Periodic Hadamard Phase Precoding for HARQ Systems Over Intersymbol Interference Channels

In this paper, the authors present a simple and effective precoding technique to mitigate inter-symbol 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. They 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.