Equalization Equalization TechniquesTechniques

By: Mohamed Osman Ahmed By: Mohamed Osman Ahmed MahgoubMahgoub

IntroductionIntroduction

Wireless communication is the mostWireless communication is the most interesting field of communication these interesting field of communication these days, because it supports mobility (mobile days, because it supports mobility (mobile users). However, many applications of users). However, many applications of wireless comm. now require high-speed wireless comm. now require high-speed communications (high-data-rates) communications (high-data-rates)..

What is What is thethe ISI ISI

Inter-symbol-interference, takes Inter-symbol-interference, takes place when a given transmitted place when a given transmitted symbol is distorted by other symbol is distorted by other transmitted symbols.transmitted symbols.

Cause of ISICause of ISI

ISI is imposed due to band-limiting ISI is imposed due to band-limiting effect of practical channel, or also effect of practical channel, or also due to the multi-path effects (delay due to the multi-path effects (delay spread).spread).

Definition of the Equalizer:Definition of the Equalizer:

the equalizer is a digital filter that the equalizer is a digital filter that provides an approximate inverse of provides an approximate inverse of channel frequency response.channel frequency response.

Need of equalization:Need of equalization:

is to mitigate the effects of ISI to is to mitigate the effects of ISI to decrease the probability of error that decrease the probability of error that occurs without suppression of ISI, but occurs without suppression of ISI, but this reduction of ISI effects has to be this reduction of ISI effects has to be balanced with prevention of noise balanced with prevention of noise power enhancement.power enhancement.

ISI-Free Transmission System:ISI-Free Transmission System:

Components of ISI-free Components of ISI-free transmission system transmission system GoGo

► Pulse shape g(t), used to improve the spectral Pulse shape g(t), used to improve the spectral properties of the transmitted signal.properties of the transmitted signal.

► Matched filter, which is matched to the pulse shape Matched filter, which is matched to the pulse shape g(t), used to maximize SNR of the received signal.g(t), used to maximize SNR of the received signal.

► Sampler, to sample the signal with higher rate than Sampler, to sample the signal with higher rate than symbol-rate, and equalizer designed for the over-symbol-rate, and equalizer designed for the over-sampled signal (fractionally-spaced-equalization).sampled signal (fractionally-spaced-equalization).

► Decision device, used to round the estimated Decision device, used to round the estimated symbol (o/p of the equalizer) to the training symbol (o/p of the equalizer) to the training sequence.sequence.

► Tap-update algorithm, to update the tap coefficients Tap-update algorithm, to update the tap coefficients to improve the performance of equalizer filter.to improve the performance of equalizer filter.

►

GoGo( ) ( )kk

d t d t kT

*( ) ( ) ( ) ( )mf t g t c t g t ( ) ( ) ( )h t g t c t

( ) ( ) ( ) ( ) ( ) ( )g k b gy t d t f t n t d f t kT n t [ ] ( ) ( ) [ ] [ ] [0] [ ] [ ]k s s g s k n k

k k k n

y n d f nT kT n nT d f n k v n d f d f n k v n

methods of implementation of methods of implementation of equalizersequalizers::

Transversal structureTransversal structure which is a digital filter with N-taps that which is a digital filter with N-taps that

have a tunable complex coefficients, have a tunable complex coefficients, and N-1 delay elements.and N-1 delay elements.

Lattice structureLattice structure which uses a sophisticated recursive which uses a sophisticated recursive

structure that has some advantages structure that has some advantages such as, better stability, flexibility to such as, better stability, flexibility to change length of equalizer.change length of equalizer.

GoGo

Types of Equalization Types of Equalization techniquestechniques

Linear Equalization techniquesLinear Equalization techniques

which are simple to implement, but which are simple to implement, but greatly enhance noise power because greatly enhance noise power because they work by inverting channel frequency they work by inverting channel frequency responseresponse..

Non-Linear Equalization techniquesNon-Linear Equalization techniques

which are more complex to implement, which are more complex to implement, but have much less noise enhancement but have much less noise enhancement than linear equalizersthan linear equalizers..

Linear Equalizers

Zero-Forcing(ZF)

Minimum-Mean-Square-Error

(MMSE)

Linear equalizer with N-taps, and (N-1) Linear equalizer with N-taps, and (N-1) delay elementsdelay elements..

GoGo

Zero-Forcing techniqueZero-Forcing technique

It cancels all ISI effect by inverting the It cancels all ISI effect by inverting the channel frequency response, andchannel frequency response, andaccordingly leads to large noise accordingly leads to large noise enhancementenhancement..

►GoGo

Minimum Mean Square Error equalizerMinimum Mean Square Error equalizer

Its goal of design is to minimize the expected MSE Its goal of design is to minimize the expected MSE between transmitted symbol and its estimationbetween transmitted symbol and its estimation..

Non-Linear Equalizers

Decision-FeedbackEqualizer

(DFE)

Maximum-LikelihoodEqualizer(MLSE)

► It consists of a feed-forward filter B(z), It consists of a feed-forward filter B(z), and a feedback filter D(z).and a feedback filter D(z).

► It suffers from Error propagation when It suffers from Error propagation when bits are decoded in error, which leads to bits are decoded in error, which leads to poor performance. poor performance. GoGo

It is the optimal equalization technique, but its It is the optimal equalization technique, but its complexity increases exponentially with the delay complexity increases exponentially with the delay spread.spread.

Difference betweenDifference between

-Adaptive Equalization-Adaptive Equalization

-Blind Equalization.-Blind Equalization.

Adaptive EqualizationAdaptive Equalization

►Definition.Definition.

►What is meant by: Training, and What is meant by: Training, and TrackingTracking

GoGo

Blind EqualizationBlind Equalization

In which the signal recovery is done In which the signal recovery is done by prior knowledge concerning by prior knowledge concerning channel, or by array calibration channel, or by array calibration information (no need for training information (no need for training sequence).sequence).

Table of various algorithms and their Table of various algorithms and their trade-offstrade-offs::

algorithalgorithmm

Multiplying-Multiplying-operationsoperations

complexitycomplexity convergenconvergencece

trackingtracking

LMSLMS LowLow slowslow poorpoor

MMSEMMSE Very highVery high fastfast goodgood

RLSRLS HighHigh fastfast goodgood

FastFast

kalmakalmann

FairlyFairly

LowLowfastfast goodgood

RLS-RLS-DFEDFE

HighHigh fastfast goodgood

2 3N toN

2 1N

22.5 4.5N N

20 5N

21.5 6.5N N

Some performance figuresSome performance figures::