A hierarchical game theoretic framework for cognitive radio networks

We consider OFDMA-based cognitive radio (CR) networks where multiple secondary users (SUs) compete for the available sub-bands in the spectrum of multiple primary users (PUs). We focus on maximizing the payoff of both SUs and PUs by jointly optimizing transmit powers of SUs, sub-band allocations of SUs, and the prices charged by PUs. To further improve the performance of SUs, we allow SUs who share the same sub-band to cooperate with each other to send and receive signals. To help us understand the interaction among SUs and PUs, we study the proposed network model from a game theoretic perspective. More specifically, we first formulate a coalition formation game to study the sub-band allocation problem of SUs and then integrate the coalition formation game into a Stackelberg game-based hierarchical framework. We propose a simple distributed algorithm for SUs to search for the optimal sub-bands. We prove that the transmit power and sub-band allocation of SUs and the price charged by PUs are interrelated by the pricing function of PUs. This makes the joint optimization possible. More importantly, we prove that if the pricing coefficients of PUs have a fixed linear relationship, the sub-band allocation of SUs will be stable and the Stackelberg equilibrium of the hierarchical game framework will be unique and optimal. We propose a simple distributed algorithm to achieve the Stackelberg equilibrium of the hierarchical game. Our proposed algorithm does not require SUs to know the interference temperature limit of each PU, and has low communication overheads between SUs and PUs