Table of Contents

\

CERTIFICATE............................................................................................................................ ii

ABSTRACT................................................................................................................................ iii

ACKNOWLEDGEMENTS.........................................................................................................iv

Table of Contents.........................................................................................................................v

List of Figures............................................................................................................................vii

List of Symbols, Abbreviations and Nomenclature...................................................................viii

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

INTRODUCTION..................................................................................................................2

Problem Statement...............................................................................................................2

Organisation of report..........................................................................................................3

2. CHANNEL EQUALIZATION............................................................................................4

INTRODUCTION TO CHANNEL EQUALIZATION.......................................................5

FUNDAMENTALS OF EQUALIZATION..........................................................................7

Introduction..........................................................................................................................7

Operating modes of an adaptive equalizer...........................................................................7

ADAPTIVE EQUALIZATION.............................................................................................8

Communication system with an adaptive equalizer.............................................................8

SURVEY ON EQUALIZATION TECHNIQUES.............................................................10

Linear Equalizer..................................................................................................................10

Non-linear Equalizer...........................................................................................................11

3. ARTIFICIAL NEURAL NETWORKS..............................................................................12

INTRODUCTION TO ANNs..............................................................................................13

What are ANNs?.................................................................................................................13

Why do we use Neural Networks?......................................................................................13

Benefits of ANN..................................................................................................................14

STRUCTURE OF ANN.......................................................................................................14

Mathematical Model of a Neuron......................................................................................14

Network Architectures........................................................................................................15

Learning Process.................................................................................................................17

i

BACK PROPAGATION ALGORITHM...........................................................................18

Introduction........................................................................................................................18

Learning Process.................................................................................................................19

4. CHANNEL EQUALIZATION USING ANNs..................................................................22

Introduction........................................................................................................................23

State of the Art...................................................................................................................24

Proposed solution methodology.........................................................................................24

Conclusion..........................................................................................................................25

REFERENCES...........................................................................................................................26

ii

List of Figures

Figure 2-1: Inter-Symbol Interference...............................................................................5

Figure 2-2: Propagation paths in an open-air radio transmission channel........................6

Figure 2-3: Communication system with an adaptive equalizer.......................................9

Figure 2-4: Equalizer located at the receiver end of the channel....................................10

Figure 2-5: Classification of the Equalizers....................................................................11

Figure 3-1: Model of an ANN.........................................................................................15

Figure 3-2: Single-layer Feed-Forward Network............................................................16

Figure 3-3: Multi-layer Feed-Forward Network.............................................................16

Figure 3-4: Recurrent Network.......................................................................................17

Figure 3-5: Three layer Neural Network with two inputs and single output...................20

Figure 4-1: Block diagram of Adaptive Equalizer..........................................................23

iii

List of Symbols, Abbreviations and Nomenclature

ISI Inter-Symbol Interference

ANN Artificial Neural Network

MLP Multi-Layer Perceptron

BPA Back Propagation

TDMA Time Division Multiple Access

LTE Linear Transversal Equalizer

DFE Decision Feedback Equalization

MLSE Maximum Likelihood Sequence Estimation

LMS Least Mean Square

RLS Recursive Least Square

iv

Chapter 1

1. INTRODUCTION

PROBLEM STATEMENT

ORGANIZATION OF REPORT

1

INTRODUCTION

In a communication system, the task of a receiver is to retrieve

the information send by the transmitter via a transmission

medium called as channel. To accomplish this task, it tries to

extract the parameters related to the transmitted information

from the received signal. The channel is central to the operation

of a communication system. Its properties determine both the

information-carrying capacity as well as the quality of service

offered by the system. Before reaching the receiver, the

transmitted signal is passes through the channel, or we can say

that the transmitted signal convolves with the channel.

Inter-Symbol Interference (ISI) caused by multipath in band-limited (frequency

selective) time dispersive channel distorts the transmitted signal, causing bit errors

at the end of the receiver. ISI has been recognized as the major obstacle to high

speed data transmission over wireless channels. Channel Equalization is a

technique used to combat inter-symbol interference.

Problem Statement

Digital communication systems are designed to transmit high

speed data over communication channels. During this process

the transmitted data is distorted, due to the effects of linear and

nonlinear distortions. So the communication system requires

signal processing techniques to improve the link performance in

mobile radio environments. Channel equalization is one of the

technique which is used to improve the quality of the received

signal and performance (i.e., to minimize the instantaneous bit

error rate) of the link over small-scale times and distances.

In mobile radio channels due to Inter-Symbol Interference, frequent

changes and multipath causes time dispersion of the digital

2

information. Also by the effect of Inter-symbol Interference,

broadening and overlapping of the pulse with its neighbour

eventually becoming indistinguishable at the receiver end.

Channel distortion calls for channel equalization techniques at

the receiver side which reconstructs the transmitted symbols

correctly since our main objective is to transmit symbols with

minimum error.

Artificial Neural Networks (ANNs) are nonlinear information

(signal) processing devices, which are built from interconnected

elementary processing devices called neurons. It has a natural

tendency for storing experimental knowledge and making it

available for use. Artificial neural networks (ANNs) can perform

complex

mapping between its input and output space and are capable of

forming complex decision regions with nonlinear decision

boundaries.

Our main goal is to design and simulate an artificial neural

network based channel equalizer and compare its performance

with existing techniques.

Organisation of report

The report is organized as follows: To get the depth of this topic, Chapter 2

introduces the fundamentals of channel equalization its requirement in field of

digital communication. Chapter 3 gives the brief introduction of the artificial

neural network, which includes the details about the mathematical model of a

neuron, different neural network architectures and the learning process of neural

network, Chapter 4 presents literature survey and state of art followed by

conclusions with future scope of the work.

3

Chapter 2

2. CHANNEL EQUALIZATION

INTRODUCTION TO CHANNEL EQUALIZATION

FUNDAMENTALS OF EQUALIZATION

ADAPTIVE EQUALIZATION

SURVEY ON EQUALIZATION TECHNIQUES

4

INTRODUCTION TO CHANNEL EQUALIZATION

In digital communication system, Inter-Symbol Interference (ISI) is one of the

main causes of degradation of system performance. Equalization is a one of the

technique which is used to improve received signal quality and link performance

over small-scale times and distances.

Equalisation compensates for Inter-Symbol Interference (ISI) created by multipath

with time dispersive channels. Basically the term equalization can be used to

describe any signal processing operation which minimizes ISI.

In radio channels, a variety of adaptive equalizers can be used to cancel

interference, because mobile fading channels are random and time-varying,

equalizers must track the time-varying characteristics of the mobile channel and

thus are called adaptive equalizers.

There are two main threats in the process of digital communication: Inter Symbol

Interference (ISI) and Multipath Propagation

Inter-Symbol Interference in Digital Transmission  

Inter-symbol interference (ISI) arises when the data transmitted through the

channel is dispersive, in which each received pulse is affected somewhat by

adjacent pulses and due to which interference occurs in the transmitted signals

[Fig 2-1]. It is difficult to recover the original data from one channel sample.

Fig 2-1: Inter-Symbol Interference

5

Multipath Propagation

Within telecommunication channels multiple paths of propagation commonly

occur. In practical terms this is equivalent to transmitting the same signal

through a number of separate channels, each having a different attenuation and

delay.

Consider an open-air radio transmission channel [Fig 2-2 (a)] that has three

propagation paths: Direct, Earth Bound, Sky Bound. Fig 2-2 (b) describes how

a receiver picks up the transmitted data. The direct signal is received firstly

whilst the earth and sky bound are delayed. All three of the signals are

attenuated with the sky path suffering the most. Multipath interference

between consecutively transmitted signals will take place if one signal is

received whilst the previous signal is still being detected. This would occur if

the symbol transmission rate is greater than 1/τ where, τ represents

transmission delay. Because bandwidth efficiency leads to high data rates,

multi-path interference commonly occurs.

Fig 2-2: Propagation paths in an open-air radio transmission channel

6

FUNDAMENTALS OF EQUALIZATION

Introduction

In a broad sense, the term equalization can be used to describe any signal

processing operation that minimizes ISI. In radio channels, a variety of adaptive

equalizers can be used to cancel interference while providing diversity [1]. Since

the mobile fading channel is random and time varying, equalizers must track the

time varying characteristics of the mobile channel, and thus are called adaptive

equalizers.

Operating modes of an adaptive equalizer

The general operating modes of an adaptive equalizer include:

a. Training (first stage)

In this first stage a known fixed-length training sequence is sent by the

transmitter so that the receiver's equalizer may average to a proper setting. The

training sequence is designed to permit an equalizer at the receiver to acquire

the proper filter coefficients in the worst possible channel conditions. The

training sequence is typically a pseudorandom binary signal or a fixed,

prescribed bit pattern. Immediately following the training sequence, the user

data is sent. The time span over which an equalizer converges is a function of

the equalizer algorithm, the equalizer structure, and the time rate of change of

the multipath radio channel. Equalizers require periodic retraining in order to

maintain effective ISI cancellation.

b. Tracking (second stage)

In second stage, immediately following the training sequence, the user data is

sent. As user data are received, the adaptive algorithm of the equalizer tracks

the changing channel and adjusts its filter characteristics over time. It is

commonly used in digital communication systems where user data is

segmented into short time blocks. Time Division Multiple Access (TDMA)

wireless systems are particularly well suited for equalizers. In TDMA data in

7

fixed-length time blocks, and the training sequence usually sent at the

beginning of a block.

ADAPTIVE EQUALIZATION

Consider a time varying channel where the receiver attains equalization by

adjusting several parameters continuously that is based on the measurements

taken on the channel characteristic. This process of continuously assessment done

in time varying natured channel is called as adaptive equalization. For example, in

mobile channels are random and time varying and often affected by signal fading,

the equalizers used in this case should possess the capability of tracking these time

varying channel to reduce interference. In simple words we can say that, an

adaptive equalizer is an equalizer that automatically adapts to time-varying

properties of the communication channel.

Adaptive equalizers compensate for signal distortion attributed to Inter-Symbol

Interference (ISI), which is caused by multipath within time-dispersive channels.

Typically, they are employed in high-speed communication systems, which do not

use differential modulation schemes or frequency division multiplexing. The

equalizer is the most expensive component of a data demodulator and can

consume over 80% of the total computations needed to demodulate a given signal.

Communication system with an adaptive equalizer

Fig 2-3 shows a block diagram of a communication system with an adaptive

equalizer in the receiver. If x (t) is the original information signal, and f(t) is the

combined complex baseband impulse response of the transmitter, channel, and the

RF/IF sections of the receiver, the signal received by the equalizer may be

expressed as

y (t )=x ( t )⨂ f ¿ (t )+nb (t) 2-1

Where,

f*(t), is the complex conjugate of f(t) ,

nb(t), is the baseband noise at the input of the equalizer, and

8

⨂, denotes the convolution operation

If the impulse response of the equalizer is heq(t), then the output of the equalizer is

d̂ (t )=x (t )⨂ f ¿ (t )⨂heq (t )+nb (t )⨂heq (t) 2-2

¿ x (t )⨂ g (t )+nb (t )⨂heq (t)

Where, g(t), is the combined impulse response of the transmitter, channel, RF/IF

sections of the receiver, and the equalizer.

The complex baseband impulse response of a transversal filter equalizer is given

by

heq ( t )=∑k

ck δ (t−n T s ) 2-3

Where, ck, are the complex filter coefficients of the equalizer.

The desired output of the equalizer is x(t), the original source data. Assume that

nb(t) = 0. Then, in order to force d̂ (t )=x ( t ) in equation (2.2), g(t) must be equal to

g ( t )=f ¿ ( t )⨂heq (t )=δ(t ) 2-4

Fig 2-3: Communication system with an adaptive equalizer

9

The goal of equalization is to satisfy equation (2.4). In the frequency domain,

equation (2.4) can be expressed as

H eq ( f ) F¿ (−f )=1 2-5Where, Heq(f) and F(f) are Fourier transforms of heq(t) and f(t), respectively.

Equation (2.5) indicates that an equalizer is actually an inverse filter of the

channel. If the channel is frequency selective, the equalizer enhances the

frequency components with small amplitudes and attenuates the strong

frequencies in the received frequency spectrum in order to provide a flat,

composite, received frequency response and linear phase response. For a time-

varying channel, an adaptive equalizer is designed to track the channel variations

so that equation (2.5) is approximately satisfied.

Equalization is the process to remove ISI and noise effects from the channel. It is

located at the receiver end of the channel as shown in below figure. It is an inverse

filter placed at the front end of the receiver. The transfer function of the equalizer

is just an inverse of the transfer function of the channel [Fig 2-4Error: Reference

source not found]. Equalization is an iterative process of reducing the mean square

error i.e. the difference between desired response and output of filter used in

equalizer.

Fig 2-4: Equalizer located at the receiver end of the channel

SURVEY ON EQUALIZATION TECHNIQUES

Equalization techniques can be sub- divided into two general categories as linear

and Non-linear equalizers.

Linear Equalizer

10

Linear equalizers aim at reducing ISI in linear channels using various algorithms

like Least Mean Square (LMS), Recursive Least Square (RLS) and normalized

LMS. The most common equalizer structure is a linear transversal equalizer

(LTE). The output of the decision maker is not used in the feedback path to adapt

the equalizer.

Non-linear Equalizer

Non-linear equalizers equalize non-linear channels. They mainly use Neural

Networks (NN) and Multilayer Perception (MLP) algorithms for equalization.

They are used in applications where the channel distortion is too severe for a

linear equalizer to handle. Decision feedback equalization (DFE) and maximum

likelihood sequence estimation (MLSE) are most commonly used non-linear

equalization techniques. The output of the decision maker is used in the feedback

path to adapt the equalizer.

Fig 2-5 provides a general categorization of the Equalization technique according

to the types, structures, and algorithms can be classified in several different ways.

Fig 2-5: Classification of the Equalizers

11

Chapter 3

3. ARTIFICIAL NEURAL NETWORKS

INTRODUCTION TO ANN

STRUCTURE OF ANN

BACK PROPAGATION ALGORITHM

12

INTRODUCTION TO ANNs

What are ANNs?

Working on artificial neural network has been motivated right from its inception

by the recognition that the human brain computes in an entirely different way

from the conventional digital computer. The brain is a highly complex, nonlinear

and parallel information processing system. It has the capability to organize its

structural constituents, known as neurons, so as to perform certain computations

many times faster than the fastest digital computer in existence today. The brain

routinely accomplishes perceptual recognition tasks, e.g. recognizing a familiar

face embedded in an unfamiliar scene, in approximately 100-200 ms, whereas

tasks of much lesser complexity may take day son a conventional computer.

A neural network is a machine that is designed to model the way in which the

brain performs a particular task. The network is implemented by using electronic

components or is simulated in software on a digital computer. A neural network

is a massively parallel distributed process or made up of simple processing units,

which has a natural propensity for storing experimental knowledge and making it

available for use. It resembles the brain in two respects:

Knowledge is acquired by the network from its environment through a

learning process.

Inter neuron connection strengths, known as synaptic weights, are used to

store the acquired knowledge.

The procedure used to perform the learning process is called a learning algorithm,

the function of which is to modify the synaptic weights of the network in an

orderly fashion to attain a desired design objective.

Why do we use Neural Networks?

Neural networks, with their remarkable ability to derive meaning from

complicated or imprecise data, can be used to extract patterns and detect trends

that are too complex to be noticed by either humans or other computer

13

techniques. A trained neural network can be thought of as an "expert" in the

category of information it has been given to analyse. This expert can then be used

to provide projections given new situations of interest and answer "what if"

questions.

Other advantages include:

a. Adaptive le a rn i ng : An ability to learn how to do tasks based on the data given

for training or initial experience.

b. Self-Organizat i o n : An ANN can create its own organization or representation

of the information it receives during learning time.

c. Real Ti m e Opera t ion : ANN computations may be carried out in parallel, and

special hardware devices are being designed and manufactured which take

advantage of this capability.

d. Fault Tolerance via Redundant Information Coding : Partial destruction of a

network leads to the corresponding degradation of performance. However,

some network capabilities may be retained even with major network damage.

Benefits of ANN

a. They are extremely powerful computational devices.

b. Massive parallelism makes them very efficient.

c. They can learn and generalize from training data–so there is no need for

enormous feats of programming.

d. They are particularly fault tolerant – this is equivalent to the “graceful

degradation” found in biological systems.

e. They are very noise tolerant - so they can cope with situations where normal

symbolic systems would have difficulty.

f. In principle, they can do anything a symbolic/logic system can do, and more

STRUCTURE OF ANN

Mathematical Model of a Neuron

A neuron is an information processing unit that is fundamental to the operation n

14

of a neural network. The three basic elements of the neuron model are [Fig 3-6]:

a. A set of weights, each of which is characterized by a strength of its own. A

signal xj connected to neuron k is multiplied by the weight wkj.The weight of

an artificial neuron may lie in a range that includes negative as well as positive

values.

b. An adder for summing the input signals, weighted by the respective weights of

the neuron.

c. An activation function for limiting the amplitude of the output of a neuron. It

is also referred to as squashing function which squashes the amplitude range

of the output signal to some finite value.

Fig 3-6: Model of a Neuron

Therefore, a vk and yk are defined as:

vk=∑j=1

p

w kj x j3-6

And

yk=φ (v k+θk ) 3-7

Network Architectures

There are three fundamental different classes of network architectures:

15

a. Single - lay e r F ee d-Forward Networks

In a layered neural network the neurons are organized in the form of layers.

In the simplest form of a layered network, we have an input layer of source

nodes that projects on to an output layer of neurons, but not vice versa [Fig 3-

7]. This network is strictly a Feed-Forward type. In single-layer network,

there is only one input and one output layer. Input layer is not counted as

layer since no mathematical calculations take place at this layer.

Fig 3-7: Single-layer Feed-Forward Network

b. Multilayer Feed-Forward Networks

The second class of a Feed-Forward neural network distinguishes itself by

the presence of one or more hidden layers, whose computational nodes are

correspondingly called hidden neurons [Fig 2-1].

Fig 3-8: Multi-layer Feed-Forward Network

16

The function of hidden neuron is to intervene between the external input and

the network output in some useful manner. By adding more hidden layers,

the network is enabled to extract higher order statistics. The input signal is

applied to the neurons in the second layer. The output signal of second layer

is used as inputs to the third layer, and so on for the rest of the network.

c. Recurrent Networks

A recurrent neural network has at least one feedback loop. A recurrent

network may consist of a single layer of neurons with each neuron feeding its

output signal back to the inputs of all the other neurons [Fig 3-9]. Self-

feedback refers to a situation where the output of a neuron is fed back into its

own input. The presence of feedback loops has a profound impact on the

learning capability of the network and on its performance.

Fig 3-9: Recurrent Network

Learning Process

By learning rule we mean a procedure for modifying the weights and biases of a

network. The purpose of learning rule is to train the network to perform some

task. They fall into three broad categories:

a. Supervis e d learning

The learning rule is provided with a set of training data of proper network

behaviour. As the inputs are applied to the network, the network outputs are

compared to the targets. The learning rule is then used to adjust the weights

and biases of the network in order to move the network outputs closer to the

targets.

17

b. Reinforcement l e arning

It is similar to supervised learning, except that, instead of being provided

with the correct output for each network input, the algorithm is only given a

grade. The grade is a measure of the network performance over some

sequence of inputs.

c. Unsupervised learning

The weights and biases are modified in response to network inputs only.

There are no target outputs available. Most of these algorithms perform

some kind of clustering operation. They learn to categorize the input patterns

into a finite number of classes.

BACK PROPAGATION ALGORITHM

Introduction

Multiple layer perceptrons have been applied successfully to solve some

difficult diverse problems by training them in a supervised manner with a highly

popular algorithm known as the error back-propagation algorithm. This

algorithm is based on the error-correction learning rule. It may be viewed as a

generalization of an equally popular adaptive filtering algorithm- the least mean

square (LMS) algorithm.

Error back-propagation learning consists of two passes through the different

layers of the network: a forward pass and a backward pass. In the forward pass, an

input vector is applied to the nodes of the network, and its effect propagates

through the network layer by layer. Finally, a set of outputs is produced as the

actual response of the network. During the forward pass the weights of the

networks are all fixed. During the backward pass, the weights are all adjusted in

accordance with an error correction rule. The actual response of the network is

subtracted from a desired response to produce an error signal. This error signal is

then propagated backward through the network, against the direction of synaptic

connections. The weights are adjusted to make the actual response of the network

18

move closer to the desired response.

A multilayer perceptron has three distinctive characteristics:

a. The model of each neuron in the network includes a nonlinear activation

function. The sigmoid function is commonly used which is defined by the

logistic function:

y= 11+exp (−x) 3-8

Another commonly used function is hyperbolic tangent:

y=1−exp (−x )1+exp (−x ) 3-9

The presence of nonlinearities is important because otherwise the input-

output relation of the network could be reduced to that of single layer

perceptron.

a. The network contains one or more layers of hidden neurons that are not part of

the input or output of the network. These hidden neurons enable the network

to learn complex tasks.

b. The network exhibits a high degree of connectivity. A change in the

connectivity of the network requires a change in the population of their

weights.

Learning Process

To illustrate the process a three layer neural network with two inputs and one

output, which is shown in the Error: Reference source not found, is used.

Signal z is adder output signal, and y = f(z) is output signal of nonlinear element.

Signal y is also output signal of neuron. The training data set consists of input

signals (x1 and x2) assigned with corresponding target (desired output) y’. The

network training is an iterative process. In each iteration weights coefficients of

nodes are modified using new data from training data set. Symbols wmn represent

19

weights of connections between output of neuron m and input of neuron n in the

next layer. Symbols yn represents output signal of neuron n.

Fig 3-10: Three layer Neural Network with two inputs and single output

y1=f 1(w11 x1+w21 x2) 3-10

y2=f 2(w12 x1+w22 x2) 3-11

y3=f 3(w13 x1+w23 x2) 3-12

y4=f 4 (w14 x1+w24 x2 )+w34 y3 3-13

y5=f 4 ( w15 x1+w25 x2 )+w35 y3 3-14

y6=f 6(w46 y4+w56 y5) 3-15

The desired output value (the target), which is found in training dataset. The

difference is called error signal δ of output layer neuron.

δ= y , ,− y 3-16

δ 4=w46δ 3-17

δ 5=w56 δ 3-18

δ 3=w34 δ4+w35 δ5 3-19

δ 2=w24 δ4+w25 δ5 3-20

20

δ 1=w14 δ4+w15 δ5 3-21

When the error signal for each neuron is computed, the weights coefficients of

each neuron input node may be modified. In formulas below df(z)/dz represents

derivative of neuron activation function.

The correction wij(n) applied to the weight connecting neuron j to neuron i is

defined by the delta rule:

Weight correction={learningrateparameter }×{ local

gradient }× {input signalof neuron i }

∆ wij ( n )=η × δi × y j(n) 3-22

The local gradient δi(n) depends on whether neuron i is an output node or a

hidden node:

a. If neuron i is an output node, δi(n) equals the product of the derivative

dfi(z)/dz and the error signal ei(n), both of which are associated with neuron

i.

b. If neuron j is a hidden node, δi(n) equals the product of the associated

derivative dfi(z)/dz and the weighted sum of the δs computed for the neurons

in the next hidden or output layer that are connected to neuron j.

21

Chapter 4

4. CHANNEL EQUALIZATION USING ANNs

INTRODUCTION

STATE OF THE ART

PROPOSED SOLUTION METHODOLOGY

CONCLUSION

22

Introduction

Designing efficient equalizers for complex, fast-varying channels

is an active area of research and development in academic.

Since recent past in field of wireless communications, the art of

using artificial neural network (ANN) has been gaining

momentum.

Linear equalizers generally employ linear filters with transversal

or lattice structure and adaptation algorithm such as recursive

least square (RLS), least mean square (LMS), fast RLS, square-

root RLS, gradient RLS, etc. However, linear equalizers do not

perform well on channels with deep spectral nulls. ANNs are

capable of forming arbitrarily nonlinear decision boundaries to

take up complex classification tasks 3, 4, 5 and 6.

Equalization refers to any signal processing technique used at

the receiver to combat Inter-Symbol Interference (ISI) in dispersive

channels. Standard equalization techniques start by modeling

communication channel as an adaptive filter with a specific

transfer function. The equalizer, which is part of the receiver,

then estimates the parameters of this unknown transfer function,

and attempts to undo the effects of this time-varying channel

distortion [7]. The equalizer extracts the desired signal by

applying adaptive algorithm using neural network (NN), which

minimizes the error between the equalizer output and the

delayed test signal, as depicted in Fig 4-11

23

Fig 4-11: Block diagram of Adaptive Equalizer

To extract the phase characteristics of the channel from the

received data, it is necessary to use higher order statistics of the

received signal. The nonlinear function of the output of the NN

equalizer gives rise to higher order statistics of the received

signal.

State of the Art

Neural equalizers have the potential for significant performance

improvements especially in severely distorted, nonlinear

channels [8, 9, 10 and 11]. Artificial Neural Networks are parallel

distributed processing systems in which many simple

interconnected elements (neurons) simultaneously process

information, adapt and learn from past patterns [12, 13, 14 and

15]. Although only capable of performing simple operations

themselves, when organized into layers, neurons are collectively

capable of performing highly sophisticated operations.

Attractive properties of ANN that are relevant to the equalization

problem at hand include massive parallelism, adaptive

processing, self-organization, universal approximation, and most

importantly, the capability of tackling highly nonlinear problems.

24

Proposed solution methodology

There are many research papers that agree on the fact that linear transversal

equalizers are not capable of equalizing highly nonlinear channels. Gibson et.al

[16] has explicitly mentioned that: “When the channel is non-minimum phase, the

decision boundary of equalizer is highly nonlinear and deviates markedly from

any decision boundary which can be formed by a linear transversal equalizer.”

Considering equalization as a geometric classification problem

rather than an inverse filter problem, our main objective

becomes the separation of the received symbols in the output

signal space whose optimal decision region boundaries are

generally highly nonlinear. The idea here is to classify the

received signal vectors by partitioning the signal space into some

decision regions. With this approach to equalization, complete

channel inversion is unnecessary, and the problem is tackled

using classification techniques.

In some aspects Artificial Neural Networks (ANN) can be used in

this field for achieving better performance than existing classical

methods. Since Artificial Neural Networks are well known for their

ability of performing classification tasks by forming complex

nonlinear decision boundaries, Neural equalizers based on neural

network have been recently receiving considerable attention in

order to increase receiver robustness.

Conclusion

In this report, neural network architectures and learning methods for solving the

problem of channel equalization has been proposed. The approach in future

research could be design a neural network structure and implementation of an

algorithm for it which can able to equalize time-varying channels with faster

convergence and simpler architecture. All the simulations will be implementing in

Matlab.

25

26

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