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In this paper, we propose a novel class of Nash problems for Cognitive Radio(CR) networks, modeled as Gaussian frequency-selective interference channels,wherein each secondary user (SU) competes against the others to maximize hisown opportunistic throughput by choosing jointly the sensing duration, thedetection thresholds, and the vector power allocation. The proposed generalformulation allows to accommodate several (transmit) power and(deterministic/probabilistic) interference constraints, such as constraints onthe maximum individual and/or aggregate (probabilistic) interference tolerableat the primary receivers. To keep the optimization as decentralized aspossible, global (coupling) interference constraints are imposed by penalizingeach SU with a set of time-varying prices based upon his contribution to thetotal interference; the prices are thus additional variable to optimize. Theresulting players' optimization problems are nonconvex; moreover, there arepossibly price clearing conditions associated with the global constraints to besatisfied by the solution. All this makes the analysis of the proposed games achallenging task; none of classical results in the game theory literature canbe successfully applied. The main contribution of this paper is to develop anovel optimization-based theory for studying the proposed nonconvex games; weprovide a comprehensive analysis of the existence and uniqueness of a standardNash equilibrium, devise alternative best-response based algorithms, andestablish their convergence.

Joint Sensing and Power Allocation in Nonconvex Cognitive Radio Games: Nash Equilibria and Distributed Algorithms