chen (University of Waikato), Prof. S. Hranilovic (McMaster University), Prof. K. Yang (University of Essex), Prof. D. B. da Costa (UFC), Dr. P. K. Upadhyay (IIT Indore), Prof. P. R. Sahu (IIT Bhubaneswar) and all the faculty colleagues of his department at IIT Guwahati. Thirdly, he is grateful to all his B.Tech., M.Tech. and Ph.D. students, especially his recently graduated Ph.D. student Dr. Anirban Bhowal for all his hard work and efforts in completing this book project in time. Last but not least, he is very thankful to his late father (in his memory), mother, brothers, wife, children, uncles, aunts and in-laws for supporting him throughout this journey of life.

xi

Contents

. . . . . . . . . . . . . .

. . . . . . . . . . . . . .

. . . . . . . . . . . . . .

. . . . . . . . . . . . . .

. . . . . . . . . . . . . .

. . . . . . . . . . . . . .

. . . . . . . . . . . . . .

. . . . . . . . . . . . . .

. . . . . . . . . . . . . .

. . . . . . . . . . . . . .

. . . . . . . . . . . . . .

. . . . . . . . . . . . . .

. . . . . . . . . . . . . .

. . . . . . . . . . . . . .

. . . . . . . . . . . . . .

1 1 3 7 10 12 14 14 15 15 17 20 21 21

2 Channel Model . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1 BAN Channel Model . . . . . . . . . . . . . . . . . . . 2.2 Channel Model for FSO Communication . . . . . 2.2.1 A G-G Channel without Pointing Error . 2.2.2 A G-G Channel with Pointing Error . . . 2.3 UOWC Channel Model . . . . . . . . . . . . . . . . . . 2.4 Hybrid FSO/RF Channel Model . . . . . . . . . . . 2.5 Mixture of Gamma Distribution . . . . . . . . . . . . 2.6 Generation of Channel Coefficients . . . . . . . . . 2.7 Appendix . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

. . . . . . . . . . .

. . . . . . . . . . .

. . . . . . . . . . .

. . . . . . . . . . .

. . . . . . . . . . .

. . . . . . . . . . .

. . . . . . . . . . .

. . . . . . . . . . .

. . . . . . . . . . .

. . . . . . . . . . .

. . . . . . . . . . .

. . . . . . . . . . .

. . . . . . . . . . .

. . . . . . . . . . .

25 25 27 28 30 32 34 35 36 37 41

1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . 1.1 BAN Communication . . . . . . . . . . . . . . 1.2 FSO Communication . . . . . . . . . . . . . . 1.3 UOWC Communication . . . . . . . . . . . . 1.4 Hybrid FSO/RF Communication . . . . . . 1.5 Cooperative Communication . . . . . . . . . 1.6 Introduction to Spatial Modulation . . . . . 1.6.1 No Network Coding Scheme . . . 1.6.2 Analog Network Coding . . . . . . 1.6.3 Physical Layer Network Coding . 1.6.4 Spatial Modulation . . . . . . . . . . . 1.7 Advanced Spatial Modulation . . . . . . . . 1.8 Performance Analysis . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . .

. . . . . . . . . . . . . .

. . . . . . . . . . . . . .

. . . . . . . . . . . . . .

xiii

xiv

3 Advanced Spatial Modulation for Body Area Network Based Communication . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1 System Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2 Performance Analysis for SISO BAN Communication . . . . 3.2.1 Performance Analysis Using Mixture of Gamma Distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3 Spatial Modulation for BAN Communication . . . . . . . . . . . 3.4 ESM for BAN Communication . . . . . . . . . . . . . . . . . . . . . 3.5 SMBM for BAN Communication . . . . . . . . . . . . . . . . . . . 3.6 Optimized SMBM for BAN Communication . . . . . . . . . . . 3.7 Performance Analysis of SM Based BAN Communication . 3.7.1 Performance Analysis Using LN-4 Distribution . . . . 3.7.2 Performance Analysis Using MG Distribution . . . . . 3.8 Results and Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.8.1 Results for SISO Based BAN Communication . . . . 3.8.2 Results of Different Types of SM Based BAN Communication . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.9 Conclusion and Scope for Future Work . . . . . . . . . . . . . . . 3.10 Appendix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Contents

..... ..... .....

43 43 46

. . . . . . . . . .

. . . . . . . . . .

. . . . . . . . . .

. . . . . . . . . .

. . . . . . . . . .

47 48 49 53 56 57 57 59 60 60

. . . .

. . . .

. . . .

. . . .

. . . .

67 73 74 84

4 Advanced Spatial Modulation for FSO Communication . . . . . . 4.1 OSM Along with PLNC for FSO Communication . . . . . . . . 4.1.1 System Model of OSM Based DFTWR . . . . . . . . . . 4.1.2 Outage Probability Analysis of DFTWR Based OSM 4.1.3 Results and Discussion of OSM Based DFTWR . . . . 4.2 TLS and Hybrid TLS for FSO Communication . . . . . . . . . . 4.2.1 TLS and TLS-OSM System Model . . . . . . . . . . . . . . 4.2.2 Performance Analysis of TLS and TLS-OSM . . . . . . 4.2.3 Results of TLS and Hybrid TLS Systems . . . . . . . . . 4.3 Advanced Optical Spatial Modulation Schemes for FSO Communication . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.3.1 System Model for Advanced Schemes of OSM . . . . . 4.3.2 Optical Enhanced Spatial Modulation . . . . . . . . . . . . 4.3.3 Optical Improved Quadrature Spatial Modulation . . . 4.3.4 Optical Generalized Spatial Modulation . . . . . . . . . . 4.3.5 Performance Analysis of Advanced OSM Schemes . . 4.3.6 Complexity Comparison of ASM Schemes . . . . . . . . 4.3.7 Results and Discussion of Advanced OSM Schemes . 4.4 Conclusion and Scope for Future Work . . . . . . . . . . . . . . . . 4.5 Appendix for Chapter 4 . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

. . . . . . . . .

. . . . . . . . .

. . . . . . . . .

. . . . . . . . .

87 87 87 89 96 101 103 104 110

. . . . . . . . . . .

. . . . . . . . . . .

. . . . . . . . . . .

. . . . . . . . . . .

113 115 115 116 119 121 126 129 131 132 137

Contents

xv

5 Advanced Spatial Modulation for Underwater Optical Wireless Communication . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.2 AF Based OWR and TWR UOWC Systems . . . . . . . . . . . . . 5.2.1 System Model of OWR and TWR UOWC Systems . . . 5.2.2 Performance Analysis of AF Based OWR UOWC System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.2.3 Performance Analysis of AF Based TWR UOWC System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.2.4 Error Analysis of AF Based UOWC Systems . . . . . . . 5.2.5 Results for AF Based UOWC Systems . . . . . . . . . . . . 5.3 OIQSM for UOWC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.3.1 OIQSM System Model . . . . . . . . . . . . . . . . . . . . . . . 5.3.2 Performance Analysis of OIQSM UOWC Systems . . . 5.3.3 Complexity Analysis of OIQSM . . . . . . . . . . . . . . . . . 5.3.4 Results of OIQSM Based UOWC Systems . . . . . . . . . 5.4 TLS Based UOWC Systems . . . . . . . . . . . . . . . . . . . . . . . . . 5.4.1 System Model for TLS and TLS-OSM Based UOWC Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.4.2 Performance Analysis of TLS and TLS-OSM UOWC System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.4.3 TLS and TLS-OSM Error Analysis . . . . . . . . . . . . . . . 5.4.4 Results of TLS and TLS-OSM UOWC System . . . . . . 5.5 Conclusion and Scope for Future Work . . . . . . . . . . . . . . . . . 5.6 Appendix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

. . . . . .

. . . . . .

. . . . . .

168 172 173 177 178 188

6 Advanced Spatial Modulation for Hybrid FSO/RF Communication . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.2 Related Literature . . . . . . . . . . . . . . . . . . . . . . . 6.3 Hybrid FSO/RF System Model . . . . . . . . . . . . . 6.4 Performance Analysis . . . . . . . . . . . . . . . . . . . . 6.4.1 Hybrid System with AF Protocol . . . . . . 6.4.2 Analysis for HSM System . . . . . . . . . . . 6.4.3 Analysis for TSS System . . . . . . . . . . . . 6.4.4 Analysis of TSS-HSM System . . . . . . . . 6.5 Complexity Analysis . . . . . . . . . . . . . . . . . . . . . 6.6 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.7 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . .

. . . . . . . . . . . . .

. . . . . . . . . . . . .

191 191 192 195 198 199 201 205 206 208 209 214 215

. . . . . . . . . . . . .

. . . . . . . . . . . . .

. . . . . . . . . . . . .

. . . . . . . . . . . . .

. . . . . . . . . . . . .

. . . . . . . . . . . . .

. . . . . . . . . . . . .

. . . . . . . . . . . . .

. . . . . . . . . . . . .

. . . . . . . . . . . . .

. . . .

. . . .

. . . .

141 141 142 143

. . . 145 . . . . . . . . .

. . . . . . . . .

. . . . . . . . .

147 149 152 156 158 159 163 164 166

. . . 168

xvi

7 Future Research Scopes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.1 Quantum Communication . . . . . . . . . . . . . . . . . . . . . . . . . 7.1.1 Quantum Entanglement . . . . . . . . . . . . . . . . . . . . . 7.1.2 How Quantum Communication Works? . . . . . . . . . 7.1.3 Quantum Repeaters for Relay Based Quantum Communication . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.1.4 Security Using Quantum Communication . . . . . . . . 7.1.5 Quantum Spatial Modulation . . . . . . . . . . . . . . . . . 7.1.6 Application of SM in Quantum Communication . . . 7.2 Ambient Backscattering . . . . . . . . . . . . . . . . . . . . . . . . . . 7.3 Reconfigurable Intelligent Surfaces . . . . . . . . . . . . . . . . . . 7.4 Future Work Related to RIS, SM and Ambient Backscatter References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Contents

. . . .

. . . .

. . . .

. . . .

. . . .

217 217 217 217

. . . . . . . .

. . . . . . . .

. . . . . . . .

. . . . . . . .

. . . . . . . .

218 219 219 221 222 223 224 226

Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 227

About the Authors

Anirban Bhowal received the Ph.D. degree from the Department of Electronics and Electrical Engineering, Indian Institute of Technology Guwahati, in 2020. He is presently associated as a postdoctoral research fellow at the INRS-EMT, Universite du Quebec, Montreal (QC), Canada. He completed his B.Tech. in electronics and communication engineering from the Heritage Institute of Technology, Kolkata, in 2012. He received his M.Tech. degree in communication engineering from the Indian Institute of Information Technology, Allahabad, in 2015. His research interests include spatial modulation in RF and FSO systems, UOWC and FSO cooperative systems, hybrid FSO/RF communication, and BAN communication. Rakhesh Singh Kshetrimayum received his Ph.D. from the School of Electrical and Electronics Engineering, Nanyang Technological University, Singapore, and B.Tech. in Electrical Engineering from the Indian Institute of Technology Bombay, India. He is currently a Professor in the Department of EEE, IIT Guwahati, India. His research interests are in the broad areas of printed antennas, passive microwave devices, spatial modulation, cooperative communications, and optical wireless communications. He has published several journal and conference papers. He is a Fellow of the IET, UK, and a senior member of the IEEE, USA.

xvii

Acronyms

NL M Rd gk gR
th mf C 2n ‚ L Re !loss hp rs wzeq hl ðzÞ ratt ND rt rs rd RL Fn I DC Bw kB T rn wz

Number of Lasers M-ary Modulation Scheme Target data rate Source Node SNR Relay Node SNR Threshold SNR Number of RF Mirrors Constant of Refractive Structure Wavelength Link Distance Photodetector Responsivity SNR Loss Factor in dB at the Optical/RF Nodes due to self-interference Fraction of power lost due to Pointing Error Pointing Error Displacement Standard Deviation Equivalent Beam Radius at the Receiver Power Loss due to Attenuation over a Distance z Attenuation coefficient Number of photodetectors Thermal Noise Shot Noise Dark Current Noise Load Resistance Noise Figure Dark Current Bandwidth Boltzmann’s constant Number of Laser Sources selected out of N L sources in TLS-OSM Standard Deviation of Noise Corresponding Beam Radius at 1 km

xix

xx

f h N SL N RL a b Po PRF Co C RF Ptr Psw Pswrf C sw C swrf C S=P L2min s að‚Þ bð‚Þ r2I  !wat gkm jf vT l r2 aMG , bMG s GS;R GR;D GS1 ;R GS2 ;R j C AF AFOWR AFTWR AP ASEP AT

Acronyms

Jitter ratio for pointing error Divergence Angle Number of Laser Sources at Source Node Number of Laser Sources at Relay Node Effective number of large-scale cells in the FSO scattering process Effective number of small-scale cells in the FSO scattering process Power Consumption of each Optical Chain Power Consumption of each RF Chain Cost of each Optical Chain Cost of each RF Chain Total Transmitted Optical Power Power Consumption of each optical switch Power Consumption of each RF switch Cost of each optical switch Cost of each RF switch Cost of each Serial-to-Parallel Converter Minimum Euclidean Distance between two Symbol Vectors Transmitted signal vector Absorption Coefficient Scattering Coefficient Scintillation Index Rate of Dissipation of Turbulent Kinteic Energy per unit Mass of Fluid Relative Strength of Temperature and Salinity Fluctuations Kolmogorov microscale Scalar spatial frequency Rate of Dissipation of Mean-Square Temperature Mean of lognormal distribution Variance of lognormal distribution Shape and scale parameters of MG distribution Path Loss Coefficient Relative Gain of the Source to Relay Link Relative Gain of the Relay to Destination Link Relative Gain of the Source S1 to Relay Link Relative Gain of the Source S2 to Relay Link Relative geometrical gain factor Gamma Function Meijer G-Function Amplify-and-Forward Amplify-and-Forward One-Way Relay Amplify-and-Forward Two-Way Relay Access Point Average Symbol Error Probability Atmospheric Turbulence

Acronyms

AUV BAN BER BMI BPSK BS CDF CF CSI D2D DCSK DF DFTWR ESM FSO G-G HSM LAN LED LN-4 LOS LSB MAN MAP MG MGF MIMO ML MRC MSB MU MZI NLOS OAMSK OESM OGSM OIQSM OISM OOK OSM PDF PEP PLNC QAM QKD

xxi

Autonomous Underwater Vehicles Body Area Network Bit Error Rate Body Mass Index Binary Phase Shift Keying Base Station Cumulative Distribution Function Compress and Forward Channel State Information Device to Device Differential Chaos Shift Keying Decode and Forward Decode-and-Forward Two-Way Relaying Enhanced Spatial Modulation Free Space Optics Gamma–Gamma Hybrid Spatial Modulation Local Area Network Light Emitting Diode LogNormal 4 Distribution Line of Sight Least Significant Bit Metropolitan Area Network Mirror Activation Pattern Mixture of Gamma Moment Generating Function Multiple-Input Multiple-Output Maximum Likelihood Maximal Ratio Combining Most Significant Bit Mobile User Mach–Zehnder Interferometer Non-Line-of-Sight Orbital Angular Momentum Shift Keying Optical Enhanced Spatial Modulation Optical Generalized Spatial Modulation Optical Improved Quadrature Spatial Modulation Optical Improved Spatial Modulation On-Off Keying Optical Spatial Modulation Probability Density Function Pairwise Error Probability Physical Layer Network Coding Quadrature Amplitude Modulation Quantum Key Distribution

xxii

QOGSM QPSK QuSM RF RIS ROV RV SINR SISO SM SMBM SNR SOA TLI TLS TSS UOWC WAN

Acronyms

Quantum Optical Generalized Spatial Modulation Quadrature Phase Shift Keying Quantum Spatial Modulation Radio Frequency Reconfigurable Intelligent Surfaces Remotely Operated Vehicles Random Variable Signal-to-Interference-plus-Noise Ratio Single-Input Single-Output Spatial Modulation Spatial Media Based Modulation Signal-to-Noise Ratio Semiconductor Optical Amplifier Transmit Laser Index Transmit Laser Selection Transmit Source Selection Underwater Optical Wireless Communication Wide Area Network

Chapter 1

Introduction

Future generation wireless communication networks require higher data rates at minimal cost and better quality of service. Hence, new technologies or devices need to be deployed in order to achieve high data rates with good efficiency. Two devices located nearby need to interact with each other without using the conventional base station. Direct interaction between devices will save resources, time, power and cost. Such communication forms an integral part of Internet of Things (IoT) and future 5G and 6G communications. Various technologies are proposed to implement interactions between devices. In the subsequent sections, we will have a brief understanding of some of the technologies available to implement such communication.

1.1 BAN Communication Radio frequency (RF) communication between wearable devices attached to the bodies of persons can take place, and this technology is termed as body area network (BAN) communication. It is a wireless network in a short range composed of devices situated in, on and around the body. The applications of BAN are quite diverse covering the healthcare industry, military, sports and entertainment industry [1–3]. A device which can be worn on the body of a person can transfer data to another such device worn on the body of another person either in short distance or separated by some farther distance. BAN communication can be used for health monitoring purposes like monitoring patients remotely, cardiovascular disease detection, sleep monitoring, etc. To prevent any major injuries or casualties, the health monitoring of an athlete in real time can also be achieved by BAN communication. If any medical emergency arises, an alarm can be sounded to an athlete. In the military domain, BAN can be beneficial in monitoring the status of a soldier on the battlefield and to exchange critical information © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021 A. Bhowal and R. S. Kshetrimayum, Advanced Spatial Modulation Systems, Signals and Communication Technology, https://doi.org/10.1007/978-981-15-9960-6_1

1

2

1 Introduction

among soldiers. The exact location and fatigue details can be tracked through such devices resulting in better management of soldiers on warfront [3]. > Important Points BAN is a form of a short-range RF wireless network taking place between wearable devices. BAN has applications in the healthcare industry, military field and sports industry.

Body movements in BAN result in shadowing effects which vary in time and correspondingly affect the data transmission at the transmitter and receiver. Hence, due to the occurrence of scatterers at the transmitter and receiver sides, it will have an impact on the data transfer. The two bodies are involved in relative motion, thereby resulting in time-varying shadowing effects. A normal indoor channel cannot model a BAN channel accurately because of the mobility of human beings and different locations of the antennas in different parts of the body thereby yielding different channel gains. BAN communication differs from device-to-device (D2D) communication in certain aspects. D2D communication usually is devoid of the shadowing effects caused by the human body. The relative height of the different body parts also plays an important role in body shadowing effects in BAN. Thus, a different channel model is required as discussed in the next chapter. > Important Points Shadowing effects in BAN are due to body movement. Relative height of the body parts causes time-varying shadowing effects.

BAN communication has been used in the healthcare industry as reported in the literature. BAN communication can be effectively used in the treatment of patients suffering from various diseases. The BAN channel for monitoring gestures, which are not normal, of patients suffering from Parkinson’s disease has been investigated in [4]. The BAN channel model taking into account the effect of different sizes/types of human bodies has been studied in [5]. S band sensing has been used to study the amplitude and phase of channel data for abnormal positions of patients suffering from dementia [6] and cerebellar abnormalities [7]. In [6], the channel’s phase and amplitude data are categorized into three wandering types—random, pacing and lapping. Using the support vector machine (SVM) algorithm, the features of the patients suffering from dementia have been classified. In [7], tremors in hand and abnormality in gait are utilized as features for amplitude and phase data categorization for patients suffering from cerebellar abnormalities . A BAN communication system with high energy efficiency has been reported in [8], which can exchange cloud-based data between the fixed access points and the patients.

1.1 BAN Communication

3

> Important Points BAN can be used in the monitoring of patients ailing from Parkinson’s disease, dementia and cerebellar anomalies. Machine learning algorithms can be used to classify amplitude and phase data depending upon disease-specific features.

BAN communication is of critical importance in the sports domain also. In sporting events, some important parameters like pulse rate, blood pressure, glucose level in blood, movement and position of body parts, etc. are required to be tracked at fixed intervals to give the best performance. The arms of athletes are equipped with different wearable sensors. Sensors can be gyroscope/accelerometer, blood pressure sensor, blood glucose sensor, electrocardiogram (ECG)/electroencephalogram (EEG)/electromyography (EMG) sensor, temperature and humidity sensor, etc. A certain physiological parameter is detected by a particular sensor which further provides post-processing data. All these data are transferred from one person’s wearable device to another person’s wearable device via relays and finally to a fixed central server for health tracking. The sensors in a cooperative manner relay the data to the central server. To deploy effective BAN communication in a particular area, sensor based communication needs to be investigated [9]. BAN communication can be effectively deployed in sports activities like running and cycling. In running, some parameters like position of gait, amount of strides taken, periodic hip movement and hand movement in oscillation are critical to yield the runner’s best performance. The storage and analysis of these data can be useful in enhancing the performance of athletes in future sporting activities. Occasionally, player casualties have been reported during sporting activities due to malfunctioning of lungs, livers, heart or kidneys [10]. During any physical activity, organs like lungs and heart toil at a higher rate, hence an increased risk of casualty. If the respiratory and heart rates can be tracked in real time during activities and in situations of these rates exceeding the danger level, then an alarm can be sounded from the monitoring center to the particular athlete’s wearable device via relay of other athlete’s wearable devices. This alarm will allow the athlete to stop all the activities immediately to prevent any casualty. This will be useful in minimizing fatalities in sporting activities.

1.2 FSO Communication Traditional RF communication suffers from the issue of limited bandwidths and lower data rates. Optical wireless communication (OWC) is a promising technology to overcome such limitations of traditional RF communication. In OWC, message transfer can take place by means of optical/light waves. OWC can be broadly classified into two types—free space optical (FSO) for outdoor communication and visible

4

1 Introduction

light communication (VLC) for indoor communication. The outdoor systems are of two types—space links and terrestrial links. Indoor communication is carried out mostly using a light emitting diode (LED) operating in the infrared (IR) wavelength region of 780–950 nm. In space link optical wireless communication, links can be air-to-ground, air-toair, aircraft to ground or to other aircraft or deep space, between different earth orbits to ground, ground to other planet links, etc. In all these links, a laser is used because of its narrow beamwidth and larger bandwidth than the RF counterpart. For terrestrial applications, FSO links can be used for distances ranging over several kilometers provided there is good line of sight (LOS) between the two devices. In the current scenario, high bandwidth connections are required between the local area network (LAN) and metropolitan area network (MAN) or wide area network (WAN). To make sure that end users receive high-speed gigabit ethernet connectivity, high bandwidth connectivity between LAN and WAN is necessary which can be achieved by using FSO links. FSO link deployment and maintenance are also cheaper than RF links. FSO communication offers benefits like ultrawide bandwidth, inherent security and ease of installation. It exceeds the data rates of traditional RF communication [11– 14]. However, FSO is affected by fluctuations in the atmosphere. As light rays travel through the atmosphere, they undergo changes in the refractive index due to variations in temperature, pressure and humidity in the atmosphere. This phenomenon is known as atmospheric turbulence. > Important Points OWC can replace RF technology by offering ultrawide bandwidths, ultrahigh data rates and more security. OWC can be classified into outdoor (FSO) and indoor (VLC) communication. Outdoor communication is again of two types—space links and terrestrial links.

The propagation of laser beam in free space is affected by beam divergence, atmospheric losses, atmospheric turbulence and ambient light. Beam divergence—The diffraction of light around the aperture at the sharp edges of the telescope causes beam divergence. The amount of useful signal energy to be collected at the receiver is determined by the amount of divergence. It is independent of the propagation medium. The divergence angle of the beam spread is given by [15]: λ , (1.1) θ= D where D is the aperture diameter and λ is the propagating wavelength. Ambient Light—Sunlight and moonlight which are natural sources of light also have spectral lines in the visible and infrared regions. So noise is induced in the FSO channels due to the presence of light sources. The peak intensity of noise caused due

1.2 FSO Communication

5

to solar radiation is generally observed at 480 nm and decreases gradually with an increase in wavelength. Atmospheric Losses—The optical beam while propagating through the atmosphere undergo losses or attenuation due to absorption and scattering. Absorption occurs due to the absorption of photons meaning that the energy of photons in the optical beam is transferred to the internal energy of the absorbing particle. Scattering occurs due to collision of the light beam with scatterers or some particles thereby causing a change in the direction of the optical signal. Attenuation of light beam propagating through the atmosphere can be described by Beer–Lambert Law. It states that at a distance x, the transmission coefficient of laser radiation T (x) in the atmosphere is given by [16] T (x) =

Ix = e−σatt x , I0

(1.2)

where Ix is the intensity of light at a distance of x whereas I0 is the original light intensity transmitted and σatt is the attenuation coefficient. Attenuation coefficient is the summation of four individual parameters—molecular and aerosol absorption coefficients αm and αa , and molecular and aerosol scattering coefficients βm and βa , respectively. These are all the functions of wavelengths. So attenuation coefficient can be evaluated as (1.3) σ = αm + αa + βm + βa . Absorption—Absorption particles can be divided into molecular and aerosol absorbers. When the laser beam interacts with the gaseous molecules in the medium like O2 , N2 , H2 , etc., then molecular absorption occurs. The particles are distinguished by their refractive index. The imaginary part of refractive index n m is involved in molecular absorption by the following equation [16]: αm =

4πn m = Aabs Nabs , λ

(1.4)

where Aabs is the cross-section of the absorption area and Nabs represents the concentration of absorption particles. Thus, molecular absorption is a function of wavelength λ. Low absorption losses take place in the spectral wavelength regions of 850, 1300 and 1550 nm. There are suspended liquid particles present in the atmosphere in the form of fog, mist, etc. which are called liquid aerosols while suspended particles in the form of dust, volcanic debris and dust particles are called solid aerosols. Aerosols can be formed as a part of industrial waste by man-made conversion of gaseous particles to solid or liquid particles. The size of the particles varies from 0.01 µm to 10 µm. Scattering—Scattering can be classified into Rayleigh and Mie scattering depending on the size of the particles. The size parameter Msc is given by Msc =

2πr , λ

(1.5)

6

1 Introduction

where the particle radius is given by r and λ is the wavelength. When Msc 1, then scattering is independent of wavelength and is of non-selective type. When the particle size is very small in comparison to the wavelength of the medium, then Rayleigh scattering dominates. The scattering is inversely proportional to λ4 meaning shorter wavelengths cause more scattering. Thus, the longer wavelength infrared region has less prominence in Rayleigh scattering. In the case of Mie scattering, the scattering is inversely proportional to λq where q varies from 1.6 to 0. q denoting the size of the scattering particle and its value is given as [17] ⎧ ⎪ ⎨1.6 for high visibility(V > 50 Km) q = 1.3 for average visibility(6 Km < V < 50 Km) ⎪ ⎩ 0.585V1/3 for low visibility(V < 6 Km) ,

(1.6)

where V denotes the visibility in Km. The Mie scattering process is mainly caused due to the presence of aerosols like fog, mist, haze, etc. > Important Points FSO communication is affected by atmospheric losses, atmospheric turbulence, beam divergence and ambient light. Atmospheric losses occur due to absorption and scattering. Absorption are of two types—molecular and aerosol. Scattering are of two types–Rayleigh and Mie.

Optical sources like LED/Laser are intensity modulated at the transmitting end while direct detection by a photodetector is performed at the receiver in an FSO system. On-off keying (OOK) and binary phase shift keying (BPSK) are the modulation schemes generally used in FSO systems. However, OOK suffers due to the requirement of an adaptive threshold in order to adjust to the time-varying atmospheric turbulences. The signal distribution is also not distinctly spaced on either side of the zero in the case of OOK. The amount of turbulence and the signal power determines the threshold for the OOK scheme. Also, the scintillation noise power in the case of OOK is concentrated at lower frequencies. BPSK on the other hand has a fixed threshold [18]. In BPSK, irrespective of the presence or absence of turbulence, the signal distribution for bits 1 and 0 are similar and are evenly spaced on either side of the zero. The threshold position can thus be fixed at zero and is unaffected by scintillation. In the spectral domain, the scintillation noise power is shifted away from the low-frequency region to the subcarrier frequency which is around 1 MHz. Therefore, it is not affected by scintillation. BPSK is the modulation scheme that has the farthest distance between constellation points, leading to minimal chances of error in detection.

1.2 FSO Communication

7

Fig. 1.1 FSO block diagram

> Important Points Intensity modulation of optical sources and direct detection by a photodetector is carried out in FSO communication. BPSK is the preferred modulation scheme for FSO communication.

In any FSO system, an electrical signal is converted to an optical signal at the transmitting end. Initially, an RF subcarrier signal is modulated by source data and the resulting signal is sinusoidal in nature which cannot drive an optical source like a laser. Thus, the signal is made positive by passing the sinusoidal signal through a DC bias adder. Now the positively modulated signal is used to drive a laser and the laser intensity is thus modulated according to the driving signal. This optical signal is sent out through an aperture/telescope. On the receiving side, direct detection by a photodetector occurs which generates an electrical signal according to the intensity of the optical signal received. The photodetector receives the signal by means of a receiving aperture/telescope. The generated electrical signal is then processed to eliminate the DC bias and undergoes subsequent demodulation. A basic block diagram of the FSO system is provided in Fig. 1.1.

1.3 UOWC Communication The concept of OWC can also be applied for underwater applications and such communication is termed as underwater optical wireless communication (UOWC). As compared to RF or acoustic based communication, UOWC can provide higher data rates, greater bandwidth and more security benefits. UOWC has many similarities with atmospheric FSO communication [19], however, the environmental conditions are different due to different scattering and absorption phenomena in the aquatic environment. UOWC constitutes multiple distributed nodes such as autonomous underwater vehicles (AUV), remotely operated underwater vehicles (ROV), relay

8

1 Introduction

Fig. 1.2 UOWC block diagram

buoys and seabed sensors. The ROVs and AUVs perform data exchange with the sensors located at the oceanic beds by means of UOWC links. The data from these ROVs and AUVs are transferred to submarines and ships through UOWC links, which perform data exchange with the data processing center located above the marine environment through RF/FSO links. This is pictorially explained in Fig. 1.2. If the nodes are located far apart, then ROVs and AUVs can also act as relay nodes and the corresponding source to relay links are labeled as indirect optical links. The direct UOWC links between source and destination nodes are labeled as direct optical links. UOWC will find use in disaster precaution, offshore exploration, environmental monitoring and military applications. > Important Points UOWC is affected by scattering and absorption effects. UOWC can be beneficial for environmental monitoring, offshore sea explorations, disaster management and military applications.

1.3 UOWC Communication

9

In UOWC, a message is sent underwater by using optical waves. The salinity of water and the presence of a variety of marine organisms affect the performance of UOWC systems. In underwater conditions, absorption takes place due to collision between the propagating photons and water molecules, and other suspended molecules, and suffer energy loss. The optical signals undergo directional change due to scattering [20]. The absorption coefficient a(λ) and scattering coefficient b(λ) take these effects into account [21]. To understand the advantages of UOWC over RF and acoustic based communication, let us have a look at the characteristics of acoustic and RF means of transmission underwater. Some of the disadvantages of underwater acoustic communication are discussed. Poorer data rates are due to the low frequency of operation. An acoustic link has a larger delay time (typically in seconds), expensive transceivers and they have low energy efficiency also. The RF version has the problem of link range which is usually short. It also utilizes costly transceivers which have low energy efficiency and antennas whose sizes are large. Hence, one can go for alternate technology such as UOWC. An optical wave has much greater speed than an acoustic wave. Thus, UOWC links have overcome the problem of link latency and enhance security also [22, 23]. The underwater environment is dynamic resulting in the need for a complex channel model. UOWC equipment are affected by turbidity of water, salinity, water flow and temperature. The power crisis in the aquatic environment requires the devices to be energy efficient. In an underwater environment, light absorption occurs because of the presence of colored dissolved organic material (CDOM) and chlorophyll. This hinders light propagation and the turbidity of water increases. The CDOM’s concentration also changes with the variations in ocean depths, correspondingly attenuation coefficients of light changes. The temperature and pressure of ocean currents vary rapidly causing fluctuations of the refractive index of water. This phenomenon is called turbulence [24]. In UOWC systems, optical sources like LED/Laser are intensity modulated at the transmitter while for a reception, direct detection by a photodetector is done [25]. BPSK or some higher constellation schemes like M-quadrature amplitude modulation (QAM) [26, 27] can be used as modulation schemes for UOWC systems. Generally, underwater explorations in the deep ocean will necessitate communications in a long range owing to the fact that the ocean depths are usually in kilometers. Hence, cooperative communication with the amplify-and-forward (AF) protocol based relay would be useful. > Important Points UOWC equipment are affected by temperature, water flow, pressure, water’s turbidity and salinity. Power shortage in the aquatic environment is an issue. Water’s refractive index fluctuates because of changing temperature and pressure of ocean currents leading to a phenomenon called turbulence.

10

1 Introduction

In the literature, several works have been carried out regarding UOWC communication systems. Optical pre-amplification for UOWC systems has been explored in [28]. In [29], a suitable channel model for UOWC systems, which considers effects like turbulence, absorption and scattering, has been proposed. UOWC systems with optical spatial modulation have been proposed in [30]. Space division multiplexing for underwater transmission has been proposed in [31]. Beer–Lambert’s Law can suitably describe the attenuation effect in seawater. It has been proven in the literature that the blue/green region of the visible spectrum having a wavelength of 450–550 nm has the minimal scattering and attenuation coefficient. The UOWC communication range is usually less than 100 m [32] which necessitates the use of cooperative UOWC communication for larger distance.

1.4 Hybrid FSO/RF Communication FSO communication is affected by fog and atmospheric turbulences and not by rain, while RF communication is affected by rain but not influenced by atmospheric turbulences [33]. The benefits of both FSO and RF communication can be combined to form a hybrid FSO/RF system. Such systems can be deployed in future generation cellular communication systems. Existing cellular communication systems support only RF communication with no provision for FSO communication. We can incorporate FSO links along with the existing RF based cellular systems to form a hybrid FSO/RF network. In this hybrid system model, the mobile user (MU) can communicate with an access point (AP) through the existing RF links while the APs can exchange data with the base stations (BSs) through FSO links. The pictorial illustration has been given in Fig. 1.3. We know that in a conventional cellular system, mobile users interact with the base stations through RF links. This concept is slightly tweaked in hybrid FSO/RF systems by incorporating an access point. The AP helps in increasing the effective link distance of the hybrid FSO/RF system. It is the node

Fig. 1.3 Hybrid FSO/RF system block diagram

1.4 Hybrid FSO/RF Communication

11

which is equipped with both optical and RF chains. This consumes more resources and escalates the system cost, but it is overshadowed by the fact that performance improves after the addition of AP, thereby justifying the use of AP. AP can be used to serve multiple mobile users also, although it is out of the scope of this book. It is difficult to incorporate FSO communication at the mobile user side since the existing mobile devices do not support FSO communication, and upgrading numerous mobiles will incur a huge cost. Hence, it is advantageous and less expensive to incorporate FSO communication at the BS, since BS are fewer in number than mobile users. It is also difficult to maintain LOS links between the MU and AP in a crowded and dense urban environment. Therefore, the use of the RF link is justified for connecting MU with AP. Thus, a hybrid FSO/RF system can exploit the benefits of both FSO and RF communication in cellular systems and achieve high data rates. > Important Points FSO communication is affected by fog and atmospheric turbulences and not by rain while RF communication is affected by rain and not by fog and atmospheric turbulences. FSO and RF communication can be combined to form hybrid FSO/RF systems and used in cellular systems. FSO links are used between BS and AP while RF links are used between AP and MU.

In the literature, many works have been reported regarding hybrid FSO/RF systems. A cost-efficient hybrid FSO/RF backhaul system has been reported in [34]. The outage analysis of a practical FSO/RF hybrid system with adaptive combining has been performed in [35], where depending on a certain threshold, an optical/RF link is chosen. Multiuser hybrid FSO/RF relaying with buffers has been proposed in [36]. The performance analysis of cooperative hybrid FSO/RF communication over generalized M channels has been analyzed in [37]. In [38], a parallel hybrid FSO/RF system has been proposed where both FSO and RF links work in parallel. Multiuser diversity using parallel hybrid FSO/RF links has been investigated in [39]. Different configurations of hybrid FSO/RF models have been used in the literature. One approach is to achieve diversity by simultaneously transmitting the same information through FSO and RF links. Such an approach ensures diversity because in case if one link fails then the other link is active to transmit the same information. Another approach is to achieve capacity enhancement by splitting the information and transmitting it through FSO and RF links. This compromises the diversity aspect and in case if any link fails, then the system performance suffers. RF link deployment as a backup link when the FSO link is down also serves as a different alternative. When atmospheric conditions are suitable, then FSO links are used but in case of severe atmospheric turbulences (i.e. beyond a threshold point) an RF link is used as an alternative. This ensures that the system does not fail in case of harsher atmospheric conditions.

12

1 Introduction

> Important Points Diversity approach is performed by the simultaneous transfer of information through FSO and RF links. Capacity approach is achieved by splitting up the information and transmitting it through FSO and RF links. RF link can be used as a backup link when the FSO link is down.

1.5 Cooperative Communication In the previous sections, we have learnt about various technologies of data transmission. All these can incorporate cooperative communication to increase the effective distance of communication. In cooperative communication, data is exchanged between two devices with the help of an intermediary device called a relay. Cooperative relaying can increase the reliability of wireless communication especially in mobile ad-hoc networks and sensor networks [40, 41]. There are many protocols and they can be broadly classified into transparent and regenerative relaying protocols. Transparent relaying protocols do not modify the samples or bits received at the relay. They are only responsible for power scaling or phase rotations. On the other hand, regenerative protocols regenerate the information received and transmit it again after performing complex baseband operations, if necessary. AF relaying is one such transparent relaying protocol, while Decode-and-Forward (DF) and Compress-andForward (CF) relaying are the most widely used regenerative protocols. In the AF protocol, the received signal at the relay is simply amplified to compensate for the power loss and then forwarded to the destination nodes. In the DF protocol, the relay first decodes the signal, encodes it again and then sends it to the destination nodes. The relays can be unidirectional or bidirectional in nature. Again the relays can have fixed or variable gain. In a unidirectional relay, the source node transmits the information to the relay in the first time slot while in the second time slot, the AF relay amplifies the information and retransmits it to the destination nodes. The end-to-end instantaneous signal-tonoise ratio (SNR) between the source and destination node can be written as [42, 43] γS R γ R D , (1.7) γeq = γS R + γ R D + 1 where γ S R and γ R D are the instantaneous SNRs of the source to relay link and relay to destination link, respectively. In bidirectional relay, two nodes (S1 and S2 ) send their information to the relay node simultaneously in the first time slot. Then, the relay combines both the signals and sends the information to both the nodes simultaneously in the second time slot. The end-to-end SNR expressions can be written as [41]

1.5 Cooperative Communication

13

γ S2→S1 =

γ S1 γ S2 , γ1 + A2PN0

(1.8)

γ S1→S2 =

γ S1 γ S2 , γ2 + A2PN0

(1.9)

where γ S1 and γ S2 are the instantaneous SNRs of the corresponding source to relay link, respectively, and A is the amplification factor and P is the power of transmission. N0 represents noise. There are two types of gain for bidirectional relay—fixed and variable. In case of fixed gain relaying, the information about both the source to relay channel links are available to the relay. The amplification factor for this fixed gain case is given by [44]  P , (1.10) A= 2 P E[| h 1 | ] + P E[| h 2 |2 ] + N0 where E[] is the expectation operator, h 1 and h 2 are the channel gain coefficients for source 1 to relay and source 2 to relay, respectively. The end-to-end instantaneous SNR expressions can then be reformulated as [44] γ S2→S1 =

γ S1 γ S2 , γ S1 + γ¯ S1 + γ¯ S2 + 1

(1.11)

γ S1→S2 =

γ S1 γ S2 , γ S2 + γ¯ S1 + γ¯ S2 + 1

(1.12)

where γ¯ S1 = E[| h 1 |2 ]/N0 ,γ¯ S2 = E[| h 2 |2 ]/N0 . In case of variable AF relaying, knowledge about the instantaneous channel coefficients of both the links is available at the relay. The amplification factor in this case would be [44]  P . (1.13) A= 2 P | h 1 | +P | h 2 |2 +N0 Thus, the end-to-end SNRs can be expressed as [44] γ S2→S1 =

γ S1 γ S2 , 2γ S1 + γ S2 + 1

(1.14)

γ S1→S2 =

γ S1 γ S2 . 2γ S2 + γ S1 + 1

(1.15)

Thus, cooperative communication holds the promise for better connectivity, increased coverage area, diversity and multiplexing gains. It can be of single hop or multi-hop. Relays can be arranged in parallel or in series. Cooperative communication can be employed with any RF or optical systems to enhance the system performance.

14

1 Introduction

> Important Points An example of transparent protocols is AF relaying, and some examples of regenerative protocols are DF and CF relaying. Relays can be unidirectional and bidirectional. Relays can have fixed and variable gains.

1.6 Introduction to Spatial Modulation Before explaining the concept of spatial modulation, let us have a brief look at the concept of RF and optical chain. An RF chain comprises electronic components and sub-modules including amplifiers, filters, mixers, attenuators, modulators and demodulators, power converters, encoders and decoders, etc. The optical chain is a similar version of the RF chain which is used for OWC systems. The optical chain comprises RF modulators, DC bias adders, intensity modulators like lasers, photodetectors, RF demodulators, etc. Let us have a basic understanding of the various network coding concepts available in the literature. We will briefly discuss no network coding, analog network coding and physical layer network coding schemes in the following subsections. In the later chapters, we are going to combine network coding along with spatial modulation in relay based communication.

1.6.1 No Network Coding Scheme In the no network coding scheme, as depicted in Fig. 1.4, node 1 sends its information packet S1 to relay node R in the first time slot. The relay node forwards this packet to node 2 in the second time slot. In the third time slot, node 2 sends its information packet S2 to relay R. Finally, the relay node forwards the packet S2 to node 1 in the fourth time slot. Thus, for the exchange of 2 packets in either direction, overall 4 time slots are required. > Important Points For the exchange of two packets, one packet in either direction, 4 time slots are required.

1.6 Introduction to Spatial Modulation

15

Fig. 1.4 No network coding scheme

Fig. 1.5 Analog network coding scheme

1.6.2 Analog Network Coding In analog network coding (ANC), for the exchange of 2 packets, total 3 time slots are required as illustrated pictorially in Fig. 1.5. The source node 1 transmits its packet S1 to the relay node R in the first time slot while source node 2 sends its packet S2 to the relay node in the second time slot. The relay node then performs network coding XOR operation as S R = S1 ⊕ S2 and transmits the packet S R to both the nodes 1 and 2 in the third time slot. Since the source nodes have information about their own packets, they can retrieve the received packet by performing an XOR operation. For example, if node 2 receives the packet S R , then it can retrieve the packet S1 as S R ⊕ S2 = (S1 ⊕ S2 ) ⊕ S2 = S1 . > Important Points For the exchange of two packets, one packet in either direction, three time slots are required. Network coding operation is performed at the relay node.

1.6.3 Physical Layer Network Coding Suppose there are 2 nodes which can exchange data with the help of a relay node as depicted in Fig. 1.6. In the first time slot, source nodes 1 and 2 send their information simultaneously to the relay node. In the second time slot, the relay node performs a mapping operation and retransmits the information to the source nodes simultaneously. It is not required for the relay node to decode the exact bit values. The source nodes are designated by node i where i ∈ (1, 2). Let the real part of the signal transmitted by node “i” be Re[(ai + jbi )e jωt ], where ω is

16

1 Introduction

Fig. 1.6 Physical layer network coding scheme

Table 1.1 Physical network coding mapping table Symbol from node 1, Symbol from node 2, Signal received at a1 a2 relay, y RI = a1 + a2 1 1 −1 −1

1 −1 1 −1

2 0 0 −2

Mapped symbol to be transmitted by relay, aR 1 −1 −1 1

the RF signal frequency. Then the real part of the signal received by the relay, which is a superposition of the signals transmitted by both the source nodes, is y R (t) = (a1 + a2 )cos(ωt) − (b1 + b2 )sin(ωt). Here, the QPSK modulated bits ai and bi can take the values of -1 and +1 as given by ai {−1, 1} , bi {−1, 1} where -1 symbol is bit-mapped to 1 and 1 symbol is bit-mapped to 0. Now the coding operation is simplified according to the mapping table given in Table 1.1. One can observe that if we convert symbol 1 to bit 0 and symbol -1 to bit 1, then the mapping table for a R gives exactly bit-level exclusive OR of a1 and a2 . The in-phase (y RI ) and quadrature phase (y RQ ) components of the signal received by the relay can be separated as y RI = a1 + a2 , y RQ = b1 + b2 . Now the relay does not have to decode the bit values, instead, it has to find the values of a1 + a2 and b1 + b2 and then find a R and b R using the following mapping function. a R = a1 a2 can be calculated from y RI as follows.  −1 i f y RI = 0, aR = 1 i f y RI = −2 or 2. Similarly, b R b R = b1 b2 can be evaluated from y RQ as follows.  −1 i f y RQ = 0, bR = 1 i f y RQ = −2 or 2. In the second time slot, relay transmits signal to nodes 1 and 2 as s R (t) = Re[(a R + jb R )e jωt ] = a R cos(ωt) − b R sin(ωt). So only the values of a R and b R are required and not the exact values of ai and bi . Thus for the exchange of two packets, one in each direction, PLNC [45] requires 2 time slots. It is because of

1.6 Introduction to Spatial Modulation

17

the network coding operation automatically performed in the superimposed electromagnetic waves for RF communication and superimposed optical waves for FSO communication. > Important Points For the exchange of two packets, one packet in either direction, two time slots are required. In the superimposed EM waves, automatically, network coding operation is performed.

1.6.4 Spatial Modulation Multiple-input multiple-output (MIMO) technology may be used in RF and optical domains to increase the data rate. But the drawback of the MIMO technique is that multiple RF/optical chains are required in the RF/optical domain leading to excessive power consumption and escalated cost. Multiple antennae/lasers operating simultaneously also leads to inter-antenna/inter-optical interference in MIMO. These problems can be mitigated by a technique called spatial modulation (SM) which uses only one RF/optical chain. SM can be employed with physical layer network coding (PLNC) for better spectral efficiency in RF and FSO systems. Power consumption and system cost are escalated considerably by the simultaneous usage of multiple transmit RF/optical chains in a MIMO based PLNC system. Due to the use of multiple antennae/lasers simultaneously, inter-antenna/inter-optical interference also increases in MIMO based PLNC. But PLNC based SM overcomes those limitations. For RF medium, a single antenna at the transmitter is activated in SM thereby eliminating the inter-antenna interference. The basic block diagram of a spatial modulation scheme is given in Fig. 1.7, in which antenna 2 is active while the remaining antennas are sitting idle. As we can see from the diagram, the transmitter has Tx antennas and the receiver has Rx antennas. From the incoming series of bits, a chunk of bits (log2 (Tx ) + log2 (M)) is taken at a time for spatial modulation, where M is the M-ary modulation scheme. The transmit antenna activation is implemented by log2 (Tx ) number of bits starting from the MSB part of the selected chunk of bits while the remaining log2 (M) bits are mapped to a symbol using a particular M-ary modulation scheme. The concept of spatial modulation is illustrated by means of an example in Fig. 1.8. Let 4-QAM be the modulation scheme and Tx = Rx = 4. Thus, a total of 4 bits enter the bit mapper out of which the first 2 bits from the MSB side, i.e. 11, are used for selecting the antenna and accordingly antenna numbered 4 is activated (since the decimal value of 11 is 4). The remaining bits, i.e. 10, enter the modulator module and are modulated as 1-i. This symbol is sent out through the fourth antenna as shown.

18

1 Introduction

Fig. 1.7 Spatial Modulation block diagram

Fig. 1.8 An example of Spatial Modulation

Similarly in optical medium, a single laser is activated and the technique is known as optical spatial modulation (OSM). The OSM concept is illustrated pictorially in Fig. 1.9, in which laser 2 is only activated while the remaining lasers are sitting idle. From the incoming series of bits, a chunk of bits (log2 (N L ) + log2 (M)) is taken at a time for OSM, where N L indicates the total number of lasers and M is the Mary modulation scheme employed. The transmit laser activation is implemented by log2 (N L ) number of bits starting from the MSB part of the selected chunk of bits while the remaining log2 (M) bits are mapped to a symbol using a particular M-ary modulation scheme. Power consumption and overall cost in SM and OSM are greatly

1.6 Introduction to Spatial Modulation

19

Fig. 1.9 Optical Spatial Modulation block diagram

reduced because of the requirement of a single RF and optical chain in SM and OSM, respectively. The concept of OSM can be pictorially described by means of an example as shown in Fig. 1.10. Let 4-QAM be the modulation scheme employed and N L = N D = 4 where N D denotes the number of photodetectors at the receiver. So a total of 4 bits enter the bit mapper out of which the first 2 bits from the MSB side, i.e. 11, are used for selecting the laser and accordingly laser numbered 4 is activated (since the decimal value of 11 is 4). The remaining bits, i.e. 10, enter the modulator module and are modulated as 1-i. The symbol is sent out through the fourth laser as shown in the diagram. > Important Points Spectral efficiency of SM—log2 (Tx ) + log2 (M). Spectral efficiency of OSM—log2 (N L ) + log2 (M).

> Important Points A single RF/optical chain is present in the SM/OSM system. Power consumption and cost are less in the SM/OSM system.

20

1 Introduction

Fig. 1.10 An example of Optical Spatial Modulation

1.7 Advanced Spatial Modulation In spatial modulation, we have seen that only one source is activated out of the multiple sources. So from the cost perspective, unnecessary money is incurred in buying and deploying the extra sources. To mitigate this issue, advanced spatial modulation techniques are introduced in which more than one source is activated to compensate for the extra cost of the other sources. These techniques also have the capability of achieving higher spectral efficiencies than conventional spatial modulation. These techniques also use multiple RF/optical chains, so there must be a compromise between cost and spectral efficiency. Activating too many sources would negate the benefit of spatial modulation such as less power, cost and inter-antenna/laser interference. Some advanced spatial modulation schemes which are described later in the book are generalized spatial modulation, enhanced spatial modulation, improved spatial modulation, improved quadrature spatial modulation, etc. Advanced spatial modulation (ASM) schemes can be used both in RF and optical domains. > Important Points Advanced spatial modulation schemes not only give better spectral efficiency than the conventional spatial modulation but also use multiple RF/optical chains. Compromise is required between cost and spectral efficiency.

1.8 Performance Analysis

21

1.8 Performance Analysis Due to the varying nature of the environments and applications for which spatial modulation is being applied, different channel models need to be selected which we will discuss further in the subsequent chapters. The main contribution of this book is to highlight the performance analysis of spectrally efficient systems which employs advanced spatial modulation schemes. These systems are proposed for RF and optical wireless domains and for various applications. Any communication system’s performance analysis is done in terms of bit error rate (BER), symbol error rate (SER), outage probability (Pout ), channel capacity (C), etc. BER is defined as the ratio of the number of bits detected with errors to the total number of bits transferred during a given time interval. SER is defined as the ratio of the number of erroneous symbols detected to the total number of symbols transferred during a given time interval. Pout refers to the probability that the system can be in an outage, i.e. the probability that the system decodes the symbols which have been transmitted unsuccessfully due to transmission at a data rate which is greater than the capacity of the channel. Channel capacity (C) provides the tight upper-bound on the information rate at which symbols can be sent over a given communication channel with minimal chances of error. In this book, performance analysis of spectrally efficient advanced spatial modulation based systems is carried out in terms of outage probability, bit error rate and symbol error rate. > Important Points BER, SER, outage probability and channel capacity are some of the performance metrics used for analyzing advanced spatially modulated systems.

References 1. M. Cheffena, M. Mohamed, The application of lognormal mixture shadowing model for B2B channels. IEEE Sens. Lett. 2(3), 1–4 (2018) 2. M. Cheffena, Time-varying on-body wireless channel model during walking. EURASIP J. Wirel. Commun. Netw. 2014(29), 1–11 (2014) 3. R. Khan, M.M. Alam, Body-to-body communication: Applications, system design aspects and performance evaluation, in 2018 12th International Symposium on Medical Information and Communication Technology (ISMICT), March 2018, pp. 1–2 4. X. Yang, S.A. Shah, A. Ren, N. Zhao, Z. Zhang, D. Fan, J. Zhao, W. Wang, M. Ur-Rehman, Freezing of gait detection considering leaky wave cable. IEEE Trans. Antennas Propag. 67(1), 554–561 (2019) 5. S. Sangodoyin, A.F. Molisch, A measurement-based model of BMI impact on UWB multiantenna PAN and B2B channels. IEEE Trans. Commun. 66(12), 6494–6510 (2018) 6. X. Yang, S.A. Shah, A. Ren, N. Zhao, D. Fan, F. Hu, M. Ur Rehman, K.M. vonDeneen, J. Tian, Wandering pattern sensing at S-band. IEEE J. Biomed. Health Inform. 22(6), 1863–1870 (2018)

22

1 Introduction

7. X. Yang, S.A. Shah, A. Ren, D. Fan, N. Zhao, S. Zheng, W. Zhao, W. Wang, P.J. Soh, Q.H. Abbasi, S-band sensing-based motion assessment framework for cerebellar dysfunction patients. IEEE Sens. J. 1–1 (2019) 8. A. Samanta, Y. Li, Distributed pricing policy for cloud-assisted body-to-body networks with optimal QoS and energy considerations. IEEE Trans Serv Comput 1–1 (2018) 9. A. Meharouech, J. Elias, A. Mehaooua, Moving towards body-to-body sensor networks for ubiquitous applications: a survey. J. Sensor Actuator Netw. 8(2), 1–27 (2019) 10. Y. Fu, J. Liu, Monitoring system for sports activities using body area networks, in Proceedings of the 8th International Conference on Body Area Networks, ser. BodyNets ’13 (2013), pp. 408–413 11. H.A. Willebrand, B.S. Ghuman, Fiber optics without fiber. IEEE Spectrum 38(8), 40–45 (2001) 12. W.P.Z. Ghassemloo, S. Rajbhandari, Optical Wireless Communications: System and channel modelling with Matlab (CRC Press, 2013) 13. M.R. Bhatnagar, Z. Ghassemlooy, Performance analysis of gamma gamma fading FSO MIMO links with pointing errors. J. Lightwave Technol. 34(9), 2158–2169 (2016) 14. I.S. Ansari, M.M. Abdallah, M.S. Alouini, K.A. Qaraqe, Outage performance analysis of underlay cognitive RF and FSO wireless channels, in 3rd International Workshop in Optical Wireless Communications (IWOW), pp. 6–10 (2014) 15. E. Friedman, L. John, Miller, Photonics Rules of Thumb (McGraw-Hill Professional, 2003) 16. H. Weichel, Laser Beam Propagation in the Atmosphere (SPIE, Bellingham, WA, 1990) 17. D. Chadha, Terrestrial Optical Wireless Communication (McGraw-Hill, 2013) 18. W. Popoola, Subcarrier intensity modulated free space optical communication systems. Ph.D. thesis (2009) 19. P. Kaur, V.K. Jain, S. Kar, Performance analysis of FSO array receivers in presence of atmospheric turbulence. IEEE Photonics Technol. Lett. 26(12), 1165–1168 (2014) 20. Z. Zeng, S. Fu, H. Zhang, Y. Dong, J. Cheng, A survey of underwater optical wireless communications. IEEE Commun. Surv. Tutori. 19(1), 204–238 Firstquarter (2017) 21. W. Cox, Simulation, modeling, and design of underwater optical communication systems. North Carolina State University, Raleigh: Ph.D. dissertation (2012) 22. M.A. Khalighi, C. Gabriel, T. Hamza, S. Bourennane, P. Léon V. Rigaud, Underwater wireless optical communication; recent advances and remaining challenges, in 2014 16th International Conference on Transparent Optical Networks (ICTON), July 2014, pp. 1–4 23. D. Pompili, I.F. Akyildiz, Overview of networking protocols for underwater wireless communications. IEEE Commun. Mag. 47(1), 97–102 (2009) 24. L.J. Johnson, F. Jasman, R.J. Green, M.S. Leeson, Recent advances in underwater optical wireless communications. Underwater Technol. 32(3), 167–175 (2014) 25. W.O. Popoola, Z. Ghassemlooy, BPSK subcarrier intensity modulated free-space optical communications in atmospheric turbulence. J. Lightwave Technol. 27(8), 967–973 (2009) 26. D.W. Dawoud, F. Heliot, M.A. Imran, R. Tafazolli, Spatial quadrature modulation for visible light communication in indoor environment, in 2017 IEEE International Conference on Communications (ICC), May 2017, pp. 1–6 27. B. Cochenour, L. Mullen, A. Laux, Phase coherent digital communications for wireless optical links in turbid underwater environments, in OCEANS 2007, September 2007, pp. 1–5 28. A.C. Boucouvalas, K.P. Peppas, K. Yiannopoulos, Z. Ghassemlooy, Underwater optical wireless communications with optical amplification and spatial diversity. IEEE Photonics Technol. Lett. 28(22), 2613–2616 (2016) 29. B. Majlesein, A. Gholami, Z. Ghassemlooy, A complete model for underwater optical wireless communications system, in 2018 11th International Symposium on Communication Systems, Networks Digital Signal Processing (CSNDSP), July 2018, pp. 1–5 30. A. Huang, L. Tao, Q. Jiang, BER performance of underwater optical wireless MIMO communications with spatial modulation under weak turbulence, in 2018 OCEANS - MTS/IEEE Kobe Techno-Oceans (OTO), May 2018, pp. 1–5 31. O.V. Sinkin, A.V. Turukhin, Y. Sun, H.G. Batshon, M.V. Mazurczyk, C.R. Davidson, J. Cai, W.W. Patterson, M.A. Bolshtyansky, D.G. Foursa, A.N. Pilipetskii, SDM for power-efficient undersea transmission. J. Lightwave Technol. 36(2), 361–371 (2018)

References

23

32. M.V. Jamali, J.A. Salehi, F. Akhoundi, Performance studies of underwater wireless optical communication systems with spatial diversity: MIMO scheme. IEEE Trans. Commun. 65(3), 1176–1192 (2017) 33. V.V. Mai, A.T. Pham, Adaptive multi-rate designs for hybrid FSO/RF systems over fading channels, in 2014 IEEE Globecom Workshops (GC Wkshps), December 2014, pp. 469–474 34. H. Dahrouj, A. Douik, F. Rayal, T.Y. Al-Naffouri, M. Alouini, Cost-effective hybrid RF/FSO backhaul solution for next generation wireless systems. IEEE Wirel. Commun. 22(5), 98–104 (2015) 35. T. Rakia, H. Yang, M. Alouini, F. Gebali, Outage analysis of practical FSO/RF hybrid system with adaptive combining. IEEE Commun. Lett. 19(8), 1366–1369 (2015) 36. Y.F. Al-Eryani, A.M. Salhab, S.A. Zummo, M. Alouini, Protocol design and performance analysis of multiuser mixed RF and hybrid FSO/RF relaying with buffers. IEEE/OSA J. Optical Commun. Netw. 10(4), 309–321 (2018) 37. L. Kong, W. Xu, L. Hanzo, H. Zhang, C. Zhao, Performance of a free-space-optical relayassisted hybrid RF/FSO system in generalized m-distributed channels. IEEE Photonics J. 7(5), 1–19 (2015) 38. A. Touati, A. Abdaoui, F. Touati, M. Uysal, A. Bouallegue, On the effects of combined atmospheric fading and misalignment on the hybrid FSO/RF transmission. IEEE/OSA J. Optical Commun. Netw. 8(10), 715–725 (2016) 39. L. Chen, W. Wang, C. Zhang, Multiuser diversity over parallel and hybrid FSO/RF links and its performance analysis. IEEE Photonics J. 8(3), 1–9 (2016) 40. G.K. Karagiannidis, N.C. Sagia, T. Mathiopoulos, The N-Nakagami fading channel model, in 2005 2nd International Symposium on Wireless Communication Systems, September 2005, pp. 185–189 41. F. Gong, Cooperative mobile-to-mobile communications over double nakagami-M fading channel. IET Commun. 6(18), 3165–3175 42. M.O. Hasna, M.S. Alouini, End-to-end performance of transmission systems with relays over Rayleigh-fading channels. IEEE Trans. Wirel. Commun. 2(6), 1126–1131 (2003) 43. L. Xu, Performance analysis of the IAF relaying M2M cooperative networks over N-nakagami fading channels. J. Commun. 10(3), 185–191 44. G. Ozcan, M.C. Gursoy, Effective capacity analysis of fixed-gain and variable-gain af two-way relaying, in 2013 IEEE 78th Vehicular Technology Conference (VTC Fall), September 2013, pp. 1–5 45. S. Liew, Physical-layer network coding: tutorial, survey and beyond. Elsevier J. Phys. Commun. 6(3), 4–42

Chapter 2

Channel Model

2.1 BAN Channel Model In BAN communication, lognormal mixture channel model is used for performance analysis of sporting activities. There is justification for the use of such a channel model. The authors in [1] have asserted that the histograms made using experimental data for different sporting activities like cycling and running exhibit skewed and mixture distribution curves. This demonstrates that distinct scattering clusters are present in BAN communication which can be modeled appropriately by a mixture distribution. Large number of scatterers are present in BAN communication due to the presence of time variant body shadowing effects, which is different from the normal environmental scattering effect. Hence, such body shadowing effects need to be modeled by a different channel model. The BAN channels for various sporting activities have been designed using a shadowing model [1, 2]. Lognormal mixture model is basically a weighted mixture of multiple lognormal channels having separate variance and mean. It has been observed that the mixture model shows better match with the original experimental data in comparison to the unimodal distributions. The weighted related mean difference (WRMD) parameter has been considered in [1] to compare the fitting of experimental data with the PDF of a specific distribution. It has been studied in literature that the lognormal mixture distribution exhibits the minimum WRMD value which proves that it has the best data fitting. Therefore, the lognormal mixture distribution can be considered as a suitable channel model for BAN communication. The PDF of the lognormal mixture distribution ( f Y (y)) can be expressed as follows [2] ∞  f Y (y) = wk f H (h) , (2.1) k=1

© The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021 A. Bhowal and R. S. Kshetrimayum, Advanced Spatial Modulation Systems, Signals and Communication Technology, https://doi.org/10.1007/978-981-15-9960-6_2

25

26

2 Channel Model

where f H (h)ε L N (μk , σk2 ) (LN representing the lognormal distribution), σk2 and component (k=1,2,...), μk are the variance and mean parameters of the k th mixture  th k th component has a weight factor denoted by wk such that ∞ k=1 wk = 1. The k component follows the lognormal distribution which can be written as given in Eq. (4) of [2]   1 −(ln h − μk )2 . (2.2) f H (h) =  exp 2σk2 h 2πσ 2 k

Let γk = h 2 E/N0 and γ¯ = E/N0 is the SNR at the source node. So the k th component will have received SNR γk which follows the PDF [3]:   −(ln ( γγ¯k ) − 2μk )2 γ¯  f (γk ) = exp . 8σk2 2γk 2πσk2

(2.3)

The lognormal mixture distribution has the received SNR (γ) whose PDF can be written as   ∞  −(ln ( γγ¯ ) − 2μk )2 γ¯ f (γ) = wk  exp . (2.4) 8σk2 2γ 2πσk2 k=1 After integration of the PDF and using the weight values, the CDF of the lognormal mixture distribution can be written as [3] ∞ 

⎛

⎛

1 wk ⎝1 − er f c ⎝ F(γ) = 2 k=1

 ln

γ γ¯

− 2μk

√ 8σk

⎞⎞ ⎠⎠ .

(2.5)

The lognormal mixture distribution is formed by mixing a finite quantity of K Gaussian kernels and K =4 yields the most suitable estimate of the original PDF, as is conclusive from the results given in [1]. Hence, for further analysis, the lognormal-4 distribution is used, and it is denoted by LN-4 in our book. Thus, the final PDF of LN-4 channel for received SNR can be written as   −(ln ( γγ¯ ) − 2μk )2 γ¯ wk  exp f (γ) = . 8σk2 2γ 2πσk2 k=1 4 

The final CDF of LN-4 channel for received SNR can be written as ⎛ γ ⎛ ⎞⎞ 4 ln − 2μ  k γ¯ 1 ⎠⎠ . wk ⎝1 − er f c ⎝ F(γ) = √ 2 8σk k=1

(2.6)

(2.7)

2.1 BAN Channel Model

27

> Important Points The lognormal mixture distribution can model the multiple scattering clusters arising due to body shadowing in BAN communication. The lognormal mixture distribution shows close match with the experimental data better than any other distributions, thereby justifying its use as channel model for BAN sporting activities. A mixture of 4 lognormal channels yields the most suitable estimate of the original PDF so LN-4 is used as the channel model for BAN sporting activities.

2.2 Channel Model for FSO Communication FSO communication is different from RF communication due to the presence of atmospheric turbulences. Before designing an appropriate channel model, we will first have to look at the requirements of the channel. Rytov theory states that a propagating optical wave at a distance of L from the source will have the field equation as  E(r, L) = E 0 (r, L) exp



 ψi (r, L)

,

(2.8)

i

where E 0 (r, L) denotes the optical field when there is no turbulence, r denotes the observation coordinate located in the transverse plane at a distance of L, ψi (r, L) indicates the complex phase perturbations resulting from random path inhomogeneities. However, this equation is limited to single scattering phenomenon only as it fails to consider the role of decreasing transverse spatial coherence radius of the propagating wave. The complex phase perturbation can be expressed as real and imaginary part as ψi (r, L) = χi (r, L) + jξi (r, L). Thus, the first-order irradiance is of the form: I = |E 0 |2 exp(2χ1 ) .

(2.9)

Second-order irradiance can similarly be expressed as I = |E 0 |2 exp(2χ1 ) exp(2χ2 ) .

(2.10)

For multiple scattering regime, Rytov theory is modified and the modified Rytov theory can be written as E(r, L) = E 0 (r, L) exp[ψx (r, L) + ψ y (r, L)] ,

(2.11)

28

2 Channel Model

where the terms ψx (r, L) and ψ y (r, L) denote complex phase deviations that are statistically independent and are caused by large scale and small scale fluctuations, respectively. Hence, the modified optical field irradiance can be written as the multiplicative effect of two random processes as I = Ix I y .

(2.12)

Thus, the modified Rytov theory states that refraction causes large scale turbulent eddies which modulate the scattering induced small scale turbulent eddies. Independent random processes can appropriately model such turbulent effects. Hence, the total irradiance of optical field can be expressed as the multiplicative effect of two independent random processes [4]. This condition is satisfied by the Gamma– Gamma (G-G) channel model formed by the multiplicative effect of two Gamma functions. The lognormal distribution fails to model atmospheric turbulences accurately. This is because only weak turbulence condition can be suitably modeled by lognormal channel model as it has to obey the criteria that the scattered optical field has a reduced magnitude in comparison to the unperturbed phase gradient. Weak turbulent conditions occur during single scattering event only. Multiple scattering phenomenon occurs in strong turbulence conditions, hence lognormal channel fails for such scenarios. Malaga channel model [5] is a prevalent generalized channel model in the literature, but all types of turbulence conditions cannot be suitably modeled by such a channel model. However, the G-G model can suitably model all the atmospheric turbulence conditions, so for further analysis of FSO systems, the G-G channel is considered as the appropriate channel model. > Important Points Large scale and small scale turbulence effects (caused by refraction and scattering, respectively) are considered as independent random processes. The irradiance effect is thus a multiplicative effect of two independent random processes. This criterion is satisfied by a G-G channel model formed by the multiplicative effect of two Gamma functions. The G-G channel considers all types of atmospheric turbulences and multi-scattering phenomenon while lognormal channel is valid only for single scattering with weak turbulence conditions.

2.2.1 A G-G Channel without Pointing Error Fading caused by atmospheric turbulences results in fluctuations of irradiance in the received optical intensity. This is termed as scintillation, and it is a consequence of the fluctuating atmospheric refractive index. Refractive index fluctuates due to rapid

2.2 Channel Model for FSO Communication

29

deviations in atmospheric temperature, pressure and humidity. A G-G channel model [6] can accurately model such fading effects. Considering the random variable ≥ 0 to be the amplitude fading coefficient of the G-G distribution as in Eq. (3) of [7], in Eq. (6) of [8] and in Eq. (6) of [9], the PDF of a G-G channel is expressed as f (ρ) =

α+β α+β (αβ)( 2 ) ρ( 2 −1) 2,0  −  G 0,2 α−β , β−α  αβρ , ρ > 0. 2 2 (α)(β)

(2.13)

Let γ = ρ2 . Considering change in random variables, PDF of received SNR (γ) is calculated as α+β α+β √ (αβ)( 2 ) γ ( 2 −2) 2,0  −  √ G 0,2 α−β , β−α  αβ γ , f γ (γ) = 2 2 2(α)(β)

(2.14)

where α and β are the effective amount of large scale cells and small scale cells of the scattering process, respectively. Gamma function is represented by the symbol . Details of Meijer G-function is provided in [10, 11]. Assuming planar wave propagation, α and β values can be estimated from experimental data and expressed as in Eq. 4 of [7]. 1  , α=  (2.15) 0.49σl2 exp −1 12/5 7/6 (1+1.11σl

β=

 exp

)

1 0.51σl2 12/5 (1+0.69σl )5/6



. −1

(2.16)

Rytov variance σl2 can be expressed as in Eq. (4) [7]. σl2 = 1.23Cn2 K 7/6 L 11/6 ,

(2.17)

, λ=1550 nm, Cn2 (constant of refractive structure prowhere L=2, 6, 8 Km, K = 2π λ −13 −17 −2/3 file) varies from 10 to 10 m . Link distance and wavelength are represented by L and λ, respectively. Cn2 takes into account the various turbulence conditions arising due to rain, fog, snow, daytime or night. During daytime, value of Cn2 is generally maximum during the afternoon. This is because the air gets heated up and hot air being lighter rises up creating turbulence effect. Rain does not impact FSO transmission because the raindrops have a radius greater than the wavelength of FSO sources. The value of Cn2 is the least at the night due to the absence of turbulence. Cn2 = 10−13 indicates strong turbulence while Cn2 = 10−17 indicates weak turbulence. The CDF of received SNR (γ) is calculated by integrating (2.14) and is written as α+β α+β √  √ (αβ)( 2 ) γ ( 2 ) 2,1  1− α+β  G 1,3 α−β , β−α 2,− α+β  αβ γ . Fγ (γ) = (α)(β) 2 2 2

(2.18)

30

2 Channel Model

Table 2.1 Turbulence parameters for different atmospheric conditions Turbulence region α β Weak Moderate Strong

11.6 4.0 4.2

10.1 1.9 1.4

Table 2.2 Turbulence parameters for different separation distances Distance of separation α β (Km) 2 6 8

4.2 8.24 10.19

1.4 1.03 1.01

σl2 0.2 1.6 3.5

σl2 3.5 26.57 45.02

The following formula is used for integration: 

m,n z μ−1 G p,q

a

1 ,a2 ,...,a p b1 ,b2 ,...,bq

    1−μ,a ,...,a  m,n+1  zw = z μ G p+1,q+1 b1 ,...,b1 q ,−μp  zw .

(2.19)

For various atmospheric scenarios, the turbulence parameters are different and the values are tabulated in Table 2.1. For various link distances, the turbulence parameters are listed in Table 2.2. The values of α and β will be used later for performance analysis of FSO systems. > Important Points β and α denote the effective quantity of large scale and small scale cells of the scattering process, respectively. Values of α and β vary with turbulence conditions and distance of separation.

2.2.2 A G-G Channel with Pointing Error In FSO communication, the line-of-sight link between lasers may be affected by many factors which might result in performance error. This is termed as pointing error. Pointing errors are the result of various incidents like laser sources misalignment, building sways and wind speeds. The detailed explanation of pointing error along with the CDF and PDF of channel model after including pointing and path loss error are derived in this section. For computation of pointing errors, certain parameters like detector aperture size, jitter variance and beamwidth have to be taken into account

2.2 Channel Model for FSO Communication

31

[12]. For this work, it is considered that the receiver has a circular aperture with radius a and the beam arriving at the receiver follows Gaussian profile. Let h p fraction of the total power that accumulate at the detector. So h p denotes the pointing error induced loss. The PDF of h p is defined as f (h p ) =

ζ2

h ζp −1 , 2

ζ2 A0

(2.20)

where h p ∈ [0, A0 ] and ζ = wzeq /2σs . ζ is calculated as the ratio between equivalent beam radius at the receiver (wzeq ) and twice the standard deviation displacement caused by pointing error at the receiver (σs ). Definition of the terms are provided as √ πer f (ν) πa , ν = , √ 2ν exp(−ν 2 ) 2wz √

A0 = [er f (ν)]2 , wz2eq = wz2

(2.21)

where a Gaussian beam propagating in atmosphere full of turbulences has a beam waist wz [12]. erf is the error function encountered while integrating the normal distribution. Beer–Lambert’s Law is utilized to compute the laser power attenuation occurring due to atmospheric laser beam propagation. The loss due to attenuation is given by P(z) (2.22) = e−σatt z , h l (z) = P(0) where attenuation coefficient is denoted by σatt , h l (z) is the power loss which occurs due to laser beam propagation over a distance z and P(z) is the laser power measured at a distance z. The term h l is assumed to be constant for a long time interval. h is the turbulence induced fading coefficient which follows (2.13). Thus, the final probability distribution of h eq = h l h p h after taking into consideration both pointing error and path loss error with the turbulent induced fading coefficient can be written as [12] ζ2 2 f (h eq ) = h ζ −1 (A0 h l )ζ 2 eq



∞ h eq /(A0 h l )

h −ζ f h (h)dh . 2

(2.23)

The PDF of a G-G channel incorporating pointing errors can be modified as [12, 13]  ∞  −  ζ 2 (αβ)(α+β)/2  ζ 2 −1 (α+β)/2−1−ζ 2 2,0 α−β β−α  αβh dh f (h eq ) = h G h 2 0,2 2 , 2 (A0 h l )ζ (α)(β) eq h eq /(A0 h l )     αβh eq ζ 2 (αβ) 3,0 ζ2  = . (2.24) G 1,3 2  A h ζ −1,α−1,β−1 (α)(β)A0 h l 0 l Let y = h 2eq . Therefore, considering change in random variables, the PDF of received SNR y is given by

32

2 Channel Model

ζ 2 (αβ) f (y) = G 3,0 (A0 h l )(α)(β)2y 1/2 1,3



   αβ y 1/2

ζ2  ζ 2 −1,α−1,β−1 

A0 h l

.

(2.25)

The CDF of received SNR y is evaluated by integrating (2.25) and is of the form: F(y) =

ζ2 G 3,1 (α)(β) 2,4



   αβ y 1/2

1,ζ 2 +1  ζ 2 ,α,β,0 

A0 h l

.

(2.26)

> Important Points Pointing error is due to laser source misalignment, wind speeds and building sways. Attenuation loss is computed by Beer Lambert Law and caused by propagation of laser beam through atmosphere. It depends upon attenuation coefficient. Pointing loss mainly depends upon jitter factor.

2.3 UOWC Channel Model UOWC effectively works for a limited distance of around 100 m, and it is less likely for pointing errors to occur within such a short line-of-sight distance. Hence, the effect of pointing errors has been neglected in the analysis. Aperture of receivers in underwater environment is also usually large. This causes a weakened turbulence effect which can be appropriately described by a lognormal channel model. Single scattering phenomenon can be modeled by lognormal model, and in weak turbulence conditions, chances of such single scattering events are high. The assumption that the scattered optical field has a magnitude which is less than the unperturbed phase gradient, is valid for underwater environments due to the existence of weak turbulence-induced fading. Hence, use of lognormal channel model is justified for UOWC under weak oceanic turbulences, as has been reported in literature [14–17]. Lognormal channel model PDF is given in (2.2). Note that UOWC experiences a single scattering phenomenon which induces weak turbulence effects as stated by Rytov theory earlier. The channel fading coefficient has an amplitude envelope which is considered to be represented by a random variable h ≥ 0 following the lognormal distribution. From the Rytov theory as seen earlier h = e2X where X is a normal random variable with μ and σ 2 as the mean and variance of X = 1/2 ln(h). Thus, the PDF of lognormal fading coefficient for UOWC link is given by   (ln(h) − 2μ)2 . exp − f (h) = √ 8σ 2 h 8πσ 2 1

(2.27)

2.3 UOWC Channel Model

33

Usually, we take the mean of h as 1. Hence, taking E[h] = μh = exp(2μ + 2σ 2 ) = 1, 2 we get μ = −σ 2 [18]. Note that variance of h, σh2 = E[h 2 ] − (E[h])2 = (e4σ − 2 2 1)e(4μx +4σ ) can be simplified as σh2 = e4σ − 1. For σ 2 1 while weak turbulence means 0 < σ I < 1. In weak turbulence environments, since the irradiance of the optical wave (I) is also modeled as e2X , where X is normal distributed with mean μ and variance σ 2 , we can show 2 that σ 2 = −μ for μ I = 1 and σ 2I = e4σ − 1 [16]. It is pertinent to note that with an 2 increment in σ , there is an increment in σ 2I value also. The parameter σ 2I is evaluated using several parameters like link distance, wavelength and refractive index which is based on turbulence and the nature of sea water. Coastal sea water is considered for our analysis which is symbolized by the parameter ω. σ 2I value is calculated using other parameters as shown below σ 2I

24.832π 5 =− 3 λ × 108



∞

κ−14/3 −1/3 [1 + 2.35(κ f ηkm )2/3 ]  2  Lκ f λ χT 2 −AT δ −As δ −A T s δ +e − 2ωe ) × sin × 2 (ω e dκ f , ω 2π 0

(2.30)

where κ f denotes the scalar spatial frequency,  denotes the dissipation rate of turbulent kinetic energy per unit mass of fluid, λ is the wavelength, ηkm represents Kolmogorov microscale, χT indicates the dissipation rate of mean-square temperature, ω indicates the relative strength of temperature and salinity fluctuations. A T , A S and A T s are all constants. δ = 8.284(κ f ηkm )4/3 + 12.978(κ f ηkm )2 . The values are later provided in the subsequent chapters. Thus, the lognormal channel model has a variance σ 2 which is dependent on σ 2I and takes into account all the channel conditions available underwater.

34

2 Channel Model

> Important Points Due to weak turbulence induced fading in oceanic underwater environment, lognormal channel model can accurately model such weak turbulence effects. The various underwater-related parameters are considered while calculating scintillation 2 index σ 2I . For weak turbulence conditions, σ 2I = e4σ − 1. Strong turbulence means σ I > 1, while weak turbulence means 0 < σ I < 1. Thus, σ 2I value indicates the nature of turbulence.

2.4 Hybrid FSO/RF Channel Model In hybrid FSO/RF communication, FSO links are modeled by the G-G channels and RF links are modeled by Rayleigh channel model. As explained in Chap. 1, line-of-sight transmission takes place between BS and AP, while non-line-of-sight (NLOS) transmission takes place between AP and MU in a crowded environment. In NLOS transmission, signal transmitted from the transmitter reaches the receiver after several reflections from the obstacles on its path. Such signal transmission can be accurately modeled by a Rayleigh channel. Whereas the LOS path between AP and BS for FSO communication can be accurately modeled by a G-G channel. A G-G channel incorporating pointing error has already been described earlier. The PDF and CDF of received SNR of a G-G channel with pointing error are given by Eq. (2.25) and (2.26), respectively. For an RF link, Rayleigh channel is used whose PDF of the SNR is expressed as [20] f (γ) =

1 − γγ¯ e , γ¯

(2.31)

where γ¯ represents average SNR. CDF of the received SNR for Rayleigh channel is of the form: γ F(γ) = 1 − e− γ¯ . (2.32) > Important Points Hybrid FSO/RF communication comprises both RF and FSO links. A G-G channel with pointing errors is used to model FSO links, whereas RF links are modeled by Rayleigh channel.

2.5 Mixture of Gamma Distribution

35

2.5 Mixture of Gamma Distribution The lognormal distribution used for BAN and UOWC communication can be simplified by means of the mixture of gamma (MG) distributions to achieve simpler expressions. For this purpose, we will first have a look at the PDF and CDF of the MG distribution. The PDF of the MG distribution [21] can be obtained as Eq. (22) of [3] MG αM G n  x αi −1 βiM G i −xβiM G Pi , (2.33) e f M G (x) = (αiM G ) i=1 where the i th Gamma distribution has a mixing coefficient denoted by Pi and the scaling and shaping parameters denoted by βiM G and αiM G , respectively. By integrating the PDF equation of the MG distribution, CDF of the MG distribution can be obtained as Eq. (23) of [3] FM G (x) =

n 

 Pi 1 −

i=1

   1 1  MG 2,0 MG  β x . G 0,αi i (αiM G ) 1,2

(2.34)

The MG distribution coefficients are calculated by applying expectation maximization (EM) algorithm which has two steps E step and M step. The algorithm complexity is analyzed. Generally, starting values of model parameters, number of iterations and stopping threshold criteria are the factors determining the complexity of the EM algorithm. If the starting values are close enough to the final solution, then the algorithm converges to a local solution in fewer iteration steps. Let us consider a particular iteration and analyze its complexity. The complexity of E step is O(m × k 2 ) where the amount of mixing coefficients is indicated by k and the quantity of model parameter values is indicated by m. The complexity of M step is O(m × k). With an increment in k value, the E step complexity increases by square of that value which amounts to a huge value for larger k values. The EM algorithm is explained in brief in Algorithm 1.

Algorithm 1: EM Algorithm An incomplete data set will be given. Accordingly, a set of initial values is considered. Expectation step (E step)- By utilizing the provided incomplete dataset, estimation algorithms are used to estimate the value of the unobserved data point or latent variable. 3 Maximization step (M step)- Using the data available after E step, the parameters are updated and stopping criteria is checked whether the error is less than a predefined value or number of steps performed is greater than a predefined value. 4 Until the stopping criteria is satisfied Step 2 and 3 are repeated.

1 2

36

2 Channel Model

> Important Points The MG distribution complexity is given by O(m × k 2 ) for E step and O(m × k) for M step.

2.6 Generation of Channel Coefficients For the benefit of the readers, we are including a section describing the codes to generate the channel coefficients required for different types of communication. For performance analysis of any system, channel coefficients need to be generated. In MATLAB, Rayleigh and lognormal channel coefficients can be generated easily. Rayleigh channel coefficients (required for RF links) can be generated by the command as shown in Algorithm 2 while lognormal channel coefficients (required for UOWC) can be generated as shown in Algorithm 3. The G-G channel coefficients required for FSO communication can be generated by acceptance rejection method [22] whose algorithm is shown in Algorithm 4. The code for the G-G channel coefficient generation is given in Mathematica.

Algorithm 2: Generation of Rayleigh channel coefficients 1

h = 1/sqr t (2) ∗ (randn + j ∗ randn)

(2.35)

Here 1/sqr t (2) is the normalizing factor. This command is used for generation of a single channel coefficient h. 2

H = 1/sqr t (2) ∗ (randn(Rx , Tx ) + j ∗ randn(Rx , Tx ))

(2.36)

This command is used to generate channel matrix H of size R x × Tx whose elements follow the Rayleigh distribution.

Algorithm 3: Generation of Lognormal channel coefficients 1

h = 1/sqr t (2) ∗ (lognr nd(m, sd) + j ∗ lognr nd(m, sd))

(2.37)

Here 1/sqr t (2) is the normalizing factor. sd and m denote the standard deviation and mean of the lognormal distribution. This command is used for generation of a single channel coefficient h. 2

H = 1/sqr t (2) ∗ (lognr nd(m, sd, Rx , Tx ) + j ∗ lognr nd(m, sd, Rx , Tx ))

(2.38)

This command is used to generate channel matrix H of size R x × Tx whose elements follow the lognormal distribution.

2.6 Generation of Channel Coefficients

37

Algorithm 4: Acceptance Rejection Method to generate G-G channel coefficients 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

α = 4.2; β = 1.4; %%% Initialize values of α and β m = MeijerG[{{}, {}}, {{(α - β)/2, (β - α)/2}, {}}, α ∗ β*y]; pd f = (αβ)((α+β)/2) /([α][β] ∗ y) ∗ y ((α+β)/2) ∗ m; %%%Initialize PDF of G-G channel with y as variable di f f = D[ pd f, y]; %%% Differentiate pdf with respect to y. ρ = y/.Find Root[di f f == 0, y, 10− 5]; %%% Set the differentiated value to 0 and find the value of y for that case. n = Mei jer G[{{}, {}}, {{(α − β)/2, (β − α)/2}, {}}, α ∗ β ∗ ρ]; bcoe f f = (αβ)((α+β)/2) /([α][β] ∗ ρ) ∗ ρ((α+β)/2) ∗ n; p = Function[var, Mei jer G[{{}, {}}, {{(α − β)/2, (β − α)/2}, {}}, αβ ∗ var ]]; F = Function[var, (α ∗ β)((α+β)/2) /([α][β] ∗ var ) ∗ var ((α+β)/2) ∗ p[var ]]; Xarray = ; mean = 1; For [i = 1, i