Quantization noise and eigenvalue statistics in the stochastic gradient polarity adjustment of an adaptive equalizer

An experimental adaptive decision feedback equalizer (DFE), with jointly adjusted sampling phase, and which employs a decision-directed stochastic gradient polarity (DDSGP) algorithm, is described. Measured performance with respect to odd-order multipath frequency response is found to be significantly worse than the calculated mean square error performance which does not include quantization noise and misadjustment noise. The discrepancy is predicted from a theorem of Gersho.
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Gersho's theorem predicts the excess noise due to the gradient polarity (GP) algorithm as a function of eigenvalue statistics, which are calculated as a function of multipath distortion.