Optimum discrete single group multicast beamforming

In this paper, transmit beamformer design for single group multicast scenario is considered. The problem is solved in discrete form where the beamformer phase and amplitude values are selected from finite discrete sets. Original optimization problem is converted to a linear form by introducing new variables. The solution of the equivalent optimization problem is always feasible as long as the total power is above a certain value. The problem in its linear form is guaranteed to return optimum solution. Proposed approach is very effective and the number of bits can be increased to obtain close to optimum continuous phase and amplitude beamformers.