Optimum design of discrete transmit phase only beamformer

Transmit beamformer design usually results suboptimum beamformers in multicast scenario. In this paper, discrete phase only beamformer design is considered. The design problem is cast in such a form that the solution is always feasible and optimum beamformer can be found using the branch and cut algorithm. Beamformer phase terms and their interrelations are expressed with a set of cosine vectors which lead to linear set of constraint equations that can be solved with mixed integer linear programming. It is shown that the proposed approach is very effective and the number of quantization bits can be increased to obtain results close to optimum continuous phase beamformers.