Rank-two transmit beamformed Alamouti space-time coding for physical-layer multicasting

In physical-layer multicasting over a multiuser MISO downlink channel, transmit beamforming using semidefinite relaxation (SDR) has been a popular approach. In this paper, we propose a rank-2 transmit beamformed Alamouti space-time code scheme, which may be seen as a generalization of the previous SDR-based beamforming framework. The beamforming problem arising from the proposed scheme is a rank-2 constrained semidefinite program (SDP).We deal with it using the SDR technique, but this time using rank-2 approximation rather than rank-1 approximation in the previous transmit beamforming. An analysis on the worst-case approximation accuracy of the rank-2 SDR approximation is provided, which reveals that the approximation accuracy degrades at a rate of √M, where M is the number of users served. This improves upon the case of transmit beamforming, where the worst-case approximation accuracy degrades at the higher rate of M. Simulation results further show that the proposed scheme performs better than the transmit beamforming scheme.