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
Introduction...18
Learning Process...19
4. CHANNEL EQUALIZATION USING ANNs...22
Introduction...23
State of the Art...24
Proposed solution methodology...24
Conclusion...25
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
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
Chapter 1
1. INTRODUCTION
PROBLEM STATEMENT
ORGANIZATION OF REPORT
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 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.
Chapter 2
2. CHANNEL EQUALIZATION
INTRODUCTION TO CHANNEL EQUALIZATION
FUNDAMENTALS OF EQUALIZATION
ADAPTIVE EQUALIZATION
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.
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.
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 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
f*(t), is the complex conjugate of f(t) ,
nb(t), is the baseband noise at the input of the equalizer, and
⨂ , denotes the convolution operation
If the impulse response of the equalizer is heq(t), then the output of the equalizer is
^d (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
ckδ
(
t−n Ts)
2-3Where, 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 ^d (t)=x (t ) in equation (2.2), g(t) must be equal
to
g (t)=f¿
Fig 2-3: Communication system with an adaptive equalizer
The goal of equalization is to satisfy equation (2.4). In the frequency domain, equation (2.4) can be expressed as
Heq(f ) F¿
(−f )=1 2-5
Where, 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
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
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.
Chapter 3
3. ARTIFICIAL NEURAL NETWORKS
INTRODUCTION TO ANN
STRUCTURE OF ANN
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 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 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 wkjxj 3-6 And yk=φ(
vk+θk)
3-7 Network Architecturesa.
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].
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.
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
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= 1
1+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
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=f1(w11x1+w21x2) 3-10 y2=f2(w12x1+w22x2) 3-11 y3=f3(w13x1+w23x2) 3-12 y4=f4
(
w14x1+w24x2)
+w34y3 3-13 y5=f4(
w15x1+w25x2)
+w35y3 3-14 y6=f6(w46y4+w56y5) 3-15The 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
δ5=w56δ 3-18 δ3=w34δ4+w35δ5 3-19 δ2=w24δ4+w25δ5 3-20 δ1=w14δ4+w15δ5 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=
{
learning rate parameter}
×{
local gradient}
×{
input signal of neuroni}
∆ wij(n)=η ×δi× yj(n) 3-22The 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
Chapter 4
4. CHANNEL EQUALIZATION USING ANNs
INTRODUCTION
STATE OF THE ART
PROPOSED SOLUTION METHODOLOGY
CONCLUSION
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
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.
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.
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