Optimization of sequences in CDMA systems: A statistical–mechanics approach

A statistical–mechanics approach is useful not only in analyzing the macroscopic system performance of wireless communication systems, but also in discussing design problems of wireless communication systems. We discuss a design problem of spreading sequences in code-division multiple-access (CDMA) systems, as an example demonstrating the usefulness of the statistical–mechanics approach. We analyze, via the replica method, the average mutual information between inputs and outputs of a randomly spread CDMA channel, and discuss the optimization problem with the average mutual information as the measure of optimization. It has been shown that the average mutual information is maximized by orthogonally-invariant random Welch bound equality (WBE) spreading sequences. This finding is an extension of the optimality of WBE spreading sequences with Gaussian inputs for non-Gaussian inputs.