Power allocation in multiantenna communication with statistical channel information at the transmitter

We characterize the power allocation that maximizes the rate per unit bandwidth supported with arbitrary reliability over single-user multiantenna channels known instantaneously by the receiver and in distribution by the transmitter. The characterization is valid for arbitrary channels and numbers of antennas. Although, in general, it leads to a fixed-point solution, at low and high signal-to-noise it provides explicit allocations. For arbitrary signal-to-noise ratios, we present an iterative algorithm that exhibits remarkable properties: robustness, rapid convergence and universal applicability. Further, when applied to the proper set of signalling eigenvectors, the algorithm converges to the power allocation that attains capacity.