Rate-Optimal MIMO Transmission with Mean and Covariance Feedback at Low SNRs

This paper considers a multiple-input–multiple-output (MIMO) wireless communication scenario in which the channel follows a block-fading model with a general spatially correlated complex Gaussian distribution with nonzero mean. We derive an explicit characterization of the (ergodic) rate-optimal input covariance for systems that operate at low signal-to-noise ratios (SNRs). In particular, we obtain a closed-form expression for the matrix whose principal eigenvector yields the optimal beamforming direction. For the class of nonzero-mean channels with Kronecker-structured covariance, we also derive a threshold on the input signal power below which the low-SNR approximation is accurate. Our numerical results show that significant improvements in the low-SNR achievable rate can be obtained by (jointly) exploiting the mean and covariance of the channel model. Our results also show that these improvements can be extended to moderate-to-high SNRs by signaling along the low-SNR optimal eigenbasis with optimized power allocation.