UNIVERSIDAD POLITÉCNICA DE MADRIDoa.upm.es/8481/1/IÑAKI_VAL_BEITIA.pdf · entorno de una red de área de hogar, donde la robustez y fiabilidad del enlace de comunicación son un

UNIVERSIDAD POLITÉCNICA DE MADRID ESCUELA TÉCNICA SUPERIOR

DE INGENIEROS DE TELECOMUNICACIÓN

TESIS DOCTORAL

LONG POLYPHASE SEQUENCES FOR ADAPTIVE MMSE DETECTOR

IN ASYNCHRONOUS CDMA PLC NETWORK WITH IMPULSIVE

NOISE

IÑAKI VAL BEITIA

INGENIERO EN AUTOMÁTICA Y ELECTRÓNICA INDUSTRIAL

2011

UNIVERSIDAD POLITÉCNICA DE MADRID

DEPARTAMENTO DE SEÑALES, SISTEMAS Y RADIOCOMUNICACIONES

ESCUELA TÉCNICA SUPERIOR DE INGENIEROS DE TELECOMUNICACIÓN

TESIS DOCTORAL

LONG POLYPHASE SEQUENCES FOR ADAPTIVE MMSE DETECTOR

IN ASYNCHRONOUS CDMA PLC NETWORK WITH IMPULSIVE

NOISE

AUTOR: Iñaki Val Beitia Ingeniero en Automática y Electrónica Industrial DIRECTOR: Francisco Javier Casajús Quirós Doctor Ingeniero de Telecomunicación

2011

Tribunal nombrado por el Mgfco. y Excmo. Sr. Rector de la Universidad Politécnica de Madrid.

PRESIDENTE:

VOCALES:

SECRETARIO:

SUPLENTES:

Realizado el acto de defensa y lectura de la Tesis en Madrid,

el día ___ de ________ de 201__.

Calificación:

EL PRESIDENTE LOS VOCALES

EL SECRETARIO

A Belén

Agradecimientos

Quiero dedicar unas líneas de agradecimiento en atención a todos aquellos que con su ayuda

y orientación han permitido la realización de este trabajo.

Mencionaré en primer lugar al Doctor Francisco Javier Casajús Quiros al que tengo que

agradecer su labor de dirección, así como sus valiosos consejos, y dedicación.

Mi más sincera gratitud va también para el Doctor Igor Armendariz, por su cuidadosa

revisión del manuscrito y sus valiosos consejos. Debo mencionar también a la institución Ikerlan-

IK4 por su soporte.

No puedo olvidarme de mi familia por todo su apoyo. Y por último, pero no por ello menos

importante, quiero agradecer a Belén sus ánimos, comprensión y apoyo incondicional, que sin ello

habría sido imposible llevar a buen puerto este trabajo.

Resumen i

Resumen

Esta tesis analiza el diseño e implementación de un dispositivo PLC Smart Grid para un

entorno de una red de área de hogar, donde la robustez y fiabilidad del enlace de

comunicación son un requisito. La red powerline es un medio de transmisión compartido

usado por todos los nodos de forma independiente. Por lo tanto, se deben emplear técnicas

de acceso múltiple para dividir las señales de transmisión, las cuales deben ser ortogonales

entre sí. Además de esto, la complejidad computacional del sistema, coste y consumo

energético deben tenerse en cuenta durante la fase de diseño. De modo que es necesario

implementar sistemas simples, de manera que todos los usuarios accedan asíncronamente

al medio de transmisión sin la necesidad de ningún nodo central.

Para entender las dificultades de las comunicaciones powerline, y diseñar sistemas de

transmisión robustos, se debe tener una buena comprensión de las características del canal

de comunicaciones. En particular, el rango de la respuesta frecuencial y las propiedades del

ruido del canal. En esta tesis se propone un modelo de simulación del canal powerline que

tiene en cuenta el ruido generado en la red así como los perfiles de atenuación frecuencial

de una red desadaptada. El modelo propuesto está basado en los resultados de una

campaña de medidas y las propuestas de otros trabajos. Un análisis del efecto del ruido

impulsional sobre las señales transmitidas revela un umbral en el rendimiento del receptor,

que depende de las propiedades estadísticas del ruido impulsional.

Los sistemas multiportadora de alta velocidad han mostrado un excelente rendimiento

en canales con efecto multitrayecto, mientras que las extensiones MC-CDMA y OFDMA han

investigado los buenos resultados en entornos síncronos de comunicaciones powerline. Esta

tesis examina el rendimiento de algunas de estas técnicas de acceso múltiple en entornos

asíncronos powerline, usando secuencias de ensanchamiento largas binarias y complejas, en

lugar de las tradicionales ortogonales cortas debido a sus malas propiedades de correlación

cruzada en entornos asíncronos.

Con el objetivo centrado en dispositivos Smart Grid, esta tesis evita el uso de técnicas

complejas de detección multiusuario (MUD) en el receptor como por ejemplo canceladores

de interferencia en paralelo, para centrarse en técnicas más simples de un único usuario

(SUD). Con respecto a sistemas CDMA monoportadora, se selecciona un receptor MMSE

debido a la facilidad de adaptación usando algoritmos adaptativos. El rendimiento de un

receptor MMSE a nivel de símbolo en sistemas asíncronos DS-CDMA con secuencias largas es

analizado y comparado con sistemas MC-CDMA empleando intervalo de guarda en forma de

Resumen

ii

prefijo cíclico. Los análisis de rendimiento se basan en el método SGA y son verificados con

simulaciones Monte Carlo para un número alto de usuarios simultáneos con ruido

impulsional, y usando diferentes tipos de secuencias. De los resultados del análisis se

muestra un superior rendimiento desechando la interferencia de acceso múltiple de los

sistemas CDMA monoportadora en entornos asíncronos. Las simulaciones Monte Carlo

también confirman el umbral de la tasa de error debido al ruido impulsional.

Se propone una estructura adaptativa para la implementación del receptor MMSE, que

requiere diferentes parámetros difíciles de estimar desde el receptor. El receptor adaptativo

está basado en un filtro cuyos coeficientes son actualizados por un algoritmo, teniendo la

capacidad de suprimir la interferencia de ruido y acceso múltiple haciendo uso de las

propiedades cicloestacionarias de las señales transmitidas. Las simulaciones Monte Carlo

muestran un buen rendimiento en sistemas DS-CDMA asíncronos comparado con los

sistemas multiportadora MC-CDMA y MC-DS-CDMA en las mismas condiciones,

especialmente usando secuencias polifásicas. Se examinan los algoritmos NLMS y RLS, y se

propone una versión mejorada de este último que resulta menos vulnerable al ruido

impulsional. Para SNR altas la interferencia de acceso múltiple degrada el rendimiento del

receptor adaptativo usando secuencias binarias largas, mientras que el ruido impulsional

prevalece sobre la interferencia en caso de usar secuencias polifásicas, las cuales obtienen el

mejor rendimiento en combinación de un receptor RLS mejorado. Para finalizar, se muestra

como los algoritmos adaptativos muestran mejores capacidades de seguimiento y mejor

rechazo de interferencia cerca-lejano con secuencias largas polifásicas.

Abstract iii

Abstract

This thesis examines the design and implementation of a Smart Grid powerline

communication device for a Home Area Network environment, where the communication

link robustness and reliability are a requirement. Powerline network represents a shared

transmission medium used by all nodes independently. Therefore, multiple–access

techniques must be employed in order to divide transmitted signals, which have to be

orthogonal to each other. In addition to this, system computational complexity, cost and

power consumption need to be taken into account during design phase. So, simple systems

need to be implemented, so that all the users access the medium asynchronously without

the coordination of any central node.

To understand the challenges of powerline communication, and to design robust data

transmission systems, one must have a good understanding of the communication channel

characteristics; in particular, the range of channel frequency response, and the

characteristics of the channel noise. In this thesis, a powerline channel model is proposed,

which takes into account the noise generated in the network as well as the frequency

attenuation profile of the unmatched network. The proposed model is based on a channel

measurement campaign results and proposals from other works. An analysis of the impulsive

noise effect over transmitted signals reveals a performance bound at the receiver side,

which depends on impulsive noise statistics.

High data rate multi–carrier systems have shown successful performance under

multipath channels, whereas its multiple–access extensions MC-CDMA and OFDMA have

probed good results under synchronous powerline communications environments. The

thesis examines the performance of some multiple–access techniques in asynchronous

powerline communications environments using long binary and complex–valued polyphase

spreading sequences, instead of short orthogonal codes due to their worse cross–correlation

properties in asynchronous environments.

This thesis avoids complex joint detection techniques at the receiver, such as multi–

user detection and parallel interference cancellers, and it focuses on single–user detection

techniques. Concerning single–carrier CDMA system, an MMSE receiver is selected due to its

advantage of ease of adaptation, since standard adaptive algorithms can be employed. The

performance of the single user detector symbol–level MMSE receiver in asynchronous long

sequences DS-CDMA systems is analyzed and compared with that of MC-CDMA receiver

employing an interval guard in the form of a CP. Performance analysis is based on the SGA

Abstract

iv

method, and validated for a large number of simultaneous nodes with Monte Carlo

simulations under powerline impulsive noise, and using different kind of long sequences.

From analysis results, it is shown the superior performance rejecting MAI of single-carrier

multiple–access technique in asynchronous environments. Monte Carlo simulations also

confirm the BER bound due to impulsive noise

An adaptive architecture is proposed for practical implementation of the MMSE

receiver, which requires several parameters difficult to estimate from the receiver side. The

adaptive receiver is based on a FSE whose tap weights are updated by an adaptive algorithm,

having the capability of performing multiple-access interference and narrowband noise

suppression taking advantage from cyclostationary properties of the transmitted signals,

requiring the knowledge of fewer parameters compared to the MMSE and RAKE receiver.

Monte Carlo simulations show the good performance of adaptive FSE receivers in

asynchronous DS-CDMA systems compared to MC-CDMA and MC-DS-CDMA systems,

especially using polyphase long sequences. Two well-known pilot-aided NLMS and RLS

adaptive algorithms are examined. An enhanced version of the RLS algorithm less vulnerable

to the impulsive noise is proposed. At high signal-to-noise ratio, the MAI degrades the

performance of adaptive FSE receiver using binary long sequences, whereas the powerline

impulsive noise prevails over the MAI in the case of using polyphase long sequences, which

achieves the best performance in combination with the enhanced RLS receiver. The adaptive

algorithms show better tracking capabilities and good near-far interference rejection with

long polyphase sequences.

Glossary v

Glossary

3G 3rd Generation

3GPP 3rd Generation Partnership Project

AC Alternating Current

ADSL Asymmetric Digital Subscriber Line

ANSI American National Standards Institute

AWGN Additive White Gaussian Noise

BER Bit Error Rate

BLE Bit Loading Estimate

BPSK Binary Phase-Shift Keying

CCo Central Coordinator

CDMA Code Division Multiple–Access

CDF Cumulative Distribution function

CDV Committee Draft for Vote

CDWMT Complex Discrete Wavelet Multi–Tone

CE Conformité Européenne

CEBus Consumer Electronics Bus

CENELEC Comité Européen de Normalisation Electrotechnique

CFO Carrier Frequency Offset

CISPR Comité International spécial des perturbations radioélectriques

CLT Central Limit Theorem

CMFB Cosine Modulated Filter Bank

CMOE Constrained Minimum Output Energy

CP Cyclic Prefix

CSMA/CA Carrier Sense Multiple–access / Collision Avoidance

CSI Channel State Information

DBPSK Differential Binary Phase–Shift Keying

DECT Digital Enhanced Cordless Telecommunication

DFT Discrete Fourier Transform

DHS Digital Home Standard

DMT Digital Multi-Tone

DQPSK Differential Quadrature Phase-Shift Keying

DS-CDMA Direct–Sequence Code Division Multiple–Access

DSL Digital Subscriber Line

DSSS Direct–Sequence Spread Spectrum

DWMT Discrete Wavelet Multi–Tone

ECC Even cross–correlation

ECG Equal Gain Combining

EHS European Home System

EHSA European Home System Association

EIB European Installation Bus

EIBA European Installation Bus Association

Glossary

vi

EMC Electromagnetic Compatibility

ETSI European Telecommunications Standards Institute

E-UTRA Evolved Universal Terrestrial Radio Access

FCC Federal Communications Commission

FDM Frequency Division Multiplexing

FDMA Frequency Division Multiple–Access

FEC Forward Error Correction

FFT Fast Fourier Transform

FH-CDMA Frequency–Hopping Code Division Multiple–Access

FHSS Frequency–Hopping Spread Spectrum

FIR Finite Impulse Response

FMT Filtered Multi–Tone

FSE Fractionally Spaced Equalizer

GHG GreenHouse Gases

GPS Global Positioning System

GSM Global System for Mobile communications

HAN Home Area Network

HD-PLC High Definition PowerLine Communications

HDTV High Definition TeleVision

HPA HomePlug Powerline Alliance

HV High Voltage

ICI Inter Carrier Interference

IDFT Inverse Discrete Fourier Transform

IEC International Electrotechnical Commission

IED Intelligent Electronic Device

IEEE Institute of Electrical and Electronics Engineers

ISI Inter Symbol Interference

ITU International Telecommunication Union

IAT Inter Arrival Time

LAN Local Area Network

LDPC Low Density Parity Check

LMS Least mean squares

LPTV Linear Periodically Time Varying

LTE Long–Term Evolution

LV Low Voltage

MAC Medium Access Control

MAI Multiple Access Interference

MC-CDMA Multi Carrier Code Division Multiple–Access

MC-DS-CDMA Multi Carrier Direct Sequence Code Division Multiple–Access

MC-SS Multi Carrier Spread Spectrum

MMSE Minimum Mean Square Error

MRC Maximum Ration Combining

MSE Mean Square Error

MUD Multi–User Detection

MV Medium Voltage

NLMS Normalized Least mean squares

Glossary

vii

OCC Odd cross–correlation

OFDM Orthogonal Frequency Division Multiplexing

OFDMA Orthogonal Frequency Division Multiple–Access

OSI Open System Interconnection

PAPR Peak–to–Average Power Ratio

PC Personal Computer

PDF Probability Density Function

PIC Parallel Interference Canceller

PLC Power Line Communication

PLT Power Line Technology

PSD Power Spectral Density

QoS Quality of Service

QPSK Quadrature Phase–Shift Keying

RF Radio Frequency

RLS Recursive Least squares

RTU Remote terminal unit

ScDMA Scattering Division Multiple–Access

SC-FDMA Single Carrier Frequency Division Multiple–Access

SCR Silicon Controlled Rectifier

SGA Standard Gaussian Approximation

SINR Signal–to–Interference Noise Ratio

SNR Signal–to–Noise Ratio

SS Spread Spectrum

SS-MC-MA Spread Spectrum Multi Carrier Multiple–Access

SUD Single–User Detection

TDMA Time Division Multiple–access

TH-CDMA Time–Hopping Code Division Multiple–Access

THSS Time–Hopping Spread Spectrum

TIA Telecommunication Industry Association

TO Time Offset

UPA Universal Powerline Association

UWB Ultra Wide Band

VDSL2 Very High Digital Subscriber Line 2

VoIP Voice over Internet Protocol

W-CDMA Wideband Code Division Multiple–Access

WSCS Wide Sense CycloStationary

WLAN Wireless Local Area Network

Index of contents ix

Index of contents

LIST OF FIGURES............................................................................................................................................ XIII

LIST OF TABLES ............................................................................................................................................ XVII

1 INTRODUCTION .........................................................................................................................................1

1.1 POWER LINES FOR COMMUNICATION ..................................................................................................... 1

1.2 SMART GRID ............................................................................................................................................. 4

1.3 OBJECTIVES .............................................................................................................................................. 7

1.4 OUTLINE OF THE THESIS ........................................................................................................................... 7

2 STATE OF THE ART REVIEW .......................................................................................................................9

2.1 POWERLINE CHANNEL ........................................................................................................................... 10

2.1.1 Topology of the network ................................................................................................................ 11

2.1.2 Frequency response ........................................................................................................................ 11

2.1.3 Channel Noise ................................................................................................................................ 16

2.1.3.1 Background and narrowband noise ........................................................................................................... 18

2.1.3.2 Impulsive noise .......................................................................................................................................... 19

2.1.4 EMC constrains and interferences .................................................................................................. 20

2.2 NARROWBAND POWERLINE .................................................................................................................. 26

2.2.1 X-10 Protocol .................................................................................................................................. 27

2.2.2 CEBus Protocol ............................................................................................................................... 28

2.2.3 LONWORKS Protocol ...................................................................................................................... 28

2.2.4 EHS Protocol ................................................................................................................................... 29

2.2.5 KONNEX Protocol ........................................................................................................................... 29

2.3 BROADBAND POWERLINE ...................................................................................................................... 29

2.3.1 HOMEPLUG POWERLINE ALLIANCE ............................................................................................... 30

Index of contents

x

2.3.1.1 HOMEPLUG 1.0 .......................................................................................................................................... 31

2.3.1.2 HOMEPLUG AV .......................................................................................................................................... 32

2.3.1.3 HOMEPLUG Green PHY .............................................................................................................................. 32

2.3.1.4 HOMEPLUG AV2 ........................................................................................................................................ 33

2.3.2 UNIVERSAL POWERLINE ASSOCIATION .......................................................................................... 33

2.3.3 HD POWERLINE COMMUNICATIONS ............................................................................................. 34

2.3.4 HOMEGRID FORUM ....................................................................................................................... 34

2.3.5 STANDARDISATION ........................................................................................................................ 35

2.3.5.1 IEEE P1901 ................................................................................................................................................. 35

2.3.5.2 ITU G.hn ..................................................................................................................................................... 36

2.4 SMART GRID ........................................................................................................................................... 37

3 STATEMENT OF THE PROBLEM ................................................................................................................ 43

3.1 TDMA ..................................................................................................................................................... 44

3.2 FDMA ..................................................................................................................................................... 49

3.3 CDMA ..................................................................................................................................................... 57

3.4 SCDMA .................................................................................................................................................... 62

3.5 SUMMARY AND CONTRIBUTIONS .......................................................................................................... 62

4 MEASUREMENT CAMPAIGN AND CHANNEL MODELING ......................................................................... 69

4.1 CHANNEL MEASUREMENTS ................................................................................................................... 70


4.1.2 Channel Noise ................................................................................................................................ 76

4.1.2.1 Background noise ...................................................................................................................................... 77

4.1.2.2 Impulsive noise .......................................................................................................................................... 78

4.2 CHANNEL MODELING ............................................................................................................................. 85


4.2.2 Noise .............................................................................................................................................. 93

4.2.2.1 Background noise ...................................................................................................................................... 93

4.2.2.2 Impulsive noise .......................................................................................................................................... 98

4.3 IMPULSIVE NOISE EFFECT ..................................................................................................................... 101

5 THEORETICAL ANALYSIS ........................................................................................................................ 103

5.1 SPREADING SEQUENCES ...................................................................................................................... 104

5.2 ANALYSIS OF ASYNCHRONOUS DS-CDMA SYSTEM .............................................................................. 108

5.3 ANALYSIS OF ASYNCHRONOUS MC-CDMA SYSTEM ............................................................................. 115

6 PERFORMANCE ANALYSIS ..................................................................................................................... 121

6.1 SPREADING SEQUENCES ...................................................................................................................... 122

6.2 NUMERICAL RESULTS ........................................................................................................................... 132

Index of contents

xi

6.3 SUMMARY ............................................................................................................................................ 137

7 ALGORITHMIC RESEARCH ...................................................................................................................... 139

7.1 ADAPTIVE RECEIVER ............................................................................................................................. 140

7.2 NUMERICAL RESULTS ........................................................................................................................... 149

7.2.1 SPREADING SEQUENCES COMPARISON ....................................................................................... 152

7.2.2 RECEIVERS COMPARISON ............................................................................................................. 159

7.2.3 NEAR–FAR EFFECT ........................................................................................................................ 164

7.3 SUMMARY ............................................................................................................................................ 166

8 CONCLUSIONS ....................................................................................................................................... 169

8.1 WORK SUMMARY ................................................................................................................................. 169

8.2 FUTURE WORK ..................................................................................................................................... 172

REFERENCES.................................................................................................................................................. 173

List of Figures xiii

List of Figures

List of Figures

Figure 1.1 European power delivery grid topology ............................................................................................. 2

Figure 1.2 PLC signal under impulsive noise [Echelon] ..................................................................................... 2

Figure 1.3 Home area network [HomeGrid] .......................................................................................................... 3

Figure 1.4 Smart Grid device complexity [HomeGrid] ........................................................................................ 6

Figure 2.1 In–home powerline topology ............................................................................................................. 11

Figure 2.2 Transmission lines ............................................................................................................................. 15

Figure 2.3 PLC channel frequency response ..................................................................................................... 15

Figure 2.4 Time variant PLC channel frequency response due to connection and disconnection of

electrical devices .................................................................................................................................................. 16

Figure 2.5 PLC channel noise classification [Zimmermann and Dostert, 2000] ............................................. 18

Figure 2.6 Background and narrowband noise PSD ......................................................................................... 18

Figure 2.7 Impulse noise parameters ................................................................................................................. 20

Figure 2.8 Electromagnetic compatibility areas [Hrasnica et al., 2004] ........................................................... 21

Figure 2.9 CENELEC Regulation for narrowband PLC ..................................................................................... 22

Figure 2.10 Occupation band 150 kHz–30 MHz.................................................................................................. 23

Figure 2.11 Home automation using narrowband EIB-PLC .............................................................................. 26

Figure 2.12 X-10 coding in a three–phase network ........................................................................................... 27

Figure 2.13 PLC standardization map ................................................................................................................ 35

Figure 2.14 Overview of Smart Grid [EPRI, 2009] .............................................................................................. 37

Figure 3.1 TDMA time slots scheduling ............................................................................................................. 44

Figure 3.2 OFDM modulation............................................................................................................................... 46

Figure 3.3 Bit loading over an OFDM symbol .................................................................................................... 47

Figure 3.4 FDMA technique ................................................................................................................................. 49

Figure 3.5 OFDMA (DMT-FDMA) technique ........................................................................................................ 51

Figure 3.6 Comparison between TDMA/OFDMA and TDMA techniques (each color represents an user) ... 52

Figure 3.7 Comparison between OFDMA and SC-FDMA techniques ............................................................. 55

List of Figures

xiv

Figure 3.8 CDMA technique ................................................................................................................................. 58

Figure 3.9 Multiple–access schemes .................................................................................................................. 63

Figure 3.10 Spread spectrum receivers for PLC................................................................................................ 66

Figure 4.1 Frequency response measurements set–up .................................................................................... 70

Figure 4.2 Powerline coupling circuit ................................................................................................................. 71

Figure 4.3 Transmission pass–band filter .......................................................................................................... 71

Figure 4.4 Reception pass–band filter ................................................................................................................ 72

Figure 4.5 Pass–band filter frequency response ............................................................................................... 72

Figure 4.6 Measured channel frequency response (Gain) ................................................................................ 73

Figure 4.7 Measured channel frequency response (Phase) ............................................................................. 73

Figure 4.8 Comparative channel responses in accordance with loads ........................................................... 74

Figure 4.9 Frequency response expansion ....................................................................................................... 74

Figure 4.10 Channel impulsive response .......................................................................................................... 75

Figure 4.11 Noise measurement set–up ............................................................................................................ 76

Figure 4.12 High–pass filter response ............................................................................................................... 76

Figure 4.13 Background noise PSD ................................................................................................................... 77

Figure 4.14 Measured impulsive noise .............................................................................................................. 78

Figure 4.15 Time between pulses PDF (20s) ..................................................................................................... 79

Figure 4.16 Time between pulses PDF (200ms) ................................................................................................ 79

Figure 4.17 Measured single pulse noise .......................................................................................................... 80

Figure 4.18 Measured single pulse noise PSD ................................................................................................. 80

Figure 4.19 Measured pulse–burst noise .......................................................................................................... 81

Figure 4.20 Measured single pulse noise PSD ................................................................................................. 82

Figure 4.21 Pulse amplitude PDF ....................................................................................................................... 83

Figure 4.22 Pulse amplitude CDF ....................................................................................................................... 84

Figure 4.23 Burst pulse duration PDF ............................................................................................................... 84

Figure 4.24 Burst pulse duration CDF ............................................................................................................... 85

Figure 4.25 Unmatched transmission line ............................................................................................................. 86

Figure 4.26 Non–ideality of the source .............................................................................................................. 89

Figure 4.27 Network topology ............................................................................................................................ 92

Figure 4.28 Random network topology ............................................................................................................. 92

Figure 4.29 Random frequency responses ....................................................................................................... 93

Figure 4.30 Randomly generated PSD shape .................................................................................................. 97

Figure 4.31 Filtered background noise PSD ..................................................................................................... 97

Figure 4.32 PSD noise and cf = 13.4MHz ....................................................................................................... 100

Figure 4.33 Impulsive noise effect over received data symbols ................................................................... 102

Figure 5.1 User even and odd cross–correlation ............................................................................................ 106

Figure 5.2 System users asynchronism ........................................................................................................... 109

Figure 5.3 Long sequence reordering for DS-CDMA interference users ....................................................... 109

Figure 5.4 Multiple–access interference for asynchronous DS-CDMA ......................................................... 110

Figure 5.5 Long sequence reordering for MC-CDMA interference users ...................................................... 116

Figure 5.6 Multiple–access interference for asynchronous MC-CDMA ......................................................... 118

Figure 6.1 ECC and OCC calculation for τ delay ............................................................................................ 123

List of Figures

xv

Figure 6.2 ECC for Walsh sequences Lc=64 .................................................................................................... 123

Figure 6.3 OCC for Walsh sequences Lc=64 .................................................................................................... 123

Figure 6.4 OCC for Gold sequences Lc=2047 .................................................................................................. 124

Figure 6.5 ECC for Gold sequences Lc=2047 ................................................................................................... 124

Figure 6.6 OCC for Song–Park sequences Lc=2048 ........................................................................................ 125

Figure 6.7 ECC for Song–Park sequences Lc=2048 ........................................................................................ 125

Figure 6.8 ECC for Oppermann sequences Lc=2039 ....................................................................................... 126

Figure 6.9 OCC for Oppermann sequences Lc=2039 ....................................................................................... 126

Figure 6.10 OCC surface for Walsh sequences Lc=64 .................................................................................... 127

Figure 6.11 ECC surface for Walsh sequences Lc=64 ..................................................................................... 127

Figure 6.12 OCC surface for Gold sequences Lc=2047 ................................................................................... 128

Figure 6.13 ECC surface for Gold sequences Lc=2047 ................................................................................... 128

Figure 6.14 OCC surface for Song–Park sequences Lc=2048 ........................................................................ 129

Figure 6.15 ECC surface for Song–Park sequences Lc=2048 ......................................................................... 129

Figure 6.16 OCC surface for Oppermann sequences Lc=2039 ....................................................................... 130

Figure 6.17 ECC surface for Oppermann sequences Lc=2039 ....................................................................... 130

Figure 6.18 Theoretical BER performance for asynchronous DS-CDMA system without impulsive noise

with 10uN = , 4=R and 0 (1 1)n uP P n N= ≤ ≤ − . ........................................................................................ 132

Figure 6.19 Theoretical and Monte Carlo BER performance for asynchronous DS-CDMA system under

impulsive noise with 10uN = , 4=R and 0 (1 1)n uP P n N= ≤ ≤ − . Monte Carlo simulations marked

with∗ . ................................................................................................................................................................. 133

Figure 6.20 Theoretical BER performance for asynchronous MC-CDMA system with 10uN = and

0 (1 1)n uP P n N= ≤ ≤ − . ..................................................................................................................................... 134

Figure 6.21 Theoretical and Monte Carlo BER performance for asynchronous MC-CDMA under impulsive

noise with 10uN = and 0 (1 1)n uP P n N= ≤ ≤ − . Monte Carlo simulations marked with∗ . ...................... 135

Figure 6.22 Theoretical BER performance comparison for asynchronous MC-DMA and DS-CDMA under

impulsive noise .................................................................................................................................................. 136

Figure 7.1 Approximated convergence rate compared with real (simulation) transient for step size µ = 0.03

............................................................................................................................................................................. 144

Figure 7.2 Training curve of the NLMS (µ=0.03) and RLS (λ=0.9995) algorithms for asynchronous DS-

CDMA system with Eb/N0 = 12 dB, 10uN = , 4R = , 64cN = , 1kV = . Solid line represents the MMSE =

0.0443. ................................................................................................................................................................. 145



0.0055. ................................................................................................................................................................. 146

Figure 7.4 RLS based FSE coefficients divergence under impulsive noise ................................................. 147

Figure 7.5 BER performance for asynchronous DS-CDMA RAKE receiver under impulsive noise with

10uN = , 1R = and 0 (1 1)n uP P n N= ≤ ≤ − . ................................................................................................. 152

Figure 7.6 BER performance for asynchronous DS-CDMA NLMS-FSE receiver (µ=0.03) under impulsive

noise with 10uN = , 4R = and0 (1 1)n uP P n N= ≤ ≤ − . ................................................................................ 153

List of Figures

xvi

Figure 7.7 BER performance with different oversampling ratios for asynchronous DS-CDMA NLMS-FSE

receiver (µ=0.03) under impulsive noise with 10uN = and 0 (1 1)n uP P n N= ≤ ≤ − . ................................. 154

Figure 7.8 BER performance for asynchronous DS-CDMA RLS-FSE receiver (λ=0.9995) under impulsive

noise with 10uN = , 4R = and 0 (1 1)n uP P n N= ≤ ≤ − . .............................................................................. 155

Figure 7.9 BER performance for asynchronous DS-CDMA RLS-FSE enhanced receiver (λ=0.9995) under

impulsive noise with 10uN = , 4R = and 0 (1 1)n uP P n N= ≤ ≤ − ............................................................. 156

Figure 7.10 MMSE and adaptive MMSE performance comparison for asynchronous DS-CDMA system

under impulsive noise with 10uN = , 4=R and 0 (1 1)n uP P n N= ≤ ≤ − . ................................................. 157

Figure 7.11 BER performance for asynchronous MC-CDMA MRC receiver under impulsive noise with

10uN = and 0 (1 1)n uP P n N= ≤ ≤ − . ............................................................................................................. 158

Figure 7.12 BER performance for asynchronous MC-DS-CDMA MRC receiver under impulsive noise with

10uN = and 0 (1 1)n uP P n N= ≤ ≤ − . ............................................................................................................. 158

Figure 7.13 BER performance comparison under impulsive noise for Walsh spreading sequences for

64cL = and 0 (1 1)n uP P n N= ≤ ≤ − . .............................................................................................................. 159

Figure 7.14 BER performance comparison under impulsive noise for Gold spreading sequences for

2047cL = and 0 (1 1)n uP P n N= ≤ ≤ − . .......................................................................................................... 160

Figure 7.15 BER performance comparison under impulsive noise for Oppermann spreading sequences

for 2039cL = and 0 (1 1)n uP P n N= ≤ ≤ − . .................................................................................................... 161

Figure 7.16 BER performance comparison under impulsive noise for Song–Park spreading sequences for

2048cL = and 0 (1 1)n uP P n N= ≤ ≤ − . .......................................................................................................... 162

Figure 7.17 BER performance for asynchronous DS-CDMA RLS-FSE enhanced receiver at 8 Mbps under

impulsive noise with 0 16V = , 2R = and

0 (1 1)n uP P n N= ≤ ≤ − . .............................................................. 163

Figure 7.18 BER performance for asynchronous DS-CDMA NLMS-FSE receiver at 8 Mbps under impulsive

noise with 0 16V = , 2R = and

0 (1 1)n uP P n N= ≤ ≤ − . ............................................................................... 164

Figure 7.19 BER performance comparison for asynchronous DS-CDMA receiver at 8 Mbps under

impulsive noise with 0 16V = , 2R = , 10uN = and

0 (1 1)n uP P n N= ≤ ≤ − . ............................................. 165

Figure 7.20 BER performance for NLMS receiver and near-far effect under impulsive noise with 4R = ,

10uN = and 02 (1 1)n uP P n N⋅ = ≤ ≤ − . ......................................................................................................... 166

Figure 7.21 BER performance for enhanced RLS receiver and near–far effect under impulsive noise with

4R = , 10uN = and 02 (1 1)n uP P n N⋅ = ≤ ≤ − . ............................................................................................ 167

List of Tables xvii

List of Tables

List of Tables

Table 2.1 Conducted emission limits (<30 MHz) ................................................................................................ 22

Table 2.2 Conducted emission limits (>30 MHz) ................................................................................................ 23

Table 2.3 Comparison between 802.11b - HomePlug 1.0 [Lee et al., 2002] ..................................................... 31

Table 2.4 Comparison between Multimedia and Smart Grid networks [HomeGrid] ....................................... 40

Table 4.1 Pulse power and energy ...................................................................................................................... 82

Table 4.2 Background noise profiles [Benyoucef, 2003] .................................................................................. 94

Table 4.3 RF services [Hrasnica et al., 2004] ..................................................................................................... 95

Table 4.4 Narrowband noise profiles [Benyoucef, 2003] .................................................................................. 96

Table 4.5 Single pulse (Nv = 1) statistical parameters [Degardin et al., 2003] and [Val et al., 2007] .............. 99

Table 4.6 Burst pulse statistical parameters [Degardin et al., 2003] and [Val et al., 2007] ............................ 99

Table 5.1 Gold preferred pairs........................................................................................................................... 105

Table 6.1 Average cross–correlation performance ......................................................................................... 131

Table 7.1 Receiver vs. sequences performance comparison ......................................................................... 167

Chapter 1. Introduction 1

1 Introduction

Chapter 1

Introduction

1.1 POWER LINES FOR COMMUNICATION

For several years there has been a great deal of interest in the utilization of power

lines as an information transmission medium. Initially, powerline communications (PLC)

technologies have been used for narrowband low data rate (<30 kbps) communication links

in the lower frequency bands using simple modulation schemes. In outdoor environment,

power distribution automation and remote meter reading [Hosono, 1982] were the target

applications for PLC, mainly in the high and medium voltage (HV and MV) lines. For in–home

network in the low voltage (LV) section, the main application was the home automation.

In PLC no additional cabling is necessary, since most industrial, office or residential

infrastructures have a very large electrical grid and wall outlets that are easy to access

throughout a building. This gives the advantage of good flexibility in use, since electronic

systems that will be connected to it, will almost always use power supply from the mains

Chapter 1. Introduction

2

network, too. However, the use of power lines for broadband applications was dismissed

because the channel was considered too noisy and unpredictable.

Figure 1.1 European power delivery grid topology

Powerline networks are not designed for communications and they do not present a

favorable transmission medium. Consequently, power lines are a very hostile medium for

communications. A power line network topology composed of large number of connections,

branches and lines with unmatched impedances gives, as a result, a received signal affected

by the multipath effect [Zimmermann and Dostert, 2002b]. Thus, the PLC transmission

channel is characterized by a large and frequency–dependent attenuation, changing

impedance and fading as well as unfavorable noise conditions. Various noise sources, acting

from the supply network, due to different electric devices being connected to the network,

and from the network environment, can negatively influence a PLC system, causing

disturbances in error–free data transmission [Zimmermann and Dostert, 2002a].

Figure 1.2 PLC signal under impulsive noise [Echelon]

After the deregulation of the European telecommunications market in a large number

of countries, new business possibilities opened for PLC technology. An alternative solution to


3

digital subscriber lines (DSL) and cable services for the realization of the access networks is

offered by the PLC technology using the MV/LV power supply grids for so–called “last mile”

communications networks. However, there is a strong competition between these providers

although PLC is a cost–effective solution.

Due to the increasing importance of networking at homes, offices and industrial

buildings, indoor PLC is considered as a candidate medium for high data rate transmissions.

Nowadays the use of high speed transmission networks is widespread inside home

environments, operating in the higher bands of the spectrum, for audio and video diffusion

as well as for personal computer data sharing. In order to utilize the in–building power

distribution grid to implement a local area network (LAN), competing directly against existing

in–home technologies such as well–known Wi–Fi and Ethernet networks.

Figure 1.3 Home area network [HomeGrid]

Unfortunately, a PLC network acts as an antenna producing electromagnetic radiation

in its environment and disturbs other services working in the same frequency range.

Therefore, the regulatory bodies specify very strong limits regarding the electromagnetic

emission from the PLC networks, with the result that PLC networks have to operate with a

limited signal power, causing performance losses.

Additionally, alternative PLC scenarios have been proposed recently, such as in–vehicle

PLC [Lienard et al., 2008] using the power supply cables of the vehicle, not only limited to

cars, but also for railway and lift systems may be possible. The idea is basically reducing costs

removing kilometers of dedicated communication cables.


4

Unlike the telephone network used by DSL, a power line network does not consist of a

point–to–point connection between two nodes. Thus, a PLC network represents a shared

transmission medium used by all nodes independently. Accordingly, the capacity of PLC

networks is furthermore reduced, requiring effective multiple–access techniques and dealing

with multiuser environments.

1.2 SMART GRID

A new concept for power delivering, named Smart Grid [Massoud Amin and

Wollenberg, 2005], is growing up during the last years, which has been promoted by many

governments as a way of addressing energy independence, global warming and emergency

resilience issues. Smart Grid refers to an improved electricity supply chain that runs from a

major power plant all the way inside your home. In short, there are thousands of power

plants throughout the country that generate electricity using wind energy, nuclear energy,

coal, hydro, natural gas, and a variety of other resources. These generating stations produce

electricity at a certain electrical voltage. This electrical energy goes through several steps

increasing and decreasing the voltage in order to transport it more efficiently.

In many countries, the electricity delivery system is getting old and worn out. In

addition, population growth in some areas has caused the entire transmission system to be

over used and fragile, taking also into account that electrical appliances are getting more

sensitive to electrical variations. Adding new transmission lines will help the utilities get

more energy from the power plants to the user. However, many communities do not want

new power lines in their areas. In addition, adding new capacity, although needed, will not

increase the reliability of all the old electrical equipment reaching the end of its useful life.

What is needed is a new approach that significantly increases the efficiency of the entire

electrical delivery system. This approach will not only increase reliability, but will also reduce

energy in the delivery process and thereby reduce greenhouse house emissions. We call this

new approach Smart Grid.

The concept of Smart Grid is to add monitoring, analysis, control, and communication

capabilities to the electrical delivery system to maximize the throughput of the system while

reducing the energy consumption. The Smart Grid will allow utilities to move electricity

around the system as efficiency and economically as possible. It will also allow the user and

business to use electricity as economically as possible, having the choice and flexibility to

manage your electrical use while minimizing the costs. Smart Grid benefits can be

categorized into 5 types [EPRI, 2009]:


5

• Power reliability and power quality: The Smart Grid provides a reliable power

supply with fewer and briefer outages, “cleaner” power, and self–healing

power systems, through the use of digital information, automated control, and

autonomous systems.

• Safety and cyber security benefits: The Smart Grid continuously monitors itself

to detect unsafe or insecure situations that could detract from its high

reliability and safe operation. Higher cyber security is built in to all systems and

operations including physical plant monitoring, cyber security, and privacy

protection of all users and customers.

• Energy efficiency benefits: The Smart Grid is more efficient, providing reduced

total energy use, reduced peak demand, reduced energy losses, and the ability

to induce end–user use reduction instead of new generation in power system

operations.

• Environmental and conservation benefits: The Smart Grid is “green”. It helps

reduce greenhouse gases (GHG) and other pollutants by reducing generation

from inefficient energy sources, supports renewable energy sources, and

enables the replacement of gasoline–powered vehicles with plug–in electric

vehicles.

• Direct financial benefits: The Smart Grid offers direct economic benefits.

Operations costs are reduced or avoided. Customers have pricing choices and

access to energy information. Entrepreneurs accelerate technology

introduction into the generation, distribution, storage, and coordination of

energy.

A smart grid is made possible by applying sensing, measurement and control devices

with two–way communications to electricity production, transmission, distribution and

consumption parts of the power grid that communicate information about grid condition to

system users, operators and automated devices, making it possible to dynamically respond

to changes in grid condition.

A home area network (HAN), shown in the Figure 1.3, extends some of the Smart Grid

capabilities into the home using powerline communications networking and/or extending

the network using wireless standards such as ZigBee, INSTEON, Zwave, WiFi or others. A


6

home area network includes an intelligent monitoring system that keeps track of all

electricity flowing in the system. When power is least expensive the user can allow the smart

grid to turn on selected home automation appliances such as washing machines or industrial

processes that can run at arbitrary hours. At peak times it could turn off selected appliances

to reduce demand.

Figure 1.4 Smart Grid device complexity [HomeGrid]

The Figure 1.4 shows the comparison of two different PLC approaches for low

complexity and high performance devices. The device power consumption and complexity is

roughly related to the supported data throughput, which is proportional to the useful

bandwidth, spectral efficiency and duty cycle of the PLC device. This performance ratio

between these two approaches establishes the difference of a Smart Grid device with the

multimedia oriented powerline modem. The most important requirements of Smart Grid

devices for HAN are for lower power, robustness, reliability, smaller size and less costly Bill

of Materials.


7

1.3 OBJECTIVES

The main objective of this thesis is to propose a multi–user powerline communications

system, which suits with the definition of a Smart Grid home device presented above. In

order to accomplish this objective, there have been defined the following particular

objectives:

i. Powerline impulsive noise measurements in order to complete a powerline

channel model and analyze the noise effect over a transmitted signal, obtaining

a closed–form probability error function.

ii. Theoretical and simulation study of asynchronous multiple–access systems with

single–carrier and multi–carrier modulations.

iii. Compare the performance of different families of spreading sequences with

several receivers’ structures and multiple–access systems in asynchronous

environments under powerline impulsive noise.

1.4 OUTLINE OF THE THESIS

The previously defined objectives will be addressed in the following chapters of this

thesis, which is organized as follows. This chapter presents the research framework in which

this work will be developed.

Chapter 2 reviews the state of the art of first powerline communication systems and

presents the current ongoing standardization processes.

Chapter 3 reviews different modulations and multiple–access techniques proposed in

the literature for powerline communication systems. Their suitability for asynchronous and

hostile environments is analyzed.

Chapter 4 presents the powerline channel measurement campaign done and propose

a channel model with background, narrowband and impulsive noise.

In the Chapter 5, a theoretical analysis is done for two asynchronous multiple–access

systems under impulsive noise, obtaining closed–form performance expression.


8

Chapter 6 analyses the performance of the previous systems with different long

spreading sequences, and Chapter 7 validates the previous analysis results with Monte Carlo

simulations under impulsive noise. In this chapter, an adaptive structure in proposed with

improved performance.

Finally, Chapter 8 gives the concluding remarks of the achievements obtained in this

thesis, and the future lines.

Chapter 2. State of the Art Review 9

2 State of the Art Review

Chapter 2

State of the Art Review

The indoor powerline is a promising medium for building in–home networks. The in–

home PLC has been drawing attention lately. There are a large number of power outlets in

any room. Therefore, we can immediately access the PLC networks by plugging the PLC

devices into power outlets without any new wiring. It has been shown that PLC technology

offers a cost–effective alternative for the realization of the access networks. On the other

hand, electrical supply networks are not designed for communications and therefore, the

transmission characteristics of powerline channels, are not entirely suited for data transfer.

There are some specific performance problems limiting the application of PLC technology

and several solutions have been presented to overcome these problems [Hrasnica et al.,

2004]:

- The powerline cables are divided in an asymmetric star topology, having many irregular

connections between network sections and transitions between overhead and

underground cables. The cable transitions cause reflections and changing characteristic

impedance, resulting in multipath signal propagation, with a frequency–selective fading

Chapter 2. State of the Art Review

10

[Zimmermann and Dostert, 2002b]. Additionally, a PLC network changes its structure,

e.g., by plugging and unplugging devices from the network [Cortes et al., 2005]. PLC

suffers from attenuation, which depends on the line, length and changing characteristic

impedance of the transmission line [Zimmermann and Dostert, 2002b].

- The low–voltage supply networks used as a transmission medium for PLC access systems

act as an antenna by producing electromagnetic radiation. On the other hand, the PLC

systems could use a frequency spectrum of up to 30-40 MHz. This frequency range is

reserved for various radio services (e.g. amateur radio) and they may be disturbed by PLC

systems. The regulatory bodies specify the limits for electromagnetic emission that is

allowed to be produced by PLC systems operating out of the frequency range defined by

the CENELEC standard [CENELEC].

- As the signal power is limited, PLC networks become more sensitive to the disturbances.

The disturbances affecting the PLC network environment are caused by other services

(e.g. shortwave radio) operating in the frequency range below 30-40 MHz [Benyoucef,

2003]. There are also disturbances coming from the PLC network itself, such as electro–

motors which could cause impulsive noise [Zimmermann and Dostert, 2002a].

- PLC access systems have to provide a very good network utilization of the shared

transmission medium and, simultaneously, a satisfactory quality of service (QoS). Both

requirements can be achieved by the application of an efficient medium access control

(MAC) layer. The task of the MAC layer is to organize the medium access between

multiple users using various services. MAC protocols for PLC systems have to achieve a

maximum utilization of the limited network capacity and realize time–critical

telecommunication services.

The following sections review the main features of the power line medium in greater

depth, gathering knowledge of the main problems involved in the use of these kinds of

networks. On the other hand, several PLC standards used in the past, present and future will

be listed.

2.1 POWERLINE CHANNEL

Users might experience unexpected trouble while they are communicating with one

another through the indoor powerline. Such trouble would be caused by significant signal


11

attenuation through the power distribution board, colored and impulsive noise generated

from electrical appliances, impedance mismatching due to the absence of electrical

terminations across the frequency band for the in–home PLC, and time–varying channel

responses synchronized to twice the electrical power frequency. The technical problems

encountered in the in–home PLC have been reported: multipath effect caused by impedance

mismatching [Zimmermann and Dostert, 2002b], colored background [Philipps, 1998],

narrowband [Benyoucef, 2003], impulsive noise [Umehara et al., 2006; Zimmermann and

Dostert, 2002a], and periodically time–varying channel frequency response [Barmada et al.,

2006; Canete et al., 2006; Cortes et al., 2005; Sancha et al., 2007].

2.1.1 Topology of the network

Unlike the telephone copper loop, the powerline in–home network does not consist of

point–to–point connections between outlets, but represents a line bus. A typical link

between two outlets consists of the distributor cable, or a series connection of distributor

cables, and the branching house connection cables, which can be modeled from the point of

view of the access network by complex termination impedance [Zimmermann and Dostert,

2002b]. Numerous reflections are caused by the joints of the house service cables, house

connection boxes, and the joints at series connections of cables with different characteristic

impedance.

Figure 2.1 In–home powerline topology

2.1.2 Frequency response

The PLC propagation medium can be seen as a transmission line. The propagation of

signals over powerline produces an attenuation, which increases with the length of the line

and the frequency. This attenuation is a function of the powerline characteristic impedance

LZ and the propagation constantγ . These two parameters can be defined by the primary

Z1

Z2

Z3

Z4

Z5 Z6

Z7

Z8

Z9

Z10 Z11

ZL4 ZL3

ZL1

ZL5

ZL7

N1

ZL6 ZL2


12

resistance R′ per unit length, the conductance G′ per unit length, the inductance L′ per

unit length and the capacitance C′ per unit length, which are generally frequency

dependent. The characteristic impedance is represented by the well–known expression

( ) ( )( ) ( )

2

2L

R f j L fZ

G f j C f

ππ

′ ′+=

′ ′+ (2.1)

and the propagation constant by

( ) ( ) ( )f f j fγ α β= + (2.2)

( ) ( ) ( )( ) ( ) ( )( )2 2f R f j L f G f j C fγ π π′ ′ ′ ′= + ⋅ + . (2.3)

Considering a matched transmission line, which is equivalent to regarding only the

propagation of the wave from source to destination, the transfer function of a line with

length l can be formulated as follows

( ) ( ) ( ) ( )f l f j fH f e e

γ α β− ⋅ − −= = . (2.4)

After different investigations and measurements of the properties of the energy

cables, it has been concluded that ( ) ( )2R f fL fπ′ ′<< and ( ) ( )2G f fC fπ′ ′<< expressions

are suitable for a considered frequency bandwidth (1–40MHz). Thus, the dependency of

L′ and C′ on frequency is neglected so that the characteristic impedance LZ and the

propagation constant γ can be determined using the following approximations

[Zimmermann and Dostert, 2002b]:

L

LZ

C

′=

′ (2.5)

and


13

( ) ( ) ( )1 12

2 2L

L

R ff G f Z j f L C

Zγ π

′′ ′ ′= ⋅ + ⋅ ⋅ + (2.6)

In order to simplify (2.6), the measurements have shown that ( )G f f′ ∼ , and ( )R f′

can be substituted by

( ) 0

2R f f

r

πµκ

′ = (2.7)

Then, the propagation constant γ is formulated as follows

( ) 0

2

12

2 2

L

L

Zf f f j f L C

Z r

πµγ π

κ′ ′= + + (2.8)

( ) ( )1 2 3f k f k f jk fγ = + + (2.9)

An approximation, as a result of different measurements, of the real part of the

propagation constant was done in order to get an equation representing the real

propagation loss behavior in frequency domain, which is expressed as

( ) 0 1Re kf a a fα γ= = + ⋅ (2.10)

Thus, by means of a suitable selection of the attenuation parameters 0a , 1a and k , the

powerline attenuation, representing the amplitude of the channel transfer function

[Zimmermann and Dostert, 2002b], can be defined by

( ) ( ) ( )0 1

,ka a f lf l

A f l e eα − + ⋅ ⋅− ⋅= = (2.11)

The PLC channel can be described by means of a discrete–time impulse response ( )h t

[Zimmermann and Dostert, 2002b] as


14

( ) ( )1

N

i i

i

h t C tδ τ=

= ⋅ −∑ (2.12)

where the channel is represented by N paths, and each path has a time delay iτ with a path

gain iC . The transformation in the frequency domain is given as

( ) 2

1

i

Nj

i

i

H f C eπτ−

=

= ⋅∑ (2.13)

From (2.3), the transfer function in the frequency domain can be rewritten as

( ) ( ) 2

1

, i

Nj

i i

i

H f g A f l eπτ−

=

= ⋅ ⋅∑ (2.14)

where ig is a weighting factor (product of transmission and reflection factors), which gets

smaller with more transitions and reflections along the path. The path delay iτ is related

with the length il of the cables by means of

ii

P

l

vτ = (2.15)

where Pv is the velocity of propagation of the wave in the cable. Using (2.11), the channel

transfer function is

( ) ( )0 1 2

1

ki i

Na a f l j

i

i

H f g e eπτ− + ⋅ ⋅ −

=

= ⋅ ⋅∑ (2.16)

The final equation of the PLC channel model is mainly composed of the weighting

term, an attenuation term and the delay term.


15

Figure 2.2 Transmission lines

Figure 2.3 shows a typical powerline frequency response following the model

proposed in (2.16). The deep narrowband notches and the attenuation along the frequency

axis can be seen.

Figure 2.3 PLC channel frequency response

As previously stated, powerline channel characteristics also exhibit a time variation

with a two–fold origin. The first is caused by the connection and disconnection of electrical

devices and represent long–term changes [Canete et al., 2003; Canete et al., 2002]. This

causes a change in the channel response, usually frequency selective as shown in the Figure

2.4. The second is due to the time–variant behavior of the electrical devices related to the

mains cycle, which produce a cyclic short–time variation in the frequency response and

cyclostationary components in the received noise [Cortes et al., 2005; Katayama et al.,

2006]. It should be noted that there also exist periodic variations of the input impedances of

the loads connected to the powerline network that translate into short–time variations of


16

the transfer function. Time variations in the channel response are usually characterized by

measuring the spectral broadening experienced by a sinusoid after traversing the channel. In

mobile radio channels this figure is usually referred to as Doppler spread.

Figure 2.4 Time variant PLC channel frequency response due to connection and disconnection of

electrical devices

Powerline communications channels are frequency selective and time variant.

Measurements have shown that they can be modeled as a linear periodically time varying

(LPTV) filter with the presence of additive cyclostationary colored noise as well [Canete et

al., 2006; Katayama et al., 2006].

2.1.3 Channel Noise

Apart from the distortion of the information signal, owing to cable losses and

multipath propagation, noise superposed on the utile signal energy make correct reception

of information more difficult. Unlike the other wireless channels, the powerline channel

does not represent an Additive White Gaussian Noise (AWGN), whose power spectral

density is constant over the whole transmission spectrum. Numerous investigations and

measurements were carried out in order to provide a detailed description of the noise

characteristics in a PLC environment. An interesting description is given in [Zimmermann and

Dostert, 2000], which classifies the noise as a superposition of five noise types, distinguished

by their origin, time duration, spectrum occupancy and intensity:


17

• Colored background noise: whose power spectral density (PSD) is relatively lower and

decreases with frequency. This type of noise is mainly caused by a superposition of

numerous noise sources of lower intensity. Contrary to the white noise, which is a

random noise having a continuous and uniform spectral density that is substantially

independent of the frequency over the specified frequency range, the colored

background noise shows strong dependency on the considered frequency. The

parameters of this noise vary over time in terms of minutes and hours.

• Narrowband noise: which most of the time has a sinusoidal form, with modulated

amplitudes. This type occupies several sub–bands, which are relatively small and

continuous over the frequency spectrum. This noise is mainly caused by the ingress

of broadcast stations over medium– and shortwave broadcast bands. Their amplitude

generally varies during the daytime, becoming higher by night when the reflection

properties of the atmosphere become stronger.

• Periodic impulsive noise, asynchronous to the main frequency: with a form of

impulses that usually has a repetition rate between 50 and 200 kHz, and which

results in the spectrum with discrete lines with frequency spacing according to the

repetition rate. This type of noise is mostly caused by switching power supplies. A

power supply is a buffer circuit that is placed between an incompatible source and

load in order to make them compatible. Because of its high repetition rate, this noise

occupies frequencies that are too close to each other, and builds frequency bundles

that are usually approximated by narrow bands.

• Periodic impulsive noise, synchronous to the main frequency: these are impulses with

a repetition rate of 50 or 100 Hz and are synchronous with the main powerline

frequency. Such impulses have a short duration, in the order of microseconds, and

have a power spectral density that decreases with the frequency. This type of noise is

generally caused by the power supply operating synchronously with the main

frequency, such as the power converters connected to the mains supply.

• Asynchronous impulsive noise: whose impulses are mainly caused by switching

transients in the networks. These impulses have durations of some microseconds up

to a few milliseconds with an arbitrary inter–arrival time. Their power spectral

density can reach values of more than 50 dB above the level of the background noise,

making them the principal cause of error occurrences in the digital communication

over PLC networks.


18

Figure 2.5 PLC channel noise classification [Zimmermann and Dostert, 2000]

2.1.3.1 Background and narrowband noise

This kind of noise is caused principally by the composition of numerous low–power

noise sources. Its PSD is relatively low and varies with the frequency and over time, although

it can be kept stationary for minutes or even hours. It has been investigated in [Benyoucef,

2003; Degardin et al., 2003; Esmailian et al., 2003; Katayama et al., 2006; Philipps, 1998].

Figure 2.6 Background and narrowband noise PSD

From the analysis of the disturbances, it is known that the distribution of the

amplitude of the disturbance is nearly Gaussian. Therefore it is sufficient to consider the

power density spectrum for the modeling. The basis of the modeling is the superposition of


19

background noise and the narrow band disturbances [Benyoucef, 2003] (Figure 2.6). In this

case, no difference is made between the shortwave radios and the other narrowband

disturbances in the form of spectral lines, because normally the spectral lines are found in

bundled form. For the modeling, these bundles of disturbers are approximated by their

envelope.

Background noise ( )NBn t is caused mainly by the composition of several low–power

noise sources, and its PSD function ( )BGS f decreases exponentially with frequency, as

shown in the following expression

0/

0 1( )f F

BGS f N N e−= + (2.17)

where 0N , 1N and 0F parameters are taken from [Benyoucef, 2003]. The average power

density of this kind of noise usually falls between a range of –160 dBV2/Hz and –120

dBV2/Hz. Narrowband noise ( )NBn t is mostly sinusoidal with modulated amplitudes This type

of noise is caused by multiple broadcast RF emissions coupled in the electrical cables

[Benyoucef, 2003]. Along the day, it may vary depending on atmospheric conditions enabling

a more propitious propagation of RF waves. Each radio emission has a Gaussian shaped PSD

[Benyoucef, 2003] and the sum ( )NBS f can be written as

2

2

( )

2

1

( )

i

i

f fN

B

NB i

i

S f A e

−−

=

= ⋅∑ (2.18)

where iA is the power density, if is the centre frequency, and iB is the narrowband

interferer bandwidth.

2.1.3.2 Impulsive noise

Impulsive noise is composed of strong peaks whose duration can vary from

microseconds to a few milliseconds. The time between occurrence events could be periodic

with electrical network frequency or totally asynchronous. Impulsive noise ( )In t has its

source in switching power electronics components and may cause burst errors in the

transmitted data. In [Zimmermann and Dostert, 2002a], the impulsive noise model is based

on classification according to different parameters such as pulse duration and inter arrival

time. This parameters are measured at the receiver side, whereas the author in [Tlich et al.,


20

2009] studies the noise directly at their source output and filtering it by the channel

frequency. From the statistical point of view, this work considers that both models have the

same effect. Then, the baseband equivalent impulsive noise in the time domain is defined as

( )

,

( ) sin(2 ) ( )k kt T kI k k k

k imp k

t Tn t A e f t T rect

T

ζ π∞

− −

=−∞

−= ⋅ ⋅ − ⋅∑ (2.19)

where ( )rect ⋅ function is a rectangular shape which is uniform in the interval [0,1]. kA ,

kζ , kf , ,imp kT , and kT are the pulse amplitude, time attenuation constant, oscillation

frequency, pulse length, and start time of the kth pulse, respectively. The parameter inter

arrival time (IAT) is defined as the time between two pulse events, i.e. , 1IAT k k kT T T −= − .

Figure 2.7 Impulse noise parameters

Each of these variables follows a statistical distribution, and they have been

investigated and modeled in [Degardin et al., 2003; Umehara et al., 2006; Zimmermann and

Dostert, 2002a]. And they will be examined more in detail in the Chapter 4.

2.1.4 EMC constrains and interferences

Powerline communications technology uses the power grid for the transmission of

information signals and from the electromagnetic point of view, the injection of the


21

electrical PLC signal into the power cables results in the radiation of an electromagnetic field

in the environment, where the power cables begin acting like antennas in transmission and

reception mode. This field is seen as a disturbance for the environment and for this reason

its level must not exceed a certain limit, in order to realize the so–called electromagnetic

compatibility. Electromagnetic compatibility means that the PLC system has to operate in an

environment without disturbing the functionality of other systems existing in this

environment. Electromagnetic immunity and radio electric disturbance are regulated by the

European regulatory standards EN 55024 [CENELEC, 1998] and EN 55022 [CENELEC, 1994],

respectively.

Figure 2.8 Electromagnetic compatibility areas [Hrasnica et al., 2004]

To be able to describe the real electromagnetic influence of the PLC system on its

environment, several measurements have been carried out. The measurements were a

starting point of the standardization efforts for PLC systems for fixing the limits of the

permitted electric (and also the magnetic in some cases) radiated field in their

environments.

PLC is not intended to communicate via radiated signals. However, a demonstration

reported in [Stott, 2004] shows that even so, a PLC in–home system does indeed do so. The

author describes the experiment as follows: a PLC network was established. One terminal

was a laptop PC using a PLC device. The latter was plugged into a mains extension lead and

from there into the mains wall socket. A set of Christmas–tree lights was also plugged into

the same mains extension lead. The PLC network functioned as expected, communicating

with a second terminal that was plugged in elsewhere. When the mains extension lead was

then unplugged from the wall, so that the laptop PC's PLC device was no longer physically

connected to the mains, the network nevertheless continued to function. It was now

functioning in effect as a wireless local area network (WLAN), using the HF frequency

spectrum. The lights acted as an antenna for the first terminal. This is possible since the

mains wiring acted as the antenna for the second terminal.


22

Figure 2.9 CENELEC Regulation for narrowband PLC

The narrowband powerline communications over the electrical power supply networks

is specified in the European standard CENELEC EN 50065 [CENELEC, 1991], providing a

frequency spectrum from 3 to 148.5 kHz for powerline communications (Figure 2.9). The

CENELEC norm significantly differs from American and Japanese standards (FCC Part 15

Subpart B and IEC 61000-3), which specify a frequency range of up to 500 kHz for the

application of powerline communications services.

Frequency in MHz Quasi-peak Average

0.15 to 0,50 66 to 56 dBµV 56 to 46 dBµV

0.50 to 5 56 dBµV 46 dBµV

5 a 30 60 dBµV 50 dBµV

Table 2.1 Conducted emission limits (<30 MHz)

On the other hand, any broadband PLC technology that requires a good signal to noise

ratio to operate must inherently generate emissions that may be in excess of the current

limits allowed. They must guarantee compliance with the regulation for emissions from

radio frequency devices valid in Europe, namely EN55022, which is the European version of

the international standard CISPR 22 [IEC, 2008]. In the USA and Canada, the regulations

concerning electromagnetic compatibility are provided by the standard FCC Part 15 [FCC,

2001]. This standard specifies limits for conducted emissions at mains ports and

telecommunication ports for frequencies up to 30 MHz (see Table 2.1) as well as limits for

radiated emissions between 30 MHz and 1000 MHz (see Table 2.2).


23

Table 2.2 Conducted emission limits (>30 MHz)

The generally accepted power level for adequate operation of a PLC system is -50 to -

40 dBm/Hz. Measured in a 9 kHz bandwidth, as is standard for interference measurements

at these frequencies, this implies a power level of around -10 to 0 dBm, which across the

differential 100 ohm impedance of the power network is 100 – 110 dBµV. This compares

with the permitted levels for conducted emissions in the domestic environment, with which

most if not all electronic product designers are familiar, of 60 dBµV in a comparable

frequency range between each phase and earth (Table 2.1).

Figure 2.10 Occupation band 150 kHz–30 MHz

Notching is the capability of using only certain parts of the spectrum. But the

technique of notching raises a further question, which is that of inter–modulation. When

multiple radio frequency signals are applied to a non–linear system (and the mains supply

network, with all its connected electronic equipment, will certainly include non–linearities)

they inter–modulate to produce frequencies that were not present in the original spectrum.

Thus although the PLC signal itself may be confined to certain parts of the spectrum and

avoid others, at the receiver the system inter–modulation effects may create interference

signals within the supposedly protected bands. Although this phenomenon has been

accepted as a possibility, there is little research available.

Another technique which can be applied in PLC modems is power management.

Widely used in the mobile phone context, it simply means that the system intelligently uses


24

only the minimum power needed over a given part of the spectrum to achieve reliable

communication. So although a figure can be quoted as above for the power level needed for

adequate operation in all kinds of mains environments, in practice this can be adjusted

downwards in any given spectrum sub–band depending on the noise level that the modem

finds, in real time, in that sub–band.

Nowadays, there is no PLC emission limit standard, but there are some PLC modems

already on the market in Europe and are CE Marked, which means that their manufacturers

believe that they meet the essential requirements of the EMC Directive. But there are no

standards specifically for such devices and for the present, no such device could actually

meet the general standard for RF emissions from IT equipment. This is because the level of

RF voltage that is put onto the mains connection is far in excess of the levels which are

allowed for conducted emissions from all such PLC modems.

The CISPR/I PLT project team are attempting to find a way to publish an amendment to

the CISPR 22 which could be applied to PLC modems. But after the failure of the PLC

amendment of CISPR 22 to reach the Committee Draft for Vote (CDV) stage, the European

Commission has asked the CENELEC to produce a European standard for emission limits for

PLC devices. This will be a stand–alone standard rather than an amendment to EN 55022

that can be listed in the Official Journal of the European Union under the EMC and R&TTE

Directives and give a presumption of agreement for emissions requirements under those

directives.

The intention is to produce two parts to the standard: part 1 for in–house apparatus

and part 2 for access apparatus. These parts will describe test methods and limits relating to

the PLC aspects, the remaining aspects will still be covered by EN 55022, which will be

referenced from the new standard. Such a standard would also allow the wired network

standard, the EN 50529 series, to be completed. Parts 1 and 2, dealing with telephone lines

and co–axial cables respectively, have recently received a positive vote, but the third part,

dealing with mains networks, cannot be completed until a standard for the terminal

apparatus is available.

The new standard will therefore fulfill the joint functions of providing a standard for

apparatus, and enabling the network standard to be completed. Timescales are tight; the

intention is for the draft for in–house apparatus to be ready for vote by July 2011 and the

draft for access apparatus to be ready for vote by December 2011.


25

It is clear that EMC is a key element for the development of PLC systems: EMC

regulations directly impact the transmitted power level, and consequently performance.

Therefore, the specification of a regulatory framework for PLC is needed.


26

2.2 NARROWBAND POWERLINE

In the 1930s, ripple carrier signaling was introduced on the medium and low voltage

distribution networks. For many years the search continued for a low–cost bi–directional

technology suitable for applications such as remote meter reading. For example, the Tokyo

Electric Power Company ran experiments in the 1970s which reported successful bi–

directional operation with several hundred units [Hosono, 1982]. Since the mid–1980s, there

has been a surge of interest in using the potential of digital communications techniques and

digital signal processing. The drive is to produce a reliable system which is cheap enough to

be widely installed and able to compete cost effectively with wireless solutions. But the

narrowband powerline communications channel presents many technical challenges.

Figure 2.11 Home automation using narrowband EIB-PLC

Approximately 30 years ago the typically home–control powerline communication

devices were operating by modulating in a carrier wave of between 20 and 200 kHz into the

household wiring at the transmitter. The carrier is modulated by digital signals. Each receiver

in the system has an address and can be individually commanded by the signals transmitted

over the household wiring and decoded at the receiver. These devices may be either plugged

into regular power outlets, or permanently wired in place. Since the carrier signal may

propagate to nearby homes (or apartments) on the same distribution system, these control

schemes have a "house address" that designates the owner.

Initially, the only way of building a home automation installation (Figure 2.11) was with

the use of sensors and actuators that were joined via a centralized architecture to a PLC or


27

controller loaded with all the intelligence required in the home. They were almost always

inflexible proprietary systems that made any attempt to increase their performance very

difficult and costly.

Thanks to the drastic fall in the price of electronic hardware, it is possible to build

sensors and actuators with sufficient intelligence to implement a distributed control local

area network using a distributed architecture and with the support of carrier current

technologies, such as X-10, European Installation Bus (EIB) and Lonworks technologies,

among others. In the case of home automation, the use of the installation became easier,

more flexible, more modular and with greater interconnectivity, in addition to reducing its

costs. But its use was not only limited to the field of home automation, it left the door open

as an alternative to wired or wireless data networks within a local environment or interiors.

Figure 2.12 X-10 coding in a three–phase network

2.2.1 X-10 Protocol

X-10 is one of the oldest protocols used in home automation devices. It was designed

in Scotland between 1976 and 1978 in order to transmit data via low voltage lines at a very

low speed (60 bps in the United States and 50 bps in Europe) and with a very low cost. The

X-10 protocol uses a very simple modulation compared with those that use other carrier

wave control protocols. The X-10 transceiver waits for the passes through zero of the 50 Hz

sine wave, typical of the electricity supply, to insert just after a very short signal burst at a

fixed frequency. This signal can be inserted in the positive and negative semicycle of the sine

wave.


28

As shown in the Figure 2.12, Coding bit '1' or bit '0' depends on how this signal is

injected in the two semicycles. One binary 1 is represented by a 120 kHz pulse for 1

millisecond, and the binary 0 for the absence of this 120 kHz pulse. In a three–phase system,

the 1 millisecond pulse is transmitted three times in order to coincide with the pass through

zero in the three phases.

2.2.2 CEBus Protocol

In 1984, several members of the North American electronics industry association (EIA)

reached the conclusion that a home automation bus that contributed more functions than

those provided by systems at that time (ON, OFF, DIMMER xx, ALL OFF, etc.) was required.

They specified and developed a standard called CEBus (Consumer Electronic Bus).

For the transmission of data via power lines, the CEBus uses an expanded spectrum

modulation, transmitting several bits within a signal burst that begins at 100 kHz and finishes

at 400 kHz (sweep) with a duration of 100 milliseconds. The average transmission speed is

7500bps.

2.2.3 LONWORKS Protocol

Echelon presented the LonWorks technology in 1992 [Echelon]. Since then a large

number of companies have been using this technology to implement security control

networks and automation. Although it is designed to cover the requirements of most control

applications, its only successful implementation has been in office buildings, hotels, etc. But,

due to its cost, LonWorks devices have not enjoyed widespread implementation in the home

particularly because there were other, much cheaper technologies with similar features.

The success that LonWorks has had in professional installations, in which reliability and

sturdiness are much more important than price, is due to the fact that since the beginning it

has offered a solution with a decentralized point to point architecture, which allows the

intelligence to be distributed between of the sensors and actuators installed in the home

and which encompasses from the physical level up to the application level.

The Neuron Chip (micro controller built into each of the nodes) provides a specific 5-

pin port which can be configured to operate like an interface between several line

transceivers and work at different binary speeds. LonWorks can work on an optoisolated RS-

485, coupled to a coaxial or braided pair cable with a transformer, on carrier currents, fiber


29

optics or even radio. Among the different transceivers that are available, the so–called PLT-

22 should be highlighted in this regard, which reaches a maximum data rate of 5.4 kbps.

2.2.4 EHS Protocol

The European home system (EHS) standard was another of the attempts made by

European industry (1984), under the auspices of the European Commission, to create a

technology that would allow the implementation of home automation in the residential

market on a massive scale. The result was the specification of the EHS in 1992. It is based on

an open system interconnection (OSI) levels topology and the following levels are specified:

physical, data link, network and application.

During the period 1992 - 1995, the EHSA (EHS Association) sponsored the development

of electronic components that would implement the first specification. This led to the

creation of the integrated circuit of ST-Microelectronics (ST7537HS1) which allowed data to

be transmitted via an asynchronous serial channel via domestic low voltage lines. This

technology, based on FSK modulation, attains speeds of up to 2400 bps.

2.2.5 KONNEX Protocol

In order to create a single European standard for the automation of homes and offices,

capable of competing with regard to quality, features and price level with other North

American systems such as Lonworks and CEBus, Konnex is the initiative of three European

associations:

• EIBA (European Installation Bus Association).

• Batibus Club International.

• EHSA (European Home System Association).

2.3 BROADBAND POWERLINE

A current snapshoot of the PLC industry reveals several consortiums and

standardization bodies. No such PLC standard has been approved yet, but the

standardization bodies institute of electrical and electronics engineers (IEEE) and


30

international telecommunication union (ITU) are currently working on two proposals, P1901

and G.hn, respectively.

Several competing organizations have developed in–home PLC specifications, including

the homeplug powerline alliance (HPA), the universal powerline association (UPA) and the

high definition PLC (HD-PLC) alliance. ITU-T adopted Recommendation G.hn as a standard for

high–speed powerline, coax and phone line communications. On the other hand, IEEE P1901

is an IEEE working group developing the global standard for high speed powerline

communications. In July 2009, the working group approved its "IEEE 1901 Draft Standard for

Broadband over Power Line Networks: Medium Access Control and Physical Layer

Specifications" as an IEEE draft standard for broadband over power lines defining medium

access control and physical layer specifications. The IEEE 1901 Draft Standard was published

by the IEEE in January 2010 and the final standard is expected to be published and ratified in

September or October of 2010.

The most established and widely deployed powerline networking standard for these

powerline modems comes from the HomePlug Powerline Alliance. HomePlug AV is the most

current of the HomePlug specifications (HomePlug 1.0, HomePlug AV and the new HomePlug

Green PHY comprise the set of published specifications) and it has been adopted by the IEEE

P1901 group as a baseline technology for their standard; it is due to be published and

ratified in September or October of 2010. Other organizations back different specifications

for power line in–home networking and these include the Universal Powerline Association,

the HD-PLC Alliance and the ITU-T’s G.hn specification.

Within homes, the HomePlug AV and IEEE P1901 standards specify how, globally,

existing AC wires should be employed for data purposes. The IEEE 1901 includes HomePlug

AV as a baseline technology, so any future IEEE 1901 products will be fully interoperable

with HomePlug AV, HomePlug Green PHY or the forthcoming HomePlug AV2 specification

(under development now and expected to be approved in Q1 2011).

2.3.1 HOMEPLUG POWERLINE ALLIANCE

The HomePlug Powerline Alliance is the largest powerline networking alliance with

over 70 members, and has developed a succession of specifications for broadband

applications such as in–home distribution of TV, gaming, broadband Internet and other

content. It also developed a high–reliability, low–power and extended temperature


31

specification to support in–home communications between electric systems and appliances

and smart meters to support the build–out of the smart grid.

2.3.1.1 HOMEPLUG 1.0

HomePlug 1.0 [HomePlug, 2001] is the first specification of the alliance for connecting

devices via power lines in the home. It provides a peak PHY–rate of 14 Mbps. It was first

introduced in June, 2001 and has since been replaced by a new specification named

HomePlug AV. In May 2008, the telecommunications industry association (TIA) incorporated

HomePlug 1.0 powerline technology into the newly published TIA-1113 international

standard. TIA-1113 specifies modem operations on user–premises electrical wiring. The new

standard was the world's first multi–megabit powerline communications standard approved

by an American National Standards Institute (ANSI) accredited organization.

Table 2.3 Comparison between 802.11b - HomePlug 1.0 [Lee et al., 2002]

The physical level is based on Orthogonal frequency–division multiplexing (OFDM)

modulation, which is widely used in digital subscriber line (DSL) technology. Over OFDM is

used differential modulation, in order to eliminate the equalization step, but losing

performance. The technical characteristics of the specification are as follows:

• Frequency band: 4.5 MHz–21 MHz.

• OFDM Modulation: 128 carriers (84 for data).

• Forward error correction: Viterbi and Reed Solomon.

• Carrier modulations supported: DQPSK, DBPSK y ROBO (robust-OFDM).

• Adaptive modulation, 3 degrees of freedom:

o Selection of carriers to be used.

o Selection of DQPSK and DBPSK modulation.

o Selection of convolutional code ½ and ¾.


32

• Access method supported: CSMA/CA.

Several performance tests have been done to modems based on HomePlug 1.0 [Lee et

al., 2002]. The results (Table 2.3) show a similar performance compared with an 802.11b

wireless link. Moreover, the PLC modem may work in places where there is no wireless

signal.

There are Turbo adapters for HomePlug 1.0 that may be found on the market. These

comply with the HomePlug 1.0 specification but feature a faster and proprietary mode that

increases the peak PHY–rate to 85 Mbps.

2.3.1.2 HOMEPLUG AV

The HomePlug AV specification [HomePlug, 2007] was introduced in August 2005 and

was designed to provide sufficient bandwidth for applications such as high definition TV

(HDTV) and voice over internet protocol (VoIP). Utilizing adaptive modulation on up to 1155

OFDM sub–carriers and turbo convolution codes for error correction, HomePlug AV can

almost achieve the theoretical maximum bandwidth across a given transmission path. Thus,

HomePlug AV is capable of reaching speeds of up to 200 Mbps in the physical level. Key

distribution techniques and the use of 128 bit AES encryption are specified as mandatory in

the specification. Furthermore, even the interception of encrypted data exchanged between

HomePlug AV devices poses a "significant challenge" for an attacker due to the adaptive

techniques used to modulate the signal between two given points.

According to the HomePlug AV specification, HomePlug AV devices may interoperate

with Homeplug 1.0 devices, but this support is optional. It is mandatory for HomePlug AV

devices to coexist with HomePlug 1.0 devices.

2.3.1.3 HOMEPLUG Green PHY

HomePlug Green PHY is a new specification that is a subset of HomePlug AV and is

specifically designed for the requirements of the Smart Grid market. It has peak rates of 10

Mbps and is designed to go into smart meters and smaller appliances such as thermostats,

home appliances and plug–in electric hybrid vehicles. For these applications, there is no

great need for high capacity broadband; the most important requirements are: for lower

power, robust, reliable coverage throughout the home, smaller size and less costly Bill of


33

Materials. HomePlug Green PHY–based products will be fully interoperable with products

based on HomePlug AV, IEEE P1901 or the upcoming HomePlug AV2 specification.

2.3.1.4 HOMEPLUG AV2

The HomePlug AV2 project is currently under development and is the prospective next

generation for the HomePlug line. According to current estimates, it will operate upon a 600

Mbps transfer capability. HomePlug AV2 is fully interoperable with HomePlug AV and will be

brought into the IEEE P1901 standard once that standard is ratified in 2010. HomePlug AV2

offers Gigabit speed at the physical layer and 600 Mbps+ at the MAC layer. The AV2 spec is

expected to be completed in late 2010. Completion of the HomePlug AV2 Marketing

Requirements Document was announced in November 2009.

2.3.2 UNIVERSAL POWERLINE ASSOCIATION

The Universal Powerline Association (UPA) is an International not–for–profit trade

association working to promote global standards and regulations in the fast developing

Powerline communications market. The UPA aims to catalyze the growth of Powerline

technology by delivering UPA plugtested and certified products that comply with these

specified standards and regulations. All products and applications designed around UPA

guidelines will communicate, from simple coexistence to full interoperability. The UPA

provides all Powerline players the opportunity to respond to key customer expectations with

open standards, based on interoperability, security and coexistence and supported by

exclusive and independent certifications; it is the only global guarantee of quality and

confidence for high–speed power line technology available today.

Members of the UPA include: AcBel Polytech Inc. Ambient Corporation, Arteche, BPL

Global, Buffalo, Comtrend, Corinex Communications Corp., Current Technologies

International, Cypress Semiconductor, D-Link, DS2, Duke Energy, Schneider Electric

Powerline Communications, Itochu Corporation, Logitec Corporation, Netgear, PCN

Technology, Pirelli Broadband, Planex, Sumitomo Electric Industries, Toshiba Electronics

Europe GmbH, Touba Telecom, TOYO Network Systems and Watteco.

The main technology provider is DS2, and the UPA digital home standard (DHS)

specification main features are:

• 1536 carrier-OFDM modulation


34

• Adaptive bit–loading, with physical layer data rate of 200 Mbps

• Collision–free and flexible TDMA MAC

• Master/slave control architecture

• Peer–to–peer data transmission architecture

• Flexible PSD mask allowing frequency band notching dynamically and remotely

• 3DES encryption

• Advanced QoS with 8 priority levels

2.3.3 HD POWERLINE COMMUNICATIONS

HD-PLC Alliance was established in 2007 to promote the world–wide adoption of HD-

PLC high–speed power line communication technology, and the interoperability of devices

that use that technology. HD-PLC Alliance is a non–profit association of more than 20

members including leading industrial organizations. The alliance encourages Japanese and

foreign companies who develop products and provide services based on HD-PLC standards,

as well as companies interested in HD-PLC to join.

Members of the HD-PLC alliance include: Panasonic, ACN, I-O DATA DEVICE, AOPEN,

APTEL, BUFFALO, Egretcom, Icron Technologies, IGRS Engineering Lab, Kawasaki

Microelectronics, Murata, OKI, OMURON NOHGATA and Qool Technologies. The main

technology provider is Panasonic, and the HD-PLC specification main features are:

• Frequency Band 4-28 MHz

• Modulation Wavelet-OFDM

• Transmission PHY Rate Maximum 190 Mbps

• Access Method CSMA/CA TDMA

• Error Correction Reed-Solomon Encoder/Decoder and Convolutional

Encoder/Viterbi

• Decoder Encryption AES 128-bit Encryption

2.3.4 HOMEGRID FORUM

The HomeGrid Forum [HomeGrid] is a global, non–profit trade group promoting the

International Telecommunication Union’s G.hn standardization efforts for next–generation

home networking. HomeGrid Forum promotes the adoption of G.hn through technical and


35

marketing efforts, it addresses certification and interoperability of G.hn–compliant products,

and cooperates with complementary industry alliances.

HomeGrid Forum members are Intel, Lantiq, Panasonic, Best Buy, British Telecom,

Texas Instruments, K-Micro, Ikanos Communications, Aware, DS2, Gigle Networks, Sigma

Designs, University of New Hampshire InterOperability Laboratory (UNH-IOL), LAN S.A.R.L, IC

Plus Corp, Korea Electrotechnology Research Institute (KERI) and Polaris Networks.

2.3.5 STANDARDISATION

As stated above, the in–home powerline networking market is badly fragmented.

There are multiple incompatible powerline technologies, where there is a lack of

interoperability and coexistence between them (UPA, HD-PLC and HomePlug devices).

Moreover, there is no interoperability between HomePlug devices. In order to solve this

problem, several initiatives are already underway in standardization proposals such as IEEE

P1901 and ITU G.hn.

Figure 2.13 PLC standardization map

2.3.5.1 IEEE P1901

The IEEE P1901, established in 2005, is an IEEE working group developing the global

standard for in–home high speed powerline communications. It was joined by both

HomePlug and the UPA, who proposed their respective powerline technologies for P1901's


36

LAN component. In 2007 the working group completed the down selection process and the

final proposal selected by the group was a combined Homeplug/Panasonic (HD-PLC)

proposal. In 2010, the working group published its "IEEE 1901 Draft Standard for Broadband

over Power Line Networks: Medium Access Control and Physical Layer Specifications" as an

IEEE draft standard for broadband over powerline networks defining medium access control

and physical layer specifications.

The P1901 Draft Standard includes two different physical layers, one based on fast

Fourier transform (FFT) OFDM modulation and another based on Wavelet-OFDM

modulation. Each PHY is optional, and implementers of the specification may include both,

but are not required to do so. Devices that use the OFDM physical layer only would not

interoperate with devices based on Wavelet physical layer. A small minority of members of

the P1901 maintain that this lack of interoperability defeats the purpose of having a

standard. The FFT-OFDM physical layer is derived from HomePlug AV technology the wavelet

physical layer comes from HD-PLC technology. The standard is expected to be approved in

2010.

2.3.5.2 ITU G.hn

In 2008, the International Telecommunication Union gave its support to G.hn, a

proposed standard for domestic networks over a range of different cable types. G.hn's goal

is to unite coax, phone lines and mains cabling into a single network capable of hosting

multiple multimedia streams over gigabit bandwidths around the home. The standard is

promoted by the HomeGrid Forum and several other organizations.

ITU Recommendation G.9960, which received approval in 2009, specifies the physical

layer and the architecture of G.hn. The data link layer specification was approved in 2010.

Over 20 companies participated regularly, representing a broad cross section of the

communications industry including some of the world's largest telephone companies, major

communication equipment companies, and some of the leading home networking

technology companies.

Unlike the P1901 standard, G.hn specifies a single physical layer based on FFT-OFDM

modulation and low–density parity–check code (LDPC) forward error correction (FEC) code.

G.hn includes the capability of notching specific frequency bands to prevent interference

with amateur radio bands and other licensed radio services. G.hn includes mechanisms to

prevent interference with legacy home networking technologies and also with other wireline


37

systems such as very high digital subscriber 2 (VDSL2) or other types of DSL used to access

the home.

Nevertheless, G.hn has been criticized because this technology is incompatible with

the established technologies on the market like HomePlug AV. Some claim that the G.hn

specification is not sufficient as a next generation technology and that G.hn will be

outperformed. HomePlug proponents say that their standard addresses such issues and that

the performance of future G.hn–based products will be in line with, or lower than, current

HomePlug AV or IEEE1901 performance.

2.4 SMART GRID

The term “Smart Grid” [Massoud Amin and Wollenberg, 2005] refers to a

modernization of the electricity delivery system so it monitors, protects and automatically

optimizes the operation of its interconnected elements – from the central and distributed

generator through the high–voltage network and distribution system, to industrial users and

building automation systems, to energy storage installations and to end–use consumers and

their thermostats, electric vehicles, appliances and other household devices.

Figure 2.14 Overview of Smart Grid [EPRI, 2009]


38

The Smart Grid is characterized by a two–way flow of electricity and information to

create an automated, widely distributed energy delivery network. It incorporates into the

grid the benefits of distributed computing and communications to deliver real–time

information and enable the near–instantaneous balance of supply and demand at the device

level. Smart Grid benefits can be categorized into 5 types [EPRI, 2009]:

• Power reliability and power quality: The Smart Grid provides a reliable power

supply with fewer and briefer outages, “cleaner” power, and self–healing

power systems, through the use of digital information, automated control, and

autonomous systems.

• Safety and cyber security benefits: The Smart Grid continuously monitors itself

to detect unsafe or insecure situations that could detract from its high

reliability and safe operation. Higher cyber security is built in to all systems and

operations including physical plant monitoring, cyber security, and privacy

protection of all users and customers.

• Energy efficiency benefits: The Smart Grid is more efficient, providing reduced

total energy use, reduced peak demand, reduced energy losses, and the ability

to induce end–user use reduction instead of new generation in power system

operations.

• Environmental and conservation benefits: The Smart Grid is “green”. It helps

reduce GHG and other pollutants by reducing generation from inefficient

energy sources, supports renewable energy sources, and enables the

replacement of gasoline–powered vehicles with plug–in electric vehicles.

• Direct financial benefits: The Smart Grid offers direct economic benefits.

Operations costs are reduced or avoided. Customers have pricing choices and

access to energy information. Entrepreneurs accelerate technology

introduction into the generation, distribution, storage, and coordination of

energy.

Technical challenges are listed below [EPRI, 2009]:

• Smart equipment: Smart equipment refers to all field equipment which is

computer–based or microprocessor–based, including controllers, remote


39

terminal units (RTUs), intelligent electronic devices (IEDs). It includes the actual

power equipment, such as switches, capacitor banks, or breakers. It also refers

to the equipment inside homes, buildings and industrial facilities. This

embedded computing equipment must be robust to handle future applications

for many years without being replaced.

• Communication systems: Communication systems refer to the media and to

the developing communication protocols. These technologies are in various

stages of maturity. The smart grid must be robust enough to accommodate

new media as they emerge from the communications industries and while

preserving interoperable, secured systems.

• Data management: Data management refers to all aspects of collecting,

analyzing, storing, and providing data to users and applications, including the

issues of data identification, validation, accuracy, updating, time–tagging,

consistency across databases, etc. Data management methods which work well

for small amounts of data often fail or become too burdensome for large

amounts of data—and distribution automation and customer information

generate lots of data. Data management is among the most time–consuming

and difficult task in many of the functions and must be addressed in a way that

will scale to immense size.

• Cyber Security: Cyber security addresses the prevention of damage to,

unauthorized use of, exploitation of, and, if needed, the restoration of

electronic information and communications systems and services (and the

information contained therein) to ensure confidentiality, integrity, and

availability.

• Information/data privacy: The protection and stewardship of privacy is a

significant concern in a widely interconnected system of systems that is

represented by the Smart Grid. Additionally, care must be taken to ensure that

access to information is not an all or nothing at all choice since various

stakeholders will have differing rights to information from the Smart Grid.

• Software applications: Software applications refer to programs, algorithms,

calculations, and data analysis. Applications range from low level control

algorithms to massive transaction processing. Application requirements are

becoming more sophisticated to solve increasingly complex problems, are


40

demanding ever more accurate and timely data, and must deliver results more

quickly and accurately. Software engineering at this scale and rigor is still

emerging as a discipline. Software applications are at the core of every function

and node of the Smart Grid.

A home area network (HAN), extends some of these capabilities into the home using

powerline networking and/or RF using standards such as ZigBee, INSTEON, Zwave, WiFi or

others. A home area network includes an intelligent monitoring system that keeps track of

all electricity flowing in the system. When power is least expensive the user can allow the

smart grid to turn on selected home automation appliances such as washing machines or

industrial processes that can run at arbitrary hours. At peak times it could turn off selected

appliances to reduce demand.

Table 2.4 Comparison between Multimedia and Smart Grid networks [HomeGrid]

The Table 2.4 summarizes the comparison between a smart grid PLC modem with a

multimedia oriented PLC system. Taking into account the above description, it can be

concluded that PLC is a suitable communication technology that can be used in a Home Grid.

These PLC modems should have specific characteristics in order to meet the requirements of

Home Grid communication devices. That is, complexity, cost and consumption must be as

low as possible, while the robustness against the disturbances found in the powerline

channel is maximized.

The two principal PLC associations, HomePlug Alliance and HomeGrid forum, started

defining their PLC modem devices for Smart Grid market. These new specifications comprise


41

a subset of previous PLC device characteristics. From HPA, HomePlug Green PHY (see

2.3.1.3) is their Smart Grid solution, which is based on the high performance HomePlug AV

specification. Whereas the HomeGrid forum has a G.hn Smart Grid profile (profile 1). Both

systems have the same characteristics: low data rates, low power consumption, low device

complexity and low cost.

Chapter 3. Statement of the problem 43

3 Statement of the Problem

Chapter 3

Statement of the Problem

A multiple–access scheme establishes a method of dividing the transmission resources

into accessible sections, which are used by multiple users using various services. A multiple–

access scheme is applied to a transmission medium within a particular frequency spectrum,

which can be used for information transfer. In the case of multiple users using a shared

transmission medium, signals from individual users have to be transmitted within separated

accessible sections, provided by a multiple–access scheme, ensuring error–free

communications. For this purpose, the signals from different users, when they are

transmitted over a shared medium, have to be orthogonal to each other [Proakis, 2000].

Focusing on a multiuser environment, several multiple–access strategies can be

employed to share the powerline network among different users, with the requisite of

allowing full asynchronism between the users and trying to achieve a robust solution that is

as simple as possible. Multiple–access schemes are used to allow many simultaneous users

to use the same fixed bandwidth spectrum and coordinate access between multiple users.

But the bandwidth that is allocated to it is always limited. Packet mode methods, like the

carrier sense multiple–access with collision avoidance (CSMA/CA) adopted in the HomePlug

1.0 PLC standards [HomePlug, 2001], do not take into account the channel characteristics of

the different users, which may be quite different. The same applies to other methods like

Aloha, Token passing or Polling. Moreover, they are not appropriate for providing the

Chapter 3. Statement of the problem

44

latency, jitter and guaranteed bandwidth needed by some streaming and industrial control

applications. These quality of service (QoS) requirements can be fulfilled by channelization

methods using time–division multiple–access (TDMA), frequency–division multiple–access

(FDMA) or code–division multiple–access (CDMA) schemes in which a centralized manager

modifies the time slots, frequency bands and codes assigned to each user. CDMA, TDMA and

FDMA have exactly the same spectral efficiency, but in practice each has its own challenges:

power control in the case of CDMA, timing in the case of TDMA, and frequency

generation/filtering in the case of FDMA.

Figure 3.1 TDMA time slots scheduling

The following are the four major methods of sharing the available bandwidth to

multiple users. There are also many extensions and hybrid techniques for these methods,

which will be listed in this chapter. However, an understanding of the four major methods is

required for understanding any extensions to these methods.

3.1 TDMA

TDMA is a type of Time–division multiplexing (TDM), with the special feature that

instead of having one transmitter connected to one receiver, there are multiple transmitters.

It is where a specific node, the central coordinator (CCo) or scheduler, has the responsibility

of coordinating the nodes of the network [Anastasiadou and Antonakopoulos, 2004]. The


45

time on the channel is divided into time slots, which are generally of fixed size. Each node of

the network is allocated a certain number of slots from where it can transmit. Slots are

usually organized in a frame, which is repeated on a regular basis. The CCo specifies the

organization of the frame in the beacon (a management frame). Each node just needs to

follow the instruction of the CCo blindly. Very often, the frame is organized as downlink

(base station to node) and uplink (node to base station) slots. A service slot allows a node to

request the allocation of a connection, by sending a connection request message in it. In

some standards, uplink and downlink frames are on different frequencies, and the service

slots could also be a separate channel.

TDMA is widely used in digital 2G cellular systems such as Global System for Mobile

Communications (GSM), IS-136 (USA), Personal Digital Cellular (Japan), iDEN (USA and

Canada), and in the Digital Enhanced Cordless Telecommunications (DECT) standard for

portable phones. It is also used extensively in satellite and military systems.

On the powerline side, the use of a TDMA scheme can be practical due to its simplicity

and reliability [Bumiller, 2001; Galda et al., 1999]. It is implemented in the current

generation of broadband powerline modems, such as HomePlug AV standard [HomePlug,

2007], which is oriented towards multimedia contents transmission, and the quality of

service (QoS) required for this kind of applications can be fulfilled with the use of a Hybrid

MAC scheme as the one employed in HomePlug AV. It can support both the connection

oriented traffic and the best effort traffic. Services that require high QoS can be offered

using a contention free MAC technique based on TDMA, while best effort traffic can be

offered using a contention based scheme as CSMA/CA. HomePlug AV uses a dynamic TDMA

scheme to satisfy the QoS based traffic. In dynamic TDMA, a scheduling algorithm

dynamically reserves a variable number of time slots in each frame for variable bit–rate data

streams, based on the traffic demand of each data stream.

A major advantage of TDMA is that the powerline modem only needs to listen and

broadcast for its own time slot. For the rest of the time, it can carry out measurements on

the network, detecting surrounding transmitters on different frequencies. This allows safe

inter frequency handovers, something which is difficult in CDMA systems. For PLC, dynamic

TDMA schemes are proposed in [Bumiller, 2001; Galda et al., 1999; Tonello et al., 2009],

where the network resources are allocated for each user in order to satisfy the QoS

parameters. In [Tonello et al., 2009], the author has studied the resource allocation problem

in an indoor PLC system with a medium access control scheme and an adaptive TDMA

region, where the presented results have been obtained by taking both the cyclostationary

noise and the cyclic behavior of the channel response into account. The system is assumed


46

to have a node in the network that acts as a CCo, which is responsible for allocating

resources by collecting information regarding the network state, i.e., number of users,

channel conditions, QoS required by each user request, etc. Once the CCo has collected all

the information needed, it allocates the resources among the users dynamically.

In order to mitigate the frequency selectivity of the powerline channel, the current

systems employ orthogonal frequency division multiplexing (OFDM) as the modulation

technique [Bingham, 1990; Kaiser, 2002], which can easily adapt to severe channel

conditions without complex equalization. The sub–carrier frequencies are chosen so that the

sub–carriers are orthogonal to each other, meaning that cross–talk between the sub–

channels is eliminated and inter–carrier guard bands are not required. This greatly simplifies

the design of both the transmitter and the receiver; unlike conventional frequency division

multiplexing (FDM), a separate filter for each sub–channel is not required. It is also robust

against inter–symbol interference (ISI) and fading caused by multipath propagation using an

interval guard in the form of CP. In such systems, when orthogonal frequency division

multiplexing (OFDM) modulation is used with TDMA, users sequentially share the available

radio resources and all carriers are assigned to the same user during a given OFDM symbol.

The TDMA approach combined with physical layer based on OFDM modulation for indoor

PLC has been studied in [Ahn and Lee, 2003; Ayyagari and Wai-chung, 2005; Bumiller, 2001;

Galda et al., 1999; Lampe, 2001; Tonello et al., 2009].

Figure 3.2 OFDM modulation

On the other hand, dynamic resource allocation strategies have been proposed for

wireless as well as wireline networks to combat the rate loss caused by interference in a

multiuser scenario. A successful example is the level–2 dynamic spectrum management

(DSM) algorithms proposed for digital subscriber–lines (DSL) [Baccarelli et al., 2002;

Papandriopoulos and Evans, 2006]. PLC has many features similar to DSL; consequently, its


47

multi–user resource allocation strategy can benefit from existing research results for DSL

networks. However, the differences in the topology between PLC and DSL need to be taken

into account. In PLC, all users transmit their signals on the same wire, while DSL users

typically transmit on separate twisted–pairs.

Figure 3.3 Bit loading over an OFDM symbol (3072 bits)

Like OFDM, discrete multi–tone (DMT) modulation is based on multi–carrier

modulation but historically comes from the DSL community [Baccarelli et al., 2002;

Papandriopoulos and Evans, 2006], and in the essence both techniques are the same.

Indeed, OFDM / DMT has many well known advantages: among others, a low complexity

channel equalizer, good resistance to narrowband noise, and the possibility to approach the

Shannon capacity by implementing coding techniques, the so–called bit–loading (or water

filling) technique. OFDM carries out energy and bit distribution across the subcarriers

yielding significant performance improvements as demonstrated in many pieces of work

[Campello, 1999; Fasano, 2003]. This is an attractive feature of OFDM, allowing practical

implementation of the water filling principle by allocating the power across the sub–

channels affected by different attenuations due to the channel frequency selectivity [Tonello

et al., 2009]. However, in the context of powerline communications, the existence, too, of

periodic variations in the input impedances of the loads connected to the network that

translate into short–time variations of the transfer function [Cortes et al., 2005] should be

noted. This behavior must in fact be incorporated in the channel state information (CSI)

which needs to be refreshed periodically. However, bit–loading is appropriate, assuming CSI

at the transmitter, because the channel is invariant for a period of time that is long in

comparison with the OFDM symbol duration [Zimmermann and Dostert, 2002b]. For indoor


48

PLC, a bit loading technique is proposed for a TDMA / OFDM system in [Ayyagari and Wai-

chung, 2005].

In [Lampe, 2001], there is discussion on the issue of medium access signaling for

powerline networks with TDMA, where all subscribers are synchronized to a TDMA framing

structure provided by a CCo. The author presents the design of transmit sequences and

signal processing of the received signal for robust medium access signaling, allowing wide

collision resolvability. As transmission request signals do not carry any payload, their

frequency and their duration should be kept as low as possible. Conversely, to ensure quality

of service, transmission requests have to be processed with high probability and short delay

by the master. These requirements prohibit the assignment of different signaling slots to

each subscriber, which in turn implies that collisions of transmission requests are possible.

Taking into account all this aspects, OFDM / DMT scheme is known to be more

efficient than single carrier schemes under frequency selective powerline channel condition

[Ahn and Lee, 2003; Galda et al., 1999; Lampe, 2001; Langfeld, 2000; Ma et al., 2005; Tlili et

al., 2003]. However, OFDM systems also show a weakness in their sensitivity to

synchronization errors. They require very accurate frequency synchronization between the

receiver and the transmitter. Thus, the major drawback of the OFDM schemes is that they

are sensitive to time misalignments and frequency offsets: ISI (channel dispersion and

asynchronous uplink links) and inter carrier interference (ICI) (cross–talk between the

subcarriers) arise and limit the performance [Tonello et al., 2000]. For this reason most of

the work on OFDM has been done for the synchronous link [Ahn and Lee, 2003; Ayyagari and

Wai-chung, 2005; Bumiller, 2001; Galda et al., 1999; Lampe, 2001; Tonello et al., 2009],

where the asynchronous links are not very suitable for this kind of modulation [Kyunbyoung

et al., 2006].

On the other hand, there are alternative propositions to the combination of FFT and

OFDM modulation. The discrete wavelet multitone (DWMT) is a type of wavelet transform

technique that has been developed recently, which is also called Wavelet-OFDM [Galli et al.,

2008] and adopted for IEEE P1901 PLC standard. This method uses a cosine modulated filter

bank (CMFB), with overlapped filters that introduce better selectivity. Wavelet-OFDM does

not need a guard interval to maintain the orthogonal characteristics between each

subcarrier, and so the spectral efficiency is better than that of FFT-OFDM using a guard

interval. In [Karamehmedovic et al., 2008], the sensitivity of DWMT transmission scheme to

the frequency offset and phase noise is addressed. The simulations performed in this piece

of work show performance comparison under frequency offset and phase noise


49

imperfections of FFT-OFDM and wavelet-OFDM, where both were found to be equally

affected by frequency offset and phase noise.

Since the DWMT it is not usually equipped with a guard interval, the main problem of

its application refers to the lack of simple and effective equalizations [Abad et al., 2005]. In

[Zbydniewski et al., 2009], the authors present a complex DWMT (CDWMT) in which the

equalization problem has been solved by the use of circularly shifted filters of the cyclic

prefix (CP). The results presented show that CDWMT modulation introducing additional

time–frequency diversity can effectively compete against FFT-OFDM standard methods

especially in powerline impulsive noise environment, but losing spectral efficiency as FFT-

OFDM. In addition, to obtain bit–rates comparable to the ones of these systems, symbols

must be overlapped in time, which in turns difficulties synchronization.

Figure 3.4 FDMA technique

Concerning PLC multiple–access techniques, Wavelet-OFDM modulation has been

used in conjunction with synchronous TDMA technique [Nakagawa et al., 2009]. In this piece

of work, the authors measure the interference immunity characteristics of high–speed PLC

modem using Wavelet-OFDM when the narrowband conducted interference signal was

injected to the network. Wavelet-OFDM modulation was shown to have good narrowband

interference immunity characteristics.

3.2 FDMA

From the point of view of dynamic resource allocation strategies and the bus topology

in PLC, a sub–channel is best assigned to an individual user and not shared by different


50

users. FDMA is a channel access method used in multiple–access protocols as a

channelization protocol. FDMA gives users an individual allocation of one or several subsets

of subcarriers, or narrower band channels, where the available bandwidth is shared among

the different users. Each user is allocated a unique frequency band, or is dynamically

assigned one in which to transmit and receive. This kind of multiple–access technique is not

vulnerable to the timing problems that TDMA has. Since a predetermined frequency band is

available for the entire period of communication, stream data (a continuous flow of data

that may not be packetized) can easily be used with FDMA. Due to the frequency filtering, it

is not sensitive to the near–far problem which is pronounced for CDMA, but requires high–

performing filters in the transmitter / receiver hardware, in contrast to TDMA and CDMA.

This process turns out to be particularly inefficient unless it employs an OFDM / DMT

modulation, since the bands assigned to the different users overlap. Moreover, since in

FDMA the protocol data units length is no longer limited by the time slots duration, the

transmitted overhead is reduced. Recent researches have focused on OFDM and FDMA

systems, where this modulation combination with the multiple–access technique is known

as DMT-FDMA [Sartenaer et al., 2000] or orthogonal frequency division multiple–access

(OFDMA) [Sari and Karam, 1998; Sofer and Segal, 2005], which is widely considered to be

one of the most efficient techniques for providing broadband services [Barbarossa et al.,

2002; Cheong Yui et al., 1999; Koffman and Roman, 2002; Li and Sollenberger, 2001; Sari and

Karam, 1998]. A different number of subcarriers can be assigned to different users, with a

view to supporting differentiated QoS, and to controlling the data rate and error probability

individually for each user. Recently, OFDM–based networks in combination with TDMA and

FDMA have become a popular choice for such an endeavor. The IEEE 802.16 standard, for

instance, has adopted OFDM-TDMA and OFDMA (OFDM-FDMA) as two transmission

schemes at the 2–11 GHz band [Eklund et al., 2002]. Indeed, it is demonstrated by analysis

and simulation that OFDMA outperforms OFDM-TDMA in terms of several QoS metrics [Yu-

Jung et al., 2007]. In addition, a QoS framework in the MAC layer has also been integrated

into the multiple–access transmission systems in the IEEE 802.16 standard [Wongthavarawat

and Ganz, 2003]. Moreover, OFDMA has been adopted in downlink by 3rd Generation

Partnership Project (3GPP) for it next generation cellular system, called Long–Term Evolution

(LTE) [ETSI].

In TDMA, each user has a number of time slots, and they can be dynamically assigned

according to its QoS requirements. During these time slots, which last several symbols, only

one user occupies the available bandwidth. Since unused carriers in one link may experience

acceptable signal–to–noise ratio (SNR) in other links, because of their low SNR, this strategy


51

may result in a waste of capacity. To overcome this pitfall, hybrid TDMA-OFDMA schemes

have been proposed for wireless communications [Eklund et al., 2002; Flikkema, 2001].

Figure 3.5 OFDMA (DMT-FDMA) technique

On the indoor powerline side, the use of a OFDMA scheme for synchronous links

(downlink) has been studied in [Sartenaer et al., 2000; Srinivasa Prasanna et al., 2009]. In

[Srinivasa Prasanna et al., 2009], the authors investigate the requirements of a low speed

smart grid monitoring system for an indoor low voltage powerline network in the CENELEC

bands A and B using a statistical time–varying channel model. It has been developed and

used with a multiple–access scheme in the form of OFDMA with appropriate sub–band

allocations. In [Sartenaer et al., 2000], the piece of work presented proposes an OFDMA

scheme for uplink multiuser transmission over a power line network, and compared with a

CDMA system, both systems achieve a similar performance.


52

Figure 3.6 Comparison between TDMA/OFDMA and TDMA techniques (each color represents an user)

In [Ayyagari and Wai-chung, 2005; Gault et al., 2005; Hao et al., 2008; Hayasaki et al.,

2009], the authors propose a bit loading algorithm which maximizes the bit rate by

optimizing not only the bit quantity on each subcarrier but also the whole code rate subject

to constraints on the total bit error rate (BER) and transmission power on each subcarrier.

Furthermore, they investigate the OFDMA scheme as a multiple–access scheme to improve

the throughput of PLC for point–to–multipoint communications. The piece of work of

[Ayyagari and Wai-chung, 2005] investigates the capacity trade–off between TDMA-OFDM

and OFDMA in an in–home powerline network, with a clear coverage improvement over the

latter system.

In [Hayasaki et al., 2009], the author evaluates an OFDMA scheme as a multiple–access

scheme with the bit loading algorithm for point–to–multipoint communications, and

proposes a bit loading algorithm which maximizes the total bit quantity on the OFDM symbol

by optimizing the data rate subject to constraints on the BER and transmission power on

each subcarrier. As a result, the proposed OFDMA scheme is superior to the conventional

TDMA scheme in terms of throughput. The work in [Hao et al., 2008] proposes a PLC

resources allocation algorithm with an FDMA constraint for multiuser OFDMA by

reformulating the weighted–sum–rate OFDMA problem into an equivalent–interference

channel problem. How the performance of TDMA degrades rapidly when multiple QoS

connections are requested is shown. The paper from [Gault et al., 2005] describes an

OFDMA based modem for multiple–access PLC over the low voltage distribution network. It

concerns in particular the data frame structure, sub–carrier allocation to users, and the bit–

loading algorithm used for symbol coding. The proposed system is evaluated through


53

simulations carried out using a simplified noise model in both downlink and uplink

directions.

In [Ser Wah et al., 2009], the throughput performance of several multiple–access

schemes is analyzed and compared with the powerline communication Homeplug 1.0

standard. This piece of work shows a modified CSMA/CA cognitive PLC system which allows

multiple users transmission at the same time. Combining with OFDMA and a cognitive

property, it could dynamically allocate subcarriers to different users in the system for

simultaneous transmissions. The proposed channel access mechanism aims to improve the

overall channel throughput by introducing subcarrier level multiple–access with cognitive

technology capability.

The previous pieces of work on PLC works were focused on synchronous systems, but

asynchronously received signals containing ISI produce ICI. It is known that OFDMA is known

to suffer from multiple–access interference (MAI) when the multiple–access channel is

asynchronous, potentially degrading the asynchronous/uplink system performance, i.e., the

users signals are received with distinct propagation delays in excess of the CP [Kaiser and

Krzymien, 1999; Tonello et al., 2000]. On the other hand, timing synchronization

requirements are much more stringent for mitigating ISI and ICI, and it requires symbol and

frequency synchronization of all terminals is required to prevent MAI among users [Cortes et

al., 2006; Sjoberg et al., 1999; van de Beek et al., 1999].

Mitigating asynchronous effects can be done with a guard period provided inherently

in the CP [Sari et al., 1995]. The CP is able to cope with ISI from frequency–selective fading,

as well as possible timing errors from all uplink users. Unfortunately, to obtain this benefit, a

long timing duration is required, which results in some reduction in data throughput.

Another mitigation approach is a downlink synchronization scheme [Kaiser and Krzymien,

1999], where an uplink user first estimates the starting point of the downlink frame by

means of a specially designed preamble or embedded redundancy (such as a CP), and then

adjusts the uplink transmission accordingly.

The feasibility performance for OFDMA uplink systems can be obtained even in high

dispersive channels. A prerequisite for this performance can be an uplink synchronization

technique at the CCo with feedback control channel to uplink users, which guarantees that

timing misalignments reside within the guard interval [Myonghee et al., 2010].

This problem associated with asynchronous OFDMA uplink systems can be addressed

in two different ways: the first focuses on mitigation/estimation of asynchronous timing


54

errors [Kaiser and Krzymien, 1999; 2004; Sari et al., 1995; van de Beek et al., 1999], and the

second involves performance evaluation: several recent papers have studied the effect of

asynchronous timing errors [El-Tanany et al., 2001; Myonghee et al., 2003; Wei and Schlegel,

1995]. Interference canceling receivers to alleviate the detrimental effects of large frequency

and timing offsets in uplink OFDMA have been proposed [Haung and Lataief, 2005;

Raghunath and Chockalingam, 2009b].

Coming back to powerline communications, in [Cortes et al., 2006], the influence of

the carrier allocation strategy in the performance of synchronous and asynchronous DMT-

FDMA systems is evaluated for an indoor powerline system. It is shown that the bit–rate loss

due to the MAI is negligible in a symbol and frequency synchronized scheme. However, its

performance is extremely sensitive to small asynchronies. System outage may even occur for

fewer than ten samples of symbol misalignment or frequency mismatches of 40ppm.

With respect to previous comments, it is clear that OFDMA is not a valid solution for

asynchronous multiple–access environments. Traditionally, TDMA has been used for

medium access in multi–carrier systems, disregarding the frequency domain for several good

reasons [Ayyagari and Wai-chung, 2005]. The performance of OFDMA is also handicapped by

several factors. Many multi–carrier modulation schemes require guard bands between tones

assigned to multiple users transmitting simultaneously, thereby reducing system capacity.

OFDMA requires significantly higher protocol overhead because users must generate,

exchange with the OFDMA scheduler and regularly maintain “tone maps” that indicate the

Bit Loading Estimate or BLE (modulation density or bit rate for a particular subcarrier). In

[Yu-Jung et al., 2007], the ideal channel state information is assumed to be available at the

CCo or scheduler. This is often achieved by feeding the estimated channel information from

the receiver back to the transmitter through a control channel.

Moreover, OFDMA scheduling is extremely complex and computationally intensive

compared with TDMA, and requires much higher processing power and memory.

Implementation issues, complexity and cost issues do give TDMA an advantage currently in

the marketplace that may not be overcome by the capacity/coverage improvements for

OFDMA [Ayyagari and Wai-chung, 2005].


55

Figure 3.7 Comparison between OFDMA and SC-FDMA techniques

On the other hand, the reduced user signal bandwidth increases sensitivity to

multipath fading, where all carriers assigned to a user may fade simultaneously, losing the

frequency diversity advantage of OFDM modulation. Another drawback of OFDM and

OFDMA systems is the high peak–to–average–power ratio (PAPR), that requires linear

transmitter circuitry, which suffers from poor power efficiency. A greater dynamic range is

required in the AFE (analog front end) making the design complex and costs higher.

In order to alleviate the PAPR problem encountered in uplink OFDMA, single carrier

frequency division multiple–access (SC-FDMA) [Czylwik, 1997; Myung et al.; Sari et al., 1994]

has been adopted for uplink transmission in evolved universal terrestrial radio access (E-

UTRA) LTE [ETSI], where the inherent loss of frequency diversity in OFDMA can be alleviated

by using some form of precoding. SC-FDMA can be viewed as a precoded OFDMA scheme,

where the precoding is done by means of a discrete Fourier transform (DFT) matrix. This M–

point DFT precoding operation at the transmitter results in all M data symbols of a user to be

mounted on all its M subcarriers, and with independent fades on these subcarriers, and

therefore, achieving frequency diversity becomes possible. In addition to providing low PAPR

compared with OFDMA and frequency diversity, SC-FDMA allows flexible sharing of the

spectrum among different users. With the adoption of SC-FDMA in E-UTRA LTE, studies

concerning different aspects of SC-FDMA are increasingly being reported in the recent

literature [Berardinelli et al., 2008; Ciochina et al., 2008; Wang et al., 2008].


56

In [Berardinelli et al., 2008], the author proposes a iterative equalization and decoding

(turbo equalization) scheme, and showed that SC-FDMA with turbo equalizer performed

better than (or the same as) OFDMA for all modulation and coding sets considered. The

author in [Ciochina et al., 2008] presents a peak–to–average power ratio (PAPR) and BER

performance comparison between SC-FDMA, OFDMA and Walsh–Hadamard precoded

OFDMA, where the PAPR advantage of SC-FDMA in the presence of power amplifier non–

linearity has been analyzed.

Large frequency and timing offsets can cause significant MAI in both, uplink OFDMA

and SC-FDMA. In the previous wireless SC-FDMA studies, perfect frequency and timing

alignment has been assumed. However, as in uplink OFDMA [Haung and Lataief, 2005],

carrier frequency offsets and timing offsets are encountered in SC-FDMA as well.

The work by [Raghunath and Chockalingam, 2009a] investigates the effect of large

frequency and time offsets on the uncoded performance of SC-FDMA systems, and

illustrates the effectiveness of the proposed multiuser detection (MUD) multistage parallel

interference canceller (PIC) and the need for such cancellers in SC-FDMA to achieve better

performance than OFDMA, even with large carrier frequency offset (CFO) and time offset

(TO) was shown to be better than that of the ideal OFDMA performance, with perfect

knowledge of frequency/time offsets and channel coefficients.

Although the interference cancellers presented in this piece of work show a good

performance under an asynchronous environment, like OFDMA this solution is extremely

complex and computationally intensive. In [Raghunath and Chockalingam, 2009a], the

author illustrate the degradation in performance due to the self interference and multiuser

interference terms caused in SC-FDMA without MUD, where SC-FDMA performed poorly

compared with OFDMA.

On the other hand, filtered multitone modulation (FMT) is a discrete time

implementation of a multi–carrier system where sub–carriers are uniformly spaced and the

sub–channel pulses are identical. OFDM / DMT can be viewed as an FMT scheme that

deploys rectangular time domain filters [Bingham, 1990; Lee et al., 2000]. The FMT system

can support user multiplexing in a FDMA fashion through the distribution of the available

tones across the users in a similar way to OFDMA, and FMT-FDMA modulation has been

originally proposed for transmission over broadband frequency selective channels both in

VDSL [Cherubini et al., 2002], and more recently in wireless [Costa et al., 2003; Tonello,

2002; Tonello, 2006a] and powerline communication [Tonello and Pecile, 2007; 2009]

scenarios. This multiple–access technique has several advantages over previous systems.


57

Robustness to frequency selective channels and to users asynchronism, sub–channel

spectral containment that makes it robust to narrow band interference, and the possibility

of shaping the spectrum by rendering undesired sub–channels null [Tonello and Pecile,

2009]. In this scenario, FMT has superior performance over OFDMA because of the sub–

channel spectral containment that allows sub–channel orthogonality in the presence of

asynchronous users as well to be mantained [Tonello, 2002; Tonello, 2006a]. FMT achieves a

high level of spectral containment with the result that the ICI is negligible compared with the

other noise signals in the system and the subcarriers can be considered close to orthogonal,

whatever the length of the multipath channel. In this way, FMT does not need the use of the

CP used in OFDM/DMT to maintain subcarrier orthogonality in the presence of multipath,

thereby, improving the total throughput. However, per sub–channel equalization is needed

in order to reduce the remaining ISI [Cherubini et al., 2002].

However, the implementation of FMT can be more complex than OFDMA because

sub–channel filtering is required. An efficient polyphase implementation of the synthesis and

analysis filter bank for single user FMT has been proposed in [Cherubini et al., 2002], and it is

based on FFT and low rate filtering. Its complexity has been evaluated in [Tonello, 2006b].

The main research problems related to FMT are the efficient digital implementation, the

design of the prototype pulse, the development of equalization schemes, the

synchronization problem, and in general the performance analysis and comparison with

other schemes.

3.3 CDMA

To cope with the impairments of powerline hostile channel, PLC systems may apply

robust and efficient modulation techniques such as spread–spectrum (SS) schemes [Biglieri,

2003]. Spread–spectrum techniques are methods by which a signal generated in a particular

bandwidth is deliberately spread in the frequency domain, resulting in a signal with a wider

bandwidth. These techniques are used for a variety of reasons, including the establishment

of secure communications, increasing resistance to natural interference and jamming.

Frequency–hopping spread spectrum (FHSS), direct–sequence spread spectrum (DSSS),

time–hopping spread spectrum (THSS) and combinations of these techniques are forms of

spread spectrum modulations. Each of these techniques employs orthogonal or

pseudorandom number sequences to determine and control the spreading pattern of the

signal across the allocated bandwidth.


58

CDMA is a spread spectrum multiple–access technique that uses neither frequency

channels nor time slots [Fazel and Kaiser, 2003]. One of the basic concepts in data

communication is the idea of allowing several transmitters to send information

simultaneously over a single communication channel. This allows several users to share a

bandwidth of different frequencies. This concept is called multiplexing. CDMA employs SS

technology and a special coding scheme (where each transmitter is assigned a code) to allow

multiple users to be multiplexed over the same physical channel. By contrast, TDMA divides

access by time, while FDMA divides it by frequency. CDMA is a form of spread–spectrum

signaling, since the modulated coded signal has a much higher data bandwidth than the data

being communicated. With CDMA, the narrow band signal is spread by a large bandwidth

signal that is a code. All users in a CDMA system use the same frequency band and transmit

simultaneously. The transmitted signal is recovered by correlating the received signal with

the orthogonal code used by the transmitter.

Figure 3.8 CDMA technique

Following the previous classification done in spread spectrum technology modulations

of FHSS, DSSS, and THSS, these technologies can be combined with CDMA multi–access

technique. FHSS is a method of transmitting signals by rapidly switching a carrier among

many frequency channels, using a pseudorandom sequence known to both transmitter and

receiver. It is utilized as a multiple–access method in the frequency–hopping code division

multiple–access (FH-CDMA) scheme. In DSSS the data signal is multiplied by a large

bandwidth signal that is a orthogonal or pseudo random noise code. Its basic principle is that

each user is allocated by a code and can communicate at any time on any frequency, where

other users interference is considered as additional channel noise. The transmitted signal is

recovered by correlating the received signal with the sequence code used by the transmitter.

This method is known as direct sequence code division multiple–access (DS-CDMA) [Verdú,


59

1998]. In THSS an orthogonal or pseudo noise sequence defines the transmission moment.

For multiple–access, time hopping code division multiple–access (TH-CDMA) uses the whole

wideband spectrum for short periods instead of parts of the spectrum all of the time.

DS-CDMA has been used widely in wireless communications and it has also been

selected by a number of standardization bodies, for instance, in third generation mobile

cellular systems like IS–95 [TIA/EIA, May 1995], 3GPP2 IS–2000 (CDMA2000) [ETSI, 2002a]

and 3GPP wideband CDMA (W-CDMA) [ETSI, 2002b] standards. It has also been used for

satellite navigation systems such as global positioning system (GPS) and the future European

Galileo.

Many multiple–access spread spectrum techniques have been proposed in the

literature for powerline communications, which include an analog spread spectrum chaotic

modulation system [Surendran and Leung, 2005]. The first synchronous DS-CDMA attempts

began in the lower frequencies (bands A and B) of the powerline channel [Okazaki and

Kawashima, 1998; van der Gracht and Donaldson, 1985]. In higher frequency bands of the

channel (1–40MHz), constrained minimum output energy (CMOE) receiver [Zsoldos et al.,

2001], maximum ratio combining (MRC) RAKE receiver [Del Re et al., 2003; Hensen and

Schulz, 1997], suboptimum minimum mean square error (MMSE) single user detection (SUD)

receiver [Hachem et al., 2001], interference cancellation detector [Tonello et al., 2004], and

multiuser detection techniques [Dai and Poor, 2003; Sartenaer et al., 2000; Tonello, 2006c]

have been used. In [Dai and Poor, 2003; Hachem et al., 2001; Sartenaer et al., 2000], users

can access the media synchronously using orthogonal binary short spreading codes, which

are optimal when all the users are synchronized. In an asynchronous environment, this is not

possible due to poor cross–correlation properties of these codes. Ignoring short–time

channel variations, powerline frequency response between two outlets may remain static

for a time changes [Canete et al., 2003; Canete et al., 2002]. So it should be pointed out that

successive symbols from the same user are spread with the same code; so for a set of users

within a relatively static channel situation, the interference signal seen by a receiver does

not change from symbol to symbol. Therefore, some users are at a disadvantage with

respect to other users [Milstein, 2001]. In pseudo–random long sequences, the interference

changes from symbol to symbol, providing higher MAI rejection and reducing its

cyclostationary statistics from symbol period to chip period. Short sequences have good

correlation properties under the assumption that the users are perfectly synchronized,

which is incorrect in this case. Therefore periodic long sequences are desirable. Some

comparisons between short and long sequences can be found in [Parkvall, 2000; Vembu and

Viterbi, 1996]. One of the most popular pseudo–random long binary sequence used in


60

wireless DS-CDMA are the Gold codes [Gold, 1967], which are used in [Zsoldos et al., 2001]

for a synchronous system. Binary pseudo–random sequences are used in [Del Re et al., 2003;

Tonello, 2006c]. Besides the binary codes, there are also other families of pseudo–random

complex–valued polyphase codes widely used in Radar systems: their correlation properties

have been shown to be better than those of classical binary sequences [Luke, 1997;

Oppermann and Vucetic, 1997; Park et al., 2002], and therefore better MAI, IQ cross–talk

and powerline narrowband noise suppression.

On the other hand, asynchronous TH-CDMA and DS-CDMA schemes based on ultra

wide band (UWB) pulses are analyzed in [Tonello et al., 2004] using orthogonal short

spreading codes, where the UWB pulses are followed by a guard time to cope with the

channel time dispersion, and consequently making the equalization easier. In [Tonello,

2006c], the author analyzes an iterative MUD frequency domain equalizer for the same

system.

Various combinations of multi–carrier and spread spectrum schemes (MC-SS), like

multi–carrier CDMA (MC-CDMA) have been introduced since 1993 [Hara and Prasad, 1997;

Yee et al., 1993]. MC-SS schemes have shown very good performances in the case of

multiuser communications in difficult environments and have been proposed for beyond 3rd

generation (3G) mobile cellular systems [Hélard et al., 2001; Kaiser, 2002]. These hybrid

techniques have also been investigated in studies in DSL context [Mallier et al., 2002], and

also represent as well potential solutions for powerline communications [Tlili et al., 2003].

MC-CDMA has been widely researched in powerline communications and takes

advantage of OFDM, which has shown very good performance in wireless and powerline

communications [Pavlidou et al., 2003]. Synchronous MC-CDMA systems are evaluated in

[Assimakopoulos and Pavlidou, 2002; Crussiere et al., 2004; Huang et al., 2008; Katsis et al.,

2003; Sartenaer et al., 2000] using short spreading codes in a powerline channel without

impulsive noise. Analytical approaches for synchronous MC-CDMA systems have been

proposed in [Huang et al., 2008] and [Navidpour et al., 2006]. However, a zero–mean

Gaussian model is used for impulsive noise in [Navidpour et al., 2006], and [Assimakopoulos

and Pavlidou, 2002] models impulsive noise with a Middleton’s class A filter. In [Zsoldos et

al., 2001], long Gold sequences have been used instead of short codes for synchronous

system without impulsive noise model. The performance of asynchronous MC-CDMA

scheme has been analyzed widely for wireless communication systems [Kyunbyoung et al.,

2006; Kyunbyoung et al., 2002; Won Mee and Moon Woo, 2006; Zhang and Guan, 2004],

where the channel conditions are different from the powerline channel. Only in [Hoque et

al., 2007], an asynchronous MC-CDMA system for powerline is proposed but without CP,


61

which is used to improve the OFDM system performance avoiding ISI and ICI caused by the

multipath effect. In [Ma et al., 2005], the background plus impulsive noise is modeled as

zero–mean Gaussian noise for the performance analysis under impulsive noise of a OFDM

system with CP, whereas the additive white Gaussian noise (AWGN) was considered as

background noise.

On the other hand, multi–carrier direct sequence code division multiple–access (MC-

DS-CDMA) system results in multi–carrier modulation applied to CDMA signal. The MC-DS-

CDMA transmitter modulates the data sub–streams on subcarriers with a carrier spacing

proportional to the inverse of the chip rate to guarantee the orthogonality between

spectrums of the sub–streams after spreading [Kondo and Milstein, 1993]. In [Crussiere et

al., 2006b], the author proposes an adaptive MC-DS-CDMA system suitable for synchronous

powerline networks. This work analyzes the performance of the system and compares the

results to those obtained with the DMT system, where it can be highlighted that for well–

chosen spreading factors, the proposed adaptive system was able to transmit higher rates

than DMT.

However, there is also the possibility of combine SS and FDMA techniques. Spread–

spectrum multi–carrier multiple–access (SS-MC-MA) [Kaiser and Krzymien, 1999] is a multi–

carrier modulation that combines SS and FDMA, which can be classified as particular linearly

precoded DMT method. The FDMA component is based on the transmission of several

subsets of subcarriers in parallel, each subset being exclusively assigned to a specific user.

The SS component allows each user to multiplex several symbols within the same subset by

spreading them in the frequency domain. For the synchronous uplink, SS-MC-MA has been

proposed to appropriately exploit the advantages of MC-CDMA evident on the downlink.

The work by [Crussiere et al., 2006a] proposes that an adaptive bit–loading algorithm

be applied to the SS-MC-MA synchronous scheme, where for well–chosen spreading factors,

it can be concluded that the proposed adaptive system was able to transmit higher rates

than DMT. In [Jingtao and Matolak, 2008], the author compares the performance of an

OFDMA, SS-MC-MA and MC-CDMA systems for a wireless synchronous uplink scenario,

showing a similar performance of these schemes under the same channel conditions.


62

3.4 ScDMA

The work by [Haumonte and Deneire, 2007] presents a method to multiplex digital

streams over powerline networks called scattering division multiple–access (ScDMA). The

principle relies on using reflections as a way to discriminate the information sent by several

transmitters. A unique feature is that the transmitter does not actually send any physical

signal, but translates the digital information to be sent directly into an impedance value. The

receiver reads the information displayed by all the transmitters by analyzing the network

scattering parameters.

This method has many advantages over TDMA methods traditionally used in cable

network multiplexing systems. Its continuous and simultaneous demodulation ability

generates very advantageous end–to–end message delays as well as a low system

complexity leading to increased robustness.

One of the key advantages of ScDMA is the fact that all transmitters send their own

data streams simultaneously and continuously. The bus is available 100% of the time for all

the transmitters at the same time. That is why the bus access is instantaneous and there is

absolutely no message request latency. Compared with existing protocols, there is no need

to define message priorities since all messages go through at the same time. Therefore there

is no message collision and no contention arbitration is needed.

This method is oriented towards low data rate transfers, such as industrial control, and

it is not scalable like other multiple–access techniques in order to satisfy quality of service

requisites.

3.5 SUMMARY AND CONTRIBUTIONS

As a summary, the following section will discuss the different advantages and

disadvantages of multiple–access schemes reviewed above for an asynchronous scenario

approach.

TDMA systems must carefully synchronize the transmission times of all the users to

ensure that they are received in the correct timeslot and do not cause interference. Since

this cannot be perfectly controlled in a multipath environment, each timeslot must have a


63

guard–time, which reduces the probability that users will interfere, but decreases the

spectral efficiency.

FDMA schemes spread user's data in the frequency dimension, so that in a multipath

channel the frequency diversity may be lost. Similar to TDMA, FDMA systems must use a

guard–band between adjacent channels, due to the frequency offsets of the signal

spectrum. The guard–bands will reduce the probability that adjacent channels will interfere,

but decrease the utilization of the spectrum.

On the other hand, most of the multi–carrier based multiple–access schemes

(Wavelet-OFDM/TDMA, FFT-OFDM/TDMA, DMT-FDMA and OFDMA) have been developed

for the synchronous downlink, due to time misalignments and frequency offset sensibility. It

is known that OFDM/DMT based schemes suffer from MAI when the multiple–access

channel is asynchronous, potentially degrading the asynchronous uplink system

performance.

Another drawback of OFDM systems is the high PAPR, requiring linear transmitter

circuitry, which suffers from poor power efficiency. SC-FDMA solves this problem, but it still

suffers from time and frequency offsets, requiring complex MUD techniques at the receiver.

Figure 3.9 Multiple–access schemes

Spread spectrum schemes take advantage of the frequency diversity in multipath

fading channels. It has been shown that MC-CDMA is a promising multiple–access scheme

for the synchronous downlink of a PLC system where it enables the deployment of efficient,

low complexity receivers employing simple channel estimation. However, this aspect does

not apply to the uplink and asynchronous environments, where more complex multiuser


64

detection techniques are necessary to counteract the MAI, since in the uplink orthogonal

spreading codes cannot be used to reduce the MAI.

On a synchronous uplink SS-MC-MA is an interesting alternative to other multi–carrier

multiple–access schemes such as OFDMA, OFDM/TDMA and MC-CDMA, as discussed in

[Kaiser, 1998]. MC-DS-CDMA is of special interest for the asynchronous uplink of mobile

radio systems, due to its close relation to asynchronous single–carrier DS-CDMA systems. On

the one hand, the synchronization of users can be avoided, but, on the other hand, the

spectral efficiency of the system decreases due to asynchronism, losing the frequency

diversity advantage. [Fazel and Kaiser, 2003].

Bit loading techniques applied to QoS requirements have been discussed. However, it

should be noted that there also exist periodic variations of the input impedances of the

loads connected to the powerline network that translate into short–time variations of the

transfer function. This behavior must in fact be incorporated in the CSI which needs to be

refreshed periodically. Some studies have advantageously applied loading principles to

spread spectrum systems [Holtzman, 2000; Terré et al., 2003], but among the existing

adaptive schemes, DMT used for DSL communications is the most popular. These techniques

require a centralized manager or CCo assuming CSI at the transmitter, which adds more

complexity to the system. Current PLC devices compliant with Smart Grid requirements

(HomePlug Green PHY and G.hn Smart Grid profile) are based on multi–carrier modulations

and TDMA schemes, which is not valid for asynchronous transmission links.

Recently proposed multiple–access schemes have been based on multi–carrier

modulations, which have demonstrated a very good performance and efficiency in

synchronous environments. But TDMA and FDMA have the drawback of being extremely

sensitive to timing/frequency asynchronism, where the behavior of some spread spectrum

multiple–access techniques could be better in an asynchronous environment. Since THSS

and FHSS are directly related to time and frequency synchronization, DSSS multiple–access

(DS-CDMA) is a logical choice taking into account its proven robustness against hostile

channels. CDMA has several advantages and disadvantages over multi–carrier methods in

hostile and asynchronous environments:

• DS-CDMA can effectively reject narrowband interference, which can be found

in powerline networks in the form of RF couplings in the wirelines. Since

narrowband interference affects only a small portion of the spread spectrum

signal, it can be ignored or easily removed through notch filtering without

much loss of information.


65

• Most modulation schemes try to minimize the signal bandwidth, since

bandwidth is a limited resource in powerline networks. However, spread

spectrum techniques use a transmission bandwidth that is several orders of

magnitude greater than the minimum required signal bandwidth. One of the

initial reasons for doing this was military applications, in order to achieve

security and resistance to jamming.

• DS-CDMA signals are resistant to multipath fading. Since the spread spectrum

signal occupies a large bandwidth only a small portion of this will undergo

fading due to multipath at any given time, through advantage of the frequency

diversity.

• Synchronous TDMA, FDMA and CDMA receivers can in theory completely reject

arbitrarily strong signals using time slots, frequency sub–channels and different

codes due to the orthogonality of these systems. However, time–frequency

misalignments produce severe MAI in these multiple–access methods, where

the asynchronous CDMA system may reject the interference in a better way.

Pseudo–random sequences are used in asynchronous CDMA systems, which

are statistically uncorrelated. That is why a lower correlation of these

sequences implies a lower MAI in the receiver. The signals of other users will

appear as noise to the signal of interest and interfere slightly with the desired

signal in proportion to the number of users. These low correlation sequences

could be polyphase sequences applied to an asynchronous CDMA system.

• The number of simultaneous user is limited by the bit error rate target, since

the signal to interference ratio varies inversely with the number of users.

• The near–far problem is a condition in which a strong signal captures a receiver

and makes it impossible for the receiver to detect a weaker signal. The near–far

problem is particularly difficult in DS-CDMA systems where transmitters share

transmission frequencies and transmission time.

• Since the transmitted signal propagates through a multipath fading channel, it

must be equalized at the receiver. While this is a relatively simple task for

multi–carrier signals, it is not the case for single–carrier signals.

Asynchronous CDMA has been widely researched for wireless Rayleigh fading channels

and additive white Gaussian noise [Mantravadi and Veeravalli, 2002; Mirbagheri and Yoon,

2002; Rapajic and Vucetic, 1994; Tomoya Urushihara, 2005; Wong et al., 1999]. However,


66

there is a lack of work on asynchronous CDMA powerline communications [Tonello et al.,

2004; Tonello, 2006c], and most of the pieces of research conducted on CDMA for powerline

communications are based on orthogonal short binary sequences [Dai and Poor, 2003;

Hachem et al., 2001; Hensen and Schulz, 1997; Okazaki and Kawashima, 1998; Sartenaer et

al., 2000; Tonello et al., 2004]. Moreover, the proposed channel noise models are usually

incomplete or simplified, where the impulsive noise is modeled the Gaussian model [Dai and

Poor, 2003; Tonello et al., 2004; Tonello, 2006c] and the remaining pieces of work simply

ignore the impulsive noise. The narrowband noise is also avoided, and the background noise

is sometimes modeled as AWGN noise [Dai and Poor, 2003; Hachem et al., 2001; Tonello,

2006c]. It must be kept in mind that the powerline noise is an important characteristic of the

network, thus it should not be disregarded.

The work presented here investigates the use of long periodic polyphase sequences in

an asynchronous DS-CDMA system under a powerline channel model with background,

narrowband and impulsive noise, analyzing its effects over CDMA signals. An MMSE receiver

is selected due to its advantage of ease of adaptation, since standard adaptive algorithms

can be employed. In order to compare the performance of such a system, the performance

of an asynchronous multi–carrier scheme is also analyzed. The selection criterion was a

similar system based on a multi–carrier modulation, which is MC-CDMA. Moreover, if the

MC-CDMA receiver does not use MUD techniques, it has been shown that its performance is

similar to OFDMA technique. As stated in previous chapters, one of the requisites of the

target system is that complex structures should be avoided in order to meet Smart Grid

requisites (Table 2.4), and asynchronous systems have been selected in order to a remove

the central coordinator.

SS

CMOEMUD[166]

ASYNCFD MUD UWB

[139]

ASYNCIC UWB

[135]

PIC MUD[34, 124]

TH-CDMAUWB[135]

MMSESUD[54]

RAKE[36, 62]

CHAOTICSS

[128]

LOWER BAND

[105, 150]

DS-CDMA

Figure 3.10 Spread spectrum receivers for PLC


67

Linking with the work description done above and remembering previously remarked

objectives of this thesis:

1. Powerline impulsive noise measurements in order to complete a powerline

channel model and analyze the noise effect over a transmitted signal, obtaining

a closed–form probability error function.

2. Theoretical and simulation study of asynchronous multiple–access systems with

single–carrier and multi–carrier modulations.

3. Compare the performance of different families of spreading sequences with

several receivers’ structures and multiple–access systems in asynchronous

environments under powerline impulsive noise.

This thesis proposes another approach for Smart Grid devices based on single–carrier

modulations with asynchronous user accesses in order to reduce complexity of the overall

system. These PLC modems should have specific characteristics in order to meet the

requirements of HAN communication devices. That is, complexity, cost and power

consumption must be as low as possible.

Chapter 4. Measurement Campaign and Channel Modeling 69

4 Measurement Campaign and Channel Modeling

Chapter 4

Measurement Campaign and Channel Modeling

Nowadays the use of high speed transmission networks is widespread inside home

environments, for audio and video diffusion as well as for data sharing. The powerline

network is an ideal media because all houses are already wired without the need to install

another medium (e.g. Ethernet cable or fiber optic) or depending on the coverage of actual

Wireless LAN modems. Even approximately 30 years ago the powerline network was used

for low speed data transmission (X-10), but these new applications require higher data rates.

To understand the challenges of powerline communication, and to design robust data



characteristics of the channel noise. These characteristics can be quite diverse among

different buildings, homes and industrial plants because of different wiring structures,

different wire types, and different appliances connected to the electric circuit. It is necessary

to understand the electrical characteristics of the network in order to adapt the transmission

system and parameters to the channel properties, since the network was not designed for

data transmission, just for power transmission.

Chapter 4. Measurement Campaign and Channel Modeling

70

In this chapter, a complete channel model that takes into account the noise generated

in the network as well as the frequency attenuation profile of the unmatched network is

proposed. The model is based on a channel measurement campaign results and proposals

from other pieces of work. For performance characterization of powerline modems, it would

be useful to have a test channel for system simulations.

4.1 CHANNEL MEASUREMENTS

Several measurements have been done in different home environments, and these

measurements were divided in two large groups. On the one hand, the channel frequency

response was measured, and on the other hand the channel noise. The data obtained after

the measurement campaign is analyzed in order to obtain a mathematical / statistical

powerline channel model.


In order to measure the frequency response of the powerline channel, a network

analyzer is used. There is interest in the band above 1 MHz, so the measurement set–up

includes a band–pass filter of 700 kHz to 32 MHz and a signal coupler (Figure 4.2) to the

powerline network for each network analyzer port. The Figure 4.1 shows the measurement

set–up composed by the network analyzer (Agilent E5070A), signal coupler and pass–band

filter for each port.

Figure 4.1 Frequency response measurements set–up

The frequency response (gain and phase) of the channel is obtained measuring the S21

parameter of the network analyzer over the whole frequency range [Rappaport, 1996]. The

band–pass filter rejects the low frequencies of the network. In order to reduce the noise


71

effect during the channel measurement, the average of the last 16 measured frequency

responses is taken.

Figure 4.2 Powerline coupling circuit

The fifth order filters from the Figure 4.3 and Figure 4.4 are tuned for a pass band of

700 kHz to 32 MHz, as the band of interests falls in the range of 1MHz to 30MHz. Figure 4.5

shows the frequency response of the band–pass passive filter for the signal reception and

transmission circuits.

Figure 4.3 Transmission pass–band filter


72

Figure 4.4 Reception pass–band filter

The channel measurements have been carried out over power lines several tens of

meters. Figure 4.6 and Figure 4.7 show a frequency response measurement done between

two power outlets in a typical home environment. To remove the effect of the noise in these

measurements, the acquired data is smoothed with the mean operation along the time.

Therefore, the short–term variations are not measured.

Figure 4.5 Pass–band filter frequency response


73

Figure 4.6 Measured channel frequency response (Gain)

Figure 4.7 Measured channel frequency response (Phase)

The channel frequency response corresponds to a low–pass filter, strong phase

nonlinearities are appreciable due to the signal multipath [Zimmermann and Dostert,

2002b]. The effect introduced by the 700 kHz cut–off pass–band filters at the signal couplers

renders the response under the 1 MHz band to be unreliable. This is due to the excessive

attenuation created by the filters in this band, and the network analyzer is incapable of

compensating it correctly. In any case, the band of interest is in the 1-30MHz region. A first

look at the amplitude frequency response of the channel suggests the use of OFDM

modulation as a transmission technique together with bit designation and power bit–loading

algorithms for each sub–channel, in order to combat selective fading.


74

Figure 4.8 shows, two powerline channels superposed; these two channels are

measured between the same outlets, but the network state was different in both cases (for

example, a vacuum cleaner switched on), where the response in some frequencies is

changed. Slight changes are observed in the amplitude response, the most severe of these

being in the 20-25 MHz band.

Figure 4.8 Comparative channel responses in accordance with loads

During the frequency response measurement process of the channel frequency

response, it is possible to observe that it remains stable for a couple of minutes or hours,

and changes when the electrical devices are plugged in and unplugged.

Figure 4.9 Frequency response expansion


75

By performing the inverse discrete Fourier transform (IDFT), an approximation of the

channel impulse response is obtained. This is only an approximation because the network

analyzer only provides information on the frequency domain above 300 kHz, to which it

would be necessary to add the effects of filters up to 1 MHz. In order to resolve the problem,

it is necessary to replace with null frequency components under 1 MHz. The impulse

response obtained does not contain information on the DC - 1MHz band, but it does contain

information on the rest of the band.

Figure 4.10 Channel impulsive response

The result of the IDFT over the frequency response is shown in Figure 4.10, where time

dispersion of the channel is less than 1 microsecond. The impulsive response obtained does

not contain information on the DC-1 MHz, but does contain information on the rest of the

band.

All the simulations are made in the time domain, so it is necessary to make a

transformation in the channel response from the frequency to the time domain, in order to

obtain the impulse response of the channel. The result obtained in the time domain can be

compared with an N–order finite impulse response (FIR) filter, which is convoluted with the

transmitted signal over the powerline media.


76

4.1.2 Channel Noise

The noise is measured with a digital oscilloscope band limited to 20 MHz and attached

to the signal coupler with a 200 kHz cut–off frequency high–pass filter (see Figure 4.11),

where its frequency response is shown in Figure 4.12. The input impedance of the coupler

should be much higher than the impedance seen in the powerline network, which is

unknown, in order not to disturb the network and obtain a reliable measurement. So, the

magnitude measurements done by an oscilloscope or spectrum analyzer should be different

due to their different input impedance (i.e. 1 MΩ and 50Ω respectively). The noise

parameters of interest are the followings.

Figure 4.11 Noise measurement set–up

The impulse noise analysis was performed by setting the oscilloscope to a sampling

rate of 15 million samples per second, while in order to analyze the distance between pulses,

the oscilloscope was set in peak detector mode, with a sampling interval of 14 microseconds,

thus obtaining, in this way, a 40-second window.

Figure 4.12 High–pass filter response


77

4.1.2.1 Background noise

This kind of noise is caused mainly by the composition of several low–power noise

sources [Zimmermann and Dostert, 2002a]. Its PSD is relatively low and varies with

frequency and time. In the absence of impulse noise, background noise samples were

captured with the oscilloscope. The capture time should be as long as possible, taking the

maximum oscilloscope memory into consideration. It must be taken into account that the

capture is done in time domain, in order to get a spectral analysis in the frequency domain.

During the background noise measurement, the noise samples are captured in absence

of impulse noise in a window of 40 milliseconds. The spectral estimation has been made

using the Welch method with a spectral resolution of 48 KHz. In order to represent the

power spectrum density in dBW/Hz, the impedance of the powerline network is needed, due

to the fact that the acquired samples are in Volts. However this parameter is unknown, so a

first approximation could be to assume a network impedance of 1Ω.

Figure 4.13 Background noise PSD

Figure 4.13 shows how the power of the noise decreases exponentially with the

frequency. The narrow band noise sources between the 5 MHz and 11 MHz bands observed

in the Figure 4.13 are RF waves of short–wave radio emissions. Background noise remains

stationary over a long period of time, even for hours. This may vary during the day

depending on the atmospheric characteristics that allow a more propitious propagation of

RF waves. It is clear that the noise produced in the power line network cannot be described

with a additive white Gaussian noise model.


78


Impulse noise has its source in switching components and devices like silicon

controlled rectifiers (SCR), linear and switching power supplies, and so on. Some of these

pulses are synchronous with the period of the electrical network, and others with the

switching period of the device. A simplified way to characterize the impulse noise is based

on the following parameters [Zimmermann and Dostert, 2002a]: kind of pulse, amplitude,

length and time interval between the pulse events. The first three parameters are captured

as in the background noise case.

In order to analyze the properties of impulsive noise, samples were taken during

several hours in different houses; after that they were processed and analyzed. Again, two

pulses with a distance of under one millisecond are regarded as belonging to a pulse–burst

event.

Figure 4.14 Measured impulsive noise

The time interval between the pulse events parameter is measured with a peak–

detector mode of the oscilloscope, in order to extend as far as possible the time–line horizon

of the measure as far as possible. The oscilloscope is given a time window of 40 seconds with

a peak detection resolution of 40 microseconds. Two pulses with a distance of less than one

millisecond are always regarded as belonging to a pulse–burst event. The probability of time

interval between pulse events decreases exponentially with time. Figure 4.15 shows a

histogram of the time intervals of captured pulses.


79

Figure 4.15 Time between pulses PDF (20s)

To obtain more detail, a zoom of the first 200 milliseconds is done and shown in Figure

4.16. The pulse events occur in a separation of time equal to the multiples of the power line

network working period (20 milliseconds in Europe), and therefore the most probable time

separation between pulses is the network period. The histogram does not show time

distances of under one millisecond because, as commented previously, it is assumed that

these pulses belong to a pulse–burst event. These data shows that there are numerous

devices in the home synchronized with the network, such as linear power supplies.

Figure 4.16 Time between pulses PDF (200ms)


80

Two different types of pulse are classified, percentage–wise, as follows:

• Single pulse noise: 48.22%

• Burst pulse noise: 51.88%

Figure 4.17 shows a measured single pulse with a specific structure mainly composed

of a oscillation attenuated in the time. On the other hand, the PSD of the previous pulse is

shown in Figure 4.18. This spectrum is a composition of background and impulsive noise,

where the pulse energy predominates in the lower frequencies.

Figure 4.17 Measured single pulse noise

Figure 4.18 Measured single pulse noise PSD


81

Figure 4.19 shows two samples of measured burst pulses. These kind of pulses are

composed of several single pulses concatenated in the time domain.

Figure 4.19 Measured pulse–burst noise

The power spectral density of the first pulse (Figure 4.19) is shown in the Figure 4.20. It

is clear that its spectrum is quite similar to the PSD that can be found in the single pulse

sample, since it is a composition of single pulses.


82

Figure 4.20 Measured single pulse noise PSD

The power and energy of a pulse is defined as follow

2

1

1 N

i

i

P xN =

= ∑ (4.1)

2

1

N

i

i

E x=

= ∑ (4.2)

where ix is the sample captured by the oscilloscope and N is number of samples.

Table 4.1 compares the power and energy of pulses shown in Figure 4.17 and Figure 4.19

with background noise. The damaging nature of this kind of noise over the signal transmitted

in the power line network should be noticed.

Length Amplitude Power Energy

Burst pulse A 65 us 0.04V -25.65dBV2 0.38dBV2

Burst pulse B 680 us 0.05V -37.34dBV2 8.57dBV2

Single pulse 4 us 0.2V -41.58dBV2 -5.56dBV2

Background noise Power: -53.04dBV2

Table 4.1 Pulse power and energy


83

From the classification done of pulse kind probability, it can be concluded that half of

the pulse events are highly destructive for the transmitted signal.

On the other hand, the amplitude of the measured impulsive noise is analyzed, and it

shown how it follows a statistical distribution which is a combination of a Rayleigh (β=0.11)

and uniform distribution, where the threshold that switches between statistical functions is

at 0.4V approximately. Figure 4.21 shows the histogram of captured amplitudes and is

compared with the probability density function (PDF) of a Rayleigh statistical distribution.

Figure 4.21 Pulse amplitude PDF

Figure 4.22 compares again the measured cumulative distribution function (CDF) with

the proposed Rayleigh statistical distribution, where both curves are very similar.


84

Figure 4.22 Pulse amplitude CDF

The same tendency can be noticed in the case of the pulse duration for a combination

of a Rayleigh (β=0.076) and uniform distribution, where the threshold that switches between

statistical functions is at approximately 250 microseconds. Figure 4.23 and Figure 4.24

compare the measured burst pulse duration PDF and CDF, respectively.

Figure 4.23 Burst pulse duration PDF


85

Figure 4.24 Burst pulse duration CDF

4.2 CHANNEL MODELING

In order to design a powerline system it is necessary to understand and characterize

the powerline network behavior through mathematical models for design and simulation.

This will allow the transmitter / receiver scheme to be validated, thus optimizing the use of

the powerline network.

Once the frequency response, the background and impulsive noise of the power line

network have been measured, and its behavior is analyzed. A powerline channel model is

proposed in this work; it is based on the measurement results presented here and on those

of other pieces of work, in order to obtain a mathematical model that is as complete as

possible, and which includes impulse response and noise model.

However, the powerline frequency response is varying over the time [Canete et al.,

2006], but the model used in this work will assume that it remains static for the entire

simulation, avoiding the long–term and short–term variations.



86

Due to the impedance mismatch between the load and the cable impedances, the

transmitted signal suffers from reflections, which are propagated through pN paths along

the powerline network. The frequency transfer function of the powerline multipath channel

[Zimmermann and Dostert, 2002b] can be written as

0 12 /( )

1

( )p

ki pi

Nj fd va a f d

i

i

G f g e eπ−− +

=

= ⋅ ⋅∑ (4.3)

where f is the frequency, ig and id are the gain parameter and the distance of each

ith path, which are calculated for a randomly built impedance network shown in Figure 2.1,

defined by cable lengths and outlet/cable impedances. k , 0a and 1a are the cable loss

parameters.

Figure 4.25 Unmatched transmission line

Reflection coefficient ρ and transmission coefficient σ are calculated from (4.4) and

(4.5), respectively.


87

a bb a

a b

Z Z

Z Zρ →

−=

+ (6) (4.4)

21 a

b a b a

a b

Z

Z Zσ ρ→ →= + =

+ (7) (4.5)

Figure 4.25 shows a simple example of multipath signal propagation which can be

easily analyzed. From the point of view of the transmitter with characteristic impedance 1T ,

the link has two branches at the intersection node 1N , one for the receiver ( 3T ) and other

for a device ( 2T ) connected to the network. Each cable segment has its own characteristic

impedance iZ and cable length il . In other words, the network studied here is a perfect

example of unmatched power line network. So, there are reflections in all 1P , 2P , 3P and 1N

junctions. With these assumptions, an infinite number of propagation paths is possible in

principle, due to multiple reflections. Each path has a weighting factor ig , representing the

product of the reflection and transmission factors along the path. All reflection and

transmission factors at power lines are basically less or equal to one. This is due to the fact

that transmission occurs only at junctions, where the load of a parallel connection of two or

more cables leads to a resulting impedance being lower than the characteristic impedance of

the feeding cable.

The path gain ig , shown in (4.3), is the product of iR reflection coefficients ρ and iT

transmission coefficients σ calculated for each ith path

∏∏==

⋅=ii T

l

li

R

l

liig1

,

1

, σρ (4.6)

The reflection coefficient 11,Nρ for a signal propagating from 1Z to the junction 1N in

the impedance network of Figure 4.25 can be written as

1

2 3 2 3 11,

2 3 2 3 1

( )

( )N

Z Z Z Z Z

Z Z Z Z Zρ

+ −=

+ + (4.7)

and the remaining reflection coefficients


88

1

1 3 1 3 22,

1 3 1 3 2

( )

( )N

Z Z Z Z Z

Z Z Z Z Zρ

+ −=

+ + (4.8)

1

1 2 1 2 33,

1 2 1 2 3

( )

( )N

Z Z Z Z Z

Z Z Z Z Zρ

+ −=

+ + (4.9)

3

3 33,

3 3

P

T Z

T Zρ

−=

+ (4.10)

2

2 22,

2 2

P

T Z

T Zρ

−=

+ (4.11)

The corresponding transmission coefficients are obtained by means of (4.5). Signal

transmission from 1T to 3T (see Figure 4.25) has several paths due to reflections, and that is

why one of these paths is described as example. According to (4.6), the gain factor of each

path is equal to the product of all the coefficients (reflection and transmission) that

comprise it. The path transitions are as follows:

Path X: 1P → 1N → 2P → 1N → 3P

Its respective path gain xg is given by

1 2 1 31, 2, 2, 3,x N P N Pg σ ρ σ σ= ⋅ ⋅ ⋅ (4.12)

and the total distance xd is computed as

1 2 2 3xd l l l l= + + + (4.13)

All the possible paths are computed in order to get the transfer function ( )G f of the

channel. A PC software is developed for this task, but the search must be limited because

there are an infinite number of paths. The path gain decrease while the number of

coefficients increase. Therefore, the first paths are more powerful, and for this reason the

weakest paths are omitted.


89

One must take into account that the expression (4.3) is the frequency–domain ratio of

the channel’s output voltage to the voltage injected into the line by an ideal generator. In

the case of a practical power–line network, as shown in Figure 4.26, calculation of the

transfer function between any two communicating devices involves an additional scaling

factor, which includes the non–ideal characteristics of the transmission system

[Anastasiadou and Antonakopoulos, 2005]. Since the transfer function of a point–to–point

channel represents the ratio of the steady state voltages measured at the two

communicating ends, another scaling factor has to be added, relating the incoming source

voltage to the total voltage measured at the transmission end, which comprises the injected

signal and the sum of all signal components that are reflected toward the source.

Figure 4.26 Non–ideality of the source

As a result, the following expression is derived for the transfer function of the channel,

which is calculated as the ratio of the voltages measured at the two communicating

termination points

11

1 1

( ) ( )rx in

tx in

V Z TZT f G f

V Z T Z

+= = ⋅ ⋅

+ (4.14)

where inZ is the total input impedance seen by the transmitter in steady state. However, the

transfer function is scaled for simulation in order to get a lossless channel, and the scaling

factor can therefore be omitted. Channel impulse response ( )g τ can be written as

[ ] ( )21( ) F ( ) ( ) cj f f

c cg G f f G f f e dfπ ττ +−= + = + ⋅ ⋅∫ (4.15)

where [ ]1F− ⋅ is the inverse Fourier transformation function. For a given signal bandwidth B,

and under the assumption of 2cf B> , the channel impulse response can be expressed as


90

( )2

2

2

( ) 2 ( ) c

B

j f f

c

B

g G f f e dfπ ττ +

−

= ⋅ + ⋅ ⋅∫ (4.16)

From (4.3), the impulse response ( )g τ is written as

( ) ( ) ( )0 1

22 /( ) 2

12

( ) 2k

c i pc i c

B Npj f f d va a f f d j f f

i

iB

g g e e e dfπ π ττ − +− + + +

=

= ⋅ ⋅ ⋅ ⋅ ⋅∑∫ (4.17)

The channel impulse response function can simplified taking the exponent of the

attenuation factor k = 1, then after some operations the impulse response is obtained as

( ) 1

0

2 22

1 2

( ) 2

i ic

pi

d a dBNp j f fv ja d

i

i B

g g e e dfπ τ

πτ

− + + −

− ⋅

=

= ⋅ ⋅ ⋅∑ ∫ (4.18)


91

( ) 1

0

2

22

11

2

( ) 2

22

i ic

p

i

B

d a dj f f

v jNpa d

i

ii i

pB

eg g e

d a dj

v j

π τπ

τ

π τπ

− + + −

− ⋅

=

−

= ⋅ ⋅ − + −

∑ (4.19)

( )

0

11

1

21 2 2

1

2 22 2 2

2

( ) 2

4

i

i i ic i c

p p

ii

Nppa d

i

ii

i

p

dB d a dBf j a d j f

v v j

da d j

vg g e

da d

v

e eπ τ π τ

π

π τ

τ

π τ

− ⋅

=

− − − − + + −

− −

= ⋅ ⋅

+ −

× −

∑

(4.20)

Channel impulse response ( )kh t in the time domain, shown in (4.21), is modeled as a

discretized version of (4.20). Hence, the channel is a L–path lossless baseband equivalent

tap–delay filter where k

lh and k

lτ are the complex tap gain and time delay respectively for

the lth path and kth user.

1

0

( ) ( )L

k k k

l l

l

h t h tδ τ−

=

= ⋅ −∑ (4.21)

where ( )δ ⋅ is the Dirac delta function. The complex tap gain k

lh is obtained from (4.20) for a

given time delay τ :

( )k k

l lh g τ= (4.22)

In order to generate a powerline network topology (Figure 4.27), the load and cable

impedances are randomly defined, where open connections are modeled with an impedance

LZ = 1 MΩ. On the hand, the characteristic impedance of each load and cable branch/stub

are modeled statistically based on a normal distribution with mean value of Z = 70 Ω (house

connection cable of the type NAYY35) and standard deviation σ = 7. The same for

branch/stub cable lengths that follow a uniform statistical distribution for a maximum

distance of d = 15 meters.


92

Branch

Stub

Z

ZL

d

Figure 4.27 Network topology

One powerline network topology randomly generated for six simultaneous

transmitting users is shown in Figure 4.28, where a coded application finds all the possible

paths for each user calculating their time delays and gains (transmission and reflection

coefficients).

Figure 4.28 Random network topology

As a result, Figure 4.29 shows the equivalent baseband frequency responses for each

user xT that are transmitting to a receiver located at the outlet R.. The carrier frequency cf

= 14.8 MHz has been randomly selected for bandwidth B = 20 MHz. The channel attenuation

parameters are fixed to 4 1

0 2 10a m− −= ⋅ and 9

1 10a s m−= .


93

-10 -8 -6 -4 -2 0 2 4 6 8 10-65

-60

-55

-50

-45

-40

-35

-30

-25

-20

-15

Frequency (MHz)

Gai

n (d

B)

T1

T2

T3

T4

T5T6

Figure 4.29 Random frequency responses

4.2.2 Noise

As stated above, measurement results reported in this work show that the powerline

noise cannot be represented using an AWGN model, widely used in wireless

communications. Powerline noise n(t) is mainly composed of colored background noise

)(tnBG , narrowband noise )(tnNB and impulsive noise )(tnI , and it can be expressed as

( ) ( ) ( ) ( )BG NB In t n t n t n t= + + (4.23)

The following sections (4.2.2.1 and 4.2.2.2) model the background and impulsive noise

based on measurements done in this work and in the literature. First, a background and

narrowband noise model for simulation is produced, and after that, one for impulsive noise.

4.2.2.1 Background noise

Background noise ( )NBn t is caused mainly by the composition of several low–power

noise sources, and its power spectral density function ( )BGS f decreases exponentially with

frequency [Benyoucef, 2003], as shown previously in (2.17). It is shifted back from the carrier

frequency as follows


94

0/

0 1( ) cf f F

BG cS f f N N e− ++ = + (4.24)

where N0 is the floor constant noise power density, N1 and F0 are the parameters of the

exponential function that are taken from [Benyoucef, 2003], which defines several profiles

depending on the selected scenario.

Table 4.2 Background noise profiles [Benyoucef, 2003]

Table 4.2 summarizes the determined parameters of the background noise as well as

the used probability densities with their values for the regarded environment types

[Benyoucef, 2003].

Narrowband noise ( )NBn t is mostly sinusoidal with modulated amplitudes This type of

noise is caused by multiple broadcast RF emissions coupled in the electrical cables.

Throughout the day, it may vary depending on atmospheric conditions enabling a more

propitious propagation of RF waves. Each radio emission has a Gaussian shaped PSD

[Benyoucef, 2003] and the sum )( fSNB can be written as

2

2

( )

2

1

( )

c i

i

f f fN

B

NB c i

i

S f f A e

+ −−

=

+ = ⋅∑ (4.25)

where iA is the power density, if is the centre frequency, and iB is the interferer

bandwidth. Table 4.3 summarizes some of the already existing services and equipment

operating in the frequency spectrum [1.3–30MHz], where the broadband PLC systems are

also operating. Carrier frequencies if are selected from this data in order to create

narrowband disturbance.


95

Table 4.3 RF services [Hrasnica et al., 2004]

Whereas the power density iA and disturbance bandwidth iB parameters are

summarized in the Table 4.4 with their respective statistical distribution depending on the

scenario and the frequency band, the power spectrum densities of the narrowband and

background noise can be added together as follows

( ) ( ) ( )N NB BGS f S f S f= + (4.26)

2

20

( )

/ 2

0 1

1

( )

c i

c i

f f fN

f f F B

N c i

i

S f f N N e A e

+ −−

− +

=

+ = + + ⋅∑ (4.27)


96

Table 4.4 Narrowband noise profiles [Benyoucef, 2003]

Figure 4.30 shows an example of background and narrowband noise spectrum

composition randomly generated by means of (4.27) and the data provided in Table 4.2,

Table 4.3 and Table 4.4. This kind of noise can be considered as a stationary random process

[Zimmermann and Dostert, 2002a], therefore a linear shift–invariant transformation

of ( )NS f can be applied filtering the signal with spectrum ( )WS f [Therrien, 1992]:

2( ) ( ) ( )N WS f S f H f= (4.28)

The power spectrum density ( )WS f is assumed to be white noise

0( )2

W

NS f = (4.29)

The filter ( )H f is obtained by applying an inverse Fourier transform to the desired

power spectrum density shape by multiplying it by a Hamming window. Figure 4.31 shows


97

the resulting spectrum of the filtered white noise, which matches the model shape from the

Figure 4.30.

0 5 10 15 20 25 30-145

-140

-135

-130

-125

-120

-115

-110

-105

-100

Frequency (MHz)

PS

D (

dBm

/Hz)

Figure 4.30 Randomly generated PSD shape

0 5 10 15 20 25 30-145

-140

-135

-130

-125

-120

-115

-110

-105

-100

PS

D (

dBm

/Hz)

Frequency (MHz)

Figure 4.31 Filtered background noise PSD


98


Impulsive noise is composed of strong peaks whose duration can vary from

microseconds to a few milliseconds. The time between occurrence events could be periodic

with the electrical network frequency or totally asynchronous. Impulsive noise ( )In t has its

source in switching power electronics components [Zimmermann and Dostert, 2002a] and

may cause burst errors in the transmitted data. Then, the baseband equivalent kth pulse

( )k

In t in the time domain is defined as

,

( ) sin(2 ) ( )ktk

I k k

imp k

tn t A e f t rect

T

ζ π−= ⋅ ⋅ ⋅ (4.30)

where ( )rect ⋅ function is a rectangular shape which is uniform in the interval [0,1],

otherwise is null. kA , kζ , kf , and ,imp kT are the pulse amplitude, time attenuation constant,

oscillation frequency and pulse length, respectively. The parameter inter arrival time ,IAT kT is

defined as the time between two pulse events

, 1IAT k k kT T T −= − (4.31)

where kT and 1kT − are the start time of the kth and (k-1)th pulse, respectively. Its statistical

probability density function (Figure 4.16) is based on the results presented in the section

4.1.2.2, which should be coded as a discrete distribution. The impulsive noise ( )In t of the

impulsive noise is shown in the following expression

2( ) ( ) cj tfk

I I k

k

n t n t T eπ

∞−

=−∞

= − ⋅∑ (4.32)

where cf is the carrier frequency. The pulse is shifted in frequency in order to obtain the

baseband equivalent signal. A binomial probability density function is used to model the

classification of the pulse, as shown in this chapter. A burst pulse ( )k

In t is defined as follows

,

1

( ) ( )vN

k k k

I i imp i

i

n t n t T=

= −∑ (4.33)

where vN is the number of consecutive single pulses, and


99

,

( ) sin(2 ) ( )kitk k

i k i k

imp i

tn t A e f t rect

T

ζ π−= ⋅ ⋅ ⋅ . (4.34)

Parameter Distribution Statistical Parameter

Pulse Kind Binomial p = 0.4812

f (MHz)

Binomial 3f MHz<

p = 0.83

3f MHz≥

p = 0.17

Weibull a = 1.26 b = 2.27

a = 10.91 b = 6.07

A (V) Normal µ = 7.73 σ = 2.97

,imp iT (µs) Weibull a = 5.14 b = 1.22

ζ Normal µ = 0.84

σ = 0.5353

Table 4.5 Single pulse (Nv = 1) statistical parameters [Degardin et al., 2003] and [Val et al., 2007]

Parameter Distribution Statistical Parameter

Pulse Kind Binomial p = 0.5188

vN Uniform discrete /

f (MHz)

Binomial 3if MHz<

p = 0.37

3if MHz≥

p = 0.63

Weibull a = 1.26 b = 2.27

a = 10.91 b = 6.07

i rf F f= ⋅

Normal µ = 1.00 σ = 0.16

A (V) Normal µ = 11.17 σ = 3.87

,imp iT (ms) Rayleigh β = 0.076 / vN

iζ

Weibull

a = 0.60 b = 1.71

Table 4.6 Burst pulse statistical parameters [Degardin et al., 2003] and [Val et al., 2007]


100

Single pulse is a particular case of burst pulse when vN = 1. All the impulsive noise

parameters follow a statistical model obtained from previous measurements done here and

other works. In [Degardin et al., 2003], several impulsive noise measurements have been

carried out, where some results are used to complete the simulation model proposed here.

Figure 4.32 shows the power spectral density of a randomly generated pulse for a

carrier frequency cf = 13.4 MHz and a bandwidth of 16 MHz. It is an example of how these

power levels turn out to be quite damaging for a transmitted signal.

-8 -6 -4 -2 0 2 4 6 8-140

-130

-120

-110

-100

-90

-80

-70

-60

Frequency (MHz)

PS

D (

dBm

/Hz)

Figure 4.32 PSD noise and cf = 13.4MHz


101

4.3 IMPULSIVE NOISE EFFECT

During impulsive noise peaks, information symbols get damaged, so proper coding and

interleaving schemes are needed in order to avoid performance loss. In this work, only

uncoded systems are taken into account. Impulsive noise can be classified into single and

burst pulses, where the latter comprises several single pulses concatenated in time. It is

known that pulse type follows a binomial probability density function defined as

1( ) (1 )x xf x p p −= − (4.35)

where x equal to 0 or 1 represents a single or burst event, respectively, and p is the

probability of being a burst pulse event. The probability of occurrence of impulsive noise

impp is expressed as

[ ]

1 1

, ,

0 0

1 1

, ,

0 0

N N

imp k imp kimpk k

imp N N

IATIAT k IAT k

k k

T T NE T

pE T

T T N

− −

= =− −

= =

= = =∑ ∑

∑ ∑ (4.36)

where impE T and [ ]IATE T are the average time length and inter arrival time of pulse

events. It is reasonable to assume that a user signal PSD is much lower than impulsive noise

PSD. Furthermore, taking into account its high number of harmonics, a pulse event may

affect the entire symbol even if pulse length is shorter than symbol time. The mean time

length of impulsive noise is given by

(1 )BP SP

imp imp impE T pE T p E T′ = + − (4.37)

where BP

impE T and SP

impE T are the average duration time of burst and single pulses,

respectively. In the worst case, each pulse event will destroy at least two symbols as seen in

Figure 4.33. Therefore, this constraint sets an upper bound to the bit error rate. The new

length mean values are

2imp imp SE T E T T′ = + (4.38)


102

Figure 4.33 Impulsive noise effect over received data symbols

The probability of bit error for a powerline system is given as

( ) ( )| (1 ) |e imp impP P e noimpulse event P P e impulse event P= ⋅ − + ⋅ (4.39)

where P(e | no impulse event) is the system probability error in the absence of impulsive

noise, and P(e | impulse event) is the system probability for impulsive noise, which in the

worst case, is equal to one half. Therefore, the BER upper bound can be expressed as

0.5e impP P= .

Chapter 5. Theoretical Analysis 103

5 Theoretical Analysis

Chapter 5

Theoretical Analysis

We consider an uplink asynchronous system with Nu users transmitting simultaneously

over the powerline network. The user delays with respect to the user of interest are

assumed to be i.i.d. and uniformly distributed in [ )0, c cT L and [ )0, s cT L N for DS-CDMA and

MC-CDMA, respectively. Therefore, the received DS-CDMA/MC-CDMA baseband equivalent

signal ( )r t at receiver input is given by

)()()()(1

1

1

0

1

0

0

0 tntxhtxhtruN

k

L

l

klk

k

l

L

l

ll +Λ−−⋅+−⋅= ∑∑∑−

=

−

=

−

=

ττ (5.1)

where kΛ is the time delay of the kth user with respect to the user of interest ( 0 0Λ = ). The

signal comprises the signal of the user of interest (k=0), the MAI term, and the powerline

noise n(t) defined in Chapter 4.

Chapter 5. Theoretical Analysis

104

5.1 SPREADING SEQUENCES

The auto–correlation property of CDMA spreading sequences is an important

parameter to take into account for initial timing synchronization and tracking. However, the

requirement is twofold, because asynchronous CDMA systems need sequences with a

minimum cross–correlation property value to reject the MAI from other users.

Various spreading sequences exist which can be distinguished with respect to

orthogonality and correlation properties, where the selection of the spreading code depends

on the scenario. In the synchronous downlink, orthogonal (or short) spreading codes are of

advantage, since they reduce the multiple–access interference compared with non–

orthogonal sequences. Orthogonal Walsh–Hadamard codes are simple to generate

recursively by using the following Hadamard matrix generation,

2 2

1

2 2

2 , 1, 1L L m

L

L L

C CC L m C

C C

= ∀ = ≥ = −

. (5.2)

The maximum number of available orthogonal spreading codes is L which determines

the maximum number of active users Nu. The Hadamard matrix generation described in (5.2)

can also be used to perform an L–ary Walsh–Hadamard modulation. However, in the

asynchronous link, the orthogonality between the spreading codes gets lost due to different

distortions of the individual codes. Moreover, the degrading effect intensifies in a multipath

environment such as a powerline network.

A short spreading sequence has a periodicity equal to the bit time, while a long

sequence is essentially pseudo–random. In a pseudo–random long code system, the

correlation between the users changes from symbol to symbol, and the MAI therefore

appears to be random in time, causing the performance for different users to be

approximately identical and determined by the average interference level. In other words,

its cyclostationary statistics are reduced from symbol period to chip period. Short codes, on

the other hand, have cross–correlations that remain unchanged over time, and an

unfortunate user might be trapped in an inferior performance scenario due to nontime–

varying cross–correlations. The variability of an asynchronous system performance with

short and long sequences has been studied in [Parkvall, 2000], where the short code system

presents a higher performance variability compared with long code system. As shown in

Chapter 4, powerline frequency response between two outlets may remain static for a time.

Consequently, the interference signal seen by a receiver does not change from symbol to

symbol when short spreading codes are used.


105

A pseudo–random sequence appears to be noise-like if the construction is not known

at the receiver. They are typically generated by using shift registers of length m with linear

feedback. These pseudo–random sequences are maximum–length shift register sequences,

known as m–sequences with a length of n = 2m

− 1 bits. The sequence has a period length of

n and each period contains 2m

− 1 ones and 2m−1 − 1 zeros.

One of the most popular pseudo–random long binary sequence are the so–called Gold

codes [Gold, 1967], which have better cross–correlation properties than m–sequences. A set

of n Gold sequences is derived from a preferred pair of m–sequences of length L = 2n − 1 by

taking the modulo-2 sum of the first preferred m–sequence with the n cyclically shifted

versions of the second preferred m–sequence. By including the two preferred m–sequences,

a family of n + 2 Gold codes is obtained. Gold codes have a three–valued cross–correlation

function with values 1, ( ), ( ) 2t m t m− − − where

( )

( )

1 2

2 2

2 1 for odd( )

2 1 for even

m

m

mt m

m

+

+

+= +

. (5.3)

Let 1f and 2f be a preferred pair of primitive polynomials of degree n whose

corresponding shift registers generate maximal linear sequences as shown in the Table 5.1.

N N 1f 2f

5 31 5 2 1x x+ + 5 4 3 2 1x x x x+ + + +

6 63 6 1 1x x+ + 6 5 2 1 1x x x x+ + + +

7 127 7 3 1x x+ + 7 3 2 1 1x x x x+ + + +

9 511 9 4 1x x+ + 9 6 4 3 1x x x x+ + + +

11 2047 11 2 1x x+ + 11 8 5 2 1x x x x+ + + +

13 8191 13 4 3 1x x x x+ + + + 13 10 9 7 5 4 1x x x x x x+ + + + + +

Table 5.1 Gold preferred pairs


106

To reduce the MAI, which is one of the main factors decreasing the practical channel

capacity and thus degrading the performance of multiple–access systems, complex

polyphase sequences are better positioned than other binary family codes, such as Walsh

and Gold sequences. These sequences are characterized as having reduced cross–

correlation.

The Song–Park (SP) sequences [Park et al., 2002] are optimized for minimal cross–

correlation value. For each , 1, 2, ,k k L= … , with L an even integer, let consider the

sequence ,0 ,1 , 1, , ,ck k k k Lc c c −=c … of length cL , defined by

cL

lRLlkj

kl ec

)1)2,(()1(22

,

−++

=δ

π

(5.4)

where 0,1, , 1cl L= −… , ( )2 1cL L= + , δ(∙) is the Dirac delta function, and ( , )R a b is the

remainder of a when divided by b . The set 1 2, , , Lc c c… of L sequences is called the

Song–Park (SP) sequence.

On the other hand, the Oppermann (OP) codes [Oppermann and Vucetic, 1997] design

is a trade–off between auto–correlation and cross–correlation properties. Let cL be the

sequence length. Let L take integer values that are relatively prime to cL such that

1 cL L≤ < . For each , 1, 2, ,k k L= … , let consider the sequence ,0 ,1 , 1, , ,ck k k k Lc c c −=c … of

length cL , defined by

, ( 1)

m p n

c

k l lj

Lkl

l kc eπ

+

= − (5.5)

where 0,1, , 1cl L= −… and p, m and n are real numbers. The triple , ,p m n specifies the

sequence set.

Figure 5.1 User even and odd cross–correlation

To fully analyze the performance of a specific kind of sequence coding in a multiuser

environment, one should consider not only the even cross–correlation (ECC) property but


107

also the odd cross–correlation (OCC) property of sequences. The OCC function affects the

correlator output when information symbols change over the integration interval, while the

ECC function affects the output when the information symbols remain unchanged. As a

result, both functions are equally important in the system design and performance analysis

[Park et al., 2002]. The ECC property function between the i and j sequences is given by

*1 1* *

, , , , ,

0 0

1 1( )

c

c

L

i j i l j l j l i l L

l lc c

c c c cL L

τ τ

τ τθ τ− − −

+ + −= =

= ⋅ + ⋅

∑ ∑ (5.6)

and the OCC property function

*1 1* *

, , , , ,

0 0

1 1ˆ ( )c

c

L

i j i l j l j l i l L

l lc c

c c c cL L

τ τ

τ τθ τ− − −

+ + −= =

= ⋅ − ⋅

∑ ∑ . (5.7)

It is important to note that because many users may be operating in the system at any

time, the cross–correlation properties of all sequences in the set should be considered when

determining the average performance. That is why, the average properties of sequences in a

set must be taken into account for any user configuration and delay τ (see Chapter 6).


108

5.2 ANALYSIS OF ASYNCHRONOUS DS-CDMA SYSTEM

Consider an asynchronous DS-CDMA system with a spreading gain factor cN . The

independent and identically distributed random data symbols of the kth user are mapped on

a QPSK constellation of the vth data multiplex for the mth symbol ,v k

ma with , 1v k

ma = . The

multiple–access scheme is based on joint utilization of short Walsh–Hadamard orthogonal

and long sequences. The data is multiplexed using a set of orthogonal Walsh codes

,1, 2,, , , kV kk kb b b… of length cN for each kth user, and scrambled by means of a long

sequence to better protect them from multipath effects and from interference of other

users. The transmitted DS-CDMA signal of the kth user is expressed by

, ,

,

1

( ) ( )kV

v k v k

k k v m m s

m v

x t P a c t mT∞

=−∞ =

= −∑ ∑ (5.8)

where sT is the symbol time, vkP , is the signal power for the vth data multiplex, and the user

symbol data rate is sk TV . Equation (5.9) shows the sequence waveform of the mth

transmitted symbol for the kth user on the vth data multiplex. The system uses a set of

QNu ≤ sequences 0 1 1, , , Q−c c c… , and each user has a sequence ,0 ,1 , 1, , ,cl l l l Lc c c −=c … of

length cL .

1, ,

,0

( ) ( )c

c

Nv k v k

m p ck p mNp

c t b c g t pT−

+=

= ⋅ −∑ (5.9)

The chip time duration is cT and )(tg is the time–limited transmitter and receiver filter

for the chip pulse shape with a group delay of D/2 chips. The operation k is the modulus

after division of k by the sequence length. The asynchronous DS-CDMA signal analysis for

MMSE receiver is carried out in absence of impulsive noise, which is conducted in the

previous chapter. From (5.1), (5.8) and (5.9) the received DS-CDMA signal ( )r t is as follows

1 1,

,

0 1 0

( ) ( ) ( )u kN V L

k v k k

k v l m l k

k m v l

r t P h c t mT n tτ− ∞ −

= =−∞ = =

= ⋅ − − − Λ +∑ ∑ ∑ ∑ (5.10)

where kΛ is the time delay of the kth user with respect to the user of interest ( 0 0Λ = ),

which are assumed to be i.i.d. and uniformly distributed in [0,LcTc).


109

k∆

... ... ......mth (m+1)th (m+2)th

1,0 −cLc

0,0c 1,0c 1,0 −NcNc ,0 1,0 +Nc 12,0 −Nc Nc 2,0 13,0 −Nc

Nc 3,0

... ... ... ...0,kc′ 1,kc′ 1, −′Nkc Nkc ,

′1, −′

cLkcNLk cc −′

,1, −−′NLk c

cNLk cc 2, −′

ckc TT Λ

kΛ

(m-1)th

NLcc −−1,0

12, −−′NLk c

c22, −−′

NLk ccNLk c

c 3, −13, −− NLk cc

(m-3)th (m-2)th (m-1)th mth

0th user

kth user

Figure 5.2 System users asynchronism

To simplify the mathematical analysis, noting that the user data is i.i.d., the long

spreading sequences are reordered to enable delays in the range [ )0, cT without any loss of

generality. As shown in the Figure 5.2, the user delay kΛ is split in two terms

k

c

kckT

T ∆+

Λ=Λ (5.11)

where ⋅ is the ceil operation and k∆ is the new kth user chip delay. The signal ( )r t at

the receiver without impulsive noise after the sequence reordering is as follows

1 1,

,

0 1 0

( ) ( ) ( )u kN V L

k v k k

k v l m l k

k m v l

r t P h f t mT n tτ− ∞ −

= =−∞ = =

= ⋅ − − − ∆ +∑ ∑ ∑ ∑ (5.12)

where the new sequence waveform ( )f t is expressed as

1, , , ,

0

( ) ( )c

k k c

Nv k v k m v k k

m p cp p mNp

f t d s c g t pT−

−Φ −Ψ +=

= ⋅ −∑ (5.13)

where k k cTΨ = Λ , k k c kN TΦ = Ψ − Λ and the vector , ,v k md is the kth user data

reordered for the new user chip delay k∆ . The Figure 5.3 shows how each symbol , ,v k md is

split into two parts as , , , ,

1

v k m v k v k

m m−=d a a where , , ,v k v k v k

m m ma a=a ⋯ and

, , ,

1 1 1

v k v k v k

m m ma a− − −=a ⋯ of length c kN − Φ and kΦ , respectively.

k∆

k

mak

ma 1−k

mak

ma 1−k

ma 1−k

ma 1−k

ma 2−k

ma 2−k

ma 2−k

mak

ma 1+k

ma

0,kc 1,kc 2,kc 1, −Nkc Nkc

, 1, +Nkc 12, +Nkc Nkc 2, 13, −Nkc1, −cLkc

1,0 −cLc

0,0c 1,0c 1,0 −Nc Nc ,0 1,0 +Nc 12,0 −Nc Nc 2,0 13,0 −NcNc 3,0

Nkc 3,12, +Nkc

k

ma 1+k

ma 1+k

ma 2+k

ma 2+k

ma 2+

ckc TT Λ

kΛ

k

ma 2+k

ma 1+

2, +Nkc 22, +Nkc

NLcc −−1,0

NLk cc −, 1, +−NLk c

c13, +Nkc2, +−NLk c

c1, −−NLk cc

TT kΛkcT Φ

Figure 5.3 Long sequence reordering for DS-CDMA interference users


110

The received signal ( )r t is filtered and sampled at sF , where c sT R F= , and R is an

integer number. The filtering is done by the transmitter filter ( )g t , and the result filter of

the convolution between the transmitter and receiver filter is the raised cosine filter

( ) ( ) ( )TRg t g t g t= ⊗ with a group delay of D chips, where ⊗ is the convolution operator.

After filtering, the output signal q(n) is supposed to be perfectly synchronized with the user

of interest. From Figure 5.4, and using a matrix representation for a window of ( 2 )cN D+

chips, the mth received vector q is defined by

1

, , , , ,

0 1

u kN V

m k v k k k v m k v m

k v

P−

= =

= +∑ ∑q S H C b n (5.14)

where S , H and C are the delay–pulse shape, channel and code matrix, respectively,

defined later. The filtered background plus narrowband noise is defined by the vectorn , and

user data symbol vector , , , , , , , ,

T

k v m k v m k v m k v m′ ′ ′=b b b b⋯ of length L, where , ,k v m

′b of length

( 4 )cN D+ is given as

, , 1 , , 1 , , , , , , 1 , , 1

, , 2 1 0 1 0 2 1c c c

v k m v k m v k m v k m v k m v k m

k v m N D N N Dd d d d d d− − + +− − − −′ =b ⋯ ⋯ ⋯ (5.15)

The matrix composition is done under the assumption that k

l slTτ = where l is an

integer number.

k∆

cDT

cc TND )12( −+

cDT

TTN cc =

0=n

Figure 5.4 Multiple–access interference for asynchronous DS-CDMA

The pulse shape and delay matrix kS of length L is expressed as


111

( )0 1 1L

k k k k

−=S S S S⋯ (5.16)

where each matrix l

kS of length ( 4 )cN D+ takes into account the lth path and user chip

delay as follows

( )( 1) (3 1)k k kc k l c k l c c k l

l

k DT D T D N Tτ τ τ− +∆ + − − +∆ + + − +∆ +=S g g g⋯ (5.17)

where each column vectorg of length ( 2 )cR N D⋅ + is expressed as

( ) ( ) ( ) ( ( 2 1) )T

TR TR s TR s TR c sg g T g nT g R N D T∆ = −∆ − ∆ − ∆ + − − ∆g ⋯ ⋯ (5.18)

which covers the entire window of ( 2 )cN D+ chips. The diagonal channel matrix kH of

length L L× is as follows

0

1

k

k

k

L−

=

h 0

H

0 h

⋯

⋮ ⋱ ⋮

⋯

(5.19)

where 0 is a rectangular null matrix of length ( 4 ) ( 4 )c cN D N D+ × + and the diagonal matrix k

nh of length ( 4 ) ( 4 )c cN D N D+ × + is given by

0

0

k

n

k

n

k

n

h

h

=

h

⋯

⋮ ⋱ ⋮

⋯

. (5.20)

The diagonal code matrix kC of length L L× is as follows

, ,

, ,

, ,

v k m

k v m

v k m

=

z 0

C

0 z

⋯

⋮ ⋱ ⋮

⋯

(5.21)

where the diagonal matrix , ,v k mz of length ( 4 ) ( 4 )c cN D N D+ × + is given by


112

, ,

2

, ,

2 1, ,

, ,

2 1

0 0

0 0

0 0c

v k m

D

v k m

Dv k m

v k m

D N

z

z

z

−

− +

− +

=

z

⋯

⋯

⋮ ⋮ ⋱ ⋮

⋯

(5.22)

where , , ,

k k c

v k m v k k

i i i mNz s c−Φ −Ψ += . Since the MMSE receiver equalizes the received signal at chip–

level, thus minimizing the mean square error of the symbol estimation. The cost function J to

minimize is

( )

−=

20,0

mm

H aEJ qww (5.23)

where ( )H⋅ is the Hermitian operation and 0w is the optimal solution given as

2

0 min HE a = − ww w q . (5.24)

Remembering that the user data a is i.i.d., it should be noted that

( ), ,1, for , ,

0, otherwise

Hi k j l

n m

n m i j k lE a a

= = = = . (5.25)

So, by substituting (5.14) in (5.23), it can be shown that

( ) ( ) ( )

( ) ( )

0,0 0,0

0,0 0,0 0,0 0,0

HH H

m m m m

H HH H H H

m m m m m m m m

J E a a

E E a a E a E a

= − ⋅ −

= + − −

w w q w q

w q q w w q q w

. (5.26)

Analyzing the Equation (5.26) term by term, it can be found that

( ) ( ) ( )

( )

10,0 0,0 0,0

, , , ,

0 1

0,0

0 0 0,0, 0,0, 0 0 0,0,

u kN VH H H

m m k k k v m k v m m m

k v

H

m m m m

E a E a E a

E a

−

= =

= +

′= =

∑ ∑q S H C b n

S H C b S H C

(5.27)

and


113

10,0 0,0 0,0

, , , ,

0 1

0,0

0,0, 0,0, 0 0 0,0, 0 0

u kN VH H H H H

m m m k v m k v m k k m

k v

H H H H H H H

m m m m

E a E a E a

E a

−

= =

= +

′ = =

∑ ∑q b C H S n

b C H S C H S

(5.28)

where 0,0

0,0, 0,0, 0,0,

H

m m m mE a′ = C C b and the correlation matrix R is given as

1 1

, , , , , , , ,

0 0

u k

H

m m

N VH H H H H

k k k v m k v m k v m k v m k k

k v

E

E E− −

= =

=

= + ∑ ∑

R q q

S H C b b C H S nn (5.29)

where HE nn is the correlation matrix of the filtered background noise. Therefore, by

substituting (5.27), (5.28) and (5.29) in (5.26), the cost function J is shown as

( ) ( )0 0 0,0,1 2HH

mJ ′= + −w w Rw S H C w . (5.30)

From (5.24) and (5.30) the optimal filter solution can be written in the form

( ) 1

0,0 0 0 0,0,( )H

mm −′=w S H C R . (5.31)

The mean square error for a given mth symbol can be written as

( )0,0 0,0 0,0 0 0 0,0, 0,0( ) ( ) 1 2HH

mMSE m J w ′= = + −w Rw S H C w (5.32)

and the relation between the SNR and mean square error (MSE) is given by 1(1 )MSE SNR −= + . Moreover, the standard Gaussian approximation (SGA) is used to

evaluate the BER performance, which relies on the observation that MAI is caused by the

sum of a large number of signals, so the MAI term can be seen as zero mean valued Gaussian

noise, applying the central limit theorem (CLT) to the sums of random variables in the

expression of (5.29). A large number of multipath components and simultaneous users in the

system are necessary to achieve good accuracy with the SGA method. The signal–to–

interference plus noise ratio 0,0SINR at the output of the receiver is presented as


114

( )( )

0,0 0,0 0 0 0,0, 0,0

0,0

0,0 0,0 0 0 0,0, 0,0

2( )

1 2

HH

m

HH

m

SINR m′−

=′+ −

w Rw S H C w

w Rw S H C w. (5.33)

Assuming that the long sequences are finite and the MAI term is repeated along the

time, the average probability bit error in absence of impulsive noise is defined as

( ) ( )0,0|P e noimpulse event E Q SINR = (5.34)

where ( )Q ⋅ is given as

2

21

( )2

u

xQ x e du

π

∞ −= ∫ (5.35)

From (4.39), the probability bit error rate for an asynchronous DS-CDMA system under

impulsive noise is as follows

( )[ ]impimpe PPSINRQEP ⋅+−⋅=

2

1)1(0,0 . (5.36)


115

5.3 ANALYSIS OF ASYNCHRONOUS MC-CDMA SYSTEM

An asynchronous MC-CDMA system is considered with a spreading gain factor of N ,

which is the number of OFDM subcarriers. The independent and identically distributed

random data symbols of the kth user are mapped on a QPSK constellation of the vth data

multiplex for the mth symbol kv

ma,

with 1, =kv

ma . The same DS-CDMA multiple–access

scheme is used here. The data is multiplexed using a set of N length orthogonal Walsh codes

,1, 2,, , , kV kk kb b b… for each kth user. The transmitted MC-CDMA signal of kth user can be

written as

12 ( ), ,

, ,1 0

1( ) ( )

k

p

V Nj f d tv k v k

k s k v m p k p mNm v p

x t p t mT P a b c eN

π∞ −

+=−∞ = =

= − ⋅ ⋅∑ ∑ ∑ (5.37)

where vkP , is the signal power, )(tp is the rectangular pulse shape in the interval [ )TTG ,− ,

T is the OFDM symbol length, Tpf p = is the frequency of the pth subcarrier, GT is the

guard interval of the symbol which is longer than the maximum multipath channel delay

MAXT , and TTT Gs += is the complete symbol length. The interval guard in the form of CP is

expressed as

+<≤−

<≤−−+=

TmTtmTmTt

mTtTmTmTTttd

sss

sGss)()( (5.38)

The system uses a set of QNu ≤ sequences 0 1 1, , , Q−c c c… , and each user has a

sequence ,0 ,1 , 1, , ,cl l l l Lc c c −=c … of length cL . The user symbol data rate is sk TV . From

(5.1) and (5.37), the received MC-CDMA signal ( )r t is as follows

1 1, ,

20 1 0

12 ( ),

,0

( ) ( )

( )

u k

p l k

N V Lk v v k k

m l l k s

k m v l

Nj f d tv k

p k p mNp

Pr t a h p t mT

N

b c e n tπ τ

τ− ∞ −

= =−∞ = =

−− −Λ

+=

= ⋅ − − Λ −

× ⋅ ⋅ +

∑ ∑ ∑ ∑

∑ (5.39)


which are assumed to be i.i.d. and uniformly distributed over [ )0, s cT L N . The asynchronous

MC-CDMA analysis is carried out in absence of impulsive noise. To simplify the mathematical

analysis, noting that the user data is i.i.d., the long spreading sequences are reordered to


116

enable delays in the range [ )sT,0 without any loss of generality. The user delay is split in two

terms

kk s k

s

TT

ΛΛ = + ∆

(5.40)

where ⋅ is the floor operation and k∆ is the new user delay for a given kth user, as shown

in Figure 5.5.

Previous studies analyzed the effect of MAI on OFDMA [Myonghee et al., 2003] and on

MC-CDMA [Kyunbyoung et al., 2002; Kyunbyoung et al., 2005] using the frequency–domain

channel transfer function. Although this approach simplifies the analysis, it cannot explicitly

present the mechanism relating ISI and ICI to MAI. In contrast to previous studies, this work

analyzes the interference in the time–domain for greater accuracy. From (5.39), after the

sequence reordering, the signal at the receiver without impulsive noise is given as

1 1, ,

20 1 0

12 ( ),

,0

( ) ( )

( )

u k

p l k

k

N V Lk v v k k

m l l k s

k m v l

Nj f d tv k

p k p mNp

Pr t a h p t mT

N

b c e n tπ τ

τ− ∞ −

= =−∞ = =

−− −∆

−Ψ +=

= ⋅ − − ∆ −

× ⋅ ⋅ +

∑ ∑ ∑ ∑

∑

(5.41)

where the code delay skk TN Λ=Ψ .

kΛ

k∆

1,, −+Ψ−Ψ− NLkLk kckccc ⋯

NT ksΨ

1,00,0 −Ncc ⋯ 12,0,0 −NN cc ⋯ 13,02,0 −NN cc ⋯

TGT

Figure 5.5 Long sequence reordering for MC-CDMA interference users

Performance analysis is done for MRC receiver, and equal gain combining (EGC)

receiver is avoided due to its worst performance [Xiang and Tung Sang, 1999]. The MRC

output for the mth symbol in perfect time synchronization with the user of interest (k=0) and

xth multiplex is given by


117

( )1 *

2 ( )* ,0

0 0 0,0

( ) ( ) ( )S

i S

S

mT TNj f t mTx x

i i i mNi mT

Z m H f b c r t e dtπ+−

− −+

=

= ⋅∑ ∫ . (5.42)

The signal from (5.41) sampled at TNTc =1 is expressed as

1 1, ,

20 1 0

1 2 ( ),

,0

( ) ( )

( )

u k

c l kc

N V Lk v v k k

m l c l k s

k m v l

pN j d nTNTv k

p k p mNp

Pr n a h p nT mT

N

b c e n nπ τ

τ− ∞ −

= =−∞ = =

− − −∆

+=

= ⋅ − − ∆ −

× ⋅ ⋅ +

∑ ∑ ∑ ∑

∑ (5.43)

and the receiver output is given as

( )11 2

,0

0 0. 0,0

0. ,

( ) ( )

( ) ( ) ( ) ( )

s

S

niN mNN jx x N

i i i mNi n mN

x I x

Z m H b c r n e

D m D m MAI m m

π

η

− +− ∗ −∗+

= =

= ⋅ ⋅ ⋅

= + + +

∑ ∑ (5.44)

where )(, pkpk fHH = , xD .0 is the desired output xth data multiplex, xID , is the interference

from the user of interest data multiplexes, MAI is the interference term from other users,

and η is assumed to be zero mean–valued complex Gaussian noise given by

( )11 2

,0

0. 0,0

( ) ( )S

S

niN mNN jx N

i i i mNi n mN

m H b c n n eπ

η− +− ∗ −∗

+= =

= ⋅ ⋅ ⋅∑ ∑ (5.45)

and the noise variance is expressed as

[ ]1 1

0 0

( ) ( ) ( , ) ( , )N N

k i

Var E n k n i M k m M i mη− −

∗ ∗

= =

= ⋅ ∑∑ (5.46)

where ( ) ( )E n k n i∗ ⋅ is the correlation of the background and narrowband noise from their

PSD defined in Chapter 4, and


118

( )1 2

,0

0. 0,0

( , )kiN j

x Ni i i mN

i

M k m H b c eπ− ∗ −∗

+=

= ⋅∑ (5.47)

The desired user signal 0D for the xth data multiplex is expressed as

12

,0

0, 0, 0,

0

( )N

x

x m x p

p

D m a P H−

=

= ∑ (5.48)

and its variance is defined as

21

2

0, 0, 0.

0

N

x x p

p

Var D P H−

=

=

∑ . (5.49)

The data multiplex interference ID for the user of interest is given as

12

,0 ,0 ,0

, 0, 0.

1; 0

( )kV N

v x v

I x m v p p p

v v x p

D m a P b b H−

= ≠ =

= ∑ ∑ (5.50)

and its variance is defined as

21

2,0 ,0

, 0, 0.

1; 0

kV Nx v

I x v p p p

v v x p

Var D P b b H−

= ≠ =

=

∑ ∑ (5.51)

TTG

mth Symbol(m-1)th Symbol (m+1)th Symbol

0th path

(L-1)th path

0th user

kth user

k∆

lτ

2=kl

SmTt =

( ) Gkl T−∆+τ

)(0

1 mMAI

)(0

2 mMAI)(1 mMAI −

0th path

(L-1)th path

Figure 5.6 Multiple–access interference for asynchronous MC-CDMA

From Figure 5.6, the received multiple–access interference MAI can be broken down

into


119

)()()()( 10

2

0

1 mMAImMAImMAImMAI −++= (5.52)

where 1−MAI is the ISI from the previous symbol, 0

1MAI and 0

2MAI are the ICI from the

same symbol. These three terms can be expressed as

( )1 1

0 ,0 1

1 0. 0,1 0

( ) ( , )uN N

x

i i ki mNk i

MAI m H b c M m i− − ∗

∗+

= =

= ⋅∑ ∑ (5.53)

( )1 1

0 ,0 2

2 0. 0,1 0

( ) ( , )uN N

x

i i ki mNk i


∗+

= =

= ⋅∑ ∑ (5.54)

( )1 1

1 ,0 1

0. 0,1 0

( ) ( , )uN N

x

i i ki mNk i


− ∗ −+

= =

= ⋅∑ ∑ (5.55)

where

1 1 1 2 ( ( ) ),1 , ,

,21 0 0

( , )k k S c l k

c

S

p niV l N mN N j d nTk v NT Nv k k v k

k m l p k p mNv l n mN p

PM m i a h b c e

N

π τ− − + − − −∆ −

+= = = =

= ⋅ ⋅∑ ∑ ∑ ∑ (5.56)

11 1 2 ( ( ) ),2 , ,

,21 ( ) 0

( , )k S c l k

c

k k S

p niV N mNL N j d nTk v NT Nv k k v k

k m l p k p mNv l l n n l mN p

PM m i a h b c e

N

π τ− +− − − −∆ −

+= = = + =

= ⋅ ⋅∑ ∑ ∑ ∑ (5.57)

( ) 11 1 2 ( ( ) ),1 , ,

1 , ( 1)21 0

( , )k k S c l k s

c

k S

p niV n l mNL N j d nT Tk v NT Nv k k v k

k m l p k p m Nv l l n mN p

PM m i a h b c e

N

π τ− +− − − −∆ + −−

− + −= = = =

= ⋅ ⋅∑ ∑ ∑ ∑ (5.58)

It is clear from Figure 5.6 that kl is the channel path that starts introducing ISI,

defined as

1 0

0 0

G k MAX

k G k c G k MAX

G k

L T T

l N T T T

T

− ∆ >

= − ∆ + ≤ − ∆ ≤ − ∆ <

(5.59)

where MAXT is the maximum channel delay defined as )max( k

lMAXT ζ= , GN is the number of

points for the OFDM interval guard expressed as cGG TTN = and )(lnk is the sample where


120

there is no more ISI defined as ( )( )k l k c Gn l T Nτ= + ∆ − , with ⋅ as the ceil operation.

The variance of the MAI term is given as

[ ] ( )1 1 1

1 1 2 2 1 1

1 0 0

( ) ( ) ( ) ( ) ( ) ( )uN N N

k k k k k k

k k i

Var MAI M k M i M k M i M k M i− − −

− − ∗ ∗ ∗

= = =

= + +∑ ∑∑ . (5.60)

Assuming that ICI and ISI signals are jointly Gaussian distributed, SGA is used to assess

the BER performance, which relies on the observation that MAI is caused by the sum of a

large number of signals, thus the MAI term can be seen as zero mean–valued Gaussian noise

[Hoque et al., 2007]. The signal–to–interference plus noise ratio 0SINR at the receiver

output for a given powerline network is expressed as

[ ][ ] [ ] [ ]

0

0

I

Var DSINR

Var MAI Var D Var η=

+ + . (5.61)

Assuming that long sequences are periodic, and that the MAI term is repeated through

time, the average probability bit error in the absence of impulsive noise is defined as

( ) ( )0|P e noimpulse event E Q SINR = (5.62)

where )(⋅Q is defined in (5.35). From (4.39), and like in the case of DS-CDMA system, the

probability bit error rate for a MC-CDMA system under impulsive noise is defined as

( )0

1(1 )

2e imp impP E Q SINR P P = ⋅ − + ⋅

. (5.63)

Chapter 6. Performance Analysis 121

6 Performance Analysis

Chapter 6

Performance Analysis

In previous chapters the term Smart Grid was introduced, which leads to the Home

Area Network (Home Grid) in order to communicate among the home appliance devices and

smart grid, where the primary means of communication is powerline networking in

collaboration with fixed wireless links. The powerline communication system must be robust

and reliable in very hostile environments, where the transmitted signal suffers from

multipath distortion, narrowband and impulsive noise. Performance feature must also be

added to the system specification, in order to achieve medium data rates. Table 2.4

summarizes the smart grid PLC modem characteristics.

The power line is a shared medium between all the devices connected to the network.

Therefore, multiple–access techniques must be employed in order to divide transmitted

signals, which have to be orthogonal to each other. there is a need to implement simple

systems, where all the users access the medium asynchronously without the coordination of

any central node, where TDMA, FDMA and multi–carrier schemes are in disadvantage with

respect to single carrier CDMA techniques. In order to compare the performance of such

systems, the performance of a multi–carrier CDMA scheme is also analyzed. So as to

decrease power consumption and overall cost, low complexity systems must be developed.

This work avoids complex joint detection techniques at the receiver, such as multi–user

detection and parallel interference cancellers, and focuses on single–user detection

Chapter 6. Performance Analysis

122

techniques. Concerning the single–carrier CDMA system, an MMSE receiver is selected due

to its advantage of ease of adaptation, since standard adaptive algorithms can be employed.

The first section of this chapter analyzes the cross–correlation properties of the

previously introduced short and long spreading sequences. The second part of the chapter

analyzes the accuracy of the analytical expressions obtained in Chapter 5 for DS-CDMA and

MC-CDMA receivers. The theoretical results are compared with those obtained from Monte

Carlo simulations in order to validate the closed–form bit error rate for asynchronous DS-

CDMA and MC-CDMA systems under coloured narrowband and impulsive noise with

different kind of long polyphase and binary spreading sequences. Finally, both systems are

compared in the same conditions.

6.1 SPREADING SEQUENCES

The performance analysis of a specific kind of spreading sequences in a asynchronous

multiuser environment is done taking into consideration the even cross–correlation and odd

cross–correlation property of sequences. Both functions are equally important in the system

design and performance analysis, as stated in Chapter 5.

From Equation (5.6), the maximum even cross–correlation ,i jθ value between the i and j

sequences is given by

, ,max ( ) , , 0 1i j i j ci j Lτ

θ θ τ τ= ≠ < < − (6.1)

and the maximum odd cross–correlation ,ˆi jθ property is as follows

, ,ˆ ˆmax ( ) , , 0 1i j i j ci j L

τθ θ τ τ= ≠ < < − (6.2)

where max v operation gives the maximum value of a vector v. The correlation is done

between a shifted sequence j of length cL , and several concatenated sequences j (Figure

6.1), where the symbol value changes depending on the desired parameter. It should be

remembered that the asynchronism is present in the uplink due to multipath components.


123

Figure 6.1 ECC and OCC calculation for τ delay

Figure 6.2 and Figure 6.3 show how the OCC and ECC values change depending on the

delay τ for a random pair of short binary Walsh sequences of length cL = 64 chips.

-60 -40 -20 0 20 40 600

0.2

0.4

0.6

0.8

1

1.2

1.4

Delay (chips)

EC

C

Figure 6.2 ECC for Walsh sequences Lc=64

-60 -40 -20 0 20 40 600

0.05

0.1

0.15

0.2

0.25

Delay (chips)

OC

C

Figure 6.3 OCC for Walsh sequences Lc=64


124

The ECC and OCC values for a random Gold pair sequence is shown in the Figure 6.4

and Figure 6.5. They show a considerably lower correlation values in contrast to the Walsh

sequences.

-2000 -1500 -1000 -500 0 500 1000 1500 20000

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

Delay (chips)

OC

C

Figure 6.4 OCC for Gold sequences Lc=2047

-2000 -1500 -1000 -500 0 500 1000 1500 20000

0.005

0.01

0.015

0.02

0.025

0.03

0.035

Delay (chips)

EC

C

Figure 6.5 ECC for Gold sequences Lc=2047

The Song–Park (Figure 6.6 and Figure 6.7) and Oppermann (Figure 6.8 and Figure 6.9)

sequences show better cross–correlation properties than binary sequences for a randomly

selected pair of sequences.


125

-2000 -1500 -1000 -500 0 500 1000 1500 20000

0.2

0.4

0.6

0.8

1

1.2

1.4x 10

-3

Delay (chips)

OC

C

Figure 6.6 OCC for Song–Park sequences Lc=2048

-2000 -1500 -1000 -500 0 500 1000 1500 20004

4.5

5

5.5

6

6.5x 10

-15

Delay (chips)

EC

C

Figure 6.7 ECC for Song–Park sequences Lc=2048

The Oppermann sequence results shown here have been obtained for design

parameters p=1, m=0.975 and n=1.575, which specify the sequence set [Oppermann and

Vucetic, 1997].


126

-2000 -1500 -1000 -500 0 500 1000 1500 20003

3.5

4

4.5

5

5.5

6

6.5x 10

-4

Delay (chips)

EC

C

Figure 6.8 ECC for Oppermann sequences Lc=2039

-2000 -1500 -1000 -500 0 500 1000 1500 20000

0.2

0.4

0.6

0.8

1

1.2

1.4x 10

-3

Delay (chips)

OC

C

Figure 6.9 OCC for Oppermann sequences Lc=2039

Comparing both families of polyphase sequences with the binary ones, it is clear how

the latter are outperformed by the polyphase sequences in the cross–correlation sense. On

the other hand, many users may be operating in the system asynchronously at any time, so

the cross–correlation properties of all sequences in the set need to be considered when

determining the average performance.

The Figure 6.10 and Figure 6.11 represent the maximum even cross–correlation ,i jθ

and odd cross–correlation ,ˆi jθ parameters surface for a Walsh sequence set of Nu = 20 users

in the worst case. In order to avoid symmetries ( , ,i j j iθ θ= ), the first ten users are correlated


127

against the next ten users. The average properties of sequences in a set for any user

configuration and delay τ must be taken into account. The ECC average performance is

given as

( )

1 1

,

0 0

1

1

u uN N

ECC i j

i ju u

K i jN N

θ− −

= =

= ≠− ∑ ∑ . (6.3)

1 2 3 4 5 6 7 8 9 10

1112

1314

1516

1718

1920

0

0.2

0.4

0.6

0.8

1

User iUser j

Max

(OC

C)

Figure 6.10 OCC surface for Walsh sequences Lc=64

1 2 3 4 5 6 7 8 9 10

1112

1314

1516

1718

1920

0

0.2

0.4

0.6

0.8

1

1.2

1.4

User iUser j

Max

(EC

C)

Figure 6.11 ECC surface for Walsh sequences Lc=64

And the OCC average performance is as follows


128

( )

1 1

,

0 0

1 ˆ1

u uN N

OCC i j

i ju u

K i jN N

θ− −

= =

= ≠− ∑ ∑ (6.4)

The same surfaces are shown for Gold, Song–Park and Oppermann sequences in Figure

6.12, Figure 6.13, Figure 6.14, Figure 6.15, Figure 6.16 and Figure 6.17. Again the best

performance is achieved by the polyphase sequences in both the ECC and OCC values.

12

34

56 7

89

1010

1112

1314

1516

1718

192020

0.06

0.065

0.07

0.075

0.08

0.085

0.09

0.095

User jUser i

Max

(OC

C)

Figure 6.12 OCC surface for Gold sequences Lc=2047

Applying (6.3) and (6.4) to the performance surface cited above, the average cross–

correlation performance is obtained for each sequence family.

12

34

56

78

910

1112

1314

1516

1718

19200

0.01

0.02

0.03

0.04

0.05

0.06

User iUser j

Max

(EC

C)

Figure 6.13 ECC surface for Gold sequences Lc=2047


129

1 2 3 4 5 6 7 8 9 10

1112

1314

1516

1718

1920

0

2

4

6

8

x 10-3

User i

User j

M

ax(O

CC

)

Figure 6.14 OCC surface for Song–Park sequences Lc=2048

12

34

56

78

910

1112

1314

1516

1718

19200

0.5

1

1.5

2

2.5

3

x 10-14

User iUser j

Max

(EC

C)

Figure 6.15 ECC surface for Song–Park sequences Lc=2048


130

1 2 3 4 5 6 7 8 9 10

1112

1314

1516

1718

1920

0

0.005

0.01

0.015

0.02

User iUser j

Max

(OC

C)

Figure 6.16 OCC surface for Oppermann sequences Lc=2039

1 2 3 4 5 6 7 8 9 10

1112

1314

1516

1718

1920

0

0.005

0.01

0.015

0.02

User iUser j

Max

(EC

C)

Figure 6.17 ECC surface for Oppermann sequences Lc=2039

Table 6.1 summarizes all the results, where the best performance is for polyphase

Song–Park sequences and the worst results are for Walsh sequences, as expected.


131

Sequence family ECCK OCCK

Walsh 0.1027 0.2243

Gold 0.0318 0.0736

Song–Park 154.1 10−⋅ 0.0019

Oppermann 0.0025 0.0021

Table 6.1 Average cross–correlation performance

As summary, the polyphase sequences have a superior cross–correlation properties

when compared with other binary sequence families


132

6.2 NUMERICAL RESULTS

This section presents the numerical results in two parts. First, the Monte Carlo

simulation results that verify the theoretical analysis of the previous chapter (Chapter 5). The

results demonstrate the accuracy of the derived probability error expressions for the MC-

CDMA and DS-CDMA receivers based on the SGA method. After that, the probability error

performance of the MC-CDMA receiver is compared with that of the DS-CDMA system.

In order to assess the performance of the previously analyzed systems, several

analytical calculations have been carried out under the powerline channel model proposed

in Chapter 4, where the carrier frequency cf has been randomly selected for each

simulation (4-20 MHz). The channel topology and noise profiles are randomly selected for

each simulation.

0 2 4 6 8 10 12 14 16 18 2010

-6

10-5

10-4

10-3

10-2

10-1

100

Eb/No (dB)

Bit

Err

or P

roba

bilit

y

MMSE-Song-Park

MMSE-Gold

MMSE-Oppermann

QPSK bound

Figure 6.18 Theoretical BER performance for asynchronous DS-CDMA system without impulsive noise

with 10uN = , 4=R and 0 (1 1)n uP P n N= ≤ ≤ − .

For a code gain 64cN = in the DS-CDMA system, the single user data rate is 128 kbps

for each multiplex. The chip pulse )(tg is the square root raised cosine pulse with α = 22%,

which gives a signal bandwidth of 5 MHz. DS-CDMA MMSE receiver processes the

oversampled signal R = 4 times the chip rate, taking advantage of the cyclostationary


133

property of the DS-CDMA signal [Adlard et al., 1998; Milstein, 2000; Parkvall, 2000]. The

performance is evaluated in terms of BER averaged over several scenarios against Eb/N0 at

the receiver input, where N0 is the equivalent mean noise power density of the colored

background noise ( )BGS f (not including narrowband noise). The media is interfered by 10

users transmitting asynchronously and one multiplex 1kV = , assuming that all the interferers

transmit the same power 0 (1 1)n uP P n N= ≤ ≤ − . Each user delay kΛ is randomly selected from

uniform distribution over [0,LcTc). The simulations were conducted for a set of Gold,

Oppermann and Song–Park sequences randomly selected with lengths of 2047, 2039 and

2048 chips, respectively.

Figure 6.18 shows the simulation results of the analytical expression of (5.34) for a

MMSE receiver in absence of impulsive noise. It is possible to conclude from the results that

Gold sequences perform better (around 5 dB) than polyphase sequences. This can be

explained from the point of view of their random nature, coding more effectively the

channel.

0 2 4 6 8 10 12 14 16 18 20

10-3

10-2

10-1

100

Eb/No (dB)

Bit

Err

or P

roba

bilit

y

MMSE-Song-Park

MMSE-Gold

MMSE-Oppermann

BER Upper bound

Figure 6.19 Theoretical and Monte Carlo BER performance for asynchronous DS-CDMA system under

impulsive noise with 10uN = , 4=R and 0 (1 1)n uP P n N= ≤ ≤ − . Monte Carlo simulations marked

with∗ .


134

The analytical results are compared with an ideal BER bound for a QPSK receiver under

AWGN, where the Gold–based receiver is 2 dB worse due to the effect of MAI and

narrowband noise. In order to evaluate the accuracy of the expression (5.34), a Monte Carlo

simulation is done for a specific scenario with Gold and Song–Park sequences. The

simulation is limited to one scenario due to the complexity in calculating the filter for each

symbol and the extremely long–time simulations. Taking a random scenario for a set of Gold

codes, frequency responses, carrier frequency, background noise and user delays, the

analytical probability error Pe is 3.39·10-5

. with Eb/N0 = 10 dB. The same random parameters

are used for a Monte Carlo simulation, obtaining a 98% confidence interval of [2.87·10-5

,

3.97·10-5

]. For Song–Park sequences, the analytical expression returns Pe = 2.28·10-3

,

whereas the Monte Carlo simulation shows a 98% confidence interval of [2.25·10-3

, 2.41·10-

3]. Therefore, the accuracy of the expression (5.34) is shown to be adequate.

0 5 10 15 20 2510

-3

10-2

10-1

100

Eb/No (dB)

Bit

Err

or P

roba

bilit

y

MC-CDMA-Gold-TH

MC-CDMA-Song-Park-TH

MC-CDMA-Walsh-TH

Figure 6.20 Theoretical BER performance for asynchronous MC-CDMA system with 10uN = and

0 (1 1)n uP P n N= ≤ ≤ − .

The previous simulations have been done in absence of impulsive noise, where the

presented curves are transformed by means of the expression (5.36). Several Monte Carlo

simulations are carried out to validate the analytical probability error expressions of the DS-


135

CDMA under impulsive noise, where Figure 6.19 shows that the analytical expression of

(5.36) accurately predicts the simulation results. The BER bound (Pe = 7.58·10-4

) due to

impulsive noise is correctly predicted using the expression (4.36). Following the noise model

presented in Chapter 4, the probability error Pe is 7.58·10-4

with an average length time 49.2938 10impE T −′ = ⋅ and average inter arrival time of pulse events [ ] 0558.0=IATTE .

The MC-CDMA system uses 64 subcarriers ( 64cN = ) for a bandwidth of 4,096 MHz,

using an interval guard of 16 samples (i.e. 3.9 microseconds), which is smaller than the

maximum spreading delay of the multipath channel (see Chapter 4). Again, the performance

of MC-CDMA receivers is evaluated in terms of BER averaged over theoretical calculations

against Eb/N0 at the receiver input. The media is interfered by 10 users transmitting

asynchronously and one multiplex 1kV = , assuming that all the interferers transmit the same

power 0 (1 1)n uP P n N= ≤ ≤ − .

0 5 10 15 20 25

10-3

10-2

10-1

100

Eb/No (dB)

Bit

Err

or P

roba

bilit

y

MC-CDMA-Gold-TH


MC-CDMA-Walsh-TH

OFDM-TH

BER Upper bound

Figure 6.21 Theoretical and Monte Carlo BER performance for asynchronous MC-CDMA under impulsive

noise with 10uN = and 0 (1 1)n uP P n N= ≤ ≤ − . Monte Carlo simulations marked with∗ .

Each user delay kΛ is randomly selected from uniform distribution over [ )0, s cT L N .

The simulations were conducted for a set of Walsh, Gold and Song–Park sequences

randomly selected with lengths of 64, 2047 and 2048 chips, respectively. Taking the


136

analytical results from the expression (5.62) without impulsive noise effects, Figure 6.20

shows how for the MC-CDMA system, the best performance is obtained with Gold

sequences, followed by the Song–Park sequences (beyond 16 dB). In asynchronous

environments, the MC-CDMA receiver suffers from MAI, even if the signal–to–noise ratio is

high. These results support the assumption of the bad behaviour of the multi–carrier system

in asynchronous environments. Finally, the worst curve is for short spreading codes.

0 5 10 15 20

10-3

10-2

10-1

100

Eb/No (dB)

Bit

Err

or P

roba

bilit

y

MMSE-Song-Park

MMSE-Gold

MMSE-Oppermann

MC-CDMA-Gold-TH


MC-CDMA-Walsh-TH

BER Upper bound

Figure 6.22 Theoretical BER performance comparison for asynchronous MC-DMA and DS-CDMA under

impulsive noise

Figure 6.21 validates the MC-CDMA analytical expression of (5.63) described in

Chapter 5 for short and long sequences, such as Walsh, Gold and Song–Park sequences. The

analytical curves match the Monte Carlo simulation results under impulsive noise, except for

polyphase sequences where a small error due to SGA approximation can be seen. Moreover,

in order to evaluate the BER upper bound for a MC-CDMA system under impulsive noise

estimation, simulation without interferer users was carried out (i.e. an OFDM system). Figure

6.21 shows how the BER upper bound matches the Monte Carlo result. It can be concluded

that the MC-CDMA system has behaved worse against MAI rejection in an asynchronous

environment, where the MAI predominates over the impulsive noise.


137

6.3 SUMMARY

The closed–form analytical probability error expressions of the DS-CDMA and MC-

CDMA receiver in (5.36) and (5.63) have been validated with their respective Monte Carlo

simulations, where the SGA approximation for a large number of users is correct, although in

the case of MC-CDMA and polyphase sequences there is a small error.

Figure 6.22 shows the BER performance for MC-CDMA and DS-CDMA systems using

different families of sequences in an asynchronous environment under impulsive noise,

where the best MC-CDMA curve is outperformed by the worst DS-CDMA curve (by nearly 15

dB), which takes advantage of the cyclostationary properties of the transmitted signal. In

asynchronous environments, the MAI is much more damaging for a multi–carrier system, as

has been stated in the results presented. The impulsive noise effect has also been studied,

showing how it limits the receiver performance. However, the implementation of the MMSE

receiver is not feasible in a practical case. Thus, the next chapter will be showing simpler

adaptive implementations of the MMSE receiver.

Chapter 7. Algorithmic Research 139

7 Algorithmic Research

Chapter 7

Algorithmic Research

The implementation of the previously presented MMSE DS-CDMA receiver (Chapter 5)

requires many parameters from other interferers that are not accessible from the receiver

side. Moreover, its extremely high computational complexity does not fit in with the Smart

Grid definition, as stated above.

However, the MMSE receiver has the advantage of ease of adaptation, since standard

algorithms such as least mean squares (LMS) or recursive least squares (RLS) can be

employed [Haykin, 2002]. On the other hand, it suffers from the disadvantage of requiring

the use of short spreading sequences, since the interference must have cyclostationary

statistics in order for the adaptation algorithms to function. That is, the statistics of the MAI

should be periodic in the update interval, which is typically once every symbol [Milstein,

2000]. Moreover, unlike high–order statistics, cyclostationarity can be exploited by means of

linear filtering.

Long sequences do not possess the cyclostationarity that makes possible many of the

advanced signal processing techniques used for blind multiuser detection and adaptive

channel estimation. However, MAI in long sequence DS-CDMA systems remains to be a

wide-sense cyclostationary (WSCS) process with its period reduced from one symbol interval

to one chip interval [Wong et al., 1999].

Chapter 7. Algorithmic Research

140

On the other hand, communications signals can be cyclostationary with cyclic

frequencies related to the carrier frequency, symbol rate, chip rate or certain combinations

of them [Gardner, 1993]. In the frequency domain this cyclostationarity manifests itself as

spectral correlation, that is, the signal is correlated with itself after frequency shifting by one

of its cyclic frequencies. It is important to note that if a signal is cyclostationary, to maintain

its spectral correlation, a sufficiently high sampling frequency must be used. A signal

sampled at one sample per symbol cannot exhibit symbol or chip rate related spectral

correlation so any processing which exploits cyclostationarity must be performed at a higher

sampling rate [Adlard et al., 1998].

In a fractionally spaced equalizer (FSE), the equalizer taps are spaced more closely than

the reciprocal of the symbol rate [Haykin, 2002]. An FSE has the capacity of compensating

for delay distortion much more effectively than a conventional synchronous equalizer does.

Another advantage of the FSE is the fact that data transmission may begin with an arbitrary

sampling phase. However, mathematical analysis of the FSE is much more complicated than

that of a conventional synchronous equalizer. Cyclostationarity introduced at the receiver by

fractional sampling is exploited by adaptive algorithms and blind equalization techniques

without resorting to higher order statistics.

7.1 ADAPTIVE RECEIVER

This section describes the proposed adaptive receiver and the error signals used by the

pilot aided LMS and RLS updating algorithms, which means that these algorithms need to be

trained during the initialization process of the receiver [Haykin, 2002]. Although the time–

varying powerline channels are not studied in this work, the use of adaptive filters may

result favourable for tracking the channel changes along the time.

From (5.1), (5.8) and (5.9), the received signal ( )r t from an asynchronous DS-CDMA

system is expressed as

1 1, ,

,

0 1 0

( ) ( ) ( )u kN V L

v k k v k k

k v m l m s l k

k m v l

r t P a h c t mT n tτ− ∞ −

= =−∞ = =

= ⋅ − − − ∆ +∑ ∑ ∑ ∑ (7.1)

which is filtered and sampled at the sampling frequency sF , where c sT R F= , and R is an

integer number. The output signal ( )q n is represented as


141

*( ) ( ) ( )sq n r t g nT t dt= −∫ (7.2)

where * denotes the complex conjugate operation. After filtering, the output signal ( )q n is

perfectly synchronized with the user of interest. The FSE comprises a (2W+1) length v

mw

filter, centred on the chip pulse. Therefore, sW F must be at least greater than the channel

delay spread. The FSE output for mth symbol and vth multiplex is given by

( )∑ ∑−

= −=+ ⋅=

1

0

**

,0

0,

0 ),()(1

)(c

c

N

p

m

W

Wi

v

mmNp

v

p

c

v ipuiwcbN

mZ (7.3)

where the input signal um is defined as

)(),( ipRmRNqipu cm ++= . (7.4)

The adaptive algorithms need the error v

mε between the FSE output )(0 mZ v and either

the training symbol v

mT (training mode) or estimated symbol ˆvma after hard–decision (blind

mode), which is given by

0

0

ˆ( ) (Blind mode)

( ) (Training mode)

v v

v m

m v v

m

Z m a

Z m Tε

−=

−. (7.5)

Starting with the LMS algorithm, it operates by adjusting the tap weights of the FSE

towards the direction of an estimate for the negative gradient of MSE. It has a low

computational complexity but leaves a relative steady–state excess MSE component above

the MMSE solution and is slow in convergence. However, an adaptive equalizer

implemented with the LMS algorithm may have better narrowband interference cancelling

capabilities than the corresponding MMSE filter due to its nonlinear effects [Reuter and

Zeidler, 1999]. On the other hand, the received signal power may vary significantly due to

powerline cable loss [Zimmermann and Dostert, 2002b], thus a normalized variation of LMS

algorithm (NLMS) based on long sequences has been selected. For the NLMS adaptive

algorithm, the FSE tap weight update is defined as


142

*

1 2

vv v v mm m m

v

m

µ ε+ = + ⋅q

w wq

(7.6)

where μ is the NLMS update step size. The NLMS input signal vector instead of being the

instantaneous value, is a time–averaged 2W+1 length vector v

mq covering the incoming mth

symbol, as suggested in [Mirbagheri and Yoon, 2002], and is given by

( ) [ ]1 *

,0

0,0

1( , ), ( , )

c

c

NTv x

m p m mp mNpc

b c u p W u p WN

−

+=

= ⋅ −∑q ⋯ . (7.7)

From [Haykin, 2002], the NLMS filter will converge to a solution if the step size

parameter follows the condition

2

20

vMAXm

µλ

< <q

(7.8)

where MAXλ is the maximum eigenvalue from the correlation matrix R of the input signal

vector q. From the eigen decomposition theory, the trace of matrix R is equal to the sum of

eigenvalues, and since the eigenvalues are all positive and real, we have

( )2 1

1

trW

i MAX

i

λ λ+

=

= >∑R . (7.9)

The correlation matrix R is nonnegative definite and Toeplitz, with all of the elements

on its main diagonal equal to r(0). Since r(0) is itself equal to the mean square value of the

input at each tap in the filter:

( ) ( ) ( ) 2tr 2 1 0 mW r E = + = R q . (7.10)

In practice, MAXλ is not known, so the expression from (7.8) is rewritten as


143

2 2

20

v vm mE

µ< <

q q. (7.11)

On the other hand, in [Haykin, 2002], it is shown that the ensemble–averaged learning

curve of the NLMS algorithm is approximated by a single exponential with time constant τ

where

2

2

v

m

av

τµλ

≈q

(7.12)

where avλ is the average eigenvalue for the correlation matrix R, which is given as

2 12

1

1 1

2 1 2 1

W

av i m

i

EW W

λ λ+

=

= = + +∑ q . (7.13)

The convergence time constant τ can be considered as a lower bound, but in the same

way that the step size has been calculated, it can be shown that

2 2

2max2 2

v v

m m

mEτ

µλ µ≈ =

q q

q (7.14)

where the Figure 7.1 shows the comparison of the convergence rate estimated from (7.14)

and the real convergence transient of a NLMS algorithm. During the first iterations, the

fastest modes dominate the behaviour of the algorithm.


144

0 50 100 1500

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Iterations

MS

E

Aprox,

Real

Figure 7.1 Approximated convergence rate compared with real (simulation) transient for step size µ = 0.03

On the other hand, the RLS update algorithm is described in a similar way, which is

based on the method of exponentially weighted least–squares which seeks to minimize the

cost function

2

1

( ) ( )m

m i

i

J m iλ ε−

=

= ⋅∑ . (7.15)

where λ is the forgetting factor [Haykin, 2002] or exponential weighting factor, chosen in the

range 0 1λ< ≤ . Instead of a single step size for the tap weight vector, the RLS algorithm

assigns a step size to every element of wm and corrects them accordingly. Hence, its speed of

convergence is much faster compared with that of the NLMS algorithm at the expense of

increased computational complexity, of order O(n2). However, there are several proposals

that reduce the computational complexity to the order of O(n) [Montazeri and Poshtan,

2009], which is equal to that of NLMS. The tap weights are updated using the following

algorithm


145

1

1

m mm H

m m mλ−

−

⋅=

+ ⋅ ⋅P q

kq P q

(7.16)

*

1m m m mε−= + ⋅w w k (7.17)

1 1

1 1

H

m m m m mλ λ− −− −= − ⋅ ⋅P P k q P (7.18)

where k, and P are the (2 1) 1W + × complex gain vector, and the (2 1) (2 1)W W+ × + inverse

correlation matrix, respectively. The matrix P needs a non–zero initialization upon start–up.

From [Haykin, 2002], the recommended choice for the initial value of P is P0 = δ−1I where I is

the (2 1) (2 1)W W+ × + identity matrix. The parameter δ is a constant which is small

compared with the power of the input signal.

0 20 40 60 80 100 120 140 160 180 200

10-1

100

Iterations

MS

E

NLMS

RLS



0.0443.


146

By invoking the independence theory, the RLS algorithm is proven in [Haykin, 2002] to

stabilize near the MMSE solution after 2(2 1)W + iterations where (2 1)W + is the number of

FSE tap weights. This can again be considered as a lower bound for convergence time of the

RLS algorithm although simulation results show that more iterations are required for the RLS

to converge.

The output SNR of the ideal MMSE receiver is formulated with the expression (5.33), or

equivalently, the MSE in (5.32). It serves as a lower bound for the performance of the

adaptive algorithms presented above. Figure 7.2 and Figure 7.3 show the averaged training

curves for both adaptive algorithms in the case of Eb/N0 = 12 dB and Eb/N0 = 22 dB,

respectively, in the same scenario. The system has 10 interferers transmitting

asynchronously using Song–Park polyphase sequences and one multiplex 1kV = , assuming

that all the interferers transmit the same power 0 (1 1)n uP P n N= ≤ ≤ − .

0 50 100 150 200 250

10-2

10-1

100

Iterations

MS

E

RLS

NLMS



0.0055.


147

The adaptive FSE receiver processes the oversampled signal R = 4 times the chip rate,

taking advantage of the cyclostationary property signal. The performance is evaluated in

terms of MSE and compared with the target solution from the ideal MMSE receiver from

Chapter 5. At lower SNR (Figure 7.2), both algorithms converge to nearly same solution,

where the relative excess MSE at the steady state for the adaptive MMSE receiver is about

44%.

0 0.5 1 1.5 2 2.5 3 3.5 4

x 104

-6

-4

-2

0

2

4

6

8x 10

10

Coe

f va

lue

Transmitted Symbols

Figure 7.4 RLS based FSE coefficients divergence under impulsive noise

The RLS algorithm, for the high SNR case shown in the Figure 7.3, converges more

accurately to the MMSE solution with a relative excess MSE of about 36%, whereas the

NLMS algorithm has a relative excess MSE of about 290%. Therefore, the RLS algorithm

based receiver has better performance, but in absence of impulsive noise. At a first

approach, the convergence rate of the RLS algorithm is superior to that of NLMS, but it

suffers from the disadvantage of being more vulnerable to the impulsive noise of the

powerline channel. Figure 7.4 shows the evolution of several RLS based filter coefficients

after the training process (blind mode) affected by powerline impulsive noise

2.3 2.4 2.5 2.6 2.7 2.8 2.9

x 103

700

600

500

400

300

200

100 0 5 0 0 1 0 0 0 1 5 0 0 2 0 0 0 2 5 0 0 3 0 0 0

- 2

0

2

4

6

8

1 0

x 1 0

7


148

In order to avoid this fatal effect over the tap filter update, the RLS algorithm can be

stopped each time that impulsive noise is detected in the received signal. This simple

solution does not improve the performance of the receiver under impulsive noise, but it

does enhance its robustness by isolating the impulsive noise from the filter update algorithm

behaviour.

The condition for detecting impulsive noise presence is defined by

2 2

1

2 2

1

0 100

1 100

m m

m m

K−

−

> ⋅=

≤ ⋅

q q

q q (7.19)

where the parameter K determines whether the filter update must be stopped. The

expression (7.19) uses the norm of the input vector q in order to have a relative estimation

of the input energy, and it is compared with the previous iteration. Afterwards, the update is

disabled until the impulsive noise disappears from the input signal, which is determined by

2 2

1

2 2

1

0 0.01

1 0.01

m m

m m

K−

−

> ⋅=

≤ ⋅

q q

q q . (7.20)

Therefore, the modified FSE tap weight update for RLS algorithm is defined as

*

1m m m mK ε+ = + ⋅ ⋅w w g . (7.21)

This section has presented two well–known adaptive algorithms and a robustness

enhancement proposal for RLS algorithm under powerline impulsive noise. Moreover, due to

its low computational complexity, these algorithms can be easily implemented in a Home

Grid modem solution for an asynchronous and hostile powerline communications

environment, where the performance and complexity need to be balanced.


149

7.2 NUMERICAL RESULTS

Monte Carlo simulation results are presented in this section, where three multiple–

access systems are evaluated. The first two systems have been previously discussed: DS-

CDMA and MC-CDMA. Additionally, a third MC-DS-CDMA multiple–access technique is

simulated in order to compare their performances with each other. For the DS-CDMA system

evaluation, RAKE, NLMS-FSE, RLS-FSE receivers plus a suboptimum MMSE-FSE receivers have

been selected, where the latter was based on the work presented in [Hachem et al., 2001].

Several simulations have been carried out under a powerline channel model with

impulsive noise, following the model proposed in the Chapter 4, where the carrier frequency

(4-20 MHz), channel topology and noise profiles were selected randomly for each

simulation. The performance is evaluated in terms of BER averaged over several scenarios

against Eb/N0 at the receiver input, where N0 is the equivalent mean noise power density of

the coloured background noise ( )BGS f (not including narrowband noise).

For a code gain 64cN = in the DS-CDMA system, the single user data rate is 128 kbps

for each multiplex. The chip pulse )(tg is the square root raised cosine pulse with α = 22%,

which gives a signal bandwidth of 5 MHz. The receiver processes the incoming oversampled

signal R times the chip rate.

In a RAKE receiver, one RAKE finger is assigned to each multipath, thus maximizing the

amount of received signal energy. Each of these different paths are combined to form a

composite signal that is expected to have substantially better characteristics for the purpose

of demodulation than just the a single path. RAKE receiver structure performs a MRC of the

received signal for one multiplex, by means of a filter matched to the channel impulse

response ( )kh t from (4.21), which maximizes the signal–to–noise ratio. The RAKE receiver

output sampled to the chip rate (R=1) and correlated with the spreading sequence is given

as

( )1 1 *

0 ,0

0, 0,0 0

1( ) ( )

c

c

N LRAKE v

v c l p p mNp lc

Z m q l p mN h b cN

− −

+= =

= + +∑ ∑ (7.22)

where in order to combine the different paths meaningfully, the RAKE receiver needs the

knowledge of channel parameters such as, number of paths, their location k

lτ and

attenuation 0

lh , under the assumption that k

l cTτ = . The received symbol estimation a is

done by the decision function [ ]D ⋅ in order to locate the symbol inside the constellation, as

shown in


150

,0

1,ˆ ( )v RAKE

m va D Z m = . (7.23)

The suboptimum MMSE receiver [Hachem et al., 2001] equalizes the received signal at

chip–level by minimizing the mean square error of the symbol estimation. The cost function

J to minimize is

−−⋅= ∑2

* )()( m

n

c anmRNwnqEJ (7.24)

where w is the Wiener filter solution [Verdú, 1998]. This paper contributes to the findings of

[Hachem et al., 2001] in evaluating the performance of the same receiver in an

asynchronous environment with impulse, narrowband and colored background noise. The

author in [Hachem et al., 2001] transforms the cost function (7.25) in a new cost function J’

(7.26) based on a training data frame 0 1 1NTT T T −=T ⋯ , in order to simplify the

optimization problem,

12

1

1

0

' ( )NT

M

m

m

J Z m T−

=

= −∑ (7.25)

1* *

1 1, ( , )

0

1( ) ( ) ( )

c

c c

NM

M p mN L c

p nc

Z m c q n w pR mRN nN

−

+=

= ⋅ + −∑ ∑ (7.26)

where NT is the number of training symbols. Focusing this optimization problem as a linear

regression, the filter w of length (2W+1) can be solved as

* 1( )H H −=w TX XX . (7.27)

The reader can find further details about the filter w and matrix X calculation in

[Hachem et al., 2001] for the cost function (7.26).

On the other hand, an asynchronous MC-DS-CDMA system is considered. The MC-DS-

CDMA transmitter modulates the data sub–streams on subcarriers with a carrier spacing

proportional to the inverse of the chip rate to guarantee orthogonality between the

spectrums of the sub–streams after spreading.


151

A mth sequence of N independent and identically distributed random complex–

valued data symbols k

pa , 0,1, , 1p N= −… , of the user k is serial–to–parallel converted into

N sub–streams, with a symbol rate of 1 cN T . Each symbol k

pa is mapped on a QPSK

constellation with 1k

pa = . The transmitted MC-DS-CDMA signal of kth user can be written as

( )1

2

0

1( ) ( ) p

Nj f tk

k c k p mN k

m p

x t p t mTN P a c t eN

π∞ −

+=−∞ =

= − ⋅ ⋅∑ ∑ (7.28)

with

( ) ( )1

,0

c

c

N

k k i mNi

c t c g t iT−

+=

= ⋅ −∑ (7.29)

where cN is the spreading gain factor, kP is the signal power, )(tp is the rectangular pulse

shape in the interval [ )0, cTN , T is the OFDM symbol length, Tpf p = is the frequency of

the pth subcarrier, and ( )g t is the chip pulse shape. The data symbol rate becomes 1 T for

cN N= . The system uses a set of QNu ≤ sequences 0 1 1, , , Q−c c c… , and each user has a

sequence ,0 ,1 , 1, , ,cl l l l Lc c c −=c … of length cL . The operation k is the modulus after

division of k by the sequence length. The received MC-DS-CDMA signal ( )r t is as follows

1 1

0 0

( ) ( ) ( )uN L

k

l k l k c

k l

r t h x t mTN n tτ− −

= =

= ⋅ − − Λ − +∑∑ (7.30)


which are assumed to be i.i.d. and uniformly distributed over [ )0, cTL . The MRC output for

the mth sequence of the pth sub–stream in perfect time synchronization with the user of

interest (k=0) is given by

( )( 1)1 *

2 ( )*

0 0 0,0

( ) ( ) ( )cc

p c

c

m TNNj f t mTNp

p i mNi mTN

Z m H f c r t e dtπ

+−− −

+=

= ⋅∑ ∫ . (7.31)

The received symbol estimation a is done by the decision function [ ]D ⋅ in order to

locate the symbol inside the constellation, as shown in


152

0

0ˆ ( )p

pa D Z m = . (7.32)

7.2.1 SPREADING SEQUENCES COMPARISON

The comparison of several receivers for Gold, Oppermann and Song–Park sequences is

shown in this section when the media is interfered by 10 users transmitting asynchronously

and one multiplex 1kV = , assuming that all the interferers transmit the same power

0 (1 1)n uP P n N= ≤ ≤ − . Each user delay kΛ is randomly selected from uniform distribution over

[ )0, c cT L . The simulations were conducted for a set of Gold, Oppermann, Song–Park and

Walsh sequences randomly selected with lengths cL of 2047, 2039, 2048 and 64 chips,

respectively.

0 2 4 6 8 10 12 14 16 18 20 22

10-3

10-2

10-1

100

Eb/No (dB)

Bit

Err

or P

roba

bilit

y

RAKE-Song-Park

RAKE-Oppermann

RAKE-Gold

BER bound

Figure 7.5 BER performance for asynchronous DS-CDMA RAKE receiver under impulsive noise with

10uN = , 1R = and 0 (1 1)n uP P n N= ≤ ≤ − .

Figure 7.5 illustrates the performance of a RAKE receiver with different kind of long

spreading sequences. The solid horizontal line is BER performance bound due to impulsive

noise effect based on statistics shown in the Chapter 4. The curves converge to the limit


153

bound, where the receiver based on polyphase Song–Park sequences achieves the best

performance, followed by Oppermann sequences (2 dB). The worst result is for binary Gold

sequences due to their worse cross–correlation properties.

0 5 10 15 20

10-3

10-2

10-1

100

Eb/No (dB)

Bit

Err

or P

roba

bilit

y

NLMS-FSE-Song-Park

NLMS-FSE-Oppermann

NLMS-FSE-Gold

BER bound

Figure 7.6 BER performance for asynchronous DS-CDMA NLMS-FSE receiver (µ=0.03) under impulsive

noise with 10uN = , 4R = and0 (1 1)n uP P n N= ≤ ≤ − .

Concerning adaptive FSE receivers, they converge to an MSE value which is above the

MMSE and randomly moves around it. The average MSE achieved after several iterations

results in an average output SNR which is known as the steady–state SNR. However, the

maximum SNR criterion is not effective when impulsive noise prevails over the MAI. So long

run time Monte Carlo simulations are needed in order to collect enough impulsive noise

statistics. Figure 7.6 shows the performance of NLMS receiver using long binary and

polyphase sequences, where the latter sequences outperform the Gold codes. At high SNR,

the MAI degrades the performance of adaptive FSE receiver using binary sequences,

whereas the powerline impulsive noise prevails over the MAI when polyphase sequences are

used. Again the simulations show the better performance of polyphase coding, which

contradicts with the MMSE results shown in Chapter 6.


154

0 2 4 6 8 10 12 14 16 18 20 22

10-3

10-2

10-1

100

Eb/No (dB)

Bit

Err

or P

roba

bilit

y

NLMS-FSE,R=1

NLMS-FSE,R=2

NLMS-FSE,R=4

NLMS-FSE,R=8

BER bound

Figure 7.7 BER performance with different oversampling ratios for asynchronous DS-CDMA NLMS-FSE

receiver (µ=0.03) under impulsive noise with 10uN = and 0 (1 1)n uP P n N= ≤ ≤ − .

Figure 7.7 shows the comparison between different oversampling ratios R at the

receiver side for a NLMS algorithm using Oppermann sequences. An increment on the

sampling rate implies a performance gain due to the advantage of cyclostationary property

of the transmitted signals. At higher SNR the difference is not so appreciable, but at lower

SNR the improvement can be up to 2 dB.

Figure 7.8 illustrates the performance curves for the RLS receiver using the filter

adaption from the expression (7.17). The effect of the impulsive noise over the RLS algorithm

performance, which is more sensitive on polyphase sequences is clear. Moreover, the

system based on binary sequences is not apparently affected by the impulsive noise. In the

previous section, an enhanced version of the RLS algorithm has been formulated in order to

prevent parameters divergence due to impulsive noise disturbance.


155

0 5 10 15 2010

-3

10-2

10-1

100

Eb/No (dB)

Bit

Err

or P

roba

bilit

y

RLS-FSE-Gold

RLS-FSE-Song-Park

RLS-FSE-Oppermann

Figure 7.8 BER performance for asynchronous DS-CDMA RLS-FSE receiver (λ=0.9995) under impulsive

noise with 10uN = , 4R = and 0 (1 1)n uP P n N= ≤ ≤ − .

Figure 7.9 shows the performance of the enhanced version of the RLS algorithm from

the expression (7.21). Comparing with the previous performance curves of Figure 7.8, the

results for polyphase sequences are greatly improved, taking an advantage of 10 dB over

Gold sequences.

On the other hand, the better performance of polyphase sequences contradicts the

MMSE receiver results shown in the Chapter 6, where the adaptive algorithms show better

tracking capabilities with polyphase sequences. Figure 7.10 compares the results obtained

from MMSE and enhanced version of the RLS receiver. It should be noted how the latter

matches the MMSE curves using polyphase Song–Park sequences. Beyond Eb/N0 = 15 dB,

there is a slight difference between them due to relative steady–state excess MSE, although

both receivers converge to the impulsive noise BER bound.


156

Alongside single–carrier systems, Figure 7.11 and Figure 7.12 illustrate the

performance curves for MC-CDMA and MC-DS-CDMA systems, respectively. Both systems

use 64 subcarriers ( 64N = ) for a bandwidth of 4,096 MHz, using an interval guard of 16

samples (i.e. 3.9 microseconds), which is lower than the maximum spreading delay of the

multipath channel (see Chapter 4). The performance of MC-CDMA receivers is evaluated in

terms of BER averaged over Monte Carlo simulations against Eb/N0 at the receiver input.

0 5 10 15 20

10-3

10-2

10-1

100

Eb/No (dB)

Bit

Err

or P

roba

bilit

y

RLS-FSE-Enhanced-Gold

RLS-FSE-Enhanced-Song-Park

RLS-FSE-Enhanced-Oppermann

BER bound

Figure 7.9 BER performance for asynchronous DS-CDMA RLS-FSE enhanced receiver (λ=0.9995) under

impulsive noise with 10uN = , 4R = and 0 (1 1)n uP P n N= ≤ ≤ −

For the MC-CDMA system, the best performance is obtained with binary Gold

sequences, followed by the polyphase Song–Park sequences. In the MC-DS-CDMA case, the

overall results are worse and each sequence displays virtually the same behaviour, including

the short spreading codes. However, in both multi–carrier systems the MAI prevails over the

impulsive and background noise effect due to user asynchronism. How sensitive the multi–

carrier systems are to asynchronous MAI becomes clear.


157

0 5 10 15 20

10-3

10-2

10-1

100

Eb/No (dB)

Bit

Err

or P

roba

bilit

y

MMSE-Song-Park

MMSE-Gold

MMSE-Oppermann

RLS-Enhanced-GoldRLS-Enhanced-Song-Park

RLS-Enhanced-Oppermann

BER Upper bound

Figure 7.10 MMSE and adaptive MMSE performance comparison for asynchronous DS-CDMA system

under impulsive noise with 10uN = , 4=R and 0 (1 1)n uP P n N= ≤ ≤ − .

MC-CDMA is a promising multiple–access scheme for the synchronous downlink of a

PLC system where it enables the deployment of efficient, low complexity receivers

employing simple channel estimation. However, it has been shown that this statement does

not apply to the uplink and asynchronous environments, where more complex multiuser

detection techniques are necessary to counteract the MAI, since the uplink orthogonal

spreading codes cannot be used to reduce the MAI.

Finally, MC-DS-CDMA was of special interest for the asynchronous uplink of mobile

radio systems due to its close relation to asynchronous single–carrier DS-CDMA systems.

However, the spectral efficiency of the system decreases due to asynchronism, and the

frequency diversity advantage is thus lost.


158

0 5 10 15 20 25

10-3

10-2

10-1

100

Eb/No (dB)

Bit

Err

or P

roba

bilit

y

MC-CDMA-Gold

MC-CDMA-Song-Park

MC-CDMA-Walsh

MC-CDMA-Oppermann

BER Upper bound

Figure 7.11 BER performance for asynchronous MC-CDMA MRC receiver under impulsive noise with

10uN = and 0 (1 1)n uP P n N= ≤ ≤ − .

0 2 4 6 8 10 12 14 16 18 20 2210

-2

10-1

100

Eb/No

Bit

Err

or P

roba

bilit

y

MC-DS-CDMA-Song-Park

MC-DS-CDMA-Walsh

MC-DS-CDMA-Gold

MC-DS-CDMA-Oppermann

Figure 7.12 BER performance for asynchronous MC-DS-CDMA MRC receiver under impulsive noise with

10uN = and 0 (1 1)n uP P n N= ≤ ≤ − .


159

7.2.2 RECEIVERS COMPARISON

The comparison of several multiple–access system receivers for Walsh, Gold,

Oppermann and Song–Park spreading sequences is shown in Figure 7.13, Figure 7.14, Figure

7.15 and Figure 7.16, respectively. The media is interfered by 10 users transmitting

asynchronously and one multiplex 1kV = , assuming that all the interferers transmit the same

power 0 (1 1)n uP P n N= ≤ ≤ − . Each user delay kΛ is randomly selected from uniform

distribution over [0,LcTc).

0 2 4 6 8 10 12 14 16 18 20 22

10-3

10-2

10-1

100

Eb/No (dB)

Bit

Err

or P

roba

bilit

y

MC-CDMA-MRC

MC-DS-CDMA-MRC

DS-CDMA-MMSE-Suboptimum-FSE

BER bound

Figure 7.13 BER performance comparison under impulsive noise for Walsh spreading sequences for

64cL = and 0 (1 1)n uP P n N= ≤ ≤ − .

The simulations were conducted for a set of Gold, Oppermann, Song–Park and Walsh

sequences randomly selected with lengths cL of 2047, 2039, 2048 and 64 chips,

respectively. Figure 7.13 illustrates three systems that use short spreading codes, where the

suboptimum MMSE receiver achieves the best results, but its performance is limited by the

asynchronous MAI, which prevails at higher SNR.


160

0 2 4 6 8 10 12 14 16 18 20 22

10-3

10-2

10-1

100

Eb/No (dB)

Bit

Err

or P

roba

bilit

y

DS-CDMA-NLMS-FSEDS-CDMA-RLS-FSE-Enhanced

DS-CDMA-RAKE

DS-CDMA-RLS-FSE

MC-CDMA-MRC

MC-DS-CDMA-MRC

BER bound

Figure 7.14 BER performance comparison under impulsive noise for Gold spreading sequences for

2047cL = and 0 (1 1)n uP P n N= ≤ ≤ − .

From the rest of the figures, it can be concluded that the enhanced version of the RLS

receiver achieves the best results for the same channel conditions and under impulsive

noise. In the Figure 7.14, the receivers using Gold sequences are still restricted by the MAI,

although the best results are for adaptive structure receivers in which a gain of 10 dB

approximately is obtained.

According to Figure 7.15, the enhanced RLS receiver outperforms the NLMS and RAKE

DS-CDMA receivers by 2 dB and 4 dB, respectively. The worst results are for multi–carrier

systems and the classic RLS algorithm, which is vulnerable to the impulsive noise influence

when using polyphase spreading sequences.


161

0 2 4 6 8 10 12 14 16 18 20 22

10-3

10-2

10-1

100

Eb/No (dB)

Bit

Err

or P

roba

bilit

y

DS-CDMA-NLMS-FSE

DS-CDMA-RLS-FSE-Enhanced

DS-CDMA-RAKE

DS-CDMA-RLS-FSE

MC-CDMA-MRC

MC-DS-CDMA-MRC

BER bound

Figure 7.15 BER performance comparison under impulsive noise for Oppermann spreading sequences

for 2039cL = and 0 (1 1)n uP P n N= ≤ ≤ − .

These results are improved by the use of Song–Park spreading sequences, as stated in

the Figure 7.16. The adaptive algorithms reach the performance bound due to impulsive

noise, which involves a good MAI rejection in asynchronous environments. Moreover, the

combination of Song–Park spreading sequences with the enhanced RLS algorithm

outperforms any other system with a margin of at least 3 dB at low signal–to–noise ratio.


162

0 2 4 6 8 10 12 14 16 18 20 22

10-3

10-2

10-1

100

Eb/No (dB)

Bit

Err

or P

roba

bilit

y

DS-CDMA-NLMS-FSE

DS-CDMA-RLS-FSE-Enhanced

DS-CDMA-RAKE

DS-CDMA-RLS-FSE

MC-CDMA-MRC

MC-DS-CDMA-MRC

BER bound

Figure 7.16 BER performance comparison under impulsive noise for Song–Park spreading sequences for

2048cL = and 0 (1 1)n uP P n N= ≤ ≤ − .

Considering an asynchronous DS-CDMA system, each data symbol of the kth user is

mapped on a QPSK constellation of the vth data multiplex, where this multiple–access

scheme is based on joint utilization of short Walsh orthogonal and long sequences. The data

is multiplexed using a set of orthogonal Walsh codes for each user and scrambled by means

of a long sequence. Therefore, the user symbol data rate is sk TV , where sT is the symbol

time and kV is the number of multiplex.


163

Several Monte Carlo simulations are executed for an user of interest data rate of 8

Mbps using 0 16V = multiplex. This is done by multiplexing the data in the transmitter using

Walsh codes prior to application of long codes. The simulation results have been obtained

for a signal bandwidth of 20 MHz, and uN interferers transmitting at 512 kbps, all of them

with the same Eb/N0 at the receiver input, oversampling the received signal by 2R = .

0 2 4 6 8 10 12 14 16 18 20 22

10-3

10-2

10-1

100

Eb/No (dB)

Bit

Err

or P

roba

bilit

y

RLS-FSE-Enhanced-Song-Park,Nu=5

RLS-FSE-Enhanced-Song-Park,Nu=10

RLS-FSE-Enhanced-Gold,Nu=10RLS-FSE-Enhanced-Gold,Nu=5

BER bound

Figure 7.17 BER performance for asynchronous DS-CDMA RLS-FSE enhanced receiver at 8 Mbps under

impulsive noise with 0 16V = , 2R = and

0 (1 1)n uP P n N= ≤ ≤ − .

Figure 7.17 shows the performance of the enhanced version of the RLS receiver and

compares its behaviour using binary and polyphase sequences under different numbers of

interferers. The better performance of Song–Park sequences for higher data rates is clear,

even if the number of interferers is superior to that of the Gold sequences. The performance

loss, by increasing from 5 to 10 simultaneous and asynchronous users in the system, in the

case of using polyphase sequences is 4 dB, whereas the performance decreases by about 8

dB for binary sequences.


164

0 2 4 6 8 10 12 14 16 18 20 22

10-3

10-2

10-1

100

Eb/No (dB)

Bit

Err

or P

roba

bilit

y

NLMS-FSE-Song-Park,Nu=5

NLMS-FSE-Song-Park,Nu=10

NLMS-FSE-Gold,Nu=5NLMS-FSE-Gold,Nu=10

BER bound

Figure 7.18 BER performance for asynchronous DS-CDMA NLMS-FSE receiver at 8 Mbps under impulsive

noise with 0 16V = , 2R = and

0 (1 1)n uP P n N= ≤ ≤ − .

Figure 7.18 illustrates the performance comparison of binary and polyphase sequences

for a NLMS receiver. As shown in the previous figure, in this case the polyphase sequences

obtain better results, and its gain loss due to users increment is about 3-4 dB. However, if

the system uses binary Gold sequences, it loses around 9 dB. On the other hand, Figure 7.19

merges the last two figures for 10 interferers, showing how the polyphase sequences

outperform the binary codes using adaptive FSE algorithms by rejecting interference under

impulsive and narrowband noise.

7.2.3 NEAR–FAR EFFECT

The near–far problem is a condition in which a strong signal captures a receiver making

it impossible for the receiver to detect a weaker signal. The near–far problem is particularly

difficult in DS-CDMA systems where transmitters share transmission frequencies and

transmission time. Figure 7.20 shows the performance curves for a NLMS FSE receiver using

binary and polyphase long sequences in a system with 10uN = simultaneous users, where


165

the interferers transmit twice the power of the user of interest, that is,

02 (1 1)n uP P n N⋅ = ≤ ≤ − .

0 2 4 6 8 10 12 14 16 18 20 22

10-3

10-2

10-1

100

Eb/No (dB)

Bit

Err

or P

roba

bilit

y

NLMS-FSE-Gold

RLS-FSE-Enhanced-Gold

NLMS-FSE-Song-Park

RLS-FSE-Enhanced-Song-Park

BER bound

Figure 7.19 BER performance comparison for asynchronous DS-CDMA receiver at 8 Mbps under

impulsive noise with 0 16V = , 2R = , 10uN = and

0 (1 1)n uP P n N= ≤ ≤ − .

Rejecting the near–far effect, the polyphase sequences (Oppermann and Song–Park) obtain

a better result than pseudo–random binary sequences, where the latter has a performance

loss of 12 dB approximately. On the other hand, the polyphase sequences lose around 6 dB,

which can be considered to be of a large magnitude.

Figure 7.21 illustrates the behaviour of the enhanced RLS receiver using both polyphase and

binary sequences, mitigating the near–far effect from the asynchronous DS-CDMA system.

The performance loss for Song–Park sequences is less than 1 dB, whereas the Gold

sequences suffer from a gain loss of about 10 dB. The Figure 7.21 also shows the curves for a

suboptimum MMSE receiver from the expression (7.27) using short spreading codes, which

shows a performance loss of 2 dB approximately.


166

0 2 4 6 8 10 12 14 16 18 20 22

10-3

10-2

10-1

100

Eb/No (dB)

Bit

Err

or P

roba

bilit

y

NLMS-FSE-Song-Park

NLMS-FSE-Oppermann

NLMS-FSE-Gold

NLMS-FSE-Song-Park-Ix2

NLMS-FSE-Oppermann-Ix2

NLMS-FSE-Gold-Ix2

BER bound

Figure 7.20 BER performance for NLMS receiver and near-far effect under impulsive noise with 4R = ,

10uN = and 02 (1 1)n uP P n N⋅ = ≤ ≤ − .

7.3 SUMMARY

This chapter examines adaptive implementation of the proposed MMSE receiver in

Chapter 5. What is proposed is an adaptive receiver which is based on an FSE whose tap

weights are updated by an adaptive algorithm; it has the capability of performing multiple-

access interference and narrowband noise suppression by taking advantage of the

cyclostationary properties of the transmitted signals. It is shown that the adaptive receiver

requires the knowledge of fewer parameters compared with the MMSE and RAKE receiver.

Only an estimate of the arrival delay of the first path of the desired user is needed as all

other multipath parameters are estimated by the adaptive FSE.

Two pilot-aided adaptive algorithms are examined: one is a slow but simple steepest

descent structure, and the other a fast but complex recursive structure, which are the well-

known NLMS and RLS algorithms, respectively. Due to the fast convergence rate of the

latter, it suffers from power line impulsive noise, falling in the tap weight update instability.


167

An enhancement of the RLS algorithm is proposed in order to perform correctly under

impulsive noise.

0 5 10 15 20

10-3

10-2

10-1

100

Eb/No (dB)

Bit

Err

or P

roba

bilit

y

RLS-FSE-Enhanced-GoldRLS-FSE-Enhanced-Song-Park

MMSE-Suboptimum-FSE

RLS-FSE-Enhanced-Gold-Ix2

RLS-FSE-Enhanced-Song-Park-Ix2

MMSE-Suboptimum-FSE-Ix2BER bound

Figure 7.21 BER performance for enhanced RLS receiver and near–far effect under impulsive noise with

4R = , 10uN = and 02 (1 1)n uP P n N⋅ = ≤ ≤ − .

Sequence

Receiver Walsh Gold Song–Park Oppermann

NLMS-FSE

Low Medium Medium

RLS-FSE

Low Low Low

Proposed RLS-FSE

Medium High High

RAKE

Low Medium Medium

MC-CDMA Low Low Low Low

MC-DS-CDMA Low Low Low Low

Table 7.1 Receiver vs. sequences performance comparison

Simulation results are presented to examine the convergence rate and steady–state

MSE performance of the proposed algorithms. Performance results are also presented to

compare single–carrier and multi–carrier multiple–access systems under impulsive noise


168

with a different set of binary and polyphase sequences. Table 7.1 shows a performance

comparison between several receivers using different families of spreading sequences,

whose BER curves have been shown in the previous performance figures. From this table,

the best performance is obtained with the proposed enhanced RLS-FSE receiver using

polyphase sequences. Within the Smart Grid framework, the computational complexity is an

important factor. However, there are smart implementations for RLS algorithms, which

reduce the computational complexity order.

Chapter 8. Conclusions 169

8 Conclusions

Chapter 8

Conclusions

8.1 WORK SUMMARY

This thesis examines the design and implementation of a Smart Grid powerline

communication device for a Home Area Network environment, where the communication

link robustness and reliability are a requirement. The power line network represents a

shared transmission medium used by all nodes independently. Therefore, multiple–access

techniques must be employed in order to divide transmitted signals, which have to be

orthogonal to each other. In addition to this, system computational complexity, cost and

power consumption need to be taken into account during the design phase. So, simple

systems need to be implemented, so that all the users access the medium asynchronously

without the coordination of any central node.

To understand the challenges of power line communication, and to design robust data



characteristics of the channel noise. In this thesis, a complete power line channel model is

proposed; it takes into account the noise generated in the network as well as the frequency

attenuation profile of the unmatched network. The proposed model is based on the results

of a channel measurement campaign and proposals from other pieces of work. An analysis

Chapter 8. Conclusions

170

of the impulsive noise effect over transmitted signals reveals a performance bound at the

receiver side, which depends on impulsive noise statistics. The results of these

measurements have been published in [Val et al., 2007].

High data rate multi–carrier systems have shown successful performance under

multipath channels, while their multiple–access extensions MC-CDMA and OFDMA have

produced good results under synchronous powerline communications environments.

Current PLC devices compliant with Smart Grid requirements (HomePlug Green PHY and

G.hn Smart Grid profile) are based on multi–carrier modulations and TDMA schemes, which

is not valid for asynchronous transmission links. The thesis examines the performance of

some multiple–access techniques in asynchronous powerline communications environments

using long binary and complex–valued polyphase spreading sequences, instead of short

orthogonal codes due to their worse cross–correlation properties in asynchronous

environments. Moreover, ignoring the short–term variations, powerline frequency response

between two outlets may remain static for a time. So it is worth pointing out that when

successive symbols from the same user are spread with the same code for a set of users

within a relatively static channel situation, the interference signal seen by a receiver does

not change from symbol to symbol. Therefore, some users are at a disadvantage with

respect to others.

The performance of the single user detector symbol-level MMSE receiver in

asynchronous long sequences of DS-CDMA systems has been analysed and compared with

that of the MC-CDMA receiver by employing an interval guard in the form of a CP. The

performance analysis was based on the SGA method, and validated for a large number of

simultaneous nodes with Monte Carlo simulations under power line impulsive noise, and

using different kinds of long sequences. From the results of the analysis, the superior

performance rejecting the MAI of the single-carrier multiple–access technique in

asynchronous environments was shown. Monte Carlo simulations also confirmed the BER

bound due to impulsive noise. The achieved results have been published in [Val et al., 2010;

Val and Casajús, 2009]

An adaptive architecture is proposed for the practical implementation of the MMSE

receiver, which requires several parameters that are difficult to estimate from the receiver

side. The adaptive receiver is based on an FSE whose tap weights are updated by an adaptive

algorithm, having the capability of performing multiple-access interference and narrowband

noise suppression by taking advantage of the cyclostationary properties of the transmitted

signals; this requires the knowledge of fewer parameters compared with the MMSE and

RAKE receiver. Monte Carlo simulations revealed the good performance of adaptive FSE

receivers in asynchronous DS-CDMA systems compared with MC-CDMA and MC-DS-CDMA


171

systems, especially using polyphase long sequences. Two well-known pilot-aided NLMS and

RLS adaptive algorithms are examined. The latter suffers from power line impulsive noise,

and a fall in the tap weight update instability. Accordingly, an enhanced version of the RLS

algorithm less vulnerable to the impulsive noise is proposed. At high signal-to-noise ratio,

the MAI degrades the performance of the adaptive FSE receiver using binary long sequences,

whereas the power line impulsive noise prevails over the MAI when using polyphase long

sequences, which achieves the best performance in combination with the enhanced RLS

receiver. The adaptive algorithms show better tracking capabilities and good near-far

interference rejection with long polyphase sequences. The simulation results have been

published in [Val and Casajus-Quiros, 2008].

This thesis avoids complex joint detection techniques at the receiver, such as multi–

user detection and parallel interference cancellers, and focuses on single–user detection

techniques. Concerning single–carrier CDMA system, an MMSE receiver is selected due to its

advantage of ease of adaptation, since standard adaptive algorithms can be employed.

Within the Smart Grid framework, the computational complexity is an important factor.

However, there are smart implementations which can reduce the computational complexity

order of the RLS algorithms.

To summarize, the main contribution of this thesis is an adaptive FSE receiver

architecture based on an enhanced RLS algorithm in an asynchronous DS-CDMA system for a

powerline network under narrowband and impulsive noise. The classic RLS algorithm is

modified in order to improve its performance under powerline impulsive noise. On the other

hand, the DS-CDMA system is based on the use of long polyphase sequences, with which the

overall performance is enhanced. Thus, by means of the modified RLS-FSE algorithm (which

takes advantage of the cyclostationary properties of the signal) and long polyphase

sequences, the MAI and narrowband noise rejection is considerably improved in an

asynchronous network without any cooperation between the transmitting users.


172

8.2 FUTURE WORK

Some of the topics worthy of further research are highlighted as follows:

a) The work presented here does not take into account the time–varying behavior

of the powerline channel due to network changes. An analysis of the adaptive

algorithms performance tracking the frequency response variations might be

interesting.

b) In addition to user asynchronism, further work should research the

impairments due to time and frequency offset combined with the use of long

polyphase spreading sequences.

References

173

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Publications related to the thesis

Journal Publications

VAL, I. and F. J. CASAJUS-QUIROS, "Long polyphase sequences for adaptive MMSE detector in asynchronous CDMA PLC system," Electronics Letters, vol. 44, pp. 918-919, 2008.

VAL, I., F. J. CASAJUS-QUIROS, and A. ARRIOLA, "Performance analysis of asynchronous multicarrier code division multiple access against direct sequence code division multiple access and long polyphase sequences for uplink powerline communication systems with impulsive noise," Communications, IET, vol. 4, pp. 606-617, 2010.

VAL, I., and F. J. CASAJUS-QUIROS, " Performance analysis of MMSE receiver for asynchronous DS-CDMA using long polyphase sequences in powerline smart grid appliances under impulsive noise," Eurasip Journal on Advances in Signal Processing (Under revision).

Conference Papers

VAL, I. and F. J. CASAJÚS, "Performance Analysis of Asynchronous MC-CDMA Long Sequences for PLC Systems with Impulsive Noise," in WSPLC'2009, Udine (Italy), 2009, pp. 60-63.

VAL, I., F. J. CASAJÚS, J. BILBAO, and A. ARRIOLA, "Measuring and Modeling an Indoor Powerline Channel," in SPECTS'2007, San Diego (USA), 2007, pp. 521-526.

VAL, I. and F. J. CASAJÚS, " Long spreading sequences for asynchronous multiple-access systems in powerline smart grid appliances under impulsive noise," in SmartGridComm'2011 (Under revision).

Documents

UNIVERSIDAD POLITÉCNICA DE MADRIDoa.upm.es/8481/1/IÑAKI_VAL_BEITIA.pdf · entorno de una red de área de hogar, donde la robustez y fiabilidad del enlace de comunicación son un