Power Minimization in MIMO Cognitive Networks

We consider the minimization of transmit power subject to rate-demand and resource constraints of a cognitive radio (CR) multi-input multi-output (MIMO) network under the framework of a noncooperative game. With spatial multiplexing over each frequency band, a multi-antenna node controls its antenna radiation directions and allocates power for each data stream by appropriately adjusting its precoding matrices. Our objective is to design the set of precoding matrices (one per channel) at each node, where power, spectrum allocation, and beamformers are optimized to minimize the transmit power. In other words, the problems of power, spectrum management, and beamforming are jointly investigated. Using recession analysis and the theory of variational inequalities, we obtain sufficient conditions that guarantee the existence and uniqueness of the game’s Nash Equilibrium (NE). Low-complexity distributed algorithms with proved and fast convergence to the NE are developed by exploiting the strong duality of the convex per-user optimization problem. To improve the efficiency of the NE, we introduce pricing policies that employ a novel network interference function. The study of the existence and uniqueness of the new NE under pricing are then given. Simulations confirm the effectiveness of our joint optimization of power, spectrum allocation, and beamforming. Our analysis and results are not limited to CR, but are also applicable to multi-carrier (e.g., OFDM) or cellular MIMO systems. Index Terms Power/spectrum efficiency, spectrum management, power allocation, beamforming, Nash Equilibrium existence and uniqueness, noncooperative game, pricing, cognitive radio, MIMO.