On Transmit Beamforming for Physical-Layer Multicasting

The paper considers transmit beamforming for physical-layer multicasting in a wireless system consisting of a single transmitter with multiple antennas and multiple single antenna users. The beamforming weights are obtained so that the transmitted power is minimized subject to meeting the minimum signal-to-noise (SNR) requirements of each user. As in previous works, semidefinite programming (SDP) relaxation is considered. The contribution of this paper lies in that it provides effective and convergent algorithms to obtain the solution for the cases in which SDP yields a solution with rank greater than one. Two methods are proposed, namely, the coordinate descent method, which is applicable for the case of at least as many transmit antennas as users, and the p-norm approximation, which is is applicable for general case. Numerical results are presented to illustrate the performance of the proposed algorithms.