Periodic Hadamard Phase Precoding for HARQ Systems over Intersymbol Interference Channels

In this paper, we present a simple and effective preceding technique to mitigate intersymbol interference in communication systems that implement automatic repeat request (ARQ) protocols over slowly time-varying frequency-selective channels. In each ARQ transmission, only the phase of modulated symbols are changed according to a specific periodic pattern in order to pre-equalize the Euclidean distance at the output of the noiseless ISI channel in the minimum square error sense. We first derive a performance criterion on the selection of precoding phases. Then, an optimal periodic pattern is built without a priori knowledge of the channel state information by the transmitter, based on orthogonal Hadamard matrices. We show that the proposed precoding scheme provides a substantial gain in terms of frame error rate performance of the joint detector without significant increase of the receiver complexity, leading to both enhanced throughput efficiency and dropping rate in ARQ systems, especially for low to medium SNR range.