Optimization of transmit-beam number and power allocation for generic correlated MIMO rayleigh channels

The optimal transmit-beam number and power allocation over generic correlated multiple-input multiple-output (MIMO) Rayleigh fading channels are investigated. By fully exploiting the algebraic structures and properties of the optimization problem, we obtain a procedure for determining the thresholds of optimal beam number and derive a set of elementary equations for optimal power allocation, which can be efficiently solved by using a Broyden-like method. A closed-form criterion for the optimality of beamforming is also proposed. Numerical results are presented for illustration.