Reduced rank signaling in spatially correlated MIMO channels

The optimal input covariance matrix Q that achieves the ergodic capacity under the coherent assumption in a point-to-point, multi-antenna setting is a function of the spatial correlation and the transmit SNR. While the eigenvectors of Q can be characterized in closed-form for many realistic correlation models, the eigenvalues have to be determined numerically. However, it is well-known that the rank of Q is a non-decreasing function of SNR. Motivated by this fact, in this work, we study communication with a low-complexity family of input covariance matrices that are characterized by their rank, assuming uniform power allocation over the smaller-dimensional eigen-space. We quantify the impact of spatial correlation on the M-th transition-SNR which is defined as the smallest SNR at which rank-M transmission becomes optimal.