Master Thesis-Ariadi Sulistyo

7/29/2019 Master Thesis-Ariadi Sulistyo

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UNIVERSITY OF DUISBURG-ESSEN

FACULTY OF ENGINEERINGINTERNATIONAL STUDIES IN ENGINEERINGMAJOR ELECTRICAL AND ELECTRONIC ENGINEERING

Master Thesis

Investigation of Space Time Block Codes

for Multipath Modeled Power Line Communication Channel

Ariadi SulistyoMatriculation Number: 2212012

Institute for Experimental Mathematics

Digital Communications GroupUniversity of Duisburg-Essen

April 24, 2008

Prof. Dr. -ir. A. J. Han VinckSupervised by: Anil Mengi, M.Sc
mailto:[email protected]:[email protected]:[email protected]:[email protected]:[email protected]:[email protected]


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i

Declaration

Herewith I declare that this thesis was composed by myself, using onlyliterature sources, and specified help tools. The work contained inside is myown, except which explicitly stated. This thesis, in same or similar form, hasnot been available to any audit authority yet.

Essen, April 24, 2008


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Acknowledgement

I would like to thank for Prof. Dr. -ir. A. J. Han Vinck for his advicesand comments, also his consistent encouragement for this thesis project. I amvery grateful to my supervisor, Mr. Anil Mengi M.Sc. for his advices, timeand his generousity for completing my thesis. His guidances and advices were

brightened my mind, and deepen my knowledge. Their support and spiritencouraged me to finish this work.

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Abstract

Powerline channel used to transmit the electricity is an alternative mediumto transfer the data. Unfortunately, by passing through the channel, dataare distorted by noises and fadings. Some examples of the noise occurred in

PLC are AWGN, impulsive noise, and narrowband interference. In this work,we investigate the performance of space time block codes to overcome thesefadings and different type of noises.

Space time coding is used to provide the diversity throughout the networkfor improving the reliability of data communication. It sends the duplicates ofeach symbol at the different time constant. Using the diversity, the character-istics of received data achieve high performance. In this thesis we assume thatthe PLC has perfect isolation between the channels. Because of this perfectisolation, the orthogonality of matrix block codes is not needed, and repetitioncodes in matrix block code can be used.

Influences of frequency non selective and frequency selective fading in spacetime coding play a major role in the transmitted data. With the same transmitpower, performances of STBC and SISO systems in the effect of Rayleighfading are compared. In PLC, instead of linear combiner used for STBC, therepetition coding with majority vote decoder is an alternative. Each combinerresults different BER characteristics. Using these two combiners, adaptivedecoder is built to enhance the reliability of the system.

Philipps channel model is used for representing the frequency selective fad-ing in PLC. The characteristics of data using SISO and STBC system insidethe Philipps channel are investigated. Frequency selective fading has a sig-

nificantly detrimental effect for transmitted data. By utilizing OFDM guardinterval and convolutional codes [177 133] the reliability of received data canbe improved.

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Contents

1 Introduction 1

1.1 Goal of The Thesis . . . . . . . . . . . . . . . . . . . . . . . . . 3

1.2 Organizational of The Thesis . . . . . . . . . . . . . . . . . . . 3

2 Space Time Block Codes 4

2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42.2 Noise Types in PLC . . . . . . . . . . . . . . . . . . . . . . . . 4

2.2.1 Additive White Gaussian Noise . . . . . . . . . . . . . . 42.2.2 Additive White Class A Noise . . . . . . . . . . . . . . . 52.2.3 Model of Fading Channel . . . . . . . . . . . . . . . . . . 6

2.3 Space-Time Transceiver . . . . . . . . . . . . . . . . . . . . . . 92.4 STBC Characteristics . . . . . . . . . . . . . . . . . . . . . . . . 102.5 Diversity Characteristic in Powerline . . . . . . . . . . . . . . . 112.6 PLC Space Time Block Codes . . . . . . . . . . . . . . . . . . . 12

2.6.1 Real Orthogonal Block Codes . . . . . . . . . . . . . . . 132.6.2 Orthogonality of Block Codes in PLC . . . . . . . . . . . 13

2.7 Detector . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152.8 Combiner . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

2.8.1 Linear Combiner . . . . . . . . . . . . . . . . . . . . . . 162.8.2 Repetition Coding with Majority Vote Decoder . . . . . 182.8.3 Adaptive Decoder . . . . . . . . . . . . . . . . . . . . . . 18

2.9 Modulator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 202.9.1 Pulse Amplitude Modulation . . . . . . . . . . . . . . . 20

2.9.2 Phase Shift Keying . . . . . . . . . . . . . . . . . . . . . 212.10 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

3 OFDM Principles 23

3.1 OFDM Orthogonality . . . . . . . . . . . . . . . . . . . . . . . . 243.2 Guard Interval . . . . . . . . . . . . . . . . . . . . . . . . . . . 253.3 OFDM-STBC Block Diagram . . . . . . . . . . . . . . . . . . . 263.4 Convolutional Coding . . . . . . . . . . . . . . . . . . . . . . . . 28

3.4.1 Encoder . . . . . . . . . . . . . . . . . . . . . . . . . . . 293.4.2 Decoder . . . . . . . . . . . . . . . . . . . . . . . . . . . 30

3.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

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CONTENTS v

4 Simulation Results and Analysis 32

4.1 Alamouti scheme . . . . . . . . . . . . . . . . . . . . . . . . . . 32

4.2 Linear Combiner . . . . . . . . . . . . . . . . . . . . . . . . . . 344.2.1 STBC with the Repetition Codes . . . . . . . . . . . . . 374.2.2 Repetition Coding with Majority Vote Decoder . . . . . 39

4.3 Adaptive Decoder . . . . . . . . . . . . . . . . . . . . . . . . . . 404.4 Guard Interval of STBC-OFDM . . . . . . . . . . . . . . . . . . 414.5 OFDM-STBC with the Convolutional Code . . . . . . . . . . . 434.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45


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List of Figures

1.1 PLC Applications in Home Appliances . . . . . . . . . . . . . . 11.2 PLC Network Distribution from Medium to Low Voltage . . . . 2

2.1 AWGN, Impulsive Noise and Symbol duration . . . . . . . . . . 52.2 Frequency Distribution of Frequency Non Selective or Flat Fading 72.3 Frequency Distribution of Frequency Selective Fading . . . . . . 72.4 Multipath Model by Holger Philipps . . . . . . . . . . . . . . . 82.5 Transfer Function of Philipps Model . . . . . . . . . . . . . . . . 92.6 PLC 3 Phase Encoder Block Diagram . . . . . . . . . . . . . . . 102.7 PLC 3 Phase Decoder Block Diagram . . . . . . . . . . . . . . . 102.8 Spatial diversity in PLC Channel . . . . . . . . . . . . . . . . . 122.9 PAM Decision Diagram on Gray Coding . . . . . . . . . . . . . 152.10 Minimum distance of the PSK Constellation . . . . . . . . . . . 16

2.11 Linear Combiner Scheme . . . . . . . . . . . . . . . . . . . . . . 162.12 Repetition Code Combiner Scheme . . . . . . . . . . . . . . . . 18

3.1 Bandwith utilization in FDM and OFDM . . . . . . . . . . . . . 243.2 OFDM intersymbol interference with Cyclic Prefix (CP) . . . . 253.3 Block Diagram of OFDM-STBC Transmitter . . . . . . . . . . . 273.4 OFDM-STBC Receiver Structure . . . . . . . . . . . . . . . . . 273.5 Circuit of generator sequences [177 133] . . . . . . . . . . . . . . 293.6 Trellis diagram of Viterbi decoding . . . . . . . . . . . . . . . . 303.7 Path sequence of Viterbi decoding . . . . . . . . . . . . . . . . . 30

4.1 Block Diagram of Alamouti Scheme under Rayleigh Fading andAWGN . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

4.2 BER performance of STBC-Alamouti scheme, Uncoded Coher-ent, MRRC in Wireless Rayleigh Channel . . . . . . . . . . . . . 33

4.3 Block Diagram of PLC STBC 3 Channel System . . . . . . . . . 344.4 BER performance of Uncoded Coherent and STBC Demodula-

tion in AWGN Channel . . . . . . . . . . . . . . . . . . . . . . . 354.5 BER performance of Uncoded Coherent and STBC with AWGN

in Rayleigh Fading Channel . . . . . . . . . . . . . . . . . . . . 354.6 BER performance of Uncoded Coherent and STBC with Class

A Noise Channel . . . . . . . . . . . . . . . . . . . . . . . . . . 36

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LIST OF FIGURES vii

4.7 BER performance of Uncoded Coherent and STBC in AWCNand Rayleigh Fading Channel . . . . . . . . . . . . . . . . . . . 36

4.8 BER performance of Uncoded Coherent and STBC-RepetitionCode in AWGN Channel . . . . . . . . . . . . . . . . . . . . . . 37

4.9 BER performance of Uncoded Coherent and STBC-RepetitionCode with AWGN and Rayleigh Fading Channel . . . . . . . . . 38

4.10 BER performance of Uncoded Coherent and STBC-RepetitionCode with Class A Noise . . . . . . . . . . . . . . . . . . . . . . 38

4.11 BER performance of Uncoded Coherent and STBC-RepetitionCode with Class A Noise and Rayleigh Fading . . . . . . . . . . 39

4.12 Block Diagram of Repetition Coding With Majority Vote De-coder . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40

4.13 BER performance of Linear Combiner and Majority Vote De-coder for Repetition Coding in in AWCN and Rayleigh FadingChannel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40

4.14 Block Diagram of Adaptive Decoder System . . . . . . . . . . . 414.15 BER performance of Adaptive Decoding in in AWCN and Rayleigh

Fading Channel . . . . . . . . . . . . . . . . . . . . . . . . . . . 424.16 OFDM Transmitter Block Diagram . . . . . . . . . . . . . . . . 434.17 OFDM Receiver Block Diagram . . . . . . . . . . . . . . . . . . 434.18 BER performance of OFDM in AWCN and Frequency Selective

Philipps Model . . . . . . . . . . . . . . . . . . . . . . . . . . . 44

4.19 Convolutional Coding Encoder . . . . . . . . . . . . . . . . . . . 444.20 Convolutional Coding Decoder . . . . . . . . . . . . . . . . . . . 454.21 OFDM STBC with Convolutional Coding [177 133] . . . . . . . 45


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List of Tables

2.1 Set parameters of echo model . . . . . . . . . . . . . . . . . . . 8

4.1 OFDM Simulation Parameters . . . . . . . . . . . . . . . . . . . 42

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Chapter 1

Introduction

Increasing demands on the internet and data communication make PowerlineCommunication as an alternative to transfer data. This inherent network isalready built which reduces the start up and installing cost. Its applicationsare at the household. Beside as Local Area Network (LAN), there are also ascommunication medium for controlling electrical units. Another application isa hybrid system which connects power line with the wireless application.

Figure 1.1: PLC Applications in Home Appliances

Since the powerline aimed to carry the electricity, it has also different phys-ical characteristics than the other wireline medium, phone line, DSL and wire-less. Current flows through the physical cable which is unshielded and un-twisted. Therefore, there can be any interference with the radio environment.If the cable is modulated, the unconditionally generated electromagnetic fieldis affecting the cable to act as antennas. Avoiding this interference, data are

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CHAPTER 1. INTRODUCTION 2

modulated by low to medium frequency. However, to modulate data with thehigh frequency, it depends on the technology used.

Figure 1.2: PLC Network Distribution from Medium to Low Voltage

Powerline is the most noisy wireline channel. The noises in powerline con-

sist of background noise, impulsive noise which comes from the householdequipment, and narrowband interference. Depend on the environment andphysical condition of powerline cable, transmitted data propagate throughdifferent path in the channel. This multipath propagation originated fromthe reflection and transmission coefficient, also characteristic impedance andmatching of the powerline channel. Using theoretical and empirical analysis,multipath model of PLC have been investigated in [6], [15], [7].

Space time block coding was first introduced by Alamouti [1] to providethe diversity of the channels in wireless communication. The basic idea isto send data and its replicas into the receiver. It uses different transmit and

received antenna at different time constant. It takes the advantage of transmit,receive, space and time diversity. Since the powerline has only three differentand independent channels to transmit data, the number of transmitter and thereceiver are the same values: three. Some works on space time block codingfocusing on reducing error rate have been proposed by [4], and [3]. Others, isproposed for OFDM and channel capacity by [5]. Especially in powerline, thecombination of space time block coding with convolutional coding as forwarderror correction (FEC) provides coding gain can result better performancethan without FEC.


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CHAPTER 1. INTRODUCTION 3

1.1 Goal of The Thesis

This master thesis addresses the application of space time block codes in pow-erline communication channel. We simulate and analyze the error rate charac-teristics of STBC in the case of PLC noises and fadings, in comparation withSISO system. Other contribution is investigation of concatenation betweenSTBC and convolutional coding as forward error correction. Then we analyzethe performance of simulation result.

1.2 Organizational of The Thesis

This thesis consists of 5 Chapters. Chapter 2 addresses to define concept and

basic of STBC, noise types, and receiver structure used in the thesis. Chapter 3discuss about OFDM used for STBC that introduces also convolutional codingas a simple forward error correction. Chapter 4 examines the simulation resultsof system built. And the Chapter 5 concludes the works and indicates futuredirections of next research based on this thesis.


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Chapter 2

Space Time Block Codes

2.1 Introduction

In this chapter, the criteria about design and analysis space time block codes(STBC) in PLC are presented. In order to get an understanding about PLCimplementation of space time coding, we introduce first the channel problems,interferences and fadings. PLC noise model is defined for realizing the channelcharacteristics. It is added to the path gained signal. Path gains are simulatedto have the characteristics of flat Rayleigh fading, and frequency selectionfading, e.g. Philipps model. Second, diversity characteristics of STBC and

the orthogonality are presented, as the implementation in PLC. There is alsoshown that non-orthogonal STBC is the same as repetition codes. Third, thedecoders used in the simulation are defined. There are 3 type of decoder usedin this thesis. The linear detector where data directly come from the linear3-phase combiner, the majority vote decoder using single detector in each 3-phase, and the adaptive decoder, which is the combination between the linearcombiner and majority vote decoder.

2.2 Noise Types in PLC

Physical environment factors cause several PLC noises and disturbances. Sev-eral noise characteristics are modeled. In this thesis, the AWGN and AWCNmodel are used. Below are the characteristics of the noises and fadings.

2.2.1 Additive White Gaussian Noise

Additive White Gaussian Noise (AWGN) is a Gaussian distributed white noisewhich is overlaid with the signal used. The white noise itself has equal powerin power spectral density of any band, and any spectral frequency. The proba-bility density function (pdf) of this Gaussian or normally distributed random

variable is:

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CHAPTER 2. SPACE TIME BLOCK CODES 5

p (x) =1

2exp(xmx)

2/22, (2.1)

where mx is the mean and 2 is the variance of the random variable x. There-

fore, pdf of the function is symmetry about its meanmx. The AWGN is appliedas a model for background noise, interference and many communication noisemodels.

2.2.2 Additive White Class A Noise

Additive White Class A Noise (AWCN) or Middleton Class A Noise is a modelof noise combination between Gaussian noise and impulsive noise. The impul-

sive noises are produced by the household electrical equipments. Time constantfor AWCN is very short, compared to the symbol duration of AWGN. AWCNhas also high amplitude, and it can distort the transmitted data. The dura-tion between AWGN, impulsive noise and symbol duration can be illustratedas [22]:

Figure 2.1: AWGN, Impulsive Noise and Symbol duration

To describe about the noise, the probability density function used is [10]:

p(x) =

1

2

m=0

1

2mmexp |x|222m , (2.2)

where m = eAAm

m!, 2m =

2 (m/A)+T1+T

, and 2 is the total variance of the

AWCN noise, i.e. 2g +2i . T=

2g2i

is coefficient of AWGN variance component

to impulsive noise variance component. On the impulsive index A, if the A issmall (e.g. A = 0.1), then the noise is highly impulsive, and if the A is high(A ) then the pdf of Class A becomes Gaussian.

In the representation, a noise sample n can be expressed as [14] [5]:

n = xG +Ky. (2.3)


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where xG is a white Gaussian background noise sequence with zero mean andvariance 2G, K is the statistically independent Poisson distributed random

sequence whose pdf is characterized by A (the mean value of Poisson distri-bution), and y is the white Gaussian sequence with zero mean and variance2i /A.

2.2.3 Model of Fading Channel

The main utilization of powerline is to distribute energy. However, for datacommunication, PLC is unfavourable because of varying impedance, variousnoises and high attenuation. In the PLC fading situation, data are not trans-mitted via direct line of sight path. They are reflected, scattered and refracted

that are causing distortion. These transmitted data are arriving at the receiverwith the varying amplitude and phase at the different time constant. Unlikewireless channel, the multipath fading in PLC depends on the reflection andtransmission factor of the channel branch and impedance characteristic of thecable. To model the fading, each channel is divided into the number of N-paths. Each path j of the channel, have an attenuation factor j, phase j ,and delay (t ).

Complex attenuation factor of each path can be defined in time domain as[6]:

v = |v| .ejv , (2.4)

where : v = arctan Im{v}Re{v}.The transfer function of the channel occurs in time domain. It is the

cumulative form of the number of all N dirac pulses which are multiplied byv and delayed by v:

h (t, ) =Nv=1

|v| .ejv .(t v) . (2.5)

Channel characteristics are also depend on the frequency range used. Infrequency used 2-30 MHz, and at Low Voltage (LV), there are many power-

line channel model proposed, such as in [15] and in [6]. From their researchand empirical analysis, the channel characteristics parameters, such as trans-fer function H(f) and noise N(f) are obtained. These parameters dependenvironmentally on the frequency used, time and location.

The channel response in the frequency domain is the Fourier transformationofh (t):

H(f) = F {h (t, )} H(f) =Nv=1

|v| .ejv .ej2fv . (2.6)

The transfer function is composed from real part and imaginer part, whichrepresents sinus and cosines wave oscillation. Each oscillation is attenuated and


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is subject to a constant phase shift. The multiplication between attenuationfactor and the phase shift form a path gain .

Based on the bandwidth used between the channel and the frequency ofthe signal, the fading can be categorized as two type, frequency non selectivefading and frequency selective fading. Frequency non selective fading also saidflat fading happens if the frequency range used in the signal is smaller thanthe coherent bandwidth of the channel. It means that the time duration ofthe signal is greater than the coherent time duration of the channel. On theother side, the frequency selective fading happens when the signal frequencyis bigger than the coherent bandwidth of the channel. Coherent bandwidthof the channel itself can be obtained from inverse of central limit delay ofthe channel, where central limit comes from the average delay duration on

the channel. Due to this correlation, coherent bandwidth can be said as afrequency range over channel fadings are correlated [20].

The illustration of flat fading and frequency non selective fading are shownbelow [21]:

Figure 2.2: Frequency Distribution of Frequency Non Selective or Flat Fading

Figure 2.3: Frequency Distribution of Frequency Selective Fading

To model the transfer function H(f), the Rayleigh fading and the Philippsmodel are investigated in this thesis.


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Rayleigh Fading

Rayleigh fading is a statistical model for the fading channel caused by multi-path. If given N-different path, the complex numbers contain in phase partsand quadrature parts are occurred. The fading modeled based on the assump-tion that the magnitude of a signal has flown through a transmission mediumvary randomly as Rayleigh distribution. Rayleigh fading is defined as flat fad-ing because, the bandwidth of data transmitted is smaller than the coherentbandwidth of channel. As a model of PLC channel, Rayleigh fading has nodominant of path gain along line of sight propagation.

Philipps Model

Another fading is multipath model which was introduced by Philipps [6]. Thismodel has a number of 5 paths in each channel. The parameters of each delaytime v is:

No. || in rad in s1. 0.151 0.691 0.1102. 0.047 -0.359 0.1543. 0.029 0.591 0.2054. 0.041 2.913 0.3115. 0.033 1.012 0.427

Table 2.1: Set parameters of echo model

The multipath system model used is 5 path or taps that represented on eachchannel:

Figure 2.4: Multipath Model by Holger Philipps

Within 1s, nearly the total amount of energy of the transmitted datareach the receiver. As it shown, the biggest complex attenuation factor is


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only 10 percentages of the original data, and the total complex attenuationnumber equals 0.201. This means the symbol energy transmitted remains only

20%, and it is far from unity. The transfer function and angular frequency ofPhilipps model are illustrated as:

Figure 2.5: Transfer Function of Philipps Model

From the characteristic above, Philipps has modeled a channel with the lossycharacteristics where the transfer function is around -10 dB and at the deepfade, it can be more than -30 dB. Therefore, the attenuation factors of thePLC channel are very high.

2.3 Space-Time Transceiver

At PLC, data in STBC are allocated into the block size where data and itsreplicas are contained in each block size. As in [2], there is two advantage in

the orthogonal matrix structure.

There is no loss in bandwidth. Orthogonal design provide maximumtransmission rate at the full diversity.

The decoding algorithm uses maximum likelihood decoding, which issimpler than other decoding algorithms regarding utilization in the or-thogonality of the columns of the orthogonal design.

The encoding system is composed as follows, the serial data are encoded andfed to modulator. Real number modulation (PAM) and complex design (BPSK

and QPSK) are applied. Modulated data are then fed into STBC block encoderto transmit by different transmitter point, Tx1, Tx2, Tx3. In the channel, data


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are disturbed by the impulsive noise and attenuated by the fading. Descriptionof encoder block diagram is shown as:

Figure 2.6: PLC 3 Phase Encoder Block Diagram

In the receiver, received data are combined with the linear combiner, de-tected, and demodulated by the PAM and PSK demodulator. The diagramblock of the decoder system is arranged as follows:

Figure 2.7: PLC 3 Phase Decoder Block Diagram

The art of detecting and combining is different, depends on 3-phase lineardetector or majority vote decoder. They will be explained in another section.

2.4 STBC Characteristics

This section is especially progressed for describing the powerline system with

space time block codes. First, parameters used for describing the terms onspace time in PLC are:

n : number of transmitter points, which is equal to m, the number ofreceiver points.

i,j : coefficient of the path gain from the transmitter point i to thereceiving point j. Criteria for i and j are 1 i N, 1 j M. Thepath gains are modeled as samples of independent complex Gaussianrandom variables with the variance 0.5 per real dimension. The channelcharacteristics are assumed quasi-static [6], so the path gains are the

same at one frame, and vary from one frame to another frame.


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l : length of the block codes.

cit : transmitted data at time t, 1 t l, from the transmitter i,

1 i n. rit : received data at time t, 1 t l, at the receiver j, 1 i m. it : noise samples in the channel. They are a complex random additive

white Class A noise which is identically and independently distributed(i.i.d).

The channel models for received data, are described on the equation below.Concentrating on perfect channel estimation, which means the path gains i,i

are known, interferences are it. The receive data at the receiving point r

it are

[2]:

rit =nt=1

i,icit +

it. (2.7)

At each time slot t sent data are cit, which are sent to the each n transmittingpoint, i = 1, 2, 3, n , . . .. Therefore, overall data sent at each time constant arec11, c

21 . . . , c

n1 , . . . c

nl .

The recovered data are obtained by minimizing the sum of decision metric.They are computed by:

lt=1

mj=1

rjt ni=1

i,icit

2

. (2.8)

2.5 Diversity Characteristic in Powerline

As a part of communication system, the processes are divided into transmitter,channel and the receiver. In PLC, the path gain of the channel can be obtainedby transmitting the independent data through each channel simultaneously.

Each path gain of the channel is assumed to be estimated coherently. Thespace time block coding system distributes the data into different time interval.Data and the replicas are sent through different transmitter point Txi. Thisrepresents a temporal diversity, because they are sent at the different time slot.But it is not considered as bandwidth efficient, since the replicas are also sent.

At the receiver, transmitted data from different channels are combinedlinearly. The signal energy of the data increases because of the path gain. Thereceiver will decode the received data reliably by using the minimum distanceof the maximum likelihood decoder at the combiner.

Another diversity method introduced is about using the multiple transmit-ter and receiver, which is called spatial diversity. Spatial diversity is used forchannel multiplexing. In PLC the terms the transmitting point and receiving


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point are used as a change of wireless antennas. Since it is the wireline channel,criteria of spacing between multiple antennas as in wireless, are not needed.

Unlike the wireless system, the powerline communication system has limi-tation in diversity. Those limitations are [4]:

Since the functionality of powerline is transferring the electricity, andalso it has three phase which are isolated to each other, then the eachchannel in powerline has independent correlation between each other.

The isolation makes no correlation within each symbols of block codessent in each different channel.

The independent noise and fading happens at each channel, and channels

are corrupted with the additive white Class A noise, caused by switchingtransient and noise in cables.

With the above reasons, the diversity in the powerline communication can-not reach the full diversity. It can only reach the number of diversity equal tothe total number of the channel, which is three.

The description for the diversity in powerline is illustrated as:

Figure 2.8: Spatial diversity in PLC Channel

2.6 PLC Space Time Block CodesOn the space time coding, the representation of the block codes are definedby G, the p x n matrix. Entries of real orthogonal matrix are the linearcombinations of the symbol sent, x1,x2,x3,...,xk, and at the complexmatrix, it also includes on the conjugates, x1, x

2, x

3,...,x

k. A detail description

about the orthogonal matrix block code, has been presented by [2]. It usesHurwitz-Radon matrix, a set of real dimensions for which the orthogonal designexists. Since powerline have only 3 coupling channel to transmit the data, thereal orthogonal matrix used is 4x3.


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2.6.1 Real Orthogonal Block Codes

Orthogonal block codes first used for this thesis are the real orthogonal blockcodes. The real orthogonal matrix design 4x3, G is:

G3 =

x1 x2 x3x2 x1 x4x3 x4 x1x4 x3 x2

(2.9)Entry matrix G above proves the orthogonality, that GTG = D where D is

the diagonal matrix with value at Dii. The diagonal matrix itself has a value ofDii = (li1x21 + li2x22 + ...+ likx2k), where i is path series, i = 1, 2,...,n, and pathgain coefficients l

i

1, li

2,...,li

k are the positive integers.Since one symbol on the modulation has a size of 2b, the transmission ratefor the modulation is represented by b bits per second per Hertz (bps/Hz).The number of data that will be encoded as symbol s1, s2, s3, , sk in oneblock matrix is kb bits. It is defined that symbol xi = si, at time t = 1, , p.Symbols sent are in time slot t, Gt1 Gtn.

At the first time slot, we send G11 = x1 via phase 1, G12 = x2 via phase2, and G13 = x3 via phase 3. At time t = 2, data in the second row, G21 =x2, G22 = x1, and G21 = x4 are sent, and continue until Gpn. Thereforetotal possible bits sent on one block are pb, and it is said that the rate R forthe coding scheme is kb/pb, that equals to k/p. Since in this simulation weintroduce 4 PAM as the modulation scheme, then the rate for coding used isone.

2.6.2 Orthogonality of Block Codes in PLC

As a criteria described on the real orthogonal block codes above, GTG = D, itcan be adapted by powerline. Because of the diversity reasons described, thespace time block codes in PLC have no differentiation between non-orthogonaland orthogonal design, even if the matrix block codes reaches full diversity,by counting the rank and determinant. However, to investigate and simu-

late the block codes in PLC, the orthogonal and non-orthogonal block codes,respectively repetition codes are the same. The proposed details of the non-orthogonal matrix block code in 3 phases are:

G3LC =

x1 x2 x3x2 x1 x4x3 x4 x1x4 x3 x2

(2.10)

In our simulation, the matrix block codes G3

LC is used for block codeswith linear combiner (LC) scheme at the receiver. As orthogonality criteria D


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explained above, a matrix L is categorized as orthogonal design ifLLT = LTL= (x21 + x

22 +

+ x2n) I. Subject to the absence of cross correlation between

each symbol at the channel, the condition of the channel fulfills the criteria of:

xixj =

0, i = j.

C, i = j.(2.11)

Formula above means that each symbol which is multiplied by another symbol,equals to zero, whereas if it is multiplied by the same symbol is equals to aconstant. Under PLC conditions, a matrix block codes GLC is searched for itsorthogonality GLCG

TLC as:

GLCGTLC =

x21 + x22 + x23 0 0 0

0 x21 + x22 + x

24 0 0

0 0 x21 + x23 + x

24 0

0 0 0 x22 + x23 + x

24

(2.12)

and also for verifying the GTLCGLC, as:

GTLCGLC =

x21 + x

22 + x

23 + x

24 0 0

0 x21 + x22 + x

23 + x

24 0

0 0 x

2

1 + x

2

2 + x

2

3 + x

2

4

(2.13)

Showing the proven for non-orthogonal codes for LC above, we have aconclusion that the repetition coding can be built as a block codes. As G3RCrepresents the repetition codes (RC), it shows that at each time slot, oneidentical symbols is transmitted 3 times via 3 different channels. Therefore,the matrix proposed for repetition block codes is:

G3RC =x1 x1 x1

x2 x2 x2x3 x3 x3x4 x4 x4

(2.14)Looking at the diagonal matrices above, we have different result in the time

processing to recover the data. With the same rate R=1, for the repetitioncodes, we can obtain the restored data directly, after the sending at timet, without waiting for entire block codes. This reduces the complexity ofcomputation. It is better than the orthogonal and non-orthogonal block codes,G3 and G3LC, since the transmitted data can only be processed until all symbolsin the matrix block codes are received.


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2.7 Detector

Before going through the combiner section, the detector should be discussedfirst. At the last stage of the receiver, the maximum likelihood decoder (MLD)is used for decoding the symbol received. For all possible symbols transmitted,the most likely received data to one symbol is decoded.

The likeliness is measured through the minimum distance of the symbolreceived to the symbol of the modulator constellation. Hence the measurementis formulated by equation (2.15):

si = argminsSM

|Ri s|2 +

1 + |1,1|2 + |2,2|2 + |3,3|2

|s|2 . (2.15)

The value of received symbol Ri is gained by the each path gain coefficient1,1, 2,2 or 3,3, where each path gain is independent, and depends on thefading inside the channel.

In this thesis we use 4-PAM constellation to represent the 4 real symbols.The 4-PSK modulation is utilized to represent the 4 complex symbols. In theQPSK, because the energy of each symbol is the same, then the second termof decoder is not needed. The equation for decoding the 4-PSK modulation isthen built as:

si

= argminsSM |

Ri s|2 . (2.16)

At the last stage of the receiver, the decision diagram for the 4-PAM con-stellation which represented by Gray coding is described below:

Figure 2.9: PAM Decision Diagram on Gray Coding

where s are 3,1, 1, 3.For QPSK modulation, the original symbols used s are complex numbers.

They are: s1 = 1 + j0, s2 = 0 + j1, s3 = 1 + j0, and s1 = 0j1. The illus-tration of minimum distance for maximum likelihood decoding at each symbolarea, where the received data are weighted by path gain can be describedas:


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Figure 2.10: Minimum distance of the PSK Constellation

2.8 Combiner

As proposed on the Alamouti paper [1], the combining technique at the receiverwhich is used for improving the signal quality will resolve the signal againstthe distortion and provide the diversity order. In the simulation, the channelsare perfectly estimated. To set the combining signals that transmitted throughthe different phases at the different time slots, 2 different combining schemesare used. One is the linear combiner, and the other one is the repetition codingwith the majority vote decoder.

2.8.1 Linear Combiner

The scheme used for linear combiner is described by:

Figure 2.11: Linear Combiner Scheme


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At the front end of receiver, transmitted data are distorted by noise andfading. They will be multiplied by the estimated channel gains. After mul-

tiplied by channel gains, each data received from different channel are thencombined in the combiner in order to get the original symbol. The result willbe sent to the maximum likelihood detector and decided.

The implementation of decision metric will be minimized as:

|r11 1,1c11|2 |r21 2,2c21|2 |r31 3,3c31|2

|r12 1,1c12|2 |r22 2,2c22|2 |r32 3,3c32|2

|r13 1,1c13|2 |r23 2,2c23|2 |r33 3,3c33|2

|r14 1,1c14|2 |r24 2,2c24|2 |r34 3,3c34|2

(2.17)

The decision variables to be detected by the maximum likelihood detector aredefined by Ri, 1 i 4. This maximum likelihood detector combines thereceived data to find the most likely transmitted data vector. R1 appropriatesto x1, R2 appropriates to x2, R3 appropriates to x3, and R4 corresponds to x4.With the received matrix rit, and path gain , the combiner operates as:

R1 = r111,1 + r222,2 + r333,3 , (2.18)R2 =

r12

1,1 + r

21

2,2 + r

34

3,3

, (2.19)

R3 =r13

1,1 + r

24

2,2 + r

31

3,3

, (2.20)

R4 =r14

1,1 + r

23

2,2 + r

32

3,3

. (2.21)

And the combiner with the repetition code matrix is:

R1 =r11

1,1 + r

21

2,2 + r

31

3,3

, (2.22)

R2 = r121,1 + r222,2 + r323,3 , (2.23)R3 =

r13

1,1 + r

23

2,2 + r

33

3,3, (2.24)

R4 =r14

1,1 + r

24

2,2 + r

34

3,3

, (2.25)

and with Ri, recovered data are decided among all the constellation symbolss. To maximize the likelihood function, the receiver has to find the optimumtransmitted data, which minimizes the relation

Mm=1 |r sm|2, where M

equals to the number of symbol used.


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2.8.2 Repetition Coding with Majority Vote Decoder

In this scheme, the receiver is assumed to have 3 ML decoders. Each 3-phases ismounted by one ML detector. Therefore, the estimation is taken individuallyon each vector received. After detection, the data recovered are comparedbetween the first, second and third phase. The majority symbol decoder takesdecision for the correct decoding through majority symbol received by thephases. In this case, numbers of errors detected are two, and numbers oferrors corrected are one. In the situation that there is no majority symbolreceived, a minimum value between these three symbols received is chosen.Optimum symbol criteria at the detector at one phase are depending on pathgain, noise, and data itself, and defined by:

si = argminsSM |Ri s|

2

+ 1 + |j,j|2 |s|2 , (2.26)where i = 1, ,M, and j are the number of channels, j = 1, 2, 3. Using themodulation PSK in the simulation, the proposed scheme [4] is:

Figure 2.12: Repetition Code Combiner Scheme

2.8.3 Adaptive Decoder

In the linear combiner, because of low SNR, data energy are weakened byAWCN. The received data in the combiner Ri are then weighted by path gain,and they are added by the noise. In the repetition coding, the receive dataare compared with the other two channel at the same time interval. In thissituation we have three decision symbols. If the absolute data energy of the

symbol at a channel is low, or data is broken, then the result is depend on thesymbols from two other channels.


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At the higher SNR, the linear combiner performs better, because signalenergy is high enough to overcome the Class A noise. Therefore, the probability

of received data at high SNR is higher than majority vote decoder.Adaptive decoder, a scheme proposed by Honary [4] is built for obtain-

ing better characteristic in detection. The decision vectors of linear combinerand repetition coding decoder are made based on the noise component, whichmakes high amplitude data restored. Detector decides one out of two schemeused through a predefined threshold. The threshold is obtained by taking aver-age power through observation of pilot data. The received energy of incomingdata are divided by the total number of pilot data. If the noise margin isgreater than threshold, the detector chooses the output from majority votedecoder, else, the detector chooses the output from the linear combiner. Ob-

tained from experiment results, it can be concluded that majority vote decoderhas lower BER characteristics at the lower SNR, whereas the linear combinerat high SNR.

In the influence of Class A noise, the received data vectors are smaller thanthe noise vector of the channel:

i,isit it rit = it. (2.27)

For detecting the received symbol, the received power |rit|2 is comparedwith the average power of symbol received.

To define the threshold, the parameters used are [4]:

p = number of time slot on block codes used, in block codes used equalsto 4.

n = number of transmitting phases, equals to 3. Le = number of blocks p used for noise estimation, they are functioned

as training period.

T0 = threshold power.

ITR = Impulse to threshold power ratio.

Algorithm for the adaptive decoding is constructed as:

1. During the transmission of Le blocks of data calculate PI and the to-tal average received power (PAVG) for t = 1, 2, . . . , p , . . . , Le, and i =1, 2, . . . , n:

ifri+1t 2 > |rit|2 set ri+1t 2 = PI.

else set |rit|2 = PI.(2.28)


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(store PI replacing the previous stored value.)

PAVG|t=1 = |r11|2

+ |r21|2

+ |r31|2

,PAVG|t=2 = |r12|2 + |r22|2 + |r32|2 + PAVG|t=1 ,PAVG|t=Le =

r1Le2 + r2Le2 + r3Le2 + PAVG|t=Le1 .(2.29)

2. At the end of the training period (Le), computes:

T0 =PAVG|t=LeLe.p.n

, (2.30)

and

Noise Margin =PIT0. (2.31)

If (Noise Margin > ITR) data are taken from an output symbol atthe RC majority vote decoder.If (Noise Margin < ITR) data are taken from an output symbol atlinear combiner detector.

Although a proper selection of T0 and ITR can be made from channelmeasurements and modeling, it has been found that choosing T

0

equals to theaverage power of all the signals received during the transmission ofLe blocksof data and ITR = 10, yields good result.

2.9 Modulator

In this thesis, for generating modulated symbols from the binary data, weuse real and complex symbol modulation. They are 4-PAM and 4-PSK. Weuse Gray code to represent the binary, because it is less susceptible to noise,because the adjacency between the constellation points differs only one bit at

each symbol. The modulator counts the signal energy of the data. In orderto distribute the energy signal to the system, the each signal energy has to beone.

2.9.1 Pulse Amplitude Modulation

Pulse Amplitude Modulation, PAM, is a real modulation. This scheme rep-resents 2 bits per one real symbol. The constellation in M-ary PAM signal isdescribed in one dimensional signal point. There is [9] :

sm = 12EgAm,m = 1, 2, 3,...,M. (2.32)


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The Eg is an energy of the basic signal pulse g(t). With M=4, the amplitudevalue of each point is as follows: A1 =

3, A2 =

1, A3 = 1, A4 = 3. Each

4-PAM point has the value ofEs which is equal to 35Eg. Es is the energy persymbol of the signal. To count average energy signal transmitted, we sum all ofeach Eg divided by the total number of symbol in the signal. The probabilityof symbol error rate for the 4-PAM signal if transmitted in the noisy channelis formulated by [9]:

P4 =6

4Q

d2EgNo

, (2.33)

where No is the noise energy, and the value of Pb depends on P4 divided k.k is log2 (M). Since Eb =

Eslog2M

, the value of SNR is EbNo

and 2 = No2

, hence

in the simulation we take the variance for Gaussian noise is1

2SNR , with eachPAM symbol energy are divided by 5.

2.9.2 Phase Shift Keying

To represent the complex signal, 4-PSK is used in the simulation. This mod-ulation scheme differs its phase by 90 degrees for each symbol changes. In theconstellation points, PSK is represented by 4 equispaced points around thecircle. The points are divided by in-phase (I) and quadrature component (Q).This recalls that on interval T in the vector representation, each symbol isdescribed as:

sm =Escos

2

M(m 1)

Es,sin

2

M(m 1)

(2.34)

where Es is the energy per symbol whose value is log2 (4)Eb. Eb is the energyper bit. With the noise applied to the signal sm, it changes the decision vector.The probability of symbol error rate of the modulation:

PM 2Q

2Es

Nosin

M

, (2.35)

and hence, the probability of bit error rate is :

PbM 2

log2MQ2log2MEb

No,sin

M

(2.36)

and so we get the probability of bit error rate for M = 4:

Pb4 Q

2EbNo

. (2.37)

In the given EbNo

we get the variance of the Gaussian noise for each I and Q

component in the simulation is 2 = No2Eb

or 2 = 12SNR

. At the last stage

demodulator, the maximum likelihood detector has the minimum distance ofPSK constellation.


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2.10 Summary

After seeing the theory and arguments above, it can be summarized that theorthogonality in matrix block codes of STBC is not needed. It is because ofindependent autocorrelation in each channel, and no cross correlation withother channel. Therefore the repetition codes as a matrix block codes can beused. As the repetition codes are used, the combiner structure at receiver hasto be changed.

For having a good BER performance and simpler decoding scheme, the rep-etition coding with majority vote decoder can be considered. Using receivedsignal power, adaptive decoding is built to choose the combining scheme, be-tween linear combiner and majority vote decoder. In order to have the same

total power in the simulation, signal energy should be adjusted to unity. Theconstellation of modulation scheme is important to contribute on this signalenergy.


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Chapter 3

OFDM Principles

Orthogonal Frequency Division Multiplexing (OFDM) is a modulation via mul-ticarrier. The motivation of OFDM is to utilize the available bandwidth bymultiplexing the numbers of N-multicarrier frequency, so the high speed par-allel data transmission can be reached. OFDM system originated from theFrequency Division Multiplexing (FDM). The difference from FDM, is thatOFDM effectively uses the spectral efficiency on the modulated data. This ef-ficiency will develop into the orthogonality between the subcarriers. In FDM,frequency guards are used as a protection from interference between subcar-riers. The large spectral bandwidth is then needed. Contrary, in OFDM,the orthogonality between signal subcarriers are utilized for preventing this

interferences. It will need then on the implementation of frequency and timesynchronization.

In the OFDM, STBC used in the transmission of the digital OFDM sym-bols and its replicas for improving the diversity needs. OFDM is using inversefast Fourier transform (IFFT) to change its frequency domain to the time do-main. OFDM can effectively overcome the frequency selective fading becauseof bandwidth distribution of carriers. The motivation that OFDM used in thisthesis is for investigating the effect for realizing of multipath fading and noisechannel at transmitted data, and the BER characteristics of received data.

OFDM applies as the standard of 4G in wireless systems. It is imple-

mented in the DAB, Digital Audio Broadcasting, and application in sendingthe multiple radio carriers in one OFDM signal. Another implementation is inthe IEEE 802.11a, about the wireless LAN. In the powerline communication,it is functioned as a standard for modulation in powerline devices to extendEthernet connections in the housing area due to the power wiring.

In other to obtain a better solution to the Space Time Coding, this chapterdescribes first about the basic of OFDM signal, the orthogonality of the fre-quency multiplexing. Second, the problems in intersymbol interference (ISI)and intercarrier interference (ICI) will be introduced. At the last, the STBC-OFDM with convolutional coding as forward error correction (FEC) proposed

will be explained.

23


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CHAPTER 3. OFDM PRINCIPLES 24

3.1 OFDM Orthogonality

OFDM allows transmission of multiple signals without interference. Orthog-onality of FDM correlates the multicarrier signals being mutual independentin frequency domain. If a set of OFDM complex signal waveform is given by[16]:

sk (t) =

1Tsejkt, for t [0, Ts] ,

0, otherwise,

(3.1)

with k = 0 + ks; k = 0, 1, 2..,Nc 1. The subcarrier frequency fk =k2

, and the lowest frequency used is fk=0. The spacing frequency between

the subcarrier is number of bandwidth divided by the number of subcarrierfrequency used, f= s

2= BW

Nc.

The signals are said orthogonal if the multiplication within the symbolperiod for each other is zero, and between itself is equal C, which is the constantof quadrat signal energy itself. It is formulated mathematically as:

T0

si (t) sj (t) dt =

C, for i = j.

0, for i = j.(3.2)

The low frequency utilization in OFDM system is described in the following

figure:

Figure 3.1: Bandwith utilization in FDM and OFDM

From input data, the inverse Fourier transform (IFFT) is used for gener-ating the OFDM signal and changing the domain into time domain. The FastFourier Transform (FFT) is for changing back the domain into its originatedfrequency domain.


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3.2 Guard Interval

In the time dispersive channel for a given data rate R symbol/s at the singlecarrier system, if an OFDM system has the number ofNc carriers, then theOFDM data rate for a single subcarriers is R

Ncsymbol/s. The symbol period

for OFDM signal increases then by the factor ofNc. If the first given channeltime length L is used in the transmission, the length of OFDM symbol Lc islonger than the time length L of the channel. This difference ofLc will affectfor distortion in the first sample of next OFDM symbol in each subcarriers,because of the longer period in the last symbol.

The intersymbol interference (ISI) is described in the figure as follows:

Figure 3.2: OFDM intersymbol interference with Cyclic Prefix (CP)

Another delay interference in OFDM is because of the orthogonality ofsubcarriers. It is known as intercarrier interference (ICI). The amplitude andphase of each OFDM subcarriers must remain constant to maintain the or-

thogonality. If there is loss of orthogonality because of the multipath fading,the signal energy, which consists of amplitude and phase of the signal will bechanged. It happens at the first of symbol period, or known as the transientperiod. Therefore, the guard interval is introduced at the transient period forovercoming these interferences.

Guard interval (GI) itself is the replica from the last part of the OFDMsymbol and positioned at the first symbol. It is also known as cyclic prefix.Cyclic prefix is implemented before the transmission, and will be erased atthe receiver after the transmission. The length of cyclic prefix Tg should beat least as long as the significant part of the impulse response experiencedby the transmitted signal. The advantages of this method are for guardingperiod of the successive symbols, and for providing a cyclic convolution with


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the channel impulse response to remain the continuity and orthogonality ofthe signal subcarriers. The cyclic convolution operates in a time domain, as a

translation of multiplication for the signals in the frequency domain. With theaddition of this interval, the loss bandwidth efficiency occurs, and data ratewill reduce. Therefore, the cyclic prefix should not be longer than needed.

The convolution between the transmit data and the channel impulse re-sponse is defined as [12]:

s (i, k) = s (i, k) k,circ h (k) F S(i, n) = DFT(k) {s (i, k)}DFT{h (k)} H(n)

(3.3)

The equalizer H(n) is built for compensating the phase signal after mul-

tiplied by channel impulse response. Therefore, output data will be obtainedfrom:

dn (i) = en.S(i, n) ; en = 1H(n)

, [PSKModulation] dn (i) = Hn.S(i, n) .(3.4)

3.3 OFDM-STBC Block Diagram

Through non orthogonality of the block codes in Chapter 2, it can be proven

that space time block coding for PLC channel is the same as repetition coding.Therefore in block diagram arrangement, the codes are sent individually viaeach phase whose channel response is uncorrelated between each other. Withthe Philipps model, the OFDM is implemented as:

The energy symbols are first checked. It must be unity. Serial data are thenconverted to parallel data. They are placed in each subcarriers. If the numberof data is not uniformly distributed data are then padded with the zeros, soeach subcarrier has the same number of data. This uniformly distributed willrepresent the same period of the symbol for transforming data in IFFT.

From output IFFT, OFDM symbols are obtained with the period Ts in

the time domain. Each subcarrier is then extended by the guard interval (GI),which is the cyclic prefix whose length depends on the need for data protectionto overcome the ISI and ICI. For having an efficient transmission, the periodof guard intervals are limited. These new symbol periods are then representedby T= Tg + Ts. After adding the guard intervals, data in parallel subcarriersare converted to the serial.

At last stage of the OFDM-STBC transmitter, serial data are transmittedparallel via 3 channels. At the channels, data experience multipath fading andtypical PLC noise, additive white Class A noise. Noisy data then receive bythe OFDM receiver in serial. Serial to parallel converter is used for chang-

ing the data to parallel. The next step is to erase the guard interval andpadded data. A number of guard intervals used in the transmission, are then


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Figure 3.3: Block Diagram of OFDM-STBC Transmitter

thrown away. After erasing, the data domain is transformed to the frequencydomain, using fast Fourier transform (FFT). The data are then equalized bythe conjugate transfer characteristics H(n) for compensating error from chan-nel fading. After equalized, the data are then combined and detected using

minimum distance maximum likelihood decoder.In the simulation the block diagram of receiver is constructed as:

Figure 3.4: OFDM-STBC Receiver Structure


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3.4 Convolutional Coding

Space time block codes use the diversity gain for improving the performance.The addition of forward error correction (FEC) enhances also the performanceof STBC for overcoming the multipath fading. Through convolutional coding,the data received can be recognized and accurately decoded. The utilizationof convolutional coding in this thesis is to determine the performance of spacetime block codes in the combination with the convolutional coding. It can alsobe compared with the effect of guard intervals used.

Convolutional coding uses a circuit contains of shift registers, to presentthe memory. It specified by number of output bits n, number of input bits k,and number of memory registers m. The specified code parameter is (n,k,m),

where n = number of data output, k = number of data input, and m = numberof register. Within GF(2), the mathematical operation is a linear combinationof information bits. Encoding process is the multiplication between genera-tor polynomial and input of information bits. Assumed that the generatorpolynomials are:

gv(x) =m=0

g,v.x, (3.5)

and sequence of information bits are:

u(x) =

r=0urx

r

, (3.6)

also the sequence of code blocks are:

a(x) = (a1(x), a2(x),...,an(x)) with av(x) =r=0

ar,vxr, (3.7)

where:

r = block number,

= memory index, v = undex of position within a code block, n = length of code blocks,

with the generator matrix G:

G (x) = (g1 (x) , g2 (x) , . . . , gn (x)) , (3.8)

then the multiplication of polynomial and incoming bits are:

av (x) = u (x) .gv (x) for v = 1, 2, . . . , n . (3.9)


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The result a(x) are:

(a1

(x) , a2

(x) , . . . , an

(x)) = u (x) . (g1

(x) , g2

(x) , . . . , gn

(x)) (3.10)

a(x) = u(x).G(x). (3.11)Therefore, the maximum of memory length m is:

m = maxlvn

degree{gv(x)} (3.12)The decoding scheme is a Viterbi decoding using a maximum likelihood

method. In order to simplify the decoding method, the binary symmetricchannel which represents the hard decision decoding is used.

3.4.1 Encoder

For encoding process, convolutional coding utilizes memory to encode and de-code the next bits using the previous code. This coding results significantlygood performance using low implementation of costs. As in Matlab, the sys-tematic convolutional encoder is used. With the number of input 1 and numberof output 2, yields rate 1/2. For simulating, the convolutional codes are [177133]. They represent the generator sequences which are the octal value ofg1 =(1,1,1,1,1,1,1) and g2 =(1,0,1,1,0,1,1).

The structure of circuit diagram to generate the output codes is describedby:

Figure 3.5:Circuit of generator sequences [177 133]

The equation for encoding system is in the special case [177 133]:

y(1) = x g1,y(2) = x g2, (3.13)

where:

y(1)l = xl + xl1 + xl2 + xl3 + xl4 + xl5 + xl6, (3.14)

y(2)l = xl + xl2 + xl3 + xl5 + xl6. (3.15)

If the input sequences convolved with the generator sequences, the code

polynomials produce two output sequences. Coded sequences are obtainedwith linear switching from the above multiplication results.


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3.4.2 Decoder

At the decoder, the maximum likelihood in Viterbi decoding is used. Basedon probability of data receive, when data are sent, Viterbi decoding searchesthe best path at minimum distance from original symbol.

max P(Y|X) = max P(X+N|X) = max P(N) (3.16)As an example, the Viterbi decoding with hard decision metric is illustrated

as:

Information vector: u = (0,0,1,1,1,1,0,1,0,1)

Code sequence vector: a = (00,01,11,01,10,01,00,10,00)

Received vector: r = (00,01,11,01,10,01,00,10,00) Error vector: f = (00,01,00,00,00,00,00,00,00) Hard decision decoding

Figure 3.6: Trellis diagram of Viterbi decoding

And the result of error correction in the decoding is:

Figure 3.7: Path sequence of Viterbi decoding


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3.5 Summary

Analyzing the problem of STBC in frequency selective fading environment,data transmission can be done alternatively with OFDM. OFDM divides datainto parallel subcarriers, so the coherent bandwidth of the channel can beidentically distributed. Although consists of parallel subcarriers, the datatransmissions are in serial, so the data are converted to serial streams. Inthe channel with Philipps model, the amplitude and phases of original signalsare changed worst. The equalization of the channel should be done to recoverthis amplitude and phase change. Guard intervals which are the cyclic prefix oflast series of data can replace the errors caused by ISI and ICI. Consequently,if there are additions of bits, the rate is reduced and lowered the efficiency of

transmission. Convolutional coding can alternatively be used for correctingthese errors.


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Chapter 4

Simulation Results and Analysis

This simulation is purposed to get characteristic of space time codes in PLCchannel. The result graphics are built to present the bit error rate (BER) ata various range of signal to noise ratio (SNR) with the noise models: additivewhite Gaussian noise, and additive white Class A noise.

First, simulation is assumed that the channel has a flat Rayleigh fading.Methods to obtain received data are divided into 3 types: (i) linear combin-ing with maximum likelihood detector, (ii) linear combining with the singlephase maximum likelihood detector, and (iii) adaptive detector which is thecombination from 2 methods above. The influences of repetition codes as nonorthogonal block codes are also investigated. At last section, the OFDM-STBC

for frequency non selective fading using Philipps model is also investigated.The implementation of adaptive decoder adopted from [4], which made the

adaptivity of the system through the noise detection. If the impulsive noiseis high, the majority vote decoder is used, but if the impulsive noise is low,the correct data are obtained from linear combiner. In order to get a goodunderstanding, we distinguish between repetition codes which proposed to usefor space time block coding, and majority vote decoder which based on therepetition coding.

4.1 Alamouti schemeIn order to differentiate with the model used in PLC, Alamouti scheme [1] ispresented. The scheme uses 2x2 matrix orthogonal block codes. This meansthat data are transmitted over 2 transmit antennas, in 2 time slots. Withthe existing cross correlation between each channel, the full diversity can bereached.

In his paper, Alamouti simulates that the total power from the two trans-mit antenna is the same as total power from the single antenna. It is alsoassumed that the amplitudes of fading from each transmit antennas to eachreceived antennas are mutually uncorrelated Rayleigh fading. Therefore, the

total transmit power of STBC in PLC system, is arranged the same as total

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CHAPTER 4. SIMULATION RESULTS AND ANALYSIS 33

power of SISO system.The implementation of Alamouti scheme used can be arranged as:

Figure 4.1: Block Diagram of Alamouti Scheme under Rayleigh Fading and AWGN

The BER characteristics of data in white Gaussian noise Rayleigh fadingchannel are shown below:

Figure 4.2: BER performance of STBC-Alamouti scheme, Uncoded Coherent,MRRC in Wireless Rayleigh Channel

As the Gaussian noise variance is 1/2SNR and Rayleigh fading variance is0.5, BER characteristics of space time block codes have better performancethan the single channel (SISO) system. That is because of the diversity of

each channel used. With the transmit power of each antenna equals to 1/2


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times the transmit power of the SISO system, the SNR difference of Alamoutischeme is 3 dB lower. The QPSK system have the worse value than BPSK

system, because in QPSK system, one symbol represents two bits and if onesymbol false detected, two bits represented are false decoded.

4.2 Linear Combiner

Based on the Alamouti scheme, the simulation on PLC begins with the realorthogonal block codes. Matrix on real orthogonal block codes contains realnumbers. The modulation used to represent real numbers are four constellatedPhase Amplitude Modulation (PAM).

Starting the simulation, the checking of symbol energy has to be done. Theenergy of each symbol must be unity. At the PAM, because of the averagequadratic symbol energy equals to 5 per symbol, then symbol energies have tobe divided by 5. First, the channel with Gaussian noise with variance 1/2SNRis presented with AWGN channel and Rayleigh fading channel. Second, ClassA noise is simulated. The AWCN parameter of impulsive index A equals 0.1,which represents the highly impulsive noise. Parameter A is generated byrandom Poisson series. Other parameter is ratio between the noise variance

T=2g2i

which equals 0.001. This realization represents as the very noisy PLC

channel.Building the system, the block diagram used is presented by:

Figure 4.3: Block Diagram of PLC STBC 3 Channel System

For comparison of performance with the uncoded coherent SISO system,the power of STBC-PAM must be the same. The total power antenna equalsto one. If the number of transmit antenna is three, then transmit power ateach antenna of STBC equals to 1/3. Performance of BER characteristic inSTBC with Gaussian noise is theoretically the same as the performance ofSISO or uncoded coherent, because of Gaussian noise have less detrimentaleffect to data transferred.


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Applying the AWGN channel, the path gain used is equals to one. Thismeans that there exists only the AWGN noise, without fading. BER charac-

teristic obtained in the AWGN channel is as follows:

Figure 4.4: BER performance of Uncoded Coherent and STBC Demodulation inAWGN Channel

From the graph, it can be seen that the characteristics of SISO and STBC

system in AWGN channel is the same. If Rayleigh fading exists, the perfor-mance of STBC compared with uncoded coherent is:

Figure 4.5: BER performance of Uncoded Coherent and STBC with AWGN inRayleigh Fading Channel

As shown, with the same total power, the performance of STBC in Rayleighchannel is better than the uncoded coherent, but the BER distributions are


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worse than AWGN channel. The BER of STBC vanishes at 25 dB, whereaswithout fading, it vanishes at 15 dB. The graphic shows that the difference

between SISO and STBC at BER of 8.104 is 13 dB.Applying Class A noise at PLC channel without fading, results:

Figure 4.6: BER performance of Uncoded Coherent and STBC with Class A NoiseChannel

BER characteristics of STBC in AWCN noise are worse than uncoded co-herent at SNR below 10 dB, because the amplitude of energy signal is not ashigh enough to overcome the influences from the amplitude of impulsive noise.Influences of Class A noise in PLC channel make error rate high at low SNR.The performance of Class A noise and Rayleigh fading is shown by:

Figure 4.7: BER performance of Uncoded Coherent and STBC in AWCN and

Rayleigh Fading Channel


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In the presence of AWCN and Rayleigh fading, it is shown that the spacetime block codes are much better than the uncoded coherent SISO system, if

the SNR are above 10 dB. At BER of 8.104, the SNR difference is 9 dB. At thehigher SNR the BER of STBC system could be even better. BER of STBCvanishes at the SNR at 30 dB. If the signal energies per transmit antennaare turned bigger, the graphic results better. Also, the difference betweenSISO and STBC characteristics are significantly increased at high SNR. Withinfluences of AWCN noise above 10 dB, the linear combiner using 3 phasesof PLC channel are better than single combiner that uses only one phases ofPLC channel.

4.2.1 STBC with the Repetition Codes

In the theory, it can be proven that the real orthogonal block codes STBC inpowerline channel is the same as the non-orthogonal repetition codes. There-fore, in the simulation, this assumption is to be proven.

The performance of STBC repetition codes with Gaussian noise is shownby:

Figure 4.8: BER performance of Uncoded Coherent and STBC-Repetition Code inAWGN Channel

As shown in the figures above, the non orthogonal block code which con-tains repetition block codes yield the same results as orthogonal block codes. Itis only in PLC, because of the perfect isolation between the channels. However,it can be concluded also, in powerline channel if we use the repetition blockcodes in the STBC matrix, then the received data can be directly detected andthe correct data can be decided, without waiting until a whole block codes aresent. Consequently, the rate is also higher than the orthogonal block codes.


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Figure 4.9: BER performance of Uncoded Coherent and STBC-Repetition Codewith AWGN and Rayleigh Fading Channel

Figure 4.10: BER performance of Uncoded Coherent and STBC-Repetition Codewith Class A Noise


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Figure 4.11: BER performance of Uncoded Coherent and STBC-Repetition Codewith Class A Noise and Rayleigh Fading

4.2.2 Repetition Coding with Majority Vote Decoder

Analyzing in the block diagram about repetition coding in Chapter two, thenumber of the maximum likelihood detector are three, because each channelhave one detector. The decision vector is depending on the majority votedecoder from all channels. If minimum two data from two channels are thesame, then the compared data is the decision data. However, if received datafrom the all three channel are not the same, the decisions depend on theminimum value between all received data. Repetition coding uses buffer to

process for their majority vote decoder. The system proposed using QPSKmodulation is:

The result from the system proposed is:

From the characteristic of repetition coding and linear combiner, it can beseen for SNR below 15 dB, the repetition coding with majority vote decoderperforms better than linear combiner. At below 15 dB, this scheme can beused.


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Figure 4.12: Block Diagram of Repetition Coding With Majority Vote Decoder

Figure 4.13: BER performance of Linear Combiner and Majority Vote Decoder forRepetition Coding in in AWCN and Rayleigh Fading Channel

4.3 Adaptive Decoder

The characteristics of real orthogonal and non-orthogonal STBC in PLC showthat for SNR below 10 dB, the BER is higher than the SISO system. This dif-ferent characteristics occur because of detector used. The difference of decoderused plays a major role in the BER result. Majority vote decoder comparesthe detected vector received from each three channel, in the contrary, linearcombiner detects vector received and combined them each to be one series ofdata received. The majority vote decoder, therefore need a buffer to store data

which to be compared.


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Based on the received data, we estimate the noise distribution and decidethe threshold. The impulse to threshold value (ITR) is decided randomly based

on the observation of BER result obtained.Within the training period, average power of received data are measured,

and used as a pilot to get the threshold power. If the received power of datais higher than ITR multiplied by threshold power, then the symbol detectedand decided are from Repetition coding.

The system block diagram is presented by:

Figure 4.14: Block Diagram of Adaptive Decoder System

The result obtained from simulation of adaptive decoder is:From the graphic shown, the detection of Class A noise works well. With

the threshold value for impulse to threshold ratio (ITR) equals to 10, thedetector of data received is chosen, and decided perfectly with the minimumdistance from original symbol.

At the SNR lower than 15 dB, data are detected by repetition coding, andabove 15 dB, output linear combiner are used. At SNR below 15 dB, therepetition coding is 12 dB better than the SISO system and 2 dB better thanlinear combiner. It is measured at BER of2.103. As for SNR higher than 15dB, the linear combiner is 13 dB better than SISO system. It is measured at

BER of 3.104.

4.4 Guard Interval of STBC-OFDM

In order to understand about the influences of frequency selective fading inspace time block codes, OFDM system is proposed. Philipps model channel isimplemented independently on each channel. The channel gain as used in theflat fading cannot be used directly. The channel equalization is applied as achange for estimated path gain channel in flat fading.

The parameters of OFDM used in the simulation are:


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Figure 4.15: BER performance of Adaptive Decoding in in AWCN and RayleighFading Channel

No. Parameter Value

1. Modulation: QPSK2. Nr.IFFT and FFT Size: 643. Nr.Carrier: 644. Nr.OFDM Symbol: 206. Index A AWCN : 0.0257. Nr. of T AWCN: 0.001

Table 4.1: OFDM Simulation Parameters

The transmit part of OFDM is shown as:The receive part of OFDM is designed as:With the 4-PSK modulation, and the Philipps model, the simulation results

yields:As shown, the space time block codes is performed better than the SISO

system, and the effect of ISI and ICI can be disabled by guard interval. Theeffective SNR for system without guard interval is 40 dB. With guard intervalis around 15 % of the OFDM symbols, the effective SNR is 45 dB. and if thenumber of GI is around 25 % of OFDM symbols, STBC error rate are vanish

at SNR 45 dB. Over all SNR, performance of STBC differs better 2.5 dB


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Figure 4.16: OFDM Transmitter Block Diagram

Figure 4.17: OFDM Receiver Block Diagram

than SISO system.Guard interval has an influence in addition of the symbol duration. This

addition can cause the loss of SNR, as TgTs+Tg

. Therefore it should be a trade

off between the time interval of data and guard interval. The length of guardinterval should not longer than the length of important data transmitted.

4.5 OFDM-STBC with the Convolutional Code

Using generator sequence [177 133], the block diagram of OFDM with convo-

lutional coding as forward error correction can be shown as:

The decoder scheme of convolutional codes is:

As in Matlab program, convolutional codes are based on the octal value.The generator bit values are then transformed to bit as g1 = (1, 1, 1, 1, 1, 1, 1)and g2 = (1, 0, 1, 1, 0, 1, 1). With the addition of white Class A noise given inall series data at the channel, after the Philipps model fading, the result shownare:

The figure shows that the concatenation between STBC and convolutional


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Figure 4.18: BER performance of OFDM in AWCN and Frequency SelectivePhilipps Model

Figure 4.19: Convolutional Coding Encoder

coding performs better than uncoded STBC at the SNR above 10 dB . Sincethe hard decision is used, at the range of 10-20 dB the performance of codeddata is worse than the uncoded case. Within the range of below 20 dB, ClassA noise contributes the addition for higher signal energy, whereas because ofPhilipps fading, data are added as well as cancelled between each other, sothe Viterbi decoder cannot decode correctly. At the SNR higher than 20 dB,the signal energy is larger than the amplitude of noise, the noise contributessmaller influences, so there exists only the fading. To overcome this fading,

convolutional coding improves better performance to correct the burst errors.


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Figure 4.20: Convolutional Coding Decoder

Figure 4.21: OFDM STBC with Convolutional Coding [177 133]

4.6 Summary

As shown in the simulation, for STBC with Rayleigh fading using perfectestimated channel, data receive are processed by linear combiner. The charac-

teristics of AWCN used in simulation are very noisy. With the impulsive indexparameter A = 0.1, and T=0.001, it is obtained that the data are worse thanthe performance in AWGN channel with Rayleigh fading. In Gaussian noise,at SNR 15 dB, the STBC BER equals to 8.104. Whereas in Class A noise,this 15 dB SNR value represent BER of 4.103.

Second, the orthogonality of block codes is not needed. It is proven thatthe repetition codes can also be used in matrix block codes. The results ofrepetition code designs are the same as orthogonal matrix block codes.

OFDM system is used to overcome against frequency selective fading. Asamplitude and phase change because of the fading, the equalization is done tocorrect this change. The guard interval plays also an important rule to protectthe data from ISI and ICI. After used for transmission, the guard interval are


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erased, and the data inside are recovered. If guard interval does not exist,data sent cannot be correctly recovered, otherwise with the number of 25 % of

transmitted data, the received data STBC can be correctly decoded at SNRabove 40 dB.

As an alternative, convolutional codes as a forward error correction coding,can be used to improve system performance. With guard interval equals zero,convolutional coding is verified to have a better result than the uncoded datawith guard interval.


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Conclusion and Future Works

Since there are 3 perfectly isolated channels in PLC, the number of maximumdiversity in STBC is three. Hence, the orthogonal design of matrix in spacetime block codes is not necessary. As we proposed in Chapter 2, the idea

of space time block codes that was proposed in [2] can be simplified to therepetition codes. With this repetition codes, the simulation results indicatesthe same performance for AWGN and AWCN channel. Consequently, datacan directly be decoded without waiting until one block matrix is received.

Repetition coding with majority vote decoder is better than linear combinerat low SNR (


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[4] C. L. Giovaneli, J. Yazdani, P. Farrell, B. Honary, Improved Space-Time

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[8] J. Haring, A. J. H. Vinck, Coding for Impulsive Noise Channels, Pro-ceeding of International Symposium on Power Line Communications andIts Applications 2001 (ISPLC 2001), pp. 103-108, 2001.

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[13] L. Litwin, M. Pugel, The Principles of OFDM, www.rfdesign.com, pp.30-48, January 2001.

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