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 thatare unused by the network’s licensed primary users (PUs),provided that the induced interference does not compromisethe PUs’ performance guarantees. To account for interferenceconstraints of this type, we consider flexible spectrum accesspricing schemes that charge SUs based on the interference thatthey cause to the system’s PUs, and we examine how SUs canreact so as to maximize their achievable transmission rate inthis setting. We show that the resulting non-cooperative gameadmits a unique Nash equilibrium under very mild assumptionson the pricing mechanism employed by the network operator, andunder both static and ergodic (fast-fading) channel conditions.In addition, we derive a dynamic power allocation policy thatconverges to equilibrium within a few iterations (even forlarge numbers of users), and which relies only on local – andpossibly imperfect –signal-to-interference-and-noise ratio (SINR)measurements; importantly, the proposed algorithm retains itsconvergence properties even in the ergodic channel regime,despite its inherent stochasticity. Our theoretical analysis is com-plemented by extensive numerical simulations which illustratethe performance, robustness and scalability properties of theproposed pricing scheme under realistic network conditions.