Adaptive Precoder Using Sign Error Feedback for FEXT Cancellation in Multichannel Downstream VDSL

Recently a novel adaptive precoder for FEXT cancellation in downstream VDSL was presented and analyzed. This precoder is intended to use low rate feedback of the error signal in order to tune the transmit precoder. However, so far no exact analysis of this precoder is applicable for the case of low rate feedback. In this paper we analyze an adaptive precoder for FEXT cancellation in downstream multichannel VDSL, which is based solely on phase quantization of the error signals sent as feedback from the receivers. This analysis holds for feedback rates as low as 1 bit per sample, and is applicable for practical implementation. We give an upper bound on the precoder error and present sufficient conditions that guarantee precoder convergence as well as a steady state approximation. We then suggest to add also a very low rate coarse power quantization feedback. We show that a minor increase of 0.5% in feedback rate, can significantly improve the performance and the convergence rate of the precoder.