Equalization Techniques By: Nader Mohammed Abdelaziz

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

 What is the ISI Inter-symbol-interference, takes place when a given transmitted symbol is distorted by other transmitted symbols. Inter-symbol-interference, takes place when a given transmitted symbol is distorted by other transmitted symbols.  Cause of ISI ISI is imposed due to band-limiting effect of practical channel, or also due to the multi-path effects (delay spread). ISI is imposed due to band-limiting effect of practical channel, or also due to the multi-path effects (delay spread).

 Definition of the Equalizer: the equalizer is a digital filter that provides an approximate inverse of channel frequency response. the equalizer is a digital filter that provides an approximate inverse of channel frequency response.  Goal of equalization: is to mitigate the effects of ISI to decrease the probability of error that occurs without suppression of ISI, but this reduction of ISI effects has to be balanced with prevention of noise power enhancement. is to mitigate the effects of ISI to decrease the probability of error that occurs without suppression of ISI, but this reduction of ISI effects has to be balanced with prevention of noise power enhancement.

 I I I I SSSS IIII ---- FFFF rrrr eeee eeee T T T T rrrr aaaa nnnn ssss mmmm iiii ssss ssss iiii oooo nnnn S S S S yyyy ssss tttt eeee mmmm ::::

Components of ISI-free transmission system: BACK> BACK> Pulse shape g(t), used to improve the spectral properties of the transmitted signal. 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. 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). 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. Decision device, used to round the estimated symbol (o/p of the equalizer) to the training sequence. Tap-update algorithm, to update the tap coefficients to improve the performance of equalizer filter. Tap-update algorithm, to update the tap coefficients to improve the performance of equalizer filter.

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methods of implementation of equalizers:  T T T T rrrr aaaa nnnn ssss vvvv eeee rrrr ssss aaaa llll s s s s tttt rrrr uuuu cccc tttt uuuu rrrr eeee which is a digital filter with N-taps that have a tunable complex coefficients, and N-1 delay elements.  L L L L aaaa tttt tttt iiii cccc eeee s s s s tttt rrrr uuuu cccc tttt uuuu rrrr eeee which uses a sophisticated recursive structure that has some advantages such as, better stability, flexibility to change length of equalizer.

Types of Equalization techniques  L L L L iiii nnnn eeee aaaa rrrr E E E E qqqq uuuu aaaa llll iiii zzzz aaaa tttt iiii oooo nnnn t t t t eeee cccc hhhh nnnn iiii qqqq uuuu eeee ssss which are simple to implement, but greatly enhance noise power because they work by inverting channel frequency response.  N N N N oooo nnnn ---- LLLL iiii nnnn eeee aaaa rrrr E E E E qqqq uuuu aaaa llll iiii zzzz aaaa tttt iiii oooo nnnn t t t t eeee cccc hhhh nnnn iiii qqqq uuuu eeee ssss which are more complex to implement, but have much less noise enhancement than linear equalizers.

Linear Equalizers Zero-Forcing (ZF) Minimum-Mean- Square-Error (MMSE)

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

Zero-Forcing technique It cancels all ISI effect by inverting the channel frequency response, and accordingly leads to large noise enhancement. B B B B B AAAA CCCC KKKK >>>>

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

Non-Linear Equalizers Decision-Feedback Equalizer (DFE) Maximum-Likelihood Equalizer (MLSE)

It consists of a feed-forward filter B(z), and a feedback filter D(z). It consists of a feed-forward filter B(z), and a feedback filter D(z). It suffers from Error propagation when bits are decoded in error, which leads to poor performance. It suffers from Error propagation when bits are decoded in error, which leads to poor performance. BACK> BACK>BACK>

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

 Difference between Adaptive Equalization, and Blind Equalization. Adaptive EqualizationBlind Equalization.Adaptive EqualizationBlind Equalization.

Adaptive Equalization Definition. Definition. What is meant by: Training, and Tracking What is meant by: Training, and Tracking

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

Table of various algorithms and their trade- offs: algorithm Multiplying- operations complexityconvergencetracking LMSLowslowpoor MMSE Very high fastgood RLSHighfastgood FastkalmanFairlyLowfastgood RLS- DFE Highfastgood

Some performance figures: