Optimum discrete max-min style broadcast beamforming design

In this paper, max-min style transmit beamformer design for single group multicast (broadcast) scenario is considered. The phase and amplitude values of beamformer vector coefficients are selected from finite discrete sets. With the help of integer variables, original optimization problem is converted to a linear form appropriate for mixed integer linear programming. The solution is always feasible as long as the total power is above a certain value. Branch and cut strategy guarantees the optimum solution. Proposed approach is very effective and with moderate number of bits, a performance closed to optimum continuous beamformer can be obtained.