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Beamforming for multi-group multicasting with statistical channel state information using second-order cone programming

We consider the problem of transmit beamforming in multi-group multicasting systems with covariance-based channel state information (CSI) available at the transmitter where the total transmitted power is minimized subject to quality-of-service (QoS) constraints at the receivers. Previous approaches for this problem are based on semidefinite relaxation (SDR) and require randomization and costly power scaling which is avoided in our approach. The proposed technique can be viewed as a non-trivial extension of the iterative second-order cone programming (SOCP) approach, which is restricted to the case of instantaneous (rank-one) CSI, to the beamforming problem with higher-rank channel covariance matrices. Computer simulations reveal that the proposed technique exhibits superior performance in terms of total transmitted power at a reduced computational complexity as compared to the SDR method.