Joint Antenna Selection and Phase-Only Beam Using Mixed-Integer Nonlinear Programming

In this paper, we consider the problem of joint antenna selection and analog beamformer design in a downlink single-group multicast network. Our objective is to reduce the hardware requirement by minimizing the number of required phase shifters at the transmitter while fulfilling given quality of constraints. We formulate the problem as an L0 minimization problem and devise a novel branch-and-cut based algorithm to solve the formulated mixed-integer nonlinear program optimally. We also propose a suboptimal heuristic algorithm to solve the above problem with a low computational complexity. Furthermore, the performance of the suboptimal method is evaluated against the developed optimal method, which serves as a benchmark.