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

TLDR

Multicast beamforming generalizes multiuser downlink beamforming by directing each stream to multiple receivers, a problem relevant to WiMAX and UMTS‑LTE, which includes the single‑group case and is NP‑hard. The study seeks computationally efficient quasi‑optimal solutions for two design goals: minimizing total transmit power while meeting per‑receiver SINR targets, and maximizing the minimum SINR under a total power budget. The authors employ Lagrangian relaxation combined with randomization and cochannel multicast power control to produce computationally efficient high‑quality approximate solutions. Numerical experiments on simulated and measured channels show that these solutions are often exactly optimal, confirming the effectiveness of the proposed approach.

Abstract

The problem of transmit beamforming to multiple cochannel multicast groups is considered, when the channel state is known at the transmitter and from two viewpoints: minimizing total transmission power while guaranteeing a prescribed minimum signal-to-interference-plus-noise ratio (SINR) at each receiver; and a "fair" approach maximizing the overall minimum SINR under a total power budget. The core problem is a multicast generalization of the 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 the emerging WiMAX and UMTS-LTE wireless networks. The joint problem also contains single-group multicast beamforming as a special case. The latter (and therefore also the former) is NP-hard. This motivates the pursuit of computationally efficient quasi-optimal solutions. It is shown that Lagrangian relaxation coupled with suitable randomization/cochannel multicast power control yield computationally efficient high-quality approximate solutions. For a significant fraction of problem instances, the solutions generated this way are exactly optimal. Extensive numerical results using both simulated and measured wireless channels are presented to corroborate our main findings.