Interior point method for optimum zero-forcing beamforming with per-antenna power constraints and optimal step size

This paper proposes a new computational procedure for solving the optimal zero-forcing beamforming problem in multiple antenna channels that maximizes user achievable rate with restriction on the per-antenna element power constraints. An interior point method with optimal step size procedure is developed in which the step size for the line search in the Newton search direction is calculated exactly for each iteration. This significantly enhances the efficiency associated with the line search. Design examples show that the proposed algorithm converges rapidly to the optimal solution with low computational complexity.