Eigenvalue-based optimum-power allocation for Gaussian vector channels

In this correspondence, we determine the optimal power allocation to antennas in a Gaussian vector channel subject to ℓ_p-norm constrained eigenvalues. Optimal solutions are characterized by using directional derivatives of the mutual information. As the central result, the optimal power assignment is obtained as the level crossing points of a set of simple monotone functions. The well-known water-filling principle for sum power constraints is retrieved as the limiting case p=1. A nested Newton type algorithm is given for finding numerical solutions.