Entropy of general gaussian distributions and MIMO channel capacity maximizing precoder and decoder

Exploiting channel state information at the transmitter and receiver to design an optimal linear precoder and decoder for a multiple-input multiple-output (MIMO) communication system is an active research area. The design is often based on the information rate criterion, that is to design the precoder and decoder such that the system capacity is maximized, subject to the average transmit power constraint. Although such an optimization problem has been considered intensively and there have been numerous proposals so far, they are not rigorously correct. We propose a mathematically rigorous framework for solving this optimization problem. Our proposed solution is applicable to both MIMO flat fading and frequency selective fading channels. Simulations verify the theoretical analysis.