Quality of Service and Max-Min Fair Transmit Beamforming to Multiple Cochannel

Abstract— The problem of transmit beamforming to multiplecochannel multicast groups is considered, when the channel stateis known at the transmitter and from two viewpoints: mini-mizing total transmission power while guaranteeing a prescribedminimum signal-to-interference-plus-noise ratio (SINR) at eachreceiver; and a “fair” approach maximizing the overall minimumSINR under a total power budget. The core problem is a multicastgeneralization of the multiuser downlink beamforming problem;the difference is that each transmitted stream is directed tomultiple receivers, each with its own channel. Such generaliza-tion is relevant and timely, e.g., in the context of the emergingWiMAX and UMTS-LTE wireless networks. The joint problemalso contains single-group multicast beamforming as a specialcase. The latter (and therefore also the former) is NP-hard. Thismotivates the pursuit of computationally efficient quasi-optimalsolutions. It is shown that Lagrangian relaxation coupled withsuitable randomization/cochannel multicast power control yieldcomputationally efficient high-quality approximate solutions. Fora significant fraction of problem instances, the solutions generatedthis way are exactly optimal. Extensive numerical results usingboth simulated and measured wireless channels are presented tocorroborate our main findings.