the desired symbol is in the mid tap
Imagine a binary sistem. Peak distortion is the ratio between the maximum absolute value of ISI and the signal alone. It is equal to the maximum closure of the eye in the eye pattern.What is peak distortion? and why it is defined the way it is defined? and what does this have to do with ZF equalization?
Imagine a binary sistem. Peak distortion is the ratio between the maximum absolute value of ISI and the signal alone. It is equal to the maximum closure of the eye in the eye pattern.
For a given support of the equalizer (span of the filter before and after the "main sample"), the equalizer that achieves the minimum peak distortion is the zero-forcing equalizer.
Regards
Z
David83,
ZF equalizer minimizes the metric D that you said, that is the peak distortion. But it can not reduce it to zero, unless the equalizer has infinite length.
Suppose that the equalizer has Nb taps before the curren symbol and Na taps after it. The set of coefficients that minimizes the metric D (with the constraint q0=1) is the set that makes that the response has Nb zeros before the current symbol and Na zeros after it. (Here is the reason of the name "zero forcing".)
The equalizer has Na+Nb+1 degrees of freedom: it can satisfy Na+Nb+1 conditions. They are:
qn=0 for -Nb<=n<=1
q0=1
qn=0 for 1<=n<=Na
Doing so, the sampes of the impuse response increase beyond the above mentioned range, i.e. for n<-Nb and n>Na. Nevertheless, the residual peak distortion is less than the original one (I don't remember exactly, but I think that this last statement is true with the condition that initially the eye is not completely closed, i.e. D<1).
Regards
Z
I came up with an idea for confusion of post#2 (future samples):
If the equalizer has N1 taps for future samples and N2 taps for previous samples, the receiver produces any output with delay of N1 samples. This delay would be enough to get all the needed future samples. So as a whole the system will produce equalized output with a delay
Correct. But I still confused about the relationship between \[\mathcal{D}\] and ZF. Why we use the absolute value in the minimization?
Well now the whitening filter has future samples in its implementation.
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