Transmit beamforming to multiple co-channel multicast groups

The problem of transmit beamforming to multiple co-channel multicast groups is considered, from the viewpoint of guaranteing a prescribed minimum signal-to-interference-plus-noise-ratio (SINR) at each receiver. The problem is a multicast generalization of the SINR-constrained multiuser downlink beamforming problem: the difference is that each transmitted stream is directed to multiple receivers, each with its own channel. Such generalization is relevant and timely, e.g., in the context of 802.16 wireless networks. Based on earlier results for a single multicast group, the joint problem is easily shown to be NP-hard, a fact that motivates the pursuit of quasi-optimal computationally efficient solutions. It is shown that Lagrangian relaxation coupled with a randomization / co-channel multicast power control loop yields a computationally efficient high-quality approximate solution. For a significant fraction of problem instances, the solutions generated this way are exactly optimal. Carefully designed and extensive simulation results are presented to support the main findings.