The Pennsylvania State University

The Graduate School

College of Engineering

OPTICAL WIRELESS COMMUNICATIONS: THEORY AND

APPLICATIONS

A Dissertation in

Electrical Engineering

by

Mohammadreza Aminikashani

© 2016 Mohammadreza Aminikashani

Submitted in Partial Fulfillment

of the Requirements

for the Degree of

Doctor of Philosophy

May 2016

The dissertation of Mohammadreza Aminikashani was reviewed and approved∗ by

the following:

Mohsen Kavehrad

W.L. Weiss Chair Professor of Electrical Engineering

Dissertation Advisor, Chair of Committee

Timothy Kane

Professor of Electrical Engineering

Julio Urbina

Associate Professor of Electrical Engineering

Jamal Rostami

Associate Professor of Energy and Mineral Engineering

Kultegin Aydin

Professor of Electrical Engineering

Head of the Department of Electrical Engineering

∗Signatures are on file in the Graduate School.

ii

Abstract

This dissertation focuses on optical communications having recently attracted sig-nificant attentions as a promising complementary technique for radio frequency(RF) in both short- and long-range communications. These systems offer signifi-cant technical and operational advantages such as higher capacity, virtually unlim-ited reuse, unregulated spectrum and robustness to electromagnetic interference.Optical wireless communication (OWC) can be used both indoors and outdoors.

Part of the dissertation contains novel results on terrestrial free-space optical(FSO) communications. FSO communication is a line-of sight technique that useslasers for high rate wireless communication over distances up to several kilometers.In comparison to RF counterparts, a FSO link has a very high optical bandwidthavailable, allowing aggregate data rates on the order of Tera bits per second (1 Terabits per second is 1000 Giga bites per second). However, FSO suffers limitations.The major limitation of the terrestrial FSO communication systems is the atmo-spheric turbulence, which produces fluctuations in the irradiance of the transmittedoptical beam, as a result of random variations in the refractive index through thelink. The existence of atmospheric-induced turbulence degrades the performanceof FSO links particularly with a transmission distance longer than 1 kilometer.The identification of a tractable probability density function (pdf) to describe at-mospheric turbulence under all irradiance fluctuation regimes is crucial in orderto study the reliability of a terrestrial FSO system. This dissertation addressesthis daunting problem and proposes a novel statistical model that accurately de-scribes turbulence-induced fading under all irradiance conditions and unifies mostof the proposed statistical models derived until now in the literature. The proposedmodel is important for the research community working on FSO communicationsbecause it allows them to fully capitalize on the potentials of currently used FSO

iii

systems. Furthermore, utilizing this new statistical channel model, closed-formexpressions for the diversity gain and the error rate performance of FSO links withspatial diversity are derived.

In addition to addressing ways to improve outdoor FSO communication sys-tems, this dissertation addresses some major challenges in indoor visible light com-munication (VLC). VLC is an advantageous technique that is proposed for wirelessindoor communications. In VLC systems, the existence of multiple paths betweenthe transmitter and receiver causes multipath distortion, particularly in links usingnon-directional transmitters and receivers, or in links relying upon non-line of-sightpropagation. This multipath distortion can lead to intersymbol interference (ISI)at high bit rates. Multicarrier modulation usually implemented by orthogonal fre-quency division multiplexing (OFDM) can be used to mitigate ISI and multipathdispersion. Nevertheless, the performance of VLC systems employing OFDM mod-ulation is significantly affected by nonlinear characteristic of light-emitting diode(LED) due to the large peak-to-average power ratio (PAPR) of OFDM signal. Inother words, signal amplitudes below the LED turn-on-voltage and above the LEDsaturation point are clipped. This dissertation targets these important issues andsuccessfully addresses them by developing some techniques to reduce high PAPRof optical OFDM signal and determining the optimum operating characteristics ofLEDs for combined lighting and communications applications.

VLC can also provide a practical solution for indoor positioning as global po-sitioning system (GPS) does not provide an accurate and rapid indoor positioningsince GPS radio signals are attenuated and scattered by walls of large buildingsand other objects. A practical VLC system would be likely to deploy the sameconfiguration for both positioning and communication purposes where high speeddata rates are desired. This dissertation also proposes a novel OFDM VLC sys-tem that provides a high data rate transmission and can be used for both indoorpositioning and communications where the multipath reflections are taken intoaccount.

Description of an experimental demonstration is also part of the dissertationwhere a software defined radio (SDR) was employed as the primary hardware andsoftware interface to verify some of the results of the topics discussed earlier.

iv

Table of Contents

List of Figures ix

List of Tables xiii

List of Abbreviations xiv

List of Symbols xvii

Acknowledgments xx

Chapter 1Introduction 11.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.2 Objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31.3 Organization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

Chapter 2Statistical Channel Model for Turbulence-Induced Fading in

Free-Space Optical Systems 72.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82.2 Double GG Distribution . . . . . . . . . . . . . . . . . . . . . . . . 102.3 Verification of the Proposed Channel Model . . . . . . . . . . . . . 15

2.3.1 Plane Wave . . . . . . . . . . . . . . . . . . . . . . . . . . . 152.3.2 Spherical Wave . . . . . . . . . . . . . . . . . . . . . . . . . 19

2.4 Performance Evaluation . . . . . . . . . . . . . . . . . . . . . . . . 212.4.1 BER Analysis of SISO FSO System . . . . . . . . . . . . . . 212.4.2 Outage Probability Analysis of SISO FSO System . . . . . . 26

2.5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

v

Chapter 3Statistical Analysis of Sum of Double Generalized Gamma Vari-

ates 293.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 293.2 An Upper-Bound for the Distribution of the Sum of Double GG

Variates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 303.3 An Approximate Distribution of the Sum of Double GG Variates . . 323.4 Verification of the Mathematical Analysis . . . . . . . . . . . . . . . 343.5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37

Chapter 4Performance Evaluation of Free-Space Optical Links with Spa-

tial Diversity 394.1 System Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 404.2 Performance Analysis of of MIMO FSO Links . . . . . . . . . . . . 404.3 Performance Analysis of FSO Links with Receive Diversity . . . . . 42

4.3.1 SIMO FSO Links with Optimal Combining . . . . . . . . . . 424.3.2 SIMO FSO Links with Selection Combining . . . . . . . . . 454.3.3 SIMO FSO Links with Equal Gain Combining . . . . . . . . 46

4.4 Performance Analysis of FSO Links with Transmit Diversity . . . . 584.4.1 MISO FSO Links . . . . . . . . . . . . . . . . . . . . . . . . 58

4.5 Performance Comparison of Diversity Techniques . . . . . . . . . . 584.6 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61

Chapter 5Performance Evaluation of Single- and Multi-carrier Modula-

tion Schemes for Indoor Visible Light CommunicationSystems 63

5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 645.2 System Model of ACO-OFDM . . . . . . . . . . . . . . . . . . . . . 655.3 System Model of ACO-SCFDE . . . . . . . . . . . . . . . . . . . . 675.4 Peak-to-Average Power Ratio . . . . . . . . . . . . . . . . . . . . . 685.5 Performance Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . 705.6 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75

Chapter 6Robust Timing Synchronization for AC OFDM Based Optical

Wireless Communications 776.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 786.2 New Timing Synchronization for AC Based OFDM Systems . . . . 79

vi

6.2.1 Timing Synchronization for ACO-OFDM . . . . . . . . . . . 796.2.2 Timing Synchronization for PAM-DMT . . . . . . . . . . . . 80

6.3 Timing Synchronization DHT Based Optical OFDM . . . . . . . . . 816.4 Simulation Results . . . . . . . . . . . . . . . . . . . . . . . . . . . 816.5 Experimental Results . . . . . . . . . . . . . . . . . . . . . . . . . . 836.6 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86

Chapter 7Indoor Location Estimation with Optical-based OFDM Com-

munications 877.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 887.2 System Configuration . . . . . . . . . . . . . . . . . . . . . . . . . . 89

7.2.1 System Model . . . . . . . . . . . . . . . . . . . . . . . . . . 897.2.2 Optical Wireless Channel . . . . . . . . . . . . . . . . . . . 907.2.3 OFDM Transmitter and Receiver . . . . . . . . . . . . . . . 93

7.3 Positioning Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . 957.4 Simulation and Analysis . . . . . . . . . . . . . . . . . . . . . . . . 98

7.4.1 Performance Comparison of Single- and Multi-carrier Mod-ulation Schemes . . . . . . . . . . . . . . . . . . . . . . . . . 99

7.4.2 Effect of Signal Power on the Positioning Accuracy . . . . . 1037.4.3 Effect of Modulation Order on the Positioning Accuracy . . 1067.4.4 Effect of Number of Subcarriers on the Positioning Accuracy 108

7.5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112

Chapter 8Conclusions and Future Work 1148.1 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1148.2 Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1168.3 Publication List . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118

Appendix ASpecial Cases of Double GG Distribution 120

Appendix BSpecial Cases of BER Expression of SISO FSO System over

Double GG Channel 123

Appendix CSpecial Cases of Outage Probability Expression of SISO FSO

System over Double GG Channel 125

vii

Appendix DSpecial Cases of BER Expression of SIMO FSO Links over Dou-

ble GG Channel 127

Bibliography 129

viii

List of Figures

2.1 Pdfs of the scaled log-irradiance for a plane wave assuming weakirradiance fluctuations. . . . . . . . . . . . . . . . . . . . . . . . . . 16

2.2 Pdfs of the scaled log-irradiance for a plane wave assuming moder-ate irradiance fluctuations. . . . . . . . . . . . . . . . . . . . . . . . 17

2.3 Pdfs of the scaled log-irradiance for a plane wave assuming strongirradiance fluctuations. . . . . . . . . . . . . . . . . . . . . . . . . . 18

2.4 Pdfs of the scaled log-irradiance for a spherical wave assuming weakirradiance fluctuations. . . . . . . . . . . . . . . . . . . . . . . . . . 19

2.5 Pdfs of the scaled log-irradiance for a spherical wave assuming mod-erate irradiance fluctuations. . . . . . . . . . . . . . . . . . . . . . . 20

2.6 Pdfs of the scaled log-irradiance for a spherical wave assumingstrong irradiance fluctuations. . . . . . . . . . . . . . . . . . . . . . 21

2.7 Average BER as a function of γ a) Plane wave - σ2Rytov = 2, l0/R0 = 0.5,

b) Plane wave-σ2Rytov = 25, l0/R0 = 1, c) Spherical wave - σ2

Rytov = 2,l0/R0 = 0, d) Spherical wave - σ2

Rytov = 5, l0/R0 = 1 . . . . . . . . . 252.8 Outage probability as a function of γ/γth for a) Plane wave - σ2

Rytov =2, l0/R0 = 0.5, b) Plane wave-σ2

Rytov = 25, l0/R0 = 1, c) Sphericalwave - σ2

Rytov = 2, l0/R0 = 0, d) Spherical wave - σ2Rytov = 5, l0/R0 = 1 27

3.1 Bounded, approximate and exact cdf of the sum of Double GGdistributed RVs assuming plane wave and moderate irradiance fluc-tuations (channel a) . . . . . . . . . . . . . . . . . . . . . . . . . . 35

3.2 Bounded, approximate and exact cdf of the sum of Double GGdistributed RVs assuming plane wave and strong irradiance fluctu-ations (channel b) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

3.3 Bounded, approximate and exact cdf of the sum of Double GGdistributed RVs assuming spherical wave and moderate irradiancefluctuations (channel c) . . . . . . . . . . . . . . . . . . . . . . . . . 36

3.4 Bounded, approximate and exact cdf of the sum of Double GG dis-tributed RVs assuming spherical wave and strong irradiance fluctu-ations (channel d) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37

ix

4.1 Comparison of the average BER between SISO and SIMO withoptimal combing for plane wave with σ2

Rytov = 25 and l0/R0 = 1. . . 444.2 Comparison of the average BER between SISO and SIMO with

optimal combing for spherical wave with σ2Rytov = 2 and l0/R0 = 0. . 45

4.3 Bounded, approximate and exact outage probability of EGC andSISO for a) Plane wave with σ2

Rytov = 2 and l0/R0 = 0.5, b) Planewave with σ2

Rytove = 25 and I0/R0 = 1. . . . . . . . . . . . . . . . . 484.4 Bounded, approximate and exact outage probability of EGC and

SISO for a) Spherical wave with σ2Rytov = 2 and l0/R0 = 0, b) Spher-

ical wave with σ2Rytov = 5 and l0/R0 = 1. . . . . . . . . . . . . . . . 49

4.5 Bounded, approximate and exact BER of EGC and SISO for a)Plane wave with σ2

Rytov = 2 and l0/R0 = 0.5, b) Plane wave withσ2

Rytove = 25 and I0/R0 = 1. . . . . . . . . . . . . . . . . . . . . . . 524.6 Bounded, approximate and exact BER of EGC and SISO for a)

Spherical wave with σ2Rytov = 2 and l0/R0 = 0, b) Spherical wave

with σ2Rytov = 5 and l0/R0 = 1. . . . . . . . . . . . . . . . . . . . . . 54

4.7 Exact, approximate and asymptotic BER of EGC over two i.n.i.d.atmospheric turbulence channels defined as plane wave with σ2

Rytov =2 and l0/R0 = 0.5, and plane wave with σ2

Rytove = 25 and I0/R0 = 1. 564.8 Exact, approximate and asymptotic BER of EGC over two i.n.i.d.

atmospheric turbulence channels defined as spherical wave withσ2

Rytov = 2 and l0/R0 = 0, and spherical wave with σ2Rytov = 5 and

l0/R0 = 1. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 574.9 Comparison of the average BER between SISO and different diver-

sity techniques for plane wave assuming i.i.d. turbulent channelwith σ2

Rytove = 25 and I0/R0 = 1. . . . . . . . . . . . . . . . . . . . 594.10 Comparison of the average BER between SISO and different diver-

sity techniques for spherical wave assuming i.i.d. turbulent channelwith σ2

Rytov = 2 and l0/R0 = 0. . . . . . . . . . . . . . . . . . . . . . 604.11 Comparison of the OC, EGC and SC receivers for SIMO FSO

links over two i.n.i.d. atmospheric turbulence channels defined asplane wave with σ2

Rytov = 2 and l0/R0 = 0.5, and plane wave withσ2

Rytove = 25 and I0/R0 = 1. . . . . . . . . . . . . . . . . . . . . . . 614.12 Comparison of the OC, EGC and SC receivers for SIMO FSO links

over two i.n.i.d. atmospheric turbulence channels defined as spher-ical wave with σ2

Rytov = 2 and l0/R0 = 0, and spherical wave withσ2

Rytov = 5 and l0/R0 = 1. . . . . . . . . . . . . . . . . . . . . . . . . 62

5.1 ACO-OFDM transmitter and receiver configuration. . . . . . . . . . 665.2 ACO-SCFDE transmitter and receiver configuration. . . . . . . . . 67

x

5.3 CCDF of PAPR comparison of ACO-OFDM and ACO-SCFDE forL = 64. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68

5.4 CCDF of PAPR comparison of ACO-OFDM and ACO-SCFDE forL = 256. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69

5.5 Impulse response of the indoor diffuse channel. . . . . . . . . . . . . 715.6 Transfer characteristics of OPTEK, OVSPxBCR4 1-Watt white

LED. (a) Fifth-order polynomial fit to the data. (b) The curvefrom the data sheet. . . . . . . . . . . . . . . . . . . . . . . . . . . 72

5.7 BER comparison of ACO-OFDM and ACO-SCFDE for bias pointof 3.2V. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72

5.8 BER of ACO-OFDM for M = 16 for different bias points. . . . . . . 735.9 BER comparison of uncoded and coded ACO-OFDM and ACO-

SCFDE for M = 16. . . . . . . . . . . . . . . . . . . . . . . . . . . 745.10 Normalized SNR versus normalized bandwidth/bit-rate required to

achieve BER of 10−9. . . . . . . . . . . . . . . . . . . . . . . . . . 76

6.1 a) Average of Schmidl’s and Park’s timing metrics with modifiedtraining symbol suitable for ACO-OFDM. b) Average of Tian’stiming metrics for ACO-OFDM. c) Average of timing metrics forbipolar correlation method for ACO-OFDM. d) Average of timingmetrics for bipolar correlation method for PAM-DMT systems. . . . 82

6.2 a) Schematic of the experimental setup. b) Real implementationwith software defined radio systems. . . . . . . . . . . . . . . . . . . 84

6.3 Average of timing metrics for bipolar correlation method for con-secutive ACO-OFDM symbols with a) L = 256 and 4-QAM modu-lation b) L = 256 and 16-QAM modulation c) L = 512 and 4-QAMmodulation b) L = 512 and 16-QAM modulation. . . . . . . . . . . 85

7.1 System configuration. . . . . . . . . . . . . . . . . . . . . . . . . . . 907.2 The contributions from different orders of reflections to the total

impulse response of a location at the center of the room (weakscatterings and multipath reflections). . . . . . . . . . . . . . . . . . 91

7.3 The contributions from different orders of reflections to the totalimpulse response of a location at the edge of the room (mediumscatterings and multipath reflections). . . . . . . . . . . . . . . . . . 92

7.4 The contributions from different orders of reflections to the totalimpulse response of a location at the corner of the room (strongscatterings and multipath reflections). . . . . . . . . . . . . . . . . . 93

7.5 OFDM transmitter and receiver configuration for both positioningand communication purposes. . . . . . . . . . . . . . . . . . . . . . 94

xi

7.6 Positioning error distribution for OFDM system with 4-QAM mod-ulation, L = 512 and Pte,k = 5 dBm. . . . . . . . . . . . . . . . . . 100

7.7 Positioning error distribution for OOK modulation with Pte,k = 5dBm. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100

7.8 Histogram of positioning errors for OFDM system with 4-QAMmodulation, L = 512 and Pte,k = 5 dBm. . . . . . . . . . . . . . . . 101

7.9 Histogram of positioning errors for OOK modulation with Pte,k =5 dBm. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102

7.10 Positioning error distribution for OFDM system with 4-QAM mod-ulation, L = 512 and Pte,k = -10 dBm. . . . . . . . . . . . . . . . . 103

7.11 Positioning error distribution for OFDM system with 4-QAM mod-ulation, L = 512 and Pte,k = 20 dBm. . . . . . . . . . . . . . . . . . 104

7.12 Histogram of positioning errors for OFDM system with 4-QAMmodulation, L = 512 and Pte,k = -10 dBm. . . . . . . . . . . . . . . 105

7.13 Histogram of positioning errors for OFDM system with 4-QAMmodulation, L = 512 and Pte,k = 20 dBm. . . . . . . . . . . . . . . 105

7.14 Positioning error distribution for OFDM system with 16-QAM mod-ulation, L = 512 and Pte,k = 5 dBm. . . . . . . . . . . . . . . . . . 106

7.15 Positioning error distribution for OFDM system with 64-QAM mod-ulation, L = 512 and Pte,k = 5 dBm. . . . . . . . . . . . . . . . . . 107

7.16 Histogram of positioning errors for OFDM system with 16-QAMmodulation, L = 512 and Pte,k = 5 dBm. . . . . . . . . . . . . . . . 107

7.17 Histogram of positioning errors for OFDM system with 64-QAMmodulation, L = 512 and Pte,k = 5 dBm. . . . . . . . . . . . . . . . 108

7.18 Positioning error distribution for OFDM system with 4-QAM mod-ulation, L = 64 and Pte,k = 5 dBm. . . . . . . . . . . . . . . . . . . 109

7.19 Positioning error distribution for OFDM system with 4-QAM mod-ulation, L = 256 and Pte,k = 5 dBm. . . . . . . . . . . . . . . . . . 109

7.20 Positioning error distribution for OFDM system with 4-QAM mod-ulation, L = 1024 and Pte,k = 5 dBm. . . . . . . . . . . . . . . . . . 110

7.21 Histogram of positioning errors for OFDM system with 4-QAMmodulation, L = 64 and Pte,k = 5 dBm. . . . . . . . . . . . . . . . 111

7.22 Histogram of positioning errors for OFDM system with 4-QAMmodulation, L = 256 and Pte,k = 5 dBm. . . . . . . . . . . . . . . . 111

7.23 Histogram of positioning errors for OFDM system with 4-QAMmodulation, L = 1024 and Pte,k = 5 dBm. . . . . . . . . . . . . . . 112

xii

List of Tables

2.1 NRMSE for different statistical models and turbulence conditionsdefined in Figs. 2.1 to 2.6 . . . . . . . . . . . . . . . . . . . . . . . . 15

5.1 Room configuration under consideration. . . . . . . . . . . . . . . . 705.2 Optical and electrical characteristics of OPTEK, OVSPxBCR4 1-

Watt white LED. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71

7.1 System parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . 917.2 Positioning error for single- and multi-carrier modulation schemes . 102

xiii

List of Abbreviations

AC asymmetrically clipped.

ACO-OFDM asymmetrically clipped optical OFDM.

AoA angle of arrival.

AWGN Additive White Gaussian noise.

BER bit error rate.

BICM bit-interleaved coded modulation.

ccdf complementary cumulative distribution function.

cdf cumulative distribution function.

CDMMC combined deterministic and modified Monte Carlo.

CP cyclic prefix.

CPC compound parabolic concentrator.

CSI channel state information.

DHT discrete Hartley transform.

Double GG Double Generalized Gamma.

EGC equal gain combining.

FFT fast Fourier transform.

xiv

FOV field of view.

FSO free-space optical.

GG Generalized Gamma.

GPS global positioning system.

i.i.d. independent and identically distributed.

i.n.i.d. independent but not necessarily identically distributed.

IBT inter-block interference.

ICT inter-carrier interference.

ID identification.

IFFT inverse fast Fourier transform.

IM/DD intensity modulation and direct detection.

IR infrared.

ISI intersymbol interference.

LBS location based services.

LED light-emitting diode.

LOS line-of-sight.

MIMO multiple-input multiple-output.

MISO multiple-input single-output.

MMC modified Monte Carlo.

MMSE minimum mean square error equalization.

NRMSE normalized root-mean-square error.

OC optimal gain combining.

OFDM orthogonal frequency division multiplexing.

xv

OOK on-off keying.

OWC optical wireless communication.

PAM-DMT PAM-modulated discrete multitone.

PAPR peak-to-average power ratio.

PC personal computer.

PD photo diode.

pdf probability density function.

RF radio frequency.

RMS root mean square.

RSS received signal strength.

RV random variable.

SC selection combining.

SCFDE single carrier frequency domain equalization.

SDR software defined radio.

SIMO single-input multiple-output.

SISO single-input single-output.

SNR signal to noise ratio.

U-OFDM unipolar OFDM.

UV ultraviole.

VLC visible light communication.

xvi

List of Symbols

I Irradiance of the received optical wave

Ux Large-scale irradiance fluctuations

Uy Small-scale irradiance fluctuations

γi Generalized Gamma (GG) distribution parameter

mi GG distribution parameter

Ωi GG distribution parameter

Gm,np,q [.] Meijer’s G-function

σ2x Large-scale fluctuations variance

σ2y Small-scale fluctuations variance

σ2Rytov Rytov parameter

R0 Fresnel zone

l0 Finite inner scale

β20 Rytov scintillation index of a spherical wave

σ2I Scintillation index

Rt Targeted transmission rate

γth Signal to noise ratio (SNR) threshold

γ Instantaneous electrical SNR

xvii

γ Average electrical SNR

Pe Bit error rate (BER) probability

Pout Outage probability

ν Additive White Gaussian noise (AWGN)

σ2n Noise variance

yn Received signal at the nth receive aperture

x Information bits

η Optical-to-electrical conversion coefficient

erfc (.) Complementary error function

Q (.) Gaussian Q-function

Kν (.) Modified Bessel function of the second kind

AN Arithmetic means

GN Geometric means

Pt,k Transmitted optical power from the kth LED bulb

Pr,k Received optical power from the kth transmitter

Hk (0) Channel DC gain

Ar Physical area of the detector

ψk Angle of incidence with respect to the receiver axis

Ts (ψk) Gain of optical filter

g (ψk) Concentrator gain

ϕk Angle of irradiance with respect to the transmitter perpendicular axis

dk Distance between transmitter k and receiver

m Lambertian order

H Transmitter height

xviii

h Receiver height

nr Refractive index of the concentrator

Ψc FOV of the concentrator

Pk,i Power attenuation of the ith symbol transmitted from the kth transmit-ter

(xc, yc) Receiver coordinates

(xck, yck) kth transmitter coordinates

xix

Acknowledgments

I would like to thank all those people who have made this dissertation possible andbecause of whom my Ph.D. experience has been one that I will cherish forever.

Foremost, I would like to sincerely thank my supervisor, Prof. Mohsen Kavehrad.It is hard to find words to describe how much I appreciate all he has done for meas a supervisor and mentor. His inspiration and guidance have motivated methroughout the course of my Ph.D. studies.

I am truly grateful to the members of my dissertation committee, ProfessorsTimothy Kane, Julio Urbina and Jamal Rostami for their time in evaluating thisdissertation and providing me valuable feedback. I would like to specially thankProf. Murat Uysal for his helpful suggestions and comments on Chapters 2 and 4.I am also thankful to all my colleagues in CICTR group for their help and support.

I sincerely thank the Penn State Graduate School for selecting me for theAlumni Association Dissertation Award. I would like to thank Prof. Kavehrad onceagain for nominating me for this award. I am also grateful to graduate committeeat the Department of Electrical Engineering who supported my nomination.

Finally, I would like to thank my beloved wife, Sepideh, for her unconditionallove, kindness, and patience, and my parents and siblings whose love, encourage-ment and prayer helped me overcome difficulties throughout my life. Withoutthem, nothing would have been possible.

xx

To my wife, Sepideh, and my dear parents.

xxi

Chapter 1Introduction

1.1 Motivation

Optical wireless communication (OWC) has been extensively studied recently as a

powerful and promising complementary and/or alternative to the existing radio fre-

quency (RF) solutions for a wide range of applications [1–4]. These systems enable

wireless connectivity within wavelengths ranging from infrared (IR) to ultraviole

(UV) including the visible light spectrum. They offer many attractive features

such as higher capacity, robustness to electromagnetic interference, excellent secu-

rity and low cost deployment. OWC comprises two main categories, indoor and

outdoor systems. Indoor OWC is free from major outdoor environmental degrada-

tions such as rain, snow, building sway, and atmospheric turbulence, and usually

characterized by short transmission range. Outdoor OWC commonly referred to

as free-space optical (FSO) communication is categorized as satellite-based and

terrestrial-based links.

Terrestrial FSO communication uses lasers or light-emitting diodes (LEDs) to

optically transmit information through atmosphere [5, 6]. These systems provide

1

high data rates comparable to fiber optics while they offer much more flexibility

in (re)deployment. Since they operate in unregulated spectrum, no licensing fee

is required making them also a cost-effective solution [1, 7, 8]. With their unique

features and advantages, FSO systems have attracted attention initially as a "last

mile" solution and can be used in a wide array of applications including cellu-

lar backhaul, inter-building connections in enterprise/campus environments, video

surveillance/monitoring, fiber back-up, redundant link in disaster recovery and

relief efforts among others.

On the other hand, IR and visible light bands are commonly used for indoor

OWC applications. OWC systems operating in the visible band (390–750 nm) are

commonly referred to as visible light communication (VLC) [9,10]. The novelty of

this technique is its dual usage. VLC makes use of light emitted from LED lamps

to both transmit data and emit light. LED lights are now favorable to incandescent

lamps because of their greater energy efficiency. As a strong candidate for high-

speed wireless networks of the next generation, VLC offers many advantages over

its RF counterparts summarized as

• Visible light, together with IR and UV spectral band, provides unregulated

and unlimited bandwidth promising a practical solution to the current spec-

trum crunch issue.

• The frequency band can be reused among different rooms and a secure com-

munication is easily achieved as light waves do not penetrate into solid walls

and therefore are confined in a room.

• Unlike the use of WiFi, the wireless technique most often currently imple-

mented, use of VLC does not involve the interference on the RF since optical

wireless utilizes optical carrier to convey data through media. Therefore, it

2

is most suitable for RF-restricted environments such as hospitals, aircrafts,

military installation and factory floors.

• The installation of a VLC wireless network is easy and cost effective as illu-

mination infrastructure exists.

VLC is also a strong candidate for indoor positioning systems considering global

positioning system (GPS) does not perform well for indoor environments since a

satellite signal suffers from severe attenuation when penetrating into solid walls

[11–13]. Indoor positioning can be used for a number of applications such as

guiding users inside large buildings, detecting location of products inside large

warehouses and location based services (LBS).

1.2 Objectives

Despite the key advantages of OWC, its widespread use has been hindered by a

number of major issues. This dissertation targets and addresses some of these

important issues for both indoor and outdoor wireless communication.

The performance of terrestrial FSO systems can be significantly diminished

by turbulence-induced fading (also called as scintillation) resulting from beam

propagation through the atmosphere. Since the calculation of detection and fade

probabilities are primarily based on the probability density function (pdf) of this

random phenomenon, identification of a unifying statistical model which is valid

under all range of turbulence conditions is vital. This dissertation addresses this

very challenging issue and proposes a novel and unifying pdf which accurately de-

scribes irradiance fluctuations over atmospheric channels under a wide range of

turbulence conditions. The proposed model called Double Generalized Gamma

3

(Double GG) distribution outperforms existing turbulence channel models in the

literature. Using this new statistical channel model, we derive closed-form expres-

sions for the outage probability and the average bit error as well as corresponding

asymptotic expressions of FSO systems over turbulence channels. We demonstrate

that our derived expressions cover many existing results in the literature earlier

reported for other channel models as special cases.

Spatial diversity techniques provide a promising approach to mitigate turbulence-

induced fading. In this dissertation, we obtain a closed-form upper-bound and a

novel and accurate approximation for the distribution of a sum of Double GG

random variables (RVs). Then, capitalizing on the derived distribution, we study

the performance of FSO links with spatial diversity over atmospheric turbulence

channels described by Double GG distribution.

On the other hand, VLC systems suffer from multipath distortion due to dis-

persion of the optical signal caused by reflections from various sources inside a

room. This dispersion leads to intersymbol interference (ISI) at high data rates

which reduces signal to noise ratio (SNR) and severely impairs the link perfor-

mance. We investigate and compare the performance of single- and multi-carrier

modulation schemes used to combat ISI effects and improve the performance of

indoor VLC systems taking into account both nonlinear characteristics of LED

and dispersive nature of optical wireless channel. We also present a robust tim-

ing synchronization scheme suitable for asymmetrically clipped (AC) orthogonal

frequency division multiplexing (OFDM) based optical wireless systems. An ex-

perimental demonstration of an indoor VLC system using software defined radio

(SDR) devices as the primary hardware is also described to verify the theoretical

results and further demonstrate the usefulness of our methods.

4

Finally, a novel OFDM VLC system is proposed which can be utilized for

both communications and indoor positioning. We calculate the positioning errors

in all the locations of a room and compare them with those using single carrier

modulation scheme. The impact of different system parameters on the positioning

accuracy of the proposed OFDM VLC system is further investigated.

1.3 Organization

The dissertation organization follows the steps mention in the previous sub-section.

In the next Chapter, we propose Double GG distribution to characterize turbulence-

induced fading and confirm the accuracy of our model through comparisons with

simulation data for plane and spherical waves. We also present the derivation of bit

error rate (BER) and outage probability for single-input single-output (SISO) FSO

systems over Double GG channel. In Chapter 3, an upper bound along with an ap-

proximate expression for the distribution of the sum of Double GG variates is pre-

sented. We confirm the accuracy of the derived expressions through comparisons

with Monte-Carlo simulation results for plane and spherical wave propagation. In

Chapter 4, we introduce the multiple-input multiple-output (MIMO) FSO system

model and provide the BER expressions for single-input multiple-output (SIMO),

multiple-input single-output (MISO) and MIMO FSO links. We present numer-

ical results to confirm the accuracy of the derived expressions and demonstrate

the advantages of employing spatial diversity over SISO links. In Chapter 5, we

briefly describe indoor VLC asymmetrically clipped optical OFDM (ACO-OFDM)

and single carrier frequency domain equalization (SCFDE) systems and compare

their peak-to-average power ratio (PAPR) performance. We study the impact of

LED bias point on the performance of multi-carrier modulation schemes. We also

5

investigate and compare the performance of single- and multi-carrier modulation

schemes and show that bit-interleaved coded modulation (BICM) can combat sig-

nal degradation due to LED nonlinearity and ISI. In Chapter 6, we present a novel

and robust timing synchronization method that works perfectly for all AC sys-

tems, namely ACO-OFDM, PAM-modulated discrete multitone (PAM-DMT) and

discrete discrete Hartley transform (DHT) based optical OFDM systems, and can

also be used for channel estimation simultaneously. We verify the accuracy of the

proposed method through simulations and experimental results. In Chapter 7, an

OFDM VLC system is proposed which can be employed for both communications

and indoor positioning. We present numerical results on the positioning accuracy

of the proposed OFDM VLC system and compare its performance with that of its

on-off keying (OOK) counterpart. The effect of different OFDM system parame-

ters on the positioning accuracy is also investigated. Finally, Chapter 8 concludes

and summarizes this thesis.

6

Chapter 2Statistical Channel Model for

Turbulence-Induced Fading in

Free-Space Optical Systems

In this Chapter, we propose a new probability distribution function which ac-

curately describes turbulence-induced fading under a wide range of turbulence

conditions. The proposed model, termed Double Generalized Gamma (Double

GG), is based on a doubly stochastic theory of scintillation and developed via

the product of two Generalized Gamma (GG) distributions. The proposed Double

GG distribution generalizes many existing turbulence channel models and provides

an excellent fit to the published plane and spherical waves simulation data. Us-

ing this new statistical channel model, we derive closed-form expressions for the

outage probability and the average bit error rate (BER) as well as corresponding

asymptotic expressions of free-space optical (FSO) communication systems over

turbulence channels. We demonstrate that our derived expressions cover many ex-

isting results in the literature earlier reported for Gamma-Gamma, Double-Weibull

7

and K channels as special cases.

2.1 Introduction

A major performance limiting factor in terrestrial FSO systems is atmospheric

turbulence-induced fading (also called as scintillation) [14]. Inhomogenities in the

temperature and the pressure of the atmosphere result in variations of the refractive

index and cause atmospheric turbulence. This manifests itself as random fluctu-

ations in the received signal and severely degrades the FSO system performance

particularly over long ranges.

In the literature, several statistical models have been proposed in an effort to

model this random phenomenon. Historically, log-normal distribution has been

the most widely used model for the probability density function (pdf) of the ran-

dom irradiance over atmospheric channels [15–17]. This pdf model is however

only applicable to weak turbulence conditions. As the strength of turbulence in-

creases, lognormal statistics exhibit large deviations compared to experimental

data. Moreover, lognormal pdf underestimates the behavior in the tails as com-

pared with measurement results. Since the calculation of detection probabilities for

a communication system is primarily based on the tails of the pdf, underestimating

this region significantly affects the accuracy of performance analysis.

In an effort to address the shortcomings of the lognormal distribution, other

statistical models have been further proposed to describe atmospheric turbulence

channels under a wide range of turbulence conditions. These include the Negative

Exponential/Gamma model (also known widely as the K channel) [18], I-K dis-

tribution [19], log-normal Rician channel (also known as Beckman) [20], Gamma-

Gamma [21], M distribution [22] and Double-Weibull [23]. Particularly worth

8

mentioning is the Gamma-Gamma model [21], [24] which has been widely used in

the literature for the performance analysis of FSO systems, see e.g., [25,26], along

with the log-normal model. This model builds upon a two-parameter distribution

and considers irradiance fluctuations as the product of small-scale and large-scale

fluctuations, where both are governed by independent gamma distributions. In a

more recent work by Chatzidiamantis et al. in [23], the Double-Weibull distribu-

tion was proposed as a new model for atmospheric turbulence channels. Similar

to the Gamma-Gamma model, it is based on the theory of doubly stochastic scin-

tillation and considers irradiance fluctuations as the product of small-scale and

large-scale fluctuations which are both Weibull distributed. It is shown in [23]

that Double-Weibull is more accurate than the Gamma-Gamma particularly for

the cases of moderate and strong turbulence.

In this Chapter, we propose a new and unifying statistical model, named Dou-

ble GG, for the irradiance fluctuations. The proposed model is valid under all

range of turbulence conditions (weak to strong) and contains most of the existing

statistical models for the irradiance fluctuations in the literature as special cases.

Furthermore, we provide comparison of the proposed model with Gamma-Gamma

and Double-Weibull models. For this purpose, we use the set of simulation data

from [27,28] for plane and spherical waves1. Our model demonstrates an excellent

match to the simulation data and is clearly superior over the other two models

which show discrepancy from the simulation data in some cases. In the second1The simulation data in [27, 28] was obtained through phase screen approach which con-

sists of approximating a three-dimensional random medium as a collection of equally spaced,two-dimensional, random phase screens that are transverse to the direction of wave propaga-tion. In [27], it was discussed in detail that such a numerical simulation approach contains allthe essential physics for accurately predicting the pdf of irradiance (or, equivalently, log-normalirradiance), and shown that the simulation results provide an excellent match to known exper-imental measurements reported in [29] for both plane and spherical waves. The same set ofsimulation data was also used in [21] and [23] which respectively introduced Gamma-Gammaand Double-Weibull distributions as turbulence channel models.

9

part of this Chapter, we use this new channel model to derive closed-form expres-

sions for the BER and the outage probability of single-input single-output (SISO)

FSO systems with intensity modulation and direct detection (IM/DD). Our per-

formance results can be seen as a generalization of the results in [30–33].

2.2 Double GG Distribution

The irradiance of the received optical wave can be modeled as [21], [23] I = UxUy,

where Ux and Uy are statistically independent random processes arising respectively

from large-scale and small scale turbulent eddies. We assume that both large-scale

and small-scale irradiance fluctuations are governed by GG distributions [34, Eq.

(1)]. The pdfs of Ux ∼ GG (γ1,m1,Ω1) and Uy ∼ GG (γ2,m2,Ω2) are given by

fUx (Ux) = γ1Um1γ1−1x

(Ω1/m1 )m1Γ (m1)exp

(−m1

Ω1Uγ1

x

)(2.1)

fUy (Uy) =γ2U

m2γ2−1y

(Ω2/m2 )m2Γ (m2)exp

(−m2

Ω2Uγ2

y

)(2.2)

where γi > 0 , mi ≥ 0.5 and Ωi i = 1, 2 are the GG parameters. The pdf of I can

be written as

fI (I) =∞∫

0

fUx (I|Uy) fUy (Uy) dUy (2.3)

where fUx (I|Uy) is obtained as

fUx (I|Uy) = γ1(I/Uy)m1γ1−1

Uy(Ω1/m1 )m1Γ (m1)exp

(−m1

Ω1

(I

Uy

)γ1). (2.4)

10

The integration in (2.3) yields

fI (I) = γ2ppm2−1/2qm1−1/2(2π)1−(p+q)/2 I−1

Γ (m1) Γ (m2)(2.5)

×G0,p+qp+q,0

(

Ω2

Iγ2

)pppqqΩq

1

mq1m

p2

|∆ (q : 1 −m1) ,∆ (p : 1 −m2)

−

where Gm,np,q [.] is the Meijer’s G-function2 defined in [35, Eq.(9.301)], p and q are

positive integer numbers that satisfy p/q = γ1/γ2 and ∆(j;x) is defined as

∆(j; x) , x/j , ..., (x+ j − 1)/j. (2.6)

We name this new distribution as Double GG. Employing [36, Eq. (10)] and

after some simplifications, the cumulative distribution function (cdf) of Double

GG distribution can be obtained as

FI (I) = pm2−1/2qm1−1/2(2π)1−(p+q)/2

Γ (m1) Γ (m2)(2.7)

×Gp+q,11,p+q+1

(Iγ2

Ω2

)p mq1m

p2

ppqqΩq1|

1

∆ (q : m1) ,∆ (p : m2) , 0

.

The distribution parameters γi and Ωi i = 1, 2 of the Double GG model can

be identified using the first and second order moments of small and large scale

irradiance fluctuations. The latter are directly tied to the atmospheric parameters.

Without loss of generality, we assume E (I) = 1 or equivalently E (Ux) = 1 and2Meijer’s G-function is a standard built-in function in mathematical software packages such

as MATLAB, MAPLE and MATHEMATICA. If required, this function can be also expressed interms of the generalized hypergeometric functions using [35, Eqs.(9.303-304)].

11

E (Uy) = 1. The second moment of irradiance is expressed as

E(I2)

= E(U2

x

)E(U2

y

)=(1 + σ2

x

) (1 + σ2

y

)(2.8)

where σ2x and σ2

y are respectively normalized variances of Ux and Uy. The nth

moment of Ux (similarly Uy) is given by

E (Unx ) =

(Ω1

m1

)n/γ1 Γ (m1 + n/γ1)Γ (m1)

. (2.9)

Therefore, by inserting the second order moment obtained from (2.9) in (2.8), and

considering that E (I) = 1, we have

σ2x = Γ (m1 + 2/γ1 ) Γ (m1)

Γ2 (m1 + 1/γ1 )− 1, (2.10a)

σ2y = Γ (m2 + 2/γ2 ) Γ (m2)

Γ2 (m2 + 1/γ2 )− 1, (2.10b)

Ωi =(

Γ (mi)Γ (mi + 1/γi)

)γi

mi, i = 1, 2 (2.11)

where mi is a distribution shaping parameter and found using curve fitting on the

simulated/measured channel data. Note that in (2.10a) and (2.10b), the variances

of small- and large-scale fluctuations (i.e., σ2x and σ2

y) are directly tied to the

atmospheric conditions. Particularly, assuming a plane wave when inner scale

effects are considered, the variances for the large- and the small-scale scintillations

12

are given by [14, Eqs. 9.46 and 9.55]

σ2x = exp

0.16σ2Rytov

2.61ηl

2.61 + ηl + 0.45σ2Rytovη

7/6l

7/6

×

1 + 1.753

2.612.61 + ηl + 0.45σ2

Rytovη7/6l

1/2

− 0.252

2.612.61 + ηl + 0.45σ2

Rytovη7/6l

7/12− 1, (2.12)

σ2y

∼= exp

0.51σ2Rytov(

1 + 0.69σ12/5Rytov

)5/6

− 1 (2.13)

where σ2Rytov is Rytov parameter, ηl = 10.89 (R0/l0), and R0/l0 denotes the ratio

of Fresnel zone to finite inner scale.

For spherical waves in the absence of inner scale, σ2x and σ2

y are given by [14,

Eqs. 9.63 and 9.70]

σ2x

∼= exp

0.49β20(

1 + 0.56β12/50

)7/6

− 1, (2.14)

σ2y

∼= exp

0.51β20(

1 + 0.69β12/50

)5/6

− 1 (2.15)

where β20 is the Rytov scintillation index of a spherical wave given by

β20 = σ2

Rytov/σ2 (l0/R0) . (2.16)

13

In (2.16), σ2 (l0/R0) is defined as

σ2 (l0/R0) ∼= 3.86[(

1 + 9/η2l

)11/12(

sin(11

6tan−1ηl

3

)+ 2.61

(9 + η2l )1/4 sin

(43

tan−1ηl

3

)

− 0.518(9 + η2

l )7/24 sin(5

4tan−1ηl

3

))− 8.75η−5/6

l

]. (2.17)

In the presence of a finite inner scale, the small-scale scintillation is again described

by (2.15) and the large-scale variance is given by [14, Eq. 78]

σ2x

∼= exp

0.04β20

(8.56ηl

8.56 + ηl + 0.195β20η

7/6l

)7/6

×

1 + 1.753(

8.568.56 + ηl + 0.195β2

0η7/6l

)1/2

−0.252(

8.568.56 + ηl + 0.195β2

0η7/6l

)7/12− 1. (2.18)

Therefore, the parameters of the Double GG distribution are readily deduced from

these expressions using only values of the refractive index structure parameter and

inner scale according to the atmospheric conditions. The scintillation index can

be further calculated as

σ2I = E (I2)

E(I)2 − 1 =(1 + σ2

x

) (1 + σ2

y

)− 1. (2.19)

We should emphasize that this distribution is very generic since it includes some

commonly used fading models as special cases. As demonstrated in Appendix A,

for γi → 0, mi → ∞, Double GG pdf coincides with the log-normal pdf. For

γi = 1, Ωi = 1, it reduces to Gamma-Gamma while for mi = 1, it becomes

14

Table 2.1: NRMSE for different statistical models and turbulence con-ditions defined in Figs. 2.1 to 2.6

Gamma-Gamma [21] Double-Weibull [23] Double GG (Proposed)Fig. 2.1 2% 7% 0.6%Fig. 2.2 2.8% 1.2% 0.8%Fig. 2.3 1.2% 1% 0.8%Fig. 2.4 0.3% 10% 0.3%Fig. 2.5 19% 8.7% 1.5%Fig. 2.6 4.8% 2.4% 1.7%

Double-Weibull. For γi = 1, Ωi = 1, m2 = 1, it coincides with the K channel.

2.3 Verification of the Proposed Channel Model

In this section, we compare the Double GG distribution model with simulation

data of plane and spherical waves provided respectively in [27] and [28]. In [27],

Flatté et al. carried out exhaustive numerical simulations and published the results

assuming plane wave propagation through homogeneous and isotropic Kolmogorov

turbulence. In [28], Hill and Frehlich presented the simulation data for the propa-

gation of a spherical wave through homogeneous and isotropic atmospheric turbu-

lence. The turbulence severity is characterized by Rytov variance (σ2Rytov) which

is proportional to the scintillation index [14]. We emphasize that the same data

set was also employed in [21] and [23] which have introduced the Gamma-Gamma

and Double-Weibull fading models.

2.3.1 Plane Wave

Figs. 2.1 to 2.3 compare the Gamma-Gamma, Double-Weibull and Double GG

models under a wide range of turbulence conditions (weak to strong) assuming

15

Figure 2.1: Pdfs of the scaled log-irradiance for a plane wave assuming weak irra-diance fluctuations.

plane wave propagation. In these figures, the vertical axis of the figure represents

the log-irradiance pdf multiplied by the square root of variance. The logarithm of

irradiance was particularly chosen to illustrate the high and low irradiance tails

[27]. Thus, sensitivity to the small irradiance fades is increased, while sensitivity to

large irradiance peaks is decreased. The pdf plots were also scaled by subtracting

the mean value to center all distributions on zero and dividing by the square

root of variance. In Fig. 2.1, we assume weak turbulence conditions which are

characterized by σ2Rytov = 0.1 and l0/R0 = 0.5. The values of the variances of small

and large scale fluctuations, (σ2x and σ2

y) are calculated from (2.12) and (2.13).

Using (2.10a), (2.10b) and (2.11), the Double GG parameters are obtained as

γ1 = 2.1, γ2 = 2.1, m1 = 4, m2 = 4.5, Ω1 = 1.0676 and Ω2 = 1.06 where p = q = 1.

16

Figure 2.2: Pdfs of the scaled log-irradiance for a plane wave assuming moderateirradiance fluctuations.

We further employ normalized root-mean-square error (NRMSE) as a statistical

goodness of fit test. Table 2.1 provides the NRMSE results for different statistical

models. According to Table 2.1 and Fig. 2.1, both Gamma-Gamma and Double-

Weibull distributions fail to match the simulation data. On the other hand, the

proposed Double GG distribution follows closely the simulation data.

In Fig. 2.2, we assume moderate irradiance fluctuations which are characterized

by σ2Rytov = 2 and l0/R0 = 0.5. The parameters of the Double GG distribution

for this case are obtained as γ1 = 2.1690, γ2 = 0.8530, m1 = 0.55, m2 = 2.35,

Ω1 = 1.5793 and Ω2 = 0.9671. In the calculations, p and q are chosen as p =

28 and q = 11 in order to satisfy p/q = γ1/γ2. Among the three distributions

under consideration, the proposed Double GG model provides the best fit to the

17

Figure 2.3: Pdfs of the scaled log-irradiance for a plane wave assuming strongirradiance fluctuations.

simulation data. It is apparent that Gamma-Gamma fails to match the simulation

data particularly in the tails. As Table 2.1 demonstrates, the accuracy of Double

Weibull is better than that of Gamma-Gamma, but slightly inferior to our proposed

distribution.

In Fig. 2.3, we assume strong irradiance fluctuations which are characterized

by σ2Rytove = 25 and I0/R0 = 1. The parameters of the Double GG distribution

are calculated as γ1 = 1.8621, γ2 = 0.7638, m1 = 0.5, m2 = 1.8, Ω1 = 1.5074 and

Ω2 = 0.9280 where p and q are chosen as 17 and 7 respectively. The Double GG

model again provides an excellent match to the simulation data and as it is clear

from Table 2.1, its accuracy is better than Gamma-Gamma and Double Weibull.

18

Figure 2.4: Pdfs of the scaled log-irradiance for a spherical wave assuming weakirradiance fluctuations.

2.3.2 Spherical Wave

Figs. 2.4 to 2.6 compare the Gamma-Gamma, Double-Weibull and Double GG

models under weak, moderate and strong turbulence conditions assuming spherical

wave propagation. These pdfs are plotted as a function of (ln I + 0.5σ2)/σ [28],

where σ is the square root of the variance of ln I. The y-axis depicts the log-

irradiance pdf multiplied by σ.

In Fig. 2.4, we consider spherical wave propagation and assume weak turbulence

which are characterized by σ2Rytov = 0.06 and l0/R0 = 0. The parameters of Double

GG are evaluated using the variances of small and large scale fluctuations, (σ2y

and σ2x) for spherical waves. The values of these variances are given by (2.14) ,

(2.15) and (2.18). Therefore, employing (2.10a), (2.10b) and (2.11), we obtain

19

Figure 2.5: Pdfs of the scaled log-irradiance for a spherical wave assuming moderateirradiance fluctuations.

m1 = 34.24, m2 = 32.79, γ1 = γ2 = Ω1 = Ω2 = 1 where p and q are equal to

1. It can be noted that in this case, the Double GG coincides with the Gamma-

Gamma distribution. It is apparent that both Gamma-Gamma and Double GG

distributions provide an excellent match to the simulation data while the Double-

Weibull distribution fails to match the simulation data.

In Fig. 2.5, we assume moderate irradiance fluctuations, which are characterized

by σ2Rytov = 2 and l0/R0 = 0. The parameters of the Double GG model for this case

are calculated as γ1 = 0.9135, γ2 = 1.4385, m1 = 2.65, m2 = 0.85, Ω1 = 0.9836

and Ω2 = 1.1745 where p and q are selected as 7 and 11 respectively. It is clearly

observed that the Double GG model provides a better fit with simulation data,

especially for small irradiance values.

In Fig. 2.6, we assume strong irradiance fluctuations which are characterized by

20

Figure 2.6: Pdfs of the scaled log-irradiance for a spherical wave assuming strongirradiance fluctuations.

σ2Rytov = 5 and l0/R0 = 1. The parameters of the Double GG model are calculated

as γ1 = 0.4205, γ2 = 0.6643, m1 = 3.2, m2 = 2.8, Ω1 = 0.8336 and Ω2 =

0.9224 where p and q are chosen as 7 and 11 respectively. It is apparent from this

figure and Table 2.1 that both Gamma-Gamma and Double-Weibull distributions

fail to match the simulation data. On the other hand, the proposed Double GG

distribution follows closely the simulation data.

2.4 Performance Evaluation

2.4.1 BER Analysis of SISO FSO System

In this section, we present the BER performance analysis of an FSO system with

on-off keying (OOK) over the proposed Double GG channel. The received optical

21

signal is written as

y = ηIx+ ν (2.20)

where x represents the information bits and can be either 0 or 1, ν is the Additive

White Gaussian noise (AWGN) term with zero mean and variance σ2n = N0/2 , η

is the optical-to-electrical conversion coefficient and I is the normalized irradiance

whose pdf follows (2.5). For the system under consideration, the instantaneous

electrical signal to noise ratio (SNR) can be defined as

γ = (ηI)2/N0. (2.21)

Therefore, the average electrical SNR is obtained as γ = η2/N0 since E (I) = 1.

Conditioned on the irradiance, the instantaneous BER for OOK is given by [32]

Pe,ins = 0.5 erfc(

ηI

2√N0

)(2.22)

where erfc (.) stands for the complementary error function defined as

erfc(x) = 2√π

∫ ∞

xe−t2

dt. (2.23)

The average BER can be then calculated by averaging (2.22) over the distribution

of I, i.e.,

Pe,SISO =∫ ∞

0fI (I)

[0.5 erfc

(ηI

2√N0

)]dI. (2.24)

The above integral can be evaluated in closed-form by expressing the erfc (.) inte-

grand via a Meijer’s G-function using [37, Eq. (8.4.14.2)], [37, Eq. (8.2.2.14)] and

22

[38, Eq. (21)]. Thus, a closed-form solution is obtained as

Pe,SISO = γ2km1+m2pm2+1/2qm1−1/2

2 32 lΓ (m1) Γ (m2) (2π)

l+k(p+q)2 −1

, (2.25)

×Gk(p+q),2l2l,k(p+q)+l

(

mq1m

p2

pP Ωp2q

qΩq1

)k (4l)l

γlkk(p+q) |∆ (l : 1) ,∆

(l : 1

2

),

Jk (q : 1 −m1) , Jk (p : 1 −m2) ,∆ (l : 0)

.

In (2.25) k and l are positive integer numbers that satisfy pγ2/2 = l/k and

Jξ (y, x) is defined as

Jξ (y, x) = ∆(ξ,y − x

y

),∆

(ξ,y − 1 − x

y

), . . . ,∆

(ξ,

1 − x

y

). (2.26)

The derived BER expression in (2.25) can be seen as a generalization of earlier

BER results in the literature. If we insert γi = 1 and Ωi = 1 in (2.25), we obtain

the BER expression derived in [31, Eq. (9)] under the assumption of Gamma-

Gamma channel. Setting mi = 1 in (2.25), we obtain Eq (15) of [23] derived for

Double-Weibull channel. On the other hand, for γi = 1, Ωi = 1 and m2 = 1, (2.25)

reduces to (12) of [32] reported for the K-channel. Appendix B provides the details

on these.

In an effort to have some further insights into system performance, we inves-

tigate the asymptotical BER performance in the following. For large SNR values,

the asymptotic BER behavior is dominated by the behavior of the pdf near the

origin, i.e. fI (I) at I → 0 [39]. Thus, employing series expansion corresponding to

the Meijer’s G-function [40, Eq. (07.34.06.0006.01)], the Double GG distribution

23

given in (2.5) can be approximated by a single polynomial term as

fI (I) ≈ Ap+q∏j=1j =k

Γ (bj − bk)Ipγ2 minm1q

,m2

p −1 (2.27)

where A is obtained as

A = γ2ppm2−1/2qm1−1/2(2π)1−(p+q)/2

Γ (m1) Γ (m2)

(mq

1mp2

(qΩ1)q(pΩ2)p

)minm1q

,m2

p . (2.28)

In (2.27), bk and bj are defined as

bk = minm1

q,m2

p

, (2.29)

bj ∈ 1 − ∆ (q : 1 −m1) , 1 − ∆ (p : 1 −m2) \ minm1

q,m2

p

. (2.30)

Therefore, based on (2.24), the average BER can be well approximated by

Pe,SISO ≈ Ap+q∏j=1j =k

Γ (bj − bk)(

2√γ

)pγ2bk Γ ((1 + pγ2bk) /2)2√πpγ2bk

. (2.31)

From (2.31), it can be readily deduced that the diversity order of SISO FSO system

is given by 0.5pγ2 min m1/q ,m2/p.

It is observed from Fig. 2.7a that an SNR of 51.1 dB is required to achieve a

BER of 10−3 for a plane wave in moderate turbulence conditions. For stronger

turbulence conditions, the required SNR to achieve the same BER performance is

68.2 dB as seen from Fig. 2.7b. For spherical waves, SNRs of 49.8 dB and 63.8 are

respectively required for moderate and strong turbulence conditions. Comparison

with the expressions presented for other channel models reveals that the Gamma-

24

(a) (b)

(c) (d)

Figure 2.7: Average BER as a function of γ a) Plane wave - σ2Rytov = 2, l0/R0 = 0.5,

b) Plane wave-σ2Rytov = 25, l0/R0 = 1, c) Spherical wave - σ2

Rytov = 2, l0/R0 = 0, d)Spherical wave - σ2

Rytov = 5, l0/R0 = 1

Gamma model significantly overestimates the performance. Also, the superiority

of Double GG is more obvious for spherical wave. As observed from Figs. 2.7c

and 2.7d, the performance plots of Double-Weibull and Gamma Gamma consid-

erably diverge particularly for strong turbulence conditions. Furthermore, it can

be clearly seen that the asymptotic results are in excellent agreement with exact

analytical results within a wide range of SNR showing the accuracy and usefulness

of the derived asymptotic expression given in (2.31).

25

2.4.2 Outage Probability Analysis of SISO FSO System

Denote Rt as a targeted transmission rate and assume γth = C−1 (Rt) as the

corresponding SNR threshold in terms of the instantaneous channel capacity for

a particular channel realization. Therefore, the outage probability is calculated

by Pout (Rt) = Pr (γ < γth) [41]. If SNR exceeds γth, no outage happens and the

receiver can decode the signal with arbitrarily low error probability. Employing

(2.21), I can be expressed as I =√γ/γ. After the transformation of the random

variable (RV), I, the cdf of γ can be easily derived from (2.7) and setting γ = γth

therein, we obtain the outage probability as

Pout = Fγ (γth) = pm2−1/2qm1−1/2(2π)1−(p+q)/2

Γ (m1) Γ (m2)(2.32)

×Gp+q,11,p+q+1

(γth

γ

)pγ2/2mq

1mp2

(Ω2p)p(Ω1q)q |1

∆ (q : m1) ,∆ (p : m2) , 0

.

(2.32) can be seen as a generalization of earlier outage analysis results in the liter-

ature. Specifically, if we insert γi = 1 and Ωi = 1 in (2.32), we obtain the outage

probability expression reported in [30, Eq. (15)] for Gamma-Gamma channel.

Setting mi = 1 in (2.32), we recover Eq (16) of [23] derived for Double-Weibull

channel. Similarly, for γi = 1, Ωi = 1 and m2 = 1, (2.32) reduces to (3) of [42]

reported for the K channel. Appendix C provides the details on these.

Based on the derived expression in (2.32), Figs. 2.8a to 2.8d present the out-

age probabilities of a SISO FSO system as a function of the normalized outage

threshold (i.e., γ/γth) for different degrees of turbulence severity. We adopt the

same parameters used in Figs. 2.2 and 2.3 and Figs. 2.5 and 2.6 and consider the

following four cases: a) Plane wave with σ2Rytov = 2 and l0/R0 = 0.5, b) Plane wave

26

(a) (b)

(c) (d)

Figure 2.8: Outage probability as a function of γ/γth for a) Plane wave - σ2Rytov = 2,

l0/R0 = 0.5, b) Plane wave-σ2Rytov = 25, l0/R0 = 1, c) Spherical wave - σ2

Rytov = 2,l0/R0 = 0, d) Spherical wave - σ2

Rytov = 5, l0/R0 = 1

with σ2Rytov = 25 and l0/R0 = 1, c) Spherical wave with σ2

Rytov = 2 and l0/R0 = 0,

d) Spherical wave with σ2Rytov = 5 and l0/R0 = 1 . It is observed from Fig. 2.8a

that an SNR of 37.8 dB is required to achieve a targeted outage probability of

10−2. As the turbulence strength gets stronger (see Fig. 2.8b), the required SNR

to maintain the same performance climbs up to 50.5 dB. Similarly, for spheri-

cal waves, SNRs of 36.8 dB and 50.9 dB are respectively required for moderate

and strong turbulence conditions. In these figures, we further include the outage

27

results for Double-Weibull and Gamma-Gamma for comparison purposes. As ex-

pected from the earlier comparisons of their pdfs, the outage performance over

Double-Weibull and Double GG for plane wave (See Figs. 2.8a and 2.8b) are sim-

ilar while the Gamma-Gamma model overestimates the outage performance. On

the other hand, the superiority of Double GG is more obvious for spherical wave

(See Figs. 2.8c and 2.8d), particularly for strong turbulence conditions, where the

outage performance plots of Double-Weibull and Gamma Gamma significantly de-

viate.

2.5 Conclusions

In this Chapter, we have introduced a new channel model, so called Double GG,

which accurately describes irradiance fluctuations over atmospheric channels under

a wide range of turbulence conditions. It is based on the theory of doubly stochastic

scintillation and considers irradiance fluctuations as the product of small-scale and

large-scale fluctuations which are both GG distributed. We have obtained closed-

form expressions for the pdf and cdf in terms of Meijer’s G-function. Comparisons

with the Gamma Gamma and Double-Weibull have shown that the new model

provides an accurate fit with numerical simulation data for both plane and spherical

waves. Using the new channel model, we have obtained closed-form expressions for

the BER and the outage probability of SISO FSO systems. We have demonstrated

that our derived expressions cover many existing results in the literature earlier

reported for Gamma-Gamma, Double-Weibull and K channels as special cases.

Based on the asymptotical performance analysis, we have further derived diversity

gains for SISO FSO systems under consideration.

28

Chapter 3Statistical Analysis of Sum of

Double Generalized Gamma Variates

3.1 Introduction

A unifying statistical distribution named Double Generalized Gamma (Double GG)

was proposed in Chapter 2 which generalizes many existing turbulence models

in a closed-form expression and covers all turbulence conditions. An analytical

solution for the distribution of the sum of Double GG random variables (RVs) is a

very cumbersome task if not impossible. Thus, in this Chapter, we derive an upper

bound and a novel and accurate approximation for the distribution of the sum of N

Double GG distributed RVs. Particularly, a useful expression for the distribution

of the product of N Double GG distributed RVs is first obtained. Then, based on

a well-known inequality between arithmetic and geometric means, a closed-form

union upper bound for the distribution of the sum of Double GG distributed RVs

is derived. As the upper bound exhibits large deviations compared to Monte-Carlo

simulation results for sufficiently large values of N , we modify the upper bound

29

and propose a novel and accurate approximation of the distribution of the sum of

Double GG distributed RVs. Extensive numerical and computer simulation results

verify the tightness of the proposed bound and the accuracy of the approximate

expression.

3.2 An Upper-Bound for the Distribution of the

Sum of Double GG Variates

Let InNn=1 be N statistically independent but not necessarily identically dis-

tributed (i.n.i.d.) Double GG RVs whose probability density function (pdf) follows

(2.5). We define a new RV R as

R ,N∏

n=1In. (3.1)

The Double GG distribution considers irradiance fluctuations as the product

of small-scale and large-scale fluctuations which are both governed by Generalized

Gamma (GG) distributions, i.e. In = Ux,nUy,n, where Ux,n and Uy,n are statistically

independent arising respectively from large-scale and small scale turbulent eddies.

Thus, R can be expressed as the product of 2N GG RVs Ul, i.e.,

R =2N∏l=1

Ul. (3.2)

The pdf of R can be obtained using the statistical model proposed in [36] as

fR (r) = αξ

rGβ,0

0,β

rα

ω

∣∣∣∣∣∣∣∣−

Jα (γ1:2N ,m1:2N)

(3.3)

30

where ξ, ω and Jα (γ1:2N ,m1:2N) are defined as

ξ =(√

2π)2N−β

2N∏l=1

(α/γl )ml−1/2

Γ (ml), (3.4)

ω =2N∏l=1

(αΩl

mlγl

)α/γl

, (3.5)

Jα (γ1:2N ,m1:2N) , ∆ (α/γ1 ;m1) ,∆ (α/γ2 ;m2) , . . . ,∆ (α/γ2N;m2N) . (3.6)

In (3.3), α and β are two positive integers defined as

α ,2N∏l=1

kl, (3.7)

β , α2N∑l=1

1γl

(3.8)

under the constraint that

ll = 1γl

l∏i=1

ki (3.9)

is a positive integer with ki being also a positive integer.

The cumulative distribution function (cdf) of R can be derived from (3.3) as

FR (r) = ξGβ,11,β+1

rα

ω

∣∣∣∣∣∣∣∣1

Jα (γ1:2N ,m1:2N) , 0

. (3.10)

Considering (3.2), the nth moment of R can be calculated utilizing the nth moment

of Ul as

E (Rn) =2N∏l=1

(Ωl

ml

)n/γl Γ (ml + n/γl)Γ (ml)

. (3.11)

The well-known inequality between arithmetic and geometric means, i.e. AN ≥

31

GN , with

AN = 1N

n∑n=1

In (3.12)

and

GN =N∏

n=1I1/N

n (3.13)

is used to obtain a lower-bound for RV Z defined as the sum of Double GG RVs,

i.e., Z ,N∑

n=1In as

Z ≥ NR1/N . (3.14)

Considering Eqs. (3.10) and (3.14), the cdf of Z is upper bounded as

FZ (z) ≤ ξGβ,11,β+1

(z/N )αN

ω

∣∣∣∣∣∣∣∣1

Jα (γ1:2N ,m1:2N) , 0

. (3.15)

3.3 An Approximate Distribution of the Sum of

Double GG Variates

As we will show later in Section 3.4, the proposed bound given in (3.15) does not

provide satisfactory accuracy for sufficiently large values of N . Thus, we obtain

an approximation for the distribution of the sum of N statistically i.n.i.d. Double

GG RVs in the following.

Let us define a new RV W such that Z = NWR1/N . Thus, an estimate of Z

can be obtained as

Z = NWR1/N (3.16)

32

where W = E [W ] is given by1

W = 1E [R1/N ]

=2N∏l=1

(ml

Ωl

)1/Nγl Γ (ml)Γ (ml + 1/Nγl)

. (3.17)

Utilizing (3.10), the cdf of Z is derived as

FZ (z) = ξGβ,11,β+1

ω−1(

z

WN

)αN

∣∣∣∣∣∣∣∣1

Jα (γ1:2N ,m1:2N) , 0

. (3.18)

Note that for W = 1 , (3.18) becomes the upper bound for the cdf of Z that

is given by (3.15). By taking the first derivative of (3.18) with respect to z, the

approximate pdf of Z can be obtained in closed-form as

fZ (z) = Nαξ

zGβ,0

0,β

ω−1(

z

WN

)αN

∣∣∣∣∣∣∣∣−

Jα (γ1:2N ,m1:2N)

. (3.19)

We should emphasize that (3.18) (similarly (3.19)) is very generic since it in-

cludes the cdf expression for the sum of some commonly used RVs used to describe

turbulence-induced fading as special cases. For γl → 0, ml → ∞, (3.18) coincides

with the cdf of the sum of N log-normal RVs. For γl = 1, Ωl = 1, it reduces to the

cdf of the sum of N Gamma-Gamma RVs while for ml = 1, it becomes the cdf of

the sum of N Double-Weibull RVs. For γl = 1, Ωl = 1, m2l = 1, it coincides with

the sum of N K distributed RVs2.1Note that without loss of generality, it is assumed in Chapter 2 that E [In] = 1 in calculating

Eqs. (2.11), (2.10a) and (2.10b)2By following the same approach, the pdf for the same spacial cases can be obtained from

(3.19).

33

3.4 Verification of the Mathematical Analysis

In this section, the previous mathematical analysis for the cdf of the sum of i.n.i.d.

Double GG RVs is verified and evaluated. We consider the following four scenarios

of atmospheric turbulence conditions reported in Chapter 2

• Channel a: Plane wave and moderate irradiance fluctuations with γ1 =

2.1690, γ2 = 0.8530, m1 = 0.55, m2 = 2.35, Ω1 = 1.5793, Ω2 = 0.9671,

p = 28 and q = 11

• Channel b: Plane wave and strong irradiance fluctuations with γ1 = 1.8621,

γ2 = 0.7638, m1 = 0.5, m2 = 1.8, Ω1 = 1.5074, Ω2 = 0.9280, p = 17 and

q = 7.

• Channel c: Spherical wave and moderate irradiance fluctuations with γ1 =

0.9135, γ2 = 1.4385, m1 = 2.65, m2 = 0.85, Ω1 = 0.9836 and Ω2 = 1.1745,

p = 7 and q = 11.

• Channel d: Spherical wave and strong irradiance fluctuations with γ1 =

0.4205, γ2 = 0.6643, m1 = 3.2, m2 = 2.8, Ω1 = 0.8336 and Ω2 = 0.9224,

p = 7 and q = 11.

Figs. 3.1 to 3.4 present the analytical results which have been obtained through

(3.15) and (3.18) assuming N = 2, 3, 4. In order to verify the tightness of the

proposed bound and the accuracy of the approximation, Monte-Carlo simulation

results for the exact cdf are also included in each figure.

In Figs. 3.1 and 3.2, we assume plane wave propagation with moderate (channel

a) and strong (channel b) irradiance fluctuations respectively. For channel a, W

is calculated through (3.17) as 1.31, 1.46 and 1.54 for N = 2, 3, 4 respectively.

34

Figure 3.1: Bounded, approximate and exact cdf of the sum of Double GG dis-tributed RVs assuming plane wave and moderate irradiance fluctuations (channela)

Figure 3.2: Bounded, approximate and exact cdf of the sum of Double GG dis-tributed RVs assuming plane wave and strong irradiance fluctuations (channel b)

35

Figure 3.3: Bounded, approximate and exact cdf of the sum of Double GG dis-tributed RVs assuming spherical wave and moderate irradiance fluctuations (chan-nel c)

Similarly for channel b, W is respectively obtained as 1.5, 1.76 and 1.92 for N =

2, 3, 4. As clearly seen from Figs. 3.1 and 3.2, our approximate expressions provide

an excellent match to the simulation results for all values of N and under all range

of turbulence conditions. However, the upper bound provides good accuracy for

small values of N , and exhibits large deviations compared to the simulation results

as N increases. Comparing Figs. 3.1 and 3.2, it is further observed that as the

turbulence condition becomes weaker, the upper bound shows better accuracy.

Figs. 3.3 and 3.4 illustrate the numerical results assuming spherical wave prop-

agation with moderate (channel c) and strong (channel d) irradiance fluctuations

respectively. For channel c, we obtain W = 1.31, 1.45, 1.53 for N = 2, 3, 4 re-

spectively. For channel d, W is respectively calculated as 1.74, 2.14 and 2.39 for

36

Figure 3.4: Bounded, approximate and exact cdf of the sum of Double GG dis-tributed RVs assuming spherical wave and strong irradiance fluctuations (channeld)

N = 2, 3, 4. It is apparent from Figs. 3.3 and 3.4 that the proposed approximation

again follows closely the exact simulation results for all values of N and under all

range of turbulence conditions. Similar to the earlier observations on the upper

bound for the plane wave propagation, the less the value of N and the weaker the

turbulence condition, the better accuracy is observed.

3.5 Conclusions

In this Chapter, we have derived a closed-form union upper bound and accurate

approximate expression for the distribution of the sum of N i.n.i.d. Double GG

distributed RVs in terms of Meijers G-function. Comparing with the computer

37

simulation results, we have shown that the proposed approximate expression pro-

vides an excellent match to the simulation results for all values of N and under all

range of turbulence conditions.

38

Chapter 4Performance Evaluation of

Free-Space Optical Links with

Spatial Diversity

In Chapter 2, we derived the bit error rate (BER) performance of single-input

single-output (SISO) free-space optical (FSO) link over Double Generalized Gamma

(Double GG) channels. As it can be noticed from Section 2.4, the performance of a

SISO FSO link over moderate and strong atmospheric turbulence is quite poor. To

address this issue, multiple transmit and/or receive apertures can be employed and

the performance can be improved via diversity gains. In this Chapter, we extend

our performance analysis to evaluate the performance of FSO links with spatial

diversity. Spatial diversity techniques provide a promising approach to mitigate

turbulence-induced fading. Some earlier results on FSO systems with spatial diver-

sity over log-normal, K, negative exponential and Gamma-Gamma channels can

be found in [26,32,33,43,44]. In this Chapter, we study the error rate performance

of multiple-input multiple-output (MIMO), single-input multiple-output (SIMO)

39

and multiple-input single-output (MISO) systems employing intensity modulation

and direct detection (IM/DD) with on-off keying (OOK) over independent but not

necessarily identically distributed (i.n.i.d.) Double GG turbulence channels.

4.1 System Model

We consider an FSO system employing IM/DD with OOK where the information

signal is transmitted via M apertures and received by N apertures over the Double

GG channel. The received signal at the nth receive aperture is then given by

yn = ηxM∑

m=1Imn + υn, n = 1, . . . , N (4.1)

where x represents the information bits and can be either 0 or 1, υn is the Additive

White Gaussian noise (AWGN) term with zero mean and variance σ2υn

= N0/2 ,

and η is the optical-to-electrical conversion coefficient. Here, Imn is the normalized

irradiance from the mth transmitter to the nth receiver whose probability density

function (pdf) and cumulative distribution function (cdf) follow (2.5) and (2.7)

respectively.

4.2 Performance Analysis of of MIMO FSO Links

The optimum decision metric for OOK is given by [33]

P (y|on,Imn)on≶offP (y|off,Imn) (4.2)

where y = (y1, y2, ..., yN) is the received signal vector. Following the same approach

as [32, 33], the conditional bit error probabilities are given by (see [33] for details

40

of derivation)

Pe(off |Imn) = Pe(on |Imn) = Q

1MN

√√√√√ γ

2

N∑n=1

(M∑

m=1Imn

)2 (4.3)

whereQ (.) is the Gaussian Q-function defined asQ (x) =(1/

√2π) ∫∞

x exp (−t2/2 )dt

[45, 46]. Therefore, the average error rate can be expressed as

Pe,MIMO =∫I

fI (I)Q

1MN

√√√√√ γ

2

N∑n=1

(M∑

m=1Imn

)2 dI (4.4)

where fI (I) is the joint pdf of vector I = (I11, I12, . . . , IMN). The factor M in (4.4)

ensures that the total transmitted powers of diversity system and SISO link are

equal for a fair comparison. On the other hand, the factor N is used to ensure that

sum of the N receive aperture areas is the same as the area of the receive aperture

of the SISO link. The integral expressed in (4.4) does not yield a closed-form

solution even for simpler turbulence distributions; however, it can be calculated

through multidimensional Gaussian quadrature rule (GQR)techniques [47].

In the following, we investigate the receive and the transmit diversity as spe-

cial cases to have further insight into the performance of FSO links with spatial

diversity.

41

4.3 Performance Analysis of FSO Links with Re-

ceive Diversity

4.3.1 SIMO FSO Links with Optimal Combining

In this Section, we assume that multiple receive apertures are employed and present

the BER derivations under the assumption that optimal gain combining (OC) with

perfect channel state information (CSI) is used where the variance of the noise in

each receiver is given by σ2n = N0/2N . Therefore, replacing M = 1 in (4.4) we

obtain

Pe,SIMO (OC) =∫I

fI (I)Q

√√√√ γ

2N

N∑n=1

I2n

dI. (4.5)

(4.5) does not yield a closed-form solution and requires N-dimensional integration.

Nevertheless, the Q-function can be well-approximated as [48]

Q(x) ≈ e− x22 /12 + e− 2x2

3 /4. (4.6)

Thus the average BER can be obtained as

Pe,SIMO (OC) ≈ 112

N∏n=1

∫ ∞

0fIn (In) exp

(−γ4N

I2n

)dIn

+ 14

N∏n=1

∫ ∞

0fIn (In) exp

(−γ3N

I2n

)dIn. (4.7)

The above integral can be evaluated by first expressing the exponential function

in terms of the Meijer G-function presented in [38, eq. (11)] as

exp (−x) = G1,00,1

[x∣∣∣−0 ] . (4.8)

42

Then, a closed-form expression for (4.7) is obtained using [38, Eq. (21)] as

Pe,SIMO (OC) ≈ 112

N∏n=1

Λ (n, 4) + 14

N∏n=1

Λ (n, 3) (4.9)

where Λ (n, c) is defined as

Λ (n, c) = αnl−0.5n k

m1,n+m2,nn

2(2π)0.5(ln−1+(kn−1)(pn+qn)) (4.10)

×Gkn(pn+qn),lnln,kn(pn+qn)

(cN)lnω−knn llnn

γlnkkn(pn+qn)n

∣∣∣∣∣∣∣∣∆ (ln, 1)

Jkn (qn, 1 −m1,n) , Jkn (pn, 1 −m2,n)

.

In (4.10), ln and kn are positive integer numbers that satisfy pnγ2,n/2 = ln/kn ,

and αn and ωn n ∈ 1, 2, . . . , N are defined as

αn = γ2,npm2,n+1/2n q

m1,n−1/2n (2π)1−(pn+qn)/2

Γ (m1,n) Γ (m2,n), (4.11)

ωn =(Ω2,npnm

−12,n

)pn(qnΩ1,nm

−11,n

)qn

. (4.12)

As detailed in Appendix D, the derived expression in (4.9) includes the previously

reported result in [32] for K channel as a special case.

Based on the approximation in (2.27), the corresponding closed-form asymp-

totic solution for (4.7) can be obtained as

Pe,SIMO (OC)_asy ≈ 112

N∏n=1

Λasy (n, 4) + 14

N∏n=1

Λasy (n, 3) (4.13)

where Λasy (n, c) is defined as

Λasy (n, c) = αn

pn+qn∏j=1j =k

Γ (bj,n − bk,n)Γ (pnγ2,nbk,n)

(√cN)pnγ2,nbk,n

2(√γ)pnγ2,nbk,n

. (4.14)

43

Figure 4.1: Comparison of the average BER between SISO and SIMO with optimalcombing for plane wave with σ2

Rytov = 25 and l0/R0 = 1.

Therefore, the diversity order of FSO links with N receive apertures employing

optimal gain combining is obtained as 0.5N∑

n=1pnγ2,n min

m1,n/qn,m2,n/pn

.

Figs. 4.1 and 4.2 illustrate the BER performance of the SIMO FSO system

under consideration assuming following two cases a) Plane wave with σ2Rytov = 25

and l0/R0 = 1, b) Spherical wave with σ2Rytov = 2 and l0/R0 = 0. We present ap-

proximate analytical results which have been obtained through (4.9) and (4.13)

along with the Monte-Carlo simulation of (4.5). As clearly seen from Figs. 4.1

and 4.2, our approximate expressions provide an excellent match to simulation re-

sults. As a benchmark, the BER of SISO FSO link is also included in these figures.

It is observed that receive diversity significantly improve the performance. For in-

stance, at a target bit error rate of 10−3, we observe performance improvements

44

Figure 4.2: Comparison of the average BER between SISO and SIMO with optimalcombing for spherical wave with σ2

Rytov = 2 and l0/R0 = 0.

of 26.8 dB and 39.6 dB respectively for with N = 2 and 3 with respect to the

SISO transmission for the plane wave scenario. Similarly, for the spherical wave

scenario, at a BER of 10−3, performance improvements of 19 dB and 25.1 dB are

achieved for SIMO links with N = 2 and 3 compared to the SISO deployment. It

can be further observed that asymptotic bounds on the BER become tighter at

high enough signal to noise ratios (SNRs) confirming the accuracy and usefulness

of the asymptotic expression given in (4.13).

4.3.2 SIMO FSO Links with Selection Combining

As an alternative to OC, we also consider selection combining (SC) which is the

least complicated of the combining schemes since it only processes one of the

45

diversity apertures. Specifically, the SC chooses the aperture with the maximum

received irradiance (or electrical SNR). Therefore, the pdf of the output of SC

receiver can be obtained as

fImax (Imax) = dFImax (Imax)dImax

=N∑

n=1

N∏k=1,k =n

fIn (Imax)FIk(Imax) . (4.15)

The average BER can be then expressed as

Pe,SIMO (SC) =N∑

n=1

N∏k=1,k =n

∫ ∞

0fIn (Imax)FIk

(Imax) Q

Imax

√γ

2N

dImax (4.16)

which can be efficiently calculated through numerical means [49].

4.3.3 SIMO FSO Links with Equal Gain Combining

Capitalizing on the mathematical analysis in Chapter 3, we now study the perfor-

mance of an FSO system with receive diversity employing equal gain combining

(EGC) where the receiver adds the receiver branches. The received signal is then

given by

y = ηxN∑

n=1In + υn, n = 1, . . . , N. (4.17)

Outage Probability Analysis: The outage probability is defined as the prob-

ability that the instantaneous SNR of the received signal falls below a predefined

threshold, that is

Pout = Pr (γEGC < γth) = FγEGC(γth) . (4.18)

For the system under consideration, the instantaneous electrical SNR can be calu-

46

lated as [50]

γEGC =

(η

N∑i=1

In

)N2N0

2

. (4.19)

Since E (In) = 1, the corresponding average electrical SNR is obtained as

γEGC = γ = η2/N0. (4.20)

Using Eqs. (4.19) and (4.20), Z, defined in Chapter 3 as Z ,N∑

n=1In, can be

expressed as

Z = N

√γEGC

γEGC

. (4.21)

Thus, the approximate cdf of γEGC can be easily derived from (3.18) and set-

ting γEGC = γth therein, an accurate closed-form approximation for the outage

probability is obtained as

Pout = FγEGC(γth) ∼= ξGβ,1

1,β+1

ω−1(

γth

γEGCW 2

)αN/2∣∣∣∣∣∣∣∣

1

Jα (γ1:2N ,m1:2N) , 0

. (4.22)

We should emphasize that if we insert W = 1 in (4.22), the upper bound expression

for the outage probability is obtained. Moreover, by setting N = 1 that results in

W = 1, we recover the exact expression for the outage probability of SISO reported

in (2.32). (4.22) can be seen as a generalization of outage analysis of SIMO FSO

systems with EGC over other atmospheric turbulence models in the literature.

Setting γl = 1 and Ωl = 1 in (4.22), we obtain the outage probability expression

under the assumption of Gamma-Gamma channel. If we insert ml = 1 in (4.22),

we derive the outage expression for Double-Weibull channel. On the other hand,

for γl = 1, Ωl = 1 and m2l = 1, the outage expression for K-channel is obtained.

47

(a)

(b)

Figure 4.3: Bounded, approximate and exact outage probability of EGC and SISOfor a) Plane wave with σ2

Rytov = 2 and l0/R0 = 0.5, b) Plane wave with σ2Rytove = 25

and I0/R0 = 1.

48

(a)

(b)

Figure 4.4: Bounded, approximate and exact outage probability of EGC and SISOfor a) Spherical wave with σ2

Rytov = 2 and l0/R0 = 0, b) Spherical wave withσ2

Rytov = 5 and l0/R0 = 1.

49

Figs. 4.3 and 4.4 present the outage probabilities as a function of the normalized

outage threshold (i.e., γEGC/γth) for different degrees of turbulence severity and

values of N based on the derived expression in (4.22). In these figures, the same

parameters used in Figs. 3.1 to 3.4 are adopted, and the outage results obtained

by Monte Carlo simulations are further included in order to verify the tightness of

the upper bound and the accuracy of (4.22). As expected from the earlier results

discussed in Section 3.4, the upper bound provides satisfactory accuracy only for

small values of N and weak turbulence conditions. However, the numerical results

of (4.22) are nearly equivalent to the simulated ones representing the exact outage

performance for all values of N and under all range of turbulence conditions. For

instance, at a target outage probability of 10−4, the gaps between the exact and

the approximate curves are 0.25 dB, 0.08 dB and 0.45 dB respectively for N = 2, 3

and 4 in Fig. 4.4b. It is also evident that for N = 1, the upper bound, approximate

and exact curves are identical. In addition, the obtained results clearly show that

outage performance significantly improves with increasing of N .

BER Performance Analysis: Following the same approach as [32, 33], the

conditional bit error probabilities are given by

Pe,SIMO (EGC)(off |In) = Pe,SIMO (EGC)(on |In) = 12

erfc(√

γEGC

2N

N∑n=1

In

). (4.23)

Therefore, the average error rate can be expressed as

Pe,SIMO (EGC) = 12

∫I

fI (I) erfc(√

γEGC

2N

N∑n=1

In

)dI. (4.24)

The integral expressed in (4.24) does not yield a closed-form solution even for

simpler turbulence distributions. However, an accurate closed-form approximation

50

of (4.24) can be obtained as

Pe,SIMO (EGC) ∼=12

∞∫0

fZ (z) erfc(√

γEGC z

2N

)dz. (4.25)

The above integral can be evaluated in closed-form by first expressing the erfc (.)

in terms of the Meijer G-function presented in [38, eq. (11)] as

erfc(√

x)

= 1√πG2,0

1,2

x∣∣∣∣∣∣∣∣

1

0, 1/2

. (4.26)

Then, a closed-form expression for (4.25) is obtained using [38, Eq. (21)] as

Pe,SIMO (EGC) ∼=Nαξqλ

2√

2s(√

2π)s+(q−1)β ,

×Gqβ,2s2s,qβ+s

Heγ−sEGC

∣∣∣∣∣∣∣∣∆ (s, 1) ,∆ (s, 1/2 )

Kq (α/γ1:2N ,m1:2N) ,∆ (s, 0)

(4.27)

where s and q are positive integer numbers that satisfy s/q = αN/2, and H, λ and

Kq (α/γ1:2N ,m1:2N) are defined as

He ,(4sN2)s

(ωqβ)q(WN

)αNq , (4.28)

Kq (α/γ1:2N ,m1:2N) , (4.29)Jα (γ1:2N ,m1:2N) q = 1

Jα(γ1:2N ,m1:2N )2 , Jα(γ1:2N ,m1:2N )−1

2

q = 2

,

51

(a)

(b)

Figure 4.5: Bounded, approximate and exact BER of EGC and SISO for a) Planewave with σ2

Rytov = 2 and l0/R0 = 0.5, b) Plane wave with σ2Rytove = 25 and

I0/R0 = 1.

52

λ ,2N∑l=1

ml −N + 1. (4.30)

Note that for N = 1 leading to W = 1, (4.27) reduces to (2.25) reported as

the BER expression of the SISO link. Furthermore, setting W = 1 in (4.27),

the upper bound expression for the BER is obtained. The derived approximate

BER expression in (4.27) for SIMO FSO systems with EGC can be seen as a

generalization of BER results over other atmospheric turbulence models as well.

Specially, if we insert γl = 1 and Ωl = 1 in (4.27), we obtain an approximate BER

expression over Gamma-Gamma channel. Setting mi = 1 in (4.27), we obtain an

approximate BER for Double Weibull channel. Similarly, for γl = 1, Ωl = 1 and

m2l = 1, an approximate BER expression for K-channel is obtained.

Figs. 4.5 and 4.6 demonstrate the average BER over independent and identi-

cally distributed (i.i.d.) Double GG channels assuming both plane and spherical

wave propagation, respectively. In order to verify the tightness of the bound and

accuracy of the approximate expression, we present analytical results obtained

through (4.27) along with the Monte-Carlo simulation of (4.24). As a benchmark,

the average BER of SISO FSO link obtained through (2.25) is also included in

these figures1. As clearly seen from Figs. 4.5 and 4.6, the approximate expres-

sion provides an excellent match to the simulation data which represent the exact

BER. For instance, at a target bit error rate of 10−4, the gaps between the ex-

act and the approximate curves are 0.16 dB, 0.3 dB and 0.6 dB respectively for

N = 2, 3 and 4 in Fig. 4.5b. This observation clearly demonstrates the accuracy of

the proposed approximation. It is also illustrated that the upper bound becomes

tighter as the number of receive apertures decreases. This is expected as the upper

bound and the exact BER curves coincide for N = 1. In addition, we observe that1The same results can be obtained by inserting N = 1 and therefore W = 1 in (4.27).

53

(a)

(b)

Figure 4.6: Bounded, approximate and exact BER of EGC and SISO for a) Spher-ical wave with σ2

Rytov = 2 and l0/R0 = 0, b) Spherical wave with σ2Rytov = 5 and

l0/R0 = 1.

54

multiple receive apertures deployment employing EGC significantly improves the

performance. Specially, in Fig. 4.5b, at a target bit error rate of 10−4, we observe

performance improvements of 23.4 dB, 33.4 dB and 41.4 dB for SIMO FSO links

with N = 2, 3 and 4 receive apertures employing EGC respectively with respect

to the SISO transmission.

Although Meijer’s G-function can be expressed in terms of more tractable gen-

eralized hypergeometric functions, (4.27) appears to be complex and the impact of

the basic system and channel parameters on performance is not very clear. How-

ever, as discussed in Section 2.4.1, for large SNR values, the asymptotic behavior

of the system performance is dominated by the behavior of the pdf near the origin,

i.e. fZ (z) at z → 0 [39]. Thus, employing a series expansion corresponding to

the Meijer’s G-function [40, Eq. (07.34.06.0006.01)], fZ (z) given in (3.19) can be

approximated by a single polynomial term as

fZ (z) ≈ Nαξ(ω(WN

)αN)minm1γ1

α,··· ,

m2N γ2Nα

β∏j=1j =k

Γ (cj − ck) zN minm1γ1,··· ,m2N γ2N −1

(4.31)

where ck and cj are defined as

ck = minm1γ1

α, · · · , m2Nγ2N

α

, (4.32)

cj ∈ ∆ (α/γ2 ;m2) , . . . ,∆ (α/γ2N;m2N) \ min

m1γ1

α, · · · , m2Nγ2N

α

. (4.33)

It must be noted that (4.31) is only valid for i.n.i.d. Double GG turbulence chan-

nels. Based on Eqs. (4.25) and (4.31) and at high SNRs, the average BER can be

55

Figure 4.7: Exact, approximate and asymptotic BER of EGC over two i.n.i.d.atmospheric turbulence channels defined as plane wave with σ2

Rytov = 2 and l0/R0 =0.5, and plane wave with σ2

Rytove = 25 and I0/R0 = 1.

well approximated as

Pe,SIMO (EGC) ≈ Γ ((1 +Nαck) /2) ξ

2√πck

(ω(WN

)αN)ck

β∏j=1j =k

Γ (cj − ck)(

2N√γEGC

)Nαck

. (4.34)

Therefore, the diversity order of FSO links with N receive apertures employing

EGC is obtained as 0.5N min m1γ1 · · · ,m2Nγ2N.

Figs. 4.7 and 4.8 illustrate the BER performance of SIMO FSO links employing

EGC receivers over i.n.i.d. Double GG channels. Similar to i.i.d. results, our

approximate closed-form expression yields a very close match to the simulation

results. For example, in Fig. 4.7 at a BER of 10−4 in SIMO links with N = 2, the

56

Figure 4.8: Exact, approximate and asymptotic BER of EGC over two i.n.i.d.atmospheric turbulence channels defined as spherical wave with σ2

Rytov = 2 andl0/R0 = 0, and spherical wave with σ2

Rytov = 5 and l0/R0 = 1.

difference between the exact and the approximate curve is 2.4 dB. In Fig. 4.8 and

at a BER of 10−4, this gap is 1.1 dB. It can be further observed that asymptotic

bounds on the BER become tighter at high enough SNR values confirming the

accuracy and usefulness of the asymptotic expression given in (4.34).

57

4.4 Performance Analysis of FSO Links with Trans-

mit Diversity

4.4.1 MISO FSO Links

In this Section, we assume that multiple transmit apertures are employed. There-

fore, replacing N = 1 in (4.4) we obtain

Pe,MISO =∫I

fI (I)Q( √

γ

M√

2

M∑m=1

Im

)dI. (4.35)

It should be noted that (4.35) is equivalent to (4.24) obtained for the SIMO FSO

links with EGC. Thus, the mathematical analysis developed in Section 4.3.3 can

be use to evaluate the performance of MISO FSO links.

4.5 Performance Comparison of Diversity Tech-

niques

In this Section, we present and compare the BER performance results of FSO sys-

tems employing different diversity techniques over Double GG channels assuming

both plane and spherical wave propagation. The performance improvements over

SISO systems are further quantified.

Figs. 4.9 and 4.10 present the average BER over i.i.d. turbulent channels as-

suming plane wave propagation with strong irradiance fluctuations and spherical

wave propagation with moderate irradiance fluctuations, respectively. As a bench-

mark, the average BER of SISO FSO link obtained through (2.25) is also included

58

Figure 4.9: Comparison of the average BER between SISO and different diversitytechniques for plane wave assuming i.i.d. turbulent channel with σ2

Rytove = 25 andI0/R0 = 1.

in these figures. As clearly seen from Figs. 4.9 and 4.10, the diversity techniques

significantly improve the performance. it is also illustrated that EGC receivers

yield nearly the same performance as OC receivers. For example, in Fig. 4.10, for

N = 2 the performance difference between OC and EGC receivers is merely 0.4

dB at a BER of 10−5. Also as expected, SIMO FSO links employing OC and EGC

outperform SC counterpart.

Figs. 4.11 and 4.12 demonstrate the BER performance of SIMO FSO links

employing OC, EGC and SC receivers over i.n.i.d. Double GG channels. Similar

to i.i.d. results, EGC receiver demonstrates nearly the same performance as OC

receiver. We further compare the performance of i.n.i.d. case with respect to i.i.d.

case presented in Figs. 4.9 and 4.10. For example, to achieve a BER of 10−5 in

59

Figure 4.10: Comparison of the average BER between SISO and different diversitytechniques for spherical wave assuming i.i.d. turbulent channel with σ2

Rytov = 2and l0/R0 = 0.

SIMO links with N = 2 over i.n.i.d. channels assuming plane wave propagation,

we need 8.2 dB, 8.5 dB and 4.9 dB less in comparison to i.i.d. case respectively

for OC, EGC and SC receivers. Note that in Fig. 4.9, we assume that both of the

two channels between the transmitter and receivers are described by a plane wave

with strong irradiance fluctuations. Thus, since in Fig. 4.11, one of the channels is

less severe, we need less SNR in comparison to i.i.d. case to obtain the same BER.

On the other hand, to achieve a BER of 10−5 for SIMO links with N = 2 over

i.n.i.d. assuming spherical wave propagation, we need 6.8 dB more for OC and

EGC receivers and 11.6 dB more for SC receiver in comparison to i.i.d. channels.

Note that in Fig. 4.10, both of the two channels between the transmitter and

receivers are described by a spherical wave with moderate irradiance fluctuations.

60

Figure 4.11: Comparison of the OC, EGC and SC receivers for SIMO FSO linksover two i.n.i.d. atmospheric turbulence channels defined as plane wave withσ2

Rytov = 2 and l0/R0 = 0.5, and plane wave with σ2Rytove = 25 and I0/R0 = 1.

Therefore, as one of the channels is more severe than those channels in Fig. 4.10,

we need more SNR in comparison to i.i.d. case to achieve the same performance.

4.6 Conclusions

In this Chapter, we have investigated the BER performance of FSO links with

spatial diversity over atmospheric turbulence channels described by the Double

GG distribution. We have obtained efficient and unified closed-form expressions

for the BER of SIMO FSO systems with OC and EGC receivers along with outage

probability of the EGC receiver which generalize existing results as special cases.

We have further obtained the diversity gains for SIMO FSO systems employing OC

61

Figure 4.12: Comparison of the OC, EGC and SC receivers for SIMO FSO linksover two i.n.i.d. atmospheric turbulence channels defined as spherical wave withσ2

Rytov = 2 and l0/R0 = 0, and spherical wave with σ2Rytov = 5 and l0/R0 = 1.

and EGC receivers based on the asymptotical performance analysis. For MIMO

and SIMO FSO systems with SC receiver, we have presented BER performance

based on numerical calculations of the integral expressions. Our numerical results

have demonstrated that spatial diversity schemes can significantly improve the

system performance and bring impressive performance gains over SISO systems.

Our comparisons among SIMO FSO links employing OC, EGC and SC receivers

have further demonstrated that EGC scheme presents a favorable trade-off between

complexity and performance.

62

Chapter 5Performance Evaluation of Single-

and Multi-carrier Modulation

Schemes for Indoor Visible Light

Communication Systems

In this Chapter, we investigate and compare the performance of single- and multi-

carrier modulation schemes for indoor visible light communication (VLC). Partic-

ularly, the performances of single carrier frequency domain equalization (SCFDE),

orthogonal frequency division multiplexing (OFDM) and on-off keying (OOK) with

minimum mean square error equalization (MMSE) are analyzed in order to mit-

igate the effect of multipath distortion of the indoor optical channel where non-

linearity distortion of light-emitting diode (LED) transfer function is taken into

account. Our results indicate that SCFDE system, in contrast to OFDM system,

does not suffer from high peak-to-average power ratio (PAPR) and can outperform

OFDM and OOK systems. We further investigate the impact of LED bias point on

63

the performance of OFDM systems and show that biasing LED with the optimum

value can significantly enhance the performance of the system. Bit-interleaved

coded modulation (BICM) is also considered for OFDM and SCFDE systems to

further compensate signal degradation due to intersymbol interference (ISI) and

LED nonlinearity.

5.1 Introduction

OFDM has been proposed in the literature to combat ISI caused by multipath re-

flections [51–56]. OFDM is capable of employing very low-complexity equalization

with single-tap equalizers in the frequency domain, and allows adaptive modula-

tion and power allocation. There have been several OFDM techniques for VLC

systems using intensity modulation and direct detection (IM/DD) including DC-

clipped OFDM [55], asymmetrically clipped optical OFDM (ACO-OFDM) [56],

PAM-modulated discrete multitone (PAM-DMT) [57], Flip-OFDM [58] and unipo-

lar OFDM (U-OFDM) [59]. In DC-clipped OFDM, a DC bias is added to the sig-

nal to make it unipolar and suitable for optical transmission. Hard-clipping on the

negative signal peaks is used in order to reduce the DC bias required. The other

techniques have been proposed to remove the biasing requirement and therefore

improve the energy efficiency of DC-clipped OFDM. Particularly, ACO-OFDM and

PAM-DMT clip the entire negative excursion of the waveform. In ACO-OFDM, to

avoid the impairment from clipping noise, only odd subcarriers are modulated by

information symbols. In PAM-DMT, only the imaginary parts of the subcarriers

are modulated such that clipping noise falls only on the real part of each subcarrier

and becomes orthogonal to the desired signal. On the other hand, U-OFDM and

Flip-OFDM extract the negative and positive samples from the real bipolar OFDM

64

symbol and separately transmit these two components over two successive OFDM

frames where the polarity of the negative samples is inverted before transmission.

As discussed in [60], all of these four non-biasing OFDM approaches exhibit the

same performance in an Additive White Gaussian noise (AWGN) channel. Among

these schemes, ACO-OFDM has been shown to be more efficient in terms of optical

power than the systems that use DC-biasing as it utilizes a large dynamic range

of the LED. Therefore, it is considered in this work.

There exist several investigations analyzing different OFDM techniques and

comparing them with SCFDE [61–63] or single carrier modulation [64,65]. To the

best of our knowledge, these previous studies were built on the assumption of ideal

AWGN channels or did not consider the nonlinear characteristics of LED. In this

Chapter, we analyze and compare performance of the aforementioned techniques

along with OOK with MMSE which is commonly used in IM/DD communication

systems considering an off-the-shelf LED model and a multipath channel. More-

over, BICM is considered for OFDM and SCFDE systems to further combat signal

degradation due to LED nonlinearity and ISI.

5.2 System Model of ACO-OFDM

ACO-OFDM is a form of OFDM that modulates the intensity of an LED. Because

ACO-OFDM modulation employs IM/DD, the time-domain transmitted signal

must be real and positive. The block diagram of an ACO-OFDM system is de-

picted in Fig. 5.1. The information stream is first parsed into a block of L/4

complex data symbols denoted by X =[X0, X1, ...XL/4−1

]Twhere the symbols are

drawn from constellations such as M -QAM or M -PSK where M is the constel-

lation size. To ensure a real output signal used to modulate the LED intensity,

65

Figure 5.1: ACO-OFDM transmitter and receiver configuration.

ACO-OFDM subcarriers must have Hermitian symmetry. In ACO-OFDM, only

odd subcarriers are modulated, and this results in avoiding the impairment from

clipping noise. Therefore, the complex symbols are mapped onto a L× 1 vector as

S = [0, X0, 0, X1, . . . , 0, XL/4−1, 0, X∗L/4−1, 0, . . . , X∗

1 , 0, X∗0 , 0]T where (.)∗ denotes

the complex conjugate and (.)T indicates the transpose of a vector. An L-point

inverse fast Fourier transform (IFFT) is then applied on the vector S to build

the time domain signal s. A cyclic prefix (CP) is added to s turning the linear

convolution with the channel into a circular one to mitigate multipath dispersion.

To make the transmitted signal unipolar, all the negative values are clipped to

zero. It is proven in [56] that since only the odd subcarriers are used to carry the

data symbols, the clipping does not affect the data-carrying subcarriers, but only

reduces their amplitude by a factor of two.

The unipolar signal is then converted to analog and filtered to modulate the

intensity of an LED. At the receiver, the signal is converted back to digital. CP

is then removed and the electrical OFDM signal is demodulated by taking a L

fast Fourier transform (FFT) and equalized with a single-tap equalizer on each

66

Figure 5.2: ACO-SCFDE transmitter and receiver configuration.

subcarrier to compensate for channel distortion. The even subcarriers are then

discarded and the transmitted data is recovered by a hard or soft decision. The

extraction of odd subcarriers along with the equalization are represented by the

Demapping block in Fig. 5.1.

5.3 System Model of ACO-SCFDE

SCFDE is a special technique which is compatible with any of OFDM techniques.

In this work, we apply ACO-OFDM to SCFDE to achieve ACO-SCFDE with

low PAPR. The block diagram of an ACO-SCFDE system is depicted in Fig. 5.2.

ACO-SCFDE and ACO-OFDM are the same except that in ACO-SCFDE, an extra

L/4-point FFT and IFFT are used at the transmitter and the receiver respectively

resulting in a single carrier transmission instead of multicarrier. As it will be shown

latter, the additional complexity of the extra FFT and IFFT blocks is offset by the

fact that SCFDE has lower PAPR and better bit error rate (BER) performance

than its OFDM counterpart when the signal is sent through the non-linear LED.

67

Figure 5.3: CCDF of PAPR comparison of ACO-OFDM and ACO-SCFDE forL = 64.

5.4 Peak-to-Average Power Ratio

In this Section, the PAPR of ACO-OFDM signals is analyzed and compared with

that of ACO-SCFDE. The PAPR is defined as the maximum power of transmitted

signal divided by the average power, that is

PAPR = max s2 (n)E [s2 (n)]

(5.1)

where E [.] denotes expectation. Due to the large number of subcarriers and occa-

sional constructive combining of them, OFDM systems have a large dynamic signal

range and exhibit a very high PAPR. Thus, the OFDM signal will be clipped when

passed through a nonlinear LED at the transmitter end which results in degrading

68

Figure 5.4: CCDF of PAPR comparison of ACO-OFDM and ACO-SCFDE forL = 256.

the BER performance. SCFDE can be used as a promising alternative technique

for OFDM to reduce the PAPR and combat the effect of nonlinear characteristics

of the LED.

PAPR is usually presented in terms of a complementary cumulative distribution

function (ccdf) which is the probability that PAPR is higher than a certain PAPR

value PAPR0, i.e. Pr (PAPR > PAPR0). Figs. 5.3 and 5.4 demonstrate the ccdf

of PAPR for L = 64 and 256 subcarriers respectively, calculated by Monte Carlo

simulation for different modulation constellations. We notice that ACO-SCFDE

has a lower PAPR as compared to ACO-OFDM system for the same number of

subcarriers. We also observe that the PAPR increases with increasing L for all of

the constellations.

69

Table 5.1: Room configuration under consideration.

Room Length 6 mWidth 5 mHeight 3 m

Reflectivity ρNorth 0.8ρSouth 0.8ρEast 0.8ρWest 0.8

ρCeiling 0.8ρFloor 0.3

Source Mode 1Azimuth 0

Elevation −90

x, y, z 0.1 m, 0.2 m, 3 mReceiver Area 1 CM2

FOV 85

x, y, z 2.5 m, 2.5 m, 1 m

5.5 Performance Analysis

Simulations are conducted assuming indoor optical multipath channel where the

transmitter and receiver are placed in a room whose configuration is summarized in

Table 5.1. The methodology developed by Barry et al [66] is employed to simulate

the impulse response of the channel where 10 reflections are taken into account.

Fig. 5.5 presents the impulse respond of a diffuse channel.

We assume an OFDM signal whose average electrical power before modulating

the LED is varied from -10 dBm to 30 dBm, and the power of AWGN is -10 dBm.

Thus, the simulated electrical signal to noise ratio (SNR) ranges from 0 dB to 40

dB matching the reported SNR values for indoor optical wireless communication

(OWC) systems [67,68]. A number of subcarriers of L = 64 with M -QAM modu-

lation are also assumed. Furthermore, OPTEK, OVSPxBCR4 1-Watt white LED

is considered in simulations whose optical and electrical characteristics are given

70

Figure 5.5: Impulse response of the indoor diffuse channel.

Table 5.2: Optical and electrical characteristics of OPTEK,OVSPxBCR4 1-Watt white LED.

Symbol Parameter MIN TYP MAX UnitsVF Forward Voltage 3.0 3.5 4 V

Φ Luminous Flux 67 90 113 lmΘ1/2 50% Power Angle — 120 — deg

in Table 5.2. A polynomial order of five is used to realistically model measured

transfer function. Fig. 5.6 demonstrates the non-linear Transfer characteristics of

the LED from the data sheet and using the polynomial function.

We first compare the BER performance of ACO-SCFDE and ACO-OFDM.

Fig. 5.7 presents the BER performance of ACO-OFDM and ACO-SCFDE for dif-

ferent modulation orders and LED bias point of 3.2V. As the results indicate,

SCFDE exhibits better BER performance in the optical multipath channel.

Furthermore, we investigate the impact of LED bias point on the performance

71

(a)(b)

Figure 5.6: Transfer characteristics of OPTEK, OVSPxBCR4 1-Watt white LED.(a) Fifth-order polynomial fit to the data. (b) The curve from the data sheet.

Figure 5.7: BER comparison of ACO-OFDM and ACO-SCFDE for bias point of3.2V.

72

Figure 5.8: BER of ACO-OFDM for M = 16 for different bias points.

of ACO-OFDM systems. According to the data sheet of the LED used in the

simulations, three different bias points (3V, 3.2V and 3.5V) are considered. Fig. 5.8

demonstrates BER performance of an ACO-OFDM system with M = 16 and

different LED bias points. As it can be clearly seen, the nonlinearity of LED

has a significant impact on the performance of optical OFDM systems. It is also

observed that there is an optimum LED bias point which is 3.2V for the case

under consideration from which deviation can significantly deteriorate the system

performance.

BICM [69] is also considered for OFDM and SCFDEs systems to further com-

pensate signal degradation due to ISI and LED nonlinearity. To demonstrate the

usefulness of BICM, we assume that the information sequence is first encoded by a

73

Figure 5.9: BER comparison of uncoded and coded ACO-OFDM and ACO-SCFDEfor M = 16.

rate 1/2 convolutional encoder with generator matrix g = (5, 7), constraint length

of 3 and minimum Hamming distance of 5. The coded information is then in-

terleaved by a bitwise interleaver. At the receiver, the Viterbi soft-decoder [70]

and the de-interleaver are used. Fig. 5.9 shows the BER of uncoded and coded

ACO-OFDM and ACO-SCFDE for the indoor VLC under consideration. As it

can be clearly observed, BICM can significantly enhance the system performance.

However, the achieved gains come at the cost of significant reduction in the data

rate due to the insertion of coded bits.

Finally, we compare the performance of ACO-OFDM, ACO-SCFDE and OOK

modulation with MMSE over an indoor VLC medium. The performance compari-

74

son is done in terms of normalized SNR and normalized bandwidth/bit-rate relative

to OOK [55]. According to [55] and [65], we define the modulation bandwidth as

the position of the first spectral null. To make a fair comparison between different

modulation schemes, the normalized bandwidth of the signal is calculated as the

modulation bandwidth which is normalized relative to OOK of the same transmit-

ted data rate. For ACO-OFDM and ACO-SCFDE, first null occurs at a normal-

ized frequency of 1+2/L. Thus, the normalized bandwidth/bit-rate is obtained as

2 (1 + 2/L) / logM2 for ACO-OFDM and ACO-SCFDE. Fig. 5.10 shows normalized

SNR required for a BER of 10−9 as a function of normalized bandwidth/bit-rate

for OOK, ACO-OFDM and ACO-SCFDE. We observe while ACO-OFDM and

ACO-SCFDE with 4-QAM modulation of each subcarrier require approximately

the same bandwidth as OOK, they are more efficient in terms of power. Partic-

ularly, ACO-OFDM and ACO-SCFDE are 2.7 dB and 3.7 dB more efficient than

OOK, respectively. For the higher orders of M , OOK outperforms ACO-OFDM

and ACO-SCFDE but it requires greater bandwidth.

5.6 Conclusions

We have evaluated and compared the performance of IM/DD single- and multi-

carrier modulation schemes for indoor VLC systems taking into account both non-

linear characteristics of LED and dispersive nature of optical wireless channel. We

have shown through the use of simulation that SCFDE system has a lower PAPR

than its counterpart OFDM system and outperforms OOK and OFDM systems

and therefore is a promising modulation technique for indoor VLC systems. We

have also investigated the performance of OFDM systems for different LED bias

points and shown that significant gain can be achieved by biasing LED with the

75

Figure 5.10: Normalized SNR versus normalized bandwidth/bit-rate required toachieve BER of 10−9.

optimum value. BICM technique has been further considered to combat signal

degradation due to LED nonlinearity and dispersive nature of the channel.

76

Chapter 6Robust Timing Synchronization for

AC OFDM Based Optical Wireless

Communications

In this Chapter, a novel timing synchronization technique suitable for asymmet-

rically clipped (AC) orthogonal frequency division multiplexing (OFDM) based

optical intensity modulation and direct detection (IM/DD) wireless systems is

presented. We demonstrate that the proposed technique can be directly applied

to asymmetrically clipped optical OFDM (ACO-OFDM), PAM-modulated dis-

crete multitone (PAM-DMT) and discrete Hartley transform (DHT) based optical

OFDM systems. In contrast to existing OFDM timing synchronization methods

which are either not suitable for AC OFDM techniques due to unipolar nature of

output signal or perform poorly, our proposed method is suitable for AC OFDM

schemes and outperforms all other available techniques. Both numerical and ex-

perimental results confirm the accuracy of the proposed method.

77

6.1 Introduction

It is well known that OFDM systems are sensitive to carrier frequency offset

and timing synchronization errors. For optical based OFDM systems employing

IM/DD timing, synchronization errors result in performance deterioration. There-

fore, an efficient timing synchronization scheme with an excellent accuracy that

can be used for all AC systems needs to be proposed.

A vast number of papers have been published in the literature on timing

synchronization schemes for radio frequency (RF) based OFDM systems [71–75].

These techniques cannot be directly adopted for optical OFDM systems employ-

ing IM/DD since the output signal is unipolar in these systems. Thus, a new

timing synchronization scheme that can be utilized for IM/DD systems needs to

be proposed. Tian et al. recently proposed a technique tailored specifically to

ACO-OFDM in [76]. Their proposed scheme may not work for other AC systems

and the detection accuracy of this scheme also depends on the choice of training

symbol used. Some training symbols may not yield perfect accuracy even at high

signal to noise ratio (SNR) and without noise and multipath. In [77], a method

using symmetry property of ACO-OFDM output signal in time domain with some

additional redundancy was presented. However, the channel cannot be estimated

using this technique. In this chapter, we address this daunting problem and present

a novel and robust timing synchronization method working accurately for all AC

systems, i.e. ACO-OFDM, PAM-DMT and DHT based optical OFDM, and can

also be used for channel estimation at the same time.

78

6.2 New Timing Synchronization for AC Based

OFDM Systems

6.2.1 Timing Synchronization for ACO-OFDM

As detailed in [78], our proposed method utilizes a very important characteristic of

ACO-OFDM output waveform which has a format [Cclip Dclip] where C represents

the first L/2 samples, D = −C represents negative part of first L/2 samples of

unclipped output time domain ACO-OFDM and L is the number of subcarriers.

Cclip and Dclip represent the first and the second half of the clipped output sym-

bol. This clearly demonstrates that the negative parts of the first L/2 samples of

unclipped time domain symbol are present in the second half of L/2 samples of

clipped symbol. Therefore, a bipolar signal of length L/2 with these two halves

can be easily reconstructed that is identical to the original unclipped bipolar signal

of length L/2. The bipolar signal is constructed as

rBP (l) = Cclip (l) − Dclip (l) (6.1)

where 0 ≤ l ≤ L/2 − 1 and subscript BP represents bipolar. This reconstructed

bipolar signal is then employed to carry out correlation with a local copy of training

symbol p (l) known at the receiver to accurately estimate the starting location of

OFDM symbols. We use timing metric obtained by

M (d) = 1K

K−1∑l=0

rBP (l + d) p (l + d) , K = 1, 2, ..., L/2 (6.2)

79

where K is the cross-correlation length that can be set based on the desired per-

formance. A higher value of K offers a better performance. The maximum of this

timing metric shows the starting location of OFDM training symbol. Without loss

of generality, we assume throughout this Chapter that average electrical power of

ACO-OFDM output training symbols before clipping is unity, i.e., E p2 (l) = 1.

6.2.2 Timing Synchronization for PAM-DMT

The output waveform of PAM-DMT has a format [0 Cclip 0 Dmirrorclip ] where C rep-

resents the first L/2−1 samples excluding the first sample and D = −C represents

negative of first L/2 − 1 samples of unclipped PAM-DMT output symbol. Cclip

and Dclip represent clipped version of C and D, respectively. In this case, the

second half of output symbol includes a mirror image of negative samples of the

first half. Therefore, we can reconstruct the received bipolar signal as

rBP (l) = Cclip (l) −(Dmirror

clip (l))mirror

(6.3)

where 0 ≤ l ≤ L/2 − 1. This bipolar signal is correlated with a local copy of

training symbol to detect the starting of OFDM training symbol. The maximum

of the same timing metric used by ACO-OFDM given in (6.2) along with the

bipolar signal reconstructed using (6.3) is employed.

80

6.3 Timing Synchronization DHT Based Optical

OFDM

Output waveform of DHT based optical OFDM has the same format as that of

ACO-OFDM, i.e. [Cclip Dclip]. Therefore, the same method used for ACO-OFDM

is adopted to reconstruct the bipolar signal. We also use the same timing metric

given in (6.2) to find the starting location of DHT based optical OFDM symbol.

6.4 Simulation Results

A total of 10,000 random training symbols are used with inverse fast Fourier trans-

form (IFFT) size of L = 256 and cyclic prefix (CP) length of L/8. To generate

more realistic results, each training symbol was followed and preceded by an-

other random ACO-OFDM or PAM-DMT symbol. Fig. 6.1a presents the average

of the timing metric for Schmidl’s and Park’s methods proposed for RF based

OFDM [73, 74] with modified training symbols suitable for ACO-OFDM. It can

be clearly seen that Schmidl’s timing metric demonstrates a flat region during the

length of CP of the training symbol. However, Park’s method does not suffer from

this flat region but has four distinct peaks one of which is at the correct timing

instant. Fig. 6.1b demonstrates the average of the timing metric for Tian’s method

proposed for ACO-OFDM systems [76]. It can be observed that in addition to the

main peak at the correct timing instance of d = L/2, there is another peak at

d = 0. As there is not a large difference between these two peaks, this can reduce

correct detection probability especially at low SNRs. Figs. 6.1c and 6.1d show

the average of the timing metric for bipolar correlation method with K = L/2

81

(a) (b)

(c) (d)

Figure 6.1: a) Average of Schmidl’s and Park’s timing metrics with modified train-ing symbol suitable for ACO-OFDM. b) Average of Tian’s timing metrics forACO-OFDM. c) Average of timing metrics for bipolar correlation method for ACO-OFDM. d) Average of timing metrics for bipolar correlation method for PAM-DMTsystems.

and K = L/2 − 1 for ACO-OFDM and PAM-DMT schemes respectively. From

these figures, we can clearly see that for both ACO-OFDM and PAM-DMT a peak

occurs at the correct location at d = 0. For ACO-OFDM system, there are two

other negative peaks at d = ±L/2 caused by the negative correlation of the first

and second half of the reference signal with the received signal. Since we are using

the maximum of the timing metric, those peaks are ignored and cannot result in

any uncertainty in the detection of the correct location. For both ACO-OFDM

and PAM-DMT schemes, there is a small peak occurring at d = −L. This is due

to the correlation of the local training symbol with the CP of the received training

82

symbol. The magnitude of this peak depends on the size of CP. Since CP length

is usually small compared to the length of useful part of symbol, the magnitude

of this peak is small compared to the main peak and thus does not cause any

uncertainty in correct location of the beginning of the training symbol and does

not result in erroneous detections. Note that, a plot of the average of the timing

metric for DHT based OFDM system with K = L/2 is identical to that obtained

for ACO-OFDM. Therefore, to avoid repetition of results, we do not show results

for DHT based OFDM system.

6.5 Experimental Results

An experimental test-bed is the perfect setup to verify the results discussed earlier.

We employ USRP210, a software defined radio (SDR), as the primary hardware

and software interface for the test-bed. The experimental setup is shown in Fig. 6.2.

As can be seen, the baseband data from the host personal computer (PC) properly

processed goes through the first USRP210 kit, where it is converted to RF signal.

Instead of feeding this signal to an antenna, it is fed to a driver circuit, which in turn

drives the light-emitting diode (LED) transmitter which is an OSRAM OSTAR

Phosphor White LED. The LED transmitter is thus properly modulated by the

data from the host PC and the light propagates through the channel. The intensity

of the light is detected by the Si PIN photodiode, which produces a current signal

proportional to this intensity. The signal is then amplified by an amplifier and fed

to a second USRP210 that sends it to the target PC as baseband data. The data

is further processed at the target PC. Figs. 6.3a to 6.3d demonstrate the timing

metric for the bipolar correlation method with K = L/2 and CP length of L/8

where L = 256, 512 . The symbols are drawn from 4-and 16-QAM constellations.

83

(a)

(b)

Figure 6.2: a) Schematic of the experimental setup. b) Real implementation withsoftware defined radio systems.

As can be clearly observed, the experimental results validate the simulation results

discussed earlier.

84

(a)

(b)

(c)

(d)

Figure 6.3: Average of timing metrics for bipolar correlation method for consecutiveACO-OFDM symbols with a) L = 256 and 4-QAM modulation b) L = 256 and16-QAM modulation c) L = 512 and 4-QAM modulation b) L = 512 and 16-QAMmodulation.

85

6.6 Conclusions

We have presented a novel and robust timing synchronization technique that can be

applied to all AC based OFDM systems using IM/DD. Our proposed timing metric

was based on the correlation of a local copy of the training symbol with a bipolar

signal reconstructed from unipolar received signal. In contrast to existing timing

synchronization methods, no special format of the training symbols is required.

Simulations and experimental results have been presented to confirm the accuracy

of the proposed method.

86

Chapter 7Indoor Location Estimation with

Optical-based OFDM

Communications

Orthogonal frequency division multiplexing (OFDM) has been applied to indoor

wireless optical communications in order to mitigate the effect of multipath dis-

tortion of the optical channel as well as increasing data rate. In this Chapter, a

novel OFDM visible light communication (VLC) system is proposed which can be

utilized for both communications and indoor positioning. A positioning algorithm

based on power attenuation is used to estimate the receiver coordinates. We fur-

ther calculate the positioning errors in all the locations of a room and compare

them with those using single carrier modulation scheme, i.e., on-off keying (OOK)

modulation. We demonstrate that our proposed OFDM positioning system out-

performs by 74% its conventional counterpart. Finally, we investigate the impact

of different system parameters on the positioning accuracy of the proposed OFDM

VLC system.

87

7.1 Introduction

In current indoor visible light positioning systems, several algorithms have been

proposed to calculate the receiver coordinates. In one approach, a photo diode

(PD) is employed to detect received signal strength (RSS) information. The dis-

tance between transmitter and receiver is then estimated based on the power atten-

uation, and the receiver coordinates are calculated by lateration algorithm [11,79].

In another approach, RSS information is pre-detected by a PD for each location

and stored as fingerprint in the offline stage. By matching the stored fingerprints

with the RSS feature of the current location, the receiver location is estimated

in the online stage [80]. In [12], proximity positioning concept has been used re-

lying on a grid of transmitters as reference points, each of which has a known

coordinate. The mobile receiver is assigned the same coordinates as the reference

point sending the strongest signal. Image sensor is another form of receiver which

detects angle of arrival (AoA) information for the angulation algorithm used to

calculate the receiver location [81]. Other techniques have been also proposed for

VLC systems to improve the indoor positioning performance. In [82], a two phase

hybrid RSS/AoA algorithm for indoor localization using VLC has been proposed.

In [83], Gaussian mixture sigma point particle filter technique has been applied to

increase the accuracy of the estimated coordinates. Accelerometer has been em-

ployed in [84] such that the information on the receiver height is not required. To

the best of our knowledge, the previous studies have been built on the assumption

of a low speed single carrier modulation or/and have not considered the multipath

reflections. However, a practical VLC system would be likely to deploy the same

configuration for both positioning and communication purposes where high speed

88

data rates are desired. Furthermore, it has been shown in [85–87] that multipath

reflections can severely degrade the positioning accuracy especially in the corner

and the edge areas of a room.

In this Chapter, to mitigate the multipath reflections as well as providing a high

data rate transmission, we propose an OFDM VLC system that can be used for

both indoor positioning and communications. The positioning algorithm employed

is based on RSS information detected by a PD and the lateration technique. We

show that our proposed system can achieve an excellent accuracy even in dispersive

optical channels and for very low signal power values.

7.2 System Configuration

7.2.1 System Model

We consider a typical room shown in Fig. 7.1 with dimensions of 6 m × 6 m × 3.5

m where four light-emitting diode (LED) bulbs are located at height of 3.3 m with

a rectangular layout. Data are transmitted from these LED bulbs after they are

modulated by driver circuits. Each LED bulb has an identification (ID) denoting

its coordinates which is included in the transmitted data. A PD as the receiver is

located at the height of 1.2 m and has a field of view (FOV) of 70 and a receiving

area of 1 cm2. The room configuration is summarized in Table 7.1.

Furthermore, strict time domain multiplexing is used where the entire OFDM

frequency spectrum is assigned to a single LED transmitter for at least one OFDM

symbol including a cyclic prefix (CP).

89

Figure 7.1: System configuration.

7.2.2 Optical Wireless Channel

We assume an indoor optical multipath channel where transmitters and a receiver

are placed in the room shown in Fig. 7.1. The baseband channel model including

noise is expressed as

y (t) = ηx (t) ∗ h (t) + ν (t) (7.1)

where y (t) is the received electrical signal, η is the photodetector responsivity,

h (t) is the multipath impulse response of the optical channel, and ν (t) denotes

ambient light shot noise and thermal noise.

Combined deterministic and modified Monte Carlo (CDMMC) method recently

developed by Chowdhury et al [88] is used to simulate the impulse response of the

optical wireless channel. Deterministic approaches [66,89] proposed to approximate

impulse response of indoor optical wireless channels divide the reflecting surfaces

90

Table 7.1: System parameters

Room dimensions Reflection coefficientslength: 6 m ρwall: 0.66width: 6 m ρCeiling: 0.35

height: 3.5 m ρF loor: 0.60Transmitters (Sources) Receiver

Wavelength: 420 nm Area (Ar): 1×10−4m2

Height (H): 3.3 m Height (h): 1.2 mLambertian mode (m): 1 Elevation: +90

Elevation: -90 Azimuth: 0

Azimuth: 0 FOV (Ψc): 70

Coordinates: (2,2) (2,4) (4,2) (4,4)Power for "1"/ "0": 5 W/3 W

Figure 7.2: The contributions from different orders of reflections to the total im-pulse response of a location at the center of the room (weak scatterings and mul-tipath reflections).

91

Figure 7.3: The contributions from different orders of reflections to the total im-pulse response of a location at the edge of the room (medium scatterings andmultipath reflections).

into small elements and provide the best accuracy, but at the cost of high comput-

ing time. On the other hand, modified Monte Carlo (MMC) approaches [90, 91]

calculate the impulse responses very fast, but the calculated impulse responses

are not as temporally smooth when compared to deterministic approaches. The

algorithm in [88] takes advantage of both deterministic and MMC methods. In

particular, the contribution of the first reflections to the total impulse response is

calculated by a deterministic method for high accuracy, while an MMC method is

employed to calculate the second and higher order reflections and achieve a lower

execution time.

We consider the line-of-sight (LOS) and first three reflections to simulate the

impulse response of the channel. For each transmitter, we generate 4096 different

channels by placing the receiver in different locations within the room with the

92

Figure 7.4: The contributions from different orders of reflections to the total im-pulse response of a location at the corner of the room (strong scatterings andmultipath reflections).

same height (i.e., 1.2 m). Figs. 7.2 to 7.4 demonstrate the contributions from

different orders of reflections to the total impulse responses for three exemplary

locations inside the room representing weak to strong scatterings and multipath

reflections.

7.2.3 OFDM Transmitter and Receiver

Different OFDM techniques have been proposed for optical wireless communica-

tions in the literature. For the sake of brevity, asymmetrically clipped optical

OFDM (ACO-OFDM) is considered in this Chapter as it utilizes a large dynamic

range of LED and thus is more efficient in terms of optical power than systems

using DC-biasing. However, the generalization to other techniques is very straight-

93

Figure 7.5: OFDM transmitter and receiver configuration for both positioning andcommunication purposes.

forward. A block diagram of an ACO-OFDM communication and positioning sys-

tem is depicted in Fig. 7.5. The data and LED ID code are combined as the

input bits which is parsed into a set of L/4 complex data symbols denoted by

X =[X0, X1, ...XL/4−1

]Twhere L is the number of subcarriers, and (.)T indicates

the transpose of a vector. These symbols are drawn from constellations such as

M -QAM or M -PSK where M is the constellation size. For VLC systems using

intensity modulation and direct detection (IM/DD), a real valued signal is required

to modulate the LED intensity. Thus, ACO-OFDM subcarriers must have Her-

mitian symmetry. As discussed in Section 5.2, in ACO-OFDM, impairment from

clipping noise is avoided by mapping the complex input symbols onto an L × 1

vector S as

S =[0, X0, 0, X1, ..., 0, XL−1, 0, X∗

L−1, 0, ..., X∗1 , 0, X∗

0 , 0]T

(7.2)

where (.)∗ denotes the complex conjugate of a vector. An L-point inverse fast

Fourier transform (IFFT) is then applied creating the time domain signal x. A

94

CP is added to the real valued output signal turning the linear convolution with

the channel into a circular one to mitigate inter-carrier interference (ICT) as well

as inter-block interference (IBT). All the negative values of the transmitted signal

are clipped to zero to make it unipolar and suitable for optical transmission. This

clipping operation does not affect the data-carrying subcarriers but decreases their

amplitude to exactly a half. The clipped signal is then converted to analog and

finally modulates the intensity of an LED.

At the receiver, the signal is detected by a PD and then converted back to a

digital signal. The CP is removed and an L-point fast Fourier transform (FFT)

is applied on the electrical OFDM signal. The training sequence is employed for

synchronization and channel estimation as discussed in Chapter 6. A single tap

equalizer is then used for each subcarrier to compensate for channel distortion and

the transmitted symbols are recovered from the odd subcarriers and denoted by

X =[X0, X1, ...XL/4 −1

]T. The LED ID is decoded and the transmitter coordinates

are obtained which are fed to the positioning block along with the estimated chan-

nel DC gain as shown in Fig. 7.5. The receiver coordinates are finally estimated

by employing the positioning algorithm detailed in the following section.

7.3 Positioning Algorithm

For the system under consideration, the received optical power from the kth trans-

mitter, k = 1, 2, 3 and 4, can be expressed as

Pr,k = Hk(0)Pt,k (7.3)

95

where Pt,k denotes the transmitted optical power from the kth LED bulb, and

Hk (0) is the channel DC gain that can be obtained as [13]

Hk (0) = m+ 12πd2

k

Arcosm(ϕk)Ts(ψk)g(ψk) cos(ψk). (7.4)

In (7.4), Ar is the physical area of the detector, ψk is the angle of incidence with

respect to the receiver axis, Ts (ψk) is the gain of optical filter, g (ψk) is the con-

centrator gain, ϕk is the angle of irradiance with respect to the transmitter per-

pendicular axis, dk is the distance between transmitter k and receiver, and m

is the Lambertian order. Assuming that both receiver and transmitter axes are

perpendicular to the ceiling, ϕk and ψk are equal and can be estimated as

cos (ψk) = cos (ϕk) = (H − h) /dk (7.5)

where H and h are the transmitter and receiver heights, respectively. For a com-

pound parabolic concentrator (CPC), g (ψk) is defined as

g (ψk) =

nr

2

sin2(Ψc) , 0 ≤ ψk ≤ Ψc

0, ψk > Ψc

(7.6)

where nr and Ψc respectively denote the refractive index and the FOV of the

concentrator.

For the proposed OFDM system, the channel DC gain can be well estimated

96

as 1

Hk (0) = 4L

L/4∑i=1

Pk,i (7.7)

where Pk,i is the power attenuation of the ith symbol transmitted from the kth

transmitter and is obtained using the training symbols used for synchronization as

Pk,i =∣∣∣∣∣Xk,i

Xk,i

∣∣∣∣∣. (7.8)

Considering (7.3)-(7.8), dk can be calculated as

dm+3k = (m+ 1)ArTs (ψk) g (ψk) (H − h)m+1

2πHk

. (7.9)

Horizontal distance between the kth transmitter and the receiver can be estimated

as

rk =√dk

2 − (H − h)2. (7.10)

Then, according to the lateration algorithm [92, 93], a set of four quadratic equa-

tions can be formed as follows

(xc − xc1)2 + (yc − yc1)2 = r2

1

(xc − xc2)2 + (yc − yc2)2 = r2

2

(xc − xc3)2 + (yc − yc3)2 = r2

3

(xc − xc4)2 + (yc − yc4)2 = r2

4

(7.11)

where (xc, yc) is the receiver coordinates to be estimated and (xck, yck) is the kth

1Note that for the other OFDM techniques, it is only required to estimate the channel DCgain similarly using the sample mean of the power attenuation of the transmitted symbols. Thus,our proposed system can be easily utilized for other OFDM techniques as well.

97

transmitter coordinates obtained from the recovered LED ID in a two-dimensional

space. By subtracting the first equation from the last three equations, we obtain

(xc1 − xcj

)xc +

(yc1 − ycj

)yc =

(r2

j − r21 − xc

2j + xc

21 − yc

2j + yc

21

)/2 (7.12)

where j = 2, 3 and 4. (7.12) can be formed in a matrix format as AX = B where

A, B and X are defined as

A =

xc2 − xC1 yc2 − yc1

xc3 − xc1 yc3 − yc1

xc4 − xc1 yc4 − yc1

, (7.13)

B = 12

(r2

1 − r22) + (xc

22 + yc

22) − (xc

21 + yc

21)

(r21 − r2

3) + (xc23 + yc

23) − (xc

21 + yc

21)

(r21 − r2

4) + (xc24 + yc

24) − (xc

21 + yc

21)

, (7.14)

X = [xc yc]T . (7.15)

The estimated receiver coordinates can then be obtained by the linear least squares

estimation approach as [92]

X = (ATA)−1ATB. (7.16)

7.4 Simulation and Analysis

In this section, we present numerical results for the proposed indoor VLC system.

In the following, we consider an OFDM system with a number of subcarriers of L =

64, 256, 512 or 1024 where the symbols are drawn from an M -QAM modulation

98

constellation. We set the CP length three times of the root mean square (RMS)

delay spread of the worst impulse response and assume a data with minimum rate

of 25 Mbps 2. The sum of ambient light shot noise and receiver thermal noise

is modeled as real baseband Additive White Gaussian noise (AWGN) with zero

mean and power of -10 dBm [67, 68]. Furthermore, to take LED nonlinearity into

account, OPTEK, OVSPxBCR4 1-Watt white LED is considered in simulations

whose optical and electrical characteristics are given in Table 5.2. A polynomial

order of five is used to realistically model the measured transfer function. The four

OPTEK LEDs are biased at 3.2V.

7.4.1 Performance Comparison of Single- and Multi-carrier

Modulation Schemes

In this subsection, the positioning performance of the proposed OFDM system is

compared with the performance of those using single carrier modulation scheme,

i.e., OOK. We assume that the average electrical power of the transmitted sig-

nal before modulating each LED is Pte,k =5 dBm. For OOK modulation, the

positioning algorithm discussed in [13] is used 3.

Fig. 7.6 demonstrates the positioning error distribution over the room for an

indoor OFDM VLC system with 4-QAM modulation and the FFT size of 512. As

it can be seen, the positioning errors are very small for the most locations inside

the room, but become larger when the receiver approaches the corners and edges

due to the severity of the multipath reflections.

Fig. 7.7, on the other hand, shows the positioning error distribution over the2The data rate is 25 Mbps for 4-QAM modulation scheme. For higher-order modulations

(i.e., M > 4), the bit rate can be achieved as R = 25 Mbps×log2 (M).3The positioning algorithm used for OOK is quite similar to the one described in Section 7.3.

The two algorithms only differ in the estimation method of the signal attenuation.

99

Figure 7.6: Positioning error distribution for OFDM system with 4-QAM modu-lation, L = 512 and Pte,k = 5 dBm.

Figure 7.7: Positioning error distribution for OOK modulation with Pte,k = 5 dBm.

100

Figure 7.8: Histogram of positioning errors for OFDM system with 4-QAM mod-ulation, L = 512 and Pte,k = 5 dBm.

room for an indoor VLC system employing OOK modulation with the same data

rate as that of the OFDM system with 4-QAM modulation (i.e., 25 Mbps). As

observed, the positioning errors are relatively small within the rectangle shown in

Fig. 7.7 where the LED bulbs are located right above its corners. However, the

positioning error becomes significantly larger when the receiver moves toward the

corners and edges as the effect of the multipath reflections increases.

Figs. 7.8 and 7.9 present the histograms of the positioning errors for OFDM

and OOK modulation schemes, respectively. For OFDM modulation, most of the

positioning errors are less than 0.1 m and only a few of them are more than 1 m

corresponding to the corner area. However, for OOK modulation, the positioning

errors are widely spread from zero to around 2.3 m, and only a few of them are

less than 0.1 m that correspond to the central area. From Figs. 7.6 to 7.9, it can

be clearly seen that the OFDM system outperforms its OOK counterpart.

Table 7.2 summarizes and compares the positioning errors of OFDM and OOK

101

Figure 7.9: Histogram of positioning errors for OOK modulation with Pte,k = 5dBm.

Table 7.2: Positioning error for single- and multi-carrier modulationschemes

Positioning error (m) OFDM modulation (m) OOK modulation (m)Corner (0, 0) 0.578 2.18Edge (3 m, 0) 0.49 1.53

Center (3 m, 3 m) 2×10−6 10−5

RMS error of 0.08 0.43the rectangular area

RMS error of 0.2609 1.01the whole room

modulation schemes. As seen, OFDM modulation provides a much better po-

sitioning accuracy than OOK modulation for all the locations inside the room.

Particularly, the RMS error is 0.08 m for the rectangular area covered perfectly

by the four LED bulbs when OFDM modulation is used while it is 0.43 m for

OOK modulation. The total RMS errors are 0.2609 m and 1.01 m for OFDM and

OOK modulation schemes as the rectangular area covered by LED bulbs is only

102

Figure 7.10: Positioning error distribution for OFDM system with 4-QAM modu-lation, L = 512 and Pte,k = -10 dBm.

11.1% of the total area. Thus, OFDM modulation decreases the RMS error by 74%

compared to OOK modulation. It should be noted that the average positioning

accuracy for can be increased by optimizing the layout design of the LED bulbs in

future.

7.4.2 Effect of Signal Power on the Positioning Accuracy

In this Subsection, we investigate the effect of the average electrical power of

the transmitted signal on the positioning accuracy of the proposed OFDM VLC

system. We consider an OFDM system with 4-QAM modulation and L = 512.

Figs. 7.10 and 7.11 present the positioning error distribution for the OFDM system

with transmitted signal power values of -10 dBm and 20 dBm, respectively. The

total RMS error is calculated as 0.384 m for the OFDM system with Pte,k = -10

103

Figure 7.11: Positioning error distribution for OFDM system with 4-QAM modu-lation, L = 512 and Pte,k = 20 dBm.

dBm and 0.2766 m for Pte,k = 20 dBm.

Figs. 7.12 and 7.13 further demonstrate the corresponding histograms of the

positioning errors for different transmitted signal power values. It is apparent from

Figs. 7.10 and 7.12 that our proposed OFDM positioning system works satisfacto-

rily even at very low transmitted signal power values resulting from dimming and

shadowing effects4. Furthermore, according to Figs. 7.6, 7.8 and 7.10 to 7.13 and as

expected, increasing the average electrical power of the transmitted signal results

in a better performance. However, at very high power values, nonlinearity dis-

tortion effects dominate the performance and the positioning accuracy decreases.

It is the main reason the performance of the VLC system with Pte,k = 20 dBm

is slightly worse than that of Pte,k = 5 dBm presented earlier. Therefore, for an4Note that the total RMS error for OOK modulation with Pte,k = -10 dBm is calculated as

1.32 m.

104

Figure 7.12: Histogram of positioning errors for OFDM system with 4-QAM mod-ulation, L = 512 and Pte,k = -10 dBm.

Figure 7.13: Histogram of positioning errors for OFDM system with 4-QAM mod-ulation, L = 512 and Pte,k = 20 dBm.

105

Figure 7.14: Positioning error distribution for OFDM system with 16-QAM mod-ulation, L = 512 and Pte,k = 5 dBm.

OFDM indoor VLC positioning system, there is an optimum power value that

depends on the LED characteristics.

7.4.3 Effect of Modulation Order on the Positioning Accu-

racy

Here, we analyze the impact of the modulation order on the positioning perfor-

mance. Figs. 7.14 and 7.15 show the positioning error distribution of the OFDM

system with the FFT size of 512 and Pte,k = 5 dBm employing 16- and 64-QAM

modulation, respectively. The corresponding histograms of the positioning errors

are shown in Figs. 7.16 and 7.17. The total RMS error is obtained as 0.2665 m

for 16-QAM and 0.2716 m for 64-QAM. By comparing these RMS error values

with the one calculated for 4-QAM modulation, we observe that all three systems

106

Figure 7.15: Positioning error distribution for OFDM system with 64-QAM mod-ulation, L = 512 and Pte,k = 5 dBm.

Figure 7.16: Histogram of positioning errors for OFDM system with 16-QAMmodulation, L = 512 and Pte,k = 5 dBm.

107

Figure 7.17: Histogram of positioning errors for OFDM system with 64-QAMmodulation, L = 512 and Pte,k = 5 dBm.

yield nearly the same positioning performance. Thus, the constellation size does

not have a significant effect on the positioning performance of the proposed OFDM

VLC system although the communication performance obviously deteriorates with

increasing the constellation size. The numerical results clearly show that our pro-

posed channel DC gain estimation works perfectly for high-order constellations as

well.

7.4.4 Effect of Number of Subcarriers on the Positioning

Accuracy

Finally, we investigate the effect of number of total subcarriers (i.e. the FFT size)

on the positioning accuracy. We consider an OFDM system with 4-QAM and Pte,k

= 5 dBm. Figs. 7.18 to 7.23 illustrate the positioning error distribution for differ-

108

Figure 7.18: Positioning error distribution for OFDM system with 4-QAM modu-lation, L = 64 and Pte,k = 5 dBm.

Figure 7.19: Positioning error distribution for OFDM system with 4-QAM modu-lation, L = 256 and Pte,k = 5 dBm.

109

Figure 7.20: Positioning error distribution for OFDM system with 4-QAM modu-lation, L = 1024 and Pte,k = 5 dBm.

ent FFT sizes providing sufficiently narrow-banded sub-channels along with their

corresponding error histograms. The total RMS errors are respectively calculated

as 0.2905 m, 0.271 m and 0.2624 m for L = 64, 256 and 1024. Considering the

results presented earlier for the FFT size of 512, it is observed that increasing the

number of subcarriers results in a better positioning performance as it improves the

estimation of the channel DC gain, i.e., Eq. (7.7). However, the peak-to-average

power ratio (PAPR) also increases with increasing the FFT size [94]. Therefore,

for sufficiently large values of L, the positioning performance is slightly degraded.

110

Figure 7.21: Histogram of positioning errors for OFDM system with 4-QAM mod-ulation, L = 64 and Pte,k = 5 dBm.

Figure 7.22: Histogram of positioning errors for OFDM system with 4-QAM mod-ulation, L = 256 and Pte,k = 5 dBm.

111

Figure 7.23: Histogram of positioning errors for OFDM system with 4-QAM mod-ulation, L = 1024 and Pte,k = 5 dBm.

7.5 Conclusions

In this Chapter, we have investigated and compared the positioning accuracy of

IM/DD single- and multi-carrier modulation schemes for indoor VLC systems tak-

ing into account both nonlinear characteristics of LED and dispersive nature of

optical wireless channel. Particularly, we have proposed an OFDM VLC system

that can be used for both indoor positioning and communications. The training se-

quence used for synchronization has been adopted to estimate the channel DC gain.

Lateration algorithm and the linear least squares estimation have been applied to

calculate the receiver coordinates. We have shown the positioning error distribu-

tion over a typical room where the impulse response has been simulated employing

CDMMC approach. Our results have demonstrated that the proposed OFDM sys-

112

tem achieves an excellent accuracy and outperforms its OOK counterpart by 74%.

Furthermore, the effect of different parameters on the positioning performance of

the OFDM system have been investigated. We have shown that our proposed

model unlike its conventional counterparts provides satisfactory performance at

low transmitted signal power values resulting from dimming and shadowing effects

and can be used for high-order constellations as well.

113

Chapter 8Conclusions and Future Work

8.1 Conclusions

Optical wireless communication (OWC) has been receiving an increasing attention

in recent years with its ability to achieve ultra-high data rates over unlicensed

optical spectrum. OWC can be both indoors and outdoors. In this dissertation

we have focused on both indoor and outdoor OWC and addressed some major

challenges for free-space optical (FSO) and indoor visible light communication

(VLC) systems.

In Chapter 2, we have proposed a unifying statistical distribution named Dou-

ble Generalized Gamma (Double GG) based on the doubly stochastic scintillation

theory that perfectly describes irradiance fluctuations over atmospheric channels

under a wide range of turbulence conditions. We have derived closed-form ex-

pressions for the Double GG’s probability density function (pdf) and cumulative

distribution function (cdf) in terms of Meijer’s G-function and shown that the

new model outperforms other existing models. Capitalizing on the new channel

model, we have obtained closed-form expressions for the outage probability and

114

the average bit error rate (BER) as well as corresponding asymptotic expressions

of single-input single-output (SISO) FSO systems over turbulence channels. It has

been shown that our derived expressions generalize many existing results in the

literature as special cases.

In Chapter 3, we have obtained a novel and accurate approximate expres-

sion for the distribution of the sum of independent but not necessarily identically

distributed (i.n.i.d.) Double GG distributed random variables (RVs) in terms of

Meijers G-function. Comparisons with the Monte-Carlo simulation results have

confirmed the accuracy of the approximate expression.

Using the statistical models proposed in Chapters 2 and 3, in Chapter 4, we have

studied the performance of multiple-input multiple-output (MIMO), single-input

multiple-output (SIMO) and multiple-input single-output (MISO) of FSO systems

with intensity modulation and direct detection (IM/DD) over Double GG turbu-

lence channels. We have shown through numerical results that spatial diversity

schemes can remarkably enhance the system performance and achieve outstand-

ing performance gains over SISO systems. We have further demonstrated that

equal gain combining (EGC) scheme presents an appropriate trade-off between

complexity and performance among different receive diversity techniques.

In Chapter 5, we have investigated and compared the performance of single-

and multicarrier modulation schemes for indoor VLC taking into account nonlinear

characteristics of light-emitting diode (LED) and dispersive nature of optical wire-

less channel. We have demonstrated that single carrier frequency domain equal-

ization (SCFDE) systems are not impaired from high peak-to-average power ratio

(PAPR) and surpass on-off keying (OOK) and orthogonal frequency division mul-

tiplexing (OFDM) systems. Therefore, SCFDE can be considered as a favorable

115

modulation technique for indoor VLC systems. The effect of LED bias point on

the performance of OFDM systems has been also studied, and it has been shown

that significant gain can be achieved by biasing LED with the optimum value.

In addition, we have added bit-interleaved coded modulation (BICM) to OFDM

and SCFDE systems to further compensate signal degradation due to intersymbol

interference (ISI) and LED nonlinearity.

Chapter 6 has proposed a novel and robust timing synchronization scheme

working for asymmetrically clipped (AC) OFDM based optical IM/DD wireless

systems. We have shown that the proposed method, in contrast to other timing

synchronization schemes, does not require any specific format of the training sym-

bols and is very computationally efficient. We have confirmed the accuracy of the

proposed method through both simulations and experimental results.

Finally, in Chapter 7, we have presented a new OFDM VLC system that can be

utilized for both indoor positioning and communications and shown it outperforms

its conventional counterpart by 74%. We have also investigated the impact of

different system parameters on the positioning accuracy of the proposed OFDM

VLC system. Extensive numerical and computer simulation results have shown

the superiority of the proposed system.

8.2 Future Work

With the ever-growing demand for high speed wireless broadband access and con-

gestion in radio frequency (RF) spectrum, the interest in OWC as a promising

complementary and/or alternative technique has been increasing. Therefore, this

technique has been rapidly developing by many researchers throughout the world.

Cooperative communication is another method to exploit spatial diversity in

116

FSO links. Although there are a number of research materials studying the perfor-

mance of cooperative communication over different atmospheric turbulence chan-

nels, a unifying and accurate approach that is valid under all range of turbulence

conditions needs to be addressed. Therefore, investigating the performance of

cooperative FSO communication using the mathematical analysis in Chapters 2

and 3 can be a topic for the future work.

In Chapter 5, we assumed that the impulse response of the channel is known to

the receiver and static during each communication session. Though these assump-

tions are appropriate where the location of the receiver is fixed, the receiver can

be mobile and have seamless communication. Therefore, the system can have dy-

namic impulse response by the move of the receiver terminal. A possible research

subject could be developing fast and accurate channel estimation algorithms and

investigating the performance of adaptive VLC systems.

In Chapter 6, we proposed a timing synchronization scheme for AC OFDM

based optical IM/DD wireless systems. Developing more efficient timing synchro-

nization techniques working for all optical OFDM systems is the subject of a future

work.

In Chapter 7, a 2-D indoor location estimation with optical-based OFDM Com-

munications was presented. Another interesting topic for future research is mod-

ifying our proposed system to develop a 3-D positioning algorithm using optical

OFDM modulation.

117

8.3 Publication List

1. M. Aminikashani and M. Kavehrad, “On the Sum of Double GeneralizedGamma Variates and Its Applications in Performance Analysis of DiversityFree-Space Optical Systems,” submitted to IEEE Transactions on WirelessCommunications, Feb. 2016.

2. W. Gu, M. Aminikashani, and M. Kavehrad, “Nonlinear Positioning Al-gorithm for Indoor OFDM VLC Systems,” submitted to Optical EngineeringLetter, Feb. 2016.

3. M. Aminikashani, M. Uysal, and M. Kavehrad, “A Novel Statistical Chan-nel Model for Turbulence-Induced Fading in Free-Space Optical Systems,”IEEE/OSA Journal of Lightwave Technology, vol.33, no.11 , pp. 2303-2312,Mar. 2015.

4. W. Gu, M. Aminikashani, and M. Kavehrad, “Impact of Multipath Re-flections on the Performance of Indoor Visible Light Positioning Systems,”IEEE/OSA Journal of Lightwave Technology, Feb. 2016.

5. M. Aminikashani, W. Gu, and M. Kavehrad, “Indoor Location Estima-tion with Optical-based OFDM Communications,” submitted to Optical En-gineering, Jan. 2016.

6. M. Aminikashani, M. Uysal, and M. Kavehrad, “A Novel Statistical Modelfor Turbulence-Induced Fading in Free-Space Optical Systems,” Invited Pa-per, 15th International Conference on Transparent Optical Networks (IC-TON), Cartagena, Spain, Jun. 2013.

7. M. Aminikashani, and M. Kavehrad, “On the Performance of Single- andMulti-carrier Modulation Schemes for Indoor Visible Light CommunicationSystems,” IEEE Globecom 2014, Austin, TX, USA, Dec. 2014.

8. W. Gu, W. Zhang, J. Wang, M. Aminikashani and M. Kavehrad, “Three-Dimensional Indoor Positioning Based on Visible Light with Gaussian Mix-ture Sigma-Point Particle Filter Technique,” SPIE Photonics West 2015, SanFrancisco, CA, USA, Feb. 2015.

9. P. Deng, M. Kavehrad and M. Aminikashani, “Nonlinear ModulationCharacteristics of White LEDs in Visible Light Communications,” OpticalFiber Communication Conference and Exposition (OFC) 2015, Los Angeles,CA, USA, Mar. 2015.

10. B. A. Ranjha, M. Aminikashani, M. Kavehrad, “Robust Timing Synchro-nization for Asymmetrically Clipped OFDM Based Optical Wireless Commu-nications,” IEEE Integrated Communications, Navigation, and Surveillance(ICNS) 2015, Herndon, VA, USA, Apr. 2015.

11. M. Aminikashani, M. Uysal, and M. Kavehrad, “On the Performance of

118

MIMO FSO Communications over Double Generalized Gamma Fading Chan-nels,” IEEE International Conference on Communications (ICC) 2015, Lon-don, United Kingdom, Jun. 2015.

12. W. Gu, M. Aminikashani, and M. Kavehrad, “Indoor Visible Light Po-sitioning System with Multipath Reflection Analysis,” IEEE InternationalConference on Consumer Electronics (ICCE), Jan. 2016.

13. M. Aminikashani, W. Gu, and M. Kavehrad, “Indoor Positioning in HighSpeed OFDM Based Optical Wireless Communication Systems,” IEEE Con-sumer Communications and Networking Conference (CCNC), Jan. 2016.

14. W. Gu, M. Kavehrad and M. Aminikashani, “Three-dimensional IndoorLight Positioning Algorithm Based on Nonlinear Estimation,” SPIE Photon-ics West OPTO, Feb. 2016.

15. M. Aminikashani, and M. Kavehrad, “Error Performance Analysis of FSOLinks with Equal Gain Diversity Receivers over Double Generalized GammaFading Channels,” SPIE Photonics West OPTO, Feb 2016.

119

Appendix ASpecial Cases of Double GG

Distribution

Proposition 1: For γi → 0 and mi → ∞, Double Generalized Gamma (Double

GG) probability density function (pdf) coincides with the log-normal pdf.

Proof : It is well known that the limiting distribution of the GG (γi,mi,Ωi) dis-

tribution is the lnN (µi, σ2i ) distribution as γi → 0 and mi → ∞ where µi → Ω1/m

2

and σ2i → 1/(miγ

2i ) [95]. Therefore, if γi → 0 and mi → ∞, the Double GG pdf

becomes lnN (µ1 + µ2, σ21 + σ2

2).

Proposition 2: For γi = 1 and Ωi = 1, Double GG pdf coincides with Gamma-

Gamma pdf.

Proof : If γi = 1, p/q = 1 and thus p = q = 1. Replacing γi = Ωi = p = q = 1 in

120

(2.5), we obtain

fI_GG (I) = I−1

Γ (m1) Γ (m2)G0,2

2,0

(m1m2I)−1|1 −m1, 1 −m2

−

= I−1

Γ (m1) Γ (m2)G2,0

0,2

m1m2I|−

m1,m2

(A.1)

= (m1m2I)(m1+m2)/2 I−1

Γ (m1) Γ (m2)G2,0

0,2

m1m2I|−

m1−m22 , m2−m1

2

.

Using [35, eq. (8.4.23.1] as

Kν (x) = 12G2,0

0,2

x2

4|

−

−ν2 ,

ν2

(A.2)

where Kν is the modified Bessel function of the second kind,(A.1) can be rewritten

as

fI_GG (I) = 2(m1m2I)(m1+m2)/2 I−1

Γ (m1) Γ (m2)Km2−m1

(2√m1m2I

)(A.3)

which coincides with (13) of [21].

Proposition 3: For mi = 1, Double GG pdf becomes Double-Weibull pdf.

Proof : Inserting mi = 1 in (2.5), we obtain

fI_DW (I) = pγ2(pq)1/2

(2π)(p+q)/2 −1IG0,p+q

p+q,0

(

Ω2

Iγ2

)p

ppqqΩq1|

∆ (q : 0) ,∆ (p : 0)

−

(A.4)

which coincides with (5) of [23].

Proposition 4: For γi = 1, Ωi = 1 and m2 = 1 Double GG pdf corresponds with

K-channel.

121

Proof : Replacing γi = Ωi = p = q = m1 = 1 in (2.5) and using (A.2), we obtain

fI_KC (I) = I−1

Γ (m2)G0,2

2,0

(m2I)−1|0, 1 −m2

−

= I−1

Γ (m2)G2,0

0,2

m2I|−

1,m2

= (m2I)(1+m2)/2 I−1

Γ (m2)G2,0

0,2

m2I|−

1−m22 , m2−1

2

= 2(m2I)(1+m2)/2 I−1

Γ (m1)Km2−1

(2√m1I

)(A.5)

which coincides with (2) of [32].

122

Appendix BSpecial Cases of BER Expression of

SISO FSO System over Double GG

Channel

Proposition 1: Inserting γi = 1 and Ωi = 1 in (2.25), the bit error rate (BER)

over Gamma-Gamma channel is obtained.

Proof : Replacing γi = Ωi = p = q = 1 and therefore l = 1 and k = 2 in (2.25),

we obtain

PSISO_GG = 2m1+m2−3

Γ (m1) Γ (m2)π32G4,2

2,5

(m1m2)2 1γl4

|1, 1

2

m12 ,

m1+12 , m2

2 ,m2+1

2 , 0

(B.1)

which coincides with (6) of [31].

Proposition 2: Inserting mi = 1 in (2.25), the BER over Double-Weibull channel

is obtained.

123

Proof : Inserting mi = 1 in (2.25), we obtain

PSISO = γ2k2p3/2q1/2

2 32 l(2π)

l+k(p+q)2 −1

×Gk(p+q),2l2l,k(p+q)+l

(ppΩp2q

qΩq1)

−k

kk(p+q)(4l)l

γl|

∆ (l : 1) ,∆(l : 1

2

)Jk (q : 0) , Jk (p : 0) ,∆ (l : 0)

(B.2)

which coincides with (15) of [23].

Proposition 3: Inserting γi = 1, Ωi = 1 and m2 = 1 in (2.25), the BER over

K-channel is obtained.

Proof : Replacing γi = Ωi = p = q = m1 = 1in (2.25), we obtain

PSISO_KC = 2m2−2

Γ (m2) π32G4,2

2,5

m22 14γl

|1, 1

2

m22 ,

m2+12 , 1

2 , 1, 0

= 2m2−2

Γ (m2) π32G2,4

5,2

4γl

m22|

2−m22 , 1−m2

2 , 12 , 0, 1

0, 12

(B.3)

which coincides with (12) of [32].

124

Appendix CSpecial Cases of Outage Probability

Expression of SISO FSO System

over Double GG Channel

Proposition 1: Inserting γi = 1 and Ωi = 1 in (2.32), the outage probability over

Gamma-Gamma channel is obtained.

Proof : Replacing γi = Ωi = 1 and therefore p = q = 1 in (2.32), we obtain

Fγ_GG (γth) = 1Γ (m1) Γ (m2)

G2,11,3

m1m2

√γth

γ|

1

m1,m2, 0

(C.1)

= (m1m2)(m1+m2)/2

Γ (m1) Γ (m2)

(γth

γ

)(m1+m2)/4

G2,11,3

m1m2

√γth

γ|

1 − m1+m22

m1−m22 , m2−m2

2 ,−m1+m22

which coincides with (15) of [30].

Proposition 2: Inserting mi = 1 in (2.32), the outage probability over Double-

Weibull channel is obtained.

125

Proof : Inserting mi = 1 in (2.32), we obtain

Fγ_DW (γth) = (pq)1/2

(2π)(p+q)/2 −1Gp+q,11,p+q+1

(γthγ−1)pγ2/2

(Ω2p)p(Ω1q)q |1

∆ (q : 1) ,∆ (p : 1) , 0

(C.2)

which coincides with (16) of [23].

Proposition 3: Inserting γi = 1, Ωi = 1 and m2 = 1 in (2.32), the outage

probability over K-channel is obtained.

Proof : Replacing γi = Ωi = p = q = m1 = 1 in (2.32), we obtain

Fγ (γ) = 1Γ (m2)

G2,11,3

m2

√γ

γ|

1

1,m2, 0

= m2(1+m2)/2

Γ (m2)

(γth

γ

)(1+m2)/4

G2,11,3

m2

√γ

γ|

1−m22

1−m22 , m2−1

2 ,−1+m22

(C.3)

which coincides with (3) of [42].

126

Appendix DSpecial Cases of BER Expression of

SIMO FSO Links over Double GG

Channel

Proposition: Inserting γi = 1, Ωi = 1 and m2 = 1 in (4.9), the BER of SIMO

FSO links over K-channel is obtained.

Proof : First, by replacing γi = Ωi = p = q = m1 = 1 in (4.11) and (4.12), we

obtain αn = 1/Γ (m2,n) and ωn = m−12,n. Then by plugging all the values in (4.10),

we obtain

ΛKC (n, υ) = 2m2,n−1

πΓ (m2,n)G4,1

1,4

(υN)m22,n

16γ

∣∣∣∣∣∣∣∣1

12 , 1,

m2,n

2 ,m2,n +1

2

(D.1)

= 2m2,n−1

πΓ (m2,n)G1,4

4,1

16γυNm2

2,n

∣∣∣∣∣∣∣∣12 , 0,

2−m2,n

2 ,1−m2,n

2

0

.

127

Therefore,

Pe,SIMO,OC_KC ≈ 112

N∏n=1

ΛKC (n, 4) + 14

N∏n=1

ΛKC (n, 3) (D.2)

which coincides with (21) of [32].

128

Bibliography

[1] S. Arnon, J. Barry, G. Karagiannidis, R. Schober, and M. Uysal, Advancedoptical wireless communication systems. Cambridge university press, 2012.

[2] M. Kavehrad, “Broadband room service by light,” Scientific American,vol. 297, no. 1, pp. 82–87, 2007.

[3] G. Keiser, “Optical communications essentials,” 2004.

[4] M. Kavehrad, “Sustainable energy-efficient wireless applications using light,”IEEE Communications Magazine, vol. 48, no. 12, pp. 66–73, 2010.

[5] H. Willebrand and B. S. Ghuman, Free space optics: enabling optical connec-tivity in today’s networks. SAMS publishing, 2002.

[6] A. K. Majumdar and J. C. Ricklin, Free-space laser communications: princi-ples and advances, vol. 2. Springer Science & Business Media, 2010.

[7] D. Kedar and S. Arnon, “Urban optical wireless communication networks: themain challenges and possible solutions,” IEEE Communications Magazine,vol. 42, no. 5, pp. S2–S7, 2004.

[8] M. A. Kashani and M. Uysal, “Outage performance of fso multi-hop parallelrelaying,” in 20th Signal Processing and Communications Applications Con-ference (SIU), 2012.

[9] S. Arnon, Visible light communication. Cambridge University Press, 2015.

[10] Z. Zhou, M. Kavehrad, and P. Deng, “Energy efficient lighting and communi-cations,” in SPIE OPTO, pp. 82820J–82820J, International Society for Opticsand Photonics, 2012.

[11] S.-H. Yang, E.-M. Jeong, D.-R. Kim, H.-S. Kim, Y.-H. Son, and S.-K. Han,“Indoor three-dimensional location estimation based on led visible light com-munication,” Electronics Letters, vol. 49, no. 1, pp. 54–56, 2013.

129

[12] Y. U. Lee and M. Kavehrad, “Two hybrid positioning system design tech-niques with lighting leds and ad-hoc wireless network,” IEEE Transactionson Consumer Electronics, vol. 58, no. 4, pp. 1176–1184, 2012.

[13] W. Zhang, M. S. Chowdhury, and M. Kavehrad, “Asynchronous indoor posi-tioning system based on visible light communications,” Optical Engineering,vol. 53, no. 4, pp. 045105–045105, 2014.

[14] L. C. Andrews and R. L. Phillips, Laser beam propagation through randommedia, vol. 52. SPIE press Bellingham, WA, 2005.

[15] M. A. Kashani, M. Safari, and M. Uysal, “Optimal relay placement and di-versity analysis of relay-assisted free-space optical communication systems,”IEEE/OSA Journal of Optical Communications and Networking, vol. 5, no. 1,pp. 37–47, 2013.

[16] M. A. Kashani and M. Uysal, “Outage performance and diversity gain anal-ysis of free-space optical multi-hop parallel relaying,” IEEE/OSA Journal ofOptical Communications and Networking, vol. 5, no. 8, pp. 901–909, 2013.

[17] M. Karimi and M. Nasiri-Kenari, “Ber analysis of cooperative systems in free-space optical networks,” Journal of Lightwave Technology, vol. 27, no. 24,pp. 5639–5647, 2009.

[18] E. Jakeman and P. Pusey, “Significance of k distributions in scattering exper-iments,” Physical Review Letters, vol. 40, no. 9, p. 546, 1978.

[19] L. Andrews and R. Phillips, “Mathematical genesis of the i–k distribution forrandom optical fields,” Journal of Optical Society of America A, vol. 3, no. 11,pp. 1912–1919, 1986.

[20] J. H. Churnside and S. F. Clifford, “Log-normal rician probability-densityfunction of optical scintillations in the turbulent atmosphere,” Journal of Op-tical Society of America A, vol. 4, no. 10, pp. 1923–1930, 1987.

[21] M. Al-Habash, L. C. Andrews, and R. L. Phillips, “Mathematical modelfor the irradiance probability density function of a laser beam propagatingthrough turbulent media,” Optical Engineering, vol. 40, no. 8, pp. 1554–1562,2001.

[22] A. Jurado-Navas, J. M. Garrido-Balsells, J. F. Paris, and A. Puerta-Notario,“A unifying statistical model for atmospheric optical scintillation,” arXivpreprint arXiv:1102.1915, 2011.

130

[23] N. D. Chatzidiamantis, H. G. Sandalidis, G. K. Karagiannidis, S. A. Kot-sopoulos, and M. Matthaiou, “New results on turbulence modeling for free-space optical systems,” in Telecommunications (ICT), 2010 IEEE 17th Inter-national Conference on, pp. 487–492, IEEE, 2010.

[24] L. C. Andrews, R. L. Phillips, C. Y. Hopen, and M. Al-Habash, “Theory ofoptical scintillation,” Journal of Optical Society of America A, vol. 16, no. 6,pp. 1417–1429, 1999.

[25] M. Uysal, J. Li, and M. Yu, “Error rate performance analysis of coded free-space optical links over gamma-gamma atmospheric turbulence channels,”IEEE Transactions on Wireless Communications, vol. 5, no. 6, pp. 1229–1233,2006.

[26] E. Bayaki, R. Schober, and R. K. Mallik, “Performance analysis of mimofree-space optical systems in gamma-gamma fading,” IEEE Transactions onCommunications, vol. 57, no. 11, pp. 3415–3424, 2009.

[27] S. M. Flatté, C. Bracher, and G.-Y. Wang, “Probability-density functionsof irradiance for waves in atmospheric turbulence calculated by numericalsimulation,” Journal of Optical Society of America A, vol. 11, no. 7, pp. 2080–2092, 1994.

[28] R. J. Hill and R. G. Frehlich, “Probability distribution of irradiance for theonset of strong scintillation,” Journal of Optical Society of America A, vol. 14,no. 7, pp. 1530–1540, 1997.

[29] J. H. Churnside and R. Hill, “Probability density of irradiance scintillationsfor strong path-integrated refractive turbulence,” Journal of Optical Societyof America A, vol. 4, no. 4, pp. 727–733, 1987.

[30] H. E. Nistazakis, T. A. Tsiftsis, and G. S. Tombras, “Performance analy-sis of free-space optical communication systems over atmospheric turbulencechannels,” IET communications, vol. 3, no. 8, pp. 1402–1409, 2009.

[31] Z. Wang, W. Zhong, S. Fu, and C. Lin, “Performance comparison of differentmodulation formats over free-space optical (fso) turbulence links with spacediversity reception technique,” IEEE Photonics Journal, vol. 1, no. 6, pp. 277–285, 2009.

[32] T. A. Tsiftsis, H. G. Sandalidis, G. K. Karagiannidis, and M. Uysal, “Op-tical wireless links with spatial diversity over strong atmospheric turbulencechannels,” IEEE Transactions on Wireless Communications, vol. 8, no. 2,pp. 951–957, 2009.

131

[33] S. M. Navidpour, M. Uysal, and M. Kavehrad, “Ber performance of free-spaceoptical transmission with spatial diversity,” IEEE Transactions on WirelessCommunications, vol. 6, no. 8, pp. 2813–2819, 2007.

[34] E. Stacy, “A generalization of the gamma distribution,” The Annals of Math-ematical Statistics, vol. 33, no. 3, pp. 1187–1192, 1962.

[35] A. Jeffrey and D. Zwillinger, Table of integrals, series, and products. AcademicPress, 2007.

[36] N. C. Sagias, G. K. Karagiannidis, P. T. Mathiopoulos, and T. A. Tsiftsis,“On the performance analysis of equal-gain diversity receivers over generalizedgamma fading channels,” IEEE Transactions on Wireless Communications,vol. 5, no. 10, pp. 2967–2975, 2006.

[37] A. Prudnikov, Y. A. Brychkov, and O. Marichev, Integrals and series. Volume3: More special functions. Transl. from the Russian by GG Gould. New York:Gordon and Breach Science Publishers, 1990.

[38] V. Adamchik and O. Marichev, “The algorithm for calculating integrals of hy-pergeometric type functions and its realization in reduce system,” in Proceed-ings of the international symposium on Symbolic and algebraic computation,pp. 212–224, 1990.

[39] A. García-Zambrana, B. Castillo-Vázquez, and C. Castillo-Vázquez, “Asymp-totic error-rate analysis of fso links using transmit laser selection over gamma-gamma atmospheric turbulence channels with pointing errors,” Optics express,vol. 20, no. 3, pp. 2096–2109, 2012.

[40] W. R. Inc., “The wolfram functions site.” http://functions.wolfram.com.

[41] M. A. Kashani, M. M. Rad, M. Safari, and M. Uysal, “All-optical amplify-and-forward relaying system for atmospheric channels,” IEEE CommunicationsLetters, vol. 16, no. 10, pp. 1684–1687, 2012.

[42] G. Karagiannidis, T. Tsiftsis, and H. Sandalidis, “Outage probability of re-layed free space optical communication systems,” Electronics Letters, vol. 42,no. 17, pp. 994–996, 2006.

[43] A. A. Farid and S. Hranilovic, “Diversity gain and outage probability for mimofree-space optical links with misalignment,” IEEE Transactions on Commu-nications, vol. 60, no. 2, pp. 479–487, 2012.

[44] A. García-Zambrana, C. Castillo-Vázquez, and B. Castillo-Vázquez, “Space-time trellis coding with transmit laser selection for fso links over strong at-mospheric turbulence channels,” Optics express, vol. 18, no. 6, pp. 5356–5366,2010.

132

[45] K. Kotobi, P. B. Mainwaring, C. S. Tucker, and S. G. Bilén, “Data-throughputenhancement using data mining-informed cognitive radio,” Electronics, vol. 4,no. 2, pp. 221–238, 2015.

[46] K. Kotobi and S. G. Bilen, “Introduction of vigilante players in cognitive net-works with moving greedy players,” in IEEE Vehicular Technology Conference(VTC Fall), pp. 1–2, IEEE, 2015.

[47] M. Abramowitz and I. A. Stegun, Handbook of mathematical functions: withformulas, graphs, and mathematical tables, vol. 55. Courier Corporation, 1964.

[48] M. Chiani, D. Dardari, and M. K. Simon, “New exponential bounds andapproximations for the computation of error probability in fading channels,”IEEE Transactions on Wireless Communications, vol. 2, no. 4, pp. 840–845,2003.

[49] A. Kurve, K. Kotobi, and G. Kesidis, “An agent-based framework for perfor-mance modeling of an optimistic parallel discrete event simulator,” ComplexAdaptive Systems Modeling, vol. 1, no. 1, pp. 1–24, 2013.

[50] K. P. Peppas, “A simple, accurate approximation to the sum of gamma–gamma variates and applications in mimo free-space optical systems,” IEEEPhotonics Technology Letters, vol. 23, no. 13, pp. 839–841, 2011.

[51] W. Shieh, X. Yi, Y. Ma, and Q. Yang, “Coherent optical ofdm: has its timecome?[invited],” Journal of Optical Networking, vol. 7, no. 3, pp. 234–255,2008.

[52] O. Gonzalez, R. Perez-Jimenez, S. Rodriguez, J. Rabadán, and A. Ayala,“Ofdm over indoor wireless optical channel,” vol. 152, no. 4, pp. 199–204,2005.

[53] H. Elgala, R. Mesleh, and H. Haas, “Indoor broadcasting via white leds andofdm,” IEEE Transactions on Consumer Electronics, vol. 55, no. 3, pp. 1127–1134, 2009.

[54] J. Armstrong, “Ofdm for optical communications,” Journal of lightwave tech-nology, vol. 27, no. 3, pp. 189–204, 2009.

[55] J. M. Kahn and J. R. Barry, “Wireless infrared communications,” Proceedingsof the IEEE, vol. 85, no. 2, pp. 265–298, 1997.

[56] J. Armstrong and A. Lowery, “Power efficient optical ofdm,” Electronics Let-ters, vol. 42, no. 6, pp. 370–372, 2006.

133

[57] S. C. J. Lee, S. Randel, F. Breyer, and A. M. Koonen, “Pam-dmt for intensity-modulated and direct-detection optical communication systems,” IEEE Pho-tonics Technology Letters, vol. 21, no. 23, pp. 1749–1751, 2009.

[58] N. Fernando, Y. Hong, and E. Viterbo, “Flip-ofdm for unipolar communi-cation systems,” IEEE Transactions on Communications, vol. 60, no. 12,pp. 3726–3733, 2012.

[59] D. Tsonev, S. Sinanovic, and H. Haas, “Novel unipolar orthogonal frequencydivision multiplexing (u-ofdm) for optical wireless,” in IEEE Vehicular Tech-nology Conference (VTC Spring), pp. 1–5, IEEE, 2012.

[60] D. Tsonev, S. Sinanovic, and H. Haas, “Complete modeling of nonlinear dis-tortion in ofdm-based optical wireless communication,” Journal of LightwaveTechnology, vol. 31, no. 18, pp. 3064–3076, 2013.

[61] R. Mesleh, “Ofdm and scfde performance comparison for indoor optical wire-less communication systems,” in 19th International Conference on Telecom-munications (ICT), pp. 1–5, IEEE, 2012.

[62] R. Mesleh, H. Elgala, and H. Haas, “On the performance of different ofdmbased optical wireless communication systems,” IEEE/OSA Journal of Opti-cal Communications and Networking, vol. 3, no. 8, pp. 620–628, 2011.

[63] S. D. Dissanayake and J. Armstrong, “Comparison of aco-ofdm, dco-ofdm andado-ofdm in im/dd systems,” IEEE Journal of Lightwave Technology, vol. 31,no. 7, pp. 1063–1072, 2013.

[64] D. J. Barros, S. K. Wilson, and J. M. Kahn, “Comparison of orthogonalfrequency-division multiplexing and pulse-amplitude modulation in indoor op-tical wireless links,” IEEE Transactions on Communications, vol. 60, no. 1,pp. 153–163, 2012.

[65] J. Armstrong and B. Schmidt, “Comparison of asymmetrically clipped opticalofdm and dc-biased optical ofdm in awgn,” IEEE Communications Letters,vol. 12, no. 5, pp. 343–345, 2008.

[66] J. R. Barry, J. M. Kahn, W. J. Krause, E. A. Lee, and D. G. Messerschmitt,“Simulation of multipath impulse response for indoor wireless optical chan-nels,” IEEE Journal on Selected Areas in Communications, vol. 11, no. 3,pp. 367–379, 1993.

[67] D. O’Brien, G. Parry, and P. Stavrinou, “Optical hotspots speed up wirelesscommunication,” Nature Photonics, vol. 1, no. 5, pp. 245–247, 2007.

134

[68] J. Grubor, S. Randel, K.-D. Langer, and J. Walewski, “Bandwidth-efficient in-door optical wireless communications with white light-emitting diodes,” in 6thInternational Symposium on Communication Systems, Networks and DigitalSignal Processing, pp. 165–169, IEEE, 2008.

[69] G. Caire, G. Taricco, and E. Biglieri, “Bit-interleaved coded modulation,”IEEE Transactions on Information Theory, vol. 44, no. 3, pp. 927–946, 1998.

[70] A. J. Viterbi, “Convolutional codes and their performance in communicationsystems,” IEEE Transactions on Communication Technology, vol. 19, no. 5,pp. 751–772, 1971.

[71] J.-J. Van de Beek, M. Sandell, M. Isaksson, and P. O. Borjesson, “Low-complex frame synchronization in ofdm systems,” in 1995 Fourth IEEE In-ternational Conference on Universal Personal Communications, pp. 982–986,IEEE, 1995.

[72] J.-J. Van de Beek, M. Sandell, P. O. Borjesson, et al., “Ml estimation of timeand frequency offset in ofdm systems,” IEEE transactions on signal processing,vol. 45, no. 7, pp. 1800–1805, 1997.

[73] T. M. Schmidl and D. C. Cox, “Robust frequency and timing synchronizationfor ofdm,” IEEE Transactions on Communications, vol. 45, no. 12, pp. 1613–1621, 1997.

[74] B. Park, H. Cheon, C. Kang, and D. Hong, “A novel timing estimation methodfor ofdm systems,” IEEE Communications Letters, vol. 7, no. 5, pp. 239–241,2003.

[75] H. Minn, V. K. Bhargava, and K. Letaief, “A robust timing and frequencysynchronization for ofdm systems,” IEEE Transactions on Wireless Commu-nications, vol. 2, no. 4, pp. 822–839, 2003.

[76] S. Tian, K. Panta, H. A. Suraweera, B. J. Schmidt, S. McLaughlin, andJ. Armstrong, “A novel timing synchronization method for aco-ofdm-basedoptical wireless communications,” IEEE Transactions on Wireless Communi-cations, vol. 7, no. 12, pp. 4958–4967, 2008.

[77] M. Freda and J. Murray, “Low-complexity blind timing synchronization foraco-ofdm-based optical wireless communications,” in 2010 IEEE GLOBE-COM Workshops, pp. 1031–1036, IEEE, 2010.

[78] B. Ranjha, M. Aminikashani, M. Kavehrad, and P. Deng, “Robust timing syn-chronization for asymmetrically clipped ofdm based optical wireless commu-nications,” in IEEE Integrated Communication, Navigation, and SurveillanceConference (ICNS), pp. 1–27, IEEE, 2015.

135

[79] W. Gu, W. Zhang, M. Kavehrad, and L. Feng, “Three-dimensional light posi-tioning algorithm with filtering techniques for indoor environments,” OpticalEngineering, vol. 53, no. 10, pp. 107107–107107, 2014.

[80] S. Hann, J.-H. Kim, S.-Y. Jung, and C.-S. Park, “White led ceiling lightspositioning systems for optical wireless indoor applications,” in 36th EuropeanConference and Exhibition on Optical Communication, 2010.

[81] T. Tanaka and S. Haruyama, “New position detection method using imagesensor and visible light leds,” in 2009 Second International Conference onMachine Vision, pp. 150–153, IEEE, 2009.

[82] G. B. Prince and T. D. Little, “A two phase hybrid rss/aoa algorithm for in-door device localization using visible light,” in Global Communications Con-ference (GLOBECOM), 2012 IEEE, pp. 3347–3352, IEEE, 2012.

[83] W. Gu, W. Zhang, J. Wang, M. A. Kashani, and M. Kavehrad, “Three di-mensional indoor positioning based on visible light with gaussian mixturesigma-point particle filter technique,” in SPIE OPTO, pp. 93870O–93870O,International Society for Optics and Photonics, 2015.

[84] M. Yasir, S.-W. Ho, and B. N. Vellambi, “Indoor localization using visiblelight and accelerometer,” in 2013 IEEE Global Communications Conference(GLOBECOM), pp. 3341–3346, IEEE, 2013.

[85] W. Gu, M. Aminikashani, and M. Kavehrad, “Indoor visible light positioningsystem with multipath reflection analysis,” in IEEE International Conferenceon Consumer Electronics (ICCE), 2016.

[86] W. Gu, M. Aminikashani, and M. Kavehrad, “Impact of multipath reflectionson the performance of indoor visible light positioning systems,” arXiv preprintarXiv:1505.07534, 2015.

[87] M. Aminikashani, W. Gu, and M. Kavehrad, “Indoor positioning in high speedofdm visible light communications,” in IEEE Annual Consumer Communica-tions & Networking Conference (CCNC), 2016.

[88] M. S. Chowdhury, W. Zhang, and M. Kavehrad, “Combined deterministic andmodified monte carlo method for calculating impulse responses of indoor op-tical wireless channels,” IEEE/OSA Journal of Lightwave Technology, vol. 32,no. 18, pp. 3132–3148, 2014.

[89] Z. Zhou, C. Chen, and M. Kavehrad, “Impact analyses of high-orderlight reflections on indoor optical wireless channel model and calibration,”IEEE/OSA Journal of Lightwave Technology, vol. 32, no. 10, pp. 2003–2011,2014.

136

[90] F. Lopez-Hernandez, R. Perez-Jimenez, and A. Santamaria, “Modified montecarlo scheme for high-efficiency simulation of the impulse response on diffuseir wireless indoor channels,” IET Electronics Letters, vol. 34, no. 19, pp. 1819–1820, 1998.

[91] F. J. Lopez-Hernandez, R. Perez-Jimenez, and A. Santamaria, “Novel ray-tracing approach for fast calculation of the impulse response on diffuse ir-wireless indoor channels,” in Photonics East’99, pp. 100–107, InternationalSociety for Optics and Photonics, 1999.

[92] A. Küpper, Location-based services: fundamentals and operation. John Wiley& Sons, 2005.

[93] A. Kushki, K. N. Plataniotis, and A. N. Venetsanopoulos, WLAN positioningsystems: principles and applications in location-based services. CambridgeUniversity Press, 2012.

[94] M. Aminikashani and M. Kavehrad, “On the performance of single-and multi-carrie modulation schemes for indoor visible light communication systems,”in IEEE Global Communications Conference (GLOBECOM), pp. 2084–2089,IEEE, 2014.

[95] C. Forbes, M. Evans, N. Hastings, and B. Peacock, Statistical distributions.John Wiley & Sons, 2011.

137

VitaMohammadreza Aminikashani

Mohammadreza Aminikashani received his B.Sc. from University of Tehran, Iran,in Electrical and Computer Engineering in 2010, and the M.Sc. degree in ElectricalEngineering as the top student from Özyegin University, Istanbul, Turkey, in 2012.He is currently a Ph.D. student in the Department of Electrical Engineering at thePennsylvania State University. He joined Center for Information and Communi-cations Technology Research (CICTR) as a research assistant working toward hisdoctorate degree under the supervision of Prof. Mohsen Kavehrad in 2012. Hiscurrent research interests include visible light communications, free-space opticalcommunications, optical fiber communications and cooperative communications.He has published twenty papers in influential scholarly journals and conferences,thirteen of which he was the lead author. He has served as a reviewer for severalprestigious journals and conferences for IEEE and OSA societies.

During his Ph.D. studies, he was awarded the grand prize of the SustainabilityInnovation Student Challenge Award (SISCA) 2014 at Penn State sponsored bythe Dow Chemical Company. SISCA recognizes and rewards students and uni-versities for their innovation and research of sustainable solutions to the world’smost pressing social, economic and environmental problems. Recently, he was alsoawarded the Penn State Alumni Association Dissertation Award, the most pres-tigious award available to Penn State graduate students. The award recognizesoutstanding achievement in scholarship and professional accomplishment, and hewas honored to be one of the two graduate students across all engineering fields atPenn State to receive the award.