Decision FeedbackEqualizer

Overview

•Overview of Decision Feedback Equalizer•Results from implementation•Conclusion

Equalization

•The process of reversing the effect of the channel to recover the input signal.•The goal of an equalizer is to eliminate the inter symbol interference and the additive noise as much as possible.

Categories of Equalizers•Linear Equalizers :• Rely on the principle of inverting the channel response.• Removes ISI but causes noise enhancement.

•Nonlinear Equalizers• Estimates ISI in the feedback path• Reconstructs ISI and removes it from the signal.

Need for Nonlinear equalizers

•Linear equalizers are simple to implement but they do not work well if the channel has both poles and zeroes.

•Nonlinear equalizer can help in counteracting these effects.

Decision Feedback EqualizerFeedforward Filter:

• If the transfer function is of the form H(z) = C(z)/A(z). It helps in removing the effects of A(z)

Feedback Filter:

• It helps in removing the Inter Symbol Interference(ISI).

• If the transfer function of the filter is H(z)=C(z)/A(z). It helps in removing the effects of C(z)

Decision Device

• It makes the decision depending upon the current estimate.

• This decision becomes the input to the feeback filter in decision directed mode.

Modes of operation• Training Mode: • Preamble: A known signal is made input to the feedback filter.• Error signal: Error signal is generated by comparing estimate and the

preamble to adjust the coefficients of the filter

•Decision Directed Mode:• The output of the decision device is made input to the feedback filter.

Input Signal

• A BPSK signal containing ten thousand samples.

• It had zero mean and unit variance.

Channel transfer function

1+ 0.078z-1 + 0.5z-2

1 - 0.5z-1

• The channel has both poles and zeroes.

Output Signal

Case 1:◦ When no noise was added to the received signal

Case 2:◦ In presence of noise with high SNR

Case 3:◦ In presence of noise with low SNR

In Absence of Noise

1+ 0.078z-1 + 0.5z-2 1 - 0.5z-1

Estimate of the input signal

Decision Feedback Equalizer Linear Equalizer

Errors in EstimationDecision Feedback Equalizer

Linear Equalizer

Errors 0 15

Instantaneous MSE

Decision Feedback Equalizer Linear Equalizer

Weight vector after trainingw =

-0.0780-0.5000-2.7883e-121.0000-0.5000

Coefficients of the feedback filter

Coefficients of the Feedforward filter

1+ 0.078z-1 + 0.5z-2 1 - 0.5z-1

Hch(z) =

• The feedback filter removes the effects of C(z).

• The feedforward filter removes the effects of A(z).

C(z) = A(z)

For High SNR

1+ 0.078z-1 + 0.5z-2 1 - 0.5z-1

Noise

Estimate of the input signal

Decision Feedback Equalizer Linear Equalizer

Errors in EstimationDecision Feedback Equalizer

Linear Equalizer

Errors 0 20

Instantaneous MSE

Linear EqualizerDecision Feedback Equalizer

For Low SNR

1+ 0.078z-1 + 0.5z-2 1 - 0.5z-1

Noise

Estimate of the input signal

Decision Feedback Equalizer Linear Equalizer

Errors in EstimationDecision Feedback Equalizer

Linear Equalizer

Errors 15 143

Instantaneous MSE

Linear EqualizerDecision Feedback Equalizer

Conclusion• Linear equalizer are simple to implement but causes noise enhancement.

• Decision Feedback equalizers should be used in applications where Linear equalizers have poor performance.

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