Precoder design for physical layer multicasting

This paper studies the design of linear precoders via instantaneous rate maximization over a K-user multicast channel, wherein multiple antennas are present at the transmitter as well as at all the receivers. We first consider the scenario wherein the linear precoder can be any complex valued matrix subject to rank and power constraints. Recognizing the resulting optimization problem to be NP-hard, we propose a cyclic alternating ascent based algorithm and establish its convergence to a stationary point. Simulation results reveal that our proposed algorithm considerably outperforms known competing solutions. We then consider a scenario in which the linear precoder can be formed by selecting and concatenating codewords from a finite codebook of precoding matrices, subject to rank and power constraints. We show that under this scenario, the instantaneous rate maximization problem is equivalent to a robust submodular maximization problem which is strongly NP-hard. We then propose a deterministic approximation algorithm and show that it yields a bicriteria approximation.