Precoding for space-time block codes in (non-)Kronecker correlated MIMO channels

A memoryless linear precoder is designed for space-time block codes (STBC) for quasi static non-frequency selective correlated Rayleigh fading multiple-input multiple-output (MIMO) channels. The precoder is designed to minimize a symbol error-based metric as function of the joint transmit-receiver channel correlation coefficients which are supposed to be fed back to the transmitter. The correlation may or may not follow the Kronecker structure. We demonstrate in particular the impact of the precoder on receive correlated channels when the Kronecker model does not hold. A numerical optimization method is proposed that can be used for invertible correlation matrices. Monte Carlo simulations show that the proposed precoder outperforms a system not having a precoder for highly correlated channels.