channel estimation techniques_last(1)

8/3/2019 Channel Estimation Techniques_last(1)

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Channel Equalization Techniques

Fernando GregorioBased on:

1-Adaptive Signal Processing, Benesty-Huang

2-Fundamentals of Adaptive Filtering, Ali H. Sayed


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Outline

Introducction

Channel equalization

Linear equalizers

Decision feedback equalizers

Adaptive algorithms for channel equalization

Adaptive linear equalizer

Adaptive DFE

Training and tracking

Simulations

Static channel

Time varying channel


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Introduction

In a communication system, the transmitter sends theinformation over an RF channel.

The channel distorts the transmitted signal befores itreaches the receiver.

The receiver task is to figure out what signal wastransmittedTurn the received signal inunderstandable information.


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Linear Equalizers

The current and the past values of the received signal arelinearly weigthed by equalizer coefficients and summed toproduce the output.

The ISI can be completely removed, without taking inconsideration the resultanting noise enhacementZeroforcing equalizer.

A substantial increment of the noise power is created using ZFequalizer.


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Introduction

Intersymbol Interference (ISI)

Noise

Channel

Noise

desired signal ISI noise


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Introduction

The purpose of an equalizer is to reduce the ISI as much aspossible to maximize the probability of correct decisions

Channel

Noise

Equalizer


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Linear Equalizers

Mean-Square Error equalizer

From the point-of-view of minimizing error probability, it isadventageous to allow some residual ISI if this can reduce thenoise power.

The MSE criterion attempts to minimize the total errorbetween the slicer input and the transmitted data symbol.

Power noiseTransmit signal


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Decision-Feedback Equalizers

Simple nonlinear equalizer which is particulary useful forchannel with severe amplitude distortion.

DFE uses desicion feedback to cancel the interferfence fromsymbols which have already have been detected.

The basic idea is that if the values of the symbols alreadydetected are known (past decisions are assumed correct),then the ISI contributed by these symbols can be canceled

exactly.


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Decision feedback equalizer structure The forward and feedback coefficients may be adjusted

simultaneously to minimize the MSE.

Feed forward

filter (FFF)

Feed backfilter (FBF)

Adjustment offilter coefficients

Input Output

++

Symboldecision


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Adaptive Equalization

The object is to adapt the coefficients to minimize the noiseand intersymbol interference (depending on the type ofequalizer) at the output.

The adaptation of the equalizer is driven by an error signal.

The aim is to minimize:2

kJ E e

EqualizerChannel

+

Errorsignal


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Adaptive Equalization

There are two modes that adaptive equalizers work; Decision Directed Mode:The receiver decisions are used to generate the error signal.

Decision directed equalizer adjustment is effective in trackingslow variations in the channel response. However, thisapproach is not effective during initial acqusition .

Training Mode:To make equalizer suitable in the initial acqusition duration, a

training signal is needed. In this mode of operation, thetransmitter generates a data symbol sequence known to the

receiver.Once an agreed time has elapsed, the slicer output is used as atraining signal and the actual data transmission begins.


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Stochastic gradient algorithm

The main idea is to minimize the mean square error betweenthe output of the equalizer, and the transmitted signal.

Since the number of samples that the receiver observe isfinite, mean square is calculated by using time averagesinstead of ensemble averages.

The resulting adaptation algorithm becomes;

Receivedsignal

Errorsignal


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Stochastic gradient algorithm

LINEAR EQUALIZERErrorsignal

EqualizerChannel

+

Trainning mode

Decision directed mode


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Decision feedback equalizer structure The forward and feedback coefficients may be adjusted

simultaneously to minimize the MSE.

Input

Feed forward

C(z)

Feedback

F(z)


Output+

+Symboldecision


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Input

Feed forward

C(z)

Feedback

F(z)


Output+

+Symboldecision


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Evaluation 1

Linear equalizer

LMS

Wiener solution

Scenarios

Channel 1

Channel 2 ( Time varying channel)


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Evaluation 1- Linear Equalizer

Static Channel h = [0.2, -0.15, 1.0, 0.21, 0.03] Lf=5

Delay=4

SNR=30dB


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Evaluation 1- Linear Equalizer

Static Channel h = [0.2, -0.15, 1.0, 0.21, 0.03] Lf=12

Delay=11

SNR=30dB


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Evaluation 1 - Linear Equalizer

Time varying channel Rayleigh

5 taps, fd=10 Hz , Ts=0.8us

Lf=8 , mu=0.1

Delay=7

SNR=30dB


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Evaluation 1 - Linear Equalizer

Time varying channel Rayleigh


Lf=8 , mu=0.1

Delay=7

SNR=30dB


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Evaluation 2

Desicion feedback equalizer

LMS

Decision direct mode and trainning mode

Scenarios

Channel 1 h = [0.2, -0.15, 1.0, 0.21, 0.03]

Channel 2 h = [0.2, -0.35, 1.0, 0.51, 0.03]


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Evaluation 2

Decision Feedback equalizer (static channel)

Channel 2Severe ISI

Channel 1


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Evaluation 3

Decision Feedback equalizer Rayleigh


Lf=8 , mu=0.015 ,Lfeed=5

Delay=7

SNR=30dB


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Evaluation 3

Decision Feedback equalizer Rayleigh


Lf=8 , mu=0.015 ,Lfeed=5

Delay=7 SNR=30dB


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Matlab examples


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Conclusions

Adaptive equalizer is an essential component ofcommunication systems.

Low complexity implementation with a good

performance in channel with low levels of ISI isobtained using linear equalizers.

In case of channels with severe ISI, DFE is the best

option.

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