  In this paper, we consider the problem of joint antenna selection and analog
beamformer design in downlink single-group multicast networks. Our objective is
to reduce the hardware costs by minimizing the number of required phase
shifters at the transmitter while fulfilling given distortion limits at the
receivers. We formulate the problem as an L0 minimization problem and devise a
novel branch-and-cut based algorithm to solve the resulting mixed-integer
nonlinear program to optimality. We also propose a suboptimal heuristic
algorithm to solve the above problem approximately with a low computational
complexity. Computational results illustrate that the solutions produced by the
proposed heuristic algorithm are optimal in most cases. The results also
indicate that the performance of the optimal methods can be significantly
improved by initializing with the result of the suboptimal method.
