Secondary Users Entering the Pool: A Joint Optimization Framework for Spectrum Pooling

Spectrum pooling has been shown to have a great potential to improve the spectrum utilization, especially when primary users (PUs) and secondary users (SUs) are allowed to utilize a common spectrum pool. This paper studies the joint optimization problem for a spectrum pooling system with both PUs and SUs. We develop a novel hierarchical game theoretic model which consists of an overlapped coalition formation game model to analyze the pricing cooperation/competition strategy among PUs and a non-cooperative game model to investigate the resource competition among SUs. These two game models are interrelated in a hierarchical game structure, in which we also study the interaction between SUs and PUs. Our model does not require SUs to have information about spectrum access scheduling of PUs. Furthermore, we propose a simple distributed joint optimization algorithm that can optimize the coalition formation of PUs as well as the sub-band allocation and transmit powers of SUs. To study different fairness criteria and their effects on the payoff divisions among PUs, we derive the optimal payoff division schemes of two popular fairness criteria, namely Nash bargaining solution and Shapley value fairness.