Optimal Transmit-Beam Number and Power Allocation for Correlated MIMO Rayleigh Fading Channels

Although optimal transmit directions over generic correlated multiple-input multiple-output (MIMO) Rayleigh fading channels are well known to be the eigen beams defined by the transmit covariance matrix, general techniques for determining optimal transmit-beam number and power allocation remain unavailable. In this paper, by formulating the problem in the framework of Lagrange multipliers and by fully exploiting the algebraic structures and properties of the optimization problem at hand, we obtain a simple criterion for optimal beam number determination and a set of elementary equations for optimal power allocation, which can be efficiently solved by using the recursive algorithm derived in this paper. Numerical results are presented for the illustration of the theory.