Distributed learning-based spectrum allocation with noisy observations in cognitive radio networks

This paper studies the medium access design for secondary users (SUs) from a game-theoretic learning perspective. In consideration of the random return of primary users (PUs), a distributed SU access approach is presented based on an adaptive carrier sense multiple access (CSMA) scheme, in which each SU accesses multiple idle frequency slots of a licensed frequency band with adaptive activity factors. The problem of finding optimal activity factors of SUs is formulated as a potential game, and the existence, feasibility, and optimality of Nash equilibrium (NE) are analyzed. Furthermore, to achieve NEs of the formulated game, learning-based algorithms are developed in which each SU independently adjusts its activity factors. Convergence properties of best-response dynamics and log-linear dynamics are studied. Subsequently, by learning other SUs' behavior from locally available information, the convergence with probability of one to an arbitrarily small neighborhood of the globally optimal solution is investigated by both analysis and simulation.