Physical-Layer Multicasting by Stochastic Transmit Beamforming and Alamouti Space-Time Coding
Consider transceiver designs in a multiuser multi-input single-output (MISO) downlink channel, where the users are to receive the same data stream simultaneously. This problem, known as physical-layer multicasting, has drawn much interest. Presently, a popularized approach is transmit beamforming, in which the beamforming optimization is handled by a rank-one approximation method called semidefinite relaxation (SDR). SDR-based beamforming has been shown to be promising for a small or moderate number of users. This paper describes two new transceiver strategies for physical-layer multicasting. The first strategy, called stochastic beamforming (SBF), randomizes the beamformer in a per-symbol time-varying manner, so that the rank-one approximation in SDR can be bypassed. We propose several efficiently realizable SBF schemes, and prove that their multicast achievable rate gaps with respect to the MISO multicast capacity must be no worse than 0.8314 bits/s/Hz, irrespective of any other factors such as the number of users. The use of channel coding and the assumption of sufficiently long code lengths play a crucial role in achieving the above result. The second strategy combines transmit beamforming and the Alamouti space-time code. The result is a rank-two generalization of SDR-based beamforming. We show by analysis that this SDR-based beamformed Alamouti scheme has a better worst-case effective signal-to-noise ratio (SNR) scaling, and hence a better multicast rate scaling, than SDR-based beamforming. We further the work by combining SBF and the beamformed Alamouti scheme, wherein an improved constant rate gap of 0.39 bits/s/Hz is proven. Simulation results show that under a channel-coded, many-user setting, the proposed multicast transceiver schemes yield significant SNR gains over SDR-based beamforming at the same bit error rate level.