Distributed optimization for cognitive radio networks using Stackelberg game

This paper considers frequency-division spatial spectrum sharing (FD-SSS) based cognitive radio (CR) networks. In this network, the spectrum of primary users (PU) can be divided into a number of sub-bands each of which can only be accessed by one secondary user (SU). This setting combines both advantages of spatial spectrum sharing and temporal spectrum sharing methods. However, there are three major problems for this system: 1) how to optimally allocate the available subbands to all SUs, 2) how to distributively optimize the transmit powers for SUs to maintain the received interference power of PUs, 3) how to control the accessibility of SUs in the licensed spectrum. In this paper, we introduce a Stackelberg game based hierarchical framework to optimize the performance of FD-SSS based CR networks. More importantly, we show that, by using a simple pricing function for PUs, the above three problems can be solved simultaneously. We prove that the proposed game has a unique Stackelberg equilibrium (SE) and then introduce a simple distributed algorithm to let SUs and PUs converge to the SE. Comparing to the existing results, our setting does not require SUs to communicate with each other or to know the interference temperature of PUs.