Transmit beamforming and admission control for multicast with uncertain user partition

In this paper, we consider the multicast beamforming problem in a downlink wireless system. Then, an optimization problem is formulated to find the optimal user-group assignment scheme and beamforming weight vectors, such that the number of admitted users is maximized with the minimum transmit power under the quality of service (QoS) requirement constraints of each individual user. Unfortunately, the constraints are nonlinear since they consist of the products of binary variables and continuous variables. As a solution, the big-M approach is adopted to transform the problem to a mixed integer quadratically constrained quadratic programming (MI-QCQP) problem. Then, an optimal and a suboptimal algorithm are proposed based on the branch and bound (BnB) method. In addition, a heuristic algorithm is designed in order to trade off the performance between computational complexity and accuracy. Simulation results are provided to demonstrate the performance of the proposed algorithms in terms of the number of admitted users and energy consumption.