Network duality and its application to multi-user MIMO wireless networks with SINR constraints

For any multiple-input and multiple-output (MIMO) network with linear beamformers, there exists a dual network that attains the same signal to interference plus noise ratio (SINR) performance. This network duality is a generalization of the virtual uplink concept investigated in R. Rashid-Farrokhi et al. (1998) in the context of cellular networks. In this paper, we develop network duality which is applicable to arbitrary multi-user MIMO networks with a generalized cost function. More importantly, we provide an optimization theoretic perspective of network duality which naturally leads to the construction of a dual network. We then consider the joint MIMO beamforming and power control problem with individual SINR constraints. We apply the network duality to this problem and propose a high performance algorithm which compared to past approaches has improved convergence behavior.