Minimum exact SER precoding of orthogonal space-time block codes for correlated MIMO channels

A memoryless precoder is designed for orthogonal space-time block codes for multiple-input multiple-output channels exhibiting joint transmit-receive correlation. Unlike most previous similar work which concentrated on transmit correlation only and pair-wise error probability (PEP) metrics, the precoder is designed to minimize the exact symbol error rate (SER) as a function of the channel correlation coefficients, which are fed back to the transmitter, and the correlation may or may not follow the so-called Kronecker structure. The proposed method can handle general propagation settings including those arising from a cooperative macro-diversity (multi-base) scenario. We present two algorithms. The first is suboptimal, but provides a simple closed-form precoder that handles the case of uncorrelated transmitters, correlated receivers. The second is a fast-converging numerical optimization which covers the general case. The results show the SER based precoder has small gains over the PEP based precoder for moderate signal-to-noise ratios (SNR). Several properties of the minimum SER precoder are given.