In multicasting networks, a multiple antenna base station transmits the same information to a single group of users. In this work we consider general rank beamforming using orthogonal space-time block codes (OSTBC)s. The beamforming problem is non-convex and generally NP hard. The semidefinite relaxation technique is employed to solve the problem. In order to control the rank of the beamforming solution we propose to replace the power minimization by a regularized volume minimization which is known as a surrogate for the rank minimization. We propose an iterative two scale algorithm to find the appropriate value for the regularization parameter that yields the desired rank and to compute stationary points of the corresponding optimization problem. The high computational complexity of the proposed algorithm is improved significantly using a one scale algorithm, where the value of the regularization variable is reduced along with the decreasing rank. Simulation results demonstrate that our algorithms outperform the state-of-the-arts procedures in terms of the transmitted power and symbol error rate (SER). For a proper setting of the regularization variable, one scale algorithm outperforms the best compared methods in terms of computational complexity.

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