Orthogonal matrix precoding for relay networks

A distributed random linear-dispersion space-time block coding for relay networks is presented. The coding matrix assigned to each relay is built by a set of columns (or rows) of an independent random Haar-distributed unitary matrix. Within each transmitter, the particular structure of the codes allows to reduce interference in the multiplexed symbols, with respect to similar codes with random i.i.d. entries. The system is shown to have an asymptotically deterministic behavior (the convergence is in probability) as the dimensions of the code grow large while keeping constant the coding rate. The limiting performance can be characterized by means of free-probability theory: more specifically, the rectangular R-transform is employed to compute the asymptotic distribution of the singular values of a sum of rectangular matrices, which completely characterizes the asymptotic spectral efficiency of the corresponding channel.