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Introduction

Wireless communication is the mostinteresting field of communication thesedays, because it supports mobility (mobileusers). However, many applications ofwireless comm. now require high-speed

communications (high-data-rates).

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What is the ISIInter-symbol-interference, takes placewhen a given transmitted symbol isdistorted by other transmitted symbols.

Cause of ISI

ISI is imposed due to band-limiting effectof practical channel, or also due to themulti-path effects (delay spread).

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Definition of the Equalizer:

the equalizer is a digital filter that providesan approximate inverse of channelfrequency response.

Need of equalization:

is to mitigate the effects of ISI to decreasethe probability of error that occurs withoutsuppression of ISI, but this reduction of

ISI effects has to be balanced withprevention of noise power enhancement.

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Free Transmission System:-ISI

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Components of ISI-free

Gotransmission system

Pulse shape g(t), used to improve the spectral

properties of the transmitted signal.

Matched filter, which is matched to the pulse shape

g(t), used to maximize SNR of the received signal.Sampler, to sample the signal with higher rate than

symbol-rate, and equalizer designed for the over-sampled signal (fractionally-spaced-equalization).

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

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

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Go( ) ( )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

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methods of implementation ofequalizers:

Transversal structure

which is a digital filter with N-taps that havea tunable complex coefficients, and N-1

delay elements.Lattice structure

which uses a sophisticated recursive

structure that has some advantages suchas, better stability, flexibility to changelength of equalizer.

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Go

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Types of Equalization techniques

Linear Equalization techniques

which are simple to implement, but greatlyenhance noise power because they work by

inverting channel frequency response.

Linear Equalization techniques-Non

which are more complex to implement, buthave much less noise enhancement than linearequalizers.

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Linear Equalizers

Zero-Forcing(ZF)

Minimum-Mean-

Square-Error(MMSE)

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

Go

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Zero-Forcing technique

It cancels all ISI effect by inverting the

channel frequency response, andaccordingly leads to large noiseenhancement.

Go

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Minimum Mean Square Error equalizer

Its goal of design is to minimize the expected MSEbetween transmitted symbol and its estimation.

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Non-LinearEqualizers

Decision-Feedback

Equalizer(DFE)

Maximum-Likelihood

Equalizer(MLSE)

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It consists of a feed-forward filter B(z),

and a feedback filter D(z).

It suffers from Error propagation whenbits are decoded in error, which leads topoor performance. Go

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

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Difference between

-Adaptive Equalization

-Blind Equalization.

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Adaptive Equalization

Definition.

What is meant by: Training, and Tracking

Go

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Blind Equalization

In which the signal recovery is done byprior knowledge concerning channel, or byarray calibration information (no need for

training sequence).

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Table of various algorithms and their trade-offs:

algorithm Multiplying-operations

complexity convergence tracking

LMS Low slow poor

MMSE Very high fast good

RLS High fast good

Fast

kalman

Fairly

Low

fast good

RLS-DFE

High fast good

2 3N toN

2 1N

22.5 4.5N N

20 5N

21.5 6.5N N

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Some performance figures:

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