Performance Analysis of an Optical Cdma Communication System Considering Space-Time Diversity Over Free Space Optical Channel

PERFORMANCE ANALYSIS OF AN OPTICAL CDMA COMMUNICATION SYSTEM CONSIDERING SPACE-TIME DIVERSITY OVER FREE SPACE OPTICAL CHANNEL

A. K. M. NAZRUL ISLAM

DOCTOR OF PHILOSOPHY

DEPARTMENT OF ELECTRICAL AND ELECTRONIC ENGINEERING

BNAGLADSEH UNIVERSITY OF ENGINEERING AND TECHNOLOGY

December 2015

PERFORMANCE ANALYSIS OF AN OPTICAL CDMA COMMUNICATION SYSTEM CONSIDERING SPACE-TIME DIVERSITY OVER FREE SPACE OPTICAL CHANNEL

A. K. M. NAZRUL ISLAM

DOCTOR OF PHILOSOPHY

DEPARTMENT OF ELECTRICAL AND ELECTRONIC ENGINEERING

BNAGLADSEH UNIVERSITY OF ENGINEERING AND TECHNOLOGY

December 2015

Performance Analysis of an Optical CDMA Communication System Considering Space-Time Diversity over Free Space Optical Channel

A thesis submitted to the Department of Electrical and Electronic Engineering of Bangladesh University of Engineering and Technology in partial fulfillment of the requirement for the degree of

DOCTOR OF PHILOSOPHY IN ELECTRICAL AND ELECTRONIC

ENGINEERING

A. K. M. Nazrul Islam

DEPARTMENT OF ELECTRICAL AND ELECTRONIC ENGINEERING

BNAGLADSEH UNIVERSITY OF ENGINEERING AND TECHNOLOGY

December 2015

The thesis titled “Performance Analysis of an Optical CDMA Communication System Considering Space-Time Diversity over Free Space Optical Channel” submitted by A. K. M. Nazrul Islam (Roll No.: 1008064002 P, Session: October/2008) has been accepted as satisfactory in partial fulfillment of the requirement for the degree of DOCTOR OF PHILOSOPHY IN ELECTRICAL AND ELECTRONIC ENGINEERING on December 30, 2015. BOARD OF EXAMINERS

1. Chairman Dr. Satya Prasad Majumder Professor, Department of Electrical and Electronic Engineering BUET, Dhaka-1205, Bangladesh

[[ 2. Member (Ex-officio) Dr. Taifur Ahmed Chowdhury Professor and Head, Department of Electrical and Electronic Engineering BUET, Dhaka-1205, Bangladesh 3. Member

Dr. Md. Saifur Rahman Professor, Department of Electrical and Electronic Engineering BUET, Dhaka-1205, Bangladesh

4. Member

Dr. Pran Kanai Saha Professor, Department of Electrical and Electronic Engineering BUET, Dhaka-1205, Bangladesh 5. Member

Dr. Md. Shah Alam Professor, Department of Electrical and Electronic Engineering BUET, Dhaka-1205, Bangladesh

6. Member

Dr. Mohammed Imamul Hassan Bhuiyan Professor, Department of Electrical and Electronic Engineering BUET, Dhaka-1205, Bangladesh

7. Member

Dr. Md. Saiful Islam Professor, Institute of Information and Communication Technology BUET, Dhaka-1205, Bangladesh 8.

Member Dr. Ranjan Gangopadhyay (External) Distinguished Professor LNM Institute of Information Technology Jaipur, Rajasthan, India (Ex-Professor IIT, Kharagpur, India)

iii CANDIDATE’S DECLARATION

It is hereby declared that, this thesis or any part of it has not been submitted elsewhere for the award of any degree or diploma.

Signature of the candidate

A. K. M. Nazrul Islam

DEDICATION

To my family

ACKNOWLEDGEMENTS

At the outset, I would like to express my heartfelt gratitude to my supervisor Prof. Satya Prasad Majumder for providing me the opportunity to work under him in the field of Free Space Optical Communication System. I would like to thank him for his constant guidance, supervision, encouragement and kind cooperation, particularly in justifying proper research direction of the thesis and ensuring that the research aims and objectives are fulfilled over the past six years.

I would then like to thank my Ph. D committee members, Prof. Taifur Ahmed Chowdhury, Prof. Md. Saifur Rahman, Prof. Pran Kanai Saha, Prof. Md. Shah Alam, Prof. Mohammed Imamul Hassan Bhuiyan and Prof. Md. Saiful Islam for their generous help and numerous advices during every stage of the program. I have learnt from them not only the knowledge but also the invaluable methodologies to solve problems. Special thanks to Dr. Ranjan Gangopadhyay, Distinguished Professor, LNM Institute of Information Technology, Jaipur, Rajasthan, India for his professional inspiration, motivation and dynamic guidance for my higher studies.

My whole-hearted thanks should go to my parents for their principles and unconditional love for me who taught me the objectives and aim in life. I sincerely pray to almighty Allah to place the departed souls of my parents to the best place of the Jannah. My sincere thanks and gratitude’s to my parents-in-law for their confidence on me, affections and constant encouragements towards the successful completion of the program.

I would like to express my sincere gratitude to the Chief of Army Staff, Commandant Military Institute of Science and Technology (MIST), Director Electrical and Mechanical Engineers for giving me the opportunities to complete the research work.

My special thanks to all the faculties and staffs of the department of EEE, BUET and department of EECE, MIST for their constant encouragement, moral support and all possible assistances. In particular, I felt indebted and thankful to all related officers and men of MIST and BUET for their administrative support and inspirations.

I am deeply thankful to my beloved wife who has persistently accompanied me in completing this journey, sharing my tears and cries and showering upon me with love, joy and laughter. I would also like to express my endless love to my daughters, Tithi and

Orthi, who always cherished me in every moment of my life with the sacrifices of their needs. I would like to express my heartfelt gratitude to my friends, colleagues and acquaintances for sharing their experiences and opinions, which have inspired me with more feasible ideas and solutions to overcome the roadblocks encountered in my research.

Finally, I would like to express my heartiest gratitude to Almighty ALLAH Sub-ha-nahu- wa-ta’la for upholding me with perseverance, wisdom and strength throughout this journey, and allowing everything to happen miraculously such that I could learn, grow and show appreciation in every aspect of my life. His blessings have brought me success and smooth accomplishment to this research program at BUET.

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ABSTRACT

The last decades have witnessed a spectacular progress on free space optical (FSO) communication, which is very much promising for future optical networking where installation of fiber is very much limited. The capacity of such wireless optical links are highly degraded due to atmospheric channel effects like rain, fog, snow, cloud, atmospheric turbulence and pointing error. As an attractive multiple access technique optical code division multiple access (OCDMA) based FSO communication will provide a high capacity FSO communication network. In this dissertation investigations are carried out to develop analytical models in order to evaluate the bit error rate (BER) performance and capacity of an OCDMA over FSO link in presence of the above channel limitations. Investigations are also carried out towards the development of a multi- wavelength (MW) OCDMA wavelength division multiplexing (MW-OCDMA-WDM) communication system for free space applications.

Primarily investigations are made to find the analytical approaches to evaluate the BER performances of an FSO system without optical encoding taking into considerations the impact of atmospheric scintillations due to refractive index variation of the optical channel with Q-ary optical PPM (Q-OPPM) with direct detection receiver using PIN and

APD. Further, investigations are carried out for FSO communication system with optical level DS-CDMA encoder and Sequence Inverse Keying (SIK) optical decoder taking into account the effect of strong and weak atmospheric turbulence to find the expressions for the signal and multi access interference at the output of a SIK dual detector receiver in presence of atmospheric turbulence considering IM/DD. Expressions for signal to interference plus noise ratio (SINR) and system BER are also developed. Analytical developments are made to find the combined influence of atmospheric turbulence and pointing error on FSO OCDMA system. Performance results are numerically evaluated in terms of SINR and BER for different turbulence variance, link distance, data rate and number of simultaneous users etc. Penalty suffered by the system at a given BER of 10-9 due to turbulence and pointing error are also evaluated numerically. The capacity of an OCDMA FSO system in terms of allowable number of simultaneous users at a given

BER, data rate and link distance are then determined. Clouds put an important limitation on the performance of an FSO link. Several research works are reported which are mostly based on experimental demonstrations. In this

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dissertation, analytical models are developed to find the signal spectrum at the output of an OCDMA FSO link considering the effect of cloud with a transfer function based on the cloud characteristics. Further analysis is extended to find the combined influence of cloud, pointing error and atmospheric turbulence on the system BER performance. Numerical BER performance results are evaluated for different cloud thickness and channel parameters. OCDMA FSO systems with diversity in transmitter and receiver are also analyzed with SIMO, MISO and MIMO configurations over the atmospheric turbulent channel with direct detection OOK receivers. Power penalty suffered by the system due to turbulence and pointing error and the improvements in receiver sensitivity and capacity enhancement due to diversity are also evaluated at a given BER of 10-9.

Finally, a novel MW-OCDMA-WDM system is proposed over the turbulence optical channel to increase the capacity of the system in presence of the above channel limitations. Analytical model of MW-OCDMA-WDM system is developed and analyses are carried out to obtain the expression of signal to noise plus multi-access interference (MAI) and cross talk ratio at the receiver output along with the BER for different turbulence conditions. Performance results are numerically evaluated at a bit rate of 1 Gbps for different turbulent conditions, number of simultaneous user, link distance, number of wavelength, code length etc. Optimum system design parameters are then determined at a BER of 10-9. It is noticed that MW-OCDM-WDM hybrid scheme can be a potential candidate for future terrestrial wireless optical communication network to overcome the channel limitations imposed by turbulence, cloud, pointing error etc. It can provide a higher capacity optical network with application of path diversity using a Rake receiver. Analytical results are validated by simulated and experimental results reported in literature.

Table of Contents

Title page i Approval page iii Declaration iv Dedication v Acknowledgements vi Abstract viii Table of contents x List of tables xv List of figures xvi List of symbols xxx List of abbreviations and acronyms xxxiii

Chapter 1 Introduction 1 1.1 Introduction to optical communications 1 1.2 Modulation and multiplexing techniques in optical 3 communications 1.2.1 Optical pulse position modulation (OPPM) 3 1.2.2 Wavelength division multiplexing (WDM) 4 1.2.2.1 Coarse WDM (CWDM) 5 1.2.2.2 Dense WDM (DWDM) 5 1.2.3 Optical code division multiple access (OCDMA) 6 1.3 Limitations of an FSO channel 8 1.3.1 Atmospheric turbulence 8 1.3.2 Refractive index variation 9 1.3.3 Scintillation 10 1.3.4 Pointing error/jitter 10 1.3.5 Cloud 10 1.3.6 Rain attenuation in FSO communication 11 1.3.7 Fog/Mist attenuation in FSO communication 13

1.4 Literature review 13 1.5 Objectives of the research 17 1.6 Outline of the thesis 18

Chapter 2 Performance Analysis of Q-ary Optical PPM FSO System over 20 Atmospheric Turbulence Channel

2.1 Introduction ` 20 2.2 FSO channel model for weak atmospheric turbulence 20 2.3 Q-OPPM FSO system model 21 2.4 Analysis of BER for Q-OPPM FSO system 22 2.4.1 Analysis of BER with PIN receiver 22 2.4.2 Analysis of BER with APD receiver 24 2.5 Results and discussions 25 2.5.1 Performance with PIN photodetector receiver 26 2.5.2 Performance with APD photodetector receiver 30 2.6 Conclusions 37

Chapter 3 Performance Analysis of an OCDMA FSO Communication System 38 with Atmospheric Turbulence and Pointing Error

3.1 Introduction 38 3.2 FSO channel model for strong atmospheric turbulence 39 3.2.1 FSO channel model for strong atmospheric 39 turbulence with Gamma-Gamma distribution and pointing error 3.2.2 FSO channel model for strong atmospheric turbulence 40 with Exponential distribution 3.2.3 FSO channel model with generalized pointing error 41 3.3 OCDMA FSO communication system model with sequence 43 inverse keying (SIK) receivers 3.4 OCDMA FSO communication system analyses 43 3.4.1 Analysis of OCDMA FSO communication system 43 with weak atmospheric turbulence 3.4.2 Analysis of OCDMA FSO communication system 46 with strong atmospheric turbulence xi

3.4.3 Analysis of OCDMA FSO communication system with 48 combined effect of atmospheric turbulence and pointing error 3.5 Results and discussions 50 3.5.1 Performance of OCDMA FSO communication system 51 with weak atmospheric turbulence 3.5.2 Performance of OCDMA FSO communication system 56 with strong atmospheric turbulence 3.5.3 Performance of OCDMA FSO communication system 60 with combined effects of atmospheric turbulence and pointing error 3.6 Conclusions 68

Chapter 4 Effect of Cloud, Fog and Pointing Error on the Performance 70 of an OCDMA FSO System

4.1 Introduction 70 4.2 Transfer function of cloud in a FSO communication system 70 4.3 Transfer Function of Fog and Channel Model 71 4.4 System model of OCDMA FSO communication system with 73 SIK receivers 4.5 System analysis 74 4.5.1 Analysis of OCDMA FSO communication system with 74 effect of cloud 4.5.2 Analysis of OCDMA FSO communication system with 76 effect of Fog 4.5.3 Analysis of OCDMA FSO communication system with 77 effect of pointing error 4.6 Results and discussions 78 4.6.1 Performance of OCDMA FSO communication system 78 with effect of cloud 4.6.2 Performance of OCDMA FSO communication system 84 with effect of Fog

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4.6.3 Performance of OCDMA FSO communication system 89 with effect of pointing error 4.7 Conclusions 95

Chapter 5 OCDMA FSO Communication System with Space Diversity 96

5.1 Introduction 96 5.2 Diversity schemes 96 5.3 Model of FSO system with and without diversity 98 5.4 FSO channel model with pointing error 100 5.5 System analysis 101 5.5.1 Analysis of BER for SISO FSO communication system 101 5.5.2 Analysis of BER for SIMO FSO communication system 101 5.5.2.1 SIMO FSO communication system: analytical 102 approach-1 5.5.2.2 SIMO FSO communication system: analytical 102 approach-2 5.5.2.3 SIMO FSO communication system: analytical 103 approach-3 5.5.2.4 SIMO FSO communication system: analytical 103 approach-4 5.5.3 Analysis of BER for MISO FSO communication system 104 5.5.4 Analysis of BER for MIMO FSO communication system 104 5.5.5 Analysis of BER for SIMO OCDMA FSO 105 Communication system 5.6 Results and discussion 108 5.6.1 Performance of SISO FSO communication system 109 5.6.2 Performance of SIMO FSO communication system 112 5.6.3 Performance of SIMO OCDMA FSO communication 126 system 5.7 Conclusions 132

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Chapter 6 Performance Analysis of Multi-Wavelength OCDMA WDM 133 System over Atmospheric Channel

6.1 Introduction 133 6.2 MW-OCDMA transmitter and receiver model 133 6.3 OCDMA-WDM channel model 134

6.4 OCDMA-WDM system analysis 135 6.5 Results and Discussion 138 6.6 Conclusions 146

Chapter 7 Conclusions and Future Works 147

7.1 Conclusions 147 7.2 Summary of the major contributions 147 7.3 Suggestions for future research 153

Bibliography 155

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List of Tables

Table 1.1 Altitude range of clouds for different regions 11

Table 2.1 System parameters 25

Table 3.1 System parameters 51

Table 4.1 System parameter 79

Table 4.2 Double Gamma function constants for cloud thickness 200 79 m to 300 m at a wavelength of 0.532 µm

Table 5.1 System parameters 109

Table 6.1 System parameter 139

List of Figures

Fig.1.1 WDM multiplexing and demultiplexing 4

Fig. 1.2 DWDM multiplexing and demultiplexing 6

Fig. 1.3 Schematic diagram of a general optical CDMA system 7

Fig. 2.1 Block diagram of a Q-OPPM FSO system with PIN or APD 22 photodiode.

Fig. 2.2 Plots of BER vs. received average optical signal intensity 26 Io(dBm) for PIN receiver without timing jitter variance and atmospheric turbulence variance using PPM order as a parameter for data rate Rb=2.4 Gbps.

Fig. 2.3 Plots of BER vs. received average optical signal intensity 27 Io(dBm) for PIN receiver with timing jitter varianceσ 2 = 0.075 and atmospheric turbulence variance ε 2 σα = 0.1 using PPM order as a parameter for data rate Rb=2.4 Gbps.

Fig. 2.4 Plots of BER vs. received average optical signal intensity 27 Io(dBm) for PIN receiver without timing jitter variance and atmospheric turbulence variance using PPM order as a parameter for data rate Rb=10 Gbps.

Fig. 2.5 Plots of BER vs. received average optical signal intensity 28 Io(dBm) for PIN receiver with timing jitter variance 2 2 σ ε = 0.075 and atmospheric turbulence variance σα = 0.1 with PPM order as a parameter for data rate Rb=10 Gbps.

Fig. 2.6 Receiver sensitivity Io(dB) vs. PPM order M at a BER of 29 -9 2 10 and atmospheric turbulence variance σα = 0.1 with timing jitter variance as a parameter for PIN receiver.

Fig. 2.7 Power penalty as a function of timing jitter variance at a 29 -9 BER 10 , data rate Rb=2.4 Gbps and atmospheric turbulence 2 variance σα = 0.1 using PPM order as a parameter for PIN receiver.

Fig. 2.8 Power penalty as function of scintillation index at a BER 30 -9 10 , data rate Rb=10 Gbps with atmospheric turbulence

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variance σ 2 = 0.1 using PPM order as a parameter for PIN α receiver.

Fig. 2.9 Plots of average BER vs. number of photon per bit of 8-PPM 31 FSO link with turbulence of scintillation index SI=0.3 at a bit rate of Rb=10 Gbps and APD Gain G=150.

Fig. 2.10 Plots of average BER vs. number of photon per bit for 256- 31 PPM FSO link with turbulence of scintillation index SI=0.3 at a bit rate of Rb=2.4 Gbps and APD Gain G=150.

Fig. 2.11 Receiver sensitivity in terms of number of photons per bit at 32 a BER of 10-9 as a function of normalized timing error ε for different PPM order with APD gain G=150, scintillation

index SI=0.3 and data rate Rb=10 Gbps.

Fig. 2.12 Plots of average BER vs. number of photons per bit for 8- 32 PPM FSO link with turbulence of scintillation index SI=0.3 at a bit rate of Rb=10 Gbps and APD Gain G=150 using timing jitter variance as a parameter.

Fig. 2.13 Plots of average BER as function of number of photons per 33 bit for 256-PPM FSO link with turbulence of scintillation index SI=0.3 at a bit rate of Rb=2.4 Gbps and APD Gain G=150 using timing jitter variance as a parameter.

Fig. 2.14 Receiver sensitivity in terms of number of photons per bit as 34 a function of variable timing jitter variance for different PPM order at a BER of 10-9 using APD gain G=150, scintillation index SI=0.3 and data rate Rb=10 Gbps.

Fig. 2.15 Penalty log10(Ks) in terms of number of photons per bit as a 34 function of different PPM order at a BER of 10-9 and APD gain G=150 using timing jitter variance as a parameter.

Fig. 2.16 Penalty log10 (Ks) in terms of photons per bit for a BER of 35 10-9 as a function of scintillation index for PPM order 32 with and without timing jitter variance for different timing error ε.

Fig. 2.17 Power penalty as a function of variance of scintillation for 35 M-OPPM [128].

Fig. 2.18 BER versus the transmitted power per bit with APD gain 36

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G = 10 using PPM order as a parameter. All turbulence effects are taken into account [46].

Fig. 3.1 Block diagram of OCDMA transmitter and OCDMA SIK 43 dual photodetector receiver.

Fig. 3.2 BER vs. average received optical intensity Io(dBm) with 52 code length Gp=256, atmospheric turbulence variance 2 σ x =0.01 and data rate Rb=1 Gbps using number of user M as a parameter.

Fig. 3.3 BER vs. average received optical intensity Io(dBm) with 52 code length Gp=1024, atmospheric turbulence variance 2 σ x =0.01 and data rate Rb=1 Gbps using number of user M as a parameter.

Fig. 3.4 BER vs. average received optical intensity Io(dBm) with 53 code length Gp=512, atmospheric turbulence variance 2 σ x =0.1 and data rate Rb=1 Gbps using number of user M as a parameter.

Fig. 3.5 BER vs. average received optical intensity Io(dBm) with 53 code length Gp=512, atmospheric turbulence variance 2 σ x =0.2 and data rate Rb=1 Gbps using number of user M as a parameter.

Fig. 3.6 BER vs. average received optical intensity Io(dBm) for 54 number of user M=8, atmospheric turbulence variance 2 σ x =0.1 and data rate Rb=1 Gbps using code length Gp as a parameter.

Fig. 3.7 BER vs. average received optical intensity Io(dBm) for 54 number of user M=8, code length Gp=512 and data rate Rb=1 Gbps using atmospheric turbulence variance as a parameter.

Fig. 3.8 Power penalty vs. number of simultaneous user with code 55 -9 length Gp=512 and data rate Rb=1 Gbps at a BER of 10 using atmospheric turbulence variance as a parameter.

Fig. 3.9 BER vs. average received optical power Pr(dBm) at a link 56 length of L=500 m corresponding to the Rytov variance=0.0559 and code length Gp=256 with number of

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user M as a parameter.

Fig. 3.10 BER vs. average received optical power Pr(dBm) at a link 57 length of L=1000 m corresponding to the Rytov variance=0.1992 and code length Gp=256 with number of user M as a parameter.

Fig. 3.11 BER vs. average received optical power Pr(dBm) at a link 57 length of L=500 m corresponding to the Rytov variance=0.0559 and code length Gp=512 with number of user M as a parameter.

Fig. 3.12 BER vs. average received optical power Pr(dBm) at a link 58 length of L=1000 m corresponding to the Rytov variance=0.1992 and code length Gp=512 with number of user M as a parameter.

Fig. 3.13 Variation of BER with number of user, M at Pr= -10 dBm for 59 code length Gp=64, 128, 256, 512 and 1024 and link length L= 500 m and 1000 m respectively.

Fig. 3.14 Power penalty in dB due to MAI in presence of atmospheric 59 turbulence as a function of link distance L at a BER = 10-9 and code length Gp=512 with number of user as a parameter.

Fig. 3.15 Plots of maximum allowable number of user as a function of 60 -6 code length Gp at a BER of 10 and Pr= -10 dBm with link length L=500 m, 1000 m and 1500 m respectively.

Fig. 3.16 BER as a function of received optical intensity Io(dBm) with 61 link length L=500 m corresponding to the Rytov variance=0.0559, code length Gp=1024, number of user M =32 at a data rate Rb=1 Gbps using normalized pointing error standard deviation as a parameter.

Fig. 3.17 BER as a function of received optical intensity Io(dBm) with 61 a link length L=1000 m corresponding to the Rytov variance=0.1992, code length Gp=256, number of user M=16 at a data rate Rb=1 Gbps using normalized pointing error standard deviation as a parameter.

Fig. 3.18 BER as a function of received optical intensity Io(dBm) with 62 a link length L=1500 m corresponding to the Rytov variance=0.4189 and code length Gp=512 with number of user M=16, data rate Rb=1 Gbps using normalized pointing xix

error standard deviation as a parameter.

Fig. 3.19 BER as a function of received optical intensity Io(dBm) with 62 a link length L=1500 m corresponding to the Rytov variance=0.4189 and code length Gp=512 with number of user M=32, data rate Rb=1 Gbps using pointing error standard deviation as a parameter.

Fig. 3.20 BER as a function of received optical intensity Io(dBm) with 63 a link length L=2000 m corresponding to the Rytov variance=0.7098 and code length Gp=1024, number of user M=32, data rate Rb=1 Gbps and normalized pointing error standard deviation as a parameter.

Fig. 3.21 BER as a function of received optical intensity Io(dBm)with 63 a link length L=3000 m corresponding to the Rytov variance=1.4928 and code length Gp=1024, number of user

M=32, data rate Rb=1 Gbps using normalized pointing error as a parameter.

Fig. 3.22 BER as a function of received optical intensity Io(dBm) at a 65 link length L=4000 m corresponding to the Rytov variance=2.5294 and code length Gp=512, number of user

M=16, data rate Rb=1 Gbps using normalized pointing error as a parameter.

Fig. 3.23 BER as a function of number of user M for code length 65

Gp=512 and link length L=1500 m at a Pr(dBm)=10 and data rate Rb=1 Gbps.

Fig. 3.24 BER as a function of link distance L at Io(dBm)=10 dB for 66 code length Gp=1024, number of user M=4, 8, 16, 32 and 64 with normalized jitter standard deviation σs/r =1.0, 1.3, 1.5, 1.8 and 2.0 respectively.

Fig. 3.25 Power penalty vs. normalized jitter standard deviation σs/r 66 for code length Gp=1024 and link length L=500 m M=4, 8, -9 16 and 32 respectively at a BER=10 and data rate Rb=1 Gbps.

Fig. 3.26 Power penalty vs. normalized jitter standard deviation σs/r 67 for code length Gp=1024 and link length L=1000 m M=4, 8,

16 and 32 respectively at a BER=10-9 and data rate 1 Gbps.

Fig. 3.27 Variation of the average BER performance versus received 68 optical power Pr with single user and multiple users interfering within all of the turbulence regimes [71].

Fig. 4.1 Block diagram of an optical CDMA (OCDMA) transmitter 73 and SIK dual photodetectors direct detector receiver over a cloudy channel.

Fig. 4.2 BER vs. average received optical intensity Io(dBm) with 80 code length Gp=256 and number of user M=8 at a data rate

Rb=1 Mbps using cloud thickness as a parameter.

Fig. 4.3 BER vs. average received optical intensity Io(dBm) with 80 code length Gp=512 and number of user M=8 at a data rate

Rb=1 Mbps using cloud thickness as a parameter.

Fig. 4.4 BER vs. average received optical intensity Io(dBm) with 81 code length Gp=1024 and number of user M=16 at a data rate Rb=1 Mbps using cloud thickness as a parameter.

Fig. 4.5 BER vs. average received optical intensity Io(dBm) with code 81 length Gp=1024 and number of user M=32 at a data rate Rb=1 Mbps using cloud thickness as a parameter.

Fig. 4.6 BER vs. average received optical intensity Io(dBm) with cloud 82 thickness of 250 m and number of user M=8 at a data rate Rb=1 Mbps using code length Gp as a parameter.

Fig. 4.7 BER vs. average received optical intensity Io(dBm) with 82 code length Gp=512, and cloud thickness of 300 m at a data rate Rb=1 Mbps using number of user M as a parameter.

Fig. 4.8 Power penalty as a function of cloud thickness for code 83 -9 length Gp=1024 and data rate Rb=1 Mbps at a BER=10 using number of user as a parameter.

Fig. 4.9 Power penalty as a function of number of user M for code 84 -9 length Gp=1024 and data rate Rb=1Mbps at a BER=10 using cloud thickness as a parameter.

Fig. 4.10 BER vs. average received optical intensity Io(dBm) with 85

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code length Gp=256 and number of user M=8 at a data rate

Rb=10 Mbps using fog thickness as a parameter.

Fig. 4.11 BER vs. average received optical intensity Io(dBm) with 85 code length Gp=512 and number of user M=8 at a data rate Rb=10 Mbps using fog thickness as a parameter.

Fig. 4.12 BER vs. average received optical intensity Io(dBm) with 86 code length Gp=1024 and number of user M=16 at a data rate Rb=10 Mbps using fog thickness as a parameter.

Fig. 4.13 BER vs. average received optical intensity Io(dBm) with 86 code length Gp=1024 and number of user M=32 at a data rate Rb=10 Mbps using fog thickness as a parameter.

Fig. 4.14 BER vs. average received optical intensity Io(dBm) with fog 87 thickness of 250 m and number of user M=16 at a data rate Rb=1 Mbps using code length Gp as a parameter.

Fig. 4.15 BER vs. average received optical intensity Io(dBm) with 87 code length Gp=512, and fog thickness of 300 m at a data rate Rb=10 Mbps using number of user M as a parameter.

Fig. 4.16 Power penalty as a function of fog thickness for code length 88 -9 Gp=1024 and data rate Rb=10 Mbps at a BER=10 using number of user as a parameter.

Fig. 4.17 Power penalty as a function of number of user M for code 88 -9 length Gp=1024 and data rate Rb=10 Mbps at a BER=10 using fog thickness as a parameter.

Fig. 4.18 BER vs. average received optical intensity Io(dBm) with 90 code length Gp=512, number of user M=32 at a data rate Rb=1Gbps using normalized pointing error σs/r as a parameter.

Fig. 4.19 BER vs. average received optical intensity Io(dBm) with 90 code length Gp=1024, number of user M=32 at a data rate Rb=1Gbps using normalized pointing error σs/r as a parameter.

Fig. 4.20 BER vs. average received optical intensity Io(dBm) with 91 code length Gp=256, number of user M=8 and data rate Rb=1

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Gbps using normalized pointing error σs/r as a parameter.

Fig. 4.21 BER vs. average received optical intensity Io(dBm) with 91 code length Gp=256, number of user M=64 and data rate Rb=1Gbps with normalized pointing error σs/r as a parameter.

Fig. 4.22 Power penalty (dB) as a function of normalized pointing 92 error σs/r for code length Gp=128, 256, 512 and 1024 -6 respectively at a BER =10 with data rate Rb=1 Gbps and number of simultaneous user M=32.

Fig. 4.23 Power penalty (dB) as a function of normalize pointing error 92 standard deviation σs/r for number of simultaneous user of 4, 8, 16, 32 and 64 respectively at a BER=10-6 with data rate

Rb=1 Gbps and code length Gp=256.

Fig. 4.24 Plots of BER vs. number of simultaneous user at a data rate 93

of Rb=5 Gbps and code length Gp=64 using normalized pointing error σs/r as a parameter.

Fig. 4.25 Plots of allowable number of user’s vs. normalized pointing 94 error for data rate of 1, 2.5, 5 and 10 Gbps respectively at a BER =10-6 and code length Gp=64.

Fig. 4.26 Power penalty (dB) as a function of normalized pointing 95 error σs/r for code length of 256, 512 and 1024 respectively -9 at a BER=10 with data rate Rb=1 Gbps and number of user M=16.

Fig.5.1(a) Block diagram of FSO link with one transmitter and one PIN 98 photodetector receiver (SISO).

Fig.5.1(b) Block diagram of FSO link with one transmitter and multiple 99 PIN photodetector receiver (SIMO).

Fig.5.1(c) Block diagram of FSO link with multiple transmitter and 99 multiple PIN photodetector receiver (MIMO).

Fig.5.1(d) Block diagram of an OCDMA FSO communication system 99 with single transmitter and multiple SIK dual photodetector receiver (SIMO).

Fig. 5.2 BER vs. transmitted power for normalized beamwidth 110 ωz/r =5 and number of photodetector receiver Nr=1 SISO

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FSO system using normalized jitter standard deviation σs/r as a parameter.

Fig. 5.3 BER vs. transmitted power for normalized beamwidth 110 ωz/r=10 and number of photodetector receiver Nr =1 for SISO FSO system using normalized jitter standard deviation σs/r as a parameter.

Fig. 5.4 BER vs. transmitted power for normalized beamwidth ωz/r=5 111 and number of photodetector receiver Nr =1 for SISO FSO system using normalized jitter standard deviation σs/r as a parameter (approach-1).

Fig. 5.5 BER vs. transmitted power for normalized beamwidth ωz/r=8 111 and number of photodetector receiver Nr =1 for SISO FSO system using normalized jitter standard deviation σs/r as a parameter (approach-1).

Fig. 5.6 BER vs. transmitted power for normalized beamwidth ωz/r=5 112 and number of photodetector receiver Nr =4 for SIMO FSO system using normalized jitter standard deviation σs/r as a parameter (approach-1).

Fig. 5.7 BER vs. transmitted power for normalized beamwidth ωz/r=8 113 and number of photodetector receiver Nr =4 for SIMO FSO system using normalized jitter standard deviation σs/r as a parameter (approach-1)

Fig. 5.8 BER vs. transmitted power for normalized beamwidth ωz/r=5 113 and number of photodetector receiver Nr =1 and 2 for SIMO FSO system using normalized jitter standard deviation σs/r as a parameter (approach-2).

Fig. 5.9 BER vs. transmitted power for normalized beamwidth ωz/r=5 114 and number of photodetector receiver Nr =4 and 8 for SIMO FSO system using normalized jitter standard deviation σs/r as a parameter (approach-2).

Fig. 5.10 BER vs. transmitted power for normalized beamwidth ωz/r=8 114 and number of photodetector receiver Nr =1 and 2 for SISO/SIMO FSO system using normalized jitter standard

deviation σs/r as a parameter (approach-2).

Fig. 5.11 BER vs. transmitted power for normalized beamwidth ωz/r=8 115

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and number of photodetector receiver Nr =4 and 8 for SIMO FSO system using normalized jitter standard deviation σs/r as a parameter (approach-2).

Fig. 5.12 BER vs. transmitted power for normalized beamwidth ωz/r=5 116 and number of photodetector receiver Nr =1 and 2 for SISO/SIMO FSO system using normalized jitter standard deviation σs/r as a parameter (approach-3).

Fig. 5.13 BER vs. transmitted power for normalized beamwidth ωz/r=5 116 and number of photodetector receiver Nr =4 and 8 for SIMO FSO system using normalized jitter standard deviation σs/r as a parameter (approach-3).

Fig. 5.14 BER vs. transmitted power for normalized beamwidth ωz/r=8 117 and number of photodetector receiver Nr =1 and 2 for SISO/SIMO FSO system using normalized jitter standard

deviation σs/r as a parameter (approach-3).

Fig. 5.15 BER vs. transmitted power for normalized beamwidth ωz/r=8 117 and number of photodetector receiver Nr =4 and 8 for SIMO FSO system using normalized jitter standard deviation σs/r as a parameter (approach-3).

Fig. 5.16 BER vs. transmitted power for normalized beamwidth ωz/r=5 118 and number of photodetector receiver Nr =2 and 4 for SIMO FSO system using normalized jitter standard deviation σs/r as a parameter (approach-4).

Fig. 5.17 BER vs. transmitted power for normalized beamwidth ωz/r=8 118 and number of photodetector receiver Nr =2 and 4 for SIMO FSO system using normalized jitter standard deviation σs/r as a parameter (approach-4).

Fig. 5.18 Required transmitted optical power Pt(dBm) vs. normalized 119 -10 jitter standard deviation σs/r to achieve a BER=10 with normalized beamwidth ωz/r=5 for a SISO and SIMO FSO system (approach-1).

Fig. 5.19 Required transmitted optical power Pt(dBm) vs. 119 normalized jitter standard deviation σs/r to achieve a -10 BER=10 and normalized beamwidth ωz/r=8 for a SISO

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and SIMO FSO system (approach-1).

Fig. 5.20 Required transmitted optical power Pt(dBm) vs. normalized 120 -10 jitter standard deviation σs/r to achieve a BER=10 and normalized beamwidth ωz/r=5 for a SISO and SIMO FSO system (approach-2).

Fig. 5.21 Required transmitted optical power Pt(dBm) vs. normalized 121 -10 jitter standard deviation σs/r to achieve a BER=10 and normalized beamwidth ωz/r=8 for a SISO and SIMO FSO system (approach-2).

Fig. 5.22 Required transmitted optical power Pt(dBm) vs. normalized 121 -10 jitter standard deviation σs/r to achieve a BER=10 and normalized beamwidth ωz/r=5 for a SISO and SIMO FSO system (approach-3).

Fig. 5.23 Required transmitted optical power Pt(dBm) vs. normalized 122 -10 jitter standard deviation σs/r to achieve a BER=10 and normalized beamwidth ωz/r=8 for a SISO and SIMO FSO system (approach-3).

Fig. 5.24 Transmitted optical power Pt(dBm) vs. normalized jitter 123 -10 standard deviation σs/r at a BER=10 and normalized beamwidth ωz/r=5 and 8 for SIMO FSO system (approach-4).

Fig. 5. 25 Maximum allowable normalized jitter standard deviation σs/r 123 vs. number of photodetector receivers at a BER=10-10, Pt(dBm) = -5 and ωz/r =5 for approach-1, 2, 3 and 4.

Fig. 5. 26 Maximum allowable normalized jitter standard deviation σs/r 124 vs. number of photodetector receivers at a BER=10-10,

Pt(dBm)= -5 and ωz/r=8 for approach-1, 2, 3 and 4.

Fig. 5. 27 Maximum allowable normalized jitter standard deviation σs/r 124 vs. number of photodetector receivers at a BER of 10-10,

Pt(dBm) = -8 and ωz/r=5 for approach-1, 2, 3 and 4.

Fig. 5. 28 Maximum allowable normalized jitter standard deviation σs/r 125 vs. number of photodetector receivers at a BER=10-10, Pt(dBm)=-8 and ωz/r=8 for approach-1, 2, 3 and 4.

Fig. 5. 29 BER vs. transmitted power for number of receiver antenna 126

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Nr=1, code length Gp=1, number of user M=1 at a data rate Rb=10 Gbps and normalized beamwidth ωz/r=8 using normalized jitter standard deviation σs/r as a parameter (SISO).

Fig. 5. 30 BER vs. transmitted power for number of receiver antenna 126

Nr=2, code length Gp=256, number of user M=8 at a data rate Rb=10 Gbps and normalized beamwidth ωz/r=10 using normalized jitter standard deviation σs/r as a parameter (SIMO).

Fig. 5. 31 BER vs. transmitted power for number of receiver antenna 127 Nr=4, code length Gp=256, number of user M=8 at a data rate Rb=10 Gbps and normalized beamwidth ωz/r=10 using normalized jitter standard deviation σs/r as a parameter.

Fig. 5. 32 BER vs. transmitted power for number of receiver antenna 128

Nr=3, number of user M=32, normalized beamwidth ωz/r=10 and normalized jitter standard deviation σs/r =1.0 at a data rate Rb=10 Gbps using code length Gp as a parameter.

Fig. 5. 33 BER vs. transmitted power for code length Gp=512, number 129 of user M=32, normalized beamwidth ωz/r=10 and normalized jitter standard deviation σs/r =1.0 at a data rate Rb=10 Gbps using number of receiver antenna Nr as a parameter.

Fig. 5. 34 BER vs. transmitted power for number of receiver antenna 129 Nr=3, code length Gp=1024, normalized beamwidth ωz/r=10 and normalized jitter standard deviation σs/r =1.0 at a data rate Rb=10 Gbps using number of user M as a parameter.

Fig. 5. 35 BER vs. transmitted power for number of receiver antenna 130 Nr=4, code length Gp=512, number of user M=16 and normalized jitter standard deviation σs/r =1.0 at a data rate Rb=10 Gbps using normalized beamwidth ωz/r as a parameter.

Fig. 5. 36 Power penalty vs. normalized jitter standard deviation for 130 number of receiver antenna Nr=4, code length Gp=512, normalized beamwidth ωz/r=10 and normalized jitter standard deviation σs/r =1.0 at a data rate Rb=10 Gbps using

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number of users M as a parameter.

Fig. 5. 37 Receiver sensitivity vs. number of receiver for normalized 131 beamwidth ωz/r=5, normalized jitter standard deviation σs/r =1.0 and number of users M=16 at a data rate Rb=10 Gbps using code length as a parameter.

Fig. 6.1(a) Multi-wavelength OCDMA transmitter. 134

Fig. 6.1(b) Multi-wavelength OCDMA SIK dual photodetectors 134 receiver.

Fig. 6.2 BER as function of average received optical power for link 140 distance L=500 m number of wavelength=8, number of users

M=1 and code length Gp=512 using normalized jitter

standard deviation σs/r as a parameter.

Fig. 6.3 BER as function of average received optical power for link 140 distance L=1000 m number of wavelength=20, number of users M=8 and code length Gp=512 using normalized jitter

standard deviation σs/r as a parameter.

Fig. 6.4 BER as function of average received optical power for 141 number of wavelength=16, number of users M=16, code

length Gp=1024 and normalized jitter standard deviation

σs/r=1.0 using link distance L as a parameter.

Fig. 6.5 BER as function of average received optical power for 142 number of users M=16, code length Gp=1024, normalized

jitter standard deviation σs/r=1.0 and link distance L=500 m using number of wavelength as a parameter.

Fig. 6.6 BER as function of average received optical power for link 142 distance L=1000 m, code length Gp=256, number of wavelength=8 and normalized jitter standard deviation

σs/r=1.0 using number of simultaneous users as a parameter.

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Fig. 6.7 BER as function of average received optical power for link 143 distance L=1500 m, number of wavelength=16, number of

simultaneous users M=12 and σs/r=1.0 using code length Gp as a Parameter.

Fig. 6.8 Power penalty as a function of normalized jitter standard 144 deviation at a link distance L=1000 m, number of simultaneous users M=8, code length Gp=512 and at a BER=10-9 with number of wavelengths as a parameter.

Fig. 6.9 Power penalty as a function of number of wavelength at a 144 link distance L=1000 m, number of simultaneous users M=8, code length Gp=512 and at a BER=10-9 using normalized

jitter standard deviation σs/r as a parameter.

Fig. 6.10 Plots of BER vs. number of wavelength for different number 146 of simultaneous users [60].

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List of Symbols

Ao Fraction of the collected power ak Q-OPPM symbol

m th th ak k bit of the m user B Receiver bandwidth Ctm () User’s code

m th Cl l chip

2 Cn Refractive index structure parameter D Receiver aperture diameter E[I] Mean irradiance e Electron charge F APD excess noise factor fc Carrier frequency G Mean gain of APD g(t) Pulse shape h(t) Temporal impulse response of cloud hmn Normalized fading channel coefficient H(f) Transfer function of temporal frequency

I0 Modified Bessel function of zero order

Is Received Optical Irradiance with atmospheric turbulence I Received optical signal irradiance

Ib Background radiation intensity

Isig Signal current

IT Average transmitted chip power

Ix Cross talk current

Iy Large scale turbulent eddies

Iz Small scale turbulent eddies id(t) Output current of the photodetector in(t) Noise current

xxx kx Wave number

Kbb Average background noise photons per PPM slot

Kb Boltzmann constant k1, k2, k3 and k4 Gamma function constant L Link distance in meter

Lc/Gp Code length/processing gain M Number of simultaneous users

Mt Number of transmitters

Nr Number of receiver photodetectors/antenna no(t) Background optical radiation n(t) Represent the photodetector shot noise, preamplifier thermal

2 noise and zero mean Gaussian noise with variance σ n .

PT Average transmitted optical power

Pr Average received optical power

Po Total beam power in watt P Atmospheric pressure

Pb Background radiation power p(t) Pulse shape of the individual chips p(I) Probability density function of irradiance I p(ε) Probability density function of timing error ε

Rb Bit rate/data rate

Rd Detector responsivity

RL Load resistance of the receiver

th rn(t) Received signal at the n receiver r Detector aperture radius s(t) Output optically coded signal T Receiver Temperature in Kelvin

Ts Slot duration

Tc Chip period

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Tb Bit period

Tr Effective absolute temperature of the APD receiver u(t) Unit impulse response wi Weight of Hermite Polynomial

Wt Effective beam radius at the transmitter

Wr Effective beam spot radius at the receiver xi Zeroes of Hermite Polynomial x(t) Transmitted signal z Distance of wave propagation from the transmitter

α Effective numbers of large scale eddies/path loss coefficient β Effective numbers of small scale eddies γ Ratio between the equivalent beam width to the pointing error standard deviation. σ Instantaneous noise variance λ Wave length ε Normalized timing error

ωc Angular optical carrier frequency

ωeff Effective beam waist

ωzeq Equivalent beamwidth

ωz Beam waist at a distance

ωo Optical carrier angular frequency

ωz/r Normalized beamwidth

σs/r Normalized pointing error standard deviation

σj Jitter standard deviation due to pointing error

Ω Resistance in ohms ζ Ionization factor for APD 2 σ x Rytov variance

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2 σn Noise variance at the output of receiver 2 σα Atmospheric turbulence variance 2 σ Timing jitter variance ε σ 2 Scintillation Index si

List of Abbreviations and Acronyms

ASK Amplitude Shift Keying ASE Amplified Spontaneous Emission APD Avalanche Photo Diode AWGN Additive White Gaussian Noise BER Bit Error Rate BPSK Binary Phase Shift Keying BPPM Binary Pulse Position Modulation CWDM Coarse Wavelength Division Multiplexing CDMA Code Division Multiple Access CMOS Metal Oxide Semiconductor DEMUX Demultiplexer DSP Digital Signal Processor DWDM Dense Wavelength Division Multiplexing EDFA Erbium Doped Fiber Amplifier EGC Equal Gain Combining FEC Forward Error Correction FSK Frequency Shift Keying FSO Free Space Optical FSP Free Space Photonics FWM Four-Wave Mixing IFFT Inverse Fast Fourier Transformation IM/DD Intensity Modulation-Direct Detection IMS Industrial, Scientific and Medical

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IR Infrared I/Q In-phase/Quadrature LAN Local Area Network LASER Light Amplification by Stimulated Emission of Radiation LD Laser Diode LED Light Emitting Diode LOS Line of Sight LO Local Oscillator LPF Low Pass Filter MAI Multiple Access Interference MC-OCDMA Multi-Carrier Optical Code Division Multiple Access MIMO Multiple Input Multiple Output MISO Multiple Input Single Output MPPM M-ary Pulse Position Modulation MUX Multiplexer MW-OCDMA Multi-wavelength OCDMA NLOS Non Line of Sight OCDMA Optical Code Division Multiple Access OFC Optical Fiber Communication OFDM Orthogonal Frequency Division Multiplexing O-OFDM Optical Orthogonal Frequency Division Multiplexing OOK On-off Keying OPPM Optical Pulse Position Modulation PAPR Peak to Average Power Ratio PDF Probability Density Function PPM Pulse Position Modulation PSD Power Spectral Density PP Pairwise Probabilities QPPM Q-ary Pulse Position Modulation Q-OPPM Q-ary Optical Pulse Position Modulation RF Radio Frequency xxxiv

SISO Single Input Single Output SI Scintillation Index SIMO Single Input Multiple Output SNR Signal to Noise Ratio SNIR Signal to Noise plus Interference Ratio SPM Self-Phase Modulation TWTA Travelling Wave Tube Amplifier WDM Wavelength Division Multiplexing WWW World Wide Web XPM Cross-phase Modulation

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Chapter 1

INTRODUCTION

1. 1 Introduction to Optical Communications

Optical communication has emerged as an alternative to RF and Microwave (MW) communications due to its inherent merits of enormous bandwidth and lower cost [1]. There are two different forms of optical communication such as optical fiber communication (OFC) and free space optical (FSO) communication. Optical fiber communication transmits information from one place to another by sending the light pulses through an optical fiber made of silica. The light pulses form an electromagnetic carrier wave that is modulated to carry information. It was first developed in the 1970s with a revolution in the telecommunication industry and played a vital role in the development of telecommunication system. Optical fibers have largely replaced copper wire communications in core networks of the world because of its merits over the electrical and RF waveguides. Optical fiber-based systems have largely replaced the radio transmitter systems for long-haul data transmission [1]. They are widely used for internet traffic, telephony and cable TV networks and high-speed local area networks (LANs) etc [2]. Optical fiber communication has also some limitations due to nonlinear refractive index of the core material which results in self-phase modulation (SPM), cross-phase modulation (XPM), and four-wave mixing (FWM) and limits the transmission rate and distance. Installation of fiber cable is also very much restricted in metropolitan areas [1, 2].

On the other hand, FSO communication does not require any fiber and can be used for communication between building to building in a metropolitan advance area. FSO communications, also called Free Space Photonics (FSP) or Optical Wireless, refers to the transmission of modulated visible or infrared (IR) beams through the atmosphere to obtain optical communication for telecommunication or computer networking. FSO uses lasers to transmit data through the free space instead of enclosing the data stream in a glass fiber. "Free space" means air, outer space, vacuum, or any such similar media. The technology is useful where the physical connections are impractical due to 2 high costs, difficult to deploy or other considerations. FSO transmits invisible, eye-safe light beams from one telescope to other telescope using low power infrared lasers in the terahertz spectrum. The beams of light in FSO systems are transmitted by laser light focused on highly sensitive photodetector receivers. These receivers are telescopic lenses able to collect the photon stream and transmit digital data containing a mixture of internet messages, video images, radio signals or computer files and so on. Commercially available systems offer capacities in the range of 100 Mbps to 2.5 Gbps, and demonstrated systems report data rates as high as 160 Gbps. FSO systems can function over a distances of several kilometers as long as there is a clear line of sight (LOS) between the source and the destination with enough transmitter power [2, 3].

FSO communication have gained sufficient interest in recent years as a serious alternatives to radio frequency (RF) links for effectively transferring data at high rates over short distances [2]. In order to provide LOS communication, the transmitter and receiver are placed on high-raise buildings separated by several hundred meters. FSO system has a numbers of merits such as communication distance upto several kilometers, immunity to electromagnetic interference, low bit error rate, lightweight, less cost and easily deployable with high data rates without any requirement for licensing for its last mile access. However, FSO systems are impaired by adverse weather conditions, such as rain, fog, cloud, snow, and atmospheric turbulences and by pointing errors due to loss of alignment between transmitter and receiver [16, 17, 19-25].

The performance of terrestrial FSO links are highly affected by beam dispersion, scattering, absorption, interference from background light sources including sun [16]. The atmospheric effect is caused by refractive index fluctuations due to temperature change which results in atmospheric turbulence classified into weak and strong turbulence. Continuous alignment between transmitter and receiver are required in FSO communication system because of pointing instability caused by the wind, dynamic and load thermal expansion and building sway due to earthquake resulting in misalignment between the transmitter and receiver [18, 19]. Spatial diversity i.e. the use of multiple transmitters and receivers, provide an attractive technique to mitigate the fades in the 3 received signal. Wavelength division multiplexing (WDM) and optical CDMA (OCDMA) system with coding and diversity over FSO channel have got a significance interests in improving the performance of a FSO communication system [6-8].

1.2 Modulation and Multiplexing Techniques in Optical Communications

1.2.1 Optical pulse position modulation (OPPM)

Optical pulse position modulation (OPPM) is a power efficient modulation technique for transmitting information over the optical free space channel [43]. According to this scheme, the encoder maps blocks of L consecutive binary symbols or bits into a single OPPM symbol by placing a single laser pulse into one of M = 2L time slots. The OPPM symbols are orthogonal, since there is no overlap between pulses in any pair of symbols. After establishing slot and symbol synchronization, the receiver detects the uncoded OPPM symbols by determining the M slots containing the laser pulses and performs the inverse mapping operation to recover the bit stream. Each correctly decoded OPPM symbol conveys L bits of information and the receiver must operate with much greater bandwidth than the actual data rate to effect the decoding operation. If each bit is Tb seconds in duration, then L bits take LTb seconds to transmit. This means the receiver must process 2L OPPM time slots in LTb seconds to avoid overflow. The processing rate of the system therefore must be a factor of 2L/L times greater than the transmitted bit rate. For large values of L, this bandwidth expansion is severe and ultimately limiting the information throughput of the system due to limitations on the sampling rate.

Due to implementation complexity issues, most current fiber optic systems use intensity modulation with direct detection (IM/DD). The on-off keying (OOK) modulation is also commonly used due to its simplicity where the presence of the transmitted light intensity represents a symbol one and its absence is a symbol zero. However, Q-ary OPPM is more efficient than OOK and IM and is more suitable for FSO link. However, the Q-OPPM requires more bandwidth than OOK at the same data transmission rate. The bandwidth requirement of higher order OPPM is not a limitation due to large bandwidth availability of FSO system. Another limitation of OPPM is that the peak-to 4 average power ration (PAPR) increases with the increase of Q for a given average transmission power.

1.2.2 Wave length division multiplexing (WDM)

WDM is a technology which multiplexes a number of optical carrier signals onto a single optical fiber by using different wavelength of laser light. This technique enables unidirectional or bidirectional communications over one strand of fiber with multiplication of capacity. For example, in a four-channel bidirectional WDM span, signals at 1549 nm and 1557 nm are multiplexed for transmission in one direction and 1533 and 1541 nm signals are multiplexed for transmission in the other directions, all on the same working fiber. On the other hand, unidirectional WDM device multiplexes a number of different frequencies for transmission in one direction on one fiber. For example, in a four-channel unidirectional WDM span, signals at 1557, 1549, 1541 and 1553 nm are multiplexed for transmission in one direction on the fiber. The block diagram of WDM multiplexing and demultiplexing is shown in Fig. 1.1:

λ1 Tx Rx λ1

λ2 Tx λ1 λ2 λ3 ...... λn Rx λ2

λ3 Tx Rx λ3

λn Tx MUX DEMUX Rx λn

Multiple Transmitters Multiple Receivers

Fig. 1.1: WDM Multiplexing and Demultiplexing

Both of these techniques allow for such fiber configurations as combining four 2.4 Gbps serial bit streams on a single fiber span for an aggregate signal speed of 10 Gbps equipment. The WDM technique can be used in the previously installed fiber base to support extremely narrowly spaced channels making maximum reuse of any existing 2.4 Gbps equipment to combine four channels. The minimum four-wavelength operation can be extended upto eight or even sixteen wavelengths and more including the capabilities to add or subtract wavelengths both in unidirectional or bidirectional operation. The term WDM is commonly applied to an optical carrier is described by its wavelength, whereas FDM applies to a radio carrier which is more often described by 5 frequency. Since wavelength and frequency are tied together through a simple directly inverse relationship, in which the product of frequency and wavelength equals the propagation speed of light, the two terms actually describe the same concept.

WDM transmission can be distinguished into two broad categories, namely coarse WDM (CWDM) and dense WDM (DWDM) with single mode fiber. Although both the categories use the same concept of multiple wavelength channels on a single fiber, they differ in the channel spacing. CWDM uses wider channel spacing and hence, provides significantly fewer channels than DWDM. Most WDM systems operate on single mode fiber which has a core diameter of 9 µm and certain forms of WDM can also be used in multi-mode fiber which has core diameters of 50 or 62.5 µm.

1.2.2.1 Coarse WDM (CWDM)

CWDM is a method of combining multiple signal or laser beams at various wavelengths for transmission along fiber optic cables such that the no of channels is fewer than that in DWDM but more that in WDM. CWDM systems have channels at wavelength spaced 20 nm apart, compared to 1 nm spacing for DWDM. This allows the use of low cost uncoded lasers for CWDM. In a typical CWDM system, laser emissions occur on eight channels at eight wavelengths of 1610 nm, 1590 nm, 1570 nm, 1550 nm, 1530 nm, 1510 nm, 1490 nm and 1470 nm. The tolerance of CWDM laser is upto ± 3 nm. A CWDM is less expensive and consumes less power than DWDM system. However, the maximum realizable distance between nodes is smaller with CWDM.

1.2.2.2 Dense WDM (DWDM)

DWDM is a technology that puts data from different sources together on an optical fiber with each signal carried at the same time on its own separate light wavelength. The major difference between WDM systems and DWDM systems is that, in DWDM the wavelengths used are packed within 1 nm or even 0.1 nm of each other, or about ten to on hundred times denser than in WDM. The current record for wavelength packing on a single fiber is 1022 channels, although the total throughput is only about 40 Gbps. Since the current serial bit transmission record on fiber is 160 Gbps, potentially DWDM systems with throughputs in excess of 160 Tbps (160000 Gbps) are possible. 6

In WDMA system the center wavelength of a channel must be tuned carefully to make sure it is exactly where it is supposed to be. This is because even simple modulation of the carrier signal will essentially double the bandwidth required and might overlap and interfere with wavelengths still within their band. The block diagram of DWDM multiplexing and demultiplexing is shown in Fig. 1.2:

DWDM refers originally to optical signals multiplexed within the 1550 nm band so as to leverage the capabilities and cost of erbium doped fiber amplifiers (EDFAs) which are effective for wavelengths between approximately 1525–1565 nm (C band), or 1570– 1610 nm (L band). EDFAs can amplify any optical signal in their operating range, regardless of the modulated bit rate. In terms of multi-wavelength (MW) signals, so long as the EDFA has enough pump energy available to it, it can amplify as many optical signals as can be multiplexed into its amplification band.

Transmitters Receivers

λ1 λ1

λ2 EDFA λ2 Dense Dense Wavelength 48 Wavelength λ3 λ3 Division Optical Fibers Virtual Division Multiplexer Fibers Demultiplexer

λn λn

Fig. 1.2: DWDM Multiplexing and Demultiplexing

DWDM systems have to maintain more stable wavelength or frequency than those needed for CWDM because of the closer spacing of the wavelengths. Precision temperature control of laser transmitter is required in DWDM systems to prevent ‘drift" off a very narrow frequency window of the order of a few GHz [4]. In addition, since DWDM provides greater maximum capacity it tends to be used at a higher level in the communications hierarchy than CWDM.

1.2.3 Optical code division multiple access (OCDMA)

Optical code division multiplexing (OCDM) or Optical code division multiple access (OCDMA) is a digital technique where the information is transmitted using a coded sequence of pulses instead of each channel occupy a given wavelength, frequency or 7 time slot. Each channel uses a specific code to transmit and recover the original signal. It utilizes basic principle of spread spectrum transmission where all users share the fiber channel bandwidth simultaneously [5-7].

OCDM is an alternate multiplexing technique that has its origins in RF communications [8-11] but has been since applied to the optical domain due to a number of inherent advantages that the technique offers. Unlike WDM that provisions a dedicated wavelength per channel or OTDM that requires strict synchronization between channels [12]. OCDM provides channels with asynchronous access to the available bandwidth. As a result each channels transmission can overlap in both the time and wavelength domain. In such a system multiplexing is achieved through the use of optical codes.

ELECTRICAL OPTICAL ELECTRICAL

CDMA CDMA #1 #1 Encoder Decoder

Star Coupler

CDMA CDMA #M #M Encoder Decoder Data Source Data Recovery Fig. 1.3: Schematic diagram of a general optical CDMA system

In OCDMA each channel is assigned a unique optical code that is impressed upon the data before it is transmitted. Fig. 1.3 shows a typical OCDMA system. Each channel modulates an optical pulse train with the data for transmission. This data signal is then encoded using an optical encoder applying the optical code unique to that channel. The data signals from all channels are multiplexed asynchronously and transmitted over the network [13].

At the receiver side, a copy of all transmitted data signals is passed to each decoder. The original signal is recovered by correlating the incoming aggregate signal with a stored version of the code used during the encoding process. The remaining data signals that do not match the decoding code remain improperly decoded. OCDMA offers several unique advantages such as asynchronous transmission, soft capacity on demand, the 8 potential for secure transmission and quality of service control [14]. However, OCDMA does suffer from two main noise sources which can severely limit system performance. Multiple access interference (MAI) noise results from the improperly decoded channels passing through the decoder and being incident on the photodetector. This MAI can limit system performance as it scales with the number of channels. The second noise source is optical beat noise (OBN) which is a result of square law photodetection used in optical systems. Since the photodetector receives the signals from each channel these incident fields are mixed in the detector and can produce beating that occupies the same bandwidth of the desired signal. OBN can often exceed MAI in terms of limiting the performance of OCDMA systems due to the fact that it scales with the number of detected fields, which is proportional to the number of channels [15].

1.3 Limitations of an FSO Channel

1.3.1 Atmospheric turbulence

Atmospheric circulation due to distribution of temperature on the surface of earth, wind flow due to the change of atmospheric pressure and velocity variation generate atmospheric turbulence. Clear air turbulence phenomena affect the propagation of optical beam by both spatial and temporal random fluctuations of refractive index due to temperature, pressure, and wind variations along the optical propagation path. Atmospheric turbulence primarily causes phase shifts of the propagating optical signals resulting in distortions in the wave front and this distortion is referred to as optical aberrations. Atmospheric turbulence also causes intensity distortion which is referred to as scintillation. Aerosols, moisture, temperature and pressure changes produce refractive index variations in the air by causing random variations in air density. These variations are referred to as eddies or air pockets having a lens effect on light passing through them [16].

The refractive index variation causes phase perturbation of the wave front isophase plane of propagating light [16]. As a result, secondary waves generated from different point of wave front have different phase, and their interference with each other gives amplitude variation. In other words, air pockets will act as lenses for propagating light having different refractive indexes, and they will focus-defocus light randomly. The net 9 result is that, intensity of received optical signal will not be constant but fluctuating randomly similar to the amplitude fading due to multipath propagation in RF wireless communication.

When a plane wave passes through these eddies, parts of it are refracted randomly causing a distorted wave front with the combined effects of variation of intensity across the wave front and warping of the isophase surface. If the size of the turbulence eddies are larger than the beam diameter, the whole laser beam bends. If the sizes of the turbulence eddies are smaller than the beam diameter and so the laser beam bends, they become distorted. Small variations in the arrival time of various components of the beam wave front produce constructive and destructive interference and result in temporal fluctuations in the laser beam intensity at the receiver.

1.3.2 Refractive index variation

2 Refractive index structure parameter (Cn ) is the most significant parameter that determines the turbulence strength and depends on the geographical location, altitude, and time of day [16]. There is the largest gradient of temperature associated with the largest values of atmospheric pressure and air density close to the ground. Therefore, the value of refractive index structure should be larger at sea level and smaller as the altitude increases, because the temperature gradient decreases with the increase of altitude and so the air density, results smaller refractive index structure. In the horizontal path even over a reasonably long distance, refractive index structure parameter may be assumed to be practically constant. Value of atmospheric refractive structure parameter depends on channel condition and for terrestrial link. Typical value of refractive index structure parameter for a weak turbulence at ground level can be as little as 10−−17 m 2/3 , while for a strong turbulence it can be up to 10−−13 m 2/3 or larger. Numbers of parametric models have been formulated to describe the refractive index structure parameter profile and among those, one of the more used models is the Hufnagel-Valley model [16, 25, 26].

1.3.3 Scintillation

2 Irradiance fluctuation due to atmospheric turbulence is known as scintillation, and σ i is used to represent scintillation index. This parameter directly indicates strength of atmospheric turbulence and defined as normalized variance of intensity fluctuation

22 2 which represents as: σ i =−EI[]/[]1 EI [16]. This scintillation index is directly

2211/6 2 related to channel parameter and system parameter as:σ inx= 1.23CLk where Cn is atmospheric refractive index structure parameter, kx=2ߨ/ߣ is known as wave number where, ߣ is the wavelength and ܮ is the link distance in meter [16]. For a constant atmospheric refractive structure parameter, scintillation index is completely dependent on link length ܮ, since wavelength of light is constant. Scintillation is the most noticeable parameter for FSO systems. Light traveling through scintillation will experience intensity fluctuations, even over relatively short propagation distance [17].

1.3.4 Pointing error/jitter

In addition to the effects of atmospheric turbulence, FSO links are also highly dependent on the pointing performance. The pointing-error is the deviation between the desired antenna orientation and its current actual position. This error can arise from mechanical misalignment, errors in tracking systems and due to mechanical vibrations present in the system. The pointing error consists of two components: a fixed error, called boresight error and a random error, called jitter. Jitter is superimposed over the fixed boresight error and modeled as a two dimensional random variables [18, 19]. Due to boresight error and jitter, each received intensity sample can be thought of as a randomly sampled point on a random irradiance profile.

1.3.5 Cloud

Clouds are the collection of droplets and crystals suspended in air and usually formed by the lifting of damp air. The lifting air parcel cools and this leads to an increase of the relative humidity. The excess vapor condenses on tiny particles called clouds nuclei, producing water droplets, which can grow due to coagulation process [20]. The clouds can travel long distances due to atmospheric air circulation and also they can be deposited on the surface of our planet due to precipitation such as snow and rain. The 11 collection of droplets can occupy large volume of troposphere at any place up to 20 km from the Earth’s surface, depending on the latitude [21, 22]. NASA has reported that, more than 50% of the Earth’s surface is covered by clouds at any given time reflecting the role that they play in atmospheric cycle and planetary radiative budget and hence their importance in studying them for communication problem. Clouds are classified not only in respect to their thermodynamic state like water, ice or mixed clouds but also in terms of their altitude ranges, in which clouds of different type called genera form most frequently. For the purpose of cloud classification, the troposphere is divided into three altitude ranges which encompass high, middle, and low as shown in Table 1.1 below:

Table 1.1: Altitude range of clouds for different regions [21]

Altitude range Polar regions Temperate regions Tropical regions High 3-8km 5-13km 6-9 km Middle 2-4km 2-7km 2-8 km Low 0-2km 0-2km 0-2km

Another important parameter for the cloud is the optical thickness. The optical thickness of the medium is a dimensionless quantity that characterizes the attenuation of optical radiation in the medium. It is the depth of the medium in which the intensity of the light of a given frequency is reduced by a factor of 1/e; approximately 1/3 of the light is absorbed within one optical thickness depth. For laser beam propagation, optical depth expresses the quantity of light removed from a beam by scattering and absorption during its path through a medium. So, in order to estimate the spectral irradiance that reaches at a given layer of cloud, the first step is to determine the total spectral extinction coefficient at each wavelength. The next step is to define the vertical component of the incremental distance along a beam of interest through which radiation travels. Integrating the spectral extinction coefficient over an incremental distance gives an optical depth [20, 22, 23].

1.3.6 Rain attenuation in FSO communication

Rain is liquid water in the form of droplets that have condensed from atmospheric water vapour and then precipitated to become heavy enough to fall under gravity. Rain is a 12 major component of the water cycle and is responsible for depositing most of the fresh water on the Earth. The major cause of rain production is moisture moving along three- dimensional zones of temperature and moisture contrasts known as weather fronts. If enough moisture and upward motion is present, precipitation falls from convective clouds those with strong upward vertical motion such as Cumulonimbus thunder clouds which can organize into narrow rain band. Rain is unpredictable attenuation and the major impairment to FSO link availability. Attenuation of the rain is independent of the wavelength and it is the function of precipitation intensity [24].

Scattering due to rainfall is called non-selective scattering, because the radius of raindrops are 100-1000 µm is significantly larger than the wavelength of typical FSO systems. The laser is able to pass through the raindrop particle with less scattering effect occurring. The haze particles are very small and stay longer in the atmosphere, but the rain particles are very large and stay shorter in the atmosphere. This is the primary reason that attenuation via rain is less than haze. An interesting point to note is that RF wireless technologies that use frequencies above approximately 10 GHz are adversely impacted by rain and little impacted by fog. This is because of the closer match of RF wavelengths to the radius of raindrops, both being larger than the moisture droplets in fog [16].

Rain is precipitation of liquid drops with diameters greater than 0.5 mm when the drops are smaller; the precipitation is usually called drizzle. The optical signal is randomly attenuated by fog and rain when it passes through the atmosphere. The main attenuation factor for optical wireless link is fog. However, rain also imposes certain attenuation. When the size of water droplets of rain becomes large enough it causes reflection and refraction. As a result, these droplets cause wavelength independent scattering. Majority of the rain drops belong to this category. The increase in rainfall rate causes linear increase in attenuation, and the mean of the raindrop sizes also increases with the rainfall rate and is in the order of a few mm [25].

1.3.7 Fog/Mist attenuation in FSO communication

Fog is a cloud of small water droplets near ground level and sufficiently dense to reduce horizontally visibility to less than 100 m. Fog is formed by the condensation of water vapor on condensation nuclei that are always present in natural air. This can result as soon as the relative humidity of the air exceeds saturation by a fraction of 1%. In highly polluted air the nuclei may grow sufficiently to cause fog at humidity’s of 95% or less [22]. Another way is to use visibility data to predict specific attenuation. The models Kruse, Kim and Al Naboulsi [20-23] use this approach and predict specific attenuation using visibility. The attenuation of 10 µm is expected to be less than attenuation of shorter wavelengths. Kim rejected such wavelength dependent attenuation for low visibility in dense fog. Al Naboulsi and et.al developed simple relations allowing the evaluation of the attenuation in the 690 to 1550 nm wavelength range and for visibilities going from 50 to 1000 m for two types of fog: advection fog and convection fog [23]:

The advection fog is generated when the warm, moist air flows over a colder surface. The air in contact with the surface is cooled below its dew point, causing the condensation of water vapour. It appears more particularly in spring when southern displacements of warm, moist air masses move over snow covered regions. The radiation or convection fog is generated by radiative cooling of an air mass during the night radiation when meteorological conditions are favourable such as very low speed winds, high humidity, clear sky etc. It forms when the surface releases the heat that is accumulated during the day and becomes colder: the air which is in contact with this surface is cooled below the dew point, causing the condensation of water vapour, which results in the formation of a ground level cloud. This type of fog occurs more particularly in valleys [25-26].

1.4 Literature Review

FSO communication has become very popular recently for effectively transferring data at high rates over short distances. In order to provide line of sight (LOS) communications, the transmitter and receiver are placed on high-raise buildings separated by several hundred meters or even kilometers. FSO has a number of merits 14 over its rivals: it is lightweight, easily deployable and provides high data rates without any requirement for licensing [26-29]. However, FSO systems are impaired by adverse weather conditions such as fog, cloud, rain, turbulences and by pointing errors due to loss of alignment between transmitter and receiver in the presence of building sway [18, 26-32].

Continuous alignment between transmitter and receiver are required in FSO communication. Dynamic load thermal expansion and earthquake cause buildings to sway resulting in misalignment between the transmitter and receiver. The effects of pointing error and atmospheric turbulence on terrestrial FSO links are reported in [29]. In these works, the detector aperture is considered negligible with respect to the beam width at the receiver. In [31], Farid and Hranilovic have derived a statistical model for FSO link which model the fading due to atmospheric turbulence and pointing errors considering beam width, pointing error variance, and detector size. In [32], Sandalidies et al. present a closed form probability density function of the statistical model considering the joint effects of K-distributed strong turbulence fading and evaluated BER in terms of the Meijer’s-G functions. In [18], Deva K. Borah et al. investigated the effect of beam pointing errors on the capacity of optical links affected by atmospheric turbulence. They have used a wave-optics based approach to evaluate the capacity expression of a FSO links affected by atmospheric turbulence and beam pointing error.

Spatial diversity i.e. the use of multiple transmitters and receivers, provide an attractive technique to mitigate the fades in the received signal. Numerous investigations on Multiple Input Multiple Output (MIMO) FSO link have been carried out during the last few years to mitigate effect of atmospheric effects on the link performance [33-42]. In [33], Navidpour et al. have evaluated the BER performances of FSO links with spatial diversity over Log-normal atmospheric turbulence fading channels, assuming both independent and correlated channels among transmitter/receiver apertures. In [34, 35], Tsiftsis et al. and Bayki et al. have studied the BER performances of MIMO FSO links in Gamma-Gamma fading by expressing pairwise probabilities (PP) as a power series with respect to the signal-to-noise ratio (SNR). 15

The authors have carried out novel analysis for an IM/DD FSO CDMA system with receive diversity, maximal ratio combining and strong atmospheric turbulence [36]. Analysis on FSO link with transmits and receives diversity considering various effects based on SIMO and MISO configurations are also reported in [36-39, 126]. Recently, coherent polarization modulated MIMO FSO link with performance is also reported under turbulence channel [40]. Use of travelling wave tube amplifier (TWTA) in a FSO link with multiple transmitter/receiver to eliminate the effect of fog is recently reported [41]. Further, the performance of FSO link with multiuser diversity is also investigated recently [42]. The performance of MIMO FSO communications over double generalized Gamma fading channels presented recently in [125]. Although, it is found that, use of diversity can be effective in minimizing the effect of atmospheric turbulence on a FSO link performance, it is highly degraded due to the effect of pointing error. Recently, analytical results are also reported on FSO system considering pointing error for SISO, SIMO, MISO and MIMO optical diversity scheme [81, 83].

Numerous woks on optical M-ary pulse position modulation (M-PPM) are also carried out to investigate the effectiveness of M-PPM in FSO links as M-PPM is an energy efficient modulation format compared to on-off keying (OOK) and other modulation schemes [43-48, 52, 68]. The effects of atmospheric turbulence and pointing error on the bit error rate performance of a PPM FSO link is reported in [43]. In [44], the authors have investigated the BER performance of M-PPM over FSO link in application of Log-normal and negative exponential distribution with and without error correction coding. The performance of optical PPM for deep space communication is also reported in [45], with multi-pulse position modulation with channel fading. The performance of Avalanche Photodiode (APD) based M-PPM receiver over atmospheric turbulence is also carried out considering different APD gain [46]. More recently, the effect of strong turbulence on the shot noise limited and thermal noise limited operations of M-PPM receivers for a FSO link is investigated with strong turbulence condition [47]. The performance of SAC-OCDMA using overlapping PPM and spectral-phase encoded optical atmospheric PPM-CDMA system is presented in [48, 50]. However, all the previous works on M-PPM FSO links are based on perfect synchronization although the performance of an optical M-PPM receiver is highly sensitive to slot synchronization error [51]. Several slot synchronizers are also reported earlier for optical M-PPM 16 system [51, 52] and the effect of imperfect slot synchronization on the performance of optical M-PPM receiver are reported earlier [51-53] without and with error correction coding.

OCDMA technique has been drawing considerable interest in fiber optic communication system with [8 ‐15]. A hybrid optical communication system of WDM and WDMA with OCDMA is also investigated recently [56-62] for its application in fiber optic communication system. Further, significant research works are also reported on OCDMA in free-space optical communication system in the presence of the above channel limitations with intensity modulation and optical pulse position modulation scheme [63-65]. Multi-carrier OCDMA (MC-OCDMA) system over atmospheric turbulence channel and time diversity OCDMA are reported [66-67] to find the bit error rate performance. Two dimensional OCDMA system and OCDMA system with turbo code has been investigated with turbulence atmospheric optical channel [69, 70]. Recently, polarization modulated direct detection OCDMA system with turbulence modeled by Gamma-Gamma distribution is reported [71, 72]. More recently, effect of pointing error and atmospheric turbulence on OCDMA FSO system using SIK dual photodetector receiver are presented [83, 116]. Although the effect of atmospheric turbulence on OCDMA system are reported, most of the above research on OCDMA- FSO considered electrical domain encoder with optical transmission and electronic domain decoder after photo detection process.

Considering the above discussions, analytical method to evaluate the performance of an OCDMA communication link over the FSO channel with different modulation schemes using direct detection optical Sequence Inverse Keying (SIK) OCDMA receiver is very important and yet to be reported. The effect of adverse weather condition on OCDMA FSO link impaired by atmospheric turbulence, cloud, rain, fog etc. and by pointing errors due to loss of alignment between transmitter and receiver needs to be studied to meet the future challenges of transmitting huge data rate at the range of hundreds of Gbps. Space-time coded OCDMA system using diversity combining technique at the receiver end is the approach to mitigate the channel impairment and to improve the system performance in a satisfactory level. Multiple numbers of PIN and APD 17 photodetector receivers can be employed to improve the system performance for space- time diversity.

Different modulation and demodulation formats depending on the specific application are also employed to analyze the systems such as IM/DD, OOK, OPPM, MPPM, WDM and DWDM etc. Each of these modulation schemes or their combination with direct, homodyne, heterodyne or diversity receivers has its own merits and demerits. IM/DD and OOK are the simplest modulation formats to implement in the FSO system. The system performance improves significantly with the higher order M-PPM format. WDM and its kind CWDM or DWDM can multiplex number of channel simultaneously [74]. The combination of these advantages allows maximum utilization of the enormous transmission capacity of OCDMA FSO system. Therefore, it is necessary to develop analytical approaches to evaluate the performance of OCDMA FSO link with space- time diversity in terms of BER using different modulation schemes.

1.5 Objectives of the Research

The objective of this research works is to provide analytical techniques to evaluate the performance of OCDMA system over FSO link in presence of channel impairments and to evaluate the performance of OCDMA system over FSO link in presence of channel impairments considering space-time diversity. The whole research work is carried out to achieve the following specific goals:

(i) To develop an analytical model for a free-space optical channel considering all the channel limitations such as fog, cloud, rain, atmospheric turbulence, pointing error and timing jitter and to find the overall channel transfer function.

(ii) To develop analytical method in order to evaluate the performance of an OCDMA communication link over the FSO channel considering different modulation schemes e.g. intensity modulation, M-PPM with direct detection optical Sequence Inverse Keying (SIK) OCDMA receiver. 18

(iii) To carryout analysis of space-time coded optical multiple input and multiple output (MIMO) transmission techniques to overcome the channel limitations and to evaluate the performance results with Alamouti code.

(iv) To carry out theoretical analysis of the signal to noise plus interference ratio (SNIR) and bit error rate (BER) for a wavelength division multiplexing (WDM) OCDMA system over FSO link considering the overall channel model developed in objective (i).

(v) To carry out numerical simulations on OCDMA FSO system with optical orthogonal and nearly orthogonal codes e.g. Walsh code, PN sequence code, Gold code to verify the analytical results.

1.6 Outline of the Thesis

The thesis is organized as follows:

Chapter 2 provides the analytical model to evaluate the effect of weak atmospheric turbulence, timing jitter and scintillation index on the performance of a single channel FSO link. FSO system model is presented using PIN and APD photodetector receivers considering weak atmospheric turbulence. Analysis is carried out to find out the average BER considering Log-normal distribution of weak turbulence using Q-OPPM modulation format.

Chapter 3 presents performance analysis for an OCDMA FSO link with weak and strong atmospheric turbulence and combined effect of atmospheric turbulence and pointing error. Analyses are carried out to find the expression for the signal current and multi access interference (MAI) current at the output of SIK receiver to find out the expression for average BER. The numerical results are evaluated for different values of processing gain, number of simultaneous users, turbulence variances and normalized pointing error standard deviations to find out the BER performance results of the proposed system including the power penalties.

In chapter 4 analytical approach is developed to evaluate the effect of cloud, fog and pointing error on OCDMA FSO link using the transfer function of cloud, fog and pdf of 19 pointing error considering a SIK dual photodetector direct detection receiver. The BER performance results are evaluated considering the cloud and fog thickness, number simultaneous user, code length and different values of jitter standard deviation.

Chapter 5 describes the analytical approaches for space-time diversity in a single channel FSO system and OCDMA FSO system considering the effect of pointing error. System models are presented for SISO, SIMO, MISO and MIMO configurations using single or multiple number of PIN photodetectors receiver. The BER performance results and power penalties are evaluated for all the analytical approaches using OOK modulation and direct detection.

Chapter 6 represents the performance of multi-wavelength OCDMA-WDM FSO system in the presence of atmospheric turbulence and pointing error considering SIK dual detector photodetector receiver. Gamma-Gamma pdf model for strong atmospheric turbulence and traditional pointing error model are used to develop analytical expression for unconditional BER.

The chapter 7 focuses on the outcome of the dissertation and summarizes the achievement and findings of the research work and gives recommendations for the scope of future research works that can be carried out. Chapter 2

PERFORMANCE ANALYSIS OF Q-ARY OPTICAL PPM FSO SYSTEM OVER ATMOSPHERIC TURBULENCE CHANNEL

2.1 Introduction

Performance of a Q-ary optical PPM (Q-OPPM) FSO system is highly limited by atmospheric turbulence and timing jitter [43]. In this chapter, an analytical approach is presented to evaluate the impact of timing jitter and the combined effect of scintillation and timing jitter on the BER performance of a Q-OPPM FSO system under the influence of weak atmospheric turbulence modeled by Log-normal distribution [54]. The expression of the conditional BER for a given turbulence and timing jitter is developed and the average BER is found by averaging the conditional BER over the probability density function (pdf) of turbulence and the timing jitter. The results are evaluated at a bit rate of 2.4 Gbps and 10 Gbps with PIN and Avalanche Photodiode (APD) receivers for different orders of Q-OPPM.

2.2 FSO Channel Model for Weak Atmospheric Turbulence

There are several models to quantify the effect of atmospheric turbulence. Log-normal distribution is a useful model for the pdf of weak atmospheric turbulence due to its simplicity [54]. As the strength of turbulence increases, multiple scattering effects become important and significant deviations from Log-normal statistics are exhibited. Log- normal pdf underestimates the behavior in the tails but an accurate detection and fade probability primarily depends on the tails of the pdf. Therefore, underestimating this region significantly affects the accuracy of the communication performance. Gamma-Gamma distribution is a two parameters distribution which is based on a doubly stochastic theory of scintillation, and assumes that small scale irradiance fluctuations are modulated by large scale irradiance fluctuations of the propagating wave and both are governed by independent Gamma distributions [52, 54]. In weak 21 atmospheric turbulence region pdf of the received irradiance I approach to the Log– normal distribution while for strong turbulence this pdf approaches to Exponential distribution [77-79]. The Gamma-Gamma pdf model is the development of Log-normal distribution which models both small and large scale eddies [75,76].

The pdf of the received irradiance I is considered as Log-normally distributed for weak turbulence and can be expressed as [80]: 1 ⎛⎞(ln(II )− ln( ))2 pI( )=− x exp⎜⎟0 (2.1) 2 2σ 2 I 2πσ α ⎝⎠α where p(I) is the pdf of the Log-normal channel, I0 is the mean received optical intensity and I is the received signal intensity with turbulence. The optical intensity of a source is defined as the optical power emitted per solid angle in units of Watts per Steradian (W/sr) [80]. The variance of the atmospheric turbulence of the channel between

2 transmitter and receiver and given byσωωα = exp(12+− ) 1, where ω1 and ω2 are given by [54] :

2 0.49σ 2 ω1 = (2.2) 212/57/6 ()1++ 0.18d 0.56σ 2

212/5−5/6 0.51σσ22() 1+ 0.69 ω = (2.3) 2 2212/5 ()1++ 0.9dd 0.62 σ 2

2 where dkDL= x /4 and kx = 2/π λ is the wave number with wave length λ, L is the

2 link distance in meter, D is the receiver aperture diameter and σ 2 is the Rytov variance for weak turbulence expressed as [54]:

27/6211/6 σ 2 = 0.492kCLxn (2.4)

2 Cn being the refractive index parameter of the turbulent channel.

2.3 Q-OPPM FSO System Model

The block diagram of the Q-OPPM FSO system with PIN and APD photodiodes is shown in Fig. 2.1. The input binary data bit streams are given input to a Q-OPPM modulator to generate the Q-OPPM symbols. The generated Q-OPPM symbols are transmitted by a laser transmitter using a collimator lens. 22

Fig. 2.1: Block diagram of a Q-OPPM FSO system with PIN or APD photodiode.

At the receiver the optical beam is received by a PIN or APD photo-detector followed by a preamplifier and a low pass filter (LPF). The slot synchronizer generates the clock using the received Q-OPPM signal. The generated clock is used by the Q-OPPM demodulator to determine the slot count over the Q-OPPM slots. Based on the slot count the demodulator takes decision of the transmitted Q-OPPM symbol and generates the output bit stream corresponding to the slot counts.

2.4 Analysis of BER for a Q-OPPM FSO System

2.4.1 Analysis of BER with PIN receiver

The Q-OPPM signal transmitted over the atmospheric channel is given by:

St( )= 2 Pejtωc . a (2.5) Tk where ak is the Q-OPPM symbol, PT is the average transmitted optical power and ωc is the angular optical carrier frequency. The received optical signal at the receiver aperture is given by:

−αL/2 rtn ( )= Sthe ( ). (2.6) where α is the path loss coefficient, L is the link distance, parameter h is the normalized fading channel coefficient which models the effect of turbulence in the channel.

The output of the photodetector can be expressed as:

2 2 −α L itddn( )== R . Re rt ( ) 2 RPhe dTkndkn. a +=+ it ( ) 2 RIait . ( ) (2.7) 23

2 −α L where IPhe= T is the received optical irradiance with atmospheric turbulence and in(t) represent the photodetector shot noise, preamplifier thermal noise and zero mean 2 Gaussian noise with variance σn .

The slot duration Ts of Q-OPPM with the modulation order Q, data rate Rb and bit duration Tb is given by [129]:

log2 Q 1 Tsb= (TQQ log2 ) /= . (2.8) QRb

2 The signal current Is over a PPM time slot Ts and the noise variance σn at the output of receiver are given by [129]: ()TT−∆ IIR==− x s IR (1ε ) (2.9) sdT d s 2 4KTb σ ndb=++2eB ( R I I ) B (2.10) RL where ε =∆TT/ s is the normalized timing error, Kb is the Boltzmann constant, T is the receiver temperature in Kelvin, B is the receiver bandwidth, RL is the load resistance of the receiver, Ib is the background radiation intensity and e is the electron charge.

The signal to noise ratio (SNR) for a given timing error ε with PPM order Q and bit rate

Rb is then given by:

2 ()IRd (1−ε ) 4KTb SNR( I ,ε )=+2 x Q log2 Q . B (2.11) 2RRbnσ L The conditional BER conditioned on a given value of irradiance I with turbulence and a given timing jitter ε is then given by: Q PI( ,εε )= xerfcSNR ⎡⎤ ( ) / 2 (2.12) b 2 ⎣⎦ 2 The pdf of the timing jitter is considered as a zero mean Gaussian with variance σε as [80]: 1 −ε 22/2σ pe(ε )= ε (2.13) 2 2πσ ε

The unconditional BER is then obtained as [94, 100]:

∞∞ BER= P( I ,εεε ) p ( I ). p ( ) dI . d (2.14) ∫∫ b −∞ −∞ 24

2.4.2 Analysis of BER with APD receiver

th We consider a Q-OPPM slot of duration Ts and slot count over k time slot with perfect synchronization is assumed to be mk. In presence of normalized timing error ε, the slot count over a signal slot is given by:

⎛⎞ TTs −∆ mmkk (εε ) ==−⎜⎟ m k(1 ) (2.15) ⎝⎠Ts

Assuming Log-normal distribution for the turbulence, the average photon per PPM slot

2 E[Ks] are function of the mean mk(ε) and variance of the Log-normal channel σ k and can be represented as [130]:

2 ⎡⎤σ k EK [sk ]=+ exp⎢⎥m (2.16) ⎣⎦2 2 2 where E is the expectation operator andσ k is a function of the scintillation index σ si as:

2 2 σσk =+ ln( si 1) (2.17)

The total noise photons per PPM slot Kn(ε) which results from background noise, thermal noise and timing error induced signal count is given by [130]: 2σ 2 KF (εε )=+n 2 (Km + . ) (2.18) nbbkGe2 where Kbb is the average background noise photons per PPM slot, G is the mean gain of APD and e is the electronic charge and F is the APD excess noise factor defined by: FG=+ 2ζ (2.19) where ζ is the ionization factor for APD.

2 The variance σn of the thermal noise in a PPM slot is defined as [129]:

2 2KTTbrs σ n = (2.20) RL where Tr is the effective noise temperature of the APD receiver and RL is the receiver load resistance.

The conditional BER conditioned on a given timing error ε, of an Q-OPPM over Log- normal channel can be expressed as [45, 129]: 25

⎡⎤exp 2( 2σεxm+ ( )) Q N ⎢⎥{ ki k } Pwerfcbi(ε )≤ ∑ . (2.21) 2πσεεiNi=−,0 ≠ ⎢⎥FxmK exp(2++ () ()) ⎣⎦ki k n

where wi and xi are the weight and zeroes of Hermite Polynomial [44].

2 Considering ε =T/T∆ s being Gaussian distributed with zero mean and varianceσ ε , the pdf of ε is given by (2.13):

The average BER can now be evaluated as [103, 115]:

∞ BER= ∫ Pb (εεε ) p ( ) d (2.22) −∞

2.5 Results and Discussions

Following the analytical approach presented in section 2.4 we evaluate the average BER for PIN photodetector receiver at a bit rate of 2.4 and 10 Gbps respectively considering weak atmospheric turbulence. Similarly, we also evaluate the average BER for APD receiver for Q-OPPM FSO link with APD gain of 150 at a bit rate of 2.4 and 10 Gbps respectively using weak turbulence for different scintillation index. The parameters of the system under investigation are presented in Table 2.1.

Table 2.1: System parameters Parameter Symbol Value Data rate Rb 2.4 &10 Gbps Receiver bandwidth B 2.4 &10 GHz Responsivity Rd 0.85 A/W Receiver temperature T 300O K Load resistance of receiver RL 50 Ω Timing jitter variance 2 0.0 to 0.15 σ n Atmospheric turbulence variance 2 0.1 σα Timing error Ε 0.0 to 0.40 PPM order Q 8 to 256 Scintillation index SI 0.1 to 0.9 APD gain G 150 Background current Ib 10 nA Ionization factor for APD ߦ 0.028 Wave length ߣ 1550 nm Power penalty at BER - 10-9

2.5.1 Performance with PIN photodetector receiver

The plots of BER as a function of received optical signal intensity are depicted in Fig. 2.2 without timing jitter and in absence of atmospheric turbulence and that in Fig. 2.3 with timing jitter and in presence of atmospheric turbulence at a data rate of 2.4 Gbps using PPM order as a parameter. It is noticed that, Q-OPPM FSO system suffers due to timing error ε, in presence of atmospheric turbulence which is significant at lower values of PPM order. It is also noticed that, BER performance improves significantly with the increase of PPM order. It is obvious from the Fig. 2.2 and Fig. 2.3 that, the required received average signal intensity Io(dBm) at a given BER reduces significantly with the increase of PPM order and provides better BER performance. Hence, significant power penalty improvement can be achieved using higher order PPM.

Fig. 2.2: Plots of BER vs. received average optical signal intensity Io(dBm) for PIN receiver without timing jitter and atmospheric turbulence using PPM order as a

parameter for data rate Rb=2.4 Gbps.

Fig. 2.3: Plots of BER vs. received average optical signal intensity Io(dBm) for PIN receiver with timing jitter variance σ 2 = 0.075 and atmospheric turbulence variance ε 2 σα = 0.1 using PPM order as a parameter for data rate Rb=2.4 Gbps.

Fig. 2.4: Plots of BER vs. received average optical signal intensity Io(dBm) for PIN receiver without timing jitter and atmospheric turbulence using PPM order as a parameter for data rate Rb=10 Gbps.

Fig. 2.5: Plots of BER vs. received average optical signal intensity Io(dBm) for 2 PIN receiver with timing jitter variance σ ε = 0.075 and atmospheric turbulence 2 variance σα = 0.1 with PPM order as a parameter for data rate Rb=10 Gbps.

For a data rate of 10 Gbps, the plots of average BER as a function of received signal intensity are shown in Fig. 2.4 in absence of timing jitter and atmospheric turbulence and that in Fig. 2.5 in presence of timing jitter variance and atmospheric turbulence variance using PPM order as a parameter. It is noticed that, Q-OPPM FSO system suffers due to both jitter variances and atmospheric turbulences, which is significant at lower values of PPM order but better performance can be achieved with the higher values of PPM order. It is observed that, higher values of signal intensity Io(dBm) are needed to maintain the same BER performance as well as to mitigate the effect of timing jitter and atmospheric turbulence.

The plots of received optical signal intensity as a function of PPM order for different values of timing jitter variances at a given BER of 10-9 and a given values of

2 atmospheric turbulence variance σα = 0.1 are shown in Fig. 2.6 for a data rate of 2.4 Gbps. It is seen that, the receiver sensitivity degrades at a higher timing jitter which is high at a lower values of PPM order and is significantly less for higher PPM order. 29

-9 Fig. 2.6: Receiver sensitivity Io(dBm) vs. PPM order at a BER of 10 and 2 atmospheric turbulence variance σα = 0.1 with timing jitter variance as a parameter for PIN receiver.

-9 Fig. 2.7: Power penalty as a function of timing jitter variance at a BER 10 , data rate 2 Rb=2.4 Gbps and atmospheric turbulence variance σα = 0.1 using PPM order as a parameter for PIN receiver.

The plots of power penalty in dB due to timing error at a given BER of 10-9 are shown in Fig. 2.7 for PPM order 8, 16, 32, 64, 128 and 256 respectively at a data rate of 2.4 Gbps. It is noticed that, penalty is significant and is higher for lower PPM order and higher timing jitter.

Fig. 2.8: Power penalty as function of scintillation index at a BER 10-9 , data rate R =10 Gbps with atmospheric turbulence variance σ 2 = 0.1 using PPM order as a b α parameter for PIN receiver.

The plots of power penalty in dB due to scintillation index at a given BER of 10-9 are shown in Fig. 2.8 for PPM order=8, 16, 32, 64, 128 and 256 respectively at a data rate of 10 Gbps. It is also noticed that, penalty is higher for lower order PPM and higher scintillation index. From Fig. 2.7 and Fig. 2.8 it is noticed that, the penalty due to timing jitter variances and scintillation can be reduced significantly by increasing the PPM order.

2.5.2 Performance with APD photodetector receiver

The plots of average BER as a function of number of photons per bit Ks are depicted in Fig. 2.9 and Fig. 2.10 for PPM order 8 and 256 and data rate 10 Gbps and 2.4 Gbps respectively with ε as a parameter using turbulence of scintillation index 0.3. It is noticed that, Q-OPPM FSO system suffers due to timing error ε in the presence of atmospheric turbulence, which is significant at higher values of timing error ε. It is also observed that, the conditional BER performance improves significantly when the PPM order increases from 8 to 256 keeping the other parameters same. It is also found from

Fig. 2.9 and Fig. 2.10 that, the BER performance and number of photons per bit Ks at a given BER largely depends on PPM order as well as the data rate.

Fig. 2.9: Plots of average BER vs. number of photon per bit of 8-PPM FSO link with turbulence of scintillation index SI=0.3 at a bit rate of Rb=10 Gbps and APD Gain G=150.

Fig. 2.10: Plots of average BER vs. number of photon per bit for 256-PPM FSO link with turbulence of scintillation index SI=0.3 at a bit rate of Rb=2.4 Gbps and APD Gain G=150. 32

Fig. 2.11: Receiver sensitivity in terms of number of photons per bit at a BER of 10-9 as a function of normalized timing error ε for different PPM order with APD

gain G=150, scintillation index SI=0.3 and data rate Rb=10 Gbps.

The plots of receiver sensitivity in number of photons per bit due to timing error at a given BER of 10-9 are shown in Fig. 2.11 for PPM order 8, 16, 32, 64, 128 and 256. It is noticed that, penalty (receiver sensitivity in terms of number of photons per bit) is increases significantly at higher timing error and penalty could be reduced reasonably using higher PPM order. In this research work the best performance is achieved using PPM with order of 256.

Fig. 2.12: Plots of average BER as a function of number of photons per bit for 8-

PPM FSO link with turbulence of scintillation index SI=0.3 at a bit rate of Rb=10 Gbps and APD Gain G=150 using timing jitter variance as a parameter. 33

Fig. 2.13: Plots of average BER as function of number of photons per bit for 256-

PPM FSO link with turbulence of scintillation index SI=0.3 at a bit rate of Rb=2.4 Gbps and APD Gain G=150 using timing jitter variance as a parameter.

The plots of average BER as a function of number of photons per bit Ks are depicted in Fig. 2.12 and Fig. 2.13 for PPM order 8 and 256 and data rate 10 Gbps and 2.4 Gbps respectively in the presence of turbulence of scintillation index 0.3 using jitter variance

2 σ ε as a parameter. It is noticed that, Q-OPPM FSO System suffers due to jitter

2 variance, which is significant at high value of σ ε in presence of atmospheric turbulence. It is found that, the BER is increases with the increase of timing jitter variances in the presence of atmospheric turbulence. It is also observed from Fig. 2.12 and Fig. 2.13 that, the BER performance improves significantly when the PPM order increases from 8 to 256 keeping the other parameters same.

The plots of receiver sensitivity in number of photons per bit due to various timing jitter variance at a given BER of 10-9 are shown in Fig. 2.14 for OPPM order 8, 16, 32, 64, 128 and 256 at a data rate of 10 Gbps in presence of atmospheric turbulence. It is

2 noticed that, penalty is significant at higher jitter variance σ ε and that reduces significantly with the increase of PPM order.

Fig. 2.14: Receiver sensitivity in terms of number of photons per bit as a function of timing jitter variance for different PPM order at a BER of 10-9 using APD gain

G=150, scintillation index SI=0.3 and data rate Rb=10 Gbps.

Fig. 2.15: Penalty log10(Ks) in terms of number of photons per bit as a function of different PPM order at a BER of 10-9 and APD gain G=150 using timing jitter variance as a parameter.

The plots of power penalty in number of photons per bit due to jitter variance versus PPM order at an average BER of 10-9 are shown in Fig. 2.15. It is noticed that, penalty 35 is significant at a lower order PPM and higher jitter variance and which reduces for higher PPM order as well as lower values of jitter variances.

Fig. 2.16: Penalty log10 (Ks) in terms of photons per bit for a BER of 10-9 as a function of scintillation index for PPM order 32 with and without timing jitter variance for different timing error ε.

Fig. 2.17: Power penalty as a function of variance of scintillation for M-OPPM [128].

Plots of penalty log10 (Ks) in terms of photons per bit for a BER of 10-9 as a function of scintillation index for PPM order 32 for a given timing jitter variance and timing error as a parameter are shown in Fig. 2.16 at a bit rate of 10 Gbps and BER=10-9. It is 36 observed that, the penalty is significantly high at the higher values of scintillation index of atmospheric turbulence.

Fig. 2.18: BER versus the transmitted power per bit with APD gain G = 10 using PPM order as a parameter. All turbulence effects are taken into account [46].

The performance of FSO communication systems adopting M-PPM techniques are investigated in [43, 45, 46, 47, 65, 128-133] considering the effects of atmospheric turbulence, pointing error and influence of noises using different modulation formats and coding. In our research work, analysis and numerical evaluations have been carried out both for APD and PIN receivers following a bit different approaches, methodologies and system parameters than that of above references. The numerically evaluated performance results of our research work in terms of BER, power penalties etc. are very much comparable with the research works [46, 128-133]. For example, we have evaluated power penalty in Fig. 2.16 as a function of scintillation at a BER of 10-9 for Q-OPPM order 32 with and without timing jitter variance for different timing error as a parameter which is very much comparable with the Fig. 2.17 which is the Fig. 7 of [128]. Similarly, the BER performance results evaluated for both for PIN and APD receivers are also comparable with [46] such as Fig. 2.18 which represents Fig. 3 of [46] for PPM order of 4 to 256 using similar system parameters. The comparative study on the similar research works reported above validates the analytical results of ours. 37

2.6 Conclusions

In this chapter, an analytical development is presented to evaluate the BER performance of a Q-OPPM FSO communication system under the influence of atmospheric turbulence, scintillation index and timing jitter with Log-normal distribution considering both PIN and APD receivers. Results are evaluated at the bit rates of 2.4 and 10 Gbps using different system parameters with weak turbulence. It is seen that, both the system suffers significant power penalties due to timing jitter and atmospheric turbulences as well as scintillation index parameter. It is also found that, the effect of the jitter variance, timing error, scintillation index parameter and turbulence on BER performance can be significantly improved using higher order PPM. The numerically evaluated results are found comparable with the other similar research works and validate the analytical approach. In the next chapter we shall discuss the performance of an OCDMA FSO system through different levels of atmospheric turbulences. Chapter 3

PERFORMANCE ANALYSIS OF AN OCDMA FSO COMMUNICATION SYSTEM WITH ATMOSPHERIC TURBULENCE AND POINTING ERROR

3.1 Introduction

Atmospheric turbulence is a phenomenon occurring in free space when there are variations in the refractive index due to inhomogeneity in temperature and pressure of the atmospheric layer [81]. Therefore, atmospheric turbulent channel is highly variable, unpredictable and vulnerable to weather effect and causes fluctuations in both the intensity and the phase of the received optical signal due to variations in the refractive index along the propagation path of the FSO communication system [82]. As a result, atmospheric turbulence results in severe bit error rates due to the random fluctuations in the received signal [81, 82]. In this chapter, an analytical approaches are presented to evaluate the effect of weak atmospheric turbulence, strong atmospheric turbulence and combined effect of atmospheric turbulence and pointing error on the BER performance of OCDMA FSO communication system using optical domain CDMA encoder and SIK balanced photodetector receiver. The analysis is presented to find the expression for the signal current and MAI current and noise current at the output of the SIK direct detection receiver in presence of the effect of atmospheric turbulence of the channel. The average BER is obtained by averaging the conditional BER over the pdf of the atmospheric turbulence. The results are evaluated for different OCDMA code length, number of simultaneous user, turbulence variances and other system and FSO channel parameters.

3.2 FSO Channel Model for Strong Atmospheric Turbulence

3.2.1 FSO channel model for strong atmospheric turbulence with Gamma- Gamma distribution and pointing error

Performance of a FSO system is highly affected by pointing error and the influences of atmospheric turbulence [32]. The pointing error occurs due to imperfect pointing of photodetector to the transmitting laser source. The pointing error consists of fixed error known as boresight error, represents by A, and random error known as jitter. Jitter is superimposed over the fixed boresight error and modeled as a two dimensional random variable with independent component u and v [18]. The random sampling point has a coordinate (A+ uv , ) such that,

222 ρ =r =(Au++ ) v (3.1)

Several probability density functions have been proposed for the intensity variation of the received optical irradiance of the optical link among which the Rayleigh model, Log-normal model, Gamma-Gamma model are the most appropriate models [18, 71]. In Gamma-Gamma model the irradiance of the received optical wave is modeled as the product of two signals, such as I=Iy .Iz, where Iy arises from large scale turbulent eddies and Iz arises from small scale eddies. Specifically, Gamma-Gamma pdf is used to model both small and large scale fluctuations [66, 81, 82]. The Gamma-Gamma pdf model is the development of the Log-normal distribution. The Gamma-Gamma pdf of atmospheric turbulence conditioned on a given value of ρ is given by [18, 71, 83-86]:

(()αρ+ βρ ())/2 2(αρβρ ( ) ( )) ⎛⎞((()αρ+− βρ ())/2)1 pI(/)ρ = x ⎜⎟Is I s ⎜⎟ γραρβρI( )ΓΓ ( ( )) ( ( )) ⎝⎠γρI()

xK (()αρ− βρ ()) (2 (αρβρ ( ) ( )) Is / γ I ( ρ )) (3.2) where Is is the optical signal intensity, Г(.) is the Gamma function and Kα(ρ)-β(ρ) is the modified Bessel function of the second kind of order α(ρ)-β(ρ). Here, α(ρ) and β(ρ) are the effective number of small and large eddies of the scattering environment. These parameters can be directly related to atmospheric conditions as given by [70, 87, 88]: 40

−1 ⎡⎤⎛⎞0.49σ 2 α ()ρ =−⎢⎥exp⎜⎟x 1 ⎢⎥⎜⎟12/5 (7/6) ⎣⎦⎝⎠()11.11+ σ x −1 ⎡⎤⎛⎞0.51σ 2 ()ρβ =−⎢⎥exp⎜⎟x 1 (3.3) ⎢⎥⎜⎟12/5 (7/6) ⎣⎦⎝⎠()10.69+ σ x

2 where σ 227=1.23Ck/6L11/6,σ is the Rytov variance for strong atmospheric turbulence. C 2 xnx x n is the index of refraction structure parameter, kx is the wave number and L is the propagation link distance [84]. In weak turbulence region pdf of Is for a given ρ, approaches to the Log–normal distribution while for strong turbulence this pdf approaches to Exponential distribution. The pdf of ρ is Rician as given by [18]:

⎧ 11⎛⎞⎛⎞A ⎪ exp⎜⎟⎜⎟−+ (ρρσAI2 ) , ≠ 0 (3.4) ⎪ 22⎜⎟⎜⎟oj 2 p()ρ =⎨22σσjj⎝⎠⎝⎠ 2 σ j ⎪ δρ−=A2 σ 0 ⎩⎪ () j where σ j is the jitter standard deviation due to pointing error, Io(.) is the modified Bessel function of first kind with zeroth order and unit impulse function is defined by δ (.) . 3.2.2 FSO channel model for strong atmospheric turbulence with Exponential distribution

As the strength of turbulence increases, multiple self-interference effects must be taken into consideration due to the greater deviation from Log-normal and Gamma-Gamma statistics [56]. The radiation field of the waves can then be approximated by a zero mean Gaussian distribution, the irradiance statics are then governed by the negative exponential distribution. The negative exponential distribution is considered as a limiting distribution for the irradiance and is therefore approaches only into the saturation regime [56, 89]. In the limit of strong irradiance fluctuation where the link length spans several kilometers, the number of independent scatterings becomes large. The amplitude fluctuation of the field traversing the turbulent medium in this situation is generally believed and experimentally verified to obey the Rayleigh distribution implying negative exponential statistics for the irradiance as [90-92]. 41

1 pII1( |oo )=− exp() II / , Io > 0 (3.5) Io where E[]II= o is the mean irradiance which is often normalized to unity. It is noted that, the Gamma-Gamma turbulence model also gives the negative exponential in the limit of strong turbulence. The unconditional pdf of the irradiance is obtained as [90-

92]:

∞ pI( )= ∫ p12 ( I | Iooo ) p ( I ) dI (3.6) 0 where pI2 ()o is the distribution function of the fluctuating mean irradiance which is assumed to be Gamma distributed.

3.2.3 FSO channel model with generalized pointing error

Performance of an FSO System is highly affected by pointing error and the influences of atmospheric turbulence. As already mentioned that the pointing error occurs due to imperfect pointing of the transmitting laser source to the receiver photodetectors and is defined as radial displacement between the detector and the received light beam on the detector plane and consists of fixed error known as boresight error, and random error known as jitter. If hp represents the attenuation due to geometric spread and pointing errors then considering a Gaussian beam and a circular detection aperture of radius r, the pdf of hp can be represented as [93-95]:

⎛⎞2r 2 hrz( , )≈ A (3.7) po⎜⎟ ⎝⎠ωzeq where r is the amplitude of radial displacement at the receiver detector, z is the distance of wave propagation from the transmitter, Ao is the fraction of the collected power at r = 0, ωzeq is the equivalent beamwidth which can be expressed as [93]. Assuming a

Gaussian beam propagating through the atmospheric turbulence, the beam waist ωz can be approximated by [93]:

2 1/2 ⎡⎤⎛⎞λz

ωωzo≈+⎢⎥1 ε⎜⎟ (3.8) πω 2 ⎣⎦⎢⎥⎝⎠o 42

22 whereωo is the beam waist at z=0 and εωρ=+(1 2oo / (z )) , where

22− 3/5 ρon()zCkz= (0.55x ) with z as the coherence length. The parameters are related as [96, 97]:

22πυerf () πr 2 ωzeq===ωυ z 2 , ,Aerf0 [ ( υ )] 2υυ exp(− ) 2ωz The radial displacement vector r can be expressed as rx= [ , y]T at the receiver aperture plane, where x and y denote the displacements located along the horizontal and vertical axes at the detector plane respectively. Assuming the amplitudes are modeled as

Gaussian distributed, the amplitude of the radial displacement rrxy is, =+22and follows the Beckmann distribution as [98]:

rrr2π ⎛⎞(cosθµ−− )22 (sin θµ ) fr( )=−− x exp⎜⎟ dθ (3.9) r ∫ ⎜⎟22 222πσxy σ0 ⎝⎠ σ x σ y

222 We define the displacement coefficient s = µxy+ µ and the jitter

222 varianceσ s ==σσxy. It follows that the amplitude radial displacement has a Rician distribution. Applying a change of variable rule to (3.9), the pdf of the generalized pointing error is given by [93]: ⎛⎞s2 γ 2 exp − ⎜⎟2 ⎛⎞2 2σ 2 s ω ln(hA / ) ⎝⎠γ −1 ⎜⎟zeq p o fhhp() = 2 h p I o 2 (3.10) p γ ⎜⎟σ 2 A0 ⎝⎠

0≤≤hAp 0 where γ = ωσzeq/2 s sand Io(.) is the modified Bessel function of the first kind with order zero. When s=0, the generalized pointing error model in (3.10) specializes to the traditional pointing error model derived as [31].

2 γ γ 2 −1 fhhp( )=≤ h p , 0 hp≤ A0 (3.11) p γ 2 A0 -2 here ωz is the beam waist i. e. radius calculated at e at a distance z from the transmitter.

3.3 OCDMA FSO Communication System Model with Sequence Inverse Keying (SIK) Receiver

The block diagram of the transmitter and the balanced photodetector SIK receiver considered for analysis are shown in Fig. 3.1. In the transmitter, the user’s data are modulated either by a unipolar signature sequence or its component depending on the input bit, either ‘1’ or ‘0’. An optically switched correlator receiver based on the principle of unipolar-bipolar correlator is used in this system. Unipolar-bipolar correlation is done optically by separating the bipolar reference sequence into two complementary unipolar reference sequences. The bipolar reference sequence is correlated directly in the receiver with the channel unipolar sequence in order to recover the user’s data [12, 14, 99].

Fig. 3.1: Block diagram of OCDMA transmitter and OCDMA SIK dual photodetector receiver.

3.4 OCDMA FSO Communication System Analyses

3.4.1 Analysis of OCDMA FSO communication system with weak atmospheric turbulence

The OCDMA signal of the mth user transmitter can be expressed as:

∞ mmjtωc StmTkb( )=− 2 I .∑ agtkTxCte ( ) ( ) (3.12) k=0 m th m where IT is the average transmitted chip power, Ct() is the code of the m user, ak denotes the kth bit of the mth user, g(t) represents the pulse shape of the information bit,

Tb is the bit period and ωc is the optical carrier angular frequency.

The mth user code Ctm () is represented by:

L −1 mmc Ct( )=−∑ CptlTlc ( ) (3.13) lo=

m th th where Cl is the l chip of the m codeword, Lc is the code length (renamed as processing gain Gp), Tc represents the chip period (Tc=Tb/Lc) and p(t) denotes the pulse shape of the individual chips.

Replacing (3.13) in (3.12), Sm(t) can be represented as:

∞ Lc mm⎧⎫jtωc StmTkbl( )=− 2 I .∑∑ agtkTx ( )⎨⎬ CptlTe ( − c ) (3.14) kl==01 ⎩⎭

We consider the effect of atmospheric turbulence on the optical signal in terms of Is. The received optical signal in the presence of atmospheric turbulence is given by:

M ∞ Lc mm⎧⎫jtωc rtooskblco( )=−−+∑∑ 2 II . agtkTx ( ) ⎨⎬ ∑ CptlTe ( ) nt ( ) (3.15) mk==10 l=1 ⎩⎭ where M is the number of simultaneous user, Io is the mean received optical power and no(t) is the background optical radiation. Considering a SIK receiver, the output current of receiver for ith user can be expressed as [14]:

T L RI b M c jtω Zt( )=−−−do IagtkTx .mmii ( ). C ( t lTxCt ) ( lT )−−+ Ct ( lTe )c dtit ( ) (3.16) iskbcccn∫ ∑∑{ } 2T 0 ml==11 b where in(t) is the total noise current due to photodetector and receiver.

ii Let, ci (.){CC (.)−= (.) } which represents the bipolar form of C iiiii(.) and BA (.) o (.)=+{ 1 ba (.) (.)} / 2 , ii i ii i where c,(.) ba (.) and (.) are the bipolar form of CB(.), (.) and A (.) respectively [12, 14].

Then, Zi(t) can now be represented as:

T mm T b M Lc−1 b RIIdos⎧⎫1(+− b t lTc c )() t − lT c i Zti( )=−−+∫∫∑∑⎨⎬ xgtlTctlTdt{} out ( c ) ( c ) itdt n ( ). (3.17) 22T 0 ml==10 0 b ⎩⎭ where g out ()tgtpt= ().()and g(t) is considered as a rectangular pulse shape.

Mean value of photo current of Zi(t) for a given value of Is can be expressed as:

T b Lc−1 RIdo. I s UI(s )=−∫ ∑ g out ( t lTdt c ) (3.18) 4T 0 l=0 b

∞ 22 and, UUIpIdI= ∫ (sss ) ( ) (3.19) 0

For a given Is the variance of MAI can be represented as [12, 14]:

222(M − 1) σ MAI(IUI s )= (s ). (3.20) 3Lc

The variance of MAI can be expressed as [14]:

∞ 2 2 σσMAI= ∫ MAI(IpIdI s ) ( s ) s (3.21) 0

The variance of noise current in(t) is represented by:

2224KTBb σσσnthshot=+ = +2eB ( I sigb + I ) (3.22) RL where Isig=RdIo and Ib=RdPb, Kb is the Boltzmann constant, T is the receiver temperature in Kelvin, B is the receiver bandwidth, RL is the load resistance of the receiver, Pb is the background radiation and e is the electron charge. The signal to noise plus interference ratio (SNIR) conditioned on a given value of turbulence Is is given by:

2 UI()s ξ(Is )= 22 (3.23) σσnMAIs+ ()I

The conditional BER conditioned on a given value of Is is then given by: 1 PI( )= erfc⎡⎤ξ ( I ) / 2 2 (3.24) bs 2 ⎣⎦s The unconditional BER is then obtained as [94]:

∞ BER= ∫ Pbs( I ) p ( I s ) dI s (3.25) 0 where p(Is) represents the pdf of Is which is considered as a Gamma-Gamma distribution given by (3.2) of sub section 3.2.1.

3.4.2 Analysis of OCDMA FSO communication system with strong atmospheric turbulence

Optical CDMA signal of the mth user transmitter can be represented as:

∞ mmjtωc SmTk( t )=− 2 P .∑ a g ( t kTb ) xC ( t ) e (3.26) k =0 th m where PT is the average transmitted power. The m user code Ct ( ) is given by equation (3.13).

Using (3.13) in (3.26), Sm(t) can be represented as:

∞ Lc mm⎧⎫jtωc StmTkbl( )=− 2 P .∑∑ agtkTx ( )⎨⎬ CptlTe ( − c ) (3.27) kl==01⎩⎭

The mean irradiance I(r) at the receiver plane is modeled as [18]:

22 Ir( )=−Ω KT exp() r /2T (3.28) where the gain constant K is defined as K =WW22/ [12] and r is the distance from the T Ttr main beam center on the transverse plane. The normalized signal Is(ρ) is obtained from unnormalized signal I(r) as:

22 IIrKrsT(ργ )== ( ) γ . exp( −Ω /2T ) (3.29) 22 WW/ Ω W where γ = rtis a normalization constant and T = r /2. Wt is the effective beam

25/61/2 radius at the transmitter and WWrx=+(1 1.33σ Λ ) is the effective beam spot radius at the receiver, W is the receiver beam radius in free space, kx is the wave number used

2 as the parameter Λ = 2 L / k xW [18]. We consider the effect of atmospheric turbulence and the channel effects on the optical signal in terms of ha. The received optical signal in presence of atmospheric turbulence is given by:

M ∞ Lc mm⎧⎫jtωc rtosrakblco( )=−−+∑∑ 2 IPht . ( ) agt ( kTx ) ⎨⎬ ∑ CptlTe ( ) nt ( ) (3.30) mk==10⎩⎭ l = 1 where Pr is the mean received optical power and no(t) is the background optical radiation.

The effect of atmospheric turbulence is modeled by the received optical intensity

I(t)= Is(ρ).ha(t) and mean optical intensity is given by:

EI{ sa()ρ . ht ()} = I (3.31)

Considering a SIK receiver, corresponding to ith user, the output current of receiver can be expressed as:

T b M Lc RPdr mm Ztisakbc()=−−∫ ∑∑ IhtagtkTx. (). ( ). C( t lT ) 2 0 ml==11

⎧⎫iijtωc xCtlTCtlTe⎨⎬(−−ccn ) ( − ) dtit + ( ) (3.32) ⎩⎭ where in(t) is the receiver total noise current.

Zi(t) can be represented by (3.33) and (3.34) as [14]:

Tmm b M Lc −1 RPIhtdrs.()1()() a⎧⎫+− btlTctlT c − c Zti ()= ∫ ∑∑⎨⎬ 220 ml==10 ⎩⎭ Tb xg( t−−+ lTc )i ( t lTdt ) itdt ( ). (3.33) {}out c c ∫ n 0

T RPIh.() t b Lc −1 Zt()=−drs a gm ( t lTct )i (− lTdt ) i∫ ∑ { out c c } 4 0 l=0 T b Lc −1 2 RPIhdrs.() a t i i +−∑ g()()() t lT b t− lT ci t− lT dt ∫ {}out c c c 4 0 l=0 T T RPIh.() t b M Lc −1 b +−drs a gmmm()()()() t lT b t− lT c t− lT ci t− lT dt+ i (). t dt (3.34) ∫∫∑∑ out c{} c c c n 2 0 ml==10 0

where, gtout ()= gtht ().a ().

Mean value of photo current Zi(t) for a given value of Is and ha can be expressed as:

T b Lc −1 RPdr UI(,)s h a=−∫ ∑ Ih s. a ( t ). g out ( t lTdt c ) (3.35) 4T 0 l=0 b

∞ 2 2 and, Uh (ass )= ∫ UIh (sa , )pI() dI ( ) (3.36) 0

The variance of MAI for a given value of Is and ha is given by [12, 14]:

222(M − 1) σ MAI(Ih s , a )= U ( Ihs , a ). (3.37) 3Lc

For a given ha, the variance of MAI can be expressed as:

∞ σσ22(hIhpIdI )= ( , ) ( ) ( ) (3.38) MAI a ∫ MAI s a s s −∞

The signal to noise plus interference ratio (SNIR) conditioned on a given value of Is and ha is given by:

2 UIh(,sa ) ξ (Ihsa , )= 22 (3.39) σσnMAIsa+ (,Ih )

The conditional BER conditioned on a given value of Is and channel coefficient ha is then given by: 1 PI( , h )= erfc⎡⎤ξ ( I , h ) / 2 2 (3.40) bsa 2 ⎣⎦sa

The average BER for a given Is then is given by:

∞ PI( )= PI ( , h ) phdh ( ) (3.41) bs∫ bsa a a −∞ The unconditional BER is then obtained as:

∞ BER= P( I ) p ( I ) dI (3.42) ∫ bs s s −∞ Finally, the equation for unconditional BER can be written as:

∞∞ BER= 0.5 erfc⎡⎤ξ ( I , h ) / 2 2 . p ( h ) p ( I ) dh dI (3.43) ∫∫ ⎣⎦sa a s as −∞ −∞

3.4.3 Analysis of OCDMA FSO communication system with combined effect of atmospheric turbulence and pointing error

We consider the effect of atmosphere on the optical signal in terms of hoc(t), which represents the overall impulse response of the atmosphere which take into account the effect of atmospheric turbulence and pointing error and hoc(t) can be represented as [100-105]:

htoc( )= hh a p (3.44) where ha represent the channel effect and atmospheric turbulence and hp is the pointing error.

The received optical signal in presence of atmospheric turbulence and pointing error is given by: 49

M ∞ Lc mm⎧⎫jtωc rtorsockblco( )=−−+∑∑ 2 PI (ρ ). h ( t ) agt ( kTx ) ⎨⎬ ∑ CptlTe ( ) nt ( ) (3.45) mk==10⎩⎭ l = 1

Considering a SIK receiver, corresponding to ith user, the output current of receiver can be expressed by:

T b M Lc RPdr mm Ztisockbc()=−∫ ∑∑ I(ρ ). h (). tagtkTx ( ). C( t− lTx ) 2 0 ml==11 ii Ct()()−− lTCt − lT dt + it( ) (3.46) {}ccn

where in(t) is the receiver total noise current.

Then following reference [14], Zi(t) can be represented by (3.47) and (3.48) as:

Tmm b M Lc −1 RPIdrs().()ρ h oc t ⎧⎫ 1+−b ( t lTc c ) ( t − lT c ) Zti ()= ∫ ∑∑⎨⎬x 220 ml==10 ⎩⎭ Tb g( t−−+ lT ) ci ( t lT ) dt i ( t ). dt (3.47) {}out c c∫ n 0

T RPI().()ρ h t b Lc−1 Z() t=−drs oc gm ( t lT ) ci ( t− lT ) dt i∫ ∑ { out c c } 4 0 l=0 T b Lc−1 2 RPIdrs().()ρ h oc t i i +−xgtlTbtlTctlTdt∑ ()()()−i − ∫ {}out c c c 4 0 l=0 T T RPI().()ρ h t b M Lc−1 b +−drs oc gmmm()()()() t lT b t− lT c t− lT ci t− lT dt+ i (tdt ). (3.48) ∫ ∑∑ out c{} c c c ∫ n 2 0 ml==10 0

where, gout (tgtht )= ( ).oc ( )

Mean value of photo current Zi(t) for a given value of ρ, Is and hoc can be expressed as:

T b Lc −1 RPdr UIh(,,)ρρs oc=−∫ ∑ I s( ). htgtlTdt oc ( ). out ( c ) (3.49) l=0 4Tb 0 ∞ 2 2 and, UI (soc ,h )= ∫ U (ρρρ , Isoc ,h ) p ( ) d (3.50) 0

The variance of multiple access interference (MAI) is given by [12, 14]:

222(M − 1) σρMAI( ,Ih s , oc )= U ( ρ , Ihs , oc ). (3.51) 3Lc

For a given Is, the variance of MAI can be expressed as: 50

∞ σσρρρ22 (Ih , )= ( , Ih , ) p ( ) d (3.52) MAI s oc∫ MAI s oc 0

The signal to noise plus interference ratio (SNIR) conditioned on a given value of turbulence and given pointing error hoc is represented by:

2 UIh(,soc ) ξ(Ihsoc , )= 22 (3.53) σσnMAIsoc+ (,Ih ,)

The conditional BER conditioned on a given value of atmospheric turbulence and pointing error hoc is then presented by: 1 PI( , h )= erfc⎡⎤ξ ( I , h ) / 2 2 (3.54) bsoc 2 ⎣⎦soc

The average BER for a given Is then is given by:

∞ PI( )= PI ( , h ) ph ( ) dh (3.55) bs∫ bsoc ococ −∞ where p(hphphoc )= ( p ). ( a ) . The pdf of hp is given in (3.11). The unconditional BER is then obtained as: ∞ BER= P( I ) p ( I ) dI (3.56) ∫ bs s s −∞ Finally, the equation for unconditional BER can be written as:

∞∞ BER= 0.5 erfc⎡⎤ξ ( I , h ) / 2 2 . p ( h ) p ( I ) dh dI (3.57) ∫∫ ⎣⎦soc oc s ocs −∞ −∞

If we consider ha=1.0 i.e. no other channel effect is present then hhoc== p and phph (oc ) ( p ) .

3.5 Results and Discussions

Following the analytical approaches presented in section 3.4, the BER performance results of an OCDMA FSO communication system with SIK receiver are evaluated numerically at a data rate of 1 Gbps for different system parameters taking the effect of weak and strong atmospheric turbulence as well as the effect of pointing error into consideration. The value of ha is considered to be unity for this calculation. The system parameters used for numerical computations are given in Table 3.1: 51

Table 3.1: System Parameters

Parameter Symbol Value Data rate Rb 1Gbps Receiver bandwidth B 1 GHz Responsivity Rd 0.85 A/W Receiver temperature T 300 0K Load resistance of receiver RL 50 Ω -23 Boltzmann’s constant Kb 1.38x10 W/K/Hz Electron charge e 1.6x10-19 C Normalized beamwidth ωz/r 1-10

Effective beam radius at the transmitter Wt 20 cm Effective beam spot radius at the receiver Wr 50 cm Detector aperture radius R 20 cm Operating wavelength ߣ 1550 nm Link distance L 500-5000 m Rytov variance (strong turbulence) 2 0.0559-3.8081 σ x 2 -14 Index of refraction structure Cn 10 Number of user M 1 – 128 Code length (processing gain) Lc (Gp) 8 – 1024 Normalized pointing error standard deviation σs/r 0.2 - 2.5 Power penalty at BER - 10-6 and 10-9 Atmospheric turbulent variance (weak 2 0.01 to 0.3 σα turbulence) Background current Ib 10 nA

3.5.1 Performance of OCDMA FSO communication system with weak atmospheric turbulence

The plots of BER as a function of received optical signal intensity are depicted in Fig. 3.2 and Fig. 3.3 for processing gain 256 and 1024 respectively for data rate 1 Gbps and

2 atmospheric turbulence variance σ x =0.01 using number of simultaneous user M as a parameter. It is noticed that, the BER of the FSO communication system suffers due to the effect of MAI with increase in number of user in presence of atmospheric turbulence. It is also noticed that, BER performance improves significantly with the increase in processing gain but again degrades with the increase number of simultaneous user. Further, it is noticed that BER floor starts to occur at a higher 52 number of user when processing gain increased from 256 to 1025 as depicted in Fig. 3.2 and Fig. 3.3.

Fig. 3.2: BER vs. average received optical intensity Io(dBm) with code length 2 Gp=256, atmospheric turbulence variance σ x =0.01 and data rate Rb=1 Gbps using number of user M as a parameter.

Fig. 3.3: BER vs. average received optical intensity Io(dBm) with code length

2 Gp=1024, atmospheric turbulence variance σ x =0.01 and data rate Rb=1 Gbps using number of user M as a parameter. 53

Fig. 3.4: BER vs. average received optical intensity Io(dBm) with code length 2 Gp=512, atmospheric turbulence variance σ x =0.1 and data rate Rb=1 Gbps using number of user M as a parameter.

Fig. 3.5: BER vs. average received optical intensity Io(dBm) with code length 2 Gp=512, atmospheric turbulence variance σ x =0.2 and data rate Rb=1 Gbps using number of user M as a parameter.

The plots of BER as a function of received optical signal intensity are depicted in Fig. 3.4 and Fig. 3.5 with the processing gain 512 for data rate 1 Gbps in presence of

2 2 atmospheric turbulence variances ofσ x = 0.1 and σ x = 0.2 respectively using number of simultaneous user M as a parameter. It is observed that, BER of the system degrades 54 with the increase of atmospheric turbulence variances for the same system parameters. It is further noticed that, the BER floor degrades with the increase in turbulence variance for the higher number simultaneous of user.

Fig. 3.6: BER vs. average received optical intensity Io(dBm) for number of user 2 M=8, atmospheric turbulence variance σ x =0.1 and data rate Rb=1 Gbps using code length Gp as a parameter.

Fig. 3.7: BER vs. average received optical intensity Io(dBm) for number of user M=8, code length Gp=512 and data rate Rb=1 Gbps using atmospheric turbulence variance as a parameter. 55

The plots of BER as a function of received optical signal intensity for with processing gain Gp as a parameter are shown in Fig. 3.6 for number of user M=8 and data rate 1

Gbps. The performance results in terms of BER as a function of Io(dBm) with respect to turbulence variances are depicted in Fig. 3.7 for M=8, Gp=512 and data rate 1 Gbps. It is noticed that the FSO system suffers due to atmospheric turbulence and the improvement of the system performance can be achieved by using higher processing gain.

Fig. 3.8: Power penalty vs. number of simultaneous user with code length Gp=512 -9 and data rate Rb=1 Gbps at a BER of 10 using atmospheric turbulence variance as a parameter.

Plots of power penalty as a function of number of simultaneous user with the

2 atmospheric turbulence variance of σ x =0.01 to 0.3 with the processing gain Gp=512 -9 and data rate Rb=1 Gbps at a BER of 10 are shown in Fig. 3.8. It is noticed that, the penalty is significant for higher number of simultaneous user and also for the higher turbulence variance. For a given number of user, the penalty due to atmospheric turbulence is found to be of the order of 1 dB to 8 dB for M=8 and increased to 3 dB to 10 dB for M=12 at a BER=10-9 with variance ranging from 0.01 to 0.3 respectively.

3.5.2 Performance of OCDMA FSO communication system with strong atmospheric turbulence

The plots of BER versus received optical power Pr(dBm) are depicted in Fig. 3.9 for Rytov variance 0.0559, link length 500 m and code length 256 with number of user as a parameter at a bit rate of 1 Gbps considering the effect of strong atmospheric turbulence. It is noticed that, the BER increases abruptly with increase in number of user M and system suffers BER floor due to the effect of MAI in presence of optical channel effect. The similar plots for link length of 1000 m with corresponding Rytov variance 0.1998 are depicted in Fig. 3.10 for code length Gp=256. It is also noticed that, BER performance further deteriorated with the increases of link length using the same parameters.

Fig. 3.9: BER vs. average received optical power Pr(dBm) at a link length of L=500 m corresponding to the Rytov variance=0.0559 and code length Gp=256 with number of user M as a parameter.

Fig. 3.10: BER vs. average received optical power Pr(dBm) at a link length of L=1000 m corresponding to the Rytov variance=0.1992 and code length Gp=256 with number of user M as a parameter.

Fig. 3.11: BER vs. average received optical power Pr(dBm) at a link length of L=500 m corresponding to the Rytov variance=0.0559 and code length Gp=512 with number of user M as a parameter.

The plots of BER versus received optical power Pr(dBm) are depicted in Fig. 3.11 and Fig. 3.12 for link length 500 m and 1000 m respectively using processing gain 512 at a bit rate of 1 Gbps with number of user as a parameter. It is noticed that, the BER have increased abruptly with increase in number of user M as well as link length L and system suffers BER floor due to the effect of MAI in presence of atmospheric 58 turbulence. Comparing Fig. 3.9 and Fig. 3.10 with Fig. 3.11 and Fig. 3.12 it noticed that, there is a significant improvement in BER performance when the code length is increased from 256 to 512.

Fig. 3.12. BER vs. average received optical power Pr(dBm) at a link length of L=1000 m corresponding to the Rytov variance=0.1992 and code length Gp=512 with number of user M as a parameter.

The variation of BER with number of simultaneous user M at a given received optical power Pr=-10 dB are depicted in Fig. 3.13 for code length ranging from 64 to 1024 corresponding to link distance of 500 m and 1000 m. The figure clearly shows the deterioration in BER performance with increase in Rytov variance which accounts for the effect of turbulence as well as link distance. Further, the improvement in BER due to increase in code length is also clearly depicted in the Fig. 3.13. BER floor is significantly noticed due to the increase of number of simultaneous user in the presence of MAI and atmospheric turbulence.

The power penalty suffered by the system due to atmospheric turbulence at a given BER of 10-9 and bit rate of 1 Gbps are shown in Fig. 3.14 as a function of link distance (Rytov variance) for code length of 512 and number of user M=2, 4, 8 and 16. It is found that, the penalty ranges from 9 dB to 11.5 dB as number of user increases from 2 to 16 at a link distance 3000 m which and can be substantially reduced by increasing the 59 code length. It is also observed during research work that, power penalty increases significantly with the increase of number of simultaneous user M, like 32, 64, 128 etc.

Fig. 3.13: Variation of BER with number of user, M at Pr= -10 dBm for code length Gp=64, 128, 256, 512 and 1024 and link length L= 500 m and 1000 m respectively.

Fig. 3.14: Power penalty due to MAI in presence of atmospheric turbulence as a function of link distance L at a BER = 10-9 and code length Gp=512 with number of user as a parameter.

Fig. 3.15: Plots of maximum allowable number of user as a function of code length -6 Gp at a BER of 10 and Pr= -10 dBm with link length L=500 m, 1000 m and 1500 m respectively.

The allowable number of simultaneous user at a BER=10-6 are depicted in Fig. 2.15 as a function of code length with the link distance (Rytov variance) as a parameter. It is clearly noticed that, the allowable number of simultaneous user can be greatly increased by increasing the code length at a given data rate and link distance. However, there is significant reduction in the number of user due to atmospheric turbulence at higher link distance as well as higher values of Rytov variance which is the function of link distance.

3.5.3 Performance of OCDMA FSO communication system with combined effects of atmospheric turbulence and pointing error

The BER performance results of a SIK OCDMA FSO communication system are evaluated numerically for different system parameters taking the combined effect of atmospheric turbulence and pointing error into consideration. The plots of BER versus received optical power Io(dBm) are depicted in Fig. 2.16 for Rytov variance 0.0559, link length 500 m and processing gain 1024 and number of user 32 using normalized pointing error as a parameter at a bit rate of 1 Gbps. It is noticed that, the BER increases significantly with increase of pointing error. The similar plots for link length of 1000 m for processing gain 256 and number of user 16 are depicted in Fig. 3.17. It is also noticed that, BER increases abruptly with the decrease of processing gain from 1024 to 61

256 and increase of pointing error and atmospheric turbulence even the number of user is reduced to 16 from 32 as in Fig. 3.16. The system suffers from BER floor due to the effect of MAI in presence of optical channel effects. It is note worthy that, the BER performance results significantly improves with the increase of processing gain which are depicted in Fig. 3.16 with processing gain of 1024 and in Fig. 3.17 with processing gain of 256.

Fig. 3.16: BER as a function of received optical intensity Io(dBm) with link length L=500 m corresponding to the Rytov variance=0.0559, code length Gp=1024,

number of user M =32 at a data rate Rb=1 Gbps using normalized pointing error standard deviation as a parameter.

Fig. 3.17: BER as a function of received optical intensity Io(dBm) with a link length L=1000 m corresponding to the Rytov variance=0.1992, code length Gp=256,

number of user M=16 at a data rate Rb=1 Gbps using normalized pointing error standard deviation as a parameter. 62

Fig. 3.18: BER as a function of received optical intensity Io(dBm) with a link length L=1500 m corresponding to the Rytov variance=0.4189 and code length Gp=512

with number of user M=16, data rate Rb=1 Gbps using normalized pointing error standard deviation as a parameter.

Fig. 3.19: BER as a function of received optical intensity Io(dBm) with a link length L=1500 m corresponding to the Rytov variance=0.4189 and code length Gp=512

with number of user M=32, data rate Rb=1 Gbps using pointing error standard deviation as a parameter.

The plots of BER versus received optical intensity Io(dBm) are depicted in Fig. 3.18 and Fig. 3.19 at the link length of 1500 m corresponding to the Rytov variance 0.4189, code length 512 and number of user 16 and 32 respectively using normalized pointing error 63 as a parameter at a bit rate of 1 Gbps. It is noticed that the BER degrades significantly with the increase of number of user 16 to 32, for the same link length and the channel effects.

Fig. 3.20: BER as a function of received optical intensity Io(dBm) with a link length L=2000 m corresponding to the Rytov variance=0.7098 and code length Gp=1024,

number of user M=32, data rate Rb=1 Gbps and normalized pointing error standard deviation as a parameter.

Fig. 3.21: BER as a function of received optical intensity Io(dBm)with a link length L=3000 m corresponding to the Rytov variance=1.4928 and code length Gp=1024,

number of user M=32, data rate Rb=1 Gbps using normalized pointing error as a parameter. 64

The plots of BER versus received optical signal intensity Io(dBm) are depicted in Fig. 3.20 for a link length of 2000 m corresponding to Rytov variance 0.7098 and Fig. 3.21 for link length of 3000 m corresponding to Rytov variance 1.4928 using code length 1024, number of user 32 and normalized pointing error as a parameter at a bit rate of 1 Gbps. It is noticed that, the BER increases with the increase of link distance with corresponding Rytov variances even all other parameters are constant.

It is noticed form Fig. 3.21 and Fig. 3.22 that, the BER performance significantly depends on the link length, Rytov variance, processing gain and number of simultaneous user in presence of the combined effects of pointing error and atmospheric turbulence with same bit rate. BER performances significantly improve with the increases of processing gain but performance detoriated with the increase of link length and number of simultaneous user. It is evident that, the BER floor is significantly reduced with increase of code length. Similar results are also observed form Fig. 3.16 to Fig. 3.20.

BER performance results with the increase of number of simultaneous user M for code length Gp=512 and link length L=1500 with corresponding Rytov variance=0.4189 at a receive optical intensity 10dB and data rate 1 Gbps are shown in Fig. 3.23 using normalized pointing error is as the parameter. It is clearly noticed that, the BER increases with the increase of number of user as well as the normalized pointing error for a given link length, Rytov variance and code length. It is also noticed that, the BER floor is significant when the user number is more than 30 due to the combined effect of atmospheric turbulence and pointing error as well as MAI.

BER performance results with the increase of link length with corresponding Rytov variances for code length Gp=1024 at a receive optical intensity 10dB and data rate 1

Gbps are shown in Fig. 3.24 using normalized pointing error σs/r and number of simultaneous user M are used as the parameter. It is clearly noticed that, the BER increases significantly with the increase of link length to the corresponding Rytov variances. It is also noticed that the BER performance depends on number of user in presence of atmospheric turbulence and pointing error for a given link length, Rytov variance and code length. It is also noticed that, the BER floor is significant when the 65 link length is more than 2000 m and Rytov variance is more than 0.7098 due to the combined effect of atmospheric turbulence and pointing error as well as MAI.

Fig. 3.22: BER as a function of received optical intensity Io(dBm) at a link length L=4000 m corresponding to the Rytov variance=2.5294 and code length Gp=512,

number of user M=16, data rate Rb=1 Gbps using normalized pointing error as a parameter.

Fig. 3.23: BER as a function of number of user M for code length Gp=512 and link

length L=1500 m at a Pr(dBm)=10 and data rate Rb=1 Gbps.

Link distance L

Fig. 3.24: BER as a function of link distance L at Io(dBm)=10 dB for code length Gp=1024, number of user M=4, 8, 16, 32 and 64 with normalized jitter standard deviation σs/r =1.0, 1.3, 1.5, 1.8 and 2.0 respectively.

Fig. 3.25: Power penalty vs. normalized jitter standard deviation σs/r for code length Gp=1024 and link length L=500 m M=4, 8, 16 and 32 respectively at a BER=10-9 and data rate Rb=1 Gbps.

Fig. 3.26: Power penalty vs. normalized jitter standard deviation σs/r for code length Gp=1024 and link length L=1000 m M=4, 8, 16 and 32 respectively at a BER=10-9 and data rate 1 Gbps.

The power penalty suffered by the system due to atmospheric turbulence, pointing error and MAI at a given BER of 10-9 and bit rate of 1 Gbps are shown in Fig. 3.25 and Fig. 3.26 for a link length 500 m and 1000 m respectively for a code length 1024 and data rate 1Gbps with number of user M=4, 8, 16 and 32. Form Fig. 3.25 it is found that, the penalty ranges from 8 dB to 11 dB for a link distance L=500 m and σs/r=1.0. Similarly, from Fig. 3.26, penalty ranges from 12.5 dB to 18 dB for a link distance L=1000 m and

σs/r=1.0 since number of user increases from 4 to 32. Further, it is found from the research work that the power penalty increases as the link distance increase upto 4000 m.

Almost similar performance results have been observed from the previous research works though the research works in the field of OCDMA FSO communication system through the atmospheric turbulence channel is limited. The analytical approaches, modulation formats, numerical evaluation methods and system parameters used in all the previous research works are in a close proximity to that of we used in our research works. The numerical results presented in [12, 14, 36, 64, 71, 87] using different approaches and similar system parameters are very close to the results obtained in our analytical approaches for weak atmospheric turbulence, strong turbulence and the combined influence of atmospheric turbulence and pointing error. For example, BER 68 performance results shown in Fig. 3.27 (Fig. 3 of [71]) for different turbulence regimes using number of simultaneous user K=1, 25, 45 are very much comparable with our numerical evaluated results which validated our analytical approaches.

Fig. 3.27: Variation of the average BER performance versus received optical power Pr with single user and multiple users interfering within all of the turbulence regimes [71].

Effects of pointing error on the FSO communication system in the presence of atmospheric turbulence have been investigated in [94, 96, 100, 115]. The combined effect of pointing error and storing atmospheric turbulence has been reported in [43, 100, 103]. The approaches we presented for OCDMA FSO link in presence of pointing error and atmospheric turbulence proved better and significantly improved performance results. The performance results for OCDMA FSO system in presence of pointing error and atmospheric turbulence are found to be in good conformity with those reported in the above references.

3.6 Conclusion

An analytical approach is presented to evaluate the BER performance limitations of an OCDMA FSO system due to effect of weak turbulence, strong turbulence and combined effect of pointing error and atmospheric turbulence with SIK dual photodetector receiver. The results show that, the system suffers from power penalty and degradation of BER significantly due to the effect of weak atmospheric turbulence, strong 69 atmospheric turbulence and combined effect of atmospheric turbulence and pointing jitter effect. Power penalty suffers by the system can be substantially reduced by using longer code length and shorter link distance. For example, in case of strong turbulence the penalty is found to be 9 dB and 11.5 dB for link distance 3000m with user number 2 and 16 respectively at a BER=10-9. And in case of weak turbulence, power penalty is 3 dB to 10 dB at a BER of 10-9 for 12 numbers of user at 1 Gbps corresponding to turbulence variance 0.01 to 0.3 respectively. Similarly for the combined influence of atmospheric turbulence and pointing error, penalty ranges from 12.5 dB to 18 dB for a link distance L=1000m and σs/r=1.0 as number of user increases from 4 to 32. However, the penalty can be reduced significantly by increasing the processing gain and reducing the link distance. Effect of cloud, fog and pointing error on the OCDMA FSO link will be presented in the coming chapter.

Chapter 4

EFFECT OF CLOUD, FOG AND POINTING ERROR ON THE PERFORMANCE OF AN OCDMA FSO COMMUNICATION SYSTEM

4.1 Introduction

Cloud and Fog being part of optical communication channel, causes temporal widening and attenuation of the optical pulse power and imposes limitations on the maximum transmission bandwidth [20-23]. Laser beam pointing is also critical for active tracking, designation and free space communications etc. In this chapter, analysis is carried out for an OCDMA system over FSO channel considering the effect of cloud, fog and pointing error between the transmitter and the receiver using optical domain encoder and SIK balanced photodetector direct detection receiver. The analysis is carried out to find the expression for the signal current and MAI current at the output of the SIK receiver in presence of cloud and fog in the channel and the effect of pointing error. The BER performance results are evaluated for different cloud thickness, fog optical thickness and different values of normalized jitter standard deviation, channel parameters, code lengths, number of simultaneous user and other system parameters.

4.2 Transfer Function of Cloud in a FSO Communication system

Optical pulses propagating through different form of clouds experiences temporal distortions and the temporal impulse response h(t) of cloud is defined by the double gamma function as [20]:

ht( )=+ k ( c ) te .−−kct21() k ( c ) te .kct41() ut ( ) (4.1) { 11 31 }

-2 where unit of h(t) is in per unit area (m ); k1, k2, k3 and k4 are the gamma function constant and depends on c1 which is the physical characteristics of the optical channel such as geometrical cloud thickness, wavelength of the radiated optical pulse, refractive index and the size distribution of the particulates and u(t) is the unit step function. 71

[ The optical pulse received by the receiver becomes broadened due the scattering effect of the cloud and thereby reduces the optical system bandwidth. The transfer function of the temporal frequency is evaluated from the temporal impulse response [20, 106] as:

∞ Hf()= ∫ hte( )(2− jftπ ) dt (4.2) −∞ where f is the temporal frequency derived from temporal impulse response.

Substituting (4.1) in (4.2) and integrating we get:

⎡⎤kc11() kc31() Hf( )=+⎢⎥22 (4.3) {()kc++ j 2ππ f )}{() kc j 2 f )} ⎣⎦21 41 The general transfer function of cloud can be derived from (4.3) [20] as:

⎪⎪⎪⎪⎪⎪⎪⎪⎧⎫⎧⎫⎛⎞fb−+ ⎛⎞ fb⎧⎫⎧⎫⎛⎞ f ⎛⎞ f Hf( )=+ G⎨⎬⎨⎬⎨⎬⎨⎬ 1 j⎜⎟ 1 + j ⎜⎟ 1 + j⎜⎟ 1 + j ⎜⎟ (4.4) ff ff ⎩⎭⎩⎭⎪⎪⎪⎪⎝⎠33 ⎝⎠⎩⎭⎩⎭⎪⎪⎪⎪⎝⎠ 12 ⎝⎠ where the parameters used in above equations can be represented as:

kk24 kk14+ kk 23 ff12==, and f 3 = (4.5) 22ππ 2() πkk13+

4(ππ22kk++ ) 4(kk ) bGk==13f22 and 13 (4.6) ()kk 2 332 24 ()kk24

4.3 Transfer Function of Fog and Channel Model

Fading of a received optical signal in an optical wireless channel is caused by absorption and spatial and temporal widening of radiation propagation in a multiple scattering. A wide accepted good model for the temporal impulse response of an optical wireless channel through fog is the double gamma function as [24]:

htfo( )= [] kt1234 exp(- ktkt )+ exp(- ktPut ) ( ) (4.7) where ki are the gamma function parameters, which are derived from experiments or simulation results; u(t ) is a unit step function and Po is the power loss due to beam divergence, optics imperfection and scintillation effects. The impulse response parameters are function of the characteristics of fog as well as the receiver and transmitter characteristics. A standard measure of fog thickness is the optical thickness

τ, expressed as τ=kextR, where kext is the scattering extinction coefficient and R is the physical thickness of fog. The optical wireless channel transfer function can be evaluated by Fourier transforming the impulse response of (4.7) as [24]: 72

∞ Hhtjtdt(ωω )=− ( )exp( ) (4.8) ff∫ 0 Substituting (4.7) in (4.8) and integrating we get:

⎡⎤k1 k3 HPfo()ω =+⎢⎥22 (4.9) ⎣⎦()()kj14−−ωω kj

When the characteristics of fog changes the fog transfer function also changes, which alters the oscillation frequency. The advantages of this system are that, the fog parameters can be directly measured and that high values of optical thickness can be dealt with. The channel power loss is described by the following formula:

⎛⎞k1 k3 HPfo(0) =+⎜⎟22 (4.10) ⎝⎠kk24 It is convenient to use a normalized impulse response model hf(t) with a power loss of unity to investigate temporal dispersion of the channel. The temporal dispersion of an optical wireless channel can be expressed by the channel rms delay spread D, calculated from (4.7), as [24]:

1/2 ⎡⎤∞ ()()thtdt− µ 22 ⎢⎥∫ f D = ⎢⎥−∞ (4.11) ⎢⎥∞ htdt2 () ⎢⎥∫ f ⎣⎦−∞ where the mean delay µ is given by [24]

∞ ⎡⎤2 ⎢⎥∫ th() t dt µ = ⎢⎥−∞ (4.12) ⎢⎥∞ ⎢⎥∫ htdt2 () ⎣⎦−∞

Using (4.7) in (4.11) and (4.12), mean delay µ and rms delay spread D can be derived by (4.13) and (4.14) as: ⎡⎤k 2 kkk2 32 3 1 ++313 ⎢⎥kk44() kk+ 4 µ = ⎣⎦24 24 (4.13) 2 2 ⎡⎤k1 kkk31316 2 ⎢⎥33++ 3 ⎣⎦kk24() kk 24+

⎛⎞kkkkkk22[3+−µµ ( 3)] [ 3 +−µµ ( 3)] ⎜⎟122344+ ⎡⎤k 2 kkk2 16 kk55 Dx=++1 313⎜⎟24 (4.14) ⎢⎥33 3⎜⎟ ⎣⎦kk24() kk 24+ 16kk13{} 12++µµ ( kk 24 )[ ( kk 24 +− ) 6] ⎜⎟+ ⎜⎟5 ⎝⎠()kk24+

The normalized delay spread DT, is defined as the rms delay spread divided by the bit duration and is a dimensionless parameter.

4.4 System Model of OCDMA FSO Communication system with SIK Receiver

The key issue to implement OCDMA communication and networking is the encoding and decoding techniques to generate and recognize appropriate code sequences reliably. The block diagram of a transmitter and a SIK direct detection receiver for the OCDMA system over a cloudy or foggy FSO channel are shown in Fig. 4.1.

Fig. 4.1: Block diagram of an optical CDMA (OCDMA) transmitter and SIK dual photodetectors direct detector receiver over a cloudy/foggy channel.

In the transmitter, the user’s data are modulated either by a unipolar signature sequence or its component depending on the bit either ‘1’ or ‘0’. An optically switched correlator receiver based on the principle of unipolar-bipolar correlator is used in this system. The bipolar reference sequence is correlated directly in the receiver with the channel unipolar sequence in order to recover the user’s data.

4.5 System Analysis

4.5.1 Analysis of OCDMA FSO communication system with effect of Cloud

The OCDMA signal of the mth user transmitter can be represented as:

∞ mmjtωc SmTkb( t )= 2 P .∑ a g ( t - kT ) xC ( t ) e (4.15) k =0 m th where PT is the average transmitted power, Ct() represents the code of the m user,

m th th ak represents the k bit of the m user, g(t) is the pulse shape of the information bit, Tb th is the bit period and ωc is the optical carrier angular frequency. The m user code Ctm ()is given by:

L −1 mmc Ct( )=−∑ CptlTlc ( ) (4.16) lo= m th th where Cl represents the l chip of the m user codeword, Lc is the code length

(processing gain, Gp), Tc is the chip period (Tc=Tb/Lc) and p(t) is the pulse shape of the individual chip.

Using (4.16) in (4.15), Sm(t) can be represented as:

∞ Lc mmjtωc StmTkblc( )= 2 P .∑∑ agtkTxCptlTe. ( - ) ( - ). (4.17) kl==01

The optical signal corresponding to mth user at the output of the cloud with impulse response h(t) can be expressed as:

∞ Lc mm jtωc YtmTkbl( )=− 2 P .∑∑ agtkTxC ( )[] ptlT ( −⊗ c ) hte ( ) . (4.18) kl==01

The equation (4.18) can be rewritten as:

∞ Lc mmjtωc YtmTkbloutc( )=− 2 P .∑∑ agtkTxCp ( ) ( tlTe − ). (4.19) kl==01

where pout ()t =⊗p ()th(t) which represents the chip shape at the receiving end of the cloud.

[ The received optical signal with the effect of cloud is then given by:

M ∞ Lc mm⎧⎫jtωc rto( )=−∑∑ 2 P r . agtkTx k ( b ) ⎨⎬ ∑ Cp l out ( t −+ lTe c ) nt b ( ) (4.20) mk==10 ⎩⎭ l=1 75 where M represents the total number of simultaneous user, Pr is the mean received power and nb(t) represent the background optical radiation. Considering a SIK correlator receiver, corresponding to ith user, the output current of receiver can be expressed as:

T RP b M Lc Zt() =−dr agtkTxmmii( ). Cp ( t −−−−+ lTxCt ) ( lT ) Ct ( lTdtit ) ( ) (4.21) i∫ ∑∑ k b l out c{ c c} n 2 0 ml==11 where in(t) is the noise current due to photodetector and receiver.

Then following reference [12, 14], Zi(t) can be represented by:

T mm T b M Lc−1 b Rdr P⎧⎫1(+− b t lT c )() c t − lT c i Ztio( )=−−+∫∫∑∑⎨⎬ xptlTctlTdt{}ut (c ) (c ) itdtn ( ). (4.22) 220 ml==10⎩⎭ 0

Equation (4.22) can be rewritten as:

TTLL−−11 RP bbccRP 2 Z() t =−−+−−−dr pmi ()() t lT c t lT dt dr pi()()() t lT b i t lT ci t lT dt i ∫∫∑∑{}out c c {}out c c c 4400ll==00 T T b M Lc−1 b RPdr mmmi +−−−−+∫∫∑∑pout( t lT c ){} b ( t lTc ) c ( t lTc ) c ( t lTc ) dt in ( t ). dt (4.23) 2 0 ml==10 0

Mean value of photo current Zi(t) can be expressed as:

T b Lc −1 RPdr UptlTdt=−∫ ∑ out( c ) (4.24) l=0 4Tb 0 The variance of multiple access interference (MAI) is given by [12, 14]:

222(M − 1) σ MAI = U . (4.25) 3Lc

The variance of noise current in(t) can be expressed as:

2224KTBb σσσnthshot=+ = +2eB ( I sigb + I ) (4.26) RL where Isig=RdPr and Ib=RdPb, Kb is the Boltzmann constant, T is the receiver temperature in Kelvin, B is the receiver bandwidth, RL is the load resistance of the receiver, Pb is the background radiation and e is the electron charge.

[ ] The signal to noise plus interference ratio (SNIR) is then given by: U 2 ξ = 22 (4.27) σσnMAI+

The BER is then given by: 1 BER= erfc ⎡⎤ξ / 2 2 (4.28) 2 ⎣⎦

4.5.2 Analysis of OCDMA FSO communication system with effect of Fog

We use equations (4.15) to (4.17) for the further analysis to evaluate the expression for BER. The optical signal corresponding to mth user at the output of the fog with impulse response hf(t) can be expressed as:

∞ Lc mm⎡⎤jtωc Ytmf( )=− 2 P T .∑∑ agtkTxCptlThte k (b ) l ( −⊗ )f ( ) . (4.29) kl==01⎣⎦c

Equation (4.29) can be rewritten as:

L ∞ c jtω mmc Ytmf( )=− 2 P T .∑∑ agtkTxCptlTe k ( b ) l f ( − c ). (4.30) kl==01

where ptff()=⊗ pt () h(t) which represents the chip shape at the receiving end of the cloud.

[ The received optical signal with the effect of fog is then given by:

L M ∞ ⎧⎫c jtω mm⎪⎪c rtorkblfb( )=−∑∑ 2 P . agtkTx ( ) ⎨⎬ ∑ Cp ( t −+ lT ) e nt ( ) (4.31) mk==10 ⎩⎭⎪⎪ l =1 c

Considering a SIK correlator receiver, corresponding to ith user, the output current of receiver can be expressed as:

T L RP b M c Zt() =−−−−−+d r agtkTxmm( ). Cpt ( lTxCtlTCt )ii ( ) ( lTdtit ) ( ) (4.32) i ∫ ∑∑kblfc{ c cn} 2 0 ml==11 where in(t) is the noise current due to photodetector and receiver.

Mean value of photo current Zi(t) can be expressed as:

T L −1 b c RPdr UptlTdt=−∫ ∑ f (c ) (4.33) 4Tb 0 l=0 The variance of multiple access interference (MAI) is given by [12, 14]:

222(M − 1) σ MAI = U . (4.34) 3Lc

The variance of noise current in(t) can be expressed as:

2224KTBb σσσnthshot=+ = +2eB ( I sigb + I ) (4.35) RL The signal to noise plus interference ratio (SNIR) is given by: U 2 ξ = 22 (4.36) σσnMAI+

The BER is then given by [94]:

1 BER= erfc ⎡⎤ξ / 2 2 (4.37) 2 ⎣⎦

4.5.3 Analysis of OCDMA FSO communication system with effect of pointing error

We consider the effect of pointing error on the optical signal in terms of hp as (1.14) of chapter 1. The received optical signal with pointing error is then given by:

M ∞ Lc mm⎧⎫jtωc rtorpkblcb( )=−−+∑∑ 2 Ph . agtkTx ( ) ⎨⎬ ∑ CptlTe ( ) nt ( ) (4.38) mk==10 ⎩⎭ l=1

Considering a SIK correlator receiver, corresponding to ith user, the output current of receiver can be expressed as:

T RP b M Lc Zt( )=−−−dr h . agtmmii ( kTx ). C ( t lTxCt ) ( lT )−−+ Ct ( lTdtit ) ( ) (4.39) ipkbcccn∫ ∑∑{ } 2 0 ml==11

Then, Zi(t) can be represented by:

T mm T b M Lc−1 b RPdr. h p ⎧⎫1(+−b t lTcc )() c t − lT i Zti()=−−+∫∫∑∑⎨⎬ xgtlTctlTdt{} out ()()(). c c itdt n (4.40) 220 ml==10⎩⎭ 0

Equation (4.40) can be rewritten as:

LL−−11T RP. h Tb ccRPh. b Z ()t dpr gmi ()() tlTctlTdt dr p g i ()()() tlTbtlTctlTdt ii 2 i=−−+−−−∫∫∑∑{} out c c{} out c c c 440 ll==000 Tb M L −1 Tb RPdr. h p c mmmi +−−−−+∫∫∑∑gout( t lT c ){} b ( t lT c ) c ( t lT c ) c ( t lT c ) dt i n ( t ). dt (4.41) 2 0 ml==10 0

Mean value of photo current Zi(t) for a given value hp can be expressed as: T b Lc −1 RPdr Uh()pp=−∫ ∑ h. gout ( t lTdtc ) (4.42) l=0 4Tb 0

The variance of multiple access interference (MAI) for a given value hp is given by [87]:

222(M − 1) σ MAI(hUh p )= (p ). (4.43) 3Lc

The signal to noise plus interference ratio (SNIR) conditioned on a given value of the channel coefficient hp is given by:

2 Uh()p ξ (hp )= 22 (4.44) σσnMAIp+ ()h

The conditional BER conditioned on a given value of channel coefficient hp is then given by:

1 Ph( )= erfc⎡⎤ξ ( h ) / 2 2 (4.45) bp 2 ⎣⎦p Finally, the average unconditional BER can be evaluated as:

∞ BER= 0.5 erfc⎡⎤ξ ( h ) / 2 2 . p ( h ) dh (4.46) ∫ ⎣⎦ppp 0 where p(hp) represents the pdf of pointing error hp as given by (3.11) of chapter 3.

4.6 Results and Discussions

4.6.1 Performance of OCDMA FSO communication system with effect of Cloud

Following the analytical approach presented in section 4.5, the BER performance results of a SIK OCDMA FSO communication system through clouds and fog are evaluated numerically for different system parameters taking the effect of cloud thickness, fog thickness (optical thickness), number of simultaneous user, code length and wavelength of transmitted optical waves into consideration. Similarly, the performance results of OCDMA FSO communication system are evaluated numerically for different system parameters taking into account the effects of pointing error. The system parameters used for evaluation are given in the following Table 4.1 and Table 4.2: 79

Table 4.1: System Parameters Parameter Symbol Value Data rate for cloud, cloud and pointing Rb 1 Mbps ~10 Gbps error Receiver bandwidth for cloud, fog and B 1 MHz ~10 GHz pointing error Responsivity Rd 0.85 A/W Receiver temperature T 300O K Load resistance of receiver RL 50 Ω Background noise current Ib 10 nA -23 Boltzmann’s constant Kb 1.38x10 W/K/Hz Electron charge e 1.602x10-19 C Cloud thickness - 200-300 m Operating wavelength through cloud λ 0.532 µm Number of user M 1 - 128 Code length (processing gain) Lc(Gp) 8 – 1024 Normalized beamwidth ωz/r 1-10 Normalized pointing error standard σs/r 0.2 - 2.5 deviation Power penalty at BER - 10-6 and 10-9

Table 4.2: Double Gamma Function Constants for Cloud Thickness 200 m to 300 m at a Wavelength of 0.532 µm [20]

Thickness k1 k2 k3 k4 200m 120.1 1.9x107 1.55 3x106 225m 34.1 1.9x107 1.6 3x106 250m 12.4 1.1x107 0.66 2.4x106 275m 5.1 0.8x107 0.28 1.8x106 300m 2.4 0.7x107 0.19 1.6x106

The plots of BER versus received average optical power Io(dBm) are depicted in Fig. 4.2 for code length 256 and number of user 8 at a bit rate of 1 Mbps using cloud thickness as a parameter. It is noticed that, due to the presence of cloud in the channel the BER increases significantly with increase of cloud thickness. The similar plots for processing gain of 512 and number of user 8 are depicted in Fig. 4.3 and it is noticed that, BER improves significantly with the increase of processing gain from 256 to 512 with the same system parameters. It is also observed from Fig. 4.2 that, the system suffers from BER floor due to the effect of MAI in presence of optical channel effects 80 which can be reduced significantly using higher processing gain shown in Fig. 4.3 where no BER floor occurs for Gp=512.

0 10 Code length, Gp=256 Data rate, Rb= 1 Mbps -2 10 Number users, M=8

-4 10 300 m

BER 275 m -6 10 250 m 225 m -8 10 Cloud thickness=200 m

-10 10 -20 -15 -10 -5 0 5 10 15 Average received optical intensity Io(dBm)

Fig. 4.2: BER vs. average received optical intensity Io(dBm) with code length Gp=256 and number of user M=8 at a data rate Rb=1 Mbps using cloud thickness as a parameter. 0 10 Code length, Gp=512 Data rate, Rb= 1 Mbps

-2 Number users, M=8 10

-4 300 m 10

BER 275 m 250 m -6 10 225 m

Cloud thickness=200 m -8 10

-20 -15 -10 -5 0 5 10 Average received optical intensity Io(dBm)

Fig. 4.3: BER vs. average received optical intensity Io(dBm) with code length Gp=512 and number of user M=8 at a data rate Rb=1 Mbps using cloud thickness as a parameter.

The plots of BER versus received optical intensity Io(dBm) are depicted in Fig. 4.4 and Fig. 4.5 with the code length 1024 and number of user 16 and 32 respectively using cloud thickness as a parameter at a bit rate of 1 Gbps. It is noticed that, the BER 81 degrades significantly with the increase of number of user from 16 to 32 for the same code length and the channel effects. Comparison of Fig. 4.4 and Fig. 4.5 reveals that, BER floor occurs due to the increased MAI at higher number of user since the number of user is increased from 16 to 32.

0 10 Code length, Gp=1024 Data rate, Rb= 1 Mbps

-2 Number users, M=16 10

-4 10 300 m

BER 275 m -6 10 250 m

225 m -8 10 Cloud thickness=200 m

-10 10 -15 -10 -5 0 5 Average received optical intensity Io(dBm)

Fig. 4.4: BER vs. average received optical intensity Io(dBm) with code length Gp=1024 and number of user M=16 at a data rate Rb=1 Mbps using cloud thickness as a parameter.

0 10

Code length, Gp=1024 Data rate, Rb= 1 Mbps -2 Number users, M=32 10

-4 300 m 10

BER 275 m 250 m -6 10 225 m

Cloud thickness=200 m -8 10

-20 -15 -10 -5 0 5 10 Average received optical intensity Io(dBm)

Fig. 4.5: BER vs. average received optical intensity Io(dBm) with code length Gp=1024 and number of user M=32 at a data rate Rb=1 Mbps using cloud thickness as a parameter. 82

0 10 Cloud thickness=250 m Data rate, Rb= 1 Mbps -2 10 Number users, M=8

Gp=64 -4 10 128

BER -6 10

-8 10 256 Gp=1024 512 -10 10 -15 -10 -5 0 5 10 15 Average received optical intensity Io(dBm)

Fig. 4.6: BER vs. average received optical intensity Io(dBm) with cloud thickness of 250 m and number of user M=8 at a data rate Rb=1 Mbps using processing gain Gp as a parameter.

Plots of BER as a function of received optical intensity with cloud thickness=250 m and number of user M=16 at a data rate Rb=1 Mbps using code length Gp as a parameter are presented in Fig. 4.6. It is noticed that, the BER performance improves with the higher values of processing gain but the performance degrades significantly with the lower values of processing gain.

0 Code length, Gp=512 10 Data rate, Rb= 1 Mbps Cloud thickness=300 m

-2 10 M=128 64

-4 48 10

BER 32

-6 10 24 20 -8 10 16 M=1 8 12

-10 10 -5 0 5 10 15 Average received optical intensity Io(dBm)

Fig. 4.7: BER vs. average received optical intensity Io(dBm) with code length Gp=512, and cloud thickness of 300 m at a data rate Rb=1 Mbps using number of user M as a parameter. 83

The plots of BER versus received optical signal intensity Io(dBm) are depicted in Fig. 4.7 for a code length Gp= 512, cloud thickness 300 m at a bit rate of 1 Mbps using number of simultaneous user as a parameter. It is noticed that, the BER increases with the increase of number of simultaneous user with even all other parameters are constant. It is also noticed from the Fig. 4.7 that, BER floor starts to occur at the numbers of simultaneous user 16 and continues to increase for the higher number of simultaneous user for the processing gain of 512.

12 Code length, Gp=1024 10 Data rate, Rb=1 Mbps At a BER=10e-9

6 M=24 16 4

Power penalty, (dB) 12 8 4 2 M=1

0 200 210 220 230 240 250 260 270 280 290 300 Cloud thickness, m

Fig. 4.8: Power penalty as a function of cloud thickness for code length Gp=1024 -9 and data rate Rb=1 Mbps at a BER=10 using number of user as a parameter.

The power penalty as function of cloud thickness is shown in Fig. 4.8. It is observed that, the power penalty depends largely on cloud thickness and number of simultaneous user in presence channel effects. Penalty is lower for the low cloud thickness which increases almost linearly with the increase of cloud thickness. It is also observed that, penalty is reasonably low for the lower number of simultaneous user which increases significantly for the user number 16 or more.

Power penalty as a function of number of simultaneous user with code length Gp=1024 -9 and data rate Rb=1 Mbps at a BER of 10 using cloud thickness as a parameter are shown in Fig. 4.9. It is noticed that, the receiver sensitivity or power penalty degrades almost linearly with the increase of number of simultaneous user for a particular cloud thickness. It is also observed from Fig. 4.9 that, penalty in the cloud thickness ranges 84 from 200 m to 225 m and 275 m to 300 m are much higher than that of thickness range 225 m to 275 m. For example, penalty for user number 16 at a cloud thickness 200 m is more than 2 dB which increases to 10 dB for the cloud thickness 300 m but penalty at 225 m is 4.7 dB, 250 m is 5.8 dB and in 275 m is 7.0 dB respectively.

12 Code length, Gp=1024 Data rate, Rb=1 Mbps 10 At a BER=10e-9 300 m

275 m 6 250 m 225m 4 Power penalty,(dB)

2 Cloud thickness=200 m 0 2 4 6 8 10 12 14 16 18 20 22 24 Number users, M

Fig. 4.9: Power penalty as a function of number of user M for code length Gp=1024 -9 and data rate Rb=1Mbps at a BER=10 using cloud thickness as a parameter.

4.6.2 Performance of OCDMA FSO communication system with effect of Fog

The plots of BER versus received optical power Io(dBm) are depicted in Fig. 4.10 for code length of 256 and number of user 8 at a bit rate of 10 Mbps using fog thickness (optical thickness) as a parameter. It is noticed that, due to the presence of fog in the channel the BER increases significantly with increase of optical thickness. The similar plots for processing gain of 512 and number of user 8 are depicted in Fig. 4.11. It is noticed that, BER improves significantly with the increase of processing gain from 256 to 512 with the same system parameters. It is also observed from Fig. 4.10 that, the system suffers from BER floor due to the effect of MAI in presence of fog and optical channel effects which can be reduced significantly using higher processing gain shown in Fig. 4.11.

0 10 Code length, Gp=256 Data rate, Rb= 10 Gbps Number users, M=8 -2 10

-4 10 300 m

BER 275 m -6 10 250 m

225 m

-8 10 Fog thickness=200 m

-10 10 -40 -35 -30 -25 -20 -15 -10 Average received optical intensity Io(dBm)

Fig. 4.10: BER vs. average received optical intensity Io(dBm) with code length Gp=256 and number of user M=8 at a data rate Rb=10 Mbps using fog thickness as a parameter.

0 10 Code length, Gp=512 Data rate, Rb= 10 Gbps Number users, M=8

-5 10

300 m

BER -10 275 m 10 250 m

225 m

-15 10 Fog thickness=200 m

-45 -40 -35 -30 -25 -20 -15 Average received optical intensity Io(dBm)

Fig. 4.11: BER vs. average received optical intensity Io(dBm) with code length Gp=512 and number of user M=8 at a data rate Rb=10 Mbps using fog thickness as a parameter.

The plots of BER versus received optical intensity Io(dBm) are depicted in Fig. 4.12 and Fig. 4.13 with the code length 1024 and number of user 16 and 32 respectively using fog thickness (optical thickness) as a parameter at a bit rate of 10 Mbps. It is noticed that, the BER degrades significantly with the increase of number of user from 16 to 32 for the same code length and the channel effects. It is again observed from Fig. 4.13 86 that, BER floor occurs due to the increased MAI at higher number of user as the number of user is increased from 16 to 32.

0 10 Code length, Gp=1024 Data rate, Rb= 10 Gbps Number users, M=16 -2 10

-4 10 300 m

BER 275 m -6 10 250 m

225 m -8 10 Fog thickness=200 m

-10 10 -50 -45 -40 -35 -30 -25 Average received optical intensity Io(dBm)

Fig. 4.12: BER vs. average received optical intensity Io(dBm) with code length Gp=1024 and number of user M=16 at a data rate Rb=10 Mbps using fog thickness as a parameter.

0 10 Code length, Gp=1024 Data rate, Rb= 10 Gbps Number users, M=32 -2 10

-4 10 300 m

BER 275 m -6 250 m 10

225 m

-8 10 Fog thickness=200 m

-10 10 -50 -45 -40 -35 -30 -25 -20 Average received optical intensisty Io(dBm)

Fig. 4.13: BER vs. average received optical intensity Io(dBm) with code length Gp=1024 and number of user M=32 at a data rate Rb=10 Mbps using fog thickness as a parameter.

Plots of BER vs. received optical intensity with fog thickness=250 m and number of user M=16 at a data rate Rb=10 Mbps using code length Gp as a parameter are presented in Fig. 4.14. It is noticed that, the BER performance improves with the higher code 87 length but the performance degrades significantly with the lower length of processing gain.

0 10

-2 10 128

-4 10 256 BER

-6 10

-8 10 Code length, Gp=64-1024 Data rate, Rb= 10 Gbps Number users, M=16 512 Fog thickness=250 m Gp=1024

-10 10 -50 -45 -40 -35 -30 -25 -20 -15 -10 Average received optical intensity Io(dBm)

Fig. 4.14: BER vs. average received optical intensity Io(dBm) with fog thickness of 250 m and number of user M=16 at a data rate Rb=1 Mbps using code length Gp as a parameter.

0 10

M=128 -2 10 64 48

-4 10 32 BER

-6 10 24

-8 Code length, Gp=512 10 Data rate, Rb= 10 Gbps 16 Number users, M=1-128 Fog thickness=300 m 12 M=1 8 -10 10 -35 -30 -25 -20 -15 -10 Average received optical intensity Io(dBm)

Fig. 4.15: BER vs. average received optical intensity Io(dBm) with code length Gp=512, and fog thickness of 300 m at a data rate Rb=10 Mbps using number of user M as a parameter.

The plots of BER versus received optical signal intensity Io(dBm) are depicted in Fig. 4.15 for a code length Gp= 512, fog thickness 300 m at a bit rate of 10 Mbps using number of simultaneous user as a parameter. It is noticed that, the BER increases with the increase of number of simultaneous user with even all other parameters are constant. 88

It is noticed from the Fig. 4.15 that, BER floor starts to occur at the numbers of simultaneous user 16 and continues to increase for higher number of users for the processing gain of 512.

20 Code length, Gp=1024 18 Data rate, Rb= 10 Gbps At a BER=10e-9 M=32 16

8 Power penalty, (dB) 6 24 16 8 4 M=1 2

0 200 210 220 230 240 250 260 270 280 290 300 Fog thickness, m

Fig. 4.16: Power penalty as a function of fog thickness for code length Gp=1024 -9 and data rate Rb=10 Mbps at a BER=10 using number of user as a parameter.

20 Code length, Gp=1024 18 Data rate, Rb= 10 Gbps 16 At a BER=10e-9

14 300 m

12 275 m 10 250 m 8 225 m Power penalty(dB) 6

2 Fog thickness=200 m 0 5 10 15 20 25 30 Number of users, M

Fig. 4.17: Power penalty as a function of number of user M for code length -9 Gp=1024 and data rate Rb=10 Mbps at a BER=10 using fog thickness as a parameter.

It is noticed form the power penalty or receiver sensitivity as function of fog thickness shown in Fig. 4.16 that, the power penalty or the receiver sensitivity depends on number 89 of simultaneous user in presence fog and channel effects. Penalty is lower for the low optical thickness which increases almost linearly with the increase of fog optical thickness. It is also observed that, penalty is reasonably low for the lower number of simultaneous user which increases significantly for the user number 24 and above.

Plots of power penalty as a function of number of simultaneous user with code length -9 Gp=1024 and data rate Rb=10 Mbps at a BER of 10 using fog optical thickness as a parameter are shown in Fig. 4.17. It is also noticed that, the receiver sensitivity or power penalty increase almost linearly with the increase of number of simultaneous user for a particular cloud thickness. It is observed from Fig. 4.17 that, penalty in the fog thickness ranges from 200 m to 225 m and 275 m to 300 m are much higher than that of thickness range 225 m to 275 m. For example: penalty for user number 15 at a fog thickness 200 m is more than 3 dB which increases to 14 dB for the fog thickness 300 m but penalty at 225 m is 7.5 dB, 250 m is 9.5 dB and in 275 m is 11.25 dB respectively.

4.6.3 Performance of OCDMA FSO communication system with effect of pointing error

The plots of BER versus average received optical intensity Io(dBm) are depicted in Fig. 4.18 for a code length Gp=512 with number of user 32 at a bit rate of 1 Gbps with normalized pointing error σs/r as a parameter. It is noticed that, the BER increases abruptly with increase σs/r and system suffers BER floor due to the effect of MAI in presence of optical channel effect.

The similar plots for code length Gp=1024 depicted in Figure 4.19 for 32 user keeping all other parameter same. It is noticed from Fig. 4.18 and Fig. 4.19 that, the BER performance has been improved significantly when the code length is increased from 512 to 1024 with all other parameters remain same. It is also evident that, the BER floor is significantly reduced with increase in code length due to reduced effect of MAI in presence of channel effects. For example, BER floor occurs in Fig. 4.18 at a BER=2.818e-10 but in case of Fig. 4.19 BER floor occurred at a BER=3.214e-14, which is approximately BER=10e-4 higher. 90

Fig. 4.18: BER vs. average received optical intensity Io(dBm) with code length Gp=512, number of user M=32 at a data rate Rb=1Gbps using normalized pointing error σs/r as a parameter.

Fig. 4.19: BER vs. average received optical intensity Io(dBm) with code length Gp=1024, number of user M=32 at a data rate Rb=1Gbps using normalized pointing error σs/r as a parameter.

For a given code length of 256, the BER performance results for number of user M=8 and 64 are shown in Fig. 4.20 and Fig. 4.21 respectively with normalized pointing error

σs/r as a parameter and all other parameters same. The figures clearly show the deterioration of BER performance in terms of BER floor with the increase in number of 91 simultaneous user and the increase of normalized pointing error parameter σs/r as well as the effect of MAI in presence of channel effects.

Fig. 4.20: BER vs. average received optical intensity Io(dBm) with code length Gp=256, number of user M=8 and data rate Rb=1 Gbps using normalized pointing error σs/r as a parameter.

Fig. 4.21: BER vs. average received optical intensity Io(dBm) with code length Gp=256, number of user M=64 and data rate Rb=1Gbps with normalized pointing error σs/r as a parameter. 92

Fig. 4.22: Power penalty as a function of normalized pointing error σs/r for code -6 length Gp=128, 256, 512 and 1024 respectively at a BER =10 with data rate Rb=1 Gbps and number of simultaneous user M=32.

Fig. 4.23: Power penalty as a function of normalize pointing error standard

deviation σs/r for number of simultaneous user of 4, 8, 16, 32 and 64 respectively at -6 a BER=10 with data rate Rb=1 Gbps and code length Gp=256.

The power penalty suffered by the system due to pointing error at a given BER of 10-6 and bit rate of 1 Gbps are shown in Fig. 4.22 with code length Gp=128, 256, 512 and 1024 respectively for a number simultaneous user M=32. Similar plots with a fixed code length Gp=256 and number of simultaneous user M=4, 8, 16, 32 and 64 respectively as a function of normalized pointing error are shown in Fig. 4.23. It is found from Fig. 93

4.22 that, the penalty is higher for lower values of code length and significantly high at higher values of normalized pointing error σs/r. For example, power penalty is about 2.4 dB when σs/r =0.2 and is about 4.3 dB when σs/r =1.5 corresponding to the number of user M=32 and Gp=128. At higher values of code length the penalty reduces significantly. From Fig. 4.23, it is noticed that, when the number of user is increased from 4 to 64 the penalty increased from 2.3 dB to 4.5 dB corresponding to σs/r =1.5 and Gp=256 which is more than 2 dB.

Fig. 4.24: Plots of BER vs. number of simultaneous user at a data rate of Rb=5 Gbps and code length Gp=64 using normalized pointing error σs/r as a parameter.

BER performance results with the increase of number of simultaneous user M are shown in Fig. 4.24 where, normalized pointing error is used as the parameter. It is clearly noticed that, the BER increases with the increase of number of user as well as the normalized pointing error. It is also noticed that, the BER floor is significant when the user number is more than 30 due to the increase of pointing error and the effect of MAI in presence of channel effects.

The performance result of the system based on maximum number of allowable user with respect to normalized pointing error at a BER of 10-6 for a code length of 64 and bit rate of 1, 2.5, 5 and 10 Gbps respectively are depicted in Fig. 4.25. Number of user decreases significantly with the increase of bit rate as well as the normalized pointing 94 error. It is noticed that, number of user have reduced from 23 to 6 at a bit rate of 10 Gbps when pointing error has increased from 0.2 to 2 and similarly the number of user is reduced from approximately 25 to 5 at a bit rate of 5 Gbps when the pointing error has increased from 0.2 to 2.5. It is also observed that, maximum number of allowable user at pointing error 1.0 are 26, 25, 23 and 21 for bit rate of 1, 2.5, 5, 10 Gbps respectively. The power penalty suffered by the system due to pointing error at a given BER of 10-9 and bit rate of 1 Gbps are shown in Fig. 4.26 with code length Gp=256, 512 and 1024 respectively for a number of simultaneous user M=16. It is found that, the penalty at BER 10-9 is 9 dB corresponding to the normalized pointing error of 1.4 for number of user M=16 with processing gain Gp=256 and is reduced to 6.9 dB when the processing gain is increased to 1024 for the same amount of pointing error and same number of simultaneous user. Similar results like Fig. 4.22 are found from Fig. 4.26 that, the penalty is noticeably higher for lower values of code length and significantly high at higher values of normalized pointing error σs/r. It is also noticed that, BER increases -9 significantly and floors earlier than BER of 10 when code length falls below 256 due to the effect of MAI and pointing error in presence of channel effects.

Fig. 4.25: Plots of allowable number of user’s vs. normalized pointing error for data rate of 1, 2.5, 5 and 10 Gbps respectively at a BER =10-6 and code length Gp=64. 95

Fig. 4.26: Power penalty as a function of normalized pointing error σs/r for code -9 length of 256, 512 and 1024 respectively at a BER=10 with data rate Rb=1 Gbps and number of user M=16.

4.7 Conclusion

An analytical approach is presented to evaluate the limitations due to cloud, fog and pointing error on the bit error rate of an OCDMA FSO communication system with SIK receiver. The results show that, the system suffers from power penalty and degradation of BER significantly due to the increase of cloud and fog thickness, pointing error standard deviation and number of simultaneous user in presence of channel effects. Power penalty suffered by the system can be substantially reduced by using longer code length and lower cloud thickness. For example in case of cloud; penalty for code length of 1024 and number user of 16 is approximately 2 dB for a cloud thickness of 200 m which increases to 10 dB for cloud thickness of 300 m at a given BER of 10-9.In case of effect of pointing error on OCDMA FSO system; penalty at BER 10-9 is found to be 9 dB corresponding to normalized pointing error of 1.4 for number of user 16 with processing gain 256 and is reduced to 6.9 dB when the processing gain is increased to 1024. In the next chapter we shall analyze and evaluate the effect of space diversity and OCDMA on the single channel FSO communication system.

Chapter 5

OCDMA FSO COMMUNICATION SYTEM WITH SPACE DIVERSITY

5.1 Introduction

In this chapter, a brief introduction on diversity schemes and the system models with and without diversity is presented. Analytical approaches are carried out to evaluate the conditional BER conditioned on a given value of pointing error for a FSO communication system with multiple PIN photodetector receivers using Equal Gain Combining (EGC) for SISO, SIMO, MISO, MIMO and SIMO OCDMA FSO communication system. The pdf of output SNR with receive diversity is also derived in presence of pointing error using EGC. The average BER of a SIMO FSO communication system and SIMO OCDMA FSO communication system is analytically evaluated by averaging the conditional BER over the pdf of the output SNR. Several analytical approaches are developed to find the average BER for SIMO FSO system. The BER performance results are evaluated based on the analytical approaches for different values of pointing error with OOK modulation and direct detection at a data rate of 10 Gbps with different system parameters.

5.2 Diversity Schemes

A diversity scheme in telecommunication refers to a method for improving the reliability of a message signal by using two or more communication channels with different characteristics. Diversity is mainly used in radio communication and is a common technique for combating fading and co-channel interference and avoiding error bursts to improve the system performance [107]. It is based on the fact that individual channels experience different levels of interference and fading. Multiple versions of the same signal may be transmitted or received to combine in the receiver. A redundant forward error correction (FEC) code may be added and different parts of the message 97 transmitted over different channels. Diversity techniques may exploit the multipath propagation resulting in a diversity gain [73, 108, 109].

In case of time diversity, multiple versions of the same signal are transmitted at different time instants. The redundant FEC code is added and the message is spread in time by means of bit interleaving before it is transmitted to avoid error bursts and to simplify the error correction. In case of frequency diversity, the signals are transmitted using several frequency channels or spread over a wide spectrum that is affected by frequency selective fading. OFDM modulation in combination with subcarrier interleaving and FEC is used in frequency diversity.

In space diversity, the signal is transmitted over several different propagation paths whereas; this can be achieved by transmitting via multiple wires for wired transmission. In wireless transmission, transmit diversity is achieved by using multiple number of transmitting antenna and reception diversity is achieved by multiple receiving antennas. A diversity combining technique is applied before further signal processing takes place. The diversity is called macro-diversity if the antennas are far apart and if the antennas are at a distance in the order of one wavelength; this is called micro-diversity.

In polarization diversity, multiple versions of a signal are transmitted and received via antennas with different polarization and a diversity combining technique is applied on the receiver side. The electric and magnetic fields of the signal carrying the information are modified and many such signals are used to send the same information and orthogonal type of polarization is obtained. The multiuser diversity is obtained by opportunistic user scheduling at either the transmitter or the receiver by selecting the best user among candidate receivers according to the qualities of each channel between the transmitter and receiver. A receiver must feedback the channel quality information to the transmitter using limited levels of resolution.

The cooperative diversity is a cooperative multiple antenna technique for maximizing total network channel capacities for any given set of bandwidths which exploits user diversity by decoding the combined signal of the relayed signal and the direct signal in wireless multi hop networks. A conventional single hop system uses direct transmission where a receiver decodes the information only based on the direct signal 98 considering the relayed signal as interference, whereas the cooperative diversity considers the other signal as contribution. That is, cooperative diversity decodes the information from the combination of two signals. Hence, it can be seen that cooperative diversity is an antenna diversity that uses distributed antennas belonging to each node in a wireless network. Most widely used diversity combining techniques are Equal gain combining, Maximal ratio combining, Switched combining, Selection combining etc.

5.3 Model of FSO System with and without Diversity

The block diagram of a single input single output SISO FSO communication system is shown in Fig. 5.1(a). In the transmitter we consider intensity modulation (IM) or on-off keying (OOK) of the transmitted laser of the incoming data bits. In the receiver, the OOK signal is detected by a PIN photodetector followed by low pass filter (LPF) and data decision. The block diagram of an FSO communication system with single transmitter and multiple photodetector output (SIMO) is shown in Fig. 5.1(b) and that of multiple transmitters with multiple photodetector output (MIMO) FSO communication system in Fig. 5.1(c). An OCDMA FSO communication system with single transmitter and multiple SIK dual photodetector receivers (SIMO) is shown in Fig 5.1(d). In case of multiple photodetector receivers we consider equal gain combining (EGC) technique with M number of transmitting laser and N number of photodetectors.

Fig. 5.1(a): Block diagram of FSO communication system with one transmitter and one PIN photodetector receiver (SISO).

Fig. 5.1(b): Block diagram of FSO communication system with one transmitter and multiple PIN photodetector receiver (SIMO).

Fig. 5.1(c): Block diagram of FSO communication system with multiple transmitter and multiple PIN photodetector receiver (MIMO).

i01 SIK Rx‐1 Tx Beam 1 C O M i02 OCDMA SIK Rx‐2 B I0 (t) Tx Tx Beam 2 I N E R 1:NR Tx Beam NR SIK Rx‐NR io NR

SIK RX‐NR

Fig. 5.1(d): Block diagram of an OCDMA FSO communication system with single transmitter and multiple SIK dual photodetector receiver (SIMO). 100

5.4 FSO Channel Model with Pointing Error

We consider a FSO communication system with Mt transmitters and Nr photodetector receivers, using IM/DD or OOK modulation format. The transmitted optical power OOK signal can be represented as:

St( )= 2 Pe− jtωc . a (5.1) tk where Pt is the average transmitted optical power, ωc is the angular optical carrier th th frequency and ak is the k bit either 1 or 0. The received signal intensity at the n photodetector receiver aperture is given by [112, 113]:

M t −αl rtnd()()=+= RSt∑ he mn nt( ) , n 1,...., N r (5.2) m=1 where Rd is the detector responsivity in A/w, α is the path loss coefficient and l is the link distance, n(t) represent the photodetectors’ shot noise, preamplifiers’ thermal noise

2 and zero mean Gaussian noise with variance σn . The normalized fading channel th coefficient hmn models the effect of pointing errors in the channel from the m transmitter aperture to the nth photodetector receiver aperture.

If hp represents the attenuation due to geometric spread and pointing errors then considering a Gaussian beam and a circular detection aperture of radius r, the pdf of hp can be represented as [26, 28]:

2 γ γ 2−1 phhp( )=≤≤ h p , 0 hp A0 (5.3) γ 2 A0 where γ = ωσzeq/2 s is the ratio of the equivalent beam radius at the receiver to the pointing error displacement standard deviation at the receiver, ωzeq is the equivalent beam width at the receiver. The equivalent beam width ωzeq is evaluated using the relations [28]:

πυerf () πr ω 22===ωυ, , Aerf[( υ )]2 zeq z 2exp(υυ− 2 ) 2ω 0 z

-2 where ωz is the beam waist i. e. radius calculated at e at a distance z from the transmitter.

101

5.5 System Analysis

The photodetector output current of nth receiver is given by:

Mt iton( )== Rrt d . n ( ) 2 RPha d t∑ mn . k + i n (t) (5.4) m=1 For a MIMO FSO communication system the output current at output of EGC can be derived as [114-117]:

NNrrMt itoondtmnkn( )==∑∑∑ i ( t ) 2 RPha . + i (t) (5.5) nmn==11=1 For a SIMO FSO communication system, the output current of EGC can be derived as:

NNrr itoondtnkn( )==∑∑ i ( t ) 2 RPha1 . + i (t) (5.6) nn==11 where in(t) represent the output noise current with zero mean Gaussian with variance

2 σ n , can be expressed as:

2 σ ndtbL=+4eR PB 4 K TB / R (5.7)

5.5.1 Analysis of BER for SISO FSO communication system

For a SISO FSO communication system, Mt=1, Nr=1 and the conditional SNR at the output of receiver at a given value of h11, can be represented as: ()2RPh 2 SNR( h )= dt11 (5.8) 11 σ 2 n

The conditional BER conditioned on a given value of h11 is given by:

Ph( )= 0.5 erfc⎡⎤ SNRh ( ) / 2 2 (5.9) b 11 ⎣⎦11 The average BER can be obtained as:

A0 BER= ∫ Pbh( h11 ) p ( h 11 ) dh 11 (5.10) 0

5.5.2 Analysis of BER for SIMO FSO communication system

For a SIMO FSO communication system with Nr receiver we consider EGC at the output. The output of the combiner is given by (5.6) and the conditional SNR at the output is given by: 102

N r 2 (2RPh ) 2 ∑ dt1 n NNrr ndt=1 (2RP ) 2 2 SNR( h11nn )==22 .∑∑ h =ζ1n (5.11) nn==11 σσnn

2RPdt where, ζ11nn= 2 .h (5.12) σ n

5.5.2.1 SIMO FSO communication system: Analytical approach-1

The conditional BER of a SIMO FSO communication system in presence of pointing error is given by:

Pbn( h11 )= 0.5 erfc SNR ( h n ) / 2 2 (5.13) The average BER can be evaluated as:

A0 BER= ∫ Pbnhn( h111 ) p ( h ) dh n (5.14) 0

5.5.2.2 SIMO FSO communication system: Analytical approach-2

Equation (5.12) can be written as:

ζ11nn= ah . (5.15)

2RPdt where a = 2 σ n

The pdf of ζ1n is derived and is found to be:

2 2 γ −1 γ ⎛⎞ζ1n 1 p(ζ1n )= 2 ⎜⎟ . (5.16) γ aa A0 ⎝⎠ ω where, γ = zeq 2σ s

The conditional SNR for a given value of ζ 1n can be defined as:

N r 2 SNR(ζζ11nn )= ∑ (5.17) n=1

The conditional BER conditioned on a given value of ζ1n can be written as:

1 ⎡⎤ PerfcSNRbn(ζζ11 )= (n ) / 2 2 (5.18) 2 ⎣⎦ The average BER can be obtained by averaging the conditional BER over the pdf of

ζ1n as:

∞ BER= ∫ Pbn(ζζζ111 ) p ( n ) d n (5.19) 0

103

5.5.2.3 SIMO FSO communication system: Analytical approach-3

2 We define, βζ11nn= and the pdf of β 1n is derived and is found to be:

⎡⎤γ 2 −1 2 ⎛⎞ 11⎢⎥γ β1n p()β1n = .⎜⎟ . (5.20) 2 β ⎢⎥γ 2 ⎜⎟aa 1n A0 ⎝⎠ ⎣⎦⎢⎥

The conditional SNR can be conditioned on a given value of β1n . Following (5.17) the conditional SNR can be expressed as:

Nr SNR(ββ11nn )= ∑ (5.21) n=1 The average BER can then be expressed as:

∞ ⎡⎤SNR()β ⎢⎥1n BER= ∫ 0.5 erfc . p (ββ11nn ) d (5.22) ⎢⎥ 0 ⎣⎦22

5.5.2.4 SIMO FSO communication system: Analytical approach-4

We define the SNR at the output of EGC as:

N βββββ==++++...... β (5.23) on∑ 1111213 1 Nr n=1 The pdf of β0 can be obtained by (Nr-1) fold convolution of the pdf of the input SNRs as: pp(β )=⊗⊗⊗⊗ (βββ ) p ( ) p ( ) ...... p ( β ) (5.24) oN11 12 13 1 r where ⊗ denotes convolution and p()β1i represents the pdf of β1i for i=1, 2……Nr The conditional BER can now be expressed as:

⎡⎤ βo Perfcbo(β )= 0.5⎢⎥ (5.25) ⎢⎥ ⎣⎦22

The average BER can be obtained as:

∞ BER= ∫ Pbo(βββ ) p ( o ) d o (5.26) 0

104

5.5.3 Analysis of BER for MISO FSO communication system

For a MISO FSO Communication system with Mt transmitter and one photodetector receivers the output of the EGC is given by:

M t 2 (2RPh ) 2 ∑ dtm1 MMtt mdt=1 (2RP ) 22 SNR( hm1 )==22∑∑hmm11 =ζ (5.27) mm==11 σσnn 2RP where ζ = dt .h (5.28) mm11σ 2 n SNR at the output of EGC can be defined as:

M t SNR(ββmm11 )= ∑ (5.29) m=1 The pdf of βm1 can be obtained by (Mt-1) fold convolution of the pdf of the input SNRs. pppp(β )=⊗⊗⊗⊗ (βββ ) ( ) ( ) ...... p ( β ) (5.30) mM111 21 31 t 1 The conditional BER can now be expressed as:

⎡⎤SNR()β Perfc(β )= 0.5⎢⎥m1 (5.31) bm1 ⎢⎥ ⎣⎦22 The average BER can be obtained as:

∞ BER= ∫ Pbm(βββ111 ) p ( m ) d m (5.32) 0

5.5.4 Analysis of BER for MIMO FSO communication system

For a MIMO FSO communication system with Mt transmitter and Nr photodetector receivers the output of the EGC is given by (5.5) and the conditional SNR at the output is given by:

M t N r 2 ∑ (2RPhdtmn ) 2 ∑ MMttNN m=1 ndt=1 (2RP ) rr22 SNR( hmn )==22∑∑∑∑ hmn =ζ mn (5.33) mm==11 σσnnnn==11 2RP where ζ = dt .h (5.34) mnσ 2 mn n SNR at the output of EGC can be defined as:

Mt Nr SNR(ββmn )= ∑∑ mn (5.35) mn==11 The pdf of βmn can be obtained by Mt.(Nr-1) fold convolution of the pdf of the input SNR as: 105

pppppp(ββββββ )=⊗⊗⊗⊗⊗⊗ ( ) ( ) ( ) ( ) ( ) ...... p β (5.36) mn 11 21 12 31 13 ( MNtr(1)− ) The conditional BER can now be expressed as:

⎡⎤SNR()β P (β )= 0.5erfc⎢⎥mn (5.37) bmn ⎢⎥ ⎣⎦22 The average BER can be obtained as:

∞ BER= ∫ Pbmnmnmn(βββ ) p ( ) d (5.38) 0

5.5.5 Analysis of BER for SIMO OCDMA FSO Communication system

The optical CDMA signal corresponding to the mth user transmitter can be represented as:

∞ mmmjtωc S( t )=− 2 PTk .∑ a. g ( t kT b ) xC ( t ) e (5.39) k =0 m th m th th Ct() represents the code of the m user, ak represents the k bit of the m user, g(t) is the pulse shape of the information bit, Tb is the bit period, PT is the average optical power transmitted by the laser diode. Ctm () is the signature sequence of the mth user and is given by:

L −1 mmc Ct( )=−∑ CptlTlc ( ) (5.40) lo= m th th where Cl represents the l chip of the m codeword, Lc is the code length (processing gain, Gp), Tc is the chip period (Tc=Tb/Lc) and p(t) is the pulse shape of the individual chip. Using (5.2) in (5.1), Sm(t) can be rewritten as:

∞ Lc mm mjtωc St( )=− 2 PTk .∑∑ agtkTxCptlTe. ( b ) l ( − c ). (5.41) kl==01

The optical signal is received by Nr number of photodetectors followed by Nr number of optical CDMA SIK receivers. The optical signal at the input of jth photodiode due to mth user signal and is given by:

mm−αdm rtjm( )= Ste ( ). . h (5.42)

th where hm represent the effect of atmospheric channel corresponding to the m user th communication system, α is the atmospheric loss coefficient, dm is the distance of the j photodiode from the mth user transmitter.

106

The optical signal at the input to jth photodiode can be represented by:

M m rtjjo( )=+∑ r ( t ) nt ( ) (5.43) m=1 where no(t) represents optical channel background noise. The output current of jth photodiode is given by:

M m itoj( )=+ R d .∑ rt j ( ) it n ( ) (5.44) m=1 The output of the jth optical CDMA decoder is represented as:

Lc −1 m ititxCptlTitout, j( )=− oj ( ) ∑ l ( c )+ n ( ) (5.45) l=0 The output of the combiner for mth user is then can be represented as:

NR M itout( )=+∑∑ G j . i out, j ( tit ) on ( ) (5.46) jm==11 where Gj represents the gain of the combiner, ion(t) represent the output noise current

2 with zero mean Gaussian with variance σ n . Inserting (5.41) to (5.45) into (5.46) we get the output current of combiner for SIMO configuration as:

M L Nr ∞ c mm−αdm it0ut( )=−− 2 RP d T∑ .∑∑ G j . agtkTxCptlThe k. ( b ) ∑ l ( c ). m .+ it on ( ) (5.47) m=1 jk==10 l = 1

The effect of atmospheric turbulence hm on the optical signal can be represented as hm=ham.hpm; where ham is the effect of atmospheric turbulence and hpm is the attenuation th due to geometric spread and pointing error. The optical signal received by the m user receiver can be expressed as:

M L Nr ∞ c mm −αdm itodTjkblcampmmon( )=−−+ 2 RP .∑ .∑∑ G . agtkTx. ( ) ∑ CptlThh ( ). . he . i ( t ) m=1 jk==10 l = 1 M N ∞ L r mmc =−− 2RPdr .∑ .∑∑ G j . a k. gt ( kTx b ) ∑ C l pt ( lTh c ). ampmon h+ i ( t ) (5.48) m=1 jk==10 l= 1

−αdm where, PPert= .

Considering SIK correlator receiver, corresponding to jth user, output current of the receiver can be expressed as: 107

T Tb N L b jmmr c ii Zt( )=−−− RP .∑∑ GagtkTxCptlTxCtlTCtlThhdtitdt . ( ). ( ) ( )−−+ ( ) . . ( ) (5.49) i d r∫ j k b l c{ c c} am pm∫ on jl==11 0 0 j Then following reference [12, 14], Z i(t) can be represented by:

T L −1 mm T RP b Nr c ⎧⎫1(+−b t lT )() c t − lT b Zj () t=−−+dr G c c x p ()(). t lT ci t lT dt h h i (). t dt (5.50) i ∫∫∑∑j ⎨⎬{}c c am pm on 220 jl==10⎩⎭ 0 Equation (5.50) can be rewritten as:

NNTT r bbLLcc−−11r 2 jmRPdr..iiRP dr i Z ()t=−−+−−− G∑∑ ptlTctlTdthh ()(). G ptlTbtlTctlTdthh ()()().i i∑∑ j∫∫{ c c} am pm j{ c cc } am pm 44jj==1100ll==00 T L −1 T RP. b Nr c b +−−−−+dr G ptlTbtlTctlTctlTdthhmmm()()()().i i (tdt). (5.51) ∫ ∑∑jcccca{}mpmn∫ 2 0 jl==10 0

For M number of users total output photocurrent is given by:

M j Ztii( )= ∑ Z ( t ) (5.52) m=1

The mean value of photo current Zi(t) for a given value of ham and hpm can be represented by:

M Nr T GRPjdrs L−1 Uh()am, h pm=−∑∑ ∫ ∑ h pm()t .().() h am t pt lTdt c (5.53) 4T l=0 mj==11 s 0 We can represent,

MM hhhhoampmm==∑∑. (5.54) mm==11

The equation (5.53) can be re-written as:

Nr T M GRPjdrs L−1 Uh()osocm=−∑∑∫ ∑ Ixh. h.( pt lTdt ) (5.55) 4T l=0 jm==11s 0 ∞ and, Uh22 ( )= Uhphdh ( ) ( ) ( ) (5.56) oooo∫ 0 The variance of noise current ion(t) is represented by:

2224KTBb σσσnthshot=+ = +2eB ( I sb + I ) (5.57) RL

The variance of MAI for a given value of ho can be represented by:

Nr 2(M − 1) σ 22(hUh )= ( ). (5.58) MAI o ∑ o 3L j=1 c 108

The SNIR conditioned on a given value of ho is then expressed by: NU.()2 h ξ (h )≅ ro (5.59) o σσ22++Nh.() σ 2 th shot r MAI o The conditional BER conditioned on a given value of channel coefficient ho can be expressed as: 1 Ph( )= erfc⎡⎤ξ ( h ) / 2 2 (5.60) bo 2 ⎣⎦o

The pdf of ho can be derived by (M-1) fold convolution as:

ph(om )= ph (123 )⊗⊗ ph ( ) ph ( )... ⊗ ph ( ) (5.61)

The average BER for a given ho can be expressed as:

M BER= P( h ) p ( h ) d ( h ) (5.62) ∫∑ bm m m m=1 Equation (5.62) has no close form solution and requires M-fold integration. To bring out approximated solution Q function can be approximated as [125]

1122 Qx( )≈+ e−−xx/2 e 2 /3 (5.63) 12 4

Thus the average BER for SIMO optimal combiner (OC) can be obtained as [125]:

MM∞∞ 11⎛⎞γγ22⎛⎞ BERSIMO, OC ≅−+−p()exp hm ⎜⎟ .hm dh m p ()exp hm ⎜⎟ .hm dh m (5.64) 12∏∏∫∫ 4MM 4 3 mm==1100⎝⎠ ⎝⎠ where γ is the distribution parameter which is assumed to be unity.

5.6 Results and Discussions

Based on the analytical approaches presented in section 5.5 we evaluate the BER performance results of a SISO and SIMO (four approaches) FSO communication system in presence of pointing error. The results are evaluated in terms of average BER and power penalties for different values of normalized jitter standard deviation σs/r and normalized beamwidth ωz/r for SISO and SIMO configurations. We also evaluate the BER performance results as well as the power penalties for SIMO OCDMA FSO communication system for different code length, number of simultaneous user in presence of pointing error utilizing the system parameters shown in Table 5.1.

109

Table 5.1: System Parameters Parameter Symbol Value Data rate Rb 10 Gbps Receiver bandwidth B 10 GHz Responsivity Rd 0.80 A/W Receiver temperature T 300o K Load resistance of receiver RL 50 Ω -23 Boltzmann’s constant Kb 1.38x10 W/K/Hz Electron charge e 1.6x10-19 C Normalized beamwidth ωz/r 5, 8, 10 Detector aperture radius r 20 cm Number of transmitter Mt 1 Number of photodetector receiver Nr 1 to 8 Normalized pointing error standard σs/r 0.2 to 2.5 deviation Operating wavelength ߣ 1550 nm Number of user M 1 – 256 Code length (processing gain) Lc (Gp) 32 – 1024 Background current Ib 10 nA Power penalty at BER - 10-9-10-10

5.6.1 Performance of SISO FSO communication system

The plots of BER versus transmitter power Pt(dBm) are depicted in Fig. 5.2 for ωz/r=5 considering SISO FSO communication systems with σs/r as a parameter. It is noticed that, system BER is sensitive to pointing jitter and the BER significantly increases with increase in normalized jitter standard deviation σs/r. However, BER decreases with increase in transmitter power. Similar results for ωz/r=10 are depicted in Fig. 5.3 with

σs/r as a parameter. Comparison of Fig. 5.2 and Fig. 5.3 revels that, the BER performance is further degraded with increase in normalized beamwidth i.e. the wider beam and a higher transmit power is required to achieve the same BER as ωz/r is increases from 5 to 10.

110

Fig. 5.2: BER vs. transmitted power for normalized beamwidth ωz/r =5 and number of photodetector receiver Nr=1 SISO FSO system using normalized jitter standard deviation σs/r as a parameter.

Fig. 5.3: BER vs. transmitted power for normalized beamwidth ωz/r=10 and number of photodetector receiver Nr=1 for SISO FSO system using normalized jitter standard deviation σs/r as a parameter.

The plots of BER versus transmit power Pt(dBm) are depicted in Fig. 5.4 for ωz/r=5 considering SISO FSO communication systems with σs/r as a parameter. It is noticed that, system BER is sensitive to pointing jitter and the BER significantly increases with increase in normalized jitter standard deviation σs/r. However, BER decreases with 111 increase in transmit power. Similar results for ωz/r=8 are depicted in Fig. 5.5 with σs/r as a parameter. Comparison of Fig. 5.4 and Fig. 5.5 reveals that the BER performance is further degraded with increase in beamwidth and a higher transmit power is required to achieve the same BER as ωz/r is increased from 5 to 8. Comparison of Fig. 5.2 and Fig. 5.3 with Fig. 5.4 and Fig. 5.5 reveals that approach-1 provides better performance results.

Fig. 5.4: BER vs. transmitted power for normalized beamwidth ωz/r=5 and number of photodetector receiver Nr=1 for SISO FSO system using normalized jitter standard deviation σs/r as a parameter (approach-1).

Fig. 5.5: BER vs. transmitted power for normalized beamwidth ωz/r=8 and number of photodetector receiver Nr=1 for SISO FSO system using normalized jitter standard deviation σs/r as a parameter (approach-1). 112

5.6.2 Performance of SIMO FSO communication system

For a SIMO FSO communication system, BER performance results are evaluated following different approaches as mentioned in section 5.5.2. Following analytical approach-1, the BER performance results for a SIMO FSO communication system are depicted in Fig. 5.6 and Fig. 5.7 for four number of photodetector receivers (Nr =4) using σs/r as a parameter with ωz/r=5 and 8 respectively. It is noticed that, there are significant improvements in BER performance with four photodetector receivers compared to SISO FSO communication system performance. Comparison of the Fig. 5.4 to Fig. 5.7 reveals that, BER reduces from10-3 to 10-9 when the number of photodetectors Nr is increased from 1 to 4 corresponding to σs/r=1.0 and ωz/r=5 at

Pt = -10 dBm. Further, there are significant reductions in required transmit power for SIMO FSO communication system compared for SISO FSO communication system for a given BER.

Fig. 5.6: BER vs. transmitted power for normalized beamwidth ωz/r=5 and number of photodetector receivers Nr=4 for SIMO FSO system using normalized jitter standard deviation σs/r as a parameter (approach-1).

113

Fig. 5.7: BER vs. transmitted power for normalized beamwidth ωz/r=8 and number of photodetector receivers Nr=4 for SIMO FSO system using normalized jitter standard deviation σs/r as a parameter (approach-1).

Fig. 5.8: BER vs. transmitted power for normalized beamwidth ωz/r=5 and number of photodetector receiver Nr=1 and 2 for SIMO FSO system using normalized jitter standard deviation σs/r as a parameter (approach-2).

Following the analytical approach-2, the BER performance results of SIMO FSO Communication system in the presence of pointing error are also evaluated at a bit rate of 10 Gbps and are presented in Fig. 5.8 through Fig. 5.11 as a function of transmit optical power Pt(dBm) for ωz/r=5 and 8 respectively and number of photodetector 114

Nr=1, 2, 4, 8 using σs/r as a parameter. It is also noticed that, there are significant improvement in BER performance as the number of receiver is increased from 1 to 8 at a given value of ωz/r and σs/r. As a consequences, the required transmit power can be greatly reduced to achieve a given BER, with increase in the number of receiver.

Fig. 5.9: BER vs. transmitted power for normalized beamwidth ωz/r=5 and number of photodetector receivers Nr=4 and 8 for SIMO FSO system using normalized jitter standard deviation σs/r as a parameter (approach-2).

Fig. 5.10: BER vs. transmitted power for normalized beamwidth ωz/r=8 and number of photodetector receiver Nr=1 and 2 for SISO/SIMO FSO system using normalized jitter standard deviation σs/r as a parameter (approach-2). 115

Fig. 5.11: BER vs. transmitted power for normalized beamwidth ωz/r=8 and number of photodetector receiver Nr=4 and 8 for SIMO FSO system using normalized jitter standard deviation σs/r as a parameter (approach-2).

The similar BER performance results are also evaluated following approach-3 as shown in Fig. 5.12 through Fig. 5.15 for ωz/r=5 and 8 using σs/r as the parameter at a bit rate of 10 Gbps. It is again observed that, the BER performances improves significantly with the increase of number of photodetector receivers and performance degrades with the increase of σs/r and ωz/r. It is also noticed from Fig. 5.12 through Fig. 5.15 that, BER performance results depend significantly on ωz/r even the other system parameters remain same.

Following the analytical approach-4, the BER performance results are also evaluated as shown in Fig. 5.16 and Fig. 5.17 for number of photodetector receivers 2 and 4 with

ωz/r=5 and 8 using σs/r as the parameter at a bit rate of 10 Gbps. It is observed that, the BER performance results improve significantly with the increase of number of photodetector receivers and performance degrades with the increase of σs/r and ωz/r. Similar observations such as Fig. 5.12 through Fig. 5.15 are found from Fig 5.16 to Fig

5.17 that, BER performance depends significantly on ωz/r even the other system parameters remain the same.

116

Fig. 5.12: BER vs. transmitted power for normalized beamwidth ωz/r=5 and number of photodetector receiver Nr=1 and 2 for SISO/SIMO FSO system using normalized jitter standard deviation σs/r as a parameter (approach-3).

Fig. 5.13: BER vs. transmitted power for normalized beamwidth ωz/r=5 and number of photodetector receiver Nr=4 and 8 for SIMO FSO system using normalized jitter standard deviation σs/r as a parameter (approach-3).

117

Fig. 5.14: BER vs. transmitted power for normalized beamwidth ωz/r=8 and number of photodetector receiver Nr=1 and 2 for SISO/SIMO FSO system using normalized jitter standard deviation σs/r as a parameter (approach-3).

Fig. 5.15: BER vs. transmitted power for normalized beamwidth ωz/r=8 and number of photodetector receiver Nr=4 and 8 for SIMO FSO system using normalized jitter standard deviation σs/r as a parameter (approach-3).

118

Fig. 5.16: BER vs. transmitted power for normalized beamwidth ωz/r=5 and number of photodetector receiver Nr=2 and 4 for SIMO FSO system using normalized jitter standard deviation σs/r as a parameter (approach-4).

Fig. 5.17: BER vs. transmitted power for normalized beamwidth ωz/r=8 and number of photodetector receiver Nr=2 and 4 for SIMO FSO system using normalized jitter standard deviation σs/r as a parameter (approach-4).

119

Fig. 5.18: Required transmitted optical power Pt(dBm) vs. normalized jitter standard -10 deviation σs/r to achieve a BER=10 with normalized beamwidth ωz/r=5 for a SISO and SIMO FSO system (approach-1).

Fig. 5.19: Required transmitted optical power Pt(dBm) vs. normalized jitter standard -10 deviation σs/r to achieve a BER=10 and normalized beamwidth ωz/r=8 for a SISO and SIMO FSO system (approach-1).

The plots of required transmit optical power to achieve a BER of 10-10 versus normalized jitter standard deviation σs/r are depicted in Fig. 5.18 and in Fig. 5.19 for SIMO FSO communication system (approach-1) using number of photodetectors

Nr=1, 2, 4, 6 and 8 with ωz/r=5.0 and 8.0 respectively. From Fig. 5.18 and Fig. 5.19 it is 120 noticed that, the system suffers power penalty as the jitter standard deviation σs/r is increases. The amount of power penalty is ranges from 0 to 12 dB as σs/r is increases from 0.2 to 1.4 for SIMO FSO system. However, the SIMO with N≥2, the penalty is found to be slightly reduced at the same value of σs/r.

Alternatively, it is also clear that, for a given transmit optical power and a given BER (say, 10-10), the SIMO system allows higher values of pointing error with increase in number of photodetector receivers at a given value of ωz/r. For example, at Pt = -5 dBm -10 and BER =10 , ωz/r=8, the allowable value of σs/r= 0.6 for SISO (Nr=1) and is almost

1.20 for SIMO (Nr=8). Thus there are significant reductions in required transmitter power for SIMO FSO communication system compared for SISO FSO communication system for a given BER.

Similar plots of required transmit power to achieve BER 10-10 is also shown in Fig. 5.20 and Fig. 5.21 derived for BER performance results of Fig. 5.8 to Fig. 5.11 using approach-2 and in Fig. 5.22 and Fig. 5.23 derived for BER performance results of Fig.

4.12 to Fig. 4.15 using approach-3 for several values of ωz/r and σs/r.

Fig. 5.20: Required transmitted optical power Pt(dBm) vs. normalized jitter standard -10 deviation σs/r to achieve a BER=10 and normalized beamwidth, ωz/r=5 for a SISO and SIMO FSO system (approach-2).

121

Fig. 5.21: Required transmitted optical power Pt(dBm) vs. normalized jitter standard -10 deviation σs/r to achieve a BER=10 and normalized beamwidth ωz/r=8 for a SISO and SIMO FSO system (approach-2).

Fig. 5.22: Required transmitted optical power Pt(dBm) vs. normalized jitter standard -10 deviation σs/r to achieve a BER=10 and normalized beamwidth ωz/r=5 for a SISO and SIMO FSO system (approach-3).

122

Fig. 5.23: Required transmitted optical power Pt(dBm) vs. normalized jitter standard -10 deviation σs/r to achieve a BER=10 and normalized beamwidth ωz/r=8 for a SISO and SIMO FSO system (approach-3).

From Fig. 5.20 through Fig. 5.23 it is clearly noticed that, as the number of photo detector receivers are increased from 1 to 8, there is a reduction in required transmit power to achieve the same BER which is the sensitivity improvement due to receiver diversity at a given value of normalized jitter standard deviation σs/r and normalized beam width ωz/r. Using multiple receivers (SIMO), the required transmitter power can further be reduced at given values of σs/r and ωz/r as shown in Fig. 5.18 through Fig. 5.23. The SIMO system shows almost 6 dB improvement in receiver sensitivity at

σs/r=0.8 and ωz/r=10 and it is found to be higher at higher values of pointing jitter variance.

Similar observation are also found in Fig. 5.24 which is obtained from Fig. 5.16 and

Fig. 5.17 using approach-4 for Nr =2, 3 and 4. It is clearly noticed that, at a given transmit power and at a given BER (say 10-10) the use of receiver diversity allows higher allowable values of σs/r corresponding to a value of ωz/r.

-10 The plots of the allowable values of σs/r at a BER=10 and at a given Pt(dBm) are shown in Fig. 5.25 and 5.26 as a function of number of receivers corresponding to

ωz/r=5 and 8 respectively for four different approaches. It is noticed that, there is a maximum allowable value of σs/r corresponding to a given value of Pt(dBm), ωz/r and number of receiver Nr. A higher value of σs/r can be obtained by increasing the number 123 of receivers. However, the results obtained by different approaches differ and it is noticed that approach-4 is more appropriate analytical approach and it offers higher value of σs/r at a given number of receiver. For example, according to Fig 5.26, results obtained by approach-4 show that, the maximum allowable value of σs/r is 1.7 corresponding to Nr=2 and can be increased to 2.75 when the number of receiver is set to Nr=4 at Pt = -5 dBm and ωz/r=8.

Fig. 5.24: Transmitted optical power Pt(dBm) vs. normalized jitter standard -10 deviation σs/r at a BER=10 and normalized beamwidth ωz/r=5 and 8 for SIMO FSO system (approach-4).

Fig. 5. 25: Maximum allowable normalized jitter standard deviation σs/r vs. number -10 of photodetector receivers at a BER=10 , Pt(dBm) = -5 and ωz/r =5 for approach-1, 2, 3 and 4. 124

Fig. 5. 26: Maximum allowable normalized jitter standard deviation σs/r vs. number -10 of photodetector receivers at a BER=10 , Pt(dBm)= -5 and ωz/r=8 for approach-1, 2, 3 and 4.

Fig. 5. 27: Maximum allowable normalized jitter standard deviation σs/r vs. number -10 of photodetector receivers at a BER of 10 , Pt(dBm) = -8 and ωz/r=5 for approach- 1, 2, 3 and 4.

125

Fig. 5. 28: Maximum allowable normalized jitter standard deviation σs/r vs. number -10 of photodetector receivers at a BER=10 , Pt(dBm)=-8 and ωz/r=8 for approach-1, 2, 3 and 4.

Similar results of Pt=-8 dBm are also shown in Fig 5.27 and 5.28 for ωz/r=5 and 8 respectively. Thus, the effect of pointing error can be overcome by applying diversity in receiving for a FSO communication system. Further, from Fig. 5.18 through Fig. 5.24 it is noticed that, at a given BER =10-10 there is an improvement in required transmit power corresponding to given value of ωz/r and σs/r. The amount of improvement in receiver sensitivity is found to be about 5 dB for Nr=4 and 10 dB for Nr=8 at ωz/r=8, -10 σs/r=1.0 and BER = 10 .

It is noticed from the plots of BER vs. transmit power of approach-1, 2, 3 and 3 (Fig. 5.2 to Fig. 5.17) that, the BER performance result is the best in approach-4 with the similar diversity scheme, same values of normalized jitter standard deviation and normalized beam width. It is also justified from Fig. 5.25 to Fig. 5.28 that, the approach-4 can tolerate much higher values of normalized jitter standard deviation for the same number of PIN photodetector receivers in comparison to the approach-1, 2 and 3.

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5.6.3 Performance of SIMO OCDMA FSO communication system

The plots of BER versus transmitted optical power Pt(dBm) are presented in Fig. 5.29 similar to the SISO configuration. It is noticed that, the BER performance results of OCDMA FSO system in presence of pointing error has improved approximately up to BER=10-5 in comparison to the SISO configuration for the similar system parameter.

Fig. 5.29: BER vs. transmitted power for number of receiver antenna Nr=1, code length Gp=1, number of user M=1 at a data rate Rb=10 Gbps and normalized beamwidth ωz/r=8 using normalized jitter standard deviation σs/r as a parameter (SISO).

Fig. 5.30: BER vs. transmitted power for number of receiver antenna Nr=2, code length Gp=256, number of user M=8 at a data rate Rb=10 Gbps and normalized beamwidth ωz/r=10 using normalized jitter standard deviation σs/r as a parameter (SIMO).

127

Fig. 5.31: BER vs. transmitted power for number of receiver antenna Nr=4, code length Gp=256, number of user M=8 at a data rate Rb=10 Gbps and normalized beamwidth ωz/r=10 using normalized jitter standard deviation σs/r as a parameter.

The plots of BER versus transmitted optical power Pt(dBm) are depicted in Fig. 5.30 and Fig. 5.31 for a code length Gp=256 with number of user 8 at a bit rate of 10 Gbps with normalized pointing error σs/r as a parameter for receiver antenna Nr=2 and 4 respectively. It is noticed that, the BER increases significantly with increase of σs/r and system suffers BER floor due to the effect of MAI in presence of optical channel effect. It is also observed that, BER performance result improves significantly with the increase of receiver antenna from 2 to 4. In comparison to the SIMO FSO system with number of photodetectors 2 to 8 the BER performance results of OCDMA FSO system using number of receiver antenna 2 to 4 have improved from 10-4 to 10-6 for the similar system parameters.

Plots of BER as a function of transmitted optical power Pt(dBm) using code length Gp as a parameter are presented in Fig. 5.32. It is noticed that, the BER performance result improves with the higher processing gain Gp but the performance degrades significantly with the lower processing gain for the same system parameters. It is also observed that, BER floor starts to occur at a processing gain 256 and continues to increase significantly since the processing gain decreases to 32.

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Fig. 5.32: BER vs. transmitted power for number of receiver antenna Nr=3, number of user M=32, normalized beamwidth ωz/r=10 and normalized jitter standard deviation σs/r=1.0 at a data rate Rb=10 Gbps using code length Gp as a parameter.

The plots of BER versus transmitted optical power Pt(dBm) are depicted in Fig. 5.33 for a code length Gp= 512, number of users 32 at a bit rate of 10 Gbps in the presence of pointing error using number of receiver antennas as a parameter. It is noticed that the BER performance result improves with the increase of number of receiver antennas

Nr=1 to 4 (SISO to SIMO) with even all other parameters are constant.

The plots of BER as a function of transmitted optical power Pt(dBm) are shown in Fig. 5.34 for a code length Gp=1024, at a bit rate of 10 Gbps using number of simultaneous users as a parameter. It is noticed that, the BER increases with the increase of number of simultaneous users with even all other parameters are constant. It is also noticed from the Fig. 5.34 that, BER floor starts to occur for the numbers of simultaneous users 100 and higher for the processing gain of 1024 in the presence of pointing error which is the significant improvement of using OCDMA FSO communication system in comparison to SISO and SIMO FSO communication system.

129

Fig. 5.33: BER vs. transmitted power for code length Gp=512, number of user

M=32, normalized beamwidth ωz/r=10 and normalized jitter standard deviation σs/r=1.0 at a data rate Rb=10 Gbps using number of receiver antenna Nr as a parameter.

Fig. 5.34: BER vs. transmitted power for number of receiver antenna Nr=3, code length Gp=1024, normalized beamwidth ωz/r=10 and normalized jitter standard deviation σs/r=1.0 at a data rate Rb=10 Gbps using number of user M as a parameter.

130

Fig. 5.35: BER vs. transmitted power for number of receiver antenna Nr=4, code length Gp=512, number of user M=16 and normalized jitter standard deviation

σs/r=1.0 at a data rate Rb=10 Gbps using normalized beamwidth ωz/r as a parameter.

Fig. 5.36: Power penalty vs. normalized jitter standard deviation σs/r for number of receiver antenna Nr=4, code length Gp=512, normalized beamwidth ωz/r=10 and normalized pointing error σs/r=1.0 at a data rate Rb=10 Gbps using number of users M as a parameter.

From Fig. 5.35, it is observed that, the BER performance result in the presence of pointing error is significantly depends on the normalized beam widths. Better 131 performance results could be achieved with the narrower beam width (ωz/r=5) than the wider one (ωz/r=25).

Fig. 5.37: Receiver sensitivity vs. number of receiver for normalized beamwidth

ωz/r=5, normalized jitter standard deviation σs/r=1.0 and number of users M=16 at a data rate Rb=10 Gbps using code length as a parameter.

It is noticed form the power penalty or receiver sensitivity as function of normalized jitter standard deviation measured at a BER of 10-9 shown in Fig. 5.36 that, the penalty depends significantly on the number of simultaneous user in presence of pointing error. Penalty is lower for the lower number of simultaneous user which increases with the increase of simultaneous user. For example, penalty for user number 8 with data rate

Rb=10 Gbps, normalized beamwidth ωz/r=10 and at a normalized pointing error σs/r=1.0 is 2.5 dB which increases to 6.5 dB for user number 64. It is also noticed that, the penalty beyond σs/r=1.5 increases abruptly with increase of number of simultaneous users. Receiver sensitivity as a function of number of receivers are shown in Fig. 5.37 plotted at a BER=10-9. It is noticed from the figure that, the receiver sensitivity increases to 2.75 dB with the increases of processing gain from 64 to 512 with the increase of number of antenna from 1 to 4 for normalized beamwidth ωz/r=5, normalized pointing error σs/r=1.0 and number of users M=16 at a data rate Rb=10 Gbps.

132

Effect of atmospheric turbulence considering receive diversity and space diversity are presented in [34, 35, 36, 70, 73, 111, 115]. Similarly, performance of FSO link in weak, moderate and severe atmospheric turbulence considering SIMO, MISO and MIMO format are reported in [39, 82, 117, 125, 126]. The BER performance results have been evaluated analytically and verified by simulation results in [42, 96, 114] in the atmospheric turbulent channel in presence of pointing error considering space diversity. The performance results presented in Fig. 5 of [42] and Fig. 2 of [96] confirms the validity of our analytical results presented for SISO and SIMO configuration. Specially, Fig. 3 to Fig. 5 of [114] presented the similar performance results for SISO and MIMO configurations in presence of atmospheric turbulence. BER performance results of Fig. 3 and 4 of [67] Fig. 3 of [87] evaluated for OCDMA FSO communication system over atmospheric turbulence channel taking the diversity into consideration is comparable to the performance results we evaluated analytically for OCDMA FSO communication system. Though the analytical methods, channel parameter and the system parameters of the above works have differences than that of ours; comparison of the plots reveals that performance results obtained by our analytical approach conform well to those reported in above references.

5.7 Conclusions

Analytical approaches are presented to evaluate the BER of a SISO, SIMO MISO, MIMO and SIMO OCDMA FSO communication system in the presence of pointing error with receive diversity by developing the pdf of the SNR at the output of PIN photodetector receiver combiner. It is observed that, FSO system suffers significantly in terms of BER due to pointing error and there is penalty due to pointing error which increases with the increases of jitter variance and equivalent beamwidth of source. An improvement in the required transmitting power at a given BER and the BER performance results are achieved using diversity in reception and SIMO OCDAM FSO system. The receive diversity and OCDMA allows higher value of pointing error at a given value of transmit power and BER. In the next chapter, the performance of multi- wavelength OCDMA WDM system over atmospheric channel will be numerically evaluated based on the analytical developments.

Chapter 6

PERFORMANCE ANALYSIS OF MULTI-WAVELENGTH OCDMA WDM SYSTEM OVER ATMOSPHERIC CHANNEL

6.1 Introduction

Performance of an OCDMA system is limited by multi-access interference and also by channel impairments. The capacity of OCDMA system can be increased with a hybrid multiple access technique like multi-wavelength OCDMA (MW-OCDMA) WDM system which can be implemented by assigning a number of wavelengths to OCDMA user along with WDM multiplexing. In this chapter, analysis is provided to evaluate the BER performance of a MW-OCDMA FSO communication link using optical encoder and SIK decoder. The analysis provides the analytical technique to evaluate the BER performance over atmospheric channel in the presence of atmospheric turbulence and pointing error and to determine the capacity enhancement of an OCDMA system using WDM technique [58, 118-121]. The numerical BER performance evaluations are carried out based on the number of wavelength, number of simultaneous users, code length, normalized jitter standard deviation and the atmospheric turbulence parameters.

6.2 MW-OCDMA Transmitter and Receiver Model

The system block diagram of a MW-OCDMA transmitter is shown in Fig 6.1(a) and MW-OCDMA SIK dual photodetectors receiver is shown in Fig 6.1(b). The data from ith channel is converted to a serial input to N number of parallel streams. The ith parallel data stream is used to modulate a laser diode (LD) of λi to set the optical input of the OCDMA encoder [122]. The output of the OCDMA encoder is generated using a code generator (CG). The outputs of OCDMA encoders are multiplexed by a WDM multiplexer of N number of wavelengths. The combined OCDMA-WDM signal is then transmitted through the FSO channel. The received optical signal from the FSO channel is amplified by an EDFA and demultiplexed by WDM demultiplexer. The outputs of 134

WDM demultiplexer are passed through OCDMA decoder. The output of each OCDMA decoder is received by a SIK receiver with dual photodetectors and data decision is carried out on each data channel.

j s1 ()t dt1() j mt1 ()

mtj ()

stj() { o } jM=1− = Sto() dtM () j j mtM () sM ()t

Fig. 6.1(a): Multi-wavelength OCDMA transmitter.

Fig. 6.1(b): Multi-wavelength OCDMA SIK dual photodetectors receiver.

6.3 OCDMA-WDM Channel Model

FSO channel model for strong atmospheric turbulence presented in sub-section 3.2.1 and generalized pointing error model presented in sub-section 3.2.3 of chapter 3 shall be followed as the channel model for the development of analytical expression for SNIR and then average BER.

135

6.4 OCDMA-WDM System Analysis

The information bits are serial to parallel converted and the data corresponding to ith th branch of the j user is used to modulate a LD of wavelength λi. The output of the

Mach-zehnder modulator (MZM) with a LD of wavelength λi can be expressed as:

jj⎡⎤2πc dtiTi( )= 2 Pmt ( )cos⎢⎥ t (6.1) ⎣⎦λi th th The encoded optical CDMA signal corresponding to i wavelength λi and j user is given by:

Lc −1 jjj jj ⎡⎤2πc stii( )== dtct ( ). ( ) 2 P Til∑ mtctptlT ( ) ( ) ( − c )cos⎢⎥ t (6.2) l=0 ⎣⎦λi j th th th where mti () represents the data of i branch of the j user, λi is the wavelength of i

th optical carrier, ctj () represents the j user code which consists of Lc chips of duration

j th th Tc, ctl ( ) represents the l chip of the j code.

The transmitted WDM signal of the jth user can then be represented as:

MMLc −1 jj jj ⎡⎤2πc Stoi( )== st ( ) 2 P Tilc mtctptlT ( ) ( ) ( − )cos⎢⎥ t (6.3) ∑∑∑ λ iil===110 ⎣⎦i

We consider the effect of atmospheric turbulence on the optical signal in terms of Is.

The optical signal received by Kth user receiver can be represented as:

K Kjd−α rtoosapc()=⊗∑ StIehhht (). . . () j=1

KM Lc −1 −αdjj ⎡⎤2πc =−⊗∑∑ 2PeTsil . I . ∑ m ( tc ) ( tpt ) ( lT c )cos⎢⎥ thh apc . ht ( ) ji==11 l = 0 ⎣⎦λi KMLc −1 ⎡⎤ jj 2πc =−∑∑∑ 2PIrs . m i ( tc ) l ( tp ) out ( t lT c ) . hh ap . cos ⎢⎥ t jil===110 ⎣⎦λi

MKLc −1 jj ⎡⎤2πc =−∑∑∑ 2PIrs . m i ( tc ) l ( tp ) out ( t lThh c ). ap . cos⎢⎥ t (6.4) iil===110 ⎣⎦λi where ha is the attenuation due to atmospheric turbulence and hp is the attenuation due to geometric spread and pointing error, hc(t) is the normalized channel fading coefficient, d is the link distance and Pr is the average received optical power represented by: 136

PPe==.−αd and Pt ( ) ptht ( )⊗ ( ) (6.5) rT out c The pth wavelength signal at the output of WDM DMUX of jth user receiver is given by:

KMLLc −−11c jjj jj rp() t=− 2 PI r . s∑∑ m p () tc l () tp out ( t lThh c ) a. p + 2 PI r . s∑ x i ∑ m i () tc l () tp out ( t − lThh c ) a. p (6.6) jl==10 i= 1 l = 0 ip≠ th where xi is the cross talk parameter for i WDM channel due to WDM multiplexer and demultiplexer.

The output of the SIK receiver corresponding to pth wavelength channel of jth user can be represented as:

T RPI. s K Lc −1 Z() t =−dr s h . h mjjj ().() t p t lT . C()() t− lT− C t− lT dt iappoutccc∫∑∑ {} 2 0 jl==10 T RPI. s MK Lc −1 +−dr s x hh. mtpjjj ( ). ( tlTCtlTCtlTdtit ) . (− )− (− )+ ( ) (6.7) ∫∑∑iapi ∑ outc{} c c n 2 0 jj==11 l = 0 ip≠

where Ts=M.Tb and Tc= Ts/Lc

Zi(t) can be re-written by (6.8) and (6.9) as [12, 14]:

T RPI.1s K Lllc −1 ⎧⎫+−btlTctlT()( −) Zt() =−dr shh. mtpj ( ). ( t lT ) . c c dt iappoutc∫∑∑ ⎨⎬ 220 jl==10 ⎩⎭ T RPI.s MK Lllc −1 ⎧⎫1()()+−btlTctlT − +−+dr sxhhmtptlT.j ( ). ( ) . c c dtit( ) (6.8) ∫∑∑iapi ∑ outc⎨⎬ n 220 jj==11 l = 0 ⎩⎭ ip≠

T RPh... h I s K Lllc −1 ⎧⎫1(+−b t lT )() c t − lT Zt()=−dr a p s mtpj (). ( t lT ) . cc dt ipoutc∫∑∑ ⎨⎬ 420 jl==10 ⎩⎭ T RPxh... h . I s MKLc −1 ⎧⎫1(+−bll t lT )() c t − lT +−+dr i a p s mtpj ( ). ( t lT ) .cc dtit ( ) (6.9) ∫∑∑∑ i out c⎨⎬ n 220 jjl===110 ⎩⎭ ip≠

137

Equation (6.9) can be simplified as [12, 14]:

T RPh... h I s Lc −1 Z() t=−dr a p s pkl ( t lT ).( c t− lT ). dt ioutcc∫ ∑{} 4 0 l=0

Ts L −1 RPh... h I c 2 +−dr a p s piil()()() t lT b t− lT c t− lT dt ∫ ∑{}out c c c 4 0 l=0 T RPh... h I s K Lc −1 +−dr a p s pkkkl()()().(). t lT b t− lT c t− lT c t− lT dt ∫∑∑ out c{} c c c 2 0 jl==10 T RP...xhh . I s K Lc −1 + dr iaps pmi()(). t−− lT c t lT dt ∫∑∑{}out c c 4 0 jl==10

Ts MKL −1 RPxh... h . I c 2 +−−−+dr i a p s piil( t lT ) b ( t lT ) c ( t lT ) dt i ( t ) (6.10) ∫∑∑∑{}out c c c n 4 0 ijl===010 ip≠

The mean value of photo current Zi(t) for a given value of ha and hp can be represented by:

Ts L−1 RPdr Uhh()IIs,, a p=−∫ ∑ s.() hhtptlTdt pt .().() a out c (6.11) 4T l=0 s 0 ∞ And, Uhh22 ( , )= UIhhpIdI ( , , ) ( ) ( ) (6.12) ap ∫ sap s s 0

The variance of noise current in(t) is represented by:

222 4KTBb σσσn =+th shot = +2eB ( I sig ++ I x I b ) (6.13) RL M 2 where Isig=RdIo and Ib=RdPb, Ix = RdPx, Px = Pxri.∑ , Kb is the Boltzmann constant, T i=1 is the receiver temperature in Kelvin, B is the receiver bandwidth, RL is the load resistance of the receiver, Pb is the background radiation and e is the electron charge.

The variance of MAI is given by: σ 22(hh , )= U ( IhhpIdI , , ) ( ) ( ) (6.14) MAI a p ∫ s a p s s

The variance of MAI for a given value of Is can be represented by: 2(M − 1) σ 22(hh , )= U ( Ihh , , ). (6.15) MAI a p s a p 3L c 138

The variance of MAI due to cross talk with cross talk parameter [123, 124] xi can be represented by: 2(M − 1) σ 222(hh , )= U ( Ihh , , ). x . (6.16) MAI/ xi a p s a p i 3L c

The signal to noise plus interference ratio (SNIR) conditioned on a given value of ha and hp is then expressed by: Uhh2 (, ) ξ (hh , )= ap (6.17) ap σσ22++ σ 2(,hh ) + σ 2 (, hh ) th shot MAI a p MAI/ xi a p

The conditional BER conditioned on a given value of channel coefficient ha and hp is expressed as: 1 Ph( , h )= erfc⎡⎤ξ ( h , h ) / 2 2 (6.18) ba p 2 ⎣⎦a p

The average BER for a given ha can be expressed as:

∞ Ph( )= Ph ( , h ) phdh ( ) ( ) (6.19) ba∫ ba p p p −∞ Finally, the unconditional BER can be found as: 1 ∞ BER= erfc⎡⎤ξ ( h , h ) / 2 2 p ( h ) d ( h ) (6.20) 2 ∫ ⎣⎦ap a a −∞

6.5 Results and Discussions

Following the analytical approach in section 6.4 we evaluate the average BER for a SIK dual photodetector receiver at a bit rate of 1Gbps considering strong atmospheric turbulence in the presence of pointing error. Numerical evaluations are carried out in terms of BER and the number of wavelengths, number of simultaneous users, code length and normalized jitter standard deviations. The system parameters used for numerical computations are presented in Table 6.1.

139

Table 6.1: System parameters Parameter Symbol Value Data rate Rb 1 Gbps Receiver bandwidth B 1 GHz Responsivity Rd 0.85 A/W Receiver temperature T 300 0K Load resistance of receiver RL 50 Ω -23 Boltzmann’s constant Kb 1.38x10 W/K/Hz Electron charge e 1.6x10-19 C Normalized beamwidth ωz/r. 10

Effective beam radius at the transmitter Wt 20 cm Effective beam spot radius at the receiver Wr 50 cm Detector aperture radius r 20 cm Operating wavelength λ 1550 nm Link distance L 500-4000 m 2 Rytov variance (strong turbulence) σx 0.0559-3.8081 2 -14 Index of refraction structure Cn 10 Number of users M 1 – 64 Code length (processing gain) Lc (Gp) 64 –1024 Normalized pointing error standard deviation σs/r 0.2 - 2.5 Power penalty at BER - 10-9 Cross talk current Ix 1 nA Background current Ib 10 nA Cross talk parameter xi 0.01

Plots of BER of a MW-OCDMA FSO link are depicted in Fig. 6.2 as a function of received optical power for link distance 500 m, number of wavelength 8, with single user and code length of 512 using normalized jitter standard deviation σs/r as a parameter. It is noticed that, there is degradation of BER performance results for 8- channel WDM system due to the effect of pointing error. The similar plots for MW-

OCDMA system with number of wavelength 20 and number of simultaneous users 8 for a link distance of 1000 m are shown in Fig. 6.3. Comparison of the figures reveals that, there is deterioration in BER performance results due to MAI, atmospheric turbulence and pointing error. It is also noticed that, the BER performance results degrades with the increase of jitter standard deviation from 0.2 to 2.5 and that of link distance from

500 m to 1000 m. Similarly, it is observed that, the BER performance result also depends on the number of wavelength and number of simultaneous users as well. 140

Fig. 6.2: BER as a function of average received optical power for link distance L=500 m number of wavelength=8, number of users M=1 and code length Gp=512 using normalized jitter standard deviation σs/r as a parameter.

Fig. 6.3: BER as a function of average received optical power for link distance L=1000 m number of wavelength=20, number of users M=8 and code length

Gp=512 using normalized jitter standard deviation σs/r as a parameter.

141

Fig. 6.4: BER as a function of average received optical power for number of wavelength=16, number of users M=16, code length Gp=1024 and normalized jitter

standard deviation σs/r=1.0 using link distance L as a parameter.

Plots of BER as a function of received optical power for number of wavelength 16, number of simultaneous users 16 and code length 1024 using link distance as a parameter are shown in Fig. 6.4. It is observed that, the BER performance results of the

OCDMA-WDM FSO system depends remarkably on the link distances and atmospheric turbulence. Since, atmospheric turbulence is the function of link distance and Rytov variance, BER performance results of the system degrades as the link distances increases from 500 m to 4000 m for a given normalized jitter standard deviation

σs/r=1.0.

Plots of BER as a function of received optical power for number of simultaneous users

16 and code length of 1024 and normalized jitter standard deviation σs/r=1.0 link distance of 500 m using number of wavelength as a parameter are shown in Fig. 6.5. It is noticed that, the BER performance improves significantly with the increase of number of wavelengths for a given pointing error, atmospheric turbulence and data rates. This is due to the fact that, bandwidths of each of the sub-channels are reduced as 142 the number of wavelength is increased which results in improvement in BER performance results. This is analogous to multi-carrier CDMA (MC-CDMA) in a wireless communication system.

Fig. 6.5: BER as a function of average received optical power for number of users

M=16, code length Gp=1024, normalized jitter standard deviation σs/r=1.0 and link distance L=500 m using number of wavelength as a parameter.

Fig. 6.6: BER as a function of average received optical power for link distance L=1000 m, code length Gp=256, number of wavelength=8 and normalized jitter

standard deviation σs/r=1.0 using number of simultaneous users as a parameter. 143

Fig. 6.7: BER as a function of average received optical power for link distance L=1500 m, number of wavelength=16, number of simultaneous users M=12 and

σs/r=1.0 using code length Gp as a Parameter.

BER as a function of received optical power for link distance 1000 m, code length 256, number of wavelength 8 and normalized jitter standard deviation σs/r=1.0 using number of simultaneous users as a parameter are shown in Fig. 6.6 and that of link distance

1500 m, number of wavelength 16, number of simultaneous users 12 and σs/r=1.0 using code length as a parameter are shown in Fig. 6.7. It is observed from Fig. 6.6 and Fig.

6.7 that, the performance results of the OCDMA-WDM FSO system significantly depends on the number of simultaneous users and code lengths. As the number of simultaneous user increases, the BER floor starts to occur for the number of users 16 and higher due to the presence of MAI and noise due to cross talk. In contrast to the number of users, it is found from Fig. 6.7 that, as the code length increases for 64 to

1024 the BER performance improves significantly and BER floor starts to occur for code length 256 and lower. This is also due to the impact of MAI and cross talk. Thus the performance results of MW-OCDMA DWM system can be significantly improved using higher code length. 144

Fig. 6.8: Power penalty as a function of normalized jitter standard deviation at a link distance L=1000 m, number of simultaneous users M=8, code length Gp=512 and at a BER=10-9 with number of wavelengths as a parameter.

Fig. 6.9: Power penalty as a function of number of wavelength at a link distance L=1000 m, number of simultaneous users M=8, code length Gp=512 and at a -9 BER=10 using normalized jitter standard deviation σs/r as a parameter.

Plots of power penalty as a function of normalized jitter standard deviation at a link distance 1000 m, number of simultaneous users 8, code length 512 and at a BER=10-9 with number of wavelength as a parameter are shown in Fig. 6.8 and that with the same parameters using normalized jitter standard deviation as a parameter are shown in 145

Fig. 6.9. It is observed from Fig. 6.8 that, the power penalty improves from 12 dB to 5 dB as the number of wave length increase from 1 to 20 at a normalized jitter standard deviation 1.0. Similarly, it is noticed from Fig. 6.9 that, the power penalty improves with the increase of number of wavelength. For example, penalty improves form 5.5 dB to 0 dB when number of wavelength increases from 1 to 20. It is also observed from

Fig. 6.9 that penalty increases drastically from 0 dB to 26 dB with the increase of normalized jitter standard deviation from 0.2 to 2.5 at the number of wavelength of 20.

OCDMA over WDM and Hybrid OCDMA WDM are experimentally presented in [59, 60, 62, 127] for single, 2, and 3-wavelengths. Specifically, [60, 127] represented experimental results for 3-wavelength OCDMA over WDM using 511-chip, 640 Gchips/s superstructured fiber Bragg grating (SSFBG) with the pulse train generated from mode-locked-laser-diode (MLLD) has a central wavelength of 1550.8 nm and repetition rate 10 GHz. In 2- and 3-wavelengths experiments maximum number of active users 16 could be achieved at a BER of 10-9 without considering atmospheric turbulence and pointing error shown in Fig 3.10 [60]. We numerically evaluate the system performance results using SIK dual photodetector receiver at a bit rate of 1 Gbps, wavelength of 1550 nm for wave number 1 to 20 with the other system parameters shown in Table 6.1. Numerical results show that (Fig. 6.6 and Fig. 6.7) 16 number of active users can be achieved at a code length of 256 and more for number of wavelength 8 and more for a link length upto 1500 m and normalized jitter standard deviation 1.0 at a BER of 10-9. The results are very much comparable with the experimental result which validates the analytical approach. 146

Fig. 6.10: Plots of BER vs. number of wavelength for different number of simultaneous users [60].

6.6 Conclusions

In this chapter, an analytical development is presented to evaluate the BER performance of an OCDMA-WDM communication system under the effect of atmospheric turbulence and pointing error considering SIK dual photodetector receiver. Results are evaluated at the data rates of 1 Gbps using different system parameters with strong atmospheric and pointing error. It is found that, the system suffers significant power penalties due to normalized jitter standard deviation and atmospheric turbulences due to link distance, number of wavelengths and number of simultaneous users. It is also found that, the power penalties due to number of simultaneous users, normalized jitter standard deviation and turbulence on BER performance can be significantly improved using higher processing gain and by increasing the number of wavelengths per user. Thus the capacity of an OCDMA system can be largely enhanced by using MW- OCDMA WDM system over atmospheric optical channel. Chapter 7

CONCLUSIONS AND FUTURE WORKS

7.1 Conclusions

FSO communication, now a day, have attracted considerable research interests due to the limitations of the fiber optic constraints imposed by the nonlinear effects. Significant amount of research works are reported recently on FSO communication system taking into account the limitations imposed by the free-space link such as atmospheric turbulence, pointing error, cloud, fog, rain etc. As the number of user in an optical communication network is increasing day by day, OCDMA is a very attractive technique for multiuser optical communication networks. Application of OCDMA in a FSO communication can enhance the capacity of a FSO system when laying of optical fiber is very much restricted. In this respect, analytical research works are presented in this dissertation to develop analytical tools for evaluating and estimating the performance limitations due to above channel impairments of an OCDMA FSO system. Further, analytical approaches are also developed for OCDMA FSO system with diversity in transmission and reception using multiple photodetectors. Analysis is also carried out on MW-OCDMA WDM FSO system to evaluate the further improvement of capacity of an OCDMA FSO system.

7.2 Summary of the Major Contributions

The principal motivation of this research work is to evaluate the effects of atmospheric impairments such as atmospheric turbulences, pointing error and effect of cloud, fog etc on the OCDMA FSO communication system. The system performance results are evaluated at a data rate of 1 Gbps to 10 Gbps taking the other system parameters into consideration. The data rate for the effect of cloud on the OCDMA FSO system is taken to be 1 Mbps and 10 Mbps for fog, since it is difficult to transmit data in the range of Gbps through the cloud, rain and dense fog. Channel impairments are the major limiting 148 factor for the propagation of high data rate through the FSO system and to improve the system capacity. Accurate system model need to be developed to optimize the system performance for FSO OCDMA system. In this respect, an analytical modeling is very much essential for a deeper comprehension and overall view of the system to estimate the optimum parameters to achieve the best performance results. Keeping this in mind, several analytical models are developed to evaluate the effect of channel impairments. The major results obtained from each approach are summarized as follows:

1. Analytical approaches are presented to evaluate the effect of weak atmospheric turbulence on the single channel FSO link considering PIN and APD photodetector receivers. The analysis is extended to include the effect of timing jitter and scintillation index. The conditional and unconditional BER expressions are formulated over the pdf of atmospheric turbulence considering optical Q-OPPM modulation format at a data rate of 2.4 Gbps and 10 Gbps respectively. In case of PIN photodetector receiver, the system performance degrades with the increase of timing jitter variance from 0.0 to 0.15 and the turbulence variance of 0.1. The system performance improves significantly with the increase of OPPM order from 8 to 256. The system also suffers from significant amount of power penalty due timing jitter variance and scintillation index variation. For example, power penalty ranges from 6 dB to 24 dB, when modulation order varies from 256 to 8 at a jitter variance of 0.1. Similarly, power penalty ranges from 8 dB to 26 dB at a scintillation index of 0.3. The APD photodetector receiver’s shows better performance results for the similar system parameters since APD gain can enhance the performance results. Results evaluated for timing error of 0.0 to 0.4 at a step of 0.05, scintillation index of 0.1 to 0.9, PPM order of 8 to 256 with the APD gain of 150. BER performance result degrades significantly with the increase of timing jitter and system suffers from substantial amount of power penalty due to the timing error and scintillation index which can be reduced by increasing optical PPM order.

2. Atmospheric turbulence is the large-scale and small-scale irregular air motions caused by the changes of atmospheric pressure and temperature, 149

velocity variation of air and different weather conditions. An analytical approach is presented to evaluate the effect of weak and strong atmospheric turbulence and the combined effect of atmospheric turbulence and pointing error on BER for OCDMA FSO system. Expressions for average BER has been formulated over the pdf of atmospheric turbulence and pointing error. It is shown that, the BER performance of the OCDMA system severely degrades due to the presence of weak and strong atmospheric turbulence as well as the combined influence of atmospheric turbulence and pointing error. System performance in terms of BER and power penalty also depends on the link distances, number of simultaneous user and presence of MAI which causes BER floor earlier. All these effects can be substantially reduced by increasing the system processing gain. For example, the penalty due to weak atmospheric turbulence is found to be in the order of 1 dB to 8 dB for 8 user and increases to 3 dB to 10 dB for 12 user for turbulence variance ranges from 0.01 to 0.3 at a processing gain of 512, data rate of 1Gbps and BER=10-9 which can be reduced substantially using processing gain 1024. It is observed that, the BER floor is significant at a code length of lower than 256 and the number of simultaneous user higher than 16.

3. The BER performance results and power penalties further deteriorates when the OCDMA FSO system switched from weak atmospheric turbulence to strong turbulence. It is found that, the penalty ranges from 9 dB to 11.5 dB as the number of user increases from 2 to 16 at a link distance of 3000 m, code length 512 and BER=10-9. The system performance in presence of strong atmospheric turbulence primarily depends on the link distance which causes to increase the Rytov variance. The BER performance is evaluated at a link distances of 500 m to 5000 m with corresponding Rytov variances of 0.0559 to 3.8081 considering both the large and small scale eddies. It is observed that, BER improves approximately from 10-2 to 10-12 when code length increases from 64 to 1024 corresponding link distances reduces from 1000 m to 500 m at a received optical power -10 dB and simultaneous user number 20. The performance of OCDMA FSO system further deteriorates when the combined effect of atmospheric turbulence and pointing error has 150

been taken into consideration with the similar system parameters. It is observed that, the pointing error has a significant impact on the OCDMA FSO system, such as BER floor occurs much earlier with the effect of pointing error standard deviation. For example, BER increases from 10-6 to approximately 10-3 when normalized jitter standard deviation increases from 0.5 to 2.5 with the code length of 512, link length 1500 m, Rytov variance 0.4189 at a received optical intensity 10 dB, data rate 1 Gbps and user number 30. Similar performance result of BER is also found for the variation of link distance from 500 m to 4000 m with code length 1024. The power penalty ranges from 12.5 dB to 18 dB for a link distance 1000 m at a normalized jitter standard deviation 1.0 when the number of user increases from 4 to 32.

4. Analysis is carried out to evaluate the effect of cloud, fog and pointing error on the performance of an OCDMA FSO system using optical domain encoder and SIK balanced photodetector direct detection receivers. Expression for BER is formulated considering the transfer function of cloud and fog and the pdf of channel coefficient for pointing error. The BER performance results and power penalties are numerically evaluated mainly based on the effect of cloud and fog thickness, normalized jitter standard deviation, code length and number of simultaneous user at a data rate of 1 Mbps for cloud, 10 Mbps for fog and 1 Gbps for the effect of pointing error. It is observed that, BER degrades with the increase of cloud thickness and fog optical thickness as well as the number of simultaneous user. For example, BER increases approximately from 10-8 to 10-2 when cloud thickness increase from 200 m to 300m with code length 256, number of users 8 at a data rate of 1Mbps and received optical intensity of 0 dBm. Similarly, BER floor is significant for the number of user more than 16 at a code length of 512 which could be substantially improved with higher code length. The power penalty also increases with the increase of cloud thickness and number of user. For example, power penalty is 2 dB for cloud thickness 200 m which increases to 10 dB for cloud thickness of 300 m when number of simultaneous user is 16 at a code length of 1024 and BER=10-9. 151

5. Similar performance results could also be achieved from OCDAM FSO channel in presence of fog. It is observed that, the BER performance results degrades as the fog optical thickness increases from 200 m to 300 m and number of simultaneous user increases from 1 to 128. The system performance in terms of BER as well as the power penalty improves significantly using higher code length. For example, BER improves from 10-2 to 10-9 when code length increases from 64 to 1024 at -10 dBm and power penalty improves from 14 dB to 3 dB for user number 15 when thickness decreases from 300 m to 200 m using code length 1024 at a BER of 10-9.

6. OCDMA FSO system is highly affected by pointing error and the system performance in terms of BER floor improves noticeably with higher processing gain similar to the effect of cloud and fog. For example, BER floor occurs at a BER=2.818x10-10, code length of 512 for user number 32 but the same is improved to 3.214x10-14 for a code length of 1024 with user number 32. It is also observed that, when the user number is increased from 8 to 64 the BER performance degrades drastically. Power penalty is calculated based on the code length and number of simultaneous user considering the effect of pointing error. It is found that, penalty is higher for the lower code length (Gp=128) and higher number of simultaneous user (M=64) and vice versa. Approximately 2 dB improvement could be achieved by using code length of 1024.

7. Space-time diversity technique is most widely accepted technique to improve the communication system performance using SIMO, MISO or MIMO arrangements in place of SISO configuration. In the transmitter OOK or intensity modulation format is used to transmit the laser information bits and at the receiver bits are detected by PIN photodetector receivers using EGC at the output. BER performance result improves significantly using SIMO space-time diversity configuration instead of SISO arrangement. Four approaches for SIMO configuration in presence of pointing error are presented to compare the performance results and to decide the best 152

approach. Comparing the overall system performance in terms of BER and power penalty, approach 4 is found to be the best approach which can tolerate higher values of normalized jitters standard deviation. For example, approach 4 could tolerate normalized jitter standard deviation as high as 2.7 for 4 receiver antennas. Analyses have been carried out on MISO and MIMO configuration without numerical evaluation.

8. Analysis and numerical evaluation is also carried out on SIMO OCDMA FSO system considering the effect of pointing error and normalized beamwidth at a data rate of 10 Gbps. It is noticed that, the BER performance results improves significantly from 10-1 to 10-6 for SISO and SIMO OCDMA FSO system. BER performance results also improve significantly since the increase of code length from 32 to 512. It is also observed that, BER significantly depends on the number of receive antennas (Fig. 5.33) and normalized beam width (Fig. 5.35) i.e. narrower the beam width better the performance results. It is found from the numerical evaluation that, the SIMO OCDMA system with 3 receive antenna could support 100 simultaneous users within the acceptable BER=10-9.

9. OCDMA is capable of providing a gigabit or even multi-gigabit/second for each user and OCDMA over WDM-PON could be one of the most promising system architecture that can break through the last mile bottleneck. Analyses are carried out to evaluate the performance of MW- OCDMA WDM system in the atmospheric turbulent channel in presence of pointing error. It is found that, the BER performance depends on the atmospheric turbulence parameter and normalized jitter standard deviations. For example, when the link distance increases from 500 m to 4000 m BER increases from 2.785e-010 to 2.097e-005 at a received optical power of 2 dB for 16 users and code length of 1024. Similar results are also found in case of pointing error and change of wavelength. BER started flooring with user number 16 and above for a code length 256 and below. Best results obtained for the user less than 16 at the code length 512 and above. It is also observed that, the power penalty increases from 0 dB to 26 dB for the increase of jitter 153

standard deviation from 0.2 to 2.5 for the similar system parameter which can be substantially reduced using higher processing gain.

The above developed system models and system analysis for the evaluation of the performances of Q-OPPM FSO system over atmospheric turbulence; OCDMA FSO system considering the effect of atmospheric turbulence and pointing error; effect of cloud and fog; space-time diversity and MW-OCDMA WDM through different atmospheric channel effects has its valid ranges of system parameters.

7.3 Suggestions for Future Research

Analytical approaches are presented considering the channel impairments due to different types of atmospheric turbulences, pointing error, combined effect of atmospheric turbulence and pointing error, effect of scintillation index and timing jitter and finally the effect cloud and fog on the OCDMA FSO system using their respective or combined probability density function or transfer functions. Specially, combined effects of atmospheric turbulence and pointing error; effect of scintillation index and timing jitter are also evaluated. Further research works can be initiated to develop an analytical model for a FSO channel considering all the channel limitations such as fog, cloud, rain, atmospheric turbulence, pointing error and timing jitter to find the overall channel transfer function to evaluate the limitations on BER performance due to above channel effects.

Mathematical analysis have been carried out to evaluate the BER performance of SISO, SIMO, MISO and MIMO space-time diversity schemes for a given value of pointing error on FSO system with multiple photodetector receivers using EGC at the output. Further research works can be carried out for optical MIMO FSO link with maximal ratio combining (MRC) and selection combining techniques. Application of different codes such as space time block code (STBC), Alamouti code etc. in combination with space-time diversity on the OCDMA FSO link under different channel effects are the scope of future research work to be completed.

Numerical simulation software’s are the essential tool to verify the analytical results with computer simulation results. Using optical orthogonal codes (OOC) numerical 154 simulations can be carried out to evaluate the performance of OCDMA system over different atmospheric conditions. The simulation can be extended to MW-OCDMA WDM FSO communication system to find the optimum codes and optimum system parameters.

Further research can be initiated for an optical FSO link with MW-OCDMA with optical orthogonal frequency division multiplexing (O-OFDM) to overcome the channel limitations and to obtain the optimum design parameters.

The effect of backscattering on a WDM FSO system is important for future work. Analytical and simulation based research work can be carried to estimate the effect of backscattering in a WDM-OCDMA system.

155

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169

LIST OF PUBLICATIONS a) Journal

1. A. K. M. N. Islam and S. P. Majumder, “Analytical Evaluation of Bit Error Rate Performance of a Free-Space Optical Communication System with Receive Diversity Impaired by Pointing Error,” Journal of Optical Communications, vol. 36, no. 2, pp. 161-168, March 2015.

2. A. K. M. N. Islam and S. P. Majumder, “Effect of Pointing Error on BER Performance of an Optical CDMA FSO Link with SIK Receiver”, Accepted by Journal of Optical Communications, 2015.

3. A. K. M. N. Islam and S. P. Majumder, “Effect of Atmospheric Turbulence on BER Performance of an Optical CDMA FSO Link with SIK Receiver”, Submitted to Optik- International Journal for Light and Electron, Elsevier 2015.

4. A. K. M. N. Islam and S. P. Majumder, “Effect of Cloud on BER Performance of an OCDMA FSO Link with SIK Receiver”, Submitted to IEEE, Photonics Technology Letters 2015.

5. A. K. M. N. Islam and S. P. Majumder, “Impact of Scintillation and Timing Jitter on BER Performance of an Optical M-ary PPM over FSO Turbulent Channel with PIN and APD Receivers”, Submitted to IET Communications, UK, 2015.

b) Conference

1. A. K. M. N. Islam and S. P. Majumder, “Performance Analysis of a Free Space Optical Link in the Presence of Pointing Errors with Space Diversity”, Proceedings of International Conference on Electrical Engineering and Information & Communication Technology (ICEEICT 2014), 10-12 April 2014, Dhaka, Bangladesh.

2. A. K. M. N. Islam and S. P. Majumder, “Effect of Timing Jitter on the BER Performance of a M-PPM FSO Link over Atmospheric Turbulence Channel”, Proceedings of International Conference on Electrical and Computer Engineering (ICECE 2014), 20-22 December 2014, Dhaka, Bangladesh.

3. A. K. M. N. Islam and S. P. Majumder, “Impact of Timing Jitter on the BER Performance of an M-PPM Free Space Optical Link in Presence of Atmospheric Turbulence”, Proceedings of International Conference on Electrical Engineering and Information & Communication Technology (ICEEICT 2015), 21-23 May 2015, Dhaka, Bangladesh. 170

4. A. K. M. N. Islam and S. P. Majumder, “Performance Analysis of a SIMO and MIMO FSO Link in Presence of Pointing Error using Equal Gain Combiner”, Proceedings of International Conference on Computer and Information Technology (ICCIT 2015), 21- 23 December 2015, Dhaka, Bangladesh.

5. A. K. M. N. Islam and S. P. Majumder, “Effect of Weak Atmospheric Turbulence on the BER Performance of an Optical CDMA FSO Link with SIK Receiver” Proceedings of International Conference on Telecommunications and Photonics (ICTP 2015), 26-28 December 2015, Dhaka, Bangladesh.