Bayesian Hierarchical Mechanism Design for Cognitive Radio Networks

Abstract

This paper considers a cognitive radio network where the licensed network, referred to as the primary user (PU) network, consists of a hierarchical structure in which multiple operators coexist in the same coverage area where each of the operators controls an exclusive set of frequency sub-bands. Unlicensed users, referred to as the secondary users (SUs), first send their requests to the operators, and can only access the sub-bands controlled by the operators that accept their requests. SUs are selfish and cannot exchange private information with each other. We model the dynamic spectrum access (DSA) problem of the SUs as a Bayesian game, referred to as the DSA game. We model the PU network as a forest where the roots represent the operators and the leaves represent the operators' sub-bands. We propose a novel forest matching market to model the interaction between the SUs and the PU network. In this market, a set of SUs can be first matched to a set of operators and the SUs matched to the same operator can then be matched to the corresponding sub-bands. We propose a distributed algorithm that results in a stable forest matching structure, which coincides with the optimal Bayesian Nash equilibrium of the DSA game. We prove that the Bayesian hierarchical mechanism associated with our proposed algorithm incentivizes truth-telling by SUs. Our algorithm does not require each SU to know the preference and conflict-solving rule of the PU network or the payoffs and actions of other SUs, and the complexity of each iteration in the worst case is given by O(L <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> N <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> K) where L is the number of operators, N is the maximum number of sub-bands of each operator, and K is the number of SUs.