Precoding of orthogonal space-time block codes in arbitrarily correlated MIMO channels: iterative and closed-form solutions

A memoryless precoder is designed for orthogonal space-time block codes (OSTBCs) for multiple-input multiple-output (MIMO) channels exhibiting joint transmit-receive correlation. Unlike most previous similar works which concentrate on transmit correlation only and pair-wise error probability (PEP) metrics, 1) the precoder is designed to minimize the exact symbol error rate (SER) as function of the channel correlation coefficients, which are fed back to the transmitter. 2) The correlation is arbitrary as it may or may not follow the so-called Kronecker structure. 3) 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 provide a simple closed-form precoder that handles the case of uncorrelated transmitters, correlated receivers. The second is a fast-converging numerical optimization of the exact SER which covers the general case. Finally, a number of novel properties of the minimum SER precoder are derived.