Joint user selection and multicast beamforming in the downlink cochannel

The problem of joint user selection and multicast beamforming design in the downlink cochannel is studied in our paper. The primary goal is to maximize the number of served users, and minimizing the transmitting power is the second one. We reformulate the problem into a form suitable for analyzing by introducing two-value auxiliary variables, then relax it into a general problem. Different approximations are discussed to turn the general problem into easy-handling problems, which covering several works in both unicast and multicast scenes. An algorithm is proposed based on analyzing two characteristics in the multicast problem, inactive signal-to-interface-noise (SINR) constraints and non-rank-one beamforming covariance matrices. In simulations, three approximate functions are chosen, and their influence on the algorithm in performance and complexity is compared. Then our algorithm and MDR algorithm in [1] is contrasted and the relation between performance gap of two algorithms and characteristics in the multicast problem is discussed at last.