Opportunistic beamforming for finite horizon multicast

Wireless multicasting suffers from the problem that the transmit rate is usually determined by the receiver with the worst channel. Composite or adaptive beamforming allows using beamforming patterns that trade off antenna gains between receivers. A common solution for wireless multicast with beamforming is to select the pattern that maximizes the minimum rate among all receivers (for a given transmit power). However, when using opportunistic multicast to transmit a finite number of packets to all receivers - the finite horizon problem - this is no longer optimal. Instead, the optimum beamforming pattern depends on instantaneous channel conditions as well as the number of received packets at each receiver. We formulate the finite horizon multicast beamforming problem as a dynamic programming problem to obtain the optimal solution. We further design a heuristic that has sufficiently low complexity to be implementable in practice and show through extensive simulations that our algorithm significantly outperforms prior solutions.