On Transceiver Beamformer Design for Multi-Source Multi-Destination Wireless Networks

In this paper, we consider the problem of designing transceiver beamforming vectors for multi-source multi-destination (MSMD) wireless networks such that the transmission power of each source is minimized while the signal-to-interference plus noise ratio (SINR) requirements of all source-destination pairs are satisfied. We propose an efficient iterative algorithm to design the transceiver beamforming vectors and address the convergence of the algorithm. We determine a necessary condition as well as a sufficient condition for the algorithm to converge to a generalized Nash equilibrium solution. Especially, if each destination has only one antenna, we obtain a necessary and sufficient condition for the algorithm to converge to a unique generalized Nash equilibrium solution. Simulation results show that the proposed iterative algorithm has higher probability of convergence compared to an iterative waterfilling (IWF) approach. For example, for a system with three source-destination pairs and SINR requirement of 2dB, the probability of convergence is 84% with the proposed algorithm while it is only 66% with the IWF algorithm.