Physical layer multicasting with linear MIMO transceivers

This paper studies the problem of linear transceiver design for multicasting in multiuser multi-input-multiple-output (MIMO) systems. We focus on a single-group multicasting scenario and consider four optimization problems: 1) minimizing the total transmit power subject to a minimum mean square error (MMSE) constraint per user, 2) minimizing the worstcase weighted MMSE among all users subject to a total power constraint, 3) minimizing the total transmit power subject to a sum-MMSE constraint, 4) minimizing the sum MMSE subject to a total power constraint. These problems can be reformulated as convex semidefinite programs (SDPs) under the assumption that the rank of the transmit covariance is unconstrained. Otherwise, these problems are non-convex. We propose iterative algorithms for these problems and analyze the convergence behavior of the algorithms. In general, due to the non-convexity of the problems, the algorithms possibly return local optima. For the special case that the returned optimal transmit filtering matrix is full rank, we prove the global convergence.