Finite Horizon Opportunistic Multicast Beamforming
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Wireless multicasting suffers from the problem that the transmit rate is usually determined by the receiver with the worst channel conditions. Composite or adaptive beamforming allows using beamforming patterns that trade off antenna gains between receivers, which can be used to overcome this problem. A common solution for wireless multicast with beamforming is to select the pattern that maximizes the minimum rate among all receivers. 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 an optimal solution. We further design a heuristic that has sufficiently low complexity to be implementable in practice. To deal with imperfect feedback, and in particular feedback delay, we extend the algorithm to work with estimated state and channel information. We show through extensive simulations that our algorithms significantly outperform prior solutions.