1. Channel Equalization Techniques
Fernando Gregorio
Based on:
1-Adaptive Signal Processing, Benesty-Huang
2-Fundamentals of Adaptive Filtering, Ali H. Sayed

2. 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
S Seminar

3. Introduction
In a communication system, the transmitter sends the information over an RF channel.
The channel distorts the transmitted signal befores it reaches the receiver.
The receiver ”task” is to figure out what signal was transmitted Turn the received signal in understandable information.
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4. Introduction Intersymbol Interference (ISI) Noise ISI Noise Channel
desired signal
noise
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5. Introduction Equalizer
The purpose of an equalizer is to reduce the ISI as much as possible to maximize the probability of correct decisions
Noise
Channel
Equalizer
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6. Linear Equalizers
The current and the past values of the received signal are linearly weigthed by equalizer coefficients and summed to produce the output.
The ISI can be completely removed, without taking in consideration the resultanting noise enhacement  Zero forcing equalizer.
A substantial increment of the noise power is created using ZF equalizer.
S Seminar

7. Linear Equalizers Mean-Square Error equalizer
From the point-of-view of minimizing error probability, it is adventageous to allow some residual ISI if this can reduce the noise power.
The MSE criterion attempts to minimize the total error between the slicer input and the transmitted data symbol.
Transmit signal
Power noise
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8. Decision-Feedback Equalizers
Simple nonlinear equalizer which is particulary useful for channel with severe amplitude distortion.
DFE uses desicion feedback to cancel the interferfence from symbols which have already have been detected.
The basic idea is that if the values of the symbols already detected are known (past decisions are assumed correct), then the ISI contributed by these symbols can be canceled exactly.
S Seminar

9. Decision-Feedback Equalizers
Decision feedback equalizer structure
The forward and feedback coefficients may be adjusted simultaneously to minimize the MSE.
Feed back filter (FBF)
Input
Output
Feed forward filter (FFF) + +
Symbol decision
Adjustment of filter coefficients
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10. Adaptive Equalization
The object is to adapt the coefficients to minimize the noise and intersymbol interference (depending on the type of equalizer) at the output.
The adaptation of the equalizer is driven by an error signal.
The aim is to minimize:
Error signal +
Channel
Equalizer
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11. 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 tracking slow variations in the channel response. However, this approach 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, the transmitter generates a data symbol sequence known to the receiver.
Once an agreed time has elapsed, the slicer output is used as a training signal and the actual data transmission begins.
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12. Stochastic gradient algorithm
The main idea is to minimize the mean square error between the output of the equalizer, and the transmitted signal.
Since the number of samples that the receiver observe is finite, mean square is calculated by using time averages instead of ensemble averages.
The resulting adaptation algorithm becomes;
Error signal
Received signal
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13. Stochastic gradient algorithm
Error signal
LINEAR EQUALIZER
Trainning mode
Decision directed mode +
Channel
Equalizer
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14. Decision-Feedback Equalizers
Decision feedback equalizer structure
The forward and feedback coefficients may be adjusted simultaneously to minimize the MSE.
Feed forward
C(z)
Feedback
F(z)
Adjustment of filter coefficients
Output +
Symbol decision
Input
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15. Decision-Feedback Equalizers
Feed forward
C(z)
Feedback
F(z)
Adjustment of filter coefficients
Output +
Symbol decision
Input
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16. Evaluation 1 Linear equalizer LMS Wiener solution Scenarios Channel 1
Channel 2 ( Time varying channel)
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17. 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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18. 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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19. 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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20. Evaluation 1 - Linear Equalizer
Time varying channel
Rayleigh
5 taps, fd=80 Hz , Ts=0.8us
Lf=8 , mu=0.1
Delay=7
SNR=30dB
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21. 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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22. Evaluation 2 Decision Feedback equalizer (static channel) Channel 2
Severe ISI
Channel 1
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23. Evaluation 3 Decision Feedback equalizer Rayleigh
5 taps, fd=20 Hz , Ts=0.8us
Lf=8 , mu=0.015 ,Lfeed=5
Delay=7
SNR=30dB
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24. Evaluation 3 Decision Feedback equalizer Rayleigh
5 taps, fd=80 Hz , Ts=0.8us
Lf=8 , mu=0.015 ,Lfeed=5
Delay=7
SNR=30dB
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25. Conclusions
Adaptive equalizer is an essential component of communication systems.
Low complexity implementation with a good performance in channel with low levels of ISI is obtained using linear equalizers.
In case of channels with severe ISI, DFE is the best option.
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