Coordinated Transmission for Visible Light Communication Systems by Hao Ma MASc., King

Coordinated Transmission for Visible Light Communication Systems

by

Hao Ma

M.A.Sc., King Abdullah University of Science and Technology, 2012

B.Eng., Xi’an Jiaotong University, 2010

A THESIS SUBMITTED IN PARTIAL FULFILLMENT OFTHE REQUIREMENTS FOR THE DEGREE OF

DOCTOR OF PHILOSOPHY

in

The Faculty of Graduate and Postdoctoral Studies

(Electrical and Computer Engineering)

THE UNIVERSITY OF BRITISH COLUMBIA(Vancouver)

October 2017

c© Hao Ma, 2017

Abstract

Visible light communication (VLC) is an emerging optical wireless communication

technology that employs the light-emitting diode (LED) as the data transmitter. It

has great potential to alleviate the strain on the radio-frequency (RF) spectrum in the

indoor environment. The integration of VLC into indoor communication networks

establishes optical attocells, responsible for the downlink traffic from the network to

user terminals. These attocells could be easily deployed wherever LEDs are adopted

for general illumination, including in electromagnetic interference sensitive areas like

hospitals and airplanes. Although opaque bounds effectively contain light signals,

VLC attocells would generally not operate free of interference. Illumination designers

aim to have a uniform illumination at a certain height in the indoor environment,

which mandates a rich overlap between the emissions of luminaires and results in

unavoidable inter-attocell interference (IAI) from a communications perspective.

This reality encourages us to propose the coordination of multiple VLC attocells

(i.e., VLC-enabled LED luminaires) to turn the problem of overlap and thus inter-

ference into an advantage. In this thesis, we study how the coordination of VLC

attocells can be employed to improve the user performance. Two coordinated VLC

architectures, both of which utilize single-carrier transmission but differ at the co-

ordination level, are investigated first. The analysis primarily focuses on the beam-

forming design subjected to the limited dynamic range of LED transmitters. The

design of robust beamformers is also considered to combat the uncertainty of channel

ii

Abstract

information at the transmitter. Finally, we propose a multi-carrier coordinated VLC

architecture that uses power lines as the backbone network for the VLC front-end.

Several subcarrier allocation schemes with varying degrees of tradeoff among hard-

ware, computational complexity and performance for meaningful variations of this

hybrid system are proposed. The system designs developed throughout the thesis

enable the collaboration among multiple LED transmitters in VLC systems, and our

results indicate that these collaborative designs can significantly improve the perfor-

mance of indoor VLC systems.

iii

Lay Summary

Visible light communication (VLC) employs the light-emitting diode (LED) as the

wireless data transmitter. Data is transmitted by varying the instantaneous power

of LEDs in time. VLC has the potential to provide high-speed communication to

indoor users at low cost via re-using LED illumination devices. On the other hand,

illumination uniformity of indoor environment generally requires the installation of

multiple wide-beam LED luminaires at the ceiling, which leads to the rich overlap

of illumination footprints, and thus strong interference from a communications per-

spective. In this thesis, we propose the coordination of multiple LED transmitters to

turn interference into an advantage. Several signal processing designs are developed

by employing the inherent multi-transmitter nature of indoor VLC system. Our re-

sults demonstrate the significant enhancement of user performance with the proposed

coordinated VLC architectures.

iv

Preface

This thesis is formatted in accordance with the regulations of the University of British

Columbia and submitted in partial fulfillment of the requirements for the Ph.D. degree

at the University of British Columbia, Vancouver, Canada. The materials presented

in this thesis are based on research performed by myself under the supervision of

Prof. Lutz Lampe in the Department of Electrical and Computer Engineering at

the University of British Columbia, Vancouver, Canada. Prof. Steve Hranilovic

from McMaster University has assisted me towards the problem formulation and the

editing of all related publications, and Dr. Ayman Mostafa from the University of

British Columbia has helped with the editing of the publication related to Chapter

3. Below is a list of publications related to the work presented in this thesis.

The content of Chapter 2 has been published in the following papers:

• H. Ma, L. Lampe, and S. Hranilovic, “Coordinated Broadcasting for Multiuser

Indoor Visible Light Communication Systems," IEEE Transaction on Commu-

nications, vol. 63, no. 9, pp. 3313-3324, Sept. 2015.

• H. Ma, L. Lampe, and S. Hranilovic, “Robust MMSE Linear Precoding for Vis-

ible Light Communication Broadcasting Systems," IEEE Globecom Workshops,

Dec. 2013.

The content of Chapter 3 has been submitted for publication.

• H. Ma, A. Mostafa, L. Lampe, and S. Hranilovic, “Coordinated Beamforming

v

Preface

for Visible Light Communication," submitted.

The content of Chapter 4 has been published in the following papers:

• H. Ma, L. Lampe, and S. Hranilovic, “Hybrid Visible Light and Power Line

Communication for Indoor Multiuser Downlink," IEEE/OSA Journal of Optical

Communications and Networking, vol. 9, no. 8, Aug. 2017.

• H. Ma, L. Lampe, and S. Hranilovic. “Subcarrier Allocation in Hybrid Visible

Light and Power Line Communication System," IEEE International Symposium

on Circuits and Systems(ISCAS), May 2016.

vi

Table of Contents

Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ii

Lay Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iv

Preface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . v

Table of Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vii

List of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xi

List of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xii

List of Abbreviations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xv

Notation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xix

Dedication . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xx

1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

1.1 Visible Light Communication Development and Applications . . . . 3

1.1.1 Visible Light Communication Development . . . . . . . . . . 3

1.1.2 Visible Light Communication Applications . . . . . . . . . . 4

1.2 Visible Light Communication Background . . . . . . . . . . . . . . . 6

1.2.1 VLC Transceivers . . . . . . . . . . . . . . . . . . . . . . . . 6

vii

Table of Contents

1.2.2 Channel Modeling . . . . . . . . . . . . . . . . . . . . . . . . 9

1.2.3 Standards and Constraints . . . . . . . . . . . . . . . . . . . 11

1.2.4 Modulation Techniques . . . . . . . . . . . . . . . . . . . . . 13

1.3 Motivation and Contributions of the Thesis . . . . . . . . . . . . . . 17

1.4 Remark on Alternating Optimization . . . . . . . . . . . . . . . . . . 22

1.5 Organization of the Thesis . . . . . . . . . . . . . . . . . . . . . . . 23

2 Joint Transmission in VLC Systems . . . . . . . . . . . . . . . . . . 24

2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

2.2 System Model and Transmission Scheme . . . . . . . . . . . . . . . . 25

2.2.1 VLC Channel . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

2.2.2 Broadcast Transmission . . . . . . . . . . . . . . . . . . . . . 28

2.2.3 Constraints on Precoding from VLC . . . . . . . . . . . . . . 29

2.2.4 Design Objectives . . . . . . . . . . . . . . . . . . . . . . . . 31

2.3 Transmitter Design with Perfect Channel Information . . . . . . . . 31

2.3.1 Sum-MSE Minimization Problem . . . . . . . . . . . . . . . . 32

2.3.2 Minimal Illumination Level Problem . . . . . . . . . . . . . . 35

2.4 Robust Transmitter Design with Channel Uncertainty . . . . . . . . 36

2.4.1 Uncertainty Models . . . . . . . . . . . . . . . . . . . . . . . 37

2.4.2 Sum-MSE Minimization Problem . . . . . . . . . . . . . . . . 40


2.5 Numerical Results and Discussions . . . . . . . . . . . . . . . . . . . 45

2.5.1 User Position with Joint Transmission Setup . . . . . . . . . 48

2.5.2 Sum-MSE Minimization with Channel Uncertainty . . . . . . 55


2.5.4 Comparison between Robust and Non-Robust Design . . . . . 57

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Table of Contents

2.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60

3 Coordinated Beamforming in VLC Systems . . . . . . . . . . . . . 62

3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62

3.2 System Model and Transmission Scheme . . . . . . . . . . . . . . . . 63

3.2.1 System Model . . . . . . . . . . . . . . . . . . . . . . . . . . 63

3.2.2 Transmission Scheme . . . . . . . . . . . . . . . . . . . . . . 64

3.2.3 Design Constraints . . . . . . . . . . . . . . . . . . . . . . . . 66

3.3 Transmitter Design with Perfect Channel Information . . . . . . . . 67

3.4 Robust Transmitter Design with Channel Uncertainty . . . . . . . . 72

3.4.1 Robust Design with the Deterministic Model . . . . . . . . . 73

3.4.2 Robust Design with the Stochastic Model . . . . . . . . . . . 76


3.5.1 Simulation Setup . . . . . . . . . . . . . . . . . . . . . . . . . 77

3.5.2 Comparison of Different Coordination Levels . . . . . . . . . 80

3.5.3 Importance of Weight . . . . . . . . . . . . . . . . . . . . . . 83

3.5.4 Comparison between Robust and Non-Robust Design . . . . . 85

3.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86

4 The Hybrid VLC-PLC System . . . . . . . . . . . . . . . . . . . . . . 91

4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91

4.2 System Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94

4.2.1 Problem Scenario . . . . . . . . . . . . . . . . . . . . . . . . 94

4.2.2 Transmitter and Receiver Model . . . . . . . . . . . . . . . . 95

4.2.3 Channel and Noise Model . . . . . . . . . . . . . . . . . . . . 96

4.3 Rate Analysis of the HVP System . . . . . . . . . . . . . . . . . . . 99

4.3.1 Signal at the PLC Hop . . . . . . . . . . . . . . . . . . . . . 99

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Table of Contents

4.3.2 Signal at the VLC Hop . . . . . . . . . . . . . . . . . . . . . 100

4.3.3 Achievable Rate Expression for Each Subcarrier Pair . . . . . 101

4.4 Subcarrier Allocation in HVP Systems . . . . . . . . . . . . . . . . . 105

4.4.1 OFDM-TDMA . . . . . . . . . . . . . . . . . . . . . . . . . . 107

4.4.2 OFDMA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110


4.5.1 Single-User System . . . . . . . . . . . . . . . . . . . . . . . . 115

4.5.2 Multi-User System . . . . . . . . . . . . . . . . . . . . . . . . 118

4.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119

5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128

5.1 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128

5.2 Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129

Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131

Appendices

A Proof of Outdated CSI Bound . . . . . . . . . . . . . . . . . . . . . . 144

x

List of Tables

1.1 Required illuminance level for different activities specified by the Eu-

ropean Norm (EN) 12464-1 Standard . . . . . . . . . . . . . . . . . . 12

2.1 Simulation parameters. . . . . . . . . . . . . . . . . . . . . . . . . . . 46

3.1 Simulation parameters . . . . . . . . . . . . . . . . . . . . . . . . . . 78

3.2 Luminaire coordinates of LS-I and LS-II . . . . . . . . . . . . . . . . 80

3.3 Illumination performance of LS-I and LS-II . . . . . . . . . . . . . . . 80

3.4 User coordinates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81

4.1 Simulation parameters. . . . . . . . . . . . . . . . . . . . . . . . . . . 116

xi

List of Figures

2.1 Illustration of indoor coordinated VLC broadcast system. . . . . . . . 26

2.2 Illustration of outdated CSI resulting from terminal mobility in a VLC

system. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38

2.3 Error bounds obtained from simulation for (a)L = 0.25 m, (b)L =

0.5 m. Illumination and VLC setup for these results are described in

Section 2.5. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40

2.4 The distribution of indoor illuminance when IDC = 500 mA. . . . . . 47

2.5 User-configurations for MU-MISO VLC are considered for numerical

results. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49

2.6 Comparison of system performance with different user positions (as

shown in Figure 2.5) as a function of illumination level. Sum-MSE

minimization with perfect CSI. . . . . . . . . . . . . . . . . . . . . . 50

2.7 Comparison of the SER calculation using Equation (2.53) with Monte

Carlo simulation result. . . . . . . . . . . . . . . . . . . . . . . . . . . 52

2.8 Different transmitter coordination levels in an MU-MISO VLC system. 53

2.9 Comparison of system performance with different transmitter coordi-

nation. Sum-MSE minimization problem with perfect CSI. . . . . . . 54

2.10 SINR as a function of user location in one quadrant of the room and

IDC = (IL + IU)/2. Sum-MSE minimization problem with perfect CSI. 55

xii

List of Figures

2.11 Robust sum-MSE minimization with outdated CSI. Setup II with x =

1.25 and y = 1.25. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57

2.12 Robust sum-MSE minimization with noisy CSI. Setup II with x = 1.25

and y = 1.25. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58

2.13 Robust illuminance minimization with perfect (L = 0) and outdated

(L > 0) CSI. Setup II with x = 1.25 and y = 1.25. . . . . . . . . . . . 59

2.14 Comparison between robust and non-robust design for sum-MSE min-

imization problem with outdated CSI. . . . . . . . . . . . . . . . . . . 61

3.1 Illustration of the CB structure. . . . . . . . . . . . . . . . . . . . . . 64

3.3 The distribution of indoor illuminance for two lighting setups when

IDC = 500 mA. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82

3.4 SINR of User I as a function of its x-axis coordinate x1. . . . . . . . . 84

3.5 Comparison of system performance with different coordination levels

for UD-II, UD-III and UD-IV. . . . . . . . . . . . . . . . . . . . . . . 87

3.6 (a) Left : w = [1, 1, 1, 1]T . (b) Right: w = [50, 10−7, 1.4, 2.2]T . . . . . 88

3.7 Comparison between robust and non-robust design with the determin-

istic model. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89

3.8 Comparison between robust and non-robust design with the stochastic

model. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90

4.1 Block diagram of the HVP system. . . . . . . . . . . . . . . . . . . . 95

4.2 Detailed block diagram of the SO-OFDM HVP downlink system for

one luminaire and one user. Blocks with dashed lines are not present

in LED luminaires operating in amplify-and-forward mode. . . . . . . 97

4.3 The setup of HVP system. . . . . . . . . . . . . . . . . . . . . . . . . 121

xiii

List of Figures

4.4 Achievable rate as a function of user location. Nc = 16, α =√

10,

β = 10. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122

4.5 Achievable rate versus relay gain (α or β). Nc = 16. User location is

x = −0.5 m, y = 1.5 m, z = 0.8 m. . . . . . . . . . . . . . . . . . . . 123

4.6 Comparison of different SA schemes with different chunk size Ns. α =√

10, β = 10. User location is x = −0.5 m, y = 1.5 m, z = 0.8 m. . . 124

4.7 NVLC_BL as a function of user location. Nc = 16. NVLC_BL is the

number of subcarrier pairs for which the VLC hop is the bottleneck

link when the maximum achievable rate is attained. . . . . . . . . . . 125

4.8 Achievable rate versus the number of users NU. SA with SP and AF-

ACO are applied. β = 10, Nc = 16. . . . . . . . . . . . . . . . . . . . 126

4.9 Comparison of multi-access schemes with and without PF for NU = 4.

The example locations are (x = −1.25, y = 1.25, z = 0.8) m, (x =

−1.25, y = −1.25, z = 0.8) m, (x = 1.25, y = 1.25, z = 0.8) m and

(x = 2.5, y = 2.5, z = 0.8) m for User 1, User 2, User 3 and User 4,

respectively. SA with SP and AF-ACO are applied. Nc = 16, β = 10. 127

xiv

List of Abbreviations

AC Alternating Current

ACO-OFDM Asymmetrically Clipped Optical Orthogonal Frequency Division Multiplexing

AF Amplify–and–Forward

AFE Analog Front–end

AP Access Point

ASE Area Spectral Efficiency

AWGN Additive White Gaussian Noise

CB Coordinated Beamforming

CoMP Coordinated Multipoint

C-RAN Cloud/Centralized Radio Access Network

CS Coordinated Scheduling

CSI Channel State Information

CSK Color Shift Keying

C-VAN Cloud/Centralized VLC Access Network

DC Direct Current

DCO-OFDM Direct Current–biased Optical Orthogonal Frequency Division Multiplexing

DD Direct Detection

DF Decode–and–Forward

DMT Discrete Multitone

DSL Digital Subscriber Line

xv


FFT Fast Fourier Transform

FoV Field of View

GPS Global Positioning System

HVP Hybrid VLC-PLC

IAI Inter–Attocell Interference

IFFT Inverse Fast Fourier Transform

IM Intensity Modulation

IoT Internet–of–Things

ISI Inter–Symbol Interference

JT Joint Transmission

LaaS Light–as–a–Service

LBS Location–Based Service

LED Light–Emitting Diode

LoS Line–of–Sight

LPTV Linear Periodically Time Varying

MHz MegaHertz

MIMO Multiple–Input Multiple–Output

MISO Multiple–Input Single–Output

MMSE Minimum Mean Squared Error

MSE Mean Squared Error

MU Multi-User

NLoS Non–Line–of–Sight

NRZ Non–Return–to–Zero

OFDM Orthogonal Frequency Division Multiplexing

OFDMA Orthogonal Frequency Division Multiple Access

xvi


OOK On-Off Keying

OW Optical Wireless

PAM Pulse Amplitude Modulation

PAPR Peak–to–Average Power Ratio

PC Partial Coordination

PD Photodiode

PLC Power Line Communication

PSD Power Spectral Density (PSD)

PWM Pulse Width Modulation

RF Radio Frequency

RGB Red–Green–Blue

SA Subcarrier Allocation

SDP Semidefinite Programming

SISO Single–Input Single–Output

SINR Signal–to–Interference–plus–Noise Ratio

SNR Signal–to–Noise Ratio

SO-OFDM Spatial Optical Orthogonal Frequency Division Multiplexing

SP Subcarrier Permutation/Pairing

THz TeraHertz

UT Uncoordinated Transmission

VLC Visible Light Communication

V-PPM Variable Pulse Position Modulation

V2I Vehicle–to–Infrastructure

V2V Vehicle–to–Vehicle

WSMSE Weighted Sum Mean Squared Error

xvii


ZF Zero–Forcing

xviii

Notation

A Matrix

a Vector

1 All–one column vector

I Identity matrix

| · | Absolute value of a real number or the cardinality of a set

(·)T Transpose

(·)H Hermitian transpose

vec(·) Vectorization

Z+ The set of positive integer

C The set of complex number

Cm×n The space of all m× n matrices with complex-valued elements

E(·) Statistical expectation operator

⊗ Kronecker product

var(·) Variance operator

‖ · ‖p p-norm

diag(x) A diagonal matrix with the elements of vector x on the main diagonal

tr(·) Trace of a matrix

xix

Dedication

To my wife, parents and families

xx

Chapter 1

Introduction

The mobile data traffic is surging at an incredible speed. A study conducted by

Cisco Systems Inc. shows that global mobile data traffic grew 63% in 2016, and the

monthly global mobile data traffic will reach 49 exabytes by 2021, compared to 7.2

exabytes per month at the end of 2016 and 4.4 exabytes per month at the end of

2015 [1]. One of the main reasons for this huge amount of traffic increment is the

increased data consumption per mobile device. This is due to the booming of data-

intensive mobile multimedia applications, especially cloud-based mobile applications

where mobile devices function as gateways for the access to services provided by the

cloud [2]. The other major reason is the explosively growing number of connected

devices. More cyber-physical systems are penetrating our life in this age of the

Internet of Things (IoT). Huawei Technologies Co. Ltd predicts that by 2025, the

total number of connected devices will reach 100 billion [3]. A significant portion

of those connected devices will be accessing the Internet wirelessly, which leads to a

higher mobile data traffic. Moreover, the introduction of new cyber-physical systems

will, in turn, drive the creation of new multimedia applications which will further

boost the aggregate data usage. In contrast, the radio-frequency (RF) spectrum

is a very limited resource, and the resulting spectrum scarcity is holding back the

capacity enhancement of wireless networks and hindering mobile network operators

from starting new wireless services [4]. Till now, the creation of small-cell networks

and operation of heterogeneous networks have been the two important means to

1

Chapter 1. Introduction

squeeze more data traffic into the limited RF spectrum. However, eventually the

usable RF spectrum is a finite resource, and the inter- and intra-cell interference will

limit the wireless network capacity.

On the other hand, the lighting industry is undergoing a major technology transi-

tion as light-emitting diode (LED) illumination devices are replacing legacy incandes-

cent and fluorescent light lamps due to the longer life expectancy and higher energy

efficiency. A McKinsey study predicts that the global LED market size in 2020 will

double that in 2016 [5]. As LED-based lamps are relatively more reliable and have a

longer lifespan, the manufacture and retail of LEDs become a less profitable business

in the long run, which is encouraging lighting companies to adjust their business

model from lighting equipment manufacturers to light-as-a-service (LaaS) providers

[6, 7].

Being at the intersection of communication and illumination, visible light com-

munication (VLC) fulfills the needs of both the wireless and lighting industries as

it turns illumination devices into wireless data transmitters. VLC uses LEDs as the

transmitting devices and operates over the nearly unlimited and license-free light

spectrum (380 nm – 780 nm), wherein the data signal is transmitted by means of

modulating the output intensity of the incoherent LED light sources, i.e., via intensity

modulation (IM). At the receiver side, direct detection (DD) is applied using simple

photodiodes (PDs) or imaging receivers. Given the ongoing widespread deployment

of LED luminaires, VLC can turn such prevalent illumination devices into wireless

access points (APs) that provide ubiquitous indoor broadband coverage, including

areas in which RF radiation is undesirable or prohibited, such as hospitals. Besides,

VLC is inherently secure as light is confined within the room that it illuminates by

opaque boundaries. Visible light is also much more eye-safe than infrared links due

2


to the inherent blink reflex of human eyes. As a result, safety regulations permit

far larger emitted optical power at visible wavelength range over infrared. Last but

not least, unlike RF front-ends and receive chains, all signals in the VLC transmit-

ter and receiver are at baseband and up/down conversion is done via inexpensive

optoelectronic components, yielding a simpler, lower power transceiver.

This chapter provides an overview of the VLC technology, and it is organized as

follows. In Sections 1.1, we briefly review the literature of VLC development and its

applications. Sections 1.2 presents an overview of the VLC channel including VLC

transceivers. System design constraints and compatible modulation schemes are also

reviewed at the end of Section 1.2. The motivations and contributions of the thesis

are provided in Section 1.3. Section 1.4 offers remarks on the alternating optimization

technique used throughout the thesis. Finally, the thesis organization is presented in

Section 1.5.

1.1 Visible Light Communication Development and

Applications

1.1.1 Visible Light Communication Development

At the time of writing of this thesis, there is substantial research interest in the area

of VLC, especially for the high data-rate indoor VLC network. The use of white

LED illumination devices for indoor communications was first proposed by Komine

et al. [8]. However, enthusiasm for this research topic has spread worldwide with

active research groups in the USA (e.g., Penn State U., Boston U., Rensellar Poly,

Georgia Tech.), Europe (e.g., Edinburgh, Oxford, Northumbria, Fraunhofer Heinrich

Hertz Inst.) and Asia (e.g., Keio U., Tsinghua U.). In addition, large research

3


projects in VLC have been launched including the Visible Light Communications

Consortium (2003, Japan), OMEGA Project (2008, EU), Smart Lighting Engineering

Research Center (2008, USA), Center on Optical Wireless Applications (2011, USA)

and Canadian Research in VLC (2012). In 2014, the Visible Light Communications

Association (VLCA) was established as a successor to Visible Light Communications

Consortium in Japan.

In 2011, the IEEE ratified 802.15.7, a wireless personal area network standard

for VLC [9]. The standardization activities were led by Samsung (Korea) and In-

tel (USA). Data rates in the standard range from 11 kbps to 96 Mbps using on-off

keying (OOK), variable pulse-position modulation (V-PPM) and colour-shift keying

(CSK). On the other hand, more modulation techniques for VLC, including orthogo-

nal frequency-division multiplexing (OFDM), have been investigated in the research

community [10, 11] and adopted by industrial companies [12]. OFDM VLC proto-

type systems developed in laboratory conditions have demonstrated the potential of

VLC in providing Gb/s transmission for indoor wireless network access. In [10], a

OFDM VLC link of 500 Mb/s is achieved over a 0.3 m distance where the employed

high-power LED possesses a 3-dB modulation bandwidth of 35 MHz. In [11], a 3

Gb/s OFDM VLC link over a 5 cm distance has been implemented utilizing a single

gallium nitride µLED whose 3-dB modulation bandwidth is 60 MHz.

1.1.2 Visible Light Communication Applications

Wireless Local Area Networks

Given the trend in the widespread deployment of LED luminaires, VLC can turn the

ubiquitous illumination devices into numerous wireless hotspots for indoor coverage.

By harnessing the vast optical spectrum resource, research [11, 13] has shown that

4


the data rate for a point-to-point VLC link can reach up to Gb/s. A typical VLC AP

covers a service area on the order of 1−10 m2. This relatively small coverage area al-

lows ultra-dense deployment of the so-called VLC attocells [14], which are analogous,

but smaller in terms of the coverage area, to RF femtocells [15]. As a consequence,

the area spectral efficiency (ASE) of VLC networks can be significantly increased,

and more users can be accommodated within the indoor environment [16, 17]. Al-

though VLC is less preferable to RF transmission (e.g., Wi-Fi, femtocell) in terms of

providing seamless connections, indoor VLC can supplement indoor RF transmission

by providing high-speed downlink transmission for data-intensive applications like

video downloading and live streaming. These applications have heavy demands on

the downlink bandwidth yet require minimal uplink capacity. Through offloading the

data traffic from RF transmission to VLC, the capacity of RF transmission available

can be enhanced and better utilized.

Indoor Positioning

The overall market of location-based services (LBS) is expected to increase five times

during the period of 2016 - 2021 [18]. The Global Positioning System (GPS) has been

widely used to provide localization service in outdoor areas, but it is not suitable for

indoor positioning due to the signal attenuation and scattering in the indoor environ-

ment. For indoor positioning, a possible solution is Wi-Fi-based indoor localization,

but it offers relatively low accuracy [19]. On the other hand, indoor positioning

based on VLC has become a popular research topic recently [20, 21]. Compared

with RF-based indoor positioning, VLC-based indoor positioning can be adopted in

electromagnetic interference sensitive areas like hospitals. As the number of LED lu-

minaires is usually greater than that of Wi-Fi APs in the indoor environment, and the

propagation of visible light is less subject to the multipath effect and thus more pre-

5


dictable, VLC-based indoor positioning techniques can generally provide localization

services of higher accuracy and are strong candidates for future indoor positioning

applications.

Vehicle Communication

The intelligent transportation system (ITS) improves the safety of transport networks

and enables better traffic management. Vehicular communication is an important

part of ITS, which falls into two categories: Vehicle to Infrastructure (V2I) and Vehi-

cle to Vehicle (V2V) communications [22]. As LED luminaires are already available

in street lights, traffic lights and signs, and automotive lighting, VLC is directly ap-

plicable for V2I and V2V communication. Due to the omnipresence of LED lights

in the transportation system, VLC-based vehicular communication reduces the huge

cost of equipment installation. Furthermore, since VLC provides a more focused

transmission and can be blocked by opaque objects, VLC-based vehicular commu-

nication experiences less interference compared with RF-based one, which is more

suitable for high traffic density areas [23].

1.2 Visible Light Communication Background

1.2.1 VLC Transceivers

Transmitter: Light-Emitting Diodes

LEDs are used as the transmitting device in a visible light communication system.

LEDs are semiconductor p-n junction diodes and emit light when activated, the

effect of which is known as electroluminescence [24]. The color of the emitted light

is determined by the band gap of the semiconductor. Among LEDs of all colors,

6


white light LEDs are most widely used for illumination purpose in both indoor and

outdoor environment. However, white light cannot be directly generated by a single

material. According to the way in which white light is generated, commercial LEDs

can primarily fall under the following two categories:

• Phosphor-based LEDs: A phosphor-based LED is a blue LED chip coated

with yellow phosphor. Phosphors are designed to absorb one specific frequency

of light and re-emit light at different frequencies. When light emitted by a blue

LED passes through the phosphor coating, part of the blue light is converted

to green, yellow and red. Together with the leaked blue light, the mixture of all

the components produces white light [24]. Phosphor-based LEDs are relatively

cheaper but suffer from low modulation bandwidth due to the slow response of

phosphor coating. Optical filters at the receiver side can be applied to retrieve

the blue component, and thus resulting in an enhanced system bandwidth [25].

• Red-Green-Blue (RGB) LEDs: The RGB LED contains three LED dices

which are jointly packaged. The three separate monochromatic LED chips emit

red, green and blue light, and the combination of the three primary colors in

appropriate portions produces white light. It omits the need for the phosphor,

so the modulation bandwidth is greater than that of phosphor-based LEDs.

However, the light output of different colored LEDs may depreciate at different

rates throughout their lifetime, leading to color drift for the RGB LED.

LEDs are current-driven devices that are able to emit incoherent light. The forward

voltage of LEDs remains approximately constant regardless of the driving current,

while the instantaneous optical power of the LED is controlled by the driving current.

VLC uses IM by modulating instantaneous output optical power of the LEDs through

the driving current signal. There exists a linear operating region for an LED wherein

7


the optical power is linearly proportional to the driving current, and the VLC-enabled

LED needs to work within the linear operating region in order to perform IM.

Though the visible light spectrum spans hundreds of terahertz (THz), the slow

modulation response of off-the-shelf LED light fixtures is the bottleneck that im-

pedes the capacity enhancement of VLC links 1. Typical white-light LEDs are mostly

phosphor-based LEDs with modulation bandwidth of several megahertz (MHz), and

employing the blue optical filter at the receiver side can improve the system band-

width to approximately 20 MHz [27]. Research of new LEDs has resulted in LEDs

with much higher modulation bandwidth [28]. Reducing the cost and accelerating the

commercialization of high-bandwidth LEDs are critical towards the wide deployment

of high-speed VLC systems.

Receiver: Photodiode

The photodiode is a semiconductor device that is able to convert incident light into

current. VLC uses photodiodes as receivers to down-convert the optical into an

electrical signal, the process of which is called DD. Another option for the VLC

receiver is the imaging sensor. It can be considered as a matrix of photodetectors

on an integrated circuitry, and VLC can utilize its rolling shutter effect for data

receiving at a fast rate [29]. In this thesis, we focus on the use of photodiode as the

VLC receiver.1The bandwidth of PDs is in general much wider than that of VLC LED transmitters [26].

8


1.2.2 Channel Modeling

Channel Response

The VLC channel response is inherently frequency-selective. While the frequency

response of VLC transmitters can be flattened through equalization to counteract the

low-pass characteristics of LEDs, the multipath propagation of visible light, which

results from reflection, will lead to delay spreads. The rays of light hit surfaces in the

environment and get reflected towards the receiver. Therefore, the channel response

hVLC comprises both a line-of-sight (LoS) component hLoS and a non-LoS (NLoS)

component hNLoS:

hVLC = hLoS + hNLoS . (1.1)

In VLC, the LoS propagation of visible light dominates the diffuse propagation in

most situations [8]. Considering the LoS propagation only, the single-tap VLC chan-

nel gain between the light source (the LED source or a reflection point on the walls)

and the receiver (the user or a reflection point on the walls) can be approximated by

a deterministic function of the emission pattern of the LED transmitters, as well as

the location and orientation of the VLC receiver. It can be expressed as below if we

assume Lambertian radiation pattern for light sources [30]:

h(D,φ, ψ) =(m+ 1)sγκ2APD

2πD2 sin2(ψc)cosm(φ) cos(ψ)IA(ψ) , (1.2)

where m is the Lambertian order and specifies the transmit beam divergence, γ is

the receiver (photodetector) responsivity [A/W], s is the conversion factor of the

light source (LED) [W/A], κ is the concentrator refractive index, D is the distance

between the receiver and the light source, ψc is the width of the field of view (FoV)

9


at the receiver, APD is the area of photodetector, ψ is the angle of incidence at which

the light is received relative to the normal vector of the receiver plane, and φ is

the angle of irradiance at which the light is emitted relative to the normal vector

of the transmitter plane. Furthermore, IA(ψ) denotes the indicator function with

A = {ψ| 0 ≤ ψ ≤ ψc}.

Research in the VLC literature generally uses two methods of modeling the VLC

channel response, namely frequency-flat channel modeling and frequency-selective

channel modeling. Frequency-flat channel modeling considers the LoS component

only and (1.2) can be applied to calculate the channel gain between the VLC trans-

mitter and the user. The neglect of NLoS components is reasonable given the fact

that the modulation bandwidth of typical off-the-shelf LED luminaires will not ex-

ceed 20 MHz, which is generally smaller than the inverse of the maximum excess

delay of the NLoS path in general indoor environment [27]. Therefore, the multipath

delay will not result in notable inter-symbol interference (ISI), and thus the VLC

channel can be treated as a single-tap channel.

On the other hand, the multipath effect has to be taken into account in case of

relatively broadband transmission, where the multipath phenomena will lead to ISI,

and NLoS components should not be neglected any more [27]. Frequency-selective

channel modeling takes both LoS and NLoS contributions into account, and the

corresponding channel response can be approximated using different algorithms. A

simple frequency-domain analytical model proposed by [31] for the indoor wireless

infrared channel has been used widely in the VLC literature due to its computational-

efficiency. However, the mismatch between the analytical model and the channel mea-

surements increases as frequency increases [31]. In comparison, approximating the

channel response by simulations, like recursive calculation methods [32] and Monte

10


Carlo ray-tracing methods [33], is of higher accuracy at the cost of higher compu-

tational complexity. In this thesis, we adopt the modified Monte Carlo ray-tracing

method [34], which is a relatively faster algorithm to obtain the VLC channel response

when the NLoS contribution needs to be considered.

Receiver Noise

The dominant noise in VLC systems comprises thermal noise generated by the re-

ceiver electronic circuits, and shot noise due to ambient light from light sources like

the sun and indoor lighting devices including VLC-enabled luminaires. The receiver

noise component can be modeled as a zero-mean Gaussian variable with variance [8]

σ2n = σ2

th + 2eB(Irp + IbgI2) , (1.3)

where σ2th is the thermal-noise variance, e is the elementary charge, B is system

bandwidth, Ibg is background current, and I2 is the noise bandwidth factor (second

Personick integral [35]). Irp is the average current due to the received signal at the

receiver, which is dependent on the illumination level of the VLC transmitter and

the user location.

1.2.3 Standards and Constraints

Appropriate lighting enables people to perform visual tasks efficiently and accurately.

A VLC-enabled LED serves the dual-purpose of illumination and communication.

Therefore, the VLC system design must follow the illumination standards, and it is

constrained by the property of LED transmitters at the same time.

11


Table 1.1: Required illuminance level for different activities specified by the EuropeanNorm (EN) 12464-1 Standard

Activity Illuminance (Lx)Stairs, escalators, travelators 100Rest rooms inside buildings 100Theaters dressing room 300

Eye or Ear examination rooms 500Classroom for evening classes 500

Normal office work 500

Illuminance and Uniformity

The indoor illuminance level is determined by the DC current of LEDs. Various stan-

dardization bodies across different countries defined the required illuminance level for

the indoor environment [36, 37, 38]. In this thesis, we follow the requirement of the

European Norm (EN) 12464-1 standard [38] for the planning and design of lighting

installations. The area planning for indoor workplaces defines both task area and

immediate surrounding area. The task area is defined as the area in which the visual

work is carried out, while the immediate surrounding area is defined as a band sur-

rounding the task area within the field of vision with a minimum width of 0.5 m. The

task area can be used to perform different types of activities which require different

illumination levels. As specified in the European Norm (EN) 12464-1 standard, Table

1.1 provides the required illuminance level for a few different activities.

Aside from the illumination level, illuminance fluctuation across the indoor en-

vironment should also be restricted in order to guarantee a comfortable luminous

environment. Therefore, the term uniformity, defined as the ratio of the lowest to

the average illuminance value in a certain area, is introduced. According to the

European Norm (EN) 12464-1 standard, the minimum uniformity of task area and

immediate surrounding area is 0.60 and 0.40, respectively.

12


Amplitude Constraint

LEDs have a limited operating region which consists of both linear region and non-

linear region. The output optical power is linear with the forward current if LEDs

operate within the linear region. Otherwise, the current/optical conversion will dis-

play nonlinear characteristics similar to the nonlinearity of RF transmitters [39].

While pre-distortion can be used to (approximately) linearize the current/optical

conversion, the driving current of LEDs still needs to stay within a limited dynamic

range, beyond which the output intensity saturates. Therefore, the channel input of

VLC systems must satisfy a certain amplitude constraint in order to avoid clipping

distortion of the transmitted signal, which is different from the power constraint that

is usually considered in RF systems.

For single-carrier modulated signals, it is easier to put a constraint on its ampli-

tude to avoid overdriving LEDs, and thus signal clipping can be prevented. While for

multi-carrier modulation, like OFDM, signal clipping is unavoidable since the time-

domain signal follows a Gaussian distribution for large Inverse Fast Fourier Transform

(IFFT) sizes according to the Central Limit Theorem [40]. In this case, the current

signal should be pre-clipped before it is injected into the LEDs so that the driving

current lies within the dynamic range of the LEDs .

1.2.4 Modulation Techniques

VLC systems utilize the LED, which is an incoherent light source, as the transmitter.

VLC-enabled LEDs send information by varying the instantaneous intensity (i.e.

power) of the optical source in time. Data are not sent in the underlying phase or

amplitude of the optical carrier but rather only in its power. This modulation scheme

is called IM. As a result, only non-negative signals can be sent from the transmitter.

13


At the receiver, a photodiode performs the DD of the signal. It integrates the envelope

of the received field and outputs an electrical current in near proportion to the optical

power impinging on it. In the following, we will have a brief review of several VLC-

compatible modulation schemes.

Single-Carrier Modulation

IEEE 802.15.7 standardized three modulation schemes, namely on-off keying (OOK),

variable pulse-position modulation (V-PPM) and color shift keying (CSK) [9]. The

first two modulation schemes are compatible with single-chip LEDs (phosphor-based

LEDs) while CSK is targeted for multi-chip light sources (RGB LEDs) and detectors.

• On-Off Keying (OOK): Due to its simplicity, on-off keying is the most pop-

ular IM/DD modulation scheme. Each OOK symbol represents either an “ON”

state or an “OFF” state. Note that "ON" and "OFF" are just two logic levels

and do not necessarily require that the light source be turned off completely.

Different line code techniques can be applied to OOK. In the simplest form of

OOK, non-return-to-zero (NRZ) OOK, digital data is represented by the pres-

ence or absence of light. The IEEE 802.15.7 standard proposes the Manchester

coding instead of NRZ for VLC OOK. The Manchester line code encodes each

data bit in either low-to-high or high-to-low transition thus it is a DC balanced

code, which can avoid possible flicker [9].

• V-PPM:V-PPM combines both 2-PPM (pulse position modulation) and PWM

(pulse width modulation). In 2-PPM, the symbol duration is divided into two

slots of equal duration and the pulse corresponding to a certain bit is trans-

mitted in one of its two time slots within the symbol period, through which

the binary bit 1 and 0 are represented. V-PPM incorporates the characteristics

14


of PWM and extends 2-PPM by making the duty cycle percentage tunable in-

stead of fixing it at 50%. Pulse width of V-PPM can be adjusted based on the

dimming requirements. V-PPM has both the advantages of flicker avoidance

(2-PPM) and dimming control capability (PWM).

• Color Shift Keying (CSK): CSK applies to VLC systems that employ RGB

LEDs as the transmitter. In CSK, signals are transmitted imperceptibly via

varying the light output of each chip in the RGB triplet. The luminous flux and

the average perceived chromaticity of the light source remain constant, making

CSK free from flicker. Also, CSK generally enables higher data throughput

since it divides the visible light spectrum into three different communication

channels, in contrast to the two modulation schemes above which modulate the

same data over the entire visible light spectrum [41].

Multi-Carrier Modulation

Besides these standardized single-carrier modulation schemes, IM/DD compatible

multi-carrier modulation schemes are gaining popularity in both the research com-

munity [10, 11] and the industry [12]. OFDM has been widely used in RF com-

munications due to its robustness towards ISI caused by the dispersive channel and

the low complexity of frequency-domain receiving equalization. The VLC channel is

inherently dispersive due to the low-pass characteristics of LEDs and the reflections

of light waves. Therefore, optical OFDM can be applied to high-speed VLC systems

to combat ISI. However, due to the nature of IM/DD, the conventional OFDM used

in RF communications needs to be modified since the time-domain optical OFDM

signals for the IM/DD channel is required to be both real and non-negative in order

to modulate light intensity. In this subsection, we will have a brief overview of two

15


popular variations of optical OFDM [42]. The former has the same requirement as for

any baseband OFDM transmission, such as for digital subscriber lines (DSLs), where

it is also referred to as discrete multitone (DMT), or for power line communication

(PLC). In comparison, the latter is truly VLC specific.

• DC-Biased Optical OFDM: In DC-biased optical OFDM (DCO-OFDM),

the signal input to the inverse Fast Fourier Transform (FFT) module should

satisfy the Hermitian symmetry so that the output is real. A DC bias is added

to ensure the unipolarity of optical OFDM signal in DCO-OFDM. However, the

time-domain OFDM signal has a high peak-to-average power ratio (PAPR). In

order to bias all negative peaks, a large DC bias is required thus the power

efficiency decreases. Therefore, typically a moderate DC bias is used to bias

most of the negative components, while the rest of the negative components will

be clipped, and every information-carrying subcarrier will be contaminated by

the resulting clipping noise.

• Asymmetrically Clipped Optical OFDM: Similar to DCO-OFDM, asym-

metrically clipped optical OFDM (ACO-OFDM) also utilizes the Hermitian

symmetry to ensure a real output. The time-domain ACO-OFDM signal is

made positive by clipping all negative signal components. As the resulting

clipping noise will only affect the even subcarriers, ACO-OFDM only employs

odd subcarriers to carry data symbols and leave even subcarriers vacant [43].

Compared with DCO-OFDM, ACO-OFDM is less spectral efficient since half

of the subcarriers are unused. However, ACO-OFDM is more power efficient in

terms of average optical power for small constellation sizes [44].

16


1.3 Motivation and Contributions of the Thesis

At the time of starting the thesis work in 2012, most research on physical layer

transmission techniques in the VLC literature focused on point-to-point communica-

tion. However, despite the often dominating LoS propagation and the confinement of

light waves by opaque surfaces, the performance of a VLC attocell downlink can still

be severely degraded by interference from neighboring attocells, i.e., inter-attocell

interference (IAI). Typical lighting systems in indoor environments utilize multiple

wide-beam luminaires to provide user-friendly uniform illumination. From a com-

munications perspective, however, the use of wide-beam luminaries gives rise to in-

creased interference levels at areas in which the illumination footprints of luminaires

from different attocells overlap.

In order to alleviate the performance degradation for attocell-edge users, several

works in the literature have considered hybrid RF-VLC systems [45, 46, 47, 48]. In

such systems, the VLC attocells are deployed with non-overlapping footprints, and

the gaps are covered with RF femtocells. In other words, users who are beyond the

coverage of the VLC attocells are served by RF base stations. Despite its benefits,

a hybrid RF-VLC system would suffer from added complexity along with increased

handover overhead for users moving across different femtocells/attocells.

A different approach towards interference management for VLC attocells is to

use the so-called coordinated multipoint (CoMP) paradigm, wherein transmitters of

different attocells are connected through backbone networks like wired Ethernet or

powerline, and design their signals in a collaborative way. In Chapter 2, we propose

the joint transmission (JT) of multiple VLC attocells (i.e., VLC-enabled LED lu-

minaries) to turn the problem of overlap and thus interference into an advantage,

with PLC used as the network backbone. In JT, all the transmitters jointly serve

17


multiple users. It removes the barriers between attocells and turns the previously

unwanted IAI into constructive signal components. We suggest that since multiple

LED luminaries in the same room are connected to the same power wires, PLC can

be used to serve as a backbone network to support the cooperation among multiple

VLC attocells. A VLC modem in an LED transmitter can receive data from the

very power line that provides its power through a PLC modem, while in comparison

an Ethernet backbone requires modifications in the existing indoor wiring. This co-

ordinated architecture2 can be considered as the VLC counterpart to RF CoMP in

cellular networks [49, 50]. Our numerical results for a typical VLC scenario clearly

demonstrate the improvements of receiver-side signal-to-interference-plus-noise ratio

(SINR) due to the proposed coordination.

Since 2013, considerable research efforts have been directed towards collaborative

designs for VLC systems, most of which focused on JT schemes [51, 52, 53, 54, 55,

56, 57, 58, 59]. JT is typically considered in the context of beamforming design or

frequency allocation among attocells. In [51], pseudo-inverse-based zero forcing (ZF)

and ZF dirty-paper coding were proposed for multi-user multi-input single-output

(MU-MISO) VLC systems, while a generalized-inverse-based ZF scheme was proposed

in [52] to maximize the system sum-rate. In addition, ZF block diagonalization

precoding3 schemes was considered for a multi-user multiple-input, multiple-output

(MU-MIMO) VLC system in [53]. Besides ZF, linear beamforming schemes that

are based on the minimum mean squared error (MMSE) criterion have also been

considered in [54, 55, 56, 57]. Other JT schemes that exploit frequency allocation

have been considered in [58, 59].

Despite their superior performance, the implementation of JT schemes brings two2We note that the backbone network of the coordinated architecture does not have to be PLC.3The concepts of precoding and beamforming are used interchangeably throughout the thesis.

18


major difficulties. First, JT requires tight synchronization among LED transmitters

of different attocells in order to ensure that the signals emitted from different lu-

minaires arrive at the intended user simultaneously. Second, information exchange

among different transmitters should involve not only downlink channel state informa-

tion (CSI), but also the data symbols intended for each user. JT may not be feasible

if the backbone network that interconnects the transmitters together is band-limited.

This is a particular concern considering the fact that PLC has been favored to be an

attractive solution as the backbone network for the VLC front-end [60, 61, 62, 63],

while the power line is a broadcast medium and thus the links to different VLC-

enabled luminaires need to share the PLC capacity.

In order to circumvent such difficulties, researchers have considered other CoMP

schemes that require lower coordination level among attocells to seek a compromise

between system performance and implementation complexity [64, 65, 66, 67, 68, 69,

70]. Unlike JT, those coordination schemes only require the sharing of CSI among

attocells. In addition, symbol-level synchronization among attocells is not required

as each user is served only by its assigned attocell. When the attocells are served by

single-luminaire transmitters, the coordination can be implemented via adaptively

allocating the time [64], frequency [64, 65, 66, 67, 68, 69, 70], or power resources

[68, 69, 70] among different attocells. Such allocation schemes restrain the resources

available to each attocell, and consequently, the overall data rate of the system is

reduced.

In Chapter 3, we propose a coordinated beamforming (CB) scheme for interference

mitigation in downlink multi-cell MU-MISO VLC systems, where different attocells

have multi-luminaire transmitters while each receiver has a single PD. The luminaires

in each transmitter are modulated independently of each other using separate drivers.

19


The excess degrees of freedom offered by such multiple luminaires allow forming more

directive beams towards the intended receivers while minimizing IAI. Compared with

the coordination schemes considered in [64, 65, 66, 67, 68, 69, 70], which are based

on time, frequency, or power allocation, our CB scheme exploits the spatial domain

for both multiplexing and interference mitigation purposes. In fact, our CB scheme

can be integrated with the time and frequency multiplexing techniques considered in

[64, 65, 66, 67, 68, 69, 70] to further enhance the overall system performance.

We also note that the concepts of JT and CB are not new and have been widely

studied for RF channels (see, e.g., [71, 72, 73, 74, 75, 76, 77]). However, since VLC

systems are typically modeled with the amplitude constraint on the channel input (see

Section 1.2.3), the beamforming schemes developed for RF channels are not directly

applicable to VLC transmitters.

Most research works in VLC focus on the downlink transmission, often assuming

the existence of a perfect uplink channel. To realize an uplink, both optical and RF

transmissions are potential candidates. An optical uplink suffers from problems like

energy inefficiency and device glare, and the link between the device and the fixed

uplink receiver can be poor due to user mobility and change in device orientation

[78]. Thus an RF uplink is preferred considering that most places are RF-insensitive.

One choice is a WiFi uplink, because most mobile devices have WiFi radio pre-

installed already. The integration of WiFi uplink with VLC has been discussed in a

number of research works in the literature, e.g., [45, 60, 78, 79, 80]. For VLC systems

using RF uplinks, channel reciprocity is absent and VLC transmitters need to obtain

the channel information from receivers through feedback channels. In a realistic

scenario, the channel information at the transmitter side will not be perfect due to

erroneous or outdated estimation and/or quantization. Imperfect CSI deteriorates

20


the performance of VLC systems, which requires robust designs to counteract the

performance loss. This motivates us to extend our proposed design methods to take

into account possible mismatches in channel information available to the transmitters,

which constitutes the second part of Chapter 2 and Chapter 3.

As has been mentioned in Section 1.2.1, the modulation response of the LED

transmitter is the bottleneck that impedes the capacity enhancement of VLC links.

The typical 3 dB modulation bandwidth of phosphor-based LEDs can be improved

to approximately 20 MHz with blue optical filters at the receiver side for better re-

ception, and the bandwidth is still smaller than the inverse of the maximum excess

delay of the NLoS path in most indoor environments [27]. When the transmit sig-

nal bandwidth is below the cutoff frequency of the LED, the VLC channel can be

approximated as frequency-flat, which is the assumption of both Chapters 2 and 3.

However, as the modulation bandwidth of LEDs gradually increases [28], the VLC

channel cannot be modeled as frequency-flat anymore and the multipath effect in

the VLC channel should be considered. Recently, there has been a growing interest

in applying OFDM to VLC due to its robustness to multipath dispersion, together

with its simple equalization and digital implementation. However, the high PAPR of

time-domain OFDM signals is a key challenge for VLC systems due to the limited

dynamic range of the LED, which will result in the clipping of time-domain OFDM

signal, leading to performance degradation of VLC systems.

In Chapter 4, we apply OFDM to combat the multipath dispersion of VLC signals,

instead of the single-carrier modulation which is considered in Chapters 2 and 3. In

particular, we propose in this chapter a hybrid VLC-PLC (HVP) system architecture

for the indoor downlink transmission and present the analytical framework for the

data rate analysis of the HVP system. To overcome the high PAPR problem, spa-

21


tial optical OFDM (SO-OFDM) [81] is applied across multiple luminaires, for which

we propose several subcarrier allocation schemes to exploit the frequency selectivity

of the VLC and PLC channels. Different possible and meaningful variations of the

HVP system, including the choice of optical OFDM transmission, relay and multi-

ple access schemes, are investigated and compared. The numerical results establish

achievable rates for relevant communication scenarios and highlight the advantages of

the proposed subcarrier allocation schemes in terms of rate and reduced peak power

of optical OFDM signals.

1.4 Remark on Alternating Optimization

The design tasks derived in this thesis are in the form of non-convex optimization

problems. Our main tool to solve these problems is alternating optimization [82, 83].

Throughout the thesis we apply an instance of alternating optimization that di-

vides optimization variables into two groups, and thus the alternation is between two

subproblems. For the problems considered in this thesis, the global optimum can

be found for each subproblem in the respective optimization step. This is because

the subproblems are either convex (Chapters 2 and 3) or classic integer program-

ming problems that can be solved with polynomial-time algorithms (Chapter 4) [84].

Hence, the value of the objective of the original problem improves with every it-

eration of the alternating optimization. Since furthermore the objective functions

considered in this thesis are bounded, we are assured that the objective function will

converge monotonically through alternating optimization [83, Theorem 4.5]. Despite

this structural convergence property, we also set a maximum number of iterations

when applying alternating optimization to the problems in Chapters 2–4, so as to

limit its computational complexity. Beyond this, however, our main focus in this the-

22


sis is the derivation of methods to enable performance-improved VLC transmission

and not the complexity analysis or optimization of computational methods applied

for this purpose.

1.5 Organization of the Thesis

The following chapters are organized as follows. In Chapter 2, we propose a JT

scheme for multiple connected VLC attocells and focus on the linear beamforming

design based on the MMSE criterion. The materials presented in this chapter have

been previously published in [54]. In Chapter 3, we propose a CB scheme for down-

link interference mitigation among coexisting VLC attocells utilizing multi-luminaire

transmitters. Compared to JT schemes, the proposed CB scheme places lower re-

quirements on the network in terms of backbone traffic, and is easier to implement

in a practical deployment, though at the cost of compromised performance. These

results have been submitted for publication. In Chapter 4, we propose a multi-carrier

HVP system as a potential indoor high-speed downlink solution employing the sym-

biotic relationship between PLC and VLC. To exploit the frequency selectivity of

HVP channels, as well as the multi-user and multi-transmitter diversity, we propose

several subcarrier allocation schemes with varying degrees of tradeoff among hard-

ware, computational complexity and performance for meaningful variations of the

HVP system. The materials presented in this chapter have been published in [85].

Finally, Chapter 5 summarizes the contributions of this thesis and outlines areas of

future research.

23

Chapter 2

Joint Transmission in VLC Systems

2.1 Introduction

Indoor environments generally utilize multiple wide-beam luminaires to ensure user-

friendly uniform illumination. From a communications perspective, however, the

use of wide-beam luminaries leads to increased interference levels. To mitigate the

interference across neighboring VLC attocells, this chapter proposes the joint trans-

mission of different transmitters, i.e., LED luminaries, through a backbone network.

The purpose of this coordination is to turn unwanted interference into constructive

signal components. The backbone could be realized by a wired Ethernet or power-

over-Ethernet link. Another convenient manner to realize the backbone is using

existing electrical power wiring for data communications, i.e., PLC [86]. The concept

of integrating PLC and VLC to form a hybrid system for fast data delivery to users

in indoor office buildings and homes is not new [87, 88, 89]. However, since multi-

ple LED luminaries in the same room are connected to the same power wires, PLC

can also be used to serve as a backbone network to support the cooperation among

multiple VLC attocell.

This chapter focuses on the signal processing required at the VLC transmitters

to benefit from coordination [62]. Multiple coordinated VLC emitters form a virtual

multiple-transmitter (or multiple-“antenna”) system. This is quite different from the

indoor multiple-input multiple-output (MIMO) VLC systems for point-to-point com-

24

Chapter 2. Joint Transmission in VLC Systems

munication studied in [90, 91], since we are dealing with the broadcasting of data

to multiple VLC receivers (e.g. cellular phones or tablets) employing single photo-

diode receivers here. Such MU-MISO systems have been widely studied for radio

communication systems, cf. e.g. [71, 72, 77]. However, different from RF wireless

communication, VLC uses IM and the transmitted signal must be non-negative and

constrained in mean amplitude, i.e., average optical power. These differences render

solutions developed for the RF case not directly applicable to VLC systems. We in-

vestigate the effect of different levels of coordination of luminaries in a room, leading

to different numbers of attocells and IAI scenarios. Within a coordinated VLC sys-

tem, linear MMSE precoder design is applied. This allows us to consider interference

from adjacent VLC transmitters that are not coordinated, as well as ambient light

from the sun and other non-VLC lighting devices. Furthermore, this chapter extends

the system design to the case of imperfect knowledge of the VLC transmission chan-

nel. The numerical results highlight the benefits of coordination for VLC attocell

systems by demonstrating significant gains in achievable SINR.

The remainder of the chapter is organized as follows. In Section 2.2, we propose

the JT VLC architecture with PLC as its backbone network. In Section 2.3, precoder

design strategies for VLC MU-MISO transmission with perfect CSI at the transmitter

are developed. In Section 2.4, the designs are extended to the case of imperfect CSI.

Simulation results are presented and discussed in Section 2.5, and finally we conclude

this chapter in Section 2.6.

2.2 System Model and Transmission Scheme

We consider an indoor environment with multiple LED luminaires deployed in a room,

office, laboratory or similar indoor space. The main elements of the coordinated

25


Figure 2.1: Illustration of indoor coordinated VLC broadcast system.

VLC broadcast system are illustrated in Figure 2.1. The luminaires function as VLC

transmitters as a secondary use, and they receive electricity and data through a PLC

backbone network. This enables some of the VLC transmitters, e.g., those connected

to the same distribution box, to operate in a coordinated fashion alike CoMP. Similar

to the definition of a CoMP-cell in the context of RF wireless systems [50], we define

a CoMP-attocell as the area covered by one VLC broadcasting system where all the

transmitters are coordinated by the PLC backbone network. In the case of multiple

CoMP-attocells in one room, there is interference from neighbouring CoMP-attocells,

which is analogous to inter-CoMP-cell interference in RF cellular systems.

2.2.1 VLC Channel

Before discussing the broadcast transmission and VLC-specific constraints, we first

briefly elaborate on channel gain and noise models applicable to the IM/DD channel

26


in VLC.

Each LED luminaire has NE LED elements with a Lambertian radiation pattern.

We assume that LoS propagation of visible light dominates the diffuse propagation

component and thus only the former is considered [90]. Utilizing Eq. (1.2), the

channel gain hkn between the kth user and the nth LED luminaire can be expressed

as [8]

hkn =

NE∑i=1

h(Dkni, φkni

, ψkni) , (2.1)

where Dkni, ψkni

and φkniare the distance, the angle of incidence and the angle

of irradiance between the kth user and the ith LED in the nth LED luminaire,

respectively.

The receiver-side noise term zk (see Eq. (2.7) below) can be written as

zk = ik + nk , (2.2)

where ik is the interference from neighbouring CoMP-attocells with average received

electrical power E(i2k) = σ2ik, and the VLC noise component nk comprises shot and

thermal noise. We assume that nk can be modelled as a zero-mean Gaussian variable

with variance calculated by Eq. (1.3). We observe that Ikrp is dependent on the

DC current and thus illumination level and on user location, via hkn. This renders

the optimization of broadcast transmission intractable. Therefore, we will use a

fixed upper bound for Ikrp in the following optimization. The accurate noise power is

however applied for all numerical results.

Finally, we denote the total interference and noise power at the kth user as

σ2k = E(z2

k) = σ2ik

+ σ2nk. (2.3)

27


2.2.2 Broadcast Transmission

In a VLC CoMP-attocell, NL LED luminaires cooperate to broadcast information

to NU single-photodiode users. OOK is applied in this work due to its popularity

in optical communications and ease of implementation4 [9]. This is accomplished by

modulating a zero-mean data signal onto the DC bias currents IDC = [I1DC, . . . , I

NLDC]T ,

which determine the brightness levels of the NL LED luminaires. In the following,

we describe the pre-processing of this data signal.

Let us denote dk ∈ {±1} the binary data symbol intended for the kth user, and

d = [d1, · · · , dNU]T is the data vector for all users with covariance matrix

Cd = I . (2.4)

The broadcast signal for VLC MU-MISO is generated through linear precoding of

the data vector with the matrix F , i.e.,

s = [s1, . . . , sNL]T = Fd . (2.5)

Finally, the transmitted current signal is given as

x = Fd+ IDC . (2.6)

We note that the conversion to a current signal and the scaling of the binary data

vector d is accomplished through matrix F . Hence, choosing dk ∈ {±1} is without

loss of generality. Furthermore, in VLC transmission, the elements of x need to be4Higher-order pulse-amplitude modulation (PAM) schemes could also be employed in the case

of high SINRs at the receivers. The precoder design would follow a similar approach as shown herefor OOK.

28


non-negative, which imposes constraints on F as we will discuss further below.

Collecting the channel gains hkn from Eq. (2.1) for all NU × NL links into the

channel matrix H = [h1, . . . ,hNU]T = {hkn}NU×NL

, the received signal at the kth

user can be written as

yk = hTkx+ zk = hTk fkdk + hTk∑i 6=k

fidi + zk + hTk IDC , (2.7)

where fk represents the kth column of F . The first term hTk fkdk is the desired signal,

while the second term hTk∑

i 6=k fidi represents the intra-CoMP-attocell interference.

The third term zk is the sum of inter-CoMP-attocell interference and noise as intro-

duced in Eq. (2.2). The fourth term hTk IDC is the DC photocurrent for illumination

that carries no data. It is removed via AC coupling at the receiver side, providing

the information-carrying signal at the kth receiver as

yk = yk − hTk IDC = hTk fkdk + hTk∑i 6=k

fidi + zk . (2.8)

2.2.3 Constraints on Precoding from VLC

Consider the precoding operation in Eq. (2.5), the data signal sn at the nth luminaire

satisfies

− ‖fn‖1 ≤ sn ≤ ‖fn‖1, (2.9)

where fn is the nth row vector of the precoding matrix F . After adding the DC bias,

InDC, to adjust the brightness of each LED luminaire, the electrical transmit signal

(drive current) at the nth LED luminaire is (see Eq. (2.6))

xn = sn + InDC . (2.10)

29


For simplicity, in the following we assume the same brightness level for every LED

luminaire, i.e.,

InDC = IDC , ∀n . (2.11)

Due to optical intensity modulation, xn ≥ 0 and thus sn ≥ −IDC from Eq. (2.10).

However, similar to the nonlinearity of RF transmitters, LEDs also have a limited

linear range [39]. While pre-distortion can be used to (approximately) linearize trans-

mission, signal clipping needs to be avoided. Furthermore, if the LED is over-driven,

not only will LED life-expectancy be reduced, but the self-heating effect will lead to

a drop in the electrical-to-optical conversion efficiency. Considering these character-

istics of LEDs, the transmit signal of each LED luminaire should satisfy

IL ≤ xn = sn + IDC ≤ IU , (2.12)

where IU > IL > 0 represent the upper and the lower bound of the LED drive current

in the linear region. Substituting this into Eq. (2.9), we get

IDC − ‖fn‖1 ≥ IL

IDC + ‖fn‖1 ≤ IU

(2.13)

and the constraint

‖fn‖1 ≤ min (IDC − IL, IU − IDC) (2.14)

for the nth row vector of the precoder matrix F . Note that, via IDC, this constraint

ties possible choices of VLC precoding matrices F to the user-selected illumination

level of the LEDs.

30


2.2.4 Design Objectives

Given the broadcast transmission model Eq. (2.8) and constraint Eq. (2.14), we

optimize the precoding represented by F in two ways. First, we consider the perhaps

more obvious design task of maximizing the performance of MU-MISO VLC under

illumination constraints, i.e., a given value of IDC. As an appropriate performance

measure for MU-MISO VLC we adopt the sum-MSE. Secondly, we consider a VLC

performance target represented by a given set of MSE thresholds for all users, and

find the minimal illumination level required to maintain performance. This design

provides a guaranteed VLC performance under different dimming levels. The two

design objectives are pursued in Section 2.3, assuming perfect CSI, i.e., channel gains

hkn (Eq. (2.1)), are available at the VLC transmitters. In Section 2.4, we extend

our derivations to the practically relevant case of imperfect channel knowledge at the

transmitter.

2.3 Transmitter Design with Perfect Channel

Information

As mentioned above, the performance metric for precoder design adopted in this sec-

tion is the sum MSE, which has widely been considered for precoding optimization in

RF wireless MIMO/MISO systems, e.g., [92]. In particular, we consider the modified

MSE [93] between the received signal yk at the kth user and original data dk given

by

MSEk = Edk,zk{‖cyk − dk‖2

2

}= Ed,zk{‖c(h

TkFd+ zk)− eTk d‖2

2} , (2.15)

31


where c is a scaling term, which does not need to be applied at the receiver but offers

a required degree of freedom in the receiver filter optimization, and ek denotes the

kth standard basis vector for the NU-dimensional space,

ek = [01×(k−1) 1 01×(NU−k)]T . (2.16)

2.3.1 Sum-MSE Minimization Problem

We first consider the sum-MSE minimization under illumination constraints. In this

case, the precoder optimization problem can be formulated as

P1 : (F ∗, c∗) = argminF ,c

NU∑k=1

MSEk

C1 : ‖fn‖1 ≤ min (IDC − IL, IU − IDC) ,∀n (2.17)

Using Eq. (2.15), the objective function in P1 can be written as

f(F , c) =

NU∑k=1

MSEk = Ed,z{‖cy − d‖2

2

}. (2.18)

The optimization problem P1 is not jointly convex in precoder F and scaling factor

c. We therefore use an alternating optimization approach to, possibly suboptimally,

solve this problem. Specifically, we iteratively optimize F and c while fixing the other

variable (see Algorithm 2.1).

32


Fixing Receiver Gain c

We assume a fixed receiver gain c and then optimize the precoder F . In this case, it

is convenient to define

σ2sum =

NU∑k=1

σ2k (2.19)

and to write the sum-MSE as

Ed,z{‖cy − d‖2

2

}= Ed,n

{‖c(HFd+ z)− d‖2

2

}= ‖c(H ⊗ I)vec(F T )− vec(I)‖2

2 + c2σ2sum .

(2.20)

Then, defining b = vec(I), A = H ⊗ I, f = vec(F T ), and V as the NLNU ×NLNU

block-diagonal matrix of the NL×NU all-one matrix, problem P1, for a fixed gain c,

can be transformed into

P2 : (f ∗, t∗) = argminf,t

‖cAf − b‖22 + c2σ2

sum

C1 : −t � f � t ,

C2 : V t ≤ min (IDC − IL, IU − IDC) 1NU×1 , (2.21)

where vector t is a slack variable. The constraints in this optimization problem are

equivalent to the L1-norm constraint (Eq. (2.14)) resulting from the limited dynamic

range of the LED. This problem is a convex quadratic programming problem and can

be efficiently solved using, e.g., the YALMIP or CVX toolbox [94, 95, 96].

33


Fixing Precoder F

Now we assume the precoder matrix F as fixed and optimize for c. The optimization

problem P1 with fixed precoder F can be simplified into

P3 : c∗ = argminc‖cAf − b‖2

2 + c2σ2sum .

The optimal c∗ can now be computed as

c∗ =sym(bTAf)

‖Af‖22 + σ2

sum

, (2.22)

where

sym(X) =X +XT

2(2.23)

represents the symmetric part of a matrix X.

Algorithm 2.1 Alternating optimization algorithm for P11. Initialization:

p⇐ 0.Update H with CSI.Initialize {F }.

2. repeat3. Update c according to Eq. (2.22).4. Solve P2 and get F .5. p⇐ p+ 1.6. until ‖MSEp+1 −MSEp‖ ≤ δ (δ is a predefined threshold) or p = pmax (pmax

is a predefined maximum iteration number), where MSE =∑NU

k=1 MSEk.

34


2.3.2 Minimal Illumination Level Problem

We now turn to the question of what is the minimal illumination level needed to

maintain a certain VLC performance. This is important for illumination systems

with dimming, for which VLC should be supported. Illumination is proportional to

IDC, which via Eq. (2.14) affects VLC precoding. Measuring VLC performance in

terms of MSE and denoting by qk the constraint for the MSE of the kth user, the

corresponding optimization problem can be formulated as

P4 : (F ∗, c∗, I∗DC) = argminF ,c,IDC

IDC

C1 : MSEk ≤ qk,∀k (2.24)

C2 : ‖fn‖1 ≤ min (IDC − IL, IU − IDC) ,∀n

Writing

MSEk = (chTkF − eTk )(chTkF − eTk )T + c2σ2k (2.25)

and defining

ζ = 1/c,

vTk = (hTkF − ζeTk ),

φk = [vTk σk],

(2.26)

the constraint MSEk ≤ qk can be expressed as

‖φk‖2 ≤√qkζ . (2.27)

35


According to the Schur complement lemma [97, 98], inequality Eq. (2.27) is equivalent

to

Θk =

√qkζ φk

φTk√qkζI

� 0 .

Thus, P4 can be reformulated as

P5 : (F ∗, ζ∗, I∗DC) = argminF ,{tk},ζ,IDC

IDC

C1 : −tk � F Tek � tk, ∀k,

C2 : 1T tk ≤ min (IDC − IL, IU − IDC) , ∀k,

C3 : Θk � 0,∀k, (2.28)

where vector tk is a slack variable. The problem is a convex semidefinite programming

problem (SDP) and can be solved efficiently numerically, e.g., [94, 95].

2.4 Robust Transmitter Design with Channel

Uncertainty

The quality of CSI at the transmitter is critical to the precoder design. While the

VLC channel is much more benign than its RF counterpart, the assumption of perfect

CSI is not necessarily practical for MU-MISO VLC. VLC systems use visible light

as the downlink medium, while the uplink medium can be RF, infrared light (IR) or

visible light [14]. In the case of VLC uplink, the uplink-downlink reciprocity will allow

CSI to be estimated at the transmitter. The more practically relevant scenario for

VLC using indoor illumination devices considered here is that an RF uplink is used.

In this case, CSI can only be estimated at the receiver and fed back to the transmitter

36


afterwards. Imperfect CSI can then arise from noisy and quantized channel estimation

and, perhaps more critically, the feedback of outdated estimates. The latter is the

case when the VLC channel varies due to terminal motion and/or changes in the

environment since the last channel update. As an example, Figure 2.2 illustrates a

scenario where the receiver terminal has moved from position p1, at which CSI is

reported, to position p2, at which precoded data using this CSI is received.

2.4.1 Uncertainty Models

Given the channel estimate hk, we can express the true channel gains for the kth

user as

hk = hk + δk , (2.29)

where the error vector δk represents the CSI uncertainty. According to the source of

estimation error, we consider two models for δk.

Noisy CSI

For noisy CSI, we use the stochastic error model [97]

δk ∼ N (0,Σk) , (2.30)

i.e., δk is zero-mean Gaussian distributed with covariance matrix Σk.

37


Figure 2.2: Illustration of outdated CSI resulting from terminal mobility in a VLCsystem.

Outdated CSI

Outdated CSI, due to e.g. a user walking with a terminal device (see Figure 2.2), is

often modelled by a bounded uncertainty model, i.e.,

‖δk‖2 ≤ εk (2.31)

for some error bound εk, which depends on the maximal changes that happened be-

tween CSI estimation and transmission using this estimation. As we show in the

following, εk should be chosen as a function of the terminal location during chan-

nel estimation, i.e., p1 in Figure 2.2. Location information could be obtained from

channel estimation itself using various positioning techniques [99, 100].

Referring to Figure 2.2, we denote L as the bound for the user movement between

two CSI updates, i.e., ‖p1−p2‖2 ≤ L. Furthermore, considering a single transmitter,

let dv and dh be the vertical and horizontal distance between transmitter and receiver,

38


respectively, as indicated in Figure 2.2. Then, for terminal movement in the horizontal

direction, horizontal planes at the LED transmitter and photodiode receiver, the error

bound

εk = max{ε+, ε−} (2.32)

can be obtained, where

ε+ = β(

(d2v + d2

1)−m+3

2 − (d2v + (d1 + L)2)−

m+32

), (2.33)

ε− = β(

(d2v + (d2 − L)2)−

m+32 − (d2

v + d22)−

m+32

), (2.34)

β =(m+ 1)NEsγκ

2APDdm+1v

2π sin2(ψc), (2.35)

and d1 and d2 satisfy

log

(d1

d1 + L

)=m+ 5

2log

(d2v + d2

1

d2v + (d1 + L)2

), (2.36)

log

(d2

d2 − L

)=m+ 5

2log

(d2v + d2

2

d2v + (d2 − L)2

). (2.37)

The details of the derivation of (2.32)–(2.37) are delegated to Appendix A. For the

more general case including multiple transmitters, the relationship between error

bound and physical system parameters is even more complicated than (2.32). We

thus resort to numerical analysis to obtain error bounds. As an example, Figure 2.3

shows εk as a function of the user location and the maximal location distance L. The

details of the room, illumination and VLC setup for this experiment are described in

Section 2.5.

In the following, we consider both uncertainty models to formulate robust precoder

designs. Similar to the RF wireless case, cf. e.g. [97, 98], we aim at optimizing average

performance for noisy CSI according to the stochastic model (2.30) and worst-case

39


−2

−1

0

1

2

−2

−1

0

1

2

0.5

1

1.5

x 10−5

x (m)y (m)

(a)

−2

−1

0

1

2

−2

−1

0

1

2

1

1.5

2

2.5

3

x 10−5

x (m)y (m)

(b)

Figure 2.3: Error bounds obtained from simulation for (a)L = 0.25 m, (b)L = 0.5 m.Illumination and VLC setup for these results are described in Section 2.5.

performance for outdated CSI with the bounded error model (2.31).

2.4.2 Sum-MSE Minimization Problem

We start with the sum-MSE minimization problem.

Robust Design with Outdated CSI

The robust broadcast precoder design for CSI uncertainty according to Eq. (2.31) is

an extension of P1 in Eq. (2.17):

P6 : (F ∗, c∗) = argminF ,c

max‖δk‖2≤εk

NU∑k=1

MSEk


40


where

MSEk = ‖c(hTk + δTk )F − eTk ‖22 + c2σ2

k . (2.39)

Using results from [97], P6 can be transformed into

P7 : (F ∗, c∗) = argminF ,{tk},λ,µ,g,c

g2

C1 : −tk � F Tek � tk, ∀k,


C3 : Ψk � 0,∀k,

C4 : Φ � 0 , (2.40)

where

Φ =

g λT cσsum

λ gI 0

cσsum 0 g

,

Ψk =

λk − µk 0T ch

T

kF − eTk

0 µkI εkcF

(chT

kF − eTk )T εk(cF )T λkI

.

Similar to the optimization problem P1, we can obtain a local optimum of this prob-

lem by alternatively optimizing over F and c. Each problem is an SDP problem and

can be efficiently solved numerically, e.g., [94, 95].

41


Robust Design with Noisy CSI

As noted above, the average sum-MSE is considered. Defining

∆ = [δ1, . . . , δNU]T , (2.41)

the optimization problem can be formulated as

P8 : (F ∗, c∗) = arg minF ,c

E∆

(NU∑k=1

MSEk

)


Following the steps in Eq. (2.18) and Eq. (2.20) and assuming Σk = σ2eI, we can

write the objective of P8 as

E∆ (f(F , c)) = (‖cAf − b‖22 +NUσ

2ec

2‖f‖22) + c2σ2

sum , (2.43)

where A = H⊗I, and H is the estimated channel matrix. While P8 is not a convex

optimization problem, again the application of alternating optimization for F and c

turns out to be a suitable approach. When fixing the receiver gain c, we can optimize

for F via

P9 : (f ∗, t∗) = argminf,t

(‖cAf − b‖22 +NUσ

2ec

2‖f‖22) + c2σ2

sum (2.44)

C1 : −t � f � t ,

C2 : V t � min (IDC − IL, IU − IDC) 1NU×1 .

42


This problem is a convex quadratic programming problem, which is solved numeri-

cally. Fixing the precoder F leads to the closed-form solution

c∗= argminc{‖cAf − b‖2

2 +NUσ2ec

2‖f‖22}+ c2σ2

sum

=sym(bT Af)

‖Af‖22 +NUσ2

e‖f‖22 + σ2

sum

.(2.45)


We finally turn to the robust design for minimizing the required illumination level

while achieving a required VLC performance.

Robust Design with Outdated CSI

To add robustness to the precoder design for minimal required brightness when CSI

is outdated, the worst-case MSE needs to satisfy the required performance qk:

max‖δk‖2≤εk

MSEk ≤ qk,∀k. (2.46)

Making use of the Schur complement lemma [97, 98] and [101, Lemma 2], Eq. (2.46)

is equivalent to ∃ λk ≥ 0,

Ψk =

√qkζ − λk vTk σk 0

vk√qkζI 0 −εkF T

σk 0√qkζ 0

0 −εkF 0 λkI

� 0,

where

vTk = (hTkF − ζeTk ) . (2.47)

43


Hence, we obtain the optimization problem

P10 : (F ∗, ζ∗, I∗DC) = argminF ,λ,ζ,IDC

IDC

C1 : −tk � F Tek � tk,∀k,


C3 : Ψk � 0, ∀k,

C4 : λk ≥ 0,∀k. (2.48)

This problem is an SDP and the global optimum can be obtained on the condition

that it is feasible.

Robust Design with Noisy CSI

In the case of noisy CSI, we need to replace C1 in P4 (2.24) by

Eδk(MSEk) = c2vTk vk + c2σ2e‖F ‖2

F + c2σ2k . (2.49)

Introducing auxiliary variable r and τ k = [vTk r σk], Eδk(MSEk) ≤ qk becomes

equivalent to

‖τ k‖2 ≤√qkζ

‖F ‖F ≤r

σe

(2.50)

44


Therefore, we can formulate the precoder design problem as

P11 : (F ∗, ζ∗, I∗DC) = argminF ,{tk},{τk},ζ,r,IDC

IDC

C1 : −tk � F Tek � tk,∀k

C2 : 1T tk ≤ min (IDC − IL, IU − IDC) ,∀k

C3 : ‖F ‖F ≤r

σe,

C4 : Υk � 0,∀k (2.51)

where

Υk =

√qkζ τ k

τ Tk√qkζI

.

This problem is again an SDP.

2.5 Numerical Results and Discussions

In this section, we present and discuss the simulation results for the proposed MU-

MISO VLC system assuming different coordination levels, user positions, interference

levels and channel uncertainty scenarios in an indoor environment. We consider an

example setup of a room with NL = 4 coordinated and VLC-enabled LED luminaires

at the ceiling. Room dimensions and luminaire locations are listed in Table 2.1. The

table also summarizes the luminaire and LED parameters, where the latter apply

to LXW8-PW40 Luxeon Rebel high power LEDs [102]. The illuminance level when

IDC = 500 mA, i.e., IDC = (IL + IU)/2, with this system setup is shown in Figure 2.4.

According to [38], the illuminance level and uniformity (0.645 in this case) is sufficient

for office work and study. The background current of Ibg = 5100 µA accounts for

45


Table 2.1: Simulation parameters.

Room SetupFixture coordinate 1 [1.25, 1.25, 3]Fixture coordinate 2 [1.25, -1.25, 3]Fixture coordinate 3 [-1.25, -1.25, 3]Fixture coordinate 4 [-1.25, 1.25, 3]Room Dimensions L × W × H 5 [m] × 5 [m] × 3 [m]

Transmitter ParametersIL 400 [mA]IU 600 [mA]Semi-angle at half power φ 1

260 [deg.]

Dimensions of LED L × W × H 3 [cm]×3 [cm]×2 [cm]LED interval 1 [cm]Number of LEDs per luminaire NE 36 (6×6)

Receiver ParametersPD area 1 cm2

Refractive index of optical concentrator κ 1.5Receiver FOV 60 [deg.]System bandwidth B 10 [MHz]Noise bandwidth factor I2 0.562Background current Ibg 5100 [µA]LED conversion factor s 0.44 [W/A]PD responsivity γ 0.30 [A/W]

ambient light from other sources such as sunlight or non-VLC enabled luminaries,

and the thermal noise is considered negligible [8].5

In the following, we assume that the VLC system transmits to NU = 4 users. For

concreteness, we further assume that the four users are centro-symmetrically located

on the plane at height z = 0.8 m, i.e., the user coordinates are (±x,±y, 0.8) m for

some x and y. We would like to emphasize that the specific system parameters, in

particular the values of NL and NU, are chosen for the sake of illustration of precoded

transmission only, and that our system design approach is applicable to any parameter5We also ran simulations assuming Ibg value of 620 µA [27]. We found that the main trends of

our results as discussed in the following are not affected by the value of the background current.

46


−2

−1

0

1

2

−2

−1

0

1

2

200

300

400

500

600

700

x (m)y (m)

Illu

min

an

ce (

lx)

Figure 2.4: The distribution of indoor illuminance when IDC = 500 mA.

pair (NL, NU).

In the subsequent sections, we report performance results for different transmis-

sion scenarios and precoder designs. Due to symmetry, the performance for the

NU = 4 users are identical, and thus we can drop the user index for the results. If

not stated otherwise, perfect CSI for the precoder design is assumed. For solving

the sum-MSE minimization problems via alternating optimization, the alternating

minimization will converge to a solution since the non-negative objective function

is minimized at each convex subproblem. The zero-forcing solution is used for ini-

47


tialization and the maximum number of iterations6 is set to 20. For solving the

convex optimization problems in this chapter, we use the YALMIP toolbox [94] in

conjunction with the MOSEK solver [103] to obtain the result numerically.

2.5.1 User Position with Joint Transmission Setup

We first investigate the achievable performance for a VLC broadcast system where

LED luminaries are fully connected by a PLC backbone network and coordinated by

a PLC controller. The users are arranged in three different setups as shown in the

first three arrangements in Fig. 2.5, where x = y = 0.5 in Setup I, x = y = 1.25 in

Setup II and x = y = 2 in Setup III, respectively. The channel matrices for these

three setups are obtained as

H I = 10−5

6.164 3.067 1.829 3.067

3.067 6.164 3.067 1.829

1.829 3.067 6.164 3.067

3.067 1.829 3.067 6.164

,

H II = 10−5

9.340 1.788 0.731 1.788

1.788 9.340 1.788 0.731

0.731 1.788 9.340 1.788

1.788 0.731 1.788 9.340

,

6The maximum number of iterations for Chapters 3 and 4 is also set to 20.

48


Figure 2.5: User-configurations for MU-MISO VLC are considered for numericalresults.

H III = 10−5

6.164 0.863 0.000 0.863

0.863 6.164 0.863 0.000

0.000 0.863 6.164 0.863

0.863 0.000 0.863 6.164

.

Figure 2.6 shows the results of the sum-MSE minimization problem as a function

of the DC bias IDC, i.e., the illumination level, for the three user-configurations from

Figure 2.5. Here we use the resulting optimal precoder to calculate the corresponding

SINR defined as

SINR =‖hTkwk‖2

2

‖hTk∑

i 6=k wi‖22 + σ2

k

. (2.52)

First, we observe that the system performance is symmetric with respect to IDC =

(IL + IU)/2. The SINR first increases as the DC bias IDC increases and then starts

to decrease after IDC surpasses (IL + IU)/2. This is because the electrical SINRs at

the receivers reach their maximal values when the precoded signal sn has the largest

dynamic range. Due to this symmetry property, we will only plot the results for IDC

ranging from IL to (IL + IU)/2 in the following figures. For varying positions of the

49


400 420 440 460 480 500 520 540 560 580 600−5

0

5

10

15

20

25

30

35

40

IDC (mA)

SIN

R (

dB

)

Setup I

Setup II

Setup III

Figure 2.6: Comparison of system performance with different user positions (as shownin Figure 2.5) as a function of illumination level. Sum-MSE minimization with perfectCSI.

50


four users, the setups in increasing order of SINR value are Setup I, Setup III and

Setup II. An intuitive explanation is that since the users in Setup I are closer to

each other than in Setup III, the channels are more similar and thus more difficult to

separate through precoding. Meanwhile, the distances between the LED luminaries

and users in Setup III are larger than those in Setup II, which leads to smaller channel

gains in Setup III than in Setup II.

The SINR defined in (2.52) can be used to approximate the symbol error rate

(SER) of the VLC transmission. For this, we assume that the interference is Gaussian

distributed, so that the SER can be expressed as [104]

SER = Q(√

2 SINR), (2.53)

where Q(·) is the Gaussian tail probability function. In Figure 2.7, we plot the SER

according to (2.53) as the function of DC bias IDC under Setup I. We also include the

SER results obtained from Monte Carlo simulations of the tranmission. We observe

that the two curves do not closely overlap, which speaks to the inaccuracy of the

Gaussian approximation for the VLC interference. We expect that this approxima-

tion becomes more accurate if more interferers are present as well as if high-order

modulation is used. Furthermore, as expected, we note that SER monotonically im-

proves with SINR also in the simulated SER case. Hence, we can well consider SINR

as a proxy for the SER performance.

We now highlight the benefit of coordination. To this end, we consider three

different coordination levels:

1. Joint Transmission (JT): Transmissions for all four LED luminaires are coordi-

nated.

51


400 405 410 41510

−6

10−5

10−4

10−3

10−2

10−1

100

IDC

(mA)

Sym

bol

Err

or

Rate

(S

ER

)

SER calculated with Equation (2.53)

SER with Monte Carlo simulation

Figure 2.7: Comparison of the SER calculation using Equation (2.53) with MonteCarlo simulation result.

52


(1) JT (2) PC (3) UT

LED Luminaire

CoMP-Attocell

Power Line PLC Controller

Figure 2.8: Different transmitter coordination levels in an MU-MISO VLC system.

2. Partial Coordination (PC): Transmissions for LED luminaires in the first and

the fourth quadrant and for LED luminaires in the second and the third quad-

rant are coordinated. Thus there exist two VLC CoMP-attocells in one room.

3. Uncoordinated Transmission (UT): Transmissions at the four LED luminaires

are not coordinated, which corresponds to four VLC CoMP-attocells in one

room.

The three coordination levels are illustrated in Fig. 2.8.

We consider two scenarios for user locations: Setup IV with x = 2, y = 1.25 and

Setup V with x = 0.5, y = 1.25. Figure 2.9 shows the SINR for precoder design

minimizing the sum-MSE as a function of IDC for different coordination levels and

user position scenarios. We observe that, since users are located closer to each other

and/or the neighbouring CoMP-attocell boundary in Setup V than for Setup IV, the

achievable SINR is generally higher for the latter. We can also see the significant SINR

increase due to coordination. In particular, the JT setup is clearly outperforming the

53


400 410 420 430 440 450 460 470 480 490 5000

5

10

15

20

25

30

35

IDC

(mA)

SIN

R (

dB

)

JT

PC

UT

Setup V

Setup IV

Figure 2.9: Comparison of system performance with different transmitter coordina-tion. Sum-MSE minimization problem with perfect CSI.

PC and UT systems, whose SINR saturates quickly due to inter-cell interference.

For Setup V, there is no performance difference for UT and PC systems, which

is due to the remaining large inter-CoMP-attocell interference in spite of the partial

coordination. In the PC system, each VLC transmitter tends to mostly communicate

to its closest receiver, which makes the PC system equivalent to a UT system.

The benefit of coordination is further demonstrated by the plots in Figure 2.10,

which show the SINR for one quadrant of the room as a function of the user’s location

(because of the symmetry of the four user’s location, the SINR plots for the other

54


0 0.5 1 1.5 2 2.50

0.5

1

1.5

2

2.5

x (m)

y (

m)

−5

0

5

10

15

20

25

30

35

40SINR (dB)

(a) JT system

0 0.5 1 1.5 2 2.50

0.5

1

1.5

2

2.5

x (m)

y (

m)

−5

0

5

10

15

20

25

30

35

40SINR (dB)

(b) UT system

Figure 2.10: SINR as a function of user location in one quadrant of the room andIDC = (IL + IU)/2. Sum-MSE minimization problem with perfect CSI.

quadrants are mirrored versions of those in Figure 2.10) and for IDC = (IL + IU)/2.

It can be seen that the SINR is severely IAI-limited in the UT case, and that this

problem can be overcome by coordination. In particular, the SINR for the JT system

is uniformly high in almost the entire service area. Note that the lower SINR at the

cell boundaries is an artifact of assuming centro-symmetrical user locations in our

experiments, which means that at cell boundaries users are close to each other and

thus interference is relatively high.

2.5.2 Sum-MSE Minimization with Channel Uncertainty

We now abandon the assumption of perfect CSI and consider channel uncertainty

according to the models from Section 2.4.1. For the case of outdated CSI, we consider

an assumed user location based on which we obtain a channel estimate hk. Then,

given a distance bound L, we obtain a CSI bound εk from numerical evaluation as

55


shown in Section 2.4.1 (see Figure 2.3). Given hk and εk, the precoder F is obtained

via P7 (2.40). Then, a set of actual channel gains h and associated SINRs (2.52) are

generated by placing users uniformly at random into the uncertainty region. For the

noisy CSI case, we use Σk = σ2eI and specify the error variance σ2

e .

Figures 2.11 and 2.12 show the SINR performance for the JT system with robust

precoder design according to the sum-MSE criterion. The results are shown as a

function of the channel uncertainty and parametrized with DC bias IDC. Setup II

from Figure 2.5 with x = 1.25 and y = 1.25 is used to calculate the channel estimate

hk and 5000 possible channel realizations hk either according to the uncertainty

bound εk or the normalized error standard deviation σe = σe/(‖vec(H)‖1/(NLNU)).

The minimum achieved SINR among channel realizations is plotted for the case of

outdated CSI, while the average SINR over channel realizations is plotted for the case

of noisy CSI. From the figures, we can see that system performance improves as the

DC bias IDC increases, until the CSI uncertainty at the transmitter limits the SINR.

Furthermore, the decline of SINR with uncertainty is less pronounced for the average

performance measure considered in Figure 2.12. The worst-case optimization for the

case of outdated CSI provides performance guarantees, which however diminish with

increasing uncertainty, as shown in Figure 2.11.


We again consider the Setup II from Figure 2.5 with x = 1.25 and y = 1.25, and

JT. Figure 2.13 shows the minimum illumination level, i.e., DC bias IDC, that is

required to meet the VLC MSE levels qk of each user terminal. The different curves

are for perfect CSI (L = 0) and outdated CSI (L > 0), and they quantify to what

extent VLC is possible when lights are dimmed. The perfect CSI case shows the best

56


0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.515

20

25

30

35

40

L (m)

SIN

R (

dB

)

IDC = 425mA

IDC = 450mA

IDC = 475mA

IDC = 500mA

IDC

Figure 2.11: Robust sum-MSE minimization with outdated CSI. Setup II with x =1.25 and y = 1.25.

possible trade-off between illumination level and achievable performance. When CSI

uncertainty comes into play, it increases the required illumination level and even-

tually limits the achievable performance. That is, the larger the uncertainty region

(quantified by L), the earlier the problem becomes infeasible, i.e., MSE constraints

cannot be met regardless of illumination level.

2.5.4 Comparison between Robust and Non-Robust Design

Finally, we illustrate the benefits of the robust design in the case of CSI uncer-

tainty. To this end, Figure 2.14 compares the SINR performances of the robust and

57


10−3

10−2

10−1

100

5

10

15

20

25

30

35

40

σe

SIN

R (

dB

)

IDC = 425mA

IDC = 450mA

IDC = 475mA

IDC = 500mA

IDC

Figure 2.12: Robust sum-MSE minimization with noisy CSI. Setup II with x = 1.25and y = 1.25.

non-robust precoder designs when CSI is outdated. Similar to Figure 2.10, SINR

performance for one quadrant of the room is plotted as a function of the assumed

user location, according to which hk is obtained. The actual user location is sampled

in a circle with radius L, from which the channel gain hk follows. Figure 2.14 shows,

for each assumed location, the minimum SINR over the uncertainty region. The DC

current IDC is fixed as IDC = (IL + IU)/2.

We observe that especially for locations close to the boundaries of two cells the

robust design significantly outperforms the non-robust approach. This is due to

the possibly large mismatch between assumed and actual channel gains, which also

58


10−4

10−3

10−2

10−1

100

400

410

420

430

440

450

460

470

480

490

500

qk

I DC

(m

A)

L = 0.00 m

L = 0.25 m

L = 0.50 m

Figure 2.13: Robust illuminance minimization with perfect (L = 0) and outdated(L > 0) CSI. Setup II with x = 1.25 and y = 1.25.

affects the expected amount of interference, and which is not taken into account

in the non-robust design approach. For example, for the case of L = 0.25 m, the

average SINR value on the boundaries of two cells is improved from −25.99 dB to

−0.69 dB via the robust design. On the other hand, closer inspection of the results

shows that for locations further from the boundaries between cells, the precoder from

the non-robust design achieves a somewhat better SINR than the robust precoder.

For example, at the location (x, y) = (0.375, 1.000), the worst-case SINR for the

robust design is 4.4 dB, while it is 6.2 dB for the non-robust design. The reason for

this is the conservativism of the robust design, which considers the worst case for

59


all hypothetical gains from the bounded region Rk ={hk

∣∣∣hk=hk+δk‖δk‖2≤εk

}, even though

only a subset of these channel gains do actually occur inside the location uncertainty

region. Nevertheless, the results in Figure 2.14 demonstrate the advantage of the

robust optimization for VLC broadcasting in the case of imperfect CSI, in that the

SINR is more consistently high over the entire attocell area and when different users

are close to each other.

2.6 Conclusion

In this chapter, we have studied transmission to multiple user terminals using VLC

attocells. Considering the inter-attocell interference as a result of the broadcast na-

ture of VLC, we have proposed the coordination of transmission in different attocells.

These coordinated VLC attocells form CoMP-attocells, similar to CoMP-cells in RF

cellular networks. We have derived new linear precoding schemes that reduce intra-

CoMP-attocell interference with the objective of optimizing system performance given

an illumination level and retaining a required performance at minimal illumination

level, respectively. Our numerical results for a typical VLC scenario have clearly

demonstrated the improvements of receiver-side SINR due to the proposed coordina-

tion. As a second important contribution, we have extended the precoding methods

to include channel uncertainty, which would occur, for example, in the case of mov-

ing terminals. Simulation results have shown that these robust precoding schemes

mitigate performance drops that stale channel information causes when assumed to

be accurate.

60


0 0.5 1 1.5 2 2.50

0.5

1

1.5

2

2.5

x (m)

y (

m)

−15

−10

−5

0

5

10

15

20

25

30

35SINR (dB)

(a) Robust Design (L=0.25m)

0 0.5 1 1.5 2 2.50

0.5

1

1.5

2

2.5

x (m)

y (

m)

−15

−10

−5

0

5

10

15

20

25

30

35SINR (dB)

(b) Non-Robust Design (L=0.25m)

0 0.5 1 1.5 2 2.50

0.5

1

1.5

2

2.5

x (m)

y (

m)

−15

−10

−5

0

5

10

15

20

25

30

35SINR (dB)

(c) Robust Design (L=0.5m)

0 0.5 1 1.5 2 2.50

0.5

1

1.5

2

2.5

x (m)

y (

m)

−15

−10

−5

0

5

10

15

20

25

30

35SINR (dB)

(d) Non-Robust Design (L=0.5m)

Figure 2.14: Comparison between robust and non-robust design for sum-MSE mini-mization problem with outdated CSI.

61

Chapter 3

Coordinated Beamforming in VLC

Systems

3.1 Introduction

As we can see from the previous chapter, uncoordinated VLC attocells will strongly

interfere with each other. In fact, it has been shown that the degradation in SINR for

users at the edge of the attocell can be as severe as 30 dB. The proposed JT scheme

can greatly enhance the user performance through transmitter cooperation. However,

both the global user data and channel state information need to be exchanged among

transmitters of different attocells in the JT scheme, which puts a high requirement

on the backbone network. What is more, in order to ensure that signals emitted from

different transmitters arrive at the receiver at the same time, tight synchronization

is required among the scattered VLC transmitters. In this chapter, we propose the

CB scheme for downlink interference mitigation among coexisting VLC attocells uti-

lizing multi-luminaire transmitters. Compared to the JT scheme, the proposed CB

scheme places lower requirements on the network in terms of backbone traffic, and

is easier to implement in a practical deployment, though at the cost of compromised

performance. In this chapter, we investigate the downlink transmission of coordi-

nated VLC attocells and focus on its transmitter design. We adopt the weighted sum

mean square error (WSMSE) as the performance metric to take into consideration

62

Chapter 3. Coordinated Beamforming in VLC Systems

interference, noise, and fairness among users in system optimization. We consider

the WSMSE minimization problem with linear beamforming restricted by amplitude

constraints. Such constraints arise from dynamic range limitations in typical LEDs.

Moreover, similar to Chapter 2, we extend our design method to take into account

possible mismatches in channel information available to the transmitters. We provide

numerical examples to illustrate the performance of the proposed CB scheme in typi-

cal VLC scenarios. We also quantify the performance gap among several coordination

schemes including JT and CB.

The remainder of the chapter is organized as follows. We introduce the system

model and transmission scheme in Section 3.2. In Section 3.3, the design algorithms

for CB are proposed assuming perfect downlink CSI at VLC transmitters. In Section

3.4, the design for CB is extended to the case of imperfect CSI. Numerical results

and discussions are provided in Section 3.5, and finally, we conclude the chapter in

Section 3.6.

3.2 System Model and Transmission Scheme

In this section, we first describe the system model and transmission scheme for the

considered multi-cell VLC system. We then specify the constraints imposed on the

linear beamformer to satisfy the amplitude constraints on the transmitted signal.

3.2.1 System Model

We consider a downlink VLC system composed of NA coordinated attocells that can

exchange information with each other through a band-limited backbone network (see

Figure 3.1). Each attocell is composed of one VLC transmitter that employs NL

LED luminaires, and each luminaire has NE LED bulbs. Such luminaires can be

63


Centralized Controller

NA VLC attocells

Backbone

Network

Multi-luminaire VLC transmitter LED luminaire Single-photodiode VLC user

NL Luminaires per

Transmitter

Figure 3.1: Illustration of the CB structure.

modulated independently of each other using separate drivers. Each attocell serves

NU single-PD users, and each user is served by a single attocell. Therefore, we have

a multi-cell MU-MISO scenario.

3.2.2 Transmission Scheme

We considerM -ary pulse amplitude modulation (M -PAM) as the modulation scheme,

with M = 2, 4, 8, 16, . . . . Let dik ∈ {−1, 3−MM−1

, 5−MM−1

, . . . , 1}, i = 1, . . . , NA, k =

1, . . . , NU, denote the data symbol intended for the kth user in the ith attocell, and

let di = [di1 , . . . , diNU]T denote the vector of data symbols intended for all the users in

the ith attocell. Note that the entries of di are independent, and thus the covariance

64


matrix of di is η2I, where I represents the identity matrix and

η =

√M + 1

3(M − 1). (3.1)

Using linear beamforming, the transmitted signal vector at the ith attocell is con-

structed as

xi = F idi + I iDC , (3.2)

where F i ∈ RNL×NU is the beamforming matrix, and I iDC = [I i1DC, Ii2DC, · · · , I

iNLDC ]T is

a DC term that sets the illumination level. Note that the zero-mean nature of the

data vector di ensures that the illumination level is unaffected by data transmission.

For the kth user in the ith attocell uik , the received signal can be decomposed into

three parts:

1) Intra-attocell Signal: We use yintraik

to represent the signal component generated

within the ith attocell and it is given by

yintraik

= hTikixi = hTikifki dik + hTiki

NU∑m=1,m 6=k

fmi dim + hTikiIiDC , (3.3)

where hikj ∈ RNL×1 denotes the channel gain vector between uik and the VLC trans-

mitter of the jth attocell, and fki is the kth column vector of F i.

2) Inter-attocell Interference: Besides the intra-attocell signal, user uik also re-

ceives interfering signals from neighboring attocells. The total interfering signal from

all the other attocells yinterik

can be expressed as

yinterik

=

NA∑j=1,j 6=i

hTikjxj =

NA∑j=1,j 6=i

NU∑m=1

hTikjfmj djm +

NA∑j=1,j 6=i

hTikjIjDC . (3.4)

65


3) Receiver noise: The dominant noise at user uik , denoted as nik , can be modelled

as a zero-mean Gaussian variable with variance calculated by Eq. (1.3), where the

average current due to the useful received signal at the user uik , Iik (Irp in Eq. (1.3)),

can be calculated by

Iik =

NA∑j=1

hTikjIjDC . (3.5)

The total received signal yik at user uik is the sum of the three components mentioned

above, and can be expressed as

yik = yintraik

+ yinterik

+ nik (3.6)

= hTikifki dik︸︷︷︸

desired signal

+ hTiki

NU∑m=1,m 6=k

fmi dim︸︷︷︸intra-attocell interference

+

NA∑j=1,j 6=i

NU∑m=1

hTikjfmj djm︸︷︷︸

inter-attocell interference

+

NA∑j=1

hTikjIjDC︸︷︷︸

DC photocurrent

+ nik︸︷︷︸noise

.

At the receiver, the DC component∑NA

j=1 hTikjIjDC is removed via AC coupling, leaving

the information-carrying signal at uik as

yik = yik −NA∑j=1

hTikjIjDC . (3.7)

3.2.3 Design Constraints

For the illumination uniformity of the indoor environment, we shall assume that all

the LEDs are driven by an equal DC bias, i.e.,

I ikDC = IDC, ∀i, k. (3.8)

66


For typical current-driven LEDs, though the nonlinear characteristic for current-

light conversion can be compensated by pre-distorters installed before the LED, the

dynamic range of LEDs is still inherently limited. Thus, the current signal should

satisfy a certain amplitude constraint to avoid signal clipping. To ensure that the

LED operates within its physical limits, the beamforming matrix F i should satisfy

the constraint (2.14):

‖fki ‖1 ≤ min (IDC − IL, IU − IDC) , ∀i, k, (3.9)

where fki represents the kth row in F i, and IU > IL > 0 represent the upper and the

lower bound of the LED drive current in the linear region.

3.3 Transmitter Design with Perfect Channel

Information

Similar to Chapter 2, we consider MMSE beamforming design in this chapter. Linear

beamformers can achieve reasonable throughput performance with considerably lower

complexity relative to their nonlinear counterparts. Two major linear beamforming

techniques are ZF beamforming and MMSE beamforming. ZF beamforming cancels

out multi-user interference through channel inversion. However, ZF is infeasible when

the number of luminaries in each attocell is less than the total number of users of all

the coordinated attocells [74]. Furthermore, ZF has relatively poor performance in

low SNR regions [105]. In comparison, MMSE beamforming has less strict require-

ments on the number of luminaires per attocell, and outperforms ZF beamforming

in noise-limited scenarios as it also takes into account the receiver noise in design

optimization [106].

67


We consider a linear receiver at the VLC user, so the estimated received signal

dik at uik can be expressed as

dik = cikyik , (3.10)

where the scaling factor cik is the receive filter for user uik . Then the mean square

error (MSE) for user uik can be calculated as

MSEik = Ed,n‖dik − dik‖22 (3.11)

= η2‖cikhTikiF i − eTk ‖2

2 + η2

NA∑j=1,j 6=i

‖cikhTikjF j‖2

2 + c2ikσ2ik,

where ek is the kth standard basis vector for the NU-dimensional space and is ex-

pressed in (2.16). Note that the second term results from the inter-attocell interfer-

ence and is absent in the MSE expression of JT (See Eq. (2.25)). In this section,

we aim at optimizing the system performance subject to the LED dynamic range

constraint (3.9) assuming the availability of perfect CSI at the transmitters. We use

the WSMSE as the performance measure so that the possibly different priorities of

different users can be considered in system design. More specifically,

WSMSE =

NA∑i=1

WSMSEi =

NA∑i=1

NU∑k=1

wikMSEik , (3.12)

where WSMSEi represents the WSMSE of the ith attocell, and wik > 0 denotes

the priority (weight) of user uik at the current scheduling slot according to some

criteria. Considering the constraint (3.9) on the beamforming matrix, the WSMSE

68


minimization problem can be formulated as

P1 : min{F i},{cik}

WSMSE (3.13)

C1 : ‖fki ‖1 ≤ min (IDC − IL, IU − IDC) , ∀i, k .

When wik = 1 ∀i, k, P1 degenerates to the sum-MSE optimization problem which

may impose unfairness across users. More generally, the weights wik can be updated

over time to maintain fairness among terminals. Designing the optimal weights for

the system is outside the scope of the chapter. Instead, we focus on obtaining the

solution to the optimization problem for a given set of weights. The objective function

in optimization problem P1 is biconvex in terms of beamforming matrices {F i} and

scaling factors {cik} [83]. Fixing either of these two groups of variables will result in

a (convex) quadratic optimization problem. Here we use the alternating optimization

method to, possibly suboptimally, solve the problem. Fixing beamforming matrices

{F i}, we can obtain the closed-form expression for the optimal MMSE receiving filter

c∗ik =η2hTikif

ki

η2∑NA

j=1

∑NU

m=1 ‖hTikj

fmj ‖22 + σ2

ik

,∀i, k. (3.14)

We also need to acquire the optimal beamforming matrices {F i} given fixed scaling

factors {cik}. For notational simplicity, we define

H ij = [hi1j,hi2j, . . . ,hiNUj]T ,

Ci = diag([ci1 , ci2 , · · · , ciNU]T ),

W i = diag([√wi1 ,√wi2 , · · · ,

√wiNU

]T ),

ni = [ni1 , ni2 , . . . , niNU]T .

69


Then WSMSEi can be expressed as

WSMSEi =

NU∑k=1

wikMSEik = Ed,ni

{∥∥W i

(Ci

( NA∑j=1

H ijF jdj + ni)− di

)∥∥2

2

}(3.15)

= η2∥∥((W iCiH ii)⊗ I) vec

(F Ti

)− vec (W i)

∥∥2

2

+ η2

NA∑j=1,j 6=i

∥∥((W iCiH ij)⊗ I) vec(F Tj

)∥∥2

2+

NU∑k=1

w2ikc2ikσ2ik.

Define wi = vec (W i), Aij = (W iCiH ij)⊗I, f j = vec(F Tj

), and V as the NLNU×

NUNL block-diagonal matrix of the NL × NU all-one matrix. With fixed {cik}, P1

can be transformed into

P2 : min{f i}

NA∑i=1

(η2 ‖Aiif i −wi‖2

2 + η2

NA∑j=1,j 6=i

∥∥Aijf j∥∥2

2+

NU∑k=1

w2ikc2ikσ2ik

)C1:− ti ≤ f i ≤ ti, ∀i ,

C2: V ti ≤ min (IDC − IL, IU − IDC) 1NLNU×1, ∀i .

P2 is a convex quadratic programming problem and can be efficiently solved by the

MOSEK solver [103]. Once P2 is solved, the optimal beamforming matrices F j can

be retrieved from vector f j.

For the suboptimal alternating optimization, the ZF beamformer can be used as

the initialization point to secure a satisfactory solution. Define the concatenation of

all channel matrices as

H = [HT11, . . . ,H

TNA1, . . . ,H

T1NA

, . . . ,HTNANA

].

When NL ≥ NANU, the general form for the transmit ZF beamformer of the ith

70


attocell can be expressed as [74]:

F ZFi =

( NA∑j=1

NA∑m=1

NU∑k=1

hjkmhTjkm

)−HT

ii diag(Λi) =(HHT

)−HT

ii diag(Λi) , (3.16)

where Λi = [Λi1 ,Λi2 , . . . ,ΛiNU]T and

(HHT

)−=(HHT

)†+(I−(HHT

)†(HHT

)U i

).

Λik > 0 represents the symbol gain for dik , and U i is an arbitrary matrix. Then we

have

HjiFZFi =

0 i 6= j ,

diag(Λi) i = j .

In this chapter, we set

U i =(HHT

)†(HHT

),

Λi =min (IDC − IL, IU − IDC)

maxm

(∑NU

k=1

∣∣∣∣((HHT)†HT

ii

)m,k

∣∣∣∣)1NU×1 ,

and we get

F ZFi =

(HHT

)†HT

ii diag(Λi) . (3.17)

Such a ZF beamforming matrix satisfies the constraint of P1 and can be used as

the initialization point for the alternating optimization algorithm. We note that

when NL < NANU, the inter-attocell and intra-attocell interference cannot be fully

canceled with the beamforming matrix (3.17). However, (3.17) still remains a wise

choice for the initialization purpose [74]. The algorithm for solving P1 is summarized

in Algorithm 3.1.

71


Algorithm 3.1 Alternating optimization algorithm for P11. Initialization:

p⇐ 0.Update H ij with CSI.Initialize {F i}.

2. repeat3. Update {cik} according to Eq. (3.14).4. Update {Aij} with {cik}.5. Solve P2 and get {F i}.6. p⇐ p+ 1.7. until ‖WSMSEp+1 −WSMSEp‖ ≤ δ (δ is a predefined threshold) or p = pmax

(pmax is a predefined maximum iteration number).

3.4 Robust Transmitter Design with Channel

Uncertainty

The linear beamforming design in the previous section is based on the premise of

perfect CSI. In practice, however, CSI at the transmitter side is usually contaminated

due to various factors like quantization, erroneous channel estimation or outdated

feedback. Assuming an additive channel uncertainty model, the actual channel gain

can be expressed as

hikj = hikj + δikj , (3.18)

where hikj represents the channel estimate, and δikj represents the error vector re-

sulting from channel uncertainty. As a result, the MSE for user uik can be expressed

72


as

MSEik = η2‖cik(hT

iki+ δTiki)F i − eTk ‖2

2 + η2

NA∑j=1,j 6=i

‖cik(hT

ikj+ δTikj)F j‖2

2 + c2ikσ2ik.

Typically, there are two classes of models to characterize δikj: the deterministic

model and the stochastic model. For the deterministic model, we assume the actual

channel gain vector, although not exactly known, lies within a certain region with

the estimated nominal value at the center of the region. In this chapter, we assume

‖δikj‖ ≤ ε, where ε is some known constant and represents the level of uncertainty7.

The goal of robust design with the deterministic model is to guarantee a certain

performance level for every possible channel realization, which is achieved through

optimizing the worst-case performance by solving a min-max optimization problem

[97, 107]. For the stochastic model, we model the elements of error vector δikj as

Gaussian distributed random variables. Particularly in this chapter, we assume δikj is

zero-mean Gaussian distributed with covariance matrix σ2eI, where σe is some known

constant. With the stochastic model, we aim at optimizing the average performance

[97, 107].

3.4.1 Robust Design with the Deterministic Model

In this subsection, we apply the deterministic model to characterize the CSI imper-

fection and aim at ensuring worst-case robustness through beamforming design. P17 We assume the same level of CSI uncertainty for each user in this chapter.

73


is modified to the min-max optimization problem

P3 : min{F i},{cik}

max‖δikj‖2≤ε

WSMSE =

NA∑i=1

NU∑k=1

wikMSEik (3.19)

C1 : ‖fki ‖1 ≤ min (IDC − IL, IU − IDC) , ∀i, k ,

Using the Schur complement lemma [108] and [101, Lemma 2], P3 can be transformed

into

P4 : min{F i},{ci},{λikj},{tikj},{gik}

z2 (3.20)

C1 : ‖fki ‖1 ≤ min (IDC − IL, IU − IDC) , ∀i, k ,

C2 : Ψikj � 0, ∀i, j, k ,

C3 : Φik � 0, ∀i, k ,

C4 : λikj ≥ 0, ∀i, j, k ,

C5 : κ � 0,

74


where

Ψikj =

tiki − λiki η(cikh

T

ikiF i − eTk ) 0

η(cik(hT

ikiF i)

T − ek) tikiI εηcikFTi

0 εηcikF i λikiI

i = j ,

tikj − λikj ηcikh

T

ikjF j 0

ηcik(hT

ikjF j)

T tikjI εηcikFTj

0 εηcikF j λikjI

i 6= j .

(3.21)

κ=

z ωT

ω zI

,

Φik =

gik tik1 . . . tikNAcikσik

tik1

... gikI

tikNA

cikσik

,

ω = [w11g11 , . . . , w1NUg1NU

, . . . , wNANUgNANU

]T .

Similar to Algorithm 3.1 for P1, a local optimum of P4 can be obtained through

alternatively optimizing over {F i} and {ci}. Each problem is an SDP and can be

solved numerically.

75


3.4.2 Robust Design with the Stochastic Model

For the stochastic error model, we would like to secure the average system perfor-

mance in the robust design. The optimization problem can be formulated as

P5 : min{F i},{cik}

E (WSMSE) =

NA∑i=1

NU∑k=1

wikE (MSEik) (3.22)

C1 : ‖fki ‖1 ≤ min (IDC − IL, IU − IDC) , ∀i, k .

Alternating optimization can also be used to solve P5 which is a non-convex opti-

mization problem. Fixing {cik}, P5 can be transformed into

P6 : min{F i}

NA∑i=1

(η2∥∥∥Aiif i −wi

∥∥∥2

2+

NA∑j=1,j 6=i

η2∥∥∥Aijf j

∥∥∥2

2+ Tr(W 2

iC2i )η

2σ2e

NA∑j=1

∥∥f j∥∥2

2

+

NU∑k=1

w2ikc2ikσ2nik

)C1:− ti � f i � ti, ∀i ,

C2: V ti ≤ min (IDC − IL, IU − IDC) 1NLNU×1, ∀i ,

where Aij =(W iCiH ij

)⊗ I and H ij =

[hi1j, hi2j, . . . , hiNU

j

]T. P6 is a convex

quadratic programming problem and can be solved numerically. Fixing {F i}, we

have

c∗ik =η2h

T

ikifki

η2∑NA

m=1

∑NU

j=1(‖hTikmf jm‖22 + σ2

e‖fjm‖2

2) + σ2ik

,∀i, k.

76



In this section, we present our simulation results to demonstrate the performance of

the proposed CB scheme. First, we compare the performance of VLC systems under

different coordination schemes. Then we show that a careful choice of the weighting

vector can significantly improve fairness among users. Finally, we demonstrate the

performance gain of the adopted robust beamforming design given imperfect CSI.

3.5.1 Simulation Setup

We consider OOK as the modulation scheme for the simulation, i.e., M = 2, and

thus η = 1. This is perhaps the most practical transmission scheme for IM systems

because of simplicity and immunity to nonlinear distortion. We consider an indoor

environment illustrated in Figure 3.2a for our simulation purposes. The coordinate

system and the area planning8 are both shown in Figure 3.2b. The room dimensions

are 10×5×3 m3. Two multi-luminaire VLC transmitters (NA = 2) are installed in the

ceiling and are interconnected through a backbone network. Simulation parameters

for VLC transmitters and receivers are listed in Table 3.1. We consider two lighting

setups, where NL = 2, NE = 64 for Lighting Setup I (LS-I) and NL = 4, NE = 36 for

Lighting Setup II (LS-II). The coordinates of LED luminaires in each setup are listed

in Table 3.2.

As the primary function of VLC transmitters is illumination, we first investigate

the illumination performance of the two lighting setups. The illuminance distribution

with LS-I and LS-II are shown in Figure 3.3a and Figure 3.3b when IDC = 500 mA,8According to the DIN EN 12464-1 standard [38] for the planning and design of lighting instal-

lations, the area planning for indoor workplaces defines both task area and immediate surroundingarea. The task area is defined as the area in which the visual task is carried out. The immediatesurrounding area is defined as a band surrounding the task area within the field of vision with aminimum width of 0.5 m.

77


Table 3.1: Simulation parameters

Transmitter ParametersIL 300 [mA]IU 700 [mA]Lambertian order m 1LED conversion factor s 0.44 [W/A]System Bandwidth B 10 [MHz]

Receiver ParametersPD area APD 1 [cm2]Concentrator refractive index κ 1.5Receiver FoV ψc 60 [deg.]Noise bandwidth factor I2 0.562Background current Ibg 100 [µA]PD responsivity γ 0.30 [A/W]

respectively. The corresponding average illuminance and uniformity of the task area

and the immediate surrounding area under both lighting setups are shown in Ta-

ble 3.3. According to the DIN EN 12464-1 standard [38], the illuminance and uni-

formity of both setups satisfy the requirements for office work and study. In this

section, we use the SINR as expressed in Eq. (3.23) as the metric for performance

comparison.

SINRik =η2‖hTikif

ki ‖2

η2∑NU

j=1,j 6=k ‖hTiki

f ji ‖2 + η2∑NA

j=1,j 6=i∑NU

m=1 ‖hTikj

fmj ‖2 + σ2ik

(3.23)

If not stated otherwise, we assume NU = 2 in the following. Note that the specific

values of the system parameters M , NU, NA and NL chosen in this section are solely

for the purpose of simulation illustration, and the system design can be applied to

any values of M , NU, NA and NL.

78


(a) Room Illustration.

10 m

5 m

y

x

z

a

b

b

a

b

b

a

a

(b) Illustration of office areas. The yellow zone is the immediate surrounding area, andthe red area is the task area. b = 0.5 m. Illuminance calculations can ignore a marginalstrip extending a = 0.5 m from the walls according to [38].

Figure 3.2: Room Setup.

79


Table 3.2: Luminaire coordinates of LS-I and LS-II

(a) Lighting Setup I (LS-I), NL = 2, NE = 64.

Attocell ILuminaire 1 [2.5, 1.25, 3]Luminaire 2 [2.5, -1.25, 3]

Attocell IILuminaire 3 [-2.5, 1.25, 3]Luminaire 4 [-2.5, -1.25, 3]

(b) Lighting Setup II (LS-II), NL = 4, NE = 36.

Attocell ILuminaire 1 [3, 1.25, 3]Luminaire 2 [3, -1.25, 3]Luminaire 3 [2, 1.25, 3]Luminaire 4 [2, -1.25, 3]

Attocell IILuminaire 5 [-2, 1.25, 3]Luminaire 6 [-2, -1.25, 3]Luminaire 7 [-3, 1.25, 3]Luminaire 8 [-3, -1.25, 3]

Table 3.3: Illumination performance of LS-I and LS-II

LS-IIlluminance (lx) Uniformity

task area 624.7 0.604immediate surrounding area 506.6 0.496

LS-IIIlluminance (lx) Uniformity

task area 695.6 0.662immediate surrounding area 571.3 0.527

3.5.2 Comparison of Different Coordination Levels

We first investigate the benefit of coordinated transmission for VLC systems. We

consider three different coordination levels:

1. Joint Transmission (JT): Both user data and CSI are shared among attocells,

and the two attocells essentially merge into one single attocell, and operate

together as a single MU-MISO system [57, 55, 54, 51, 56].

2. Coordinated Beamforming (CB): Different from JT, only CSI is shared among

the attocells. Based on the shared channel information, beamforming matrices

for different attocells are designed collaboratively to alleviate IAI.

80


Table 3.4: User coordinates

(a) User Distribution I (UD-I)

Attocell IUser 1 [x1, 1.25, 0.8]User 2 [2.5, -1.25, 0.8]

Attocell IIUser 3 [-2.5, 1.25, 0.8]User 4 [-2.5, -1.25, 0.8]

(b) User Distribution II (UD-II)

Attocell IUser 1 [0.25, 0.25, 0.8]User 2 [0.25, -0.25, 0.8]


(c) User Distribution III (UD-III)



(d) User Distribution IV (UD-IV)



3. Uncoordinated Transmission (UT): Attocells are uncoordinated, and each atto-

cell operates as an independent MU-MISO system when NL ≥ 2 and NU ≥ 2.

In this subsection, we consider User Distribution I (UD-I) listed in Table 3.4. We set

wik = 1,∀i, k, and thus P1 reduces to a sum-MSE minimization problem. We focus

on the area wherein users will suffer from IAI, namely the region of −2 m ≤ x ≤ 2 m

under our system setup (see Figure 3.2b).

The benefit of the CB scheme is demonstrated in Figure 3.4. Figure 3.4a and

Figure 3.4b plot the SINR of User 1 as a function of its x-axis coordinate x1 with

LS-I and LS-II, respectively. In Figure 3.4a with LS-I, we can observe that JT

produces the best performance among the three schemes. As User 1 moves closer to

the edge of the neighboring attocell, i.e., x1 approaches zero, the achievable SINR

81


y (m) x (m)

02.5

5

500

Illu

min

an

ce (

lx)

0

1000

0

-2.5 -5

(a) LS-I

x (m)y (m)

02.5

5

500

Illu

min

an

ce (

lx)

0

1000

0

-2.5 -5

(b) LS-II

Figure 3.3: The distribution of indoor illuminance for two lighting setups when IDC =500 mA.

decreases dramatically due to the increasing interference from neighboring attocell,

and the UT scheme suffers the most significant performance degradation due to the

lack of coordination. For LS-I with NL = 2, CB provides an intermediate achievable

SINR between that of JT and UT. For LS-II with NL = 4, as can be seen from

Figure 3.4b, the achievable SINR of User 1 with CB is almost the same as that with

JT. In comparison to LS-I, LS-II has more transmission power and more degrees of

freedom in the beamforming design, thus the resulting beamformer can direct more

transmission power onto the targeted user and leak relatively less interference to

neighboring users at the same time.

From Figure 3.4, it may seem that CB can replace JT as long as NL is large

enough. However, CB does have its limitations. In Figure 3.5, we consider three user

distributions for each lighting setup: UD-II, UD-III and UD-IV as listed in Table 3.4.

The similarity of the three setups is that all users are located at the attocell edge

and are close to users in the neighboring attocell. For LS-I, we can observe that JT

significantly outperforms CB and UT schemes, and the CB scheme can barely improve

82


the performance to a decent level. For LS-II, while CB can significantly increase the

SINR in UD-III, the performance of UD-II still barely improves with CB. An intuitive

explanation is that all users in UD-II are closer to each other, making the beamformer

difficult to target one user without interfering with another one. While for UD-IV,

CB provides no improvement compared with UT for both lighting setups. The reason

is that each user in UD-IV can only be reached by one single luminaire of its belonging

attocell, making interference mitigation through beamforming impossible.

From the above results, we can see that although CB often displays comparable

performance with JT, the performance gap between JT and CB may become large

with specific user distributions. A possible solution is to apply Coordinated Schedul-

ing (CS) jointly with the CB scheme across attocells to make sure that users with

such distribution do not get served in the same time slot, so that we can enjoy the

architectural benefit of CB while maintaining a comparable performance to JT.

3.5.3 Importance of Weight

Fairness considerations are of particular importance for multiuser VLC systems. Un-

like RF wireless communication, indoor VLC channels are free from multipath fading

due to the large photodiode size compared with the optical wavelength. Consequently,

the deterministic nature of the VLC channel will fix attocell-edge users in an infe-

rior position if sum-MSE maximization is the only objective in system optimization.

Therefore, the WSMSE design criterion is a desirable feature to ensure some level of

fairness among the users. In the WSMSE optimization problem P1, the weight vari-

able wik represents the priority of user uik . The weight provides a tradeoff between

maximizing the total system throughput and balancing the fairness among users. In

this subsection, we consider UD-I with x1 = 1 m and define w = [w11 , w12 , w21 , w22 ]T .

83


0 0.5 1 1.5 2

x1 (m)

0

20

40

60

80S

INR

of

Use

r 1

(d

B)

UT

CB

JT

(a) LS-I (NL = 2)

0 0.5 1 1.5 2

x1(m)

0

20

40

60

80

SIN

R o

f U

ser 1

(d

B)

UT

CB

JT

(b) LS-II (NL = 4)

Figure 3.4: SINR of User I as a function of its x-axis coordinate x1.

84


When w = [1, 1, 1, 1]T , the user scheduling reduces to sum-MSE minimizing schedul-

ing. The SINR values of 4 users when w = [1, 1, 1, 1]T are shown in Figure 3.6a. We

can observe that SINR of User 1 is much lower than the rest of users. This is because

the location of User 1 leads to strong inter-attocell interference from Attocell II. User

1 will continuously suffer from low SINR as long as all users remain still. To maintain

a level of fairness across users, we can adjust the weights of the users. For example,

the SINR plot when w = [50, 10−7, 1.4, 2.2]T is shown in Figure 3.6b. We can observe

that by tuning the weight, fairness across the users can be greatly improved, though

the sum-MSE is slightly compromised.

3.5.4 Comparison between Robust and Non-Robust Design

In this section, we assume NU = 1 for the ease of illustration, and present the benefit

of robust design under CSI uncertainty. We plot the minimum SINR value as a

function of the assumed user location, according to which we obtain {hikj}. For a

fixed assumed user location, 105 realizations of actual channel vectors are generated

according to the error model Eq. (3.18) given a fixed ε or σe. The minimum SINR

value among those realizations can then be obtained. For concreteness, we further

assume that the two users are symmetrically located on the plane of z = 0.8 m, i.e.,

the user coordinates are (±x, y, 0.8) m for some x and y. Due to the symmetry,

we only plot the SINR performance for one quadrant of the room in Figure 3.7 and

Figure 3.8. From Figure 3.7 and Figure 3.8, we can observe that the expansion of

uncertainty region will deteriorate the system performance, and the robust design can

improve the performance of CB compared with the non-robust approach, especially

in the region where attocell boundaries lie. The robust approach improves the VLC

transmitter design to avoid the large beamformer mismatch with the actual channels

85


in spite of the CSI uncertainty, and keeps the SINR consistently high over the indoor

environment, including attocell boundaries.

3.6 Conclusion

Attocell-edge users suffer from serious inter-attocell interference if universal frequency

reuse is applied in VLC systems. Although joint transmission can be applied as a so-

lution to this problem, it puts high requirement on the VLC infrastructure in terms

of backbone capacity and inter-attocell synchronization. In this chapter, an alter-

native solution, i.e., coordinated beamforming, has been proposed for interference

mitigation in VLC downlinks, which requires less collaboration among attocells as

compared to joint transmission. We focused on the beamforming design subject to

the limited dynamic range of LED transmitters. Robust beamforming designs have

also been investigated to combat the uncertainty in CSI. Numerical results show that

the coordinated beamforming scheme provides a good tradeoff between system per-

formance and complexity, and validate the capability of the robust design against

channel uncertainty.

86


UD-II UD-III UD-IV-10

0

10

20

30

40

50S

INR

(d

B)

JT

CB

UT

(a) LS-I (NL = 2)

UD-II UD-III UD-IV-10

0

10

20

30

40

50

SIN

R (

dB

)

JT

CB

UT

(b) LS-II (NL = 4)

Figure 3.5: Comparison of system performance with different coordination levels forUD-II, UD-III and UD-IV.

87


User 1 User 2 User 3 User 40

10

20

30

40

50

60

70

SIN

R (

dB

)


10

20

30

40

50

60

70

SIN

R (

dB

)

Figure 3.6: (a) Left : w = [1, 1, 1, 1]T . (b) Right: w = [50, 10−7, 1.4, 2.2]T .

88


0 1 2 3 4 5x (m)

0

0.5

1

1.5

2

2.5

y (

m)

-20

-10

0

10

20

30SINR (dB)

(a) Non-Robust Design (ε = 10−5)

0 1 2 3 4 5x (m)

0

0.5

1

1.5

2

2.5

y (

m)

-20

-10

0

10

20

30SINR (dB)

(b) Robust Design (ε = 10−5)

0 1 2 3 4 5x (m)

0

0.5

1

1.5

2

2.5

y (

m)

-20

-10

0

10

20

30SINR (dB)

(c) Non-Robust Design (ε = 2× 10−5)

0 1 2 3 4 5x (m)

0

0.5

1

1.5

2

2.5

y (

m)

-20

-10

0

10

20

30SINR (dB)

(d) Robust Design (ε = 2× 10−5)

Figure 3.7: Comparison between robust and non-robust design with the deterministicmodel.

89


0 1 2 3 4 5x (m)

0

0.5

1

1.5

2

2.5

y (

m)

-20

-10

0

10

20

30

40SINR (dB)

(a) Non-Robust Design (σe = 10−6)

0 1 2 3 4 5x(m)

0

0.5

1

1.5

2

2.5

y(m

)

-20

-10

0

10

20

30

40

x (m)

SINR (dB)

(b) Robust Design (σe = 10−6)

0 1 2 3 4 5x (m)

0

0.5

1

1.5

2

2.5

y (

m)

-20

-10

0

10

20

30

40

SINR (dB)

(c) Non-Robust Design (σe = 5× 10−6)

0 1 2 3 4 5x (m)

0

0.5

1

1.5

2

2.5

y (

m)

-20

-10

0

10

20

30

40

SINR (dB)

(d) Robust Design (σe = 5× 10−6)

Figure 3.8: Comparison between robust and non-robust design with the stochasticmodel.

90

Chapter 4

The Hybrid VLC-PLC System

4.1 Introduction

Moving forward from the previous chapters, we specifically consider the PLC back-

bone network for VLC front-ends in this chapter. PLC seems a more pragmatic choice

than Ethernet given that PLC is possible to leverage existing infrastructure already

in place at each luminaire [109, 110]. We note that the integration of VLC and PLC

is not new, e.g., [87, 88]. However, the coordinating role of PLC for VLC in such

a hybrid HVP system, in which the PLC modem is connected to the outside access

network and acts not only as a data source for VLC luminaires but also as a cen-

tral controller for multiple luminaires, has only been presented recently [51, 55, 62].

Backbone PLC systems are typically broadband in nature and employ OFDM [111].

OFDM has also been adopted for VLC transmission, e.g., [11, 12, 112], to deal with

the frequency selectivity of the VLC channel. One of the challenges for an optical

OFDM implementation is the high PAPR of the time-domain signal. It leads to signal

distortion due to the non-negativity constraint for the optical time-domain signal and

a reduced energy-efficiency for practical LED drivers with limited dynamic range. To

alleviate the PAPR problem, recently [81] designed and analyzed SO-OFDM schemes,

in which (possibly overlapping) subsets of OFDM subcarriers are transmitted over

subsets of LEDs of a luminaire, and the entire OFDM signal results from spatial

summing. In the extreme case of a single subcarrier per LED, this leads to a PAPR

91

Chapter 4. The Hybrid VLC-PLC System

of only 3 dB.

In this chapter, we propose an HVP system for indoor downlink optical wireless

access utilizing the SO-OFDM technique. Compared to traditional VLC-PLC in-

tegration, our system enables end-to-end use of OFDM modulation, alleviates the

high PAPR problem of OFDM for LED transmitters, and enables the cooperation

of multiple spatially distributed luminaires to overcome inter-luminaire interference

and increase robustness against possible signal obstruction from a single luminaire.

To this end, we make the following contributions.

1. We develop the HVP system together with an analytical framework for its

achievable rate. Inspired by cooperative transmission techniques widely stud-

ied in the RF domain, we consider the HVP system as a relay-assisted two-hop

communication system without a direct link between the source and the des-

tination. The LED luminaires act as full-duplex relays (transmit and receive

signals at the same time) and retransmit the received PLC signal to the user

via VLC. Considering the channel characteristics of PLC and VLC and the fact

that VLC uses intensity modulation, i.e., the transmitted signal must be non-

negative and operates under a peak amplitude constraint, we derive expressions

for the rate that can be supported by the HVP system.

2. We generalize SO-OFDM proposed in [81] by considering the joint subcarrier

allocation (SA) among multiple spatially distributed LED luminaires, and we

propose several SA schemes for this SO-OFDM HVP system to exploit the fre-

quency diversity of PLC and VLC channels, and multi-user diversity in the case

of multiple users. This includes a subcarrier pairing method that adaptively

matches between incoming and outgoing subcarriers at the LED luminaire to

account for the frequency selectivity of the two channels.

92


3. For multi-user HVP systems, the SA schemes are developed for two possible

multiple access schemes: OFDM time-division multiple access (OFDM-TDMA)

and orthogonal frequency-division multiple access (OFDMA). SA of multi-user

HVP systems is a non-trivial task due to the coupling of subcarrier pairing,

relay selection and user selection, and the limited number of subcarriers per

LED luminaire set by SO-OFDM. To reduce the computational complexity of

SA, we investigate the performance of chunk-based SA [113] and propose several

suboptimal polynomial-time SA algorithms. We note that the contribution of

our work is not dependent on any specific OFDM signal format employed by

the VLC link. We adopt two variations of OFDM signal formats as the VLC

multicarrier solutions in this chapter due to their popularity. However, the

proposed optimization framework can be easily extended to any other OFDM

signal formats in SO-OFDM-based HVP systems.

The remainder of the chapter is organized as follows. In Section 4.2, we introduce

the SO-OFDM-based HVP system, and present the channel and noise models for

the PLC and VLC links. In Section 4.3, different optical OFDM formats and relay

protocols are investigated for the HVP system, and the corresponding achievable rate

expressions are presented. In Section 4.4, computationally efficient SA algorithms,

with and without SP, are proposed for the two multi-access schemes. Simulation

results for different variations of HVP systems are presented and discussed in Sec-

tion 4.5. Finally, the conclusions are drawn in Section 4.6.

93


4.2 System Model

4.2.1 Problem Scenario

We propose an SO-OFDM-based HVP system for downlink transmission to NU users

located in the same room and served via the cooperation of NL LED luminaires,

and each luminaire consists of NE LEDs. Figure 4.1 illustrates the system structure

showing a single user. The power line acts as the backbone network that feeds data

to and coordinates cooperation among the multiple VLC-equipped LED luminaires,

which in turn operate as full-duplex relays which process the received PLC signal and

forward it via VLC to indoor users. Applying SO-OFDM across multiple luminaires,

each luminaire only emits a subset of the data symbols from the received PLC OFDM

signal. The VLC signals from multiple LED luminaires superpose at the photo-diode

detectors of the users, where a conventional OFDM receiver can be used to decode the

information. To achieve this, accurate time and frequency synchronization is required

for the VLC hop. Since both VLC and PLC OFDM are baseband modulated, carrier

frequency offset is absent and only timing needs to be taken care of. To resolve the

time synchronization problem resulting from the time difference of arrivals of users’

signal at the luminaires, we can ensure that the cyclic prefix length of the OFDM

symbol is longer than the time difference of arrivals. Further considering the fact

that the LoS link plays the major role in VLC systems [8], and the inter-luminaire

distances between VLC transmitters in the indoor environment are relatively small,

the situation here is relatively simpler compared to CoMP systems with RF imple-

mentation [114]. In the rest of the chapter, we assume VLC transmitters are perfectly

synchronized. For the HVP uplink, one preferred choice is WiFi uplink (see Section

1.3). The WiFi uplink, for the HVP system specifically, can be implemented through

94


LED Luminary 1

WiFi Uplink

PLC

modem

OFDM

Demodulation

Subcarrier

Selection

Subcarrier

Permutation

OFDM

Modulation

LED Luminary 2

OFDM

Demodulation

Subcarrier

Selection

Subcarrier

Permutation

OFDM

Modulation

OFDM

Demodulation

Subcarrier

Selection

Subcarrier

Permutation

OFDM

Modulation

LED Luminary NL

PLC-WiFi

integrated

modem

PLC

Network

...

Figure 4.1: Block diagram of the HVP system.

a PLC-WiFi integrated modem (which could act as the coordinator point), as illus-

trated in Figure 4.1. Such an uplink would provide the CSI about the VLC links to

the coordinator point for system optimization.

4.2.2 Transmitter and Receiver Model

Figure 4.2 shows a detailed block diagram of the SO-OFDM HVP system with respect

to a specific luminaire relay. We note that the baseband OFDM signals transmit-

ted over the PLC and VLC links satisfy the Hermitian symmetry property in the

frequency domain, and in the following, we will only describe the processing for the

independent information-carrying subcarrier sets (Pinfo and Vinfo in Section 4.3).

In the PLC hop, the PLC modem broadcasts the same wideband OFDM signal

to every LED luminaire containing Np independent information-carrying subcarriers.

In the VLC hop, SO-OFDM is applied, and the kth luminaire re-modulates Nk of the

received PLC data symbols onto Nk of Nv available VLC subcarriers. The Nv −Nk

unused subcarriers are set to zero. The subcarrier subsets across different luminaires

95


are disjoint and we have∑NL

k=1Nk = Np. At each LED luminaire, we consider a

subcarrier pairing approach which adaptively matches incoming with outgoing sub-

carriers to fully exploit the frequency diversity of both PLC and VLC channels. The

number of subcarriers Nk and thus subcarrier pairs assigned to the kth luminaire

cannot exceed an upper limit in order to limit the PAPR of the OFDM signal at each

LED luminaire.

We consider two operating modes for the LED luminaire relay, namely amplify-

and-forward (AF) and decode-and-forward (DF). An AF-mode VLC relay demodu-

lates the PLC signal, scales the selected subcarrier signals, and re-modulates them

applying subcarrier pairing. In addition to this, a DF-mode relay also decodes the re-

ceived signal. Only if decoding is deemed successful, based on an outer error-detection

code, the DF-mode relay will re-encode and re-modulate the data, and then forward

it to the destination.

At the user side, the VLC analog front-end (AFE) consists of a photo-diode

detector to convert the optical to an electrical received signal and an AC coupler to

remove the DC signal component, which is responsible for the primary illumination

function of the LED luminaires. This is followed by a conventional OFDM receiver.

4.2.3 Channel and Noise Model

Power Line Communication

To faithfully model the signal transfer over the low-voltage power line network, we

apply the bottom-up approach based on transmission-line theory as presented in

[115, 116] and implemented in a simulator in [117], which leads to a distinctive PLC

channel for each LED luminaire based on the cable characteristics of its corresponding

power line branch. The noise in PLC systems consists of colored background noise,

96


Cyclic prefix

removalFFT

QAM

Modulation

Data

input Hermitian

symmetry

InsertionIFFT

PLC

AFE

Cyclic prefix

insertion

PLC

AFE

PLC

Channel

PLC noise

S/P P/S

S/PP/SDemodulationDecode

Encode

S/P

Modulation

Subcarrier

PairingIFFT P/S

Cyclic prefix

insertion

Power

scalingClipping D/A

DC bias

VLC AFE

VLC

Channel

VLC noise

Cyclic prefix

removalFFT

VLC

AFES/PP/SDemodulationDecode

Data

output

PLC Transmitter

LED Luminary

VLC Receiver

Subcarrier

Selection

Figure 4.2: Detailed block diagram of the SO-OFDM HVP downlink system for oneluminaire and one user. Blocks with dashed lines are not present in LED luminairesoperating in amplify-and-forward mode.

narrowband disturbance, and impulsive noise [111]. We model the first two terms

through the combined power spectral density (PSD) of the shape as in [118, Eq.

(4)], as also adopted in the IEEE 1901 standard [119, Annex F.3.5.2]. Impulse noise

is modeled as a non-stationary random process. For the purpose of mathematical

tractability, we disregard the impulse noise in the rate optimization. This is justified

as the impulse noise events occur with relatively low probability (see. e.g. [120]) and

if significant lead to outage events. Furthermore, one of the major components of

impulse noise in the low-voltage power line is random aperiodic impulse noise. In this

case, rate optimization considering the aperiodic noise for the purpose of adaptive

transmission is ineffective. Note that in all the numerical results presented in Section

4.5, we will consider the impulse noise for the purpose of simulation accuracy, and we

apply the two-state approximation as in [121, Eq. (19)] to calculate the achievable

97


rate. To enable the reproducibility of the numerical results, we have made the PLC

noise simulator available online [122].

Visible Light Communication

The VLC channel is frequency selective due to the low-pass characteristics of the

LED emission and the multipath dispersion of the VLC signal. The latter starts

to play a role when the transmitted signal is broadband [27], which is the case for

the considered HVP system. In this chapter, we take both the LoS link and NLoS

link (reflections) into consideration for the VLC channel modeling. We assume that

propagation from either the LED source or a reflection point on the walls follows the

Lambertian radiation pattern. The channel gain h between the receiver (the user or a

reflection point on the walls) and the light source (the LED source or a reflection point

on the walls) can then be expressed using Eq. (1.2). Based on Eq. (1.2), we apply

the modified Monte Carlo method presented in [34] to obtain the frequency-domain

channel gain HCL(f) in our simulations, and our source code written in MATLAB

is available at [123]. The first three reflections are taken into account as they carry

most of the VLC signal power. Together with the frequency response for the LED

emissions which can be approximated by [124]

HLED(f) =1

1 + j ffLED

, (4.1)

with fLED representing the 3 dB cutoff frequency of the LED low-pass characteristics,

the overall VLC channel gain can be expressed as

Hv(f) = HLED(f)HCL(f). (4.2)

98


The noise in VLC systems comprises shot noise, which is induced by ambient light,

and thermal noise. The variance of the total VLC noise can be modeled as a zero-

mean Gaussian random variable with variance σ2vn calculated by Eq. (1.3).

4.3 Rate Analysis of the HVP System

In this section, we derive the expressions for the achievable rates for downlink trans-

mission with the HVP system using different relaying strategies. More specifically,

we consider the rate associated with a single OFDM subcarrier pair of the PLC-VLC

link to a single user. Since different subcarriers are orthogonal and users are multi-

plexed over orthogonal subcarriers or time slots, rate expressions of the total HVP

system follow then immediately.

4.3.1 Signal at the PLC Hop

The baseband PLC OFDM signal uses the set Pinfo of information-carrying subcarri-

ers, where |Pinfo| = Np. Denoting the PLC frequency-domain transmitted symbol at

subcarrier l as Xp(l), and with the usual assumptions about sufficient cyclic-prefix

length, synchronization, and channel time-invariance, the PLC frequency-domain sig-

nal Y kp (l) at subcarrier l received by the kth LED luminaire can be expressed as

Y kp (l) = Hk

p(l)Xp(l) +Nkp (l) , (4.3)

where Hkp(l) and Nk

p (l) are the PLC channel gain and noise for subcarrier l at the

kth LED luminaire, respectively. The corresponding SNR is

SNRkp(l) =

∣∣Hkp(l)∣∣2σ2

p

σ2pn,k(l)

, (4.4)

99


where σ2p = E

[|Xp(l)|2

]and σ2

pn,k(l) = E[∣∣Nk

p (l)∣∣2].

4.3.2 Signal at the VLC Hop

The kth VLC transmitter modulates Nk subcarriers from the set Vinfo of active

information-carrying subcarriers, and |Vinfo| = Nv. Denoting the frequency-domain

transmitted symbol over subcarrier l as Xkv (l) and the size of the discrete Fourier

transform applied for VLC as Nvfft, the time-domain samples at each element of the

kth luminaire can be expressed as

xkv,info(n) =1√Nv

fft

Nvfft−1∑l=0

Xkv (l)exp

(j2πnl

Nvfft

), (4.5)

where Hermitian symmetry Xkv (l) =

(Xk

v (Nvfft − l)

)∗ holds, and only 2Nk out of Nvfft

Xkv (l) are non-zero due to SO-OFDM (see Section 4.2.2). The signal xkv,info(n) is

used to modulate the intensity of the LED luminaire. To make the signal compatible

with the IM/DD channel, in the following we consider both DCO-OFDM and ACO-

OFDM, which are the two popular forms of intensity-modulated optical OFDM [43,

44].

Since an LED as a transmitter has a limited dynamic range, the time-domain

OFDM signal may be clipped due to a high PAPR [39]. Let IL and IU represent the

lower and upper bound of the LED forward current, respectively, and IDC be the DC

bias current. Then, the clipped signal can be expressed as

xkv,clip(n) = FCLIP(xkv,info(n)) , (4.6)

100


where [40]

FCLIP(x) =

b, x ≤ b ,

t, x ≥ t ,

x, otherwise ,

(4.7)

and t = IU−IDC, b = IL−IDC for DCO-OFDM, and t = IU−IDC, b = max(IL−IDC, 0)

for ACO-OFDM. Neglecting possible differences among LEDs located at the same

luminaire, we obtain the equivalent transmitted signal of the kth LED luminaire as

xkv,sum(n) = NE

(xkv,clip(n) + IDC

). (4.8)

We note that the level of the bias current, which together with clipping ensures the

non-negativity of the transmit signal, is determined by the illumination requirement

on the luminaire.

To proceed with formulating the received signal after the VLC link, we need

to distinguish between the OFDM modalities used at the VLC transmitter (DCO-

OFDM or ACO-OFDM) and the relaying methods (DF or AF) to obtain Xkv (l).

This is done in the next subsection, where we derive the associated expressions for

achievable rates for a single subcarrier pair of the HVP system.

4.3.3 Achievable Rate Expression for Each Subcarrier Pair

DCO-OFDM

For DCO-OFDM, Vinfo = {1, 2, . . . , Nv}. According to Bussgang’s theorem [125], the

clipped signal at the kth luminaire can be modeled as an attenuation of the original

101


signal plus a non-Gaussian uncorrelated noise component [126]:

xkv,clip(n) = Akxkv,info(n) + nkc(n) , (4.9)

where nkc(n) is the non-Gaussian clipping noise term with variance σ2clip,k and Ak

is the attenuation factor. Given the electrical power of the VLC signal P kv =∑Nv

fft−1

l=0 E[|Xk

v (l)|2]/Nv

fft and the constants from the clipping function (4.7), and

defining the normalized clipping levels bk = b/√P k

v and tk = t/√P k

v , we have

[40, 127]

Ak = Q(bk)−Q

(tk), (4.10)

and

σ2clip,k =P k

v

(Ak −

(φ(bk)− φ(tk) + (1−Q(bk)

)bk +Q(tk)tk)2 − (Ak)2

+(1−Q(bk)

)(bk)2 +Q(tk)(tk)2 + φ(bk)bk − φ(tk)tk

), (4.11)

where Q(·) and φ(·) are the tail probability function and the probability density

function of the standard normal distribution.

Substituting (4.9) into (4.8) gives the output signal at the kth LED luminaire as

xkv,sum(n) = NEAkxkv,info(n) +NEn

kc(n) +NEIDC . (4.12)

Correspondingly, we can write for the frequency-domain signal at the lth subcarrier

Xkv,sum(l) = NEA

kXkv (l) +NEN

kclip(l) , (4.13)

where the DC component NEIDC is not present for l ∈ Vinfo and Nkclip is the discrete

102


Fourier transform of nkc . According to the central limit theorem (CLT), Nkclip can

be modeled as an additive complex-valued Gaussian variable with zero mean and

variance of σ2clip,k [40]. We now consider the two relaying schemes.

DF Scheme In DF, the relay will only forward the message if it was detected

correctly as verified by an outer error-detection code. Then, we will have Xkv (l) =

αXp(m), where subcarrier m ∈ Pinfo from the PLC link is paired with subcarrier l ∈

Vinfo for the VLC link, and the factor α adjusts the VLC signal strength. The pairing

will be discussed in more detail in Section 4.4. The received signal on subcarrier l at

user u when served from luminaire k follows as

Y k,uv (l) = Hk,u

v (l)Xkv,sum(l) +Nu

v (l) (4.14)

= NEαAkHk,u

v (l)Xp(m) +NEHk,uv (l)Nk

clip(l) +Nuv (l) ,

where Hk,uv (l) is the VLC channel gain for subcarrier l between the kth luminaire

and user u, and Nuv (l) is the VLC noise on subcarrier l at user u. The corresponding

subcarrier SNR is

SNRk,uv (l) =

|NEαAkHk,u

v (l)|2σ2p

|NEHk,uv (l)|2σ2

clip,k + σ2vn,u

, (4.15)

where σ2vn,u = E

[|Nu

v (l)|2]. As both clipping and VLC receiver noise can be approxi-

mated as i.i.d. Gaussian noise when Nk ≥ 64 [126], the corresponding per-subcarrier

rate can be calculated as (in bit per use)9 [128]

Rk,u(l,m) = min(log2(1 + SNRk

p(m)), log2(1 + SNRk,uv (l))

).

9Both Eq. (4.16) and Eq. (4.18) can be derived from [128, Eq. (15)] and [128, Eq. (12)], respec-tively, via setting the direct link channel gain to 0. The absence of the coefficient 1

2 is due to thefull-duplex property of the luminaire relay.

103


AF Scheme For AF, we have Xkv (l) = βYp(m), where β is the amplification factor

for the AF scheme. Similar to (4.14), Y k,uv (l) can be expressed as

Y k,uv (l) = NEA

kβHk,uv (l)Hk

p(m)Xp(m) +NEAkβHk,u

v (l)Nkp (m) (4.16)

+NEHk,uv (l)Nk

clip(l) +Nuv (l) ,

and the corresponding SNR at user u is given by

SNRk,uv (l,m) =

∣∣NEAkβHk,u

v (l)Hkp(m)

∣∣2 σ2p∣∣∣NEAkβH

k,uv (l)

∣∣∣2 σ2pn,k(m) +

∣∣∣NEHk,uv (l)

∣∣∣2 σ2clip,k + σ2

vn,u

. (4.17)

Using again the fact that the total noise is Gaussian, the achievable rate follows as

Rk,u(l,m) = log2

(1 + SNRk,u

v (l,m)). (4.18)

ACO-OFDM

Different than DCO-OFDM, only odd subcarriers in ACO-OFDM carry information,

i.e., Vinfo = {1, 3, . . . , 2Nv − 1}, which allows for zero-level clipping and reduces the

minimum level of DC bias at the cost of reduced bandwidth efficiency [43]. The

clipped ACO-OFDM signal can be expressed as

xkv,clip(n) = 2AkU(xkv,info(n))xkv,info(n) + nkc(n) , (4.19)

104


where U(·) is the Heaviside step function [129] and the variance of the clipping noise

nkc(n) is [40]

σ2clip,k = P k

v

(Ak((bk)2 + 1

)− 2(Ak)2 − bk

(φ(bk)− φ(tk)

)− φ(tk)(tk − bk) +Q(tk)(tk − bk)2

). (4.20)

With this, the expression for the frequency-domain signal at the lth subcarrier for

l ∈ Vinfo is the same as in Eq. (4.13). Accordingly, the SNR expressions for DF

relaying in (4.15) and AF relaying in (4.17) also apply to ACO-OFDM and can be

used in the rate expression (4.16) and (4.18), respectively, to obtain the associated

achievable rate.

4.4 Subcarrier Allocation in HVP Systems

We now use the rate expressions from the previous section to optimize the rate of the

overall HVP system. Since multiple users compete for resources, we integrate a notion

of fairness into the rate optimization. In particular, we introduce a weight variable wu

that represents the priority of user u. For example, in the case of a proportional fair

(PF) scheduling policy that prioritizes the user with the lowest average data-rate, we

have wu = 1/Ruavg(n) for long-term fairness consideration, where Ru

avg(n) is computed

as

Ruavg(n) =

(1− 1

Nres

)Ru

avg(n− 1) +1

Nres

Ru(n− 1) , (4.21)

and Ru(n) is the data rate at instance n and Nres is the response time of the low-pass

filter [130]. We note that the optimization framework presented in this section is

105


independent of the specific scheduling policy that is applied.

The optimization of the achievable rate of the HVP system is accomplished

through SA schemes, for which we propose two variants. The first variant, which

we refer to as SA without subcarrier permutation (SP), retains the subcarrier as-

signment when transitioning from PLC to VLC link. Assuming for simplicity and

without loss of generality that Nv = Np, we have Pinfo = Vinfo and thus l = m in

(4.16) and (4.18) for DCO-OFDM. Since Vinfo = {1, 3, . . . , 2Nv−1} for ACO-OFDM,

we have l = 2m − 1, m ∈ Pinfo, in this case. The second scheme applies subcarrier

permutation at the relays, and we refer to it as SA with SP. It makes use of the fact

that the per-subcarrier link qualities of the PLC and VLC hop are independent of

each other.

Since the number of subcarriers in broadband HVP systems can be very large, an

SA scheme considering each individual subcarrier will not only have large computa-

tional complexity, but also requires significant signaling overhead. To mitigate the

computational and coordination complexity, a chunk-based SA scheme can be applied

[113]. This means that a set of Ns adjacent subcarriers is grouped into a chunk, and

the chunk is used as the minimum unit in SA. Hence, in the following we consider

that Nc chunks are available in total, where Np = Nv = NsNc, of which Ck chunks

are assigned to kth luminaire, i.e., Nk = NsCk. Obviously, Ns = 1 is the special case

of single-subcarrier-based allocation. Given that a codebook of size Sc (Sc = 2q) is

employed for the channel gain vector space Huv(l) = [H1,u

v (l), H2,uv (l), . . . , HNL,u

v (l)],

qNc bits of CSI feedback are required for one OFDM block per VLC user. We define

the binary variable xk,ui,j ∈ {0, 1}, i, j ∈ {1, 2, . . . , Nc}, with xk,ui,j = 1 indicating that

ith chunk in the PLC hop together with the jth chunk in the VLC hop are assigned

to user u with the assistance of the kth VLC-enabled luminaire. Furthermore, we will

106


need in the following xu = [xk,ui,j ]i,j=1,...,Nc, k=1,...,NLas the Nc ×Nc ×NL SA tensor for

user u and x = [x1, . . . ,xNU] as the Nc×Nc×NLNU tensor for SA across all users, and

we will use the sets Nc = {1, 2, . . . , Nc}, NL = {1, 2, . . . , NL} and NU = {1, . . . , NU}

in the following, where Nc, NL and NU are the sets of chunk indices, luminaire indices

and user indices, respectively.

Next, we present the SA methods first for HVP with OFDM-TDMA and then for

HVP with OFDMA.

4.4.1 OFDM-TDMA

With OFDM-TDMA, the whole frequency spectrum is owned exclusively by the user

with the highest priority weight wu in a certain time slot. Hence, SA is performed

for one user only at a time.

SA without SP

For SA without SP, we have xk,ui,j = 0 for i 6= j, and the rate maximization problem

can be formulated as

P1 : x∗u = argmax{xu}

∑i∈Nc

∑k∈NL

xk,ui,i Rk,ui,i (4.22)

C1 :∑k∈NL

xk,ui,i = 1,∀i ∈ Nc,

C2 :∑i∈Nc

xk,ui,i = Ck,∀k ∈ NL,

C3 : xk,ui,i ∈ {0, 1}, ∀i ∈ Nc, ∀k ∈ NL ,

where Rk,ui,j represents the rate of the chunk pair (i, j) for user u and PLC-VLC relay

k. Constraint C1 guarantees that each subcarrier pair is assigned to one and only one

107


relay, and C2 ensures the number of subcarriers pairs allocated to each relay. P1 can

be categorized as a linear semi-assignment problem and can be solved with a time

complexity of O(N2cNL) [131]. For the simulation results in the next section, we use

the YALMIP [94] toolbox in conjunction with the MOSEK solver [103] to obtain a

solution numerically.

SA with SP

Here we generalize P1 and allow subcarrier permutation at the relays. In this case,

the optimization problem for user u can be formulated as

P2 : x∗u = argmax{xu}

∑i∈Nc

∑j∈Nc

∑k∈NL

xk,ui,j Rk,ui,j (4.23)

C1 :∑j∈Nc

∑k∈NL

xk,ui,j = 1,∀i ∈ Nc ,

C2 :∑i∈Nc

∑k∈NL

xk,ui,j = 1,∀j ∈ Nc ,

C3 :∑i∈Nc

∑j∈Nc

xk,ui,j = Ck,∀k ∈ NL ,

C4 : xk,ui,j ∈ {0, 1},∀i, j ∈ Nc, ∀k ∈ NL ,

where C1 and C2 guarantee that each subcarrier is assigned to exactly one relay for

the PLC and VLC hop, respectively, and C3 controls the number of assigned subcar-

rier pairs per relay. P2 can be categorized as a constrained linear 0-1 programming

problem, which is NP-hard. We therefore apply a heuristic alternating optimization

method to solve P2 suboptimally within polynomial time [132]. To this end, we

108


introduce vectors {yui,j} and {zk,ui } with x

k,ui,j = yui,jz

k,ui , and P2 is transformed into

P2.1 : (y∗u, z∗u) = argmax

{yu,zu}

∑i∈Nc

∑j∈Nc

∑k∈NL

yui,jzk,ui Rk,u

i,j

C1 :∑j∈Nc

yui,j = 1,∀i ∈ Nc,

C2 :∑i∈Nc

yui,j = 1,∀j ∈ Nc,

C3 :∑k∈NL

zk,ui = 1,∀i ∈ Nc,

C4 :∑i∈Nc

zk,ui = Ck,∀k ∈ NL,

C5 : yui,j, zk,ui ∈ {0, 1},∀i, j ∈ Nc, ∀k ∈ NL ,

where yu = [yui,j]i,j∈Nc and zu = [zk,ui ]i∈Nc,k∈NL. P2.1 is a bilinear 0-1 programming

problem, and we obtain a suboptimal solution by alternately optimizing on yu and

zu. When yu is fixed, we can ignore constraints C1 and C2, and P2.1 will degenerate

to P1 with Rk,ui,i replaced by T k,ui =

∑j∈Nc

yui,jRk,ui,j , which will be referred to as P2.2.

When zu is fixed, we define Sui,j =∑

k∈NLzk,ui Rk,u

i,j and P2.1 becomes

P2.3 : y∗u = argmax{yu}

∑i∈Nc

∑j∈Nc

yui,jSui,j

C1 :∑j∈Nc

yui,j = 1,∀i ∈ Nc,

C2 :∑i∈Nc

yui,j = 1, ∀j ∈ Nc,

C3 : yui,j ∈ {0, 1},∀i, j ∈ Nc ,

which is a classic assignment problem and can be solved by the Hungarian algorithm

with a computational complexity of O(N3c ) [133, 134]. The algorithm of the alter-

109


nating optimization for P2 is summarized in Algorithm 4.1 and the time complexity

is O(N3c +N2

cNL).

Algorithm 4.1 Alternating Optimization for P21. Initialization:

u∗ = argmaxu∈NU{wu}.

Calculate {Rk,u∗

i,j }.y0u∗ ⇐ INc×Nc , p⇐ 0.

2. repeat3. Update {T k,u

∗

i } with ypu∗ .4. Solve P2.2 according to [131] and get zpu∗ .5. Update {Su∗i,j} with z

pu∗ .

6. Solve P2.3 and get yp+1u∗ .

7. p⇐ p+ 1.8. until ‖yp+1

u∗ − ypu∗‖ ≤ δ (δ is a predefined threshold)

9. Compute xu∗ according to xk,u∗

i,j = yu∗i,jz

k,u∗

i .10. Update {wu}u∈NU

according to rate update (4.21).

4.4.2 OFDMA

OFDMA accomplishes multiple access by assigning different subcarriers to different

users. This allows for a more flexible SA scheme that can exploit multi-user diversity.

110


SA without SP

Without SP at the relays, again xk,ui,j = 0 for i 6= j, and the maximization problem

for the weighted sum rate is

P3 : x∗ = argmax{x}

∑u∈NU

wu∑i∈Nc

∑k∈NL

xk,ui,i Rk,ui,i (4.24)

C1 :∑u∈NU

∑k∈NL

xk,ui,i = 1,∀i ∈ Nc,

C2 :∑u∈NU

∑i∈Nc

xk,ui,i = Ck,∀k ∈ NL ,

C3 : xk,ui,i ∈ {0, 1},∀i ∈ Nc, k ∈ NL, u ∈ NU .

Similar to problem P2, we introduce vectors {ai,u} and {bi,k} with xk,ui,i = ai,ubi,k, and

suboptimally solve P3 with alternating optimization based on the transformation into

P3.1 : (a∗, b∗) = argmax{a,b}

∑u∈NU

wu∑i∈Nc

∑k∈NL

ai,ubi,kRk,ui,i

C1 :∑u∈NU

ai,u = 1,∀i ∈ Nc ,

C2 :∑k∈NL

bi,k = 1,∀i ∈ Nc ,

C3 :∑i∈Nc

bi,k = Ck, ∀k ∈ NL ,

C4 : ai,u, bi,k ∈ {0, 1}, ∀i ∈ Nc, k ∈ NL, u ∈ NU ,

where a = [ai,u]i∈Nc,u∈NUand b = [bi,k]i∈Nc,k∈NL

. Let Eui =

∑k∈NL

bi,kRk,ui,i , F k

i =∑u∈NU

ai,uwuRk,u

i,i , and function u∗i = argmaxu∈NU{wuEu

i }. We observe that the

optimal solution of P3.1 with b fixed is a vector a∗ with ai,u∗i = 1 and zero otherwise.

When a is fixed, we can ignore constraints C1 in P3.1, and P3.1 will degenerate to P1

111


with Rk,ui,i replaced by F k

i and xk,ui,i replaced by bi,k, which will be referred to as P3.2.

The algorithm of the alternating optimization for P3 is summarized in Algorithm 4.2,

and the time complexity is O(N2cNL +NcNUNL).

Algorithm 4.2 Alternating Optimization for P31. Initialization:

Calculate {Rk,ui,i }.

a0 ⇐ INc×NU, p⇐ 0.

2. repeat3. Update {F k

i } with ap.4. Solve P3.2 according to [131] and get bp.5. Update {Eu

i } with bp.6. Find u∗i and obtain ap+1.7. p⇐ p+ 1.8. until ‖ap+1 − ap‖ ≤ δ (δ is a predefined threshold)9. Compute x according to xk,ui,i = ai,ubi,k.10. Update {wu}u∈NU

according to rate update in (4.21).

SA with SP

Allowing subcarrier permutation at the relays, the weighted sum rate maximization

problem can be expressed as

P4 : x∗ = argmax{x}

∑u∈NU

wu∑i∈Nc

∑j∈Nc

∑k∈NL

xk,ui,j Rk,ui,j

C1 :∑u∈NU

∑j∈Nc

∑k∈NL

xk,ui,j = 1,∀i ∈ Nc ,

C2 :∑u∈NU

∑i∈Nc

∑k∈NL

xk,ui,j = 1,∀j ∈ Nc ,

C3 :∑u∈NU

∑i∈Nc

∑j∈Nc

xk,ui,j = Ck, ∀k ∈ NL ,

C4 : xk,ui,j ∈ {0, 1}, ∀i, j ∈ Nc, k ∈ NL, u ∈ NU .

112


P4 is a constrained linear 0-1 programming problem, which is NP-hard. Here we

propose a heuristic subcarrier offloading algorithm that can solve the problem sub-

optimally within polynomial time. First we relax the constraints of P4 and consider

P4 without C3, which will be referred to as P4.1. P4.1 can be solved with the al-

gorithm proposed in [135] within a polynomial time of O(NLNUN2c + N3

c ), and the

solution is denoted as {xk,ui,j }. Define NL1 and NL2 as the sets of luminaires that

do and do not exceed the assigned value Ck, respectively, with NL1 = {k|ck > Ck},

NL2 = {k|ck < Ck}, where ck =∑

u∈NU

∑i∈Nc

∑j∈Nc

xk,ui,j . Define Rk,ui,j = wuRk,u

i,j

and set R = {Rk,ui,j |x

k,ui,j = 1, k ∈ NL1}. Then we can execute the subcarrier offload-

ing algorithm summarized in Algorithm 4.3 and obtain the solution x∗ to P4. The

time complexity of Algorithm 4.3 is O(NcNLNU + Nc log(Nc)). So the total time

complexity of solving P4 will be O(NLNUN2c +N3

c ).

Algorithm 4.3 Subcarrier Offloading Algorithm1. Sort R in increasing order and store it in array AR2. for Rk,u

i,j in AR3. Initialize Rmax

i,j ⇐ 0, (k∗, u∗)⇐ (0, 0)

4. for k′ ∈ NL2, u′ ∈ NU

5. if Rk′,u′

i,j > Rmaxi,j

6. Rmaxi,j ⇐ Rk′,u′

i,j , (k∗, u∗)⇐ (k′, u′)

7. end if8. end for9. xk,ui,j ⇐ 0, xk

∗,u∗

i,j ⇐ 1, update ck, NL1 and NL2.10. if NL1 = ∅11. break12. end if13. end for14. update {xk,ui,j } ⇐ {x

k,ui,j }.

113



We now evaluate the performance of the proposed SO-OFDM-based HVP system.

We consider an example setup of a 5 m × 5 m room with NL = 4 coordinated

VLC-enabled LED luminaires, each of which contains NE = 36 LEDs. The setup

of the HVP system and the applied coordinate system are illustrated in Figure 4.3.

Denoting the length of the power line connecting the ith luminaire and the PLC

modem as li, we consider an example setup where l1 = 7 m, l2 = 8 m, l3 = 9 m,

l4 = 10 m. The LEDs have an operating range of IL = 300 mA to IU = 700 mA, with

a 3 dB bandwidth WLED = 10 MHz with blue filtering [102]. The DC bias is set to

IDC = (IL + IU)/2 = 500 mA, which provides a sufficient illumination for office work

and study with this system setup [54].

The HVP system has Np = 1024 independent information-carrying subcarriers,

and we set Ck = 256, k = 1, . . . , 4. For the PLC link, the minimum subcarrier fre-

quency is 2.026 MHz and the subcarrier spacing is 24.4 kHz [119]. For the VLC link,

we adopt the same subcarrier spacing as the PLC link, but the first data carrying

subcarrier is at frequency 24.4 kHz. The PLC transmit PSD is set to -50 dBm/Hz ac-

cording to the HomePlug AV standard [136] so that conducted and radiated emission

limits are met. The PLC noise in the simulation includes background, narrowband,

and impulse noise, where the PSDs and the corresponding measurement-based param-

eters of the former two are described in [137] and [118], respectively. For the impulse

noise, we adopt the model from the IEEE 1901 standard [119, Annex F.3.5.2], which

includes periodic synchronous, periodic asynchronous and aperiodic noise compo-

nents, and we apply the parameters from measurements provided in [138]. The PLC

noise simulator we developed and used here is available online [122]. For simulation

accuracy, we apply the two-state approximation as in [121, Eq. (19)] to calculate

114


the average achievable rate, which takes into account all of colored background noise,

narrowband disturbance and impulsive noise. The average achievable rate can be cal-

culated as the weighted sum of the achievable rates of the system with and without

impulse noise:

Ravg = (1− p)Rwithout_imp + pRwith_imp , (4.25)

where Ravg denotes the average achievable rate, Rwithout_imp denotes the achievable

rate of the system when impulse noise is absent and only colored background noise

and narrowband disturbance are considered, and Rwith_imp denotes the achievable

rate of the system when impulse noise is present. p denotes the probability of im-

pulse noise occurrence, and we let p = 0.01 in the simulation based on the PLC

noise measurement [120]. According to the measurement, p < 0.01 in even heavily

disturbed power line environment, thus our simulation results can be considered as a

lower bound of the average achievable rate. Further system parameters are listed in

Table 4.1.

4.5.1 Single-User System

We first consider the single-user scenario and focus on analyzing the system perfor-

mance with different optical OFDM, relay and SA schemes. In the following, we use

DF-DCO, DF-ACO, AF-DCO and AF-ACO to identify the cases where DF or AF

relaying at the luminaires is used together with DCO-OFDM or ACO-OFDM for the

optical OFDM scheme, respectively.

Figure 4.4 compares the achievable rates of the four transmission schemes as a

function of the user location in the x-y plane. The user height is assumed to be

z = 0.8 m. We observe that for all four schemes, the system achieves the highest rate

115


Table 4.1: Simulation parameters.

Room SetupFixture coordinate 1 [1.25, 1.25, 3]Fixture coordinate 2 [1.25, -1.25, 3]Fixture coordinate 3 [-1.25, -1.25, 3]Fixture coordinate 4 [-1.25, 1.25, 3]Room Length L × W × H 5 [m] × 5 [m] × 3 [m]

VLC ParametersLambertian order m 1PD area APD 1 [cm2]Concentrator refractive index κ 1.5Receiver FOV ψc 85 [deg.]Noise bandwidth factor I2 0.562Background current Ibg 100 [µA]LED conversion factor s 0.44 [W/A]PD responsivity γ 0.30 [A/W]

when the user is near the center of the room and rate decreases as the user moves

closer to the walls. SA without SP and SA with SP can improve the achievable

rate notably across the room compared with a random SA at the luminaire relays,

which we refer to as Random SA. In Figure 4.4, we also notice that the DCO-OFDM

scheme achieves a higher system rate than ACO-OFDM. This is due to the fact

that ACO-OFDM only utilizes odd subcarriers for data transmission, which makes

it less bandwidth-efficient than DCO-OFDM. In particular, for the same number

of information-carrying subcarriers in DCO-OFDM and ACO-OFDM, ACO-OFDM

uses a broader frequency spectrum and thus suffers from stronger channel attenuation

at higher frequencies. For the results in Figure 4.4, we set α =√

10 and β = 10,

which is a reasonable choice as will be discussed next.

For the results in Figure 4.5 and Figure 4.6, we fix the user location to x = −0.5 m,

y = 1.5 m, and z = 0.8 m. In Figure 4.5, we show the achievable rate as a function

of the relay gain α and β, respectively. When the relay gain is small and thus the

116


transmission power for the VLC hop is relatively low, the system performance is VLC-

noise limited. Increasing the relay gain will increase the SNR, but at some point LED

clipping distortion becomes the dominant noise source and curbs further performance

improvements. Hence, there is an optimal relay gain for each of the four transmissions

schemes, which depends on the magnitude of VLC noise, VLC channel (e.g., receiver

orientation, etc). Figure 4.6 compares the performance of Random SA, SA without SP

and SA with SP as a function of chunk size Ns. We can observe that SA without SP

and SA with SP can greatly enhance the system performance compared with Random

SA. Note that for SA without SP in the AF-DCO system, modulation/demodulation,

FFT/IFFT and encode/decode blocks shown in Figure 4.2 are not required, and the

signal transition between PLC and VLC can be done in the analogue domain. Based

on the results, a chunk size of Ns = 16 seems to provide close to optimal performance,

while providing computational complexity savings when solving the SA optimization

problem.

We next investigate whether the PLC or the VLC hop is limiting the performance

of the HVP system, for which we focus on the DF-mode and SA with SP. Since the

PLC and VLC channels are frequency selective, we count the number NVLC_BL of

subcarrier pairs for which the VLC hop is the bottleneck link when the maximum

achievable rate is attained. Figure 4.7 plots the NVLC_BL as a function of the user

location in the x-y plane with z = 0.8 m for both DF-DCO and DF-ACO. The 3 dB

bandwidth of WLED = 10 MHz used for the results in Figure 4.7a corresponds to the

current system setup with a blue filter at the photodiode, and WLED = 2 MHz for

the results in Figure 4.7b corresponds to a photodiode receiver without blue filtering

[139]. We observe that NVLC_BL of DF-DCO is generally smaller than that of DF-

ACO due to the stronger channel attenuation of ACO-OFDM at higher frequencies.

117


In Figure 4.7a, NVLC_BL is typically less than 60 out of Np = 1024 subcarrier pairs

for both DF-DCO and DF-ACO, which shows that the PLC link is the main bottle-

neck for the end-to-end performance of the HVP system. This changes notably and

especially for the system operating in the DF-ACO mode when the LED bandwidth

is reduced to 2 MHz. Here, the VLC hop limits the system performance, as shown

in Figure 4.7b.

4.5.2 Multi-User System

We now consider the scenario of multiple VLC users. We perform simulations for

both OFDM-TDMA and OFDMA to evaluate the corresponding achievable rate and

user fairness. In this section, we use AF-ACO as the example transmission scheme.

Figure 4.8 shows the average sum achievable rate against the number of VLC users.

For a given value of NU, a set of sum achievable rates are calculated and averaged by

distributing NU users uniformly at random over the indoor environment. For a fixed

location of NU users, we evaluate the average sum achievable rate over 100 time slots,

and the weights {wu} in schemes with PF scheduling are updated with Nres = 20 in

(4.21). For schemes without PF, OFDM-TDMA without PF represents an OFDM-

TDMA scheme with wu set to 1 and the user scheduling degrades to a Round-Robin

(RR) scheme. OFDMA without PF represents an OFDMA scheme with wu set to 1,

and the user scheduling degrades to a sum-rate maximizing scheduling and fairness

across users is neglected. From Figure 4.8, we can see that as NU increases, the sum

achievable rates of OFDMA schemes grow monotonically while the sum achievable

rates of OFDM-TDMA remain almost unchanged. OFDMA outperforms OFDM-

TDMA since it exploits the multi-user diversity. Not imposing the PF constraint

provides further gains due to the increased multi-user diversity.

118


The benefit of schemes with PF is illustrated in Figure 4.9. We consider a fixed

location profile forNU = 4 users and plot the average achievable rate for each user over

100 time slots (we assume that users remain static during this time period). We can

see that PF can improve the data rate fairness across users for both OFDM-TDMA

and OFDMA schemes, and PF is significantly important for OFDMA scheme. For

the setup in Figure 4.9, due to the poor channel conditions, no subcarrier is allocated

to User 4 in the OFDMA scheme without PF. Unlike RF wireless communication,

there is no multipath fading for indoor VLC channels due to the large photodiode size

compared with the optical wavelength. The deterministic nature of the VLC channel

will fix users in low SNR channels to become complete neglected in user scheduling

if PF scheduling is not applied. As expected, although PF results in lower overall

rate, it is a desirable feature to ensure some level of fairness among the users of the

proposed HVP system.

4.6 Conclusion

In this chapter, we have proposed a multicarrier HVP system as a potential indoor

high-speed downlink solution employing the symbiotic relationship between PLC and

VLC. Compared with traditional multicarrier-based VLC-PLC integration, the pro-

posed HVP system alleviates the PAPR problem for VLC transmitters and elim-

inates the inter-luminaire interference through the cooperation of LED luminaires

piggybacked on the powerline backbone. We have considered the HVP system as a

two-hop relay system and investigated different approaches of signal transition be-

tween PLC and VLC systems. To exploit the frequency selectivity of HVP channels,

as well as the multi-user and multi-transmitter diversity, we have proposed several

subcarrier allocation schemes with varying degrees of tradeoff among hardware, com-

119


putational complexity and performance for meaningful variations of the HVP sys-

tem. As another important contribution, we have investigated and compared two

multi-access schemes for the HVP system, i.e., OFDMA and OFDM-TDMA. Several

polynomial-time SA algorithms are proposed correspondingly. At the cost of higher

computational complexity, OFDMA has been shown to outperform OFDM-TDMA

for the HVP system in multi-user situations. For future work, power and bit loading

for the SO-OFDM-based HVP system can be investigated, where the linear period-

ically time varying (LPTV) properties of PLC channels can be exploited to reduce

the complexity of implementation [140].

120


LED luminary

Access

Network

VLC User PLC modem

12

3

4

Powerline

zx

y

Figure 4.3: The setup of HVP system.

121


0

2.5

5

0

2.5

5120

140

160

180

x (m)

(a) AF−DCO

y (m)

Ach

ievab

le r

ate

(M

bit

s/s)

0

2.5

5

0

2.5

580

100

120

140

160

x (m)

(b) AF−ACO

y (m)

Ach

ievab

le r

ate

(M

bit

s/s)

0

2.5

5

0

2.5

5100

150

200

x (m)

(d) DF−ACO

y (m)

Ach

ievab

le r

ate

(M

bit

s/s)

SA with SP

SA without SP

Random SA

0

2.5

5

0

2.5

5160

170

180

190

200

x (m)

(c) DF−DCO

y (m)

Ach

ievab

le r

ate

(M

bit

s/s)

Figure 4.4: Achievable rate as a function of user location. Nc = 16, α =√

10, β = 10.

122


100

101

102

60

80

100

120

140

160

180

β

Ach

ievab

le r

ate

(M

bit

s/s)

(a) AF−DCO

100

101

102

20

40

60

80

100

120

140

160

β

Ach

ievab

le r

ate

(M

bit

s/s)

(b) AF−ACO

100

101

102

80

100

120

140

160

180

200

α

Ach

ievab

le r

ate

(M

bit

s/s)

(c) DF−DCO

SA with SP

SA without SP

Random SA

100

101

102

80

100

120

140

160

180

200

α

Ach

ievab

le r

ate

(M

bit

s/s)

(d) DF−ACO

Figure 4.5: Achievable rate versus relay gain (α or β). Nc = 16. User location isx = −0.5 m, y = 1.5 m, z = 0.8 m.

123


Figure 4.6: Comparison of different SA schemes with different chunk size Ns. α =√10, β = 10. User location is x = −0.5 m, y = 1.5 m, z = 0.8 m.

124


0

2.5

5

0

2.5

5

0

10

20

30

40

50

60

70

80

DF−DCO

NV

LC

_B

L

0

2.5

5

0

2.5

5

0

20

40

60

80

100

120

DF−ACO

NV

LC

_B

L

(a) WLED = 10 MHz.

0

2.5

5

0

2.5

5

0

20

40

60

80

100

120

140

DF−DCO

NV

LC

_B

L

0

2.5

5

0

2.5

5

0

100

200

300

400

500

600

700

800

DF−ACO

NV

LC

_B

L

(b) WLED = 2 MHz.

Figure 4.7: NVLC_BL as a function of user location. Nc = 16. NVLC_BL is the numberof subcarrier pairs for which the VLC hop is the bottleneck link when the maximumachievable rate is attained. 125


Nu = 1 Nu = 2 Nu = 3 Nu = 4 Nu = 5145

150

155

160

165

170

175

180

Number of users

Ach

iev

ab

le r

ate

(M

bit

s/s)

OFDM−TDMA without PF

OFDM−TDMA with PF

OFDMA without PF

OFDMA with PF

OFDM−TDMA

OFDMA

Figure 4.8: Achievable rate versus the number of users NU. SA with SP and AF-ACOare applied. β = 10, Nc = 16.

126



10

20

30

40

50

(a) OFDM−TDMA without PF

Ach

iev

ab

le r

ate

(M

bit

s/s)


5

10

15

20

25

30

35

40

(b) OFDM−TDMA with PF

Ach

iev

ab

le r

ate

(M

bit

s/s)


10

20

30

40

50

60

70

80

(c) OFDMA without PF

Ach

iev

ab

le r

ate

(M

bit

s/s)


10

20

30

40

50

(d) OFDMA with PF

Ach

iev

ab

le r

ate

(M

bit

s/s)

Figure 4.9: Comparison of multi-access schemes with and without PF for NU = 4.The example locations are (x = −1.25, y = 1.25, z = 0.8) m, (x = −1.25, y =−1.25, z = 0.8) m, (x = 1.25, y = 1.25, z = 0.8) m and (x = 2.5, y = 2.5, z = 0.8) mfor User 1, User 2, User 3 and User 4, respectively. SA with SP and AF-ACO areapplied. Nc = 16, β = 10.

127

Chapter 5

Conclusion

5.1 Summary

Most research in physical-layer VLC transmission schemes focus on point-to-point

communication, however, typical rooms are usually equipped with multiple LED

luminaires instead of just one to ensure the uniformity of indoor illumination level.

Multiple independent point-to-point links will lead to strong interference among users

as the illumination footprints of neighboring LED luminaires usually have significant

overlap. To mitigate the co-channel interference, the simplest method is traditional

frequency planning that assigns different sub-bands to neighbouring attocells. An-

other method is to position VLC luminaires separately to avoid overlapping foot-

prints, and the gap between attocells is covered by RF base stations. In comparison

with frequency planning, this hybrid RF-VLC scheme allows full frequency reuse

among VLC attocells.

Different from the previous methods, the research work in this thesis presented an

alternative approach which achieves interference mitigation through coordination of

different VLC attocells. The thesis focused on developing transmission schemes for

coordinated VLC attocells. We considered three different coordinated architectures

for VLC downlink transmission. Chapter 2 proposed the full cooperation among

VLC attocells and the multiple coordinated VLC emitters form a virtual multiple-

transmitter system. The system design in Chapter 2 focused on the MMSE precoder

128

Chapter 5. Conclusion

design subject to lighting constraint. Chapter 3 extends the work in Chapter 2 by

considering looser coordination among neighboring attocells with multiple luminaires

each, which puts less requirement on the inter-attocell communication and synchro-

nization, though at the cost of compromised system performance. Numerical results

show that the coordination scheme proposed in Chapter 3 provides a good tradeoff

between system performance and complexity. While Chapter 2 and 3 assumed the

existence of backbone network for VLC transmitter, Chapter 4 delved deeper into the

power line backbone network for the proposed hybrid VLC-PLC system. In addition,

SO-OFDM was applied across multiple neighboring VLC transmitters to alleviate the

PAPR problem for each VLC transmitter, and several subcarrier allocation schemes

are proposed to exploit the frequency selectivity of the VLC and PLC channels. Dif-

ferent possible and meaningful variations of the HVP system, including the choice of

optical OFDM transmission, relay and multiple access schemes, are investigated and

compared.

5.2 Future Work

In Chapter 2 and Chapter 3, we focus on developing the spatial multiplexing tech-

niques at the transmitter side to serve multiple indoor VLC users simultaneously. It

will be interesting to investigate the joint optimization of user scheduling and beam-

forming to enhance the system performance when the number of users exceeds that

of VLC-enabled LED luminaires. What’s more, the designs proposed by Chapter 2

and Chapter 3 only apply to the single-carrier modulation, more specifically, PAM.

The optimal multi-carrier beamforming designs for both JT and CB, to the author’s

knowledge, have yet to be studied.

In fact, our ultimate goal is to build a Cloud VLC Access Network (C-VAN) which

129

Chapter 5. Conclusion

is similar to its counterpart Cloud Radio Access Network (C-RAN) in RF systems

[141]. Individual signal processing units for different VLC attocells are replaced by

a centralized unit. The LED luminaires operate as access points for the users, and

are connected to the centralized unit which coordinates the transmission for all the

attocells. The advantages of deploying C-VAN for indoor VLC systems are multi-fold.

First, smoother handover across different VLC attocells can be realized. Second, C-

VAN increases system adaptability to non-uniform indoor traffic by dynamic resource

allocation at the centralized unit. Third, C-VAN reduces the deployment cost for

VLC-enabled luminaires since luminaires in C-VAN require no baseband processing

module. Last, and most importantly, C-VAN can achieve higher system capacity

and lower IAI through collaboration among VLC transmitters. The research work

in this thesis is the first step towards a practical C-VAN system. In this thesis, we

focus on the (robust) precoder design and various resource allocation algorithms, and

assume perfect synchronization, unlimited backbone capacity and negligible delay for

coordinated VLC systems, which is not the case in reality. Factors, like time and

frequency synchronization across different VLC transmitters, backbone requirement

for a predefined VLC data rate and the effect of delay in the backbone network are

vital to the successful implementation of a working system. Future research is needed

to address these issues.

130

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143

Appendix A

Proof of Outdated CSI Bound

For the terminal movement in the horizontal direction, the terminal can either move

away from or towards the VLC transmitter. In the former case, the resulting differ-

ence in the scalar channel gain between two consecutive CSI updates can be expressed

as a function of dh and calculated according to Equation (1.2):

ε+(dh) = hp1− hp2

(A.1)

=(m+ 1)NEsγκ

2APD

2π(d2v + d2

h)

(dv√d2v + d2

h

)m+1

− (m+ 1)NEsγκ2APD

2π(d2v + (dh + L)2)

(dv√

d2v + (dh + L)2

)m+1

= β

((d2v + d2

h

)−m+32 −

(d2v + (dh + L)2)−m+3

2

),

where

β =(m+ 1)NEsγκ

2APDdm+1v

2π sin2(ψc). (A.2)

Based on the three facts:

1. ε+(0) > 0 ,

2. d ε+(dh)d dh

∣∣∣dh=0

> 0 ,

3. limdh→+∞ ε+(dh)→ 0 ,

144

Appendix A. Proof of Outdated CSI Bound

it can be deduced that there exists one maximum in (0, +∞). Therefore, there exists

at least one d1 ∈ (0,+∞) that satisfies d ε+(dh)d dh

∣∣∣dh=d1

= 0, and one of those d1 is

corresponding to the maximum. To obtain d1, we calculate the derivative of equation

(A.1):

d ε+(dh)

d dh

∣∣∣∣dh=d1

= 0

⇒ log

(d1

L+ d1

)=m+ 5

2log

(d2v + d2

1

d2v + (L+ d1)2

). (A.3)

So the maximum channel gain difference between two consecutive CSI updates when

the user terminal moves away from the VLC transmitter is

ε+ = maxdh

ε+(dh) = β(

(d2v + d2

1)−m+3

2 − (d2v + (d1 + L)2)−

m+32

), (A.4)

where d1 satisfies (A.3). Similarly, if the user terminal moves towards the VLC trans-

mitter, the maximum difference in the scalar channel gain between two consecutive

CSI updates can be expressed as

ε− = β(

(d2v + (d2 − L)2)−

m+32 − (d2

v + d22)−

m+32

), (A.5)

where d2 satisfies

log

(d2

d2 − L

)=m+ 5

2log

(d2v + d2

2

d2v + (d2 − L)2

). (A.6)

So the error bound for the kth user can be expressed as εk = max{ε+, ε−}, together

with (A.3)–(A.6).

145

Documents

Coordinated Transmission for Visible Light Communication Systems by Hao Ma MASc., King