Interference-Based Pricing for Opportunistic Multi-Carrier Cognitive Radio Systems

Cognitive radio (CR) systems allow opportunistic, secondary users (SUs) to access portions of the spectrum that are unused by the network’s licensed primary users (PUs), provided that the induced interference does not compromise the PUs’ performance guarantees. To account for interference constraints of this type, we consider flexible spectrum access pricing schemes that charge SUs based on the interference that they cause to the system’s PUs, and we examine how SUs can react so as to maximize their achievable transmission rate in this setting. We show that the resulting non-cooperative game admits a unique Nash equilibrium under very mild assumptions on the pricing mechanism employed by the network operator, and under both static and ergodic (fast-fading) channel conditions. In addition, we derive a dynamic power allocation policy that converges to equilibrium within a few iterations (even for large numbers of users), and which relies only on local – and possibly imperfect –signal-to-interference-and-noise ratio (SINR) measurements; importantly, the proposed algorithm retains its convergence properties even in the ergodic channel regime, despite its inherent stochasticity. Our theoretical analysis is complemented by extensive numerical simulations which illustrate the performance, robustness and scalability properties of the proposed pricing scheme under realistic network conditions.