Spectrum sharing and power allocation in multiple-in multiple-out cognitive radio networks via pricing

In the cognitive radio (CR) networks consisting of selfish users competing for spectrum resources, the social optimum is usually not achieved at the Nash equilibrium (NE) of the power control game, since selfish users are only interested in their own benefit. In this study with the aim of improving the NE efficiency, the authors extend the pricing concept to a multi-channel multiple-in multiple-out (MIMO) CR scenario and propose two iterative algorithms for power control and channel allocation in such systems. Specially, the authors consider both linear and non-linear pricing methods and derive the optimal pricing factor for both scenarios and prove the existence and uniqueness of the NE. Simulation results prove the outstanding performance of the proposed MIMO cognitive system considering price-based power control over the non-price-based MIMO cognitive systems.