Rank-Two Beamforming and Stochastic Beamforming for MISO Physical-Layer Multicasting with Finite-Alphabet Inputs

This letter considers multi-input single-output (MISO) downlink multicasting with finite-alphabet inputs when perfect channel state information is known at the transmitter. Two advanced transmit schemes, namely the beamformed (BF) Alamouti scheme and the stochastic beamforming (SBF) scheme, for maximizing the finite-alphabet-constrained multicast rate are studied. We show that the transmit optimization for these two schemes can be formulated as an SNR-based max-min-fair (MMF) problem with Gaussian inputs, which can be handled via the semidefinite relaxation (SDR) technique. Apart from transmit optimization, we analyzed the rate performance of the two schemes. Our analytical results show that for BF Alamouti, the multicast rate degrades with the number of users M at a rate of root M, which is better than the traditional transmit beamforming scheme. For SBF, the multicast rate degradation is less sensitive to the increase in the number of users and outperforms BF Alamouti for large M. All the results were verified by numerical simulations.