Equalization Techniques By: Nader Mohammed Abdelaziz.
-
Upload
frank-woods -
Category
Documents
-
view
228 -
download
0
description
Transcript of Equalization Techniques By: Nader Mohammed Abdelaziz.
Equalization TechniquesEqualization Techniques
By: Nader Mohammed By: Nader Mohammed AbdelazizAbdelaziz
IntroductionIntroduction Wireless communication is the most Wireless communication is the most
interesting field of communication interesting field of communication these days, because it supports these days, because it supports mobility (mobile users). However, mobility (mobile users). However, many applications of wireless comm. many applications of wireless comm. now require high-speed 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.
Goal of equalization:Goal 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: BACK> BACK>
• 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 symbol Decision device, used to round the estimated symbol (o/p of the equalizer) to the training sequence.(o/p of the equalizer) to the training 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.
BACK> BACK> ( ) ( )k
k
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 equalizers:equalizers: 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.
BACK>BACK>
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 response.response.
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 equalizers.than linear equalizers.
Linear Equalizers
Zero-Forcing(ZF)
Minimum-Mean-Square-Error
(MMSE)
• Linear equalizer with N-taps, and (N-Linear equalizer with N-taps, and (N-1) delay elements.1) delay elements.
BACK>BACK>
Zero-Forcing techniqueZero-Forcing technique• It cancels all ISI effect by inverting It cancels all ISI effect by inverting
the channel frequency response, and the channel frequency response, and accordingly leads to large noise accordingly leads to large noise enhancement.enhancement.
BACK>BACK>
• Its goal of design is to minimize the Its goal of design is to minimize the expected MSE between transmitted expected MSE between transmitted symbol and its estimation.symbol and its estimation.
Non-Linear Equalizers
Decision-FeedbackEqualizer
(DFE)
Maximum-LikelihoodEqualizer(MLSE)
• It consists of a feed-forward filter It consists of a feed-forward filter B(z), and a feedback filter D(z).B(z), and a feedback filter D(z).
• It suffers from Error propagation It suffers from Error propagation when bits are decoded in error, when bits are decoded in error, which leads to poor performance.which leads to poor performance.
BACK>BACK>
• It is the optimal equalization technique, It is the optimal equalization technique, but its complexity increases but its complexity increases exponentially with the delay spread.exponentially with the delay spread.
Difference between Difference between Adaptive Equalization, and Adaptive Equalization, and Blind Equalization.Blind Equalization.
Adaptive EqualizationAdaptive Equalization• Definition.Definition.
• What is meant by: Training, and What is meant by: Training, and TrackingTracking
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-offs:trade-offs:
algorithalgorithmm
Multiplying-Multiplying-operationsoperations
complexitycomplexity convergenconvergencece
trackingtracking
LMSLMS LowLow slowslow poorpoorMMSEMMSE Very highVery high fastfast goodgoodRLSRLS HighHigh fastfast goodgoodFastFastkalmakalmann
FairlyFairlyLowLow
fastfast goodgood
RLS-RLS-DFEDFE
HighHigh fastfast goodgood
2 3N toN2 1N
22.5 4.5N N
20 5N
21.5 6.5N N
Some performance figures:Some performance figures: