Power Minimization in Multi-Band Multi-Antenna Cognitive Radio Networks

This paper aims to design an optimal set of beam-vectors for multi-band multi-antenna cognitive radio networks that jointly allocate power over both space and frequency, so that the sum power of secondary users (SUs) is minimized, subject to rate demands at the SUs, as well as the interference constraints imposed by primary users. Unlike the rate maximization problems, which are always feasible, this power minimization (PM) problem may be infeasible due to the rate constraints. Therefore, we provide a complete analysis of the PM problem by splitting the solution into two separate phases. In phase I, a novel method is developed to check the feasibility of the PM problem by considering an alternative problem, where one additional variable is introduced. This alternative problem is always feasible and one algorithm based on network duality and geometric programs is developed to solve it. In phase II, a novel algorithm is developed to solve the PM problem. This algorithm can be implemented in an online fashion. Furthermore, this algorithm is proved to converge to a Karush-Kuhn-Tucker point of the PM problem. Simulation results show that the proposed algorithms converge in only a few iterations and significantly outperform the existing single-band method in terms of both the feasibility probabilities and power savings.