MMSE analysis of certain large isometric random precoded systems

Linear precoding consists in multiplying by a N×K matrix a K-dimensional vector obtained by serial to parallel conversion of a symbol sequence to be transmitted. We analyse the performance of MMSE receivers for certain large random isometric precoded systems on fading channels. Using new tools, borrowed from the so-called free probability theory, it can be shown that the signal to interference plus noise ratio at the equalizer output converges almost surely to a deterministic value depending on the probability distribution of the channel coefficients when N→+∞ and K/N→α⩽1. These asymptotic results are used to optimally balance the redundancy introduced between linear precoding and classical convolutional coding, while preserving a simple MMSE equalization scheme at the receiver