An outage-based game design for cognitive radio

This paper addresses the power control problem in an underlay cognitive radio network where N selfish secondary users (SUs) sharing a frequency band with a primary user. The problem is studied from two perspectives: system level and user level. At the system level, a secondary network manager (SNM) is interested in minimizing the secondary network outage probability subject to peak power constraints on SU transmission power levels and a constraint on the maximum interference generated at the primary receiver. The resulting system level optimization problem is converted to a convex one. At the user level, SUs selfishly increase their transmission power levels to maximize their outage-based utility functions, and SNM imposes a cost on each SU based on its interference power at the primary receiver. The system level optimization problem is converted to a convex one. The user level optimization problem is formulated as a strategic (non-cooperative) power control game, which admits a unique Nash equilibrium. A distributed algorithm for computing the Nash equilibrium is proposed. Finally, an optimal pricing scheme is presented which eliminates the gap between network and user level performances by aligning the optimal solution of system level problem with the Nash equilibrium of the user level problem.