An iterative convex approximation approach for transmit beamforming in multi-group multicasting

We propose a novel algorithm for transmit beamforming to multiple cochannel multicast groups. The problem of minimizing the total power transmitted by the antenna array subject to quality-of-service (QoS) constraints at the receivers is considered. We show that this problem, which is known to be NP-hard, can be approximated by a second-order cone programming (SOCP) problem. We propose an iterative scheme in which the SOCP approximation is successively improved in each iteration. Earlier state-of-the-art techniques for this problem are based on semidefinite relaxation (SDR) and require randomization and power scaling which is avoided in our approach. Computer simulations show that the proposed technique exhibits superior performance in terms of total transmitted power and feasibility at a reduced computational complexity as compared to the SDR method.