Analysis of Zero-Padded Optimal Transceivers

Abstract

This paper analyzes both the mean-square error (MSE) and the mutual information in block-based transceivers that employ zero-padding. We consider both linear transceivers and decision-feedback equalizers (DFE) that minimize the MSE of symbols. These systems may enjoy the zero-forcing property or not, and may use unitary precoder or not. We demonstrate mathematically that the MSE/mutual information related to these transceivers are: (i) monotone increasing/decreasing functions of the number of transmitted symbols per block; (ii) monotone decreasing/increasing functions of the number of redundant data used in the equalization process of a block; and (iii) increased/decreased whenever non-minimum phase channels are utilized, instead of their minimum phase counterparts, assuming that one does not use the whole received data block to estimate the transmitted signal. As consequence of the former results, we also prove that, for both DFE and minimum error-probability systems, the average error-probability of symbols maintains the same monotonic behavior as the average MSE of symbols. The theoretical results do not include pure minimum MSE-based systems.