Power allocation in multi-antenna 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 multi-antenna 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.