Energy Efficient Spectrum Sharing Strategy Selection for Cognitive MIMO Interference Channels

In this paper, we propose a promising discrete gametheoretic framework for distributed energy efficient discrete spectrum sharing strategy selection (i.e., joint discrete power control and multimode precoding strategy selection) with limited feedback for cognitive MIMO interference channels. Given the competitive nature, the secondary users are assumed to be selfish and noncooperative, each of whom attempts to maximize its individual energy efficiency under a minimum data rate constraint and an interference power constraint. A mechanism for shutting down links is proposed to reduce interference and save energy. A payoff function is designed to guarantee the feasibility of the pure strategy Nash equilibrium with no need to know the infeasible strategy profiles (a spectrum sharing strategy profile is said to be feasible if the stated constraints are satisfied; otherwise, the spectrum sharing strategy profile is said to be infeasible, i.e., they may not satisfy the interference power constraint and minimum data rate constraint) in advance. We then investigate the existence and the feasibility of the pure strategy Nash equilibrium, and further devise a pricing-based distributed algorithm for spectrum strategy selection. The proposed algorithm is proved to converge to a feasible pure strategy Nash equilibrium under specific conditions. Moreover, by studying the relationship between our proposed game and the social optimum, we find that the pricing mechanism can result in Pareto improvement and lead to better convergence for the proposed distributed algorithm. Numerical results show that our designed algorithm significantly outperforms the random selection algorithm and the pricing mechanism has a dramatic effect in improving the system performance.