  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.
