Transmission of OFDM-UWB radio signals in FTTH … of OFDM-UWB radio signals in ... radio signals in future wireless personal area ... radio signals in FTTH networks using chirp-managed

Transmission of OFDM-UWB radio signals in FTTH networksusing chirp-managed lasers

Pedro Luís Benito Canêlhas

Dissertação para obtenção do Grau de Mestre em

Engenharia Electrotécnica e de Computadores

Júri

Presidente: Prof. José Manuel Bioucas DiasOrientador: Prof. Adolfo da Visitação Tregeira CartaxoVogal: Prof. António Luís Jesus Teixeira

Outubro 2010

Acknowledgments

I would like to express my gratitude to my supervisor, Professor Adolfo Cartaxo, whose expertise, de-

manding requirements and patience were relevant to my dissertation. I appreciate his vast technical

knowledge in the field of optical communications, and his assistance in the evaluation of my reports.

I would like also to thank the PhD students at the Group of Research on Optical Fiber Telecommunication

Systems (GROFTS) of Instituto de Telecomunicações, Tiago Alves, Nelson Costa and Filipe Wiener, for

their prompt availabitlity and continued support during the many weeks we worked side by side in the

optical laboratory at Instituto Superior Técnico.

An acknowledgement is addressed to Instituto de Telecomunicações in recognition for the scolarship and

the use of their facilities.

Lastly, and most importantly, I am extremely grateful to my family and friends for the encouragement

and support they provided me through my entire life.

I dedicate this dissertation to my mother and father for their consistent guiding and strong commitment

providing me with all the educational tools to achieve my academic goals, and to my brother, whose

example and advice were also determinant in the choices I had to make in my life.

i

Abstract

Fiber-to-the-home (FTTH) networks have been proposed as a means to extend the application of ultra-

wideband (UWB) radio signals in future wireless personal area networks (WPAN) to the delivery of

high data-rate applications. In this dissertation, it is investigated, using numerical simulation through

MATLAB R©, the transmission of orthogonal frequency-division multiplexing ultra-wideband (OFDM-

UWB) radio signals in FTTH networks using chirp-managed lasers (CML). The main parameters that

influence the performance degradation of the OFDM-UWB signals distribution in FTTH networks are

identified and optimized. The main transmission impairments are discussed and the maximum transmis-

sion distance for a required minimum quality is assessed.

The performance optimization shows that the optical transmitter originates a half-clipped OFDM-UWB

signal. A half-clipped OFDM-UWB signal has reduced distortion although half of its amplitude was

removed. The optical transmitter applies a higher gain to the OFDM-UWB signal balancing an increase

of signal distortion and the raise of the power level of the UWB subbands.

The chirp-managed-based transmission achieves an improvement of 10 km of the maximum transmis-

sion distance compared to the use of a directly-modulated laser (DML). It is concluded that the quality

OFDM-UWB optical signal shows a higher resilience to the fiber chromatic dispersion in the CML-based

transmission.

keywords: Chirp-managed lasers, directly-modulated lasers, fiber-to-the-home networks, optical com-

munications, orthogonal frequency-division multiplexing ultra-wideband radio signals.

ii

Resumo

A utilização de redes de fibra até à casa do cliente (FTTH) tem sido proposta como o meio de distribuição

de sinais rádio de banda ultra-larga (UWB) nas futuras redes pessoais sem fios (WPAN) para a difusão

de aplicações de alto débito. Nesta dissertação, investiga-se a transmissão de sinais rádio de banda

ultra-larga usando multiplexagem ortogonal por divisão na frequência (OFDM-UWB) em redes FTTH

utilizando lasers com chirp controlado (CML). Os principais parâmetros que influenciam a degradação

do desempenho da transmissão de sinais OFDM-UWB em redes FTTH são identificados e optimizados.

Os principais problemas associados à transmissão são analisados e a distância máxima alcançada para

uma qualidade mínima requirida é avaliada.

A optimização do desempenho mostra que o transmissor óptico origina um sinal OFDM-UWB semi-

cortado. Este sinal apresenta distorção reduzida apesar de ter sido removida metade da sua amplitude.

O transmissor aplica um maior ganho ao sinal OFDM-UWB equilibrando uma maior distorção de sinal

com o aumento do nível de potência das sub-bandas UWB.

Obtém-se uma melhoria de 10 km no alcance máximo de transmissão usando CML em vez de lasers

modelados directamente. Conclui-se que o sinal óptico OFDM-UWB mostra maior resistência à disper-

são cromática da fibra quando se usa CML.

Palavras-chave: Comunicações ópticas, laser com chirp controlado, laser modulado directamente, re-

des de fibra até à casa do cliente (FTTH), sinais de rádio de banda ultra-larga usando multiplexagem

ortogonal por divisão na frequência.

iii

Contents

Acknowledgments i

Abstract ii

Resumo iii

Contents iii

List of figures vi

List of tables ix

List of acronyms xii

List of symbols xiv

1. Introduction 1

1.1. Scope of the work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

1.2. Objectives and structure of the dissertation . . . . . . . . . . . . . . . . . . . . . . . . . 4

1.3. Original contributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

2. OFDM-UWB Radio Signals 6

2.1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

2.2. OFDM-UWB radio signals mathematical formulation . . . . . . . . . . . . . . . . . . . 6

2.2.1. Baseband and bandpass OFDM . . . . . . . . . . . . . . . . . . . . . . . . . . 6

2.2.2. Cyclic prefix introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

2.2.3. Discrete Fourier transform implementation of OFDM . . . . . . . . . . . . . . . 8

2.2.4. OFDM transmitter and receiver . . . . . . . . . . . . . . . . . . . . . . . . . . 9

2.2.5. UWB standard for OFDM (OFDM-UWB) . . . . . . . . . . . . . . . . . . . . . 10

2.3. Time and frequency analysis of OFDM-UWB radio signals . . . . . . . . . . . . . . . . 12

2.4. Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

iv

3. OFDM-UWB FTTH network model 18

3.1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

3.2. FTTH network architecture . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

3.2.1. OFDM-UWB transmitter, gain and DC current . . . . . . . . . . . . . . . . . . 20

3.2.2. Clipper . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

3.2.3. Directly modulated laser . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

3.2.4. Optical Spectrum Reshaping filter . . . . . . . . . . . . . . . . . . . . . . . . . 22

3.2.5. Optical filter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

3.2.6. Optical amplifier EDFA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

3.2.7. Optical fiber . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

3.2.8. Power splitter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

3.2.9. PIN Photodetector . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

3.2.10. Receiving filter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

3.2.11. OFDM-UWB receiver . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

3.3. Performance evaluation methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

3.3.1. Error Vector Magnitude . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

3.3.2. Semi-analytical Gaussian approach . . . . . . . . . . . . . . . . . . . . . . . . 28

3.4. Effects of clipping in an OFDM-UWB radio signal . . . . . . . . . . . . . . . . . . . . 29

3.5. Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

4. OFDM-UWB FTTH Network Optimization 34

4.1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34

4.2. Model of the system to be optimized . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

4.3. Optimization of the currents in single subband transmission . . . . . . . . . . . . . . . . 36

4.3.1. Back-to-back configuration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36

4.3.2. Performance with fiber transmission . . . . . . . . . . . . . . . . . . . . . . . . 38

4.4. Optimization of the currents in multi-subband transmission . . . . . . . . . . . . . . . . 41

4.4.1. Subbands used: 1,2 and 1,2,3 . . . . . . . . . . . . . . . . . . . . . . . . . 42

4.4.2. Subbands used: 1,2,3,4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47

4.5. Optical spectrum reshaper filter optimization . . . . . . . . . . . . . . . . . . . . . . . . 50

4.6. Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54

5. Transmission performance of the multi-subband OFDM-UWB signal in the optimized FTTH

network 56

5.1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56

v

5.2. Results and discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56

5.2.1. Assessment of the distortion inflicted by the OFDM-UWB FTTH network . . . . 59

5.2.2. Influence of the optical noise generated by the EDFA at the central node . . . . . 60

5.2.3. Influence of optical and electrical noise . . . . . . . . . . . . . . . . . . . . . . 62

5.3. Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62

6. Final conclusion 64

6.1. Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64

6.2. Suggestions for future work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66

A. Directly-modulated laser 67

A.1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67

A.2. Description of the directly modulated laser . . . . . . . . . . . . . . . . . . . . . . . . . 67

A.3. Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72

B. Optimization results 73

C. References 82

vi

List of Figures

2.1. OFDM symbol with cyclic prefix. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

2.2. Block diagram of the OFDM transmitter. . . . . . . . . . . . . . . . . . . . . . . . . . . 9

2.3. Block diagram of the OFDM receiver. . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

2.4. Frequency band allocation for the OFDM-UWB system. . . . . . . . . . . . . . . . . . 10

2.5. Amplitude response of a 6th-order low-pass Bessel filter. . . . . . . . . . . . . . . . . . 12

2.6. OFDM-UWB signal using subband 1. . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

2.7. OFDM-UWB current signal using subband 1 with a mean of 60 mA and a peak-to-peak

current of 80 mA. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

2.8. PSD of an OFDM-UWB signal using subband 1. . . . . . . . . . . . . . . . . . . . . . 14

2.9. Close-up of the PSD of an OFDM-UWB signal using subband 1. . . . . . . . . . . . . . 14

2.10. Mean, maximum and minimum values of the PAPR for a 2lseq deBruijn bit sequence

mapped into QPSK symbols in an OFDM-UWB signal using subband 1. . . . . . . . . . 15

3.1. Schematic of the FTTH network. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

3.2. Block diagram of the FTTH network. . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

3.3. Block diagram of the equivalent model of the FTTH network from single wavelength

view point. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

3.4. Static response of the directly modulated laser. . . . . . . . . . . . . . . . . . . . . . . . 21

3.5. Constellation diagram for QPSK. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

3.6. OFDM-UWB current signal using subbands 1,2,3,4. . . . . . . . . . . . . . . . . . . 30

3.7. PSD of OFDM-UWB current signal without clipping using subbands 1,2,3,4. . . . . . 30

3.8. EVM of the OFDM-UWB signal using subbands 1,2,3,4 as a function of the percent-

age of the bottom half removal. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

3.9. Example of an OFDM-UWB current signal using subbands 1,2,3,4 after clipping. . . . 31

3.10. PSD of the OFDM-UWB current signal using subbands 1,2,3,4 with 40%, 80% and

100% of bottom half clipped. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32

4.1. Block diagram of the equivalent FTTH network adequate for an optimization. . . . . . . 36

vii

4.2. Contour of the representation of the required OSNR as a function of the current level in

the back-to-back configuration for subband 1. . . . . . . . . . . . . . . . . . . . . . . . 37

4.3. OFDM-UWB current signal of three consecutive OFDM-UWB symbols for subband 1

using optimal current levels for the back-to-back configuration. . . . . . . . . . . . . . . 38

4.4. OSNR and EVM as a function of the SSMF length for the optimal current levels in

single-subbands 1, 2, 3 and 4. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40

4.5. Psb of single subbands 1, 2, 3 and 4 for optimal current levels as a function of the SSMF

length. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41

4.6. Required OSNR as a function of the SSMF length for the optimal current levels for

subbands 1,2 and 1,2,3. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45

4.7. Psb as a function of the SSMF length for multi-subband transmission of 1,2 and 1,2,3. 45

4.8. Required OSNR as a function of the SSMF length for the optimal current levels for

subbands 1,2 and 1,2,3 comparing to the single subband transmission of 2 and 3. 46

4.9. Required OSNR as a function of the SSMF length for the optimal current levels for sub-

bands 1,2 and 1,2,3 comparing the Bessel and rectangular filters use at the OFDM-

UWB transmitter and receiver. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46

4.10. BER contour for an OSNR = 15 dB as a function of the bias and peak-to-peak current in

the back-to-back configuration for subband group 1,2,3,4. . . . . . . . . . . . . . . . 47

4.11. Required OSNR and EVM as a function of the SSMF length for the optimal current

levels in transmission of subbands 1,2,3,4. . . . . . . . . . . . . . . . . . . . . . . . . 49

4.12. Required OSNR as a function of the SSMF length for the optimal current levels in trans-

mission of subband groups 1,2,3,4 with maximum and minimum PAPR. . . . . . . . . 49

4.13. OSNR as a function of the SSMF length for the optimal current levels in multi-subband

groups 1,2, 1,2,3 and 1,2,3,4. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50

4.14. Frequency chirp of the DML output when modulated by an OFDM-UWB signal using

subband group 1,2,3,4. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51

4.15. OFDM-UWB current signal of three consecutive OFDM-UWB symbols for subband

group 1,2,3,4. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51

4.16. Required OSNR for BER = 10−4 as a function of the peak-to-peak current in 80 km fiber

transmission with an optimized OSR. . . . . . . . . . . . . . . . . . . . . . . . . . . . 52

4.17. Required OSNR for BER = 10−4 as a function of the peak-to-peak current in 100 km

fiber transmission with an optimized OSR. . . . . . . . . . . . . . . . . . . . . . . . . . 52

4.18. PSD of the OFDM-UWB signal in several points of the network. . . . . . . . . . . . . . 54

5.1. BER as a function of the SSMF length of the FTTH network considering N=64. . . . . . 58

viii



5.4. EVM value at the OFDM-UWB receiver for the CML and DML-based transmission. . . 60

5.5. Constellation of the received symbols from subbands 1, 2, 3 and 4 of CML and DML-

based 100 km transmission. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60

A.1. Frequency characteristics of the assemblage effects on the DML. . . . . . . . . . . . . . 70

A.2. Static response of the MQW laser. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70

A.3. Dynamic response of the DML when modulated by small current signals. . . . . . . . . 71

B.1. Contour of the representation of the required OSNR as a function of the current level for

subband 1 considering a fiber transmission from 0 to 100 km. . . . . . . . . . . . . . . . 74








subbands 1 and 2 considering a fiber transmission from 0 to 100 km. . . . . . . . . . . . 78


subbands 1, 2 and 3 considering a fiber transmission from 0 to 100 km. . . . . . . . . . . 79


subbands 1, 2, 3 and considering a fiber transmission from 0 to 80 km. . . . . . . . . . . 80

B.8. BER contour for an OSNR = 15 dB as a function of the current levels for subbands 1, 2,

3 and 4 considering a fiber transmission from 0 to 100 km. . . . . . . . . . . . . . . . . 81

ix

List of Tables

2.1. PAPR mean, maximum and minimum values for different subbands used. . . . . . . . . 16

4.1. Noiseless EVM of the single subband OFDM-UWB signal in several points of the system

in the back-to-back configuration. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38

4.2. Optimal current levels for single subband transmission and corresponding required OSNR

for BER=10−4 for the back-to-back configuration. . . . . . . . . . . . . . . . . . . . . . 38

4.3. Optimal current levels for the fiber transmission using subband 1 and corresponding

required OSNR. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39


required OSNR. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39


required OSNR. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40

4.6. Optimal current levels for the fiber transmission using subband 4 and the corresponding

required OSNR. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40

4.7. Noiseless EVM of the OFDM-UWB signal in several points of the system for the multi

subband transmission 1,2 in the back-to-back configuration. . . . . . . . . . . . . . . 43


subband transmission 1,2,3 in the back-to-back configuration. . . . . . . . . . . . . . 43

4.9. Optimal current levels for the multi-subband fiber transmission of 1,2 and the corre-

sponding minimum required OSNR. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44

4.10. Optimal current levels for the multi-subband fiber transmission of 1,2,3 and the corre-



subband transmission 1,2,3,4 in the back-to-back configuration. . . . . . . . . . . . . 48

4.12. Optimal current levels for a multi-subband fiber transmission of 1,2,3,4 and the corre-


4.13. OSR filter optimization results. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53

x

5.1. OSNR calculated at the DEMUX input in the CML-based transmission. . . . . . . . . . 61

A.1. Ortel MQW laser parameter values. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69

xi

List of acronyms

ASE Amplified Spontaneous Emission

BER Bit Error Ratio

BPSK Binary PSK

CML Chirp-Managed Laser

DAB Digital Audio Broadcasting

DAC Digital-to-Analog Conversion

DC Direct Current

DFT Discrete Fourier Transform

DML Directly-Modulated Laser

DVB Digital Video Broadcasting

DWDM Dense Wavelength Division Multiplexing

ECMA European Computer Manufacturers Association

EDFA Erbium-Doped Fiber Amplifier

ER Extinction Ratio

EVM Error Vector Magnitude

FCC Federal Communications Comission

FFT Fast Fourier Transform

FM Frequency Modulation

FTTH Fiber-To-The-Home

HDTV High-Definition Television

IDFT Inverse Discrete Fourier Transform

IEEE Institute of Electrical and Electronics Engineers

IFFT Inverse Fast Fourier Transform

IM Intensity Modulation

IR-UWB Impulse Radio Ultra-Wideband

xii

ISI Inter-Symbol Interference

LP Low-Pass

LR-PON Long-Reach Passive Optical Network

MC Monte Carlo

M-PSK M-ary Phase Shift Keying

MQW Multiple Quantum Wells

NRZ Non-Return-to-Zero

OFDM Orthogonal Frequency Division Multiplexing

OFDM-UWB Orthogonal Frequency Division Multiplexing Ultra-Wideband

OFDM-UWB RX OFDM-UWB Receiver

OFDM-UWB TX OFDM-UWB Transmitter

OSNR Optical Signal-to-Noise Ratio

OSR Optical Spectrum Reshaper

PAM Pulse Amplitude Modulation

PAPR Peak-to-Average Power Ratio

PON Passive Optical Networks

PSD Power Spectrum Density

PSK Phase Shift Keying

QAM Quadrature Amplitude Modulation

QPSK Quadrature PSK

PIN Positive-Intrinsic-Negative

RF Radio Frequency

RIN Relative Intensity Noise

RMS Root-Mean-Square

SAGA Semi-Analytical Gaussia Approach

SSMF Standard Single Mode Fiber

UWB Ultra-Wideband

VA Variable Attenuator

WPAN Wireless Personal Area Network

xiii

List of symbols

Amux losses from the multiplexer/demultiplexer

Anr nonradiative recombination rate coefficient

Aspl losses from the splitter

Atotal minimum losses from the FTTH network

Ax losses from connectors and splices

B radiative recombination rate coefficient

B -10 dB bandwidth of a signal

B0 reference optical bandwidth of 0.1 nm

C Auger recombination coefficient

I DC current applied to the OFDM-UWB signal in the FTTH network

c light velocity

D dispersion parameter of the SSMF

Ein(t) electrical field at the EDFA input

Eout(t) electrical field at the EDFA output

fc center frequency of a signal

fn,e noise factor

fRF central frequency of a OFDM passband signal

f equivalent baseband frequency

gedfa gain of an EDFA

gedfa, CN gain of the EDFA at the central node

gedfa, LE gain of the EDFA at the local exchange

g gain applied to the OFDM-UWB signal in the FTTH network

gc gain parameter

h constant of Planck

xiv

iPIN(t) output current of the PIN photodetector

kB Boltzmann constant

lseq length of the bit sequence to be mapped in an OFDM signal

L length of the optical fiber

n order of the OSR filter

N number of subscribers in the FTTH network

N0 carrier density at transparency

Nsc number of subcarriers in an OFDM symbol

nsp spontaneous emission noise factor

PCN imposed mean power at the output of the central node

pPIN(t) optical power at the PIN input

POF mean power of the signal at the output of the optical filter that simulates the multiplexer

Popt mean optical power at the VA input

Psb mean power of a subband

Rb bias resistor of the photodetector

Rλ responsivity of the PIN

Sideal,r expected complex value of a demodulated symbol

Smeas,r complex of the demodulated value of the actual received symbol

sk Complex symbol that modulate an OFDM subcarrier

sRF (t) passband OFDM signal

S dispersion slope of the SSMF

s(t) baseband OFDM signal

xv

Tg guard interval of an OFDM symbol

T room temperature

t time signal

Ts duration of an OFDM symbol

Ts sampling period of an OFDM signal

Ttot duration of an OFDM symbol with cyclic extension

Vact volume of the active region

α loss coefficient of the SSMF

αc linewidth enhancement factor

β spontanerous emission factor

β2 group-velocity dispersion coefficient

∆ f separation in frequency of OFDM subcarriers

η differential quantum efficiency

ηi internal quantum efficiency

ε gain compression factor

δ [k− l] Kronecker delta symbol

Γ confinement factor

λ optical wavelength

ν optical frequency

νc central frequency of the OSR filter

νg bandwidth at -3 dB of the OSR filter

ν0 optical carrier frequency

τp photon lifetime

υ optical frequency

ϕk function in time that defines a OFDM subcarrier

xvi

1. Introduction

1.1. Scope of the work

In the near future, indoor communications will be supported by a single digital wireless network. Such

network requires: high data rates, so that several high-definition television (HDTV) channels and new

advanced multimedia-based applications could be provided; low cost, for a consumer massification;

and low power consumption, for applications using battery-powered devices. Due to its inherent high

capacity, ultra-wideband (UWB) signals have been proposed as a solution to satisfy these requirements

[1].

The UWB technology has been standardized by the U.S. Federal Communications Comission (FCC) [2],

which defines UWB as any transmission scheme that occupies a fractional bandwidth greater than 0.2

or a signal bandwidth of more than 500 MHz. The fractional bandwidth is defined as B/ fc, where B

represents the -10 dB bandwidth and fc is the center frequency of a signal.

There has been a growing interest in this technique due to its features such as high bit-rate over short-

range broadcasting, low self interference, tolerance to multi-path fading, low probability of interception

and the possibility of coexistence with other deployed wireless technologies [3].

UWB signals are suited for high-data-rate wireless personal area networks (WPAN) which can be defined

as networks that transmit at data rates ranging from 100 to 500 Mbps within a distance of 20 m. Recently,

IEEE 802.15.3 standard task group has established a study group [4] to define a new physical layer

concept for high-data-rate WPAN applications.

Although FCC has regulated the spectrum and transmitter power levels for an UWB signal, there is

currently no standard for an UWB transmission scheme. A possible approach for the implementation

of UWB technology is based on single-carrier system or impulse radio communications. Impulse radio

UWB (IR-UWB) refers to the generation of a series of impulselike waveforms of very short duration.

Each pulse occupies a bandwidth that fits the FCC requirements. The information is modulated directly

1

into the sequence of pulses using, for example, pulse amplitude modulation (PAM) [5]. However, a

receiver of the single-carrier system requires a complex receiver with RF and analog circuits.

A multi-carrier approach has been proposed to overcome the drawback of single-carrier systems. It

consists in dividing the UWB frequency band from 3.1 to 10.6 GHz into several smaller bands, named as

subbands [1]. A part of the information to be transmitted is given to each subband. Within each subband,

different types of data modulation can be adopted. WiMedia Alliance suggested selecting Orthogonal

Frequency Division Multiplexing (OFDM) for high-speed UWB wireless [6], leading to OFDM-UWB

signals. Later, European Computer Manufacturers Association (ECMA) adopted the WiMedia Approach

and ratified ECMA-368 standard [7].

One great advantage of multi-carrier UWB is that it is software configurable, so any frequency bands

can be turned off to meet specific spectral requirements. The OFDM-UWB solution shows flexibility

to provide multiple access, tolerance to multi-path fading and inter-symbol interference. The OFDM

technique has been used in digital video broadcasting (DVB) and digital audio broadcasting (DAB)

which allows achieving a fast and low cost integration.

Due to very low-power, wide bandwidth and high frequency signals characteristic of UWB, the trans-

mission of UWB over coaxial cable is not feasible because of its exceedingly high cost and high rate

of attenuation for a wideband signal. However, optical fiber provides an efficient alternative for the

transmission of UWB signals due to its low cost, wide bandwidth and low loss.

The distribution of OFDM-UWB radio signals over a fiber-to-the-home (FTTH) network has been pro-

posed in [8],[9]. This approach present several advantages: FTTH networks provide enough bandwidth

to distribute a large number of UWB signals; no transmodulation and frequency up-conversion is re-

quired for a fiber-to-wireless conversion at the subscriber premises; and, FTTH networks are transparent

to the UWB implementation employed.

One of the most attractive architectures of FTTH networks is the passive optical network (PON). PON

consists in a network shared among many costumers which increases its cost-effectiveness. Research

attention has been recently focused on new types of optically amplified long-reach (100 km) PONs (LR-

PONs) [10]. These LR-PONs would replace the separate metro and access portions of the network with

a single, integrated, all-optical communication system. The European Union-funded project PIEMAN

is performing physical layer research aimed at achieving a bandwidth per wavelength of up to 10 Gbps

downstream and upstream, where each 10 Gbps is shared by up to 512 costumers [11].

An experimental demonstration of OFDM-UWB distribution in FTTH networks is shown in [8],[12],[13].

2

In these works, significant performance degradation was observed when the optical fiber length in-

creases.

External modulation schemes, using for example Mach Zehnder modulator, have been adopted in optical

transmitters. In addition to the expensive use of external modulators, dispersion compensation modules

are required to overcome the transmission dispersion effects along a standard single-mode fiber (SSMF).

The use of external modulation is very inconvenient in FTTH networks where cost-effectiveness is a key

issue. In [14] the operation of a gigabit-PON (GPON) with 2.488 Gbps downstream and 1.244 Gbps

upstream over 135 km using external modulation techniques has been reported.

Currently, there has been a growing interest in utilizing directly modulated lasers (DML) because of their

potentially low cost, compact size, low power consumption and high optical output power characteristics.

Therefore, DML becomes a solution to overcome the cost issue of the optical transmitters.

The transmission of OFDM-UWB signals over single-mode fiber of 5 km length [15] and multimode fiber

of 400 meters length [16][17] using directly modulated lasers has been experimentally demonstrated and

the performance degradation of OFDM-UWB transmission over fiber has been experimentally investi-

gated and theoretically analyzed in [18]. In this case, the optical transmission was accomplished for a

maximum distance of 40 km while, in this dissertation, a maximum optical link of 100 km is established.

It was shown that direct modulation is limited by laser bandwidth, linewidth, stability, and relative inten-

sity noise (RIN) [19]. In [20], it was shown that RIN significantly degrades the OFDM-UWB over fiber

system, particularly for the higher frequency UWB channels.

The directly-modulated laser has been investigated as optical transmitter in FTTH networks [21]. It

reduces the network complexity, the installation and maintenance cost without compromising the flex-

ibility of the network [22]. However, the DML current modulation gives rise to high frequency chirp:

the intensity modulation is accompanied by frequency modulation [23]. This results in a broad spectrum

that severely limits the transmission distance due to the effect of chromatic dispersion.

Through a tuned optical spectrum reshaper filter (OSR) placed after the DML, bandwidth and chirp

reductions are achieved after the DML modulation. This filter performs a frequency modulation (FM) to

intensity modulation (IM) conversion, leading to a signal more robust to the dispersion of the fiber.

The grouping of the DML and the OSR composes the chirp-managed laser (CML) as presented in [24].

The optical signal obtained at the OSR output is more resilient to inter-symbol interference caused by

the dispersion effects associated with the transmission through the fiber.

The CML technique has been demonstrated in 10 Gbps transmission over 200 km of single-mode fiber

without dispersion compensation [25] and 675 km transmission using a combination of electronic dis-

3

persion compensation and tunable dispersion compensation [26]. Recently, it has been experimentally

demonstrated the 40 Gbps CML transmission over 20 km of single-mode fiber [27]. It was also achieved

a bit error ratio (BER) of 10−6 in the CML transmission of 40 Gbps in the metro network consisting of

a 240 km long link with dispersion compensating fiber.

In this work, the transmission of OFDM-UWB signals through a FTTH network using chirp-managed

lasers is proposed and investigated as a means to overcome the cost issue of the optical transmitter

and extend the transmission distance achieved by using conventional directly modulated lasers. The

CML transmitter is a highly practical solution to meet simultaneously the size, power, capacity and cost

requirements of the optical links in FTTH networks.

1.2. Objectives and structure of the dissertation

The objective of this dissertation is the analysis and performance optimization of the transmission of

OFDM-UWB radio signals in FTTH networks using chirp-managed lasers. The time and frequency

characteristics of OFDM-UWB signals are investigated. The influence of the each component of the

FTTH network on the OFDM-UWB signal quality is assessed. The key system parameters that influence

the transmission performance are identified and optimized through extensive numerical simulations and

the maximum transmission distance achieved for a given minimum quality is assessed.

The dissertation is structured as follows. Chapter 2 presents a detailed description of OFDM-UWB

signals. The mathematical formulation of OFDM-UWB signals is presented and the FCC standard for

UWB is detailed. A time and frequency analysis of OFDM-UWB signals is accomplished and the main

characteristics of the signals are identified.

In chapter 3, the FTTH network is analyzed as a means to transmit OFDM-UWB signals. An equivalent

model of the network is presented and each component is described - a careful description of the DML

operation is performed in Appendix A. The methods of performance evaluation of OFDM-UWB signals

in FTTH networks are presented in order to be used in the following chapters. At the end, chapter 3

analyzes the time and frequency effects of the non-linear operation of clipping performed at the FTTH

network transmitter.

Chapter 4 accomplishes the optimization of the current levels that modulate the optical transmitter in

the DML-based single and multi-subband transmission in the back-to-back configuration and with fiber

transmission. The influence of each component of the network is assessed and the impact of the si-

multaneous transmission of several subbands is analyzed. Based on the results from the current levels

4

optimization, the optical spectrum reshaper filter is introduced in the system and its characteristics are

optimized.

Chapter 5 analyzes the performance of the transmission of OFDM-UWB signals in the FTTH network

based on the outcome of chapter 4. The maximum transmission distance assuring a defined minimum

quality is calculated, and the DML and CML-based transmissions are compared.

Chapter 6 draws the main conclusions of this dissertation and topics for further investigations are sug-

gested.

1.3. Original contributions

In the analysis performed in this work, several original contributions were introduced relative to other

studies in the field. In the following, the list of the most important contributions of this work are pre-

sented:

1. time and frequency analysis of the non-linear operation (clipping) accomplished to OFDM-UWB

signals at the FTTH transmiter and its influence on the error vector magnitude.

2. optimization of the input currents of the DML in the single and multiple subband OFDM-UWB

transmission in the back-to-back configuration and in the configuration with fiber transmission for

lengths up to 100 km.

3. analysis of the distortion experienced by the OFDM-UWB signal in the clipper, in the DML and

by the fiber transmission.

4. analysis of the performance degradation of a single and multiple subband OFDM-UWB DML-

based transmission in the back-to-back configuration and in the configuration with fiber transmis-

sion for lengths up to 100 km with optimized input currents.

5. optimization of the optical spectrum reshaper filter parameters in the multi-subband OFDM-UWB

transmission in the configuration with fiber transmission of 80 and 100 km.

6. analysis of the performance degradation improvement of the multi-subband OFDM-UWB CML-

based transmission compared to the DML-based transmission.

7. analysis of the maximum transmission distance of an OFDM-UWB signal along FTTH network

achieved for a minimum defined quality for the CML-based and the DML-based optical transmit-

ters.

5

2. OFDM-UWB Radio Signals

2.1. Introduction

As mentioned in the Chapter 1, OFDM-UWB radio signals have been proposed to support high data rate

applications in the near future.

In this chapter, OFDM-UWB signals are introduced analytically in section 2.2: the general definition

of baseband and bandpass OFDM is detailed along with the implementation of OFDM in the UWB

standard. A time and frequency analysis of OFDM-UWB signals is presented in section 2.3.

2.2. OFDM-UWB radio signals mathematical formulation

2.2.1. Baseband and bandpass OFDM

OFDM is a form of multicarrier modulation, where a single data stream is transmitted over a number of

lower rate subcarriers [28],[29]. OFDM increases the robustness of the signal against frequency selective

channels and narrowband interference.

Let skk=0,1,... be the complex information symbols to be transmitted, obtained by mapping the binary

input data into a symbol stream using a signal format such as quadrature amplitude modulation (QAM)

or phase-shift keying (PSK). Each information symbol modulates different subcarriers separated by ∆ f

during a limited period of time.

The baseband OFDM signal is formed by a sequence of OFDM symbols, each one with a fixed duration

of Ts. Each OFDM symbol has Nsc subcarriers, corresponding to a group of Nsc information symbols,

and it can be expressed as

s(t) =Nsc−1

∑k=0

ske j2π fkt =Nsc−1

∑k=0

skϕk, for 0≤ t ≤ Ts, (2.1)

where fk = k∆ f , and

6

ϕk =

e j2π fkt , if 0≤ t ≤ Ts

0, otherwise(2.2)

The orthogonality condition, characteristic of OFDM signals, imposes an OFDM symbol duration given

by

Ts ·∆ f = K , K ∈ N (2.3)

It is easily proven that the set of functions ϕk are orthogonal along an OFDM symbol:

1Ts

∫ Ts

0ϕkϕ

∗l dt

=1Ts

∫ Ts

0e j2π( fk− fl)tdt

=1Ts

∫ Ts

0e j2π(k−l)∆ f ·tdt

= δ [k− l] (2.4)

where δ [k− l] is the Kronecker delta symbol defined by

δ [k− l] =

1, if k = l

0, otherwise(2.5)

Using the property of orthogonality, an OFDM symbol can be easily demodulated.

2.2.2. Cyclic prefix introduction

A guard interval with duration Tg is introduced between consecutive OFDM symbols to prevent Inter-

Symbol Interference (ISI) due to the delay spread of the transmission channel. A fraction of the guard

interval is used for transmitting a copy of the final part of the OFDM symbol in order to eliminate

intersubcarrier interference (see figure 2.1). This copy is named cyclic prefix. Thus, the baseband OFDM

signal can be written as

s(t) =

s(t +Ts), if −Tg ≤ t ≤ 0

s(t), if 0≤ t ≤ Ts

(2.6)

With the cyclic extension, the actual OFDM symbol duration is increased to Ttot = Ts +Tg, resulting in

7

the symbol rate of

RS =Nsc

Ttot=

Nsc

Ts +Tg(2.7)

Figure 2.1.: OFDM symbol with cyclic prefix.

In order to obtain OFDM bandpass signals, a carrier with frequency fRF is modulated by the OFDM

baseband signal. This frequency upconversion makes a complex-to-real conversion of s(t) as follows

sRF(t) = ℜ

s(t)e j2π fRF t= ℜs(t) · cos(2π fRFt)−ℑs(t) · sin(2π fRFt) (2.8)

where sRF (t) is the OFDM symbol transmitted with carrier frequency fRF .

2.2.3. Discrete Fourier transform implementation of OFDM

If s(t) is sampled with a sampling period of Tsa = Ts/Nsc it follows that

Sn = s(nTsa) =Nsc−1

∑k=0

ske j2π fknTsNsc =

Nsc−1

∑k=0

ske j 2πknNsc = IDFTsk (2.9)

where IDFT denotes the inverse discrete Fourier transform.

Thus, the discrete values of s(t) are the Nsc-point IDFT of the information symbols sk. The IDFT/DFT

approach simplifies the implementation of an OFDM transmitter and receiver (OFDM-TX and OFDM-

RX, respectively). It avoids an extremely complex architecture, involving many oscillators and filters,

that would be necessary at both OFDM-TX and OFDM-RX in the case of an implementation based on a

large number of subcarriers modulated by each symbol sk.

The s(t) signal is generated by a digital-to-analog conversion (DAC) of the samples coming from the

IDFT calculation of the sequence sk. The efficient implementation of the IDFT/DFT is the fast Fourier

8

transform (IFFT/FFT) which reduces the number of multiplications from N2sc to (Nsc/2)· log2(Nsc).

A zero padding is introduced within the input sequence s0, ...,sNsc−1 before computing the inverse

Fourier transform due to an intolerable aliasing from the DAC. The zero padding is implemented by

introducing additional subcarriers with zero amplitude. The zeroes are inserted in the middle of the

symbol sequence since, after the IFFT calculation, it corresponds to the output edges of the signal band,

minimizing the aliasing resulting from the DAC.

2.2.4. OFDM transmitter and receiver

In figures 2.2 and 2.3, the block diagrams of the OFDM transmitter and receiver are presented, respec-

tively.

The OFDM transmitter illustrated in figure 2.2, shows that the bit sequence generated is mapped into a

symbol stream using a signal format such as M-PSK. Afterwards, the IFFT is calculated to the symbol

stream with the insertion of the zero-padding. After the digital-to-analog conversion, s(t) is obtained and

will modulate a carrier with frequency fRF .

The OFDM receiver, shown in figure 2.3, performs backwardly the same operations as the transmitter

with the insertion of an equalizer after the FFT block. The equalization is used to compensate for the

amplitude and phase distortion induced by the transmission channel and its transfer function is estimated

from the pilot carriers information of the OFDM signal received.

Figure 2.2.: Block diagram of the OFDM transmitter.

9

Figure 2.3.: Block diagram of the OFDM receiver.

In figure 2.2, the low-pass filter placed after the digital-to-analog converter is used to reduce, or even

eliminate, the influence of the aliasing components on the system performance. At the OFDM receiver

(figure 2.3), the low-pass filters, after the beating with RF oscillators, are used to reduce the noise power

added by the transmission system and they present, usually, the same characteristics as the low-pass

filters used in the OFDM transmitter.

2.2.5. UWB standard for OFDM (OFDM-UWB)

FCC allocated a bandwidth of 7.5 GHz (3.1∼10.6 GHz) for the use by UWB signals. In the OFDM-

UWB approach, the spectrum is divided into subbands that are 528 MHz wide, forming a total of 14 (as

shown in figure 2.4), with central frequencies given by [1]

fRF [n] = 2904+528n [MHz] n = 1,2, ...,14 (2.10)

Figure 2.4.: Frequency band allocation for the OFDM-UWB system.

Each OFDM symbol in an UWB subband consists in 128 subcarriers:

• 100 data subcarriers: e.g. with BPSK, QPSK or QAM modulation.

• 12 pilot subcarriers: to provide information for the equalizer.

10

• 6 null subcarriers: to relax filter requirements.

• 10 guard subcarriers: used for different purposes.

The time duration of an OFDM-UWB symbol in one subband is defined as 312.5 ns. A 9.5 ns guard

interval is sufficient for a safe switching between two subbands and a 60.6 ns zero-padded prefix provides

both robustness against multi-path and decreases the power needs.

In this work, a quadrature phase-shift keying (QPSK) is chosen as modulation format to generate the

symbols from the bit sequence that modulate each subcarrier in an OFDM subband and its data rate per

subband is 640 Mbit/s.

A single subband OFDM-UWB signal is generated by an OFDM transmitter as presented in subsection

2.2.4. The transmitter adopts the UWB standard, namely the number of subcarriers and the OFDM-

UWB symbol duration time. The carrier frequency fRF , given by (2.10), is assigned to the transmitter

according to desired subband.

A multiple subband OFDM-UWB signal is obtained by summing the output of single subband OFDM-

UWB transmitters.

The most adequate low-pass filters for both OFDM-UWB transmitter and receiver would be a rectangular

filter with a 264 MHz bandwidth - matching the used frequencies of each subband - because it would

minimize the crosstalk between adjacent subbands and fully eliminate the noise outside the subband of

interest. However, the forementioned filter is not realizable and a 6th-order Bessel filter is adopted with

an optimized bandwidth of 315 MHz as given in [21]. This filter bandwidth reduces the distortion within

each subband caused by the filter not having a totally flat passband. It also reduces the crosstalk between

subbands and out-of-subband noise which comes from the slow transition between the passband and

stopband. The amplitude response of the filter is drawn in figure 2.5. Considering the frequencies of the

UWB subband, the amplitude response of the 6th-order Bessel filter shows a 2.5 dB difference between

the center of the subband and its edges (±264 MHz), which contributes to the distortion of the subband

of the OFDM-UWB signal.

11

Figure 2.5.: Amplitude response of a 6th-order low-pass Bessel filter.

2.3. Time and frequency analysis of OFDM-UWB radio signals

Figure 2.6 shows an example of an OFDM-UWB symbol in time using the first UWB subband ( fRF

= 3432 MHz). The signal is obtained directly from the OFDM-UWB transmitter from mapping a bit

sequence into QPSK symbols that modulate the 128 subcarriers of the UWB subband.

Considering an optical network using intensity modulation and direct detection (as in this work), the

transmitting signal modulates the intensity (power) of the carrier frequency of the optical transmitter, not

its amplitude or phase. This means that the transmitting signal must be positive and real. As observed

in figure 2.6, a signal obtained by an OFDM-UWB transmitter has both positive and negative values.

Therefore, a gain should be applied along with the adding of a DC component in order to fit the OFDM-

UWB transmitter output to the optical transmitter input restrictions.

Figure 2.7 shows an example of an OFDM-UWB current signal when a gain is applied and a DC com-

ponent added so that it has a peak-to-peak current of 80 mA and mean current of 60 mA. This current

signal meets the restrictions of the optical transmitter used in this work - a directly modulated laser.

From the OFDM-UWB current signal shown in figure 2.7, it was estimated that during 87% of the time,

the signal has an amplitude in the region of 50∼70 mA. The estimation suggests that most of the electrical

power of the signal has a low current amplitude when compared with its peaks. This result comes from

the high peak-to-average power ratio (PAPR) typical of OFDM signals which will be discussed later.

12

Figure 2.6.: OFDM-UWB signal using subband 1.

Figure 2.7.: OFDM-UWB current signal using subband 1 with a mean of 60 mA and a peak-to-peakcurrent of 80 mA.

Figure 2.8a shows the power spectrum density (PSD) of an OFDM-UWB signal. The first UWB subband

is assigned to the OFDM-UWB signal which centers the PSD in 3432 MHz with a bandwidth of 528

MHz. It is observed power outside the subband of interest that comes from the aliasing of the digital-to-

analog conversion at the OFDM-UWB transmitter. The aliasing is limited by a 6th order Bessel low-pass

filter with 315 MHz of bandwidth. If not attenuated, the aliasing power could interfere with adjacent

subbands.

The PSD shown in figure 2.8b is calculated by doing the mean over a 10 samples window of the actual

PSD - shown in figure 2.8a. This approach facilitates the analysis of the spectrum due to the smaller

variation of the samples. From this point on, all the PSD representations will be a mean over a 10

samples window of the original PSD.

13

(a) Original PSD (b) 10-samples window mean PSD

Figure 2.8.: PSD of an OFDM-UWB signal using subband 1.

Figure 2.9a shows a close-up to the PSD of the UWB subband. It is observed that there is an approx-

imately 3 dB difference between the center of the UWB subband and its edge. The round top of each

subband comes from the low-pass filters used in the OFDM-UWB transmitter not having a totally flat

passband as already discussed in section 2.2.5. Figure 2.9b shows the PSD of the OFDM-UWB current

signal when rectangular filters with a 264 MHz bandwidth are used at the OFDM-UWB transmitter. This

bandwidth fits thoroughly the UWB subband which is approximately flat due to the ideal characteristics

of the filters.

(a) Bessel filter used at OFDM-TX (b) Rectangular filter used at OFDM-TX

Figure 2.9.: Close-up of the PSD of an OFDM-UWB signal using subband 1.

As mentioned above, the high peak-to-average power ratio (PAPR) is known as one of the major draw-

backs of the OFDM signals [29].

14

The PAPR of the OFDM signal is defined as

PAPR =max

|s(t)|2

mean|s(t)|2

, (2.11)

where s(t) is given by (2.1).

As explained in [29], the theoretical PAPR maximum is 10log10(Nsc) in dB, obtained by setting sk = 1

and t = 0 in (2.1). For a system with Nsc = 128, the theoretical maximum PAPR is 21 dB.

The PAPR theoretical maximum value is excessively high, especially if it modulates a directly modulated

laser: each laser has its own limited region of modulation and an OFDM signal can be severely distorted

if it has a high PAPR 1.

Several values of PAPR were calculated when a deBruijn bit sequence of length 2lseq is mapped into

QPSK symbols that modulate each OFDM subcarrier. For a given deBruijn sequence of length 2lseq ,

the PAPR value was computed for sequences resulting from circular shifting of the original deBruijn bit

sequence 2lseq times. Figure 2.10 shows the PAPR mean, maximum and minimum for different values

of lseq using the first subband. It is observed that, for a longer deBruijn bit sequence, the PAPR mean

value increases. The maximum value found was 16.5 dB which is below the theoretical maximum, but

the graph from figure 2.10 suggests higher PAPR values for longer deBruijn bit sequences.

Figure 2.10.: Mean, maximum and minimum values of the PAPR for a 2lseq deBruijn bit sequence mappedinto QPSK symbols in an OFDM-UWB signal using subband 1.

The OFDM-UWB symbol sequence used in this work comes from the deBruijn sequence of lseq = 11

(signal format of QPSK) with the highest PAPR found. The PAPR of each OFDM-UWB signal depends

on which and how many subbands are used.

1The optical transmitter used in this work is detailed in chapter 3.

15

An OFDM-UWB signal with a high peak is more likely to be distorted by the optical transmitter and,

therefore, it represents, possibly, the worst case scenario for the optical network.

Table 2.1 shows the PAPR mean and maximum values for different subbands used. For a single-subband

transmission, the PAPR value is independent of the subband used. For multiple-subband transmission, it

is observed that the PAPR value increases with the number of subbands assigned.

Table 2.1.: PAPR mean, maximum and minimum values for different subbands used.

Subbands used meanPAPR maxPAPR minPAPR

1 13.90 15.48 12.24

2 13.91 15.49 12.32

3 13.91 15.50 12.29

4 13.90 15.49 12.33

1,2 16.67 18.45 14.97

1,3 16.61 18.32 14.92

1,2,3 18.36 20.16 16.70

1,2,3,4 19.56 21.30 17.94

2.4. Conclusion

In this chapter, OFDM-UWB radio signals were introduced and described. An analitycal approach was

followed for the definition of this type of signals in section 2.2. It was demonstrated that a general OFDM

signal can be easily obtained by calculating the IDFT of the symbol sequence to be transmitted which

substantially reduces the complexity of the OFDM implementation.

It was discussed that the original OFDM-UWB signal is not suited for optical transmission using intensity

modulation and that a modification in the mean and amplitude of the signal should be performed.

The OFDM transmitter and receiver block diagram was presented and each function block explained.

The FCC specifications were detailed to the OFDM-UWB approach, namely the 14 UWB subbands used

frequencies, the 128 subcarriers per subband and the duration of 312.5 ns of an OFDM-UWB symbol.

Time and frequency analysis of OFDM-UWB radio signals were performed in section 2.3. The power

spectrum density of a single subband OFDM-UWB signal showed that the 6th order Bessel low-pass

filters used in the OFDM-TX and OFDM-RX reduce the aliasing coming from the digital-to-analog

16

conversion although it introduces distortion to the subband caused by the filter not having a totally flat

passband. The high PAPR was mentioned as one of the major drawbacks of the OFDM-UWB radio

signals reaching 21.3 dB for an OFDM-UWB signal using subbands 1, 2, 3 and 4.

17

3. OFDM-UWB FTTH network model

3.1. Introduction

The transmission of OFDM-UWB radio signals in a fiber-to-the-home (FTTH) network is a cost-effective

solution to extend the coverage of these signals. It can support a transparent electro-optical signal conver-

sion, avoids using some expensive high-frequency electronic components required during signal trans-

mission and the optoelectronic integration technologies have their size and power consumption of the

optical UWB transmitters and receivers decreased.

For the evaluation of the impact of the transmition along the FTTH network on the OFDM-UWB signal

quality, a model of the network adapted to the OFDM-UWB signal transmission is presented and each

component of the network is described. The methods that measure the quality of an OFDM-UWB signal

are detailed and discussed.

In this Chapter, section 3.2 presents the FTTH network and each of its elements are described. In section

3.3, the methods of performance evaluation of the FTTH system are introduced and discussed, and in

section 3.4, the effects of the non-linear operation performed in the FTTH network (clipping) is anal-

ysed.

3.2. FTTH network architecture

Fiber-to-the-home is defined as a telecommunications network in which an optical path is estabilished

from the switching equipment of the telecom operator (designated as central node) to the home premises

of the subscriber. A simplified block diagram of this network is drawn in figure 3.1.

18

Figure 3.1.: Schematic of the FTTH network.

As mentioned in the Chapter 1, FTTH networks are usually based on existing passive optical networks

(PONs). A PON-based FTTH network consists of an optical line terminal (OLT) at the central node

of the service provider and a number of optical network units (ONUs) near end users. A PON is a

point-to-multipoint network which reduces the amount of fiber used.

In figure 3.2, the block diagram of the LR-PON is shown. As observed, the central node generates and

multiplexes the OFDM-UWB signal making use of dense wavelength division multiplexing (DWDM).

This technology is used for the transport of several optical carrier signals onto a single optical fiber of 80

km from the central node until the local exchange [10].

The erbium-doped fiber amplifier (EDFA) at the central node is used to impose a defined mean optical

power before the fiber transmission. At the local exchange, the EDFA compensates for the losses inflicted

by the transmission and, afterwards, the optical signal is demultiplexed and distributed to N subscribers

by a N-splitter. Depending on the geographic location of each subscriber, the optical path between the

local exchange and the premises of the subscriber may have a length between 0 and 20 km.

Since the analysis of wavelength multiplexing/demultiplexing technology is out of scope for this work,

an equivalent model of the FTTH network is adopted which neglects the crosstalk between different

wavelengths.

The goal of this dissertation is to evaluate the impact of the transmission along the FTTH network on the

OFDM-UWB signal quality. Thus, from this point on, the discussion will be focused on an individual

wavelength channel. The multiplexers/demultiplexers represented in figure 3.2 are replaced by the equiv-

alent model from the single-wavelength view point. The equivalent FTTH network model is represented

in figure 3.3.

19

Figure 3.2.: Block diagram of the FTTH network.

Figure 3.3.: Block diagram of the equivalent model of the FTTH network from single wavelength viewpoint.

3.2.1. OFDM-UWB transmitter, gain and DC current

Figure 3.3 shows, in the central node, the OFDM-UWB transmitter as described in chapter 2. Its output

is approximately symmetric around zero and its amplitude is not suited for the modulation of the directly

modulated laser. Therefore, an adaptation of the OFDM-UWB original signal to the restrictions of the

optical transmitter is necessary.

The gain g in figure 3.3 imposes the swing of the current that modulates the laser and I sets its bias. These

parameters alter the OFDM-UWB transmitter output in order to meet the optical transmitter input current

restrictions. Thus, I and g have a strong influence on the performance of the system and, therefore, should

be optimized.

3.2.2. Clipper

A clipping operation is performed to the current signal before the DML modulation in order to ensure

the variation of the OFDM-UWB current signal inside the laser linear operating region defined as the

range between 18 and 100 mA. The lower limit of the region is 18 mA because a shorter proximity

to the threshold current of the laser could lead to a slower operation of the DML. The upper value of

20

the modulation region sets the transition to a multimode emission which should avoided (the general

operation of the laser is detailed in subsection 3.2.3).

The non-linear operation of clipping introduces some distortion to the signal, but it has the advantage of

reducing the PAPR of the signal. A deeper analysis of the clipping effect is presented in section 3.4.

3.2.3. Directly modulated laser

The DML used in the FTTH network is a Multiple Quantum Wells (MQW) and it is operating at the

wavelength of 1550.2 nm. Its behaviour characteristics are well described by the rate equations that gov-

ern the interaction of photons and electrons inside the active region of the laser [31]. The rate equations

are carefully detailed in Appendix A.

The static response of the laser is shown in figure 3.4 and derived in Appendix A. It relates the output

power when a constant current is modulating the laser. It is observed that, for a current below 14.34

mA, the output power is approximately 0 because there is only spontaneous emission of photons. Above

this threshold, there is stimulated emission of photons and, therefore, the output power shows a linear

increase with the input current. This linear region is limited until 100 mA, which is the maximum input

current value before the laser presents multi-mode emission. Thus, for OFDM-UWB signal transmission

through this DML, the input current levels should remain inside the forementioned region.

Figure 3.4.: Static response of the directly modulated laser.

The DML model also considers the effects originated from the assemblage of the laser. These effects are

represented by a first order low-pass filter with a bandwidth of 6 GHz.

The dynamic response of the laser to a small current signal modulation is also shown and derived in

Appendix A. It is observed that the bandwidth of the DML depends on the bias input current: for an

21

increase of the bias current from 20 mA to 60 mA, the bandwidth at -3 dB increases approximately from

10 GHz to 25 GHz. Thus, the overall bandwidth of the DML is the result of the effects of its assemblage

and the input bias current. Due to the bandwidth limitation of the DML, the transmission of OFDM-

UWB signals is accomplished only for the first four UWB subbands ( fRF = 3.43 GHz; 3.96 GHz; 4.49

GHz; 5.02 GHz).

A simultaneous modulation in intensity (IM) and frequency (FM) is observed in the dynamic response of

the DML. This simultaneous modulation becomes a drawback when a IM signal is sent through the fiber:

the signal becomes wider in frequency due to FM and more sensitive to the dispersion of the fiber.

The instanteous frequency shift is related to carrier-induced index changes caused by different levels of

input currents. The frequency chirp is also influenced by small oscillations of the carriers number as

shown in Appendix A.

By placing a tuned optical filter at the laser output, FM to IM conversion is accomplished, increasing the

resilience to the dispersion of the fiber and reducing the inter-symbol interference caused by the optical

transmission. As demonstrated in [24], the CML reaches higher performances in the transmission of a

10 Gbps non-return-to-zero (NRZ) signal through a direct-detection optical fiber communication system,

when compared to the use of the DML.

3.2.4. Optical Spectrum Reshaping filter

As mentioned above, the optical spectrum reshaper filter plays an essential part in the chirp control.

Many possiblities for the filter type have been considered [27]:

• Butterworth: flat response in the pass band; overshoot and ringing in the step response.

• Chebyshev: better rate of attenuation in the stop-bands than Butterworth; more ringing in step

response than Butterworth.

• Bessel: minimal overshoot and ringing in the step response; slowest rate of attenuation beyond the

pass band.

• Super-Gaussian: transfer function without dispersion; easily implemented.

The super-Gaussian filter is selected to be the OSR filter because it is easily implemented and is also the

type of filter suggested in [27]. The transfer function of the filter is given by

T (ν) = exp

(− ln

(√2)∣∣∣∣ν−νc

νg/2

∣∣∣∣2n)

(3.1)

22

where ν is the optical frequency, νc is the central frequency of the OSR, νg is the bandwidth at - 3dB of

the filter and n the filter order. The bandwidth and central frequency of the OSR are optimized choosing

the first-order Gaussian filter (n = 1) for an optimal chirp control.

3.2.5. Optical filter

The optical filter placed after the CML is the equivalent model of the multiplexer from the single-

wavelength point of view. This filter has the same transfer function as the one of the demultiplexer

at the local exchange.

The optical filter at the local exchange narrows the noise spectrum of the amplified spontaneous emission

(ASE) generated by the EDFA reaching the OFDM-UWB receiver, but it also distorts the optical signal

if not wide enough. The optimal bandwidth of the filter constitutes a balance between the two mentioned

factors. Based on the outcome of [21], a 2nd order super-Gaussian filter with an optimized bandwidth of

35 GHz is considered.

An insertion loss of 2.5 dB, as given in [32], is also taken into account in the equivalent model of both

multiplexer and demultiplexer.

3.2.6. Optical amplifier EDFA

For the compensation of the power losses induced by the OSR and the optical filter that simulates the

multiplexer, an erbium-doped fiber amplifier (EDFA) sets the mean power of the optical signal at the

output of the central node to a defined value of, typically 0, 3 or 5 dBm. Thus, independently of the input

current levels of the optical transmitter, the transmission of OFDM-UWB signals have the same mean

optical power at the central node output.

The gain of this optical amplifier is given by

gedfa, CN =POF

PCN(3.2)

where POF is the mean power of the signal at the output of the optical filter that simulates the multiplexer

and PCN the imposed mean power at the output of the central node.

At the local exchange, the role of the EDFA is to compensate for the losses inflicted by the fiber trans-

mission from the central node to the local exchange, splices, connectors, multiplexer, demultiplexer and

splitter present in the FTTH network.

23

Considering the cost of an EDFA with a gain higher than 35 dB and the loss inflicted by the FTTH

network (minimum 30 dB as demonstrated later), it is considered a 30 dB gain in the optical amplifier at

the local exchange (gedfa, LE = 1000). Thus, the EDFA will not compensate totally the losses inflicted by

the network from the central node to the facilities of the subscriber.

An ideal model of the EDFA was considered: constant gain along frequency and no amplifier saturation.

The electrical field at the EDFA output is then given by

Eout(t) = Ein(t)√

gedfa (3.3)

where Ein(t) is the electrical field at the EDFA input, and gedfa is the power gain.

Along with the amplification of the optical signal, there is introduction of noise by the EDFA from

amplified spontaneous emission. The noise field is assumed zero mean additive white Gaussian noise

with a power density per polarization mode defined by the optical gain of the EDFA (gedfa) as

SASE = hν0nsp (gedfa−1) (3.4)

where h is the constant of Planck, nsp = 1.26 is the spontaneous emission noise factor and ν0 is the

optical carrier frequency.

3.2.7. Optical fiber

A standard single mode fiber (SSMF) was considered for the FTTH network.

The equivalent baseband transfer function of the SSMF is given by [33]

H f (∆ω) = exp(− jβ (∆ω)L) · exp(−α

L2

), (3.5)

where α is the loss coefficient of the fiber with a value of 0.21 dB/km, L is the fiber length and β (∆ω) is

approximated by a Taylor series as

β (∆ω)≈ β0 +β1 (∆ω)+12

β2 (∆ω)2 +16

β3 (∆ω)3 , (3.6)

in which ∆ω is given by

∆ω = ω−ω0 = 2π f , (3.7)

24

where f is the equivalent baseband frequency.

β2 is the group-velocity dispersion coefficient and is given by [33]

β2 =−λ 2D2πc

, (3.8)

where λ is the optical wavelength (1550.2 nm), c is the light velocity and D is the dispersion parameter

with a value of 17 ps/(km-nm).

β3 is given by [33],

β3 =−S−(4πc/λ 3

)β2

(2πc/λ 2)2 , (3.9)

where S is the dispersion slope with a value of 0.09 ps/(km-nm2).

3.2.8. Power splitter

The power splitter at the local exchange output divides equally the power by the N subscribers using the

same wavelength. The power loss inflicted by the splitter is given in dB by

Aspl = 10log10(N)+0.5log2(N) (3.10)

The first term represents the losses from dividing the input power by N and the second term, the losses

from insertion: 0.5 dB from each level of division.

Assuming, in this work, that N = 16, 32 or 64, the losses inflicted by the splitter (Aspl) vary from 14 to

19 dB.

Defining Amux as the losses from the multiplexer and demultiplexer, and Ax the losses from connectors

and splices with an assumed value of 3 dB, the minimum total loss inflicted by the FTTH network

from the central node until the local exchange is given by Atotal = α · 80+Ax +Amux +minAspl =

16.8+3+5+14 = 38.8 dB.

3.2.9. PIN Photodetector

The optical-to-electrical conversion is performed by a photodetector PIN due to low cost, compared to

other optical receivers type (e.g. avalanche photodiode). The low cost is essential for the implementation

of a FTTH network.

25

The output current of a PIN photodetector iPIN(t) is given by

iPIN(t) = Rλ pPIN(t) (3.11)

where pi(t) is the optical power at the PIN input and Rλ is responsivity of the PIN with a value of 1

A/W.

3.2.10. Receiving filter

The receiving filter before the OFDM-UWB receiver is a 5th-order Bessel low-pass filter with a band-

width of 10 GHz. This bandwidth ensures the filtering until the 4th UWB subband (5 GHz) without

adding distortion. This filter performs a signal conversion from current to voltage and limits the noise

generated by the optical amplification.

3.2.11. OFDM-UWB receiver

As mentioned in chapter 2, the OFDM-UWB receiver demodulates the electrical signal and, according

to the information from the pilots subcarriers, an equalization is performed. This process adjusts the

strength of certain frequencies within the received signal and it improves the performance of the system.

The equalizer uses the information from the 12 pilot subcarriers of the UWB subband - 6 subcarriers

with frequencies above fRF and 6 subcarriers below - and estimates the transfer function of the channel

by using a polynomial of degree 2.

The electrical-to-optical conversion and amplification accomplished at the premises of the subscribers

contribute to raise the level of noise. The electrical noise is generated by the resistive and active elements

present in the receiver. The power spectrum density (one-sided) of the electrical generated noise is given

by

Sc =4kBT

Rbfn,e (3.12)

where kB is the Boltzmann constant, T is the room temperature with an assumed value of 290 Kelvin, Rb

is the bias resistor of the photodetector (50 Ω) and fn,e is the noise factor that represents the influence of

the active elements of the receiver.

Typical values of the electrical power spectrum density are in the range from 1·10−24 A2/Hz to 1·10−22

A2/Hz [34]. In this case, a PSD of 2.5·10−23 A2/Hz was considered, leading to the fn,e value of 11.1

dB.

26

3.3. Performance evaluation methods

The two major causes of performance limitation of the OFDM-UWB optical system are noise and dis-

tortion. It leads to incorrect demodulation at the receiver and, consequently, to bit errors. It is indeter-

minable which has a heavier weight on the system performance because none has a dominant role and

their influence changes with the system parameterization.

Although noise is present in every component of the real system it is considered in the numerical sim-

ulations, for simplicity, that is generated optically at the EDFA and electrically at the OFDM-UWB

receiver.

The presence of non-ideal components, non-linear operations performed (e.g. clipping) and the fiber

transmission change the shape of the signal introducing distortion to the signal. In this work, the er-

ror vector magnitude (EVM) is adopted as a measure of the distortion inflicted by the system and its

definition is detailed below.

For a complete performance evaluation of the optical transmission system, which accounts for the noise

and distortion, it is used the semi-analytical Gaussian approach [35]. This method gives the bit error

ratio, which is the most common performance assessment method of a digital transmission system. This

method is also detailed in the subsection below.

3.3.1. Error Vector Magnitude

The EVM is a common figure of merit that evaluates the quality of a digital transmission. Its value ex-

presses the difference between the value of the actual received symbol (Smeas,r) and the expected complex

voltage/current value of the demodulated symbol (Sideal,r), demonstrated in figure 3.5.

Generally, the EVM takes into consideration the noise introduced by the system. In the numerical simu-

lations performed, each symbol is obtained after the equalization at the OFDM receiver and its complex

value is not affected by noise.

27

Figure 3.5.: Constellation diagram for QPSK.

The definition of EVM is the root-mean-square (RMS) value of the difference between a collection of

measured symbols and ideal symbols. The EVM can be expressed mathematically as

EVMRMS =

√√√√ 1N ∑

Nr=1 |Sideal,r−Smeas,r|2

1N ∑

Nr=1 |Sideal,r|2

(3.13)

The EVM is usually adopted as a general performance of the system. Nevertheless, since it does not take

into account the noise generated by the system, it is just a measure of the distortion inflicted on the signal

at the OFDM receiver input.

3.3.2. Semi-analytical Gaussian approach

The semi-analytical Gaussian approach (SAGA) allows evaluating the BER of each OFDM subcarrier in

direct detection optical communication systems through numerical simulation.

There are three approaches that can be followed in order to calculate the BER in a digital communication

system:

• Monte Carlo (MC) simulation: the noise is introduced in the system and propagated with the

signal. The BER is obtained by direct error counting. Although this method gives an accurate

BER estimation, it requires unacceptable computation time for low BER levels.

• semi-analytical method: the signal is propagated through the optical system. The BER and noise

are characterized analytically by using the statistical properties of the noise.

• analytical methods: signal and noise are both characterized analytically. This method neglects the

distortion inflicted by the optical system but provides a fast estimation of the BER.

28

The semi-analytical approach constitutes a balance between the MC simulation method and the analytical

method.

The SAGA method takes into account the distortion induced by the components of the system (e.g.

filter shapes) and considers both optical and electrical noise introduced at the EDFA and the receiver,

respectively.

The SAGA closed-form analytical expressions for the mean and variance of signal-noise and noise-noise

beat terms of each subcarrier at the equalizer output are detailed in [35]. The noise field is assumed zero

mean additive white Gaussian noise with a power density with contributions from the circuit generated

noise and the noise originated at the EDFA.

This method is a powerful tool for the optimization of the network under analysis and its estimates have

shown excellent agreements with the MC simulation.

3.4. Effects of clipping in an OFDM-UWB radio signal

The clipping operation accomplished before the electro-optical conversion fits the OFDM-UWB current

signal into the linear operating region of the laser. Although it causes an increase of distortion, a benefit

that comes from removing the peaks of the signal is the reduction of the PAPR.

In this section, the distortion inflicted by the clipping is assessed in terms of the EVM. It is considered

an multi-subband OFDM-UWB signal sequence transmitting simultaneously in the first 4 subbands with

a PAPR of 21 dB. The current at the clipper input is defined by a mean of 60 mA and a peak-to-peak

current of 80 mA so that the electrical signal fits the linear operating region of the laser (18∼100 mA).

Figure 3.6 presents the mentioned OFDM-UWB current signal. As observed, most of the electrical

power of the signal has a low current amplitude when compared with its peaks due to the high PAPR

(mentioned in chapter 1).

29

Figure 3.6.: OFDM-UWB current signal using subbands 1,2,3,4.

The power spectrum density of the mentioned OFDM-UWB current signal is shown in figure 3.7. It is

observed that the PSD is composed by the DC component which carries the highest power (50 dB above

the UWB subbands) and the UWB subbands.

Figure 3.7.: PSD of OFDM-UWB current signal without clipping using subbands 1,2,3,4.

The effect on the EVM of each subband in removing a percentage of the bottom half of the current is

represented in figure 3.8. It is observed that the subbands at the borders of the subband group (subbands

1 and 4) present a lower EVM than the subbands in the middle (subbands 2 and 4) due to an interference

coming from only one adjacent subbands instead of two.

As expected, figure 3.8 shows that the absence of clipping results in the lowest value of EVM of each

subband and as the bottom of the signal begins to be removed, the corresponding EVM increases. For a

clipping percentage near 100%, the EVM of each subband shows an abrupt decrease, showing a similar

value to the non-clipped signal. Figure 3.9 shows two examples of the OFDM-UWB current signal after

the clipper.

30

Figure 3.8.: EVM of the OFDM-UWB signal using subbands 1,2,3,4 as a function of the percentage ofthe bottom half removal.

(a) 50% of bottom half clipped (b) 80% of bottom half clipped

Figure 3.9.: Example of an OFDM-UWB current signal using subbands 1,2,3,4 after clipping.

Figures 3.10a, 3.10b and 3.10c show that the percentage increase of the removal of the bottom half of the

signal causes the growing of power outside the subband group. This power raising comes from intermod-

ulation products at frequencies multiple of the sum or difference between the original used frequencies

(multiples of an UWB subband bandwidth). The appearance of unwanted frequencies is a consequence

of the non-linear operation performed and, as observed for 100% removal, the possible introduction of

higher-frequency subbands (namely for subbands 10 and 11) would be affected by clipping noise gener-

ated by the first four subbands.

The result of a low EVM for a half-clipped OFDM signal was also obtained previously in [36]. For an

OFDM signal with only the odd index subcarriers modulated, half-clipping reduces the amplitude of the

subcarriers by exactly one half and all intermodulation products fall on the even subcarriers, reducing

the distortion of the signal although half of the signal amplitude was removed. Figure 3.8 shows that the

31

effect of low distortion for half-clipping an OFDM signal is replicated when modulating both odd and

even indexed subcarriers.

(a) 40% of bottom half clipped (b) 80% of bottom half clipped

(c) 100% of bottom half clipped

Figure 3.10.: PSD of the OFDM-UWB current signal using subbands 1,2,3,4 with 40%, 80% and 100%of bottom half clipped.

In conclusion, a half-clipped OFDM signal is good solution for the high PAPR problem and it shows

reduced distortion. This result is interesting for fiber transmission where there are restrictions in the

amplitude of the input current.

The optimization performed in chapter 3 combine the current characteristics of the OFDM-UWB signal

via the gain g, the DC input current I and the clipping operation. In addition to fitting the current signal to

the DML linear operating region, the clipper reduces the PAPR minimizing the distortion of the signal.

32

3.5. Conclusion

In this chapter, the FTTH architecture was described as an optical fiber network that links the switching

equipment of the operator to the facilities of the subscriber. An equivalent single-wavelength model of

the FTTH was detailed and each element characterized.

The directly modulated laser general behavior was described and its main drawbacks were identified:

high frequency chirp and limited input region of operation. The high frequency chirp effect can be

minimized by the filtering the DML output by a optical spectrum reshaping filter. This filter performs

a frequency to intensity conversion, increasing the tolerance of the optical signal to the fiber dispersion

effect.

Two performance methods were introduced: error vector magnitude and semi-analytical gaussian ap-

proach. The first one refers to a measure of the distortion inflicted by the FTTH network to the trans-

mitting signal. The SAGA method, gives the bit error ratio as the main performance measure. This

method considers the distortion inflicted by the system and the optical and electrical noise added by the

amplifiers.

The effect of clipping an OFDM-UWB was analysed. It was concluded that a half-clipped OFDM-UWB

shows low distortion and it represents a solution for the limited region of modulation of the DML and

the high peak-to-average power ratio typical of OFDM signals. However, it was demonstrated that clip-

ping originates out-of-subband noise which can significantly affect the introduction of higher frequency

subbands.

33

4. OFDM-UWB FTTH Network Optimization

4.1. Introduction

The FTTH network for OFDM-UWB signal distribution was presented in chapter 2, being the directly

modulated laser announced as the optical transmitter. Although the adoption of a DML reduces the

complexity of the network, cost of implementation and power consumption, it has a limited region of

linear operation (18-100 mA) and it exhibits an instantaneous frequency shift caused by different levels

of input current.

The limited region of linear operation is a drawback for the distribution of OFDM-UWB signals due to

the high PAPR typical of these signals as discussed in section 2.3. The frequency shifting broadens the

frequency spectrum making the transmitting signal more sensitive to the fiber chromatic dispersion.

The clipping operation accomplished before the electrical-to-optical conversion, imposes the levels of

current inside the linear operating region of the laser. The gain g and the added DC current I determine

which part of the amplitude of the original signal is clipped and, therefore, represent key parameters of

the system. In this chapter, gain g and I are optimized in order to obtain the levels of current that, along

with the clipping operation, lead to the best performance of the system.

As mentioned in chapter 2, the use of an OSR after the DML minimizes the chirp produced by the

electrical-to-optical conversion. The chirp-managed approach performs a frequency to intensity conver-

sion, making the optical signal more resilient to the fiber dispersion. For an optimal chirp control, in this

chapter, the central frequency and bandwidth of the OSR filter are optimized.

This chapter is structured as follows: in section 4.2 is presented a simplified, yet equivalent, model of

the FTTH network that is more adequate for the optimization. Sections 4.3 and 4.4, the results of the

optimization of single subband and multi-subband transmission are presented and discussed, respectively.

Section 4.5 shows the performance improvement of an optimal chirp control through the use of an OSR

filter.

34

4.2. Model of the system to be optimized

Figure 4.1 shows the block diagram of the equivalent FTTH network adequate for an optimization. The

corresponding OFDM-UWB transmitter and receiver block diagrams are detailed in chapter 1.

As mentioned before, the gain g and the DC current I in figure 4.1 impose the swing and bias current that

along with the clipping operation determine the levels of current that modulate the DML. The non-linear

operation of clipping will introduce some distortion to the OFDM-UWB signal with the advantage of

reducing the PAPR. Since these parameters have a strong influence on the performance of the system,

they are simultaneously optimized.

The OSR filter, which accomplishes the chirp control, is a 1st order Gaussian filter (n = 1 in expression

(3.1)). Its parameters are also optimized, namely bandwidth (νg) and central frequency (νc).

As in FTTH network model, a standard single mode fiber is used but it is only characterized by its

dispersive effects: D = 17 ps/nm/km and S = 0.09 ps/(km· nm2).

The photodetector and the receiving filter have the same characteristics as presented in chapter 2.

At the optical fiber end, a variable attenuator (VA) and an erbium-doped fiber amplifier (EDFA) compose

the noise loader. The noise loader is used to adjust the noise power at the PIN photodetector input so

that a defined optical signal-to-noise ratio (OSNR) is obtained. The value of the amplified spontaneous

emission density power noise per polarization and per component (phase and quadrature) is given by

SASE =Popt

4 ·osnr ·B0(4.1)

where Popt is the mean optical power at the VA input and B0 is the reference optical bandwidth of 0.1

nm. The SAGA method, detailed in section 3.3, gives the BER in terms of a desired OSNR.

In the optimization process, the metric used to determine the performance of the system is the required

OSNR value for a BER value of 10−4. This metric is well-known and it is used in similar optimizations.

In the following sections, wherever the required OSNR is mentioned, it means the required OSNR value

for BER = 10−4.

35

Figure 4.1.: Block diagram of the equivalent FTTH network adequate for an optimization.

4.3. Optimization of the currents in single subband transmission

In this section, the values of g and I are set in order to minimize the required OSNR for a BER of 10−4 at

the PIN input, calculated using the SAGA method when only a single subband is used. The optimization

was performed simultaneously for both gain g and I.

As mentioned before, I is the DC current added to the OFDM-UWB signal that defines the bias point

of the current signal in the linear operating region of the DML. The gain g determines the peak-to-peak

current of the OFDM-UWB current signal around the bias current before the clipping operation.

The OSR was not introduced yet in this analysis. The improvements of using the OSR are analyzed in

section 4.5.

4.3.1. Back-to-back configuration

Figure 4.2 represents the contour of the required OSNR value as a function of the bias and peak-to-peak

current for the system in a back-to-back configuration (no fiber transmission) using subband 1. A bias

current of 18 mA and peak-to-peak current of 350 mA was the result of the optimization with a required

OSNR value of 5.08 dB.

A bias current of 18 mA originates a half-clipped OFDM-UWB current signal. Table 4.1 presents the

noiseless EVM of the OFDM-UWB signal in several points of the network1. It shows that the difference

between the EVM of the OFDM-UWB current signal at the clipper input (-41 dB) and after half-clipping

(-40.8 dB) is negligible. Thus, a similar distortion was obtained although half of the amplitude of the

current signal was removed. This result was expected after the discussion presented in section 3.4.

An optimal peak-to-peak current of 350 mA for a back-to-back transmission exceeds the upper limit of

the linear operating region of the DML (100 mA). An increase in g and the corresponding higher clipping

1Each EVM value in Table 4.1 was calculated by demodulating the electrical OFDM-UWB signal obtained at the desiredpoint of the network.

36

of the peaks of the current signal, severely distorts the signal at the clipper output: the EVM increases

from -41 dB to -21.3 dB after the clipping operation, as shown in table 4.1. Nevertheless, a higher value

in g raises the power level of the UWB subbands increasing the resilience to the noise added by the

EDFA. The optimal g sets the balance between increasing the distortion introduced by the clipper and

raising the power level of the UWB subband.

The optimized DML input current for the back-to-back configuration using subband 1 is represented in

figure 4.3.

Figure 4.2.: Contour of the representation of the required OSNR as a function of the current level in theback-to-back configuration for subband 1.

As demonstrated in Appendix B, the transmission of single subbands 2, 3 and 4 in the back-to-back

configuration show similar optimal current levels: a bias current that leads to a half-clipped signal and

a gain g that imposes a peak-to-peak of current before the clipping operation of 350 mA. Table 4.2

shows the optimal current levels for single subband transmission of the first four UWB subbands with

the corresponding minimum required OSNR for BER = 10−4.

It is observed that subbands with higher frequencies have worse performance in terms of the required

OSNR value. The required OSNR decrease results from the larger distortion inflicted by the DML on

the OFDM-UWB current signal using higher frequency subbands. As in [20], a higher degradation was

achieved for higher frequency UWB subbands due to the RIN generated by the laser.

Table 4.1 shows that the difference in dB between the EVM of the OFDM-UWB signal at the DML

input and the EVM calculated at the receiver is increasing with the frequency of the subbands. Thus, it

is demonstrated that an OFDM-UWB current signal using higher frequency subbands experience more

distortion by the DML leading to worse performance.

37

Table 4.1.: Noiseless EVM of the single subband OFDM-UWB signal in several points of the system inthe back-to-back configuration.

Single subband used 1 2 3 4

EVM [dB] @ clipper input -41 -41 -41 -41

EVM [dB] @ clipper input (but) half-clipped -40.8 -40.5 -30.2 -30.3

EVM [dB] @ DML input -21.32 -21.38 -19.41 -19.39

EVM [dB] @ OFDM-RX -18.25 -17.82 -15.57 -14.43

EVM difference between of DML input and OFDM-RX [dB] 3.07 3.57 3.84 4.94

Figure 4.3.: OFDM-UWB current signal of three consecutive OFDM-UWB symbols for subband 1 usingoptimal current levels for the back-to-back configuration.

Table 4.2.: Optimal current levels for single subband transmission and corresponding required OSNR forBER=10−4 for the back-to-back configuration.

Single subband used 1 2 3 4

Optimal bias current 18 18 20 20

Optimal peak-to-peak current 350 350 350 350

Required OSNR [dB] for BER = 10−4 5.08 5.35 5.92 6.31

4.3.2. Performance with fiber transmission

The bias and peak-to-peak current were optimized for an OFDM-UWB signal using the first four single

subbands in the configuration with fiber transmission from 0 to 100 km.

38

As shown in Appendix B, similar results were obtained in the optimal current levels comparing with

the back-to-back configuration. Tables 4.3, 4.4, 4.5 and 4.6 present the optimal bias and peak-to-peak

current for single subbands 1, 2, 3 and 4, respectively. Figure 4.4a exhibits the performance degradation

in terms of the required OSNR for BER=10−4 for the configuration with fiber transmission. It is observed

that the transmission with a higher fiber length increases the required OSNR value leading to worse

performance. This results from the fiber dispersion effects that are stronger for fiber transmission with a

higher length.

Figure 4.4b shows the noiseless EVM of the OFDM-UWB RX signal input as a function of the SSMF

length. It can be noticed a slight decrease of the EVM value for the fiber transmission until 60 km. This

means that the fiber compensates for the distortion inflicted to the signal although, in the end, it causes a

higher performance degradation.

Table 4.3.: Optimal current levels for the fiber transmission using subband 1 and corresponding requiredOSNR.

SSMF length [km] 0 20 40 60 80 100

Optimal bias current [mA] 18 18 18 18 18 19

Optimal peak-to-peak current [mA] 350 350 350 350 350 350

Required OSNR [dB] for BER=10−4 5.08 5.19 5.42 5.73 6.14 6.66


SSMF length [km] 0 20 40 60 80 100




39


SSMF length [km] 0 20 40 60 80 100




Table 4.6.: Optimal current levels for the fiber transmission using subband 4 and the corresponding re-quired OSNR.

SSMF length [km] 0 20 40 60 80 100




(a) OSNR (b) EVM

Figure 4.4.: OSNR and EVM as a function of the SSMF length for the optimal current levels in single-subbands 1, 2, 3 and 4.

For this work, the mean power of a subband (Psb) is defined as the mean power of the signal obtained by

filtering the OFDM-UWB RX input by an ideal band-pass filter centered at the frequency center of the

subband with a 528 MHz bandwidth.

Figure 4.5 presents the Psb of each single subband as a function of the SSMF length. It shows that the Psb

decreases with the length of the fiber transmission.

40

Although the losses induced by the fiber are not introduced in the optical fiber numerical model, its

dispersion effects influence the power of the optical signal through chromatic dispersion. The decrease

of Psb when the level of added noise by the EDFA is the same, makes the required OSNR increase in

order to maintain the BER = 10−4. This leads to the performance degradation demonstrated in figure

4.4a.

It can be noticed from figure 4.4a that the fiber transmission degrades the performance more severely

for higher-frequency subbands. Figure 4.5 shows that the Psb of subband 1 decreases 2 dB between the

back-to-back configuration and the configuration with 100 km fiber transmission, while Psb of subband 4

decreases 8 dB. A higher decrease in Psb leads to worse performance in terms of the required OSNR.

The results here obtained contradict the outcome of [21], in which higher frequency subbands reached

a higher performance due to the gain induced by the fiber intensity transfer function being higher for

subband 4 and lower for subband 1. It seems that the different behaviour results from the transmission

of half-clipped OFDM-UWB signals instead of non-clipped OFDM-UWB signals

Figure 4.5.: Psb of single subbands 1, 2, 3 and 4 for optimal current levels as a function of the SSMFlength.

4.4. Optimization of the currents in multi-subband transmission

In this section, the optimization is performed in a similar way as in the single-subband case, changing the

number of subbands used. The use of multiple subbands raises the interference level between subbands

that leads to a higher performance degradation.

The role of the low-pass (LP) filters in the OFDM-UWB transmitter and receiver is essential in minimiz-

ing the crosstalk between subbands and it is assessed below.

41

Since a required OSNR value for BER=10−4 is computed for each subband, the required OSNR that

indicates the performance of the multi-subband transmission, corresponds to the one of the subband with

the highest required OSNR.

4.4.1. Subbands used: 1,2 and 1,2,3

Back-to-back configuration

As demonstrated in Appendix B, a bias current of 18 mA and a peak-to-peak current of 400 mA constitute

the optimal current levels for the transmission of both subband groups, 1,2 and 1,2,3, in the back-

to-back configuration. For subband group 1,2 a required OSNR of 7.36 dB was obtained, and for the

subband group 1,2,3, 9.13 dB.

The introduction of additional subbands increase the interference between subbands which raises the

level of distortion leading to worse performance compared to the single subband transmission.

Tables 4.7 and 4.8 present the EVM value in dB in several points of the system for both groups of

subbands considered in the back-to-back configuration.

Considering the subband group 1,2, and comparing with the equivalent EVM of the single subbands

(detailed in table 4.1), it can be noticed that the EVM value at the OFDM-UWB receiver increases

approximately 1.5 dB for both subbands 1 and 2. A higher noiseless EVM value at the receiver implies

that the level of distortion is higher and therefore a worse performance is achieved in terms of required

OSNR value for BER = 10−4.

Due to the crosstalk between subbands, the required OSNR for the transmission of the single subband 2

increases from 5.35 dB to 7.36 dB when transmitted simultaneously with subband 1.

Considering subband group 1,2,3, and comparing with the single subband case, it is also observed an

increase of the EVM at the OFDM-UWB RX of 1.5 dB to subbands 1 and 3, and a 2 dB increase to

subband 2. A larger EVM increase to the middle subband results from the higher interference experi-

enced from adjacent subbands at both sides of the frequency spectrum. However, it is subband 3 the one

that imposes the lowest performance due to the more intense distortion inflicted by the laser, which can

be noticed from table 4.8. As in the single subband case, higher frequency subbands experience more

distortion when modulating a DML.

The higher distortion inflicted by the DML along with the crosstalk of the adjancent subbands make the

required OSNR of single subband 3 increase from 5.92 dB to 9.13 dB when transmitted simultaneously

with subband 1 and 2.

42

Table 4.7.: Noiseless EVM of the OFDM-UWB signal in several points of the system for the multi subbandtransmission 1,2 in the back-to-back configuration.

Subband 1 2

EVM [dB] @ clipper input -41 -41

EVM [dB] @ DML input -19.4 -19.7

EVM [dB] @ OFDM-RX -16.7 -16.1

Difference between EVM [dB] of DML input and EVM [dB] of OFDM-RX 2.7 3.6

Table 4.8.: Noiseless EVM of the OFDM-UWB signal in several points of the system for the multi subbandtransmission 1,2,3 in the back-to-back configuration.

Subband 1 2 3

EVM [dB] @ clipper input -39.5 -41 -39.8

EVM [dB] @ DML input -19.3 -19.0 -19.9

EVM [dB] @ OFDM-RX input -16.9 -15.6 -14.3

Difference between EVM [dB] of DML input and EVM [dB] of OFDM-RX 2.4 3.4 5.6

Performance with fiber transmission

Tables 4.9 and 4.10 show the optimal current levels for the fiber transmission of both subband groups

1,2 and 1,2,3 at different SSMF lengths.

The optimal peak-to-peak currents in both cases have a higher value, compared to the single subband

case, due to a higher PAPR: 15.5 dB for single subband 1, 2 or 3, 18 dB for 1,2, and 20 dB for 1,2,3

(shown in table 2.1).

Considering the subband group 1,2,3, a fiber transmission with a length higher than 60 km makes

the optimal peak-to-peak current value increase from 400 to 450 mA. This higher value in g adds more

distortion to the signal, but it also increases the power corresponding to each subband which compensates

for the stronger dispersion effects caused by a longer fiber transmission. These effects are more intense

because, in this case of the multi-subband transmission of 1,2,3, the overall bandwidth of the signal is

wider.

43

Table 4.9.: Optimal current levels for the multi-subband fiber transmission of 1,2 and the correspondingminimum required OSNR.

SSMF length [km] 0 20 40 60 80 100



Required OSNR for BER=10−4 7.36 7.54 7.90 8.41 9.11 10.05

Table 4.10.: Optimal current levels for the multi-subband fiber transmission of 1,2,3 and the correspond-ing minimum required OSNR.

SSMF length [km] 0 20 40 60 80 100




Figure 4.6 shows the required OSNR for BER = 10−4 as a function of the SSMF length with the opti-

mized current levels for multi-subband groups 1,2 and 1,2,3. In both cases, the subband with the

highest frequency in each group imposes the highest OSNR: for subband group 1,2, subband 2 has

the lowest performance, and for 1,2,3, subband 3 imposes the highest OSNR. An inferior performance

in higher-frequency subbands, results from the stronger distortion inflicted by the DML to the OFDM-

UWB current, which was demonstrated in the back-to-back configuration, and the higher decrease of the

Psb for higher frequencies, as concluded in section 4.3.

Figure 4.7 presents the Psb of each subband in the subband groups 1,2 and 1,2,3. As expected, it

shows a larger decrease for higher-frequency subbands which leads to a worse performance.

44

(a) subband group 1,2 (b) subband group 1,2,3

Figure 4.6.: Required OSNR as a function of the SSMF length for the optimal current levels for subbands1,2 and 1,2,3.

(a) subband group 1,2 (b) subband group 1,2,3

Figure 4.7.: Psb as a function of the SSMF length for multi-subband transmission of 1,2 and 1,2,3.

Comparing with the single subband transmission - figures 4.8a and 4.8b - the introduction of another

subband increases by approximately 2 dB the required OSNR value when changing from single subband

2 to subband group 1,2, and approximately 3 dB from single subband 3 to subband group 1,2,3.

The higher performance degradation, compared to the single subband transmission case, results from the

higher level of crosstalk between the used subbands, as observed for the back-to-back configuration. The

lower Psb also contributes substancially to a performance decrease.

45

(a) subbands 1,2 (b) subbands 1,2,3

Figure 4.8.: Required OSNR as a function of the SSMF length for the optimal current levels for subbands1,2 and 1,2,3 comparing to the single subband transmission of 2 and 3.

As mentioned before, the crosstalk between subbands is a major drawback and, as seen in figure 4.9, the

use of ideal rectangular low-pass filters in the OFDM-UWB transmitter and receiver improves the system

performance. The use of rectangular LP filter in the OFDM-UWB transmitter and receiver reduces by

approximately 0.5 dB the required OSNR value when comparing with the adoption of 6th order Bessel

LP filters.

(a) subbands 1,2 (b) subbands 1,2,3

Figure 4.9.: Required OSNR as a function of the SSMF length for the optimal current levels for subbands1,2 and 1,2,3 comparing the Bessel and rectangular filters use at the OFDM-UWB transmitter andreceiver.

46

4.4.2. Subbands used: 1,2,3,4

Back-to-back configuration

The contour of the BER for OSNR = 15 dB 2 as a function of the bias and peak-to-peak current is

represented in figure 4.10. In terms of the required OSNR, a bias current of 18 mA and a peak-to-peak

current of 400 mA constitute the optimal current levels for the simultaneous transmission of subbands 1,

2, 3 and 4.

Figure 4.10.: BER contour for an OSNR = 15 dB as a function of the bias and peak-to-peak current in theback-to-back configuration for subband group 1,2,3,4.

The simultaneous transmission of 4 UWB subbands show a lower performance in terms of required

OSNR (12.39 dB) comparing with the transmission of 1,2,3 (9.13 dB) due to more interference be-

tween subbands and the use of higher-frequency subbands which, as demonstrated in the previous sub-

sections, experiences a stronger distortion and have the corresponding Psb lower.

Table 4.11 presents the EVM value of the OFDM-UWB signal at several points of the system. Comparing

with the single subband transmission case (Table 4.1) the EVM at the OFDM-UWB receiver increases

around 1.5 dB in each subband. It can be noticed, also for the multi-subband transmission of 1,2,3,4,

that the distortion inflicted by the DML is substantially stronger for higher frequency subbands.

2The optimization was performed minimizing the required OSNR for BER = 10−4 but, for the current values considered, thecontour of the required OSNR did not fit the limits of the figure. Nevertheless, the contour of the BER shows a similarbehaviour.

47

Table 4.11.: Noiseless EVM of the OFDM-UWB signal in several points of the system for the multisubband transmission 1,2,3,4 in the back-to-back configuration.

Subband 1 2 3 4

EVM [dB] @ clipper input -39.5 -39.5 -39.8 -39.8

EVM [dB] @ DML input -22.5 19.8 -19.2 -22.1

EVM [dB] @ OFDM-RX -18.7 -16.2 -13.9 -12.9

EVM difference between of DML input and OFDM-RX [dB] 3.8 3.6 5.3 9.2

Performance with fiber transmission

Figure 4.11 shows the required OSNR for BER=10−4 for subbands 1, 2, 3 and 4 when simultaneously

transmitted with optimal current levels as presented in table 4.12.

Subbands 3 and 4 impose the lowest performance: subband 3 experiences a higher level of interference

from subbands at the both sides of the frequency spectrum, but the higher frequency subbands have the

Psb decrease more and are submitted to a higher distortion inflicted by the DML.

For a configuration with no fiber transmission, subband 4 sets the highest required OSNR. For a transmis-

sion with an increasing fiber length, the crosstalk between subbands increase due to the chromatic dis-

persion effects, making subband 3 the one that imposes the lowest performance of the subband group.

Figure 4.11b presents the EVM value of each subband of the OFDM-UWB signal at the receiver. It can

be noticed that the EVM of subband 2 and 3 substantially increase for the 100 km fiber transmission. The

level of interference raises significantly due to the crosstalk from both sides of the frequency spectrum

which is amplified by the fiber dispersion effects, making subband 3 impose the lowest performance.

Table 4.12.: Optimal current levels for a multi-subband fiber transmission of 1,2,3,4 and the correspond-ing minimum required OSNR.

SSMF length [km] 0 20 40 60 80 100




48

(a) OSNR (b) EVM

Figure 4.11.: Required OSNR and EVM as a function of the SSMF length for the optimal current levelsin transmission of subbands 1,2,3,4.

Figure 4.12 compares the performance of the subband group 1,2,3,4 transmission when the bit se-

quence that originates the QPSK symbols leads to an OFDM-UWB signal with the highest PAPR (as in

any other case analyzed before) and the lowest PAPR (17.9 dB). The OFDM-UWB signal corresponding

to the maximum PAPR shows a 0.5 dB higher OSNR, leading to a worse performance. Since there is a 3

dB PAPR difference, the distortion caused by the system to the maximum PAPR OFDM-UWB signal is

higher.

Figure 4.12.: Required OSNR as a function of the SSMF length for the optimal current levels in transmis-sion of subband groups 1,2,3,4 with maximum and minimum PAPR.

Figure 4.13 shows the performance degradation of multi-subband groups 1,2, 1,2,3 and 1,2,3,4.

As expected, due to higher interference from crosstalk and the use of higher frequency subbands, the

required OSNR for BER = 10−4 increases with the number of subbands used by the multi-subband

OFDM-UWB signal. The performance degradation of the transmission of subband group 1,2,3,4 is

49

approximately value is 5 dB higher than the transmission of 1,2,3, and 10 dB higher than the transmis-

sion of 1,2.

Figure 4.13.: OSNR as a function of the SSMF length for the optimal current levels in multi-subbandgroups 1,2, 1,2,3 and 1,2,3,4.

The performance degradation can be minimized with the use of an OSR at the DML output which reduces

the effect of the fiber dispersion to the optical signal. In section 4.5, the OSR filter is presented and its

performance analyzed.

4.5. Optical spectrum reshaper filter optimization

The electrical-to-optical conversion by the DML of a current signal occurs simultaneously in intensity

and frequency. The output spectrum of the laser becomes wider due to frequency chirp and the optical

signal is more sensible to the fiber dispersion, limiting the performance of the system. Figure 4.14

shows an example of the frequency shift after the optical conversion of an OFDM-UWB current signal

transmitting the first four subbands. The OFDM-UWB current signal that modulates the DML is shown

in figure 4.15.

50

Figure 4.14.: Frequency chirp of the DML output when modulated by an OFDM-UWB signal using sub-band group 1,2,3,4.

Figure 4.15.: OFDM-UWB current signal of three consecutive OFDM-UWB symbols for subband group1,2,3,4.

As mentioned in chapter 3, with a tuned optical spectrum reshaper filter (OSR) placed after the DML,

bandwidth and chirp reduction are achieved after the DML modulation. The optical signal obtained at

the OSR output is more resilient to inter-symbol interference caused by the dispersion effects associated

with the transmission through the fiber.

Since the optimization of the OSR parameters is an extensive process, the optimization was performed

for the transmission of multi-subband OFDM-UWB signal using subbands 1,2,3,4 in a configuration

with fiber transmission of length 80 and 100 km. The optimization process accomplished for the levels of

current around the optimal values obtained in subsection 4.4.2 and are simultaneous for both bandwidth

νg and central frequency νc.

Figures 4.16 and 4.17 compare the non-managed chirp approach with the introduction of the OSR filter

at the DML output, showing the OSNR for BER = 10−4 values as a function of the peak-to-peak current

51

with I = 18 mA and I = 19 mA.

In terms of the required OSNR for BER = 10−4, there is a performance improvement with the use of the

OSR: a 3 dB decrease in the required OSNR for BER = 10−4 value for the fiber transmission of 80 km

and a 5.8 dB decrease for fiber transmission of 100 km - the optimal OSR parameters for 80 and 100 km

of fiber transmission are presented in table 4.13 3.

(a) I = 18 mA (b) I = 19 mA

Figure 4.16.: Required OSNR for BER = 10−4 as a function of the peak-to-peak current in 80 km fibertransmission with an optimized OSR.

(a) I = 18 mA (b) I = 19 mA

Figure 4.17.: Required OSNR for BER = 10−4 as a function of the peak-to-peak current in 100 km fibertransmission with an optimized OSR.

3The results obtained for the OSR optimization shown in figure 4.17 suggest a lower required OSNR for a decreasing peak-to-peak current, however, the required OSNR obtained was unexpectedly high and did not fit the limit of the figure.

52

Table 4.13.: OSR filter optimization results.

SSMF length [km] 80 100

Optimal required OSNR for BER = 10−4 [dB] 13.70 14.30

Optimal peak-to-peak current [mA] 550 500

Optimal mean current [mA] 18 18

Optimal OSR bandwidth [GHz] 5 4.6

Optimal OSR central frequency [GHz] 5 4

Figures 4.18a, 4.18b, 4.18c and 4.18d show the PSD of the OFDM-UWB signal at different points of the

system represented in figure 4.1.

Figure 4.18a shows the PSD at the DML input. It is observed power outside the subband group caused

by intermodulation products coming from the clipping operation as already discussed in section 3.4. In

figure 4.18b, it is presented the PSD of the OFDM-UWB signal after the DML modulation. It can be

noticed that the DML introduces distortion to OFDM-UWB signal: each subband shows different power

levels and there is approximately 15 dB increase of the out-of-subband power in the close proximity of

the UWB subband group borders.

The use of the OSR filter decreases the power outside the subband group as shown in figure 4.18c. It

reduces by approximately 10 dB the DC component. Thus, the mean power of the OFDM-UWB signal

decreases making the power associated with the UWB subband group higher relatively to the mean.

Thus, the interference from power outside the subband group is lower leading to a better performance of

the system.

At the OFDM-UWB receiver, the PSD of the signal shows an approximately 30 dB loss when compar-

ing to the signal at the fiber input as seen in figure 4.18d. This power decrease comes from the fiber

transmission and the optical-to-electrical conversion performed by the PIN.

53

(a) DML input (b) DML output

(c) OSR output (d) OFDM-UWB RX

Figure 4.18.: PSD of the OFDM-UWB signal in several points of the network.

In conclusion, the introduction of the OSR filter leads to an improvement that reaches 6 dB in terms

of the required OSNR when compared to the transmission using only the DML for the 100 km fiber

transmission. The chirp-managed method reduces the chirp generated by the DML modulation and

raises the subband group power level relative to the unwanted power outside the subband group.

4.6. Conclusion

In this chapter, the transmission of OFDM-UWB signals in an optical fiber was optimized: the bias and

peak-to-peak currents that minimize the required OSNR for BER = 10−4 were calculated.

The optimal bias current for both single and multi-subband transmission, originated a half-clipped OFDM-

UWB signal which shows reduced distortion although half of the amplitude of the signal was removed.

54

The optimal peak-to-peak current sets the balance between increasing the distortion introduced by the

clipper and raising the power level of the UWB subband. Its value increases with the number of subbands

used due to the higher PAPR shown in OFDM-UWB signals using more subbands.

It was concluded that the performance degradation is severely damaged by: the distortion inflicted by the

laser, which is more intense for higher frequency subbands; the larger decrease of Psb also for higher fre-

quency subbands which is enhanced by the fiber transmission; and the higher interference from crosstalk

between subbands in multi-subband transmission which is raised by the chromatic dispersion of the

fiber.

A required OSNR of 20 dB for BER = 10−4 was obtained when transmitting subbands 1, 2, 3 and

4 simultaneously through the configuration with 100 km of fiber. This value is 5 dB higher than the

transmission of 1,2,3, and 10 dB higher than the transmission of 1,2

The chirp-managed laser technology was introduced and an improvement of 5.8 dB in the required OSNR

for BER = 10−4 was achieved in the simultaneous transmission of subbands 1, 2, 3 and 4, through the

configuration with 100 km of fiber. The method reduces the chirp generated by the DML modulation

and raises the subband group power level relative to the unwanted power outside the subband group.

55

5. Transmission performance of the multi-subband

OFDM-UWB signal in the optimized FTTH

network

5.1. Introduction

The analysis of transmission performance of OFDM-UWB signals (detailed in chapter 2) along a FTTH

network (presented in chapter 3) is accomplished in this chapter.

The chirp-managed-based approach for the optical transmitter is compared to the use of DML. The

performance improvement is quantified from the maximum transmission distance for a required level of

BER.

The outcome of chapter 4, namely the optimal current levels that modulate the DML and the optimal

bandwidth and central frequency that characterize the OSR filter, are adopted to the transmission of the

multi-subband OFDM-UWB signal using subbands 1, 2, 3 and 4.

The analysis is performed for the power levels of 0, 3 and 5 dBm, at the central node output (PCN), and a

number of subscribers (N) of 16, 32 and 64.

5.2. Results and discussion

Figures 5.1, 5.2 and 5.3 show the BER as a function of the SSMF length of the FTTH network transmit-

ting an OFDM-UWB signal using subband group 1,2,3,4 considering N = 64, 32 and 16, respectively.

As expected, the power level of the received signal substantially influences the performance of the sys-

tem. Figures 5.1, 5.2 and 5.3 show that the BER increases with the number of subscribers due to a higher

loss inflicted by the N-splitter. For higher PCN , the BER of the system decreases: considering N = 16 in

the CML-based transmission of 80 km, the BER decreases approximately 7 orders of magnitude when

PCN increases from 0 to 3 dBm, and 10 orders of magnitude when PCN increases from 3 to 5 dBm. This

56

result is expected because an OFDM-UWB signal experiences the same level of distortion independently

of its mean power and, as demonstrated in section 5.2.3, the level of introduced noise does not increase

significantly with the mean power of the OFDM-UWB signal.

As concluded in Chapter 4, the transmission using the chirp-managed laser improves the performance

of the system compared to the use of the DML. A 6 dB improvement in the required OSNR for BER =

10−4 was obtained for the transmission of an OFDM-UWB signal using subband group 1,2,3,4 with

a fiber length of 100 km. This technology reduces the frequency shift generated by the DML and raises

the subband power level relative to the unwanted power outside the subband group.

Considering the FTTH configuration with 64 subscribers, the chirp-managed-based transmission does not

ensure the minimum quality of BER = 10−3 for PCN = 0 dBm, but this minimum quality is achieved for

the maximum distance of 81 and 90 km for the fiber transmission with PCN of 3 and 5 dBm, respectively.

As observed in figure 5.1, the DML-based transmission only assures a BER not exceeding 10−3 for

the maximum fiber length of 83 km with PCN = 5 dBm. Thus, the CML-based transmission improves

the maximum reach of the network that ensures a minimum quality of BER = 10−3, compared to the

DML-based transmission, by approximately 1 and 7 km, respectively for PCN of 3 and 5 dBm.

For N = 32, as considered in figure 5.2, the transmission using the DML only assures the minimum

quality of BER = 10−4 for the maximum distance of 83 km for PCN of 3 dBm and 89 km for PCN of 5

dBm. The transmission using the CML ensuring the minimum quality of BER = 10−4 is accomplished

for a maximum distance of 90 km for PCN of 3 dBm, and 100 km for PCN of 5 dBm. The CML-based

transmission with PCN of 0 dBm does not ensure the minimum quality of BER = 10−4. An improvement

of 7 and 11 km is achieved for the cases with a PCN of 3 and 5 dBm.

As it can be noticed in figure 5.3, for N = 16 the transmission using the DML only assures the minimum

quality of BER = 10−9 for a maximum transmission length of 80 km with PCN of 3 dBm, and 86 km with

PCN of 5 dBm. The CML based transmission ensures the minimum required quality for the transmission

length of 87 and 96 km with PCN of 3 and 5 dBm, respectively. For both DML and CML-based trans-

mission the minimum quality not exceeding BER = 10−9 is not achieved with PCN of 0 dBm. Thus, an

improvement of 7 and 10 km is achieved for PCN of 3 and 5 dBm.

57

Figure 5.1.: BER as a function of the SSMF length of the FTTH network considering N=64.


58


5.2.1. Assessment of the distortion inflicted by the OFDM-UWB FTTH network

Although the same power level is assigned to both CML and DML-based approaches, the chirp-controlled

optical OFDM-UWB signal is more resilient to the fiber transmission. Figure 5.4 shows the noiseless

EVM of the OFDM-UWB signal at the receiver as a function of the SSMF length. It can be observed that

the chromatic dispersion associated with the fiber transmission has a stronger effect on the DML-based

OFDM-UWB signal: there is a higher increase of the EVM value compared to the EVM of the CML-

based transmission. The subbands in the middle of the subband group have an EVM increase mainly

due to a larger crosstalk coming from subbands at both sides of the spectrum. The distortion coming

from crosstalk is enhanced by the higher sensitivity of the non-chirp-controlled OFDM-UWB signal to

the fiber dispersion.

Figures 5.5a and 5.5b show the difference between the received constellation of a chirp-managed and a

non-chirp-managed OFDM-UWB signal. As expected, the demodulated symbols of the chirp-managed

OFDM-UWB signal are less spread than the demodulated symbols of the OFDM-UWB signal without

controlled chirp.

As in Chapter 4, subband 3 and 4 impose the lowest performance: subband 3 experiences a higher level

of interference from subbands at the both sides of the frequency spectrum, but higher frequency subbands

have their Psb decrease more due to the fiber dispersion and are submitted to a higher distortion by the

DML (as Chapter 4). For the DML-based transmission, the subband with worst performance varies

between 3 and 4. The higher level of crosstalk caused by a longer fiber transmission makes the subband

with worst performance change from 4 to 3.

59

In the CML-based transmission, subband 4 imposes the highest distortion. As observed in figure 5.4a,

the fiber dispersion effect does not influence the EVM value as much as in the transmission using the

DML. A chirp-controlled OFDM-UWB signal exhibits a higher resilience to the chromatic dispersion

of the fiber. Chapter 4 demonstrated that higher frequency subbands experience more distortion by the

DML and, in this case, it determines the subband with worst performance.

(a) CML-based transmission (b) DML-based transmission

Figure 5.4.: EVM value at the OFDM-UWB receiver for the CML and DML-based transmission.

(a) CML-based transmission (b) DML-based transmission

Figure 5.5.: Constellation of the received symbols from subbands 1, 2, 3 and 4 of CML and DML-based100 km transmission.

5.2.2. Influence of the optical noise generated by the EDFA at the central node

As explained in chapter 3, the role of the EDFA prior to the fiber transmission is to impose a defined

mean optical power in order to compensate for the losses inflicted by the OSR. Along with the optical

60

amplification, the EDFA increases the level of noise power.

In this subsection, the influence of the optical noise generated by the post-amplifier at the central node is

assessed in the OSNR value at the local exchange.

The noise originated by the EDFA depends on its gain as given in (3.4). The gain of the EDFA at the

central node is influenced by the mean optical power imposed at the central node output (PCN). A higher

level of mean optical power imposed at the central node output increases the gain of the first EDFA

raising the ASE noise power at its output.

Table 5.1 shows the OSNR calculated at the splitter input neglecting the noise generated at the central

node, and the OSNR considering both the noise generated from the EDFA at the local exchange and the

noise coming from the EDFA at the central node 1. As expected, the influence of the noise generated

at the central node increases with PCN. However, the OSNR difference does not exceed 0.1 dB for

OSNR values near 30 dB, which means that the noise generated by the first EDFA does not influence the

performance of the CML-based system.

Table 5.1.: OSNR calculated at the DEMUX input in the CML-based transmission.

SSMF length after the splitter [km] 80 85 90 95 100

OSNR neglecting the noise from the 1st EDFA

for PCN = 0 dBm [dB]21.67 21.67 21.67 21.67 21.67

OSNR accounting for the noise from the 1st

EDFA for PCN = 0 dBm [dB]21.67 21.67 21.67 21.67 21.67


for PCN = 3 dBm [dB]24.67 24.67 24.67 24.67 24.67




for PCN = 5 dBm [dB]26.67 26.67 26.67 26.67 26.67



Since for the DML-based transmission there is no loss from the chirp control, the EDFA gain is lower

than in the CML-based transmission. Therefore, it can be concluded that the ASE noise of the EDFA at

1The OSNR value shown in Table 5.1 varies with the fiber length because the OSR considered for each fiber length hasdifferent characteristics.

61

the central node does not influence the OSNR at the receiver and, consequently, the overall performance

of the system.

5.2.3. Influence of optical and electrical noise

As explained in Chapter 3, the noise in the FTTH network is originated by the EDFAs at the central node

and local exchange, and by the electrical circuitry at the premises of the user.

It is considered that the optical noise is dominant, when the variance (that affects each OFDM-UWB

subcarrier) of the optical noise is one order of magnitude higher than the variance of electrical noise.

The electrical noise is dominant, if the variance of electrical noise is one order of magnitude higher than

the variance of optical noise.

As presented in Chapter 3, the power spectral density of the electrical noise is constant and its value is

given by expression (3.12). The power spectral density of the noise generated by the EDFA is given by

(3.4), and it is influenced by the number N of subscribers and the length of the second section of fiber.

An increasing number of subscribers or a longer fiber transmission raises the level of loss inflicted by the

FTTH, reducing the PSD of the optical noise incident on the PIN. A lower value of the power spectrum

density of the optical noise reduces its influence on the performance of the system.

Considering N = 16, the variances of electrical and optical noise have the same order of magnitude

in most of the configurations. Due to a higher loss from a longer fiber transmission noise generated

electrically prevails over the optical noise.

For N = 32 and 64, the electrical noise is dominant for all configurations. The PSD of noise generated by

the EDFA is significantly reduced by the 32 and 64-splitter, making the noise generated by the electrical

circuitry have a dominant role in determining the performance of the system.

5.3. Conclusion

The performance of transmission of OFDM-UWB signals along the FTTH network was analyzed in this

chapter. The chirp-managed-based approach for the optical transmitter was compared to the use of the

DML, reaching an improvement of 10 km of the maximum transmission distance for a minimum quality

of BER = 10−9 in the configuration with 16 subscribers. It is concluded that the chirp-controlled OFDM-

UWB optical signal is more resilient to the fiber dispersion, showing a noiseless EVM that is not much

influenced by fiber transmission compared to the EVM of the DML-based transmission.

62

The impact of the noise originated from the EDFA at the central node was assessed. It was concluded

that noise originated by ASE of the first EDFA is neglectable since the maximum difference between

the OSNR of the OFDM-UWB optical signal at the splitter input taking into account the noise from the

central node and neglecting it, does not exceed 0.1 dB for the power levels at the central node output of

0, 3 and 5 dBm.

The weight on the FTTH performance of optical generated noise and electrical generated noise was

evaluated. It was concluded that, for most cases, the electrical noise has a dominant role. The high loss

inflicted by the FTTH network along with the increase of the number of subscribers and the longer second

section of fiber significantly reduces the noise generated by the EDFA, making the electrical circuit noise

have a dominant role in determining the performance of the system.

63

6. Final conclusion

6.1. Conclusion

The objective of this dissertation was the analysis and performance optimization of the transmission of

OFDM-UWB radio signals in FTTH networks using the chirp-managed laser.

In chapter 2, OFDM-UWB radio signals were introduced and described. An analitycal approach was fol-

lowed for the definition of this type of signals and it was presented the IFFT/FFT-based implementation

of the OFDM-UWB transmitter and receiver which significantly reduces its complexity. It was discussed

that the original OFDM-UWB signals are not suited for the optical transmission using intensity mod-

ulation and that the mean and amplitude of the signal should be adequately modified. The time and

frequency analysis of OFDM-UWB radio signals demonstrated that the 6th order Bessel low-pass filters

used in the OFDM-TX and OFDM-RX reduce the aliasing coming from the digital-to-analog conversion

although introduces distortion to the subband caused by the filter not having a totally flat passband. The

high PAPR was mentioned as one of the major drawbacks of the OFDM-UWB radio signals. Higher

PAPR values were obtained for OFDM-UWB signals originated by longer bit sequences and using more

subbands. A PAPR of 21.3 dB was reached for an OFDM-UWB signal using simultaneously subbands

1, 2, 3 and 4.

In chapter 3, the FTTH architecture was presented and each of its components was described: the general

behavior of the directly modulated laser was detailed and its main drawbacks were identified: high

frequency chirp and limited input region of operation. The high frequency chirp effect can be reduced

by filtering the DML output by an optical spectrum reshaping filter. This filter performs a frequency to

intensity conversion, increasing the tolerance of the optical signal to the fiber dispersion effect. The main

characteristics of the optical spectrum reshaper were discussed being chosen a 1storder Gaussian filter to

control the chirp generated by the DML modulation.

There were introduced two performance methods: noiseless error vector magnitude and semi-analytical

Gaussian approach (SAGA). The first one refers to a measure of the distortion inflicted by the FTTH net-

64

work on the transmitting signal. The SAGA method gives the bit error ratio and considers the distortion

inflicted by the system and the optical and electrical noise added by the amplifiers.

The effect of the non-linear operation of clipping in the OFDM-UWB signal was analysed and it was

concluded that a half-clipped OFDM-UWB signal shows a reduced distortion and it represents a solution

for the limited region of modulation of the DML and the high peak-to-average power ratio typical of

OFDM signals. However, it was demonstrated that clipping originates out-of-subband noise which can

significantly affect the introduction of higher frequency subbands.

In chapter 4, the transmission of OFDM-UWB signals in a DML-based system was optimized: the bias

and peak-to-peak currents that minimize the required OSNR for BER = 10−4 were calculated. The

optimization was performed for both single and multi-subband transmission of OFDM-UWB signals

in the configuration with fiber transmission from 0 to 100 km. For all cases, the optimal bias current

originated a half-clipped OFDM-UWB signal. The half-clipped OFDM-UWB signal shows reduced

distortion although half its amplitude was removed. The optimal peak-to-peak current sets the balance

between increasing the distortion introduced by the clipper and raising the power level of the UWB

subband. The optimal current amplitude increases with the number of subbands used due to the higher

PAPR of OFDM-UWB signals using more subbands. The performance degradation was analyzed and

it was demonstrated that it is imposed by the distortion inflicted by the laser, which is more intense for

higher frequency subbands. The larger decrease of Psb for higher frequency subbands significantly limits

the performance of the system and it was shown that this effect is augmented by the fiber transmission.

The higher interference from crosstalk between subbands in multi-subband transmission substantially

degrades the performance of the system and it is also augmented by the chromatic dispersion of the fiber.

A required OSNR of 20 dB for BER = 10−4 was obtained when transmitting subbands 1, 2, 3 and 4

simultaneously through a configuration with 100 km of fiber transmission. This value is 5 dB higher

than the transmission of subbands 1, 2 and 3, and 10 dB higher than the transmission of subbands 1 and

2.

The chirp-managed laser was optimized and an improvement of 6 dB in the required OSNR for BER =

10−4 was achieved when subbands 1, 2, 3 and 4 are simultaneously transmitted along 100 km of fiber.

The method reduces the chirp generated by the DML modulation and raises the subband group power

level relative to the unwanted power outside the subband group, making the optical OFDM-UWB signal

more resilient to the chromatic dispersion of the fiber.

The transmission performance of OFDM-UWB signals along the FTTH network using chirp-managed

lasers was investigated in chapter 5. The chirp-managed-based approach for the optical transmitter was

compared to the use of the DML, reaching an improvement of 10 km of the maximum transmission

65

distance for a minimum quality of BER = 10−9. It was concluded that the chirp-controlled OFDM-UWB

optical signal is more tolerant to the fiber dispersion, showing a noiseless EVM that is approximately

constant with the fiber transmission compared to the EVM of the DML-based transmission.

The impact of the noise originated from the EDFA at the central node was assessed. It was concluded

that noise originated by ASE of the first EDFA can be neglected since the maximum difference between

the OSNR of the OFDM-UWB optical signal at the splitter input taking into account the noise from the

central node and neglecting it, does not exceed 0.1 dB.

The weight on the FTTH performance of optical generated noise and electrical generated noise was

evaluated. It was concluded that, for most cases, the electrical noise has a dominant role. The high

loss inflicted by the FTTH network along with the increase of the number of subscribers and the longer

second section of fiber significantly reduces the noise generated by the EDFA, making the electrical noise

have a dominant role in determining the performance of the system.

6.2. Suggestions for future work

Following the conclusions drawn above, some topics of work are suggested as interesting to investigate

in order to complement or continue the work accomplished in this dissertation:

• optimization of the equalizer and analysis of its impact on the performance of the CML-based

transmission of OFDM-UWB transmission in FTTH networks;

• experimental demonstration of the CML-based transmission of OFDM-UWB transmission in FTTH

networks;

• theoretical analysis of the half-clipped OFDM-UWB signals and its transmission in a DML-based

optical system;

• analysis of the transmission along CML-based FTTH networks of OFDM-UWB signals using

other modulation formats (e.g. 64-QAM);

• analysis of the transmission in CML-based FTTH networks of IR-UWB signals.

66

A. Directly-modulated laser

A.1. Introduction

The description and analysis of the directly-modulated laser used in this work is performed in this chapter.

The analytical model of laser is detailed, being derived and analyzed its static and dynamic response.

A.2. Description of the directly modulated laser

The DML used in this dissertation is a Multiple Quantum Wells from Ortel Corporation and it is operating

at the wavelength of 1550.2 nm. Its behaviour characteristics are well described by the rate equations

that govern the interaction of photons and electrons inside the laser’s active region [31].

The rate equations take the form of (A.1), (A.2) and (A.3), where N is the carrier density, S is the photon

density and ∆ν is the instantaneous frequency shift, also designated as frequency chirp.

dNdt

=ηiIA

qVact−R(N)−g(N,S)S (A.1)

dSdt

= Γg(N,S)S− Sτp

+RS(N) (A.2)

∆ν =1

2π

dφ

dt=

αc

2Γg0(N−Nbias) (A.3)

In (A.1), ηi represents the internal quantum efficiency, IA the current applied to the active region, q is the

electric charge of an electron and Vact is the volume of the active layer. R(N) is a function that defines

the total recombination rate,

R(N) = AnrN +BN2 +CN3, (A.4)

67

where Anr is the nonradiative recombination rate coefficient, B, the radiative recombination rate coeffi-

cient, and C is the Auger recombination coefficient. g(N,S) is designated as optical gain and it is given

by,

g(N,S) =g(N)

1+ εS, (A.5)

in which ε is the nonlinear gain compression factor and g(N) is expressed as,

g(N) = gc ln(

R(N)

R(N0)

)= gc ln

(AnrN +BN2 +CN3

AnrN0 +BN20 +CN3

0

), (A.6)

where gc is the gain parameter and N0 is carrier density at transparency.

In (A.2), τp represents the photon lifetime and RS(N) the rate of spontaneous emission which is related

to the carrier density N by,

RS(N) = ΓβBN2, (A.7)

where β is the fraction of spontaneous emission noise coupled into the lasing mode.

Finally, in (A.3), αc is the linewidth enhancement factor, Nbias is the carrier density for the polarization

current Ibias and g0 is the differential gain coefficient.

Table A.1 shows the values of the laser intrinsic parameters.

68

Table A.1.: Ortel MQW laser parameter values.

Parameters Value

Carrier Density at Transparency, N0 1.7× 1024 m−3

Volume of the Active Region, Vact 29.2× 10−18 m3

Confinement Factor, Γ 0.13

Internal Quantum Efficiency, ηi 1

Differential Quantum Efficiency, η 0.139

Gain Parameter, gc 10.6× 1012 s−1

Gain Compression Factor, ε 5× 10−23 m3

Photon Lifetime, τp 0.98 ps

Linewidth Enhancement Factor, αc 2.8

Spontanerous Emission Factor, β 2.5× 10−5

Nonradiative Recombination Rate Coefficient, Anr 5× 107 s−1

Radiative Recombination Rate Coefficient, B 4.6× 10−16 m3s−1

Auger Recombination Coefficient, C 1.08× 10−41 m6 s−1

The optical power at the laser output is related with the photon density through the expression

P(t) =Vactηhυ

ΓτpηiS(t), (A.8)

where h is Planck’s constant, η is the differential quantum efficiency and υ is the optical frequency.

The DML model also considers the effects originated from the assemblage of the laser. These effects are

simulated by a first order low-pass filter with a time constant of τ=26 ps (as deduced in [37]):

H( jω) =1

1+ jωτ(A.9)

The bandwidth at -3 dB of filter is 6.1 GHz and its frequency characteristics are shown in figure A.1.

69

(a) Magnitude Response (b) Phase Response (c) Delay Response

Figure A.1.: Frequency characteristics of the assemblage effects on the DML.

The static response of the DML is shown in figure A.2. It shows the output power of the DML when a

constant current is modulating the laser.

The analytical results were obtained by solving the rate equations in steady-state mode (d/dt = 0) using

the method of Newton (the analytical solution is derived in [37]). The simulated results come from

solving the rate equations for a constant input current and getting the output power after the transient

period passed.

It is observed that for a current below 14.34 mA the output power is approximately 0 because there is

only spontaneous emission of photons. Above this threshold, there is stimulated emission of photons

and, therefore, the output power increases and it shows a linear dependence with the input current. This

linear region is limited until 100 mA, which is the maximum input current value before the laser reaches

a multi-mode emission. Thus, the current levels should only vary inside the forementioned region.

Figure A.2.: Static response of the MQW laser.

The dynamic response of the laser to a small current signal modulation is shown in figure A.3. When

this input current, defined by

70

I(t) = Ibias + i(ω)e jωt and i(ω)<< Ibias, (A.10)

modulates the laser, the output shows

• Intensity Modulation (figure A.3a): defined as the relation between the optical output power and

the input current (responses derived by [37]),

HIM =pout(ω)

i(ω). (A.11)

• Frequency Modulation (figure A.3b): defined as the relation between the frequency shift of the

output signal, or frequency chirp, and the input current (responses derived by [37]),

HFM =∆ν(ω)

i(ω). (A.12)

Figure A.3a shows that the IM response has a larger bandwidth for a higher bias current. From a Ibias =

20 mA to Ibias = 60 mA, the bandwidth at -3 dB increases approximately from 10 GHz to 25 GHz. The

FM response (figure A.3b) exhibits higher bandwidths for the same bias current, for example, for Ibias =

60 mA, the bandwidth at -3 dB is 30 GHz higher than the corresponding IM, reaching 55 GHz.

This parallel modulation becomes a drawback when a IM signal is sent through the fiber: a signal with

a wide spectrum due to FM is more sensitive to the dispersion of the fiber, limiting the transmission

distance without a compensator.

(a) IM response of the DML (b) FM response of the DML

Figure A.3.: Dynamic response of the DML when modulated by small current signals.

71

A.3. Conclusion

In this appendix, the directly-modulated laser rate equations were presented and detailed. The static

response of the laser was derived and it shows a linear region of operation between 14.34 mA and 100

mA. The dynamic response of the laser exhibits a simultaneous intensity and frequency modulation

which broadens the optical signal spectrum making it more vulnerable to the fiber dispersion effect.

72

B. Optimization results

In this appendix, it is shown the optimization results accomplished for single UWB subbands 1, 2, 3 and

4, and subband groups 1,2, 1,2,3 and 1,2,3,4 with fiber transmission of 0, 20, 40, 60, 80 and 100

km. The results presented follow the description performed in Chapter 4.

The optimization process is demonstrated in terms of the contour of the required OSNR for BER = 10−4

as a function of the mean and peak-to-peak current. For the subband group 1,2,3,4 it is presented the

contour of the BER for an OSNR OF 15 dB as a function of the current levels.

Since the optimization process is an extensive process, for most of the cases the range in the bias and

peak-to-peak current is limited to the bottom of the linear operating region of the laser, leading to half-

clipped OFDM-UWB signals.

73

(a) 0 km (b) 20 km

(c) 40 km (d) 60 km

(e) 80 km (f) 100 km

Figure B.1.: Contour of the representation of the required OSNR as a function of the current level forsubband 1 considering a fiber transmission from 0 to 100 km.

74

(a) 0 km (b) 20 km

(c) 40 km (d) 60 km

(e) 80 km (f) 100 km


75

(a) 0 km (b) 20 km

(c) 40 km (d) 60 km

(e) 80 km (f) 100 km


76

(a) 0 km (b) 20 km

(c) 40 km (d) 60 km

(e) 80 km (f) 100 km


77

(a) 0 km (b) 20 km

(c) 40 km (d) 60 km

(e) 80 km (f) 100 km

Figure B.5.: Contour of the representation of the required OSNR as a function of the current level forsubbands 1 and 2 considering a fiber transmission from 0 to 100 km.

78

(a) 0 km (b) 20 km

(c) 40 km (d) 60 km

(e) 80 km (f) 100 km

Figure B.6.: Contour of the representation of the required OSNR as a function of the current level forsubbands 1, 2 and 3 considering a fiber transmission from 0 to 100 km.

79

(a) 0 km (b) 20 km

(c) 40 km (d) 60 km

(e) 80 km

Figure B.7.: Contour of the representation of the required OSNR as a function of the current level forsubbands 1, 2, 3 and considering a fiber transmission from 0 to 80 km.

80

(a) 0 km (b) 20 km

(c) 40 km (d) 60 km

(e) 80 km (f) 100 km

Figure B.8.: BER contour for an OSNR = 15 dB as a function of the current levels for subbands 1, 2, 3and 4 considering a fiber transmission from 0 to 100 km.

81

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