An Investigation of Stochastic Market Equilibrium in Cognitive Radio Networks

In this letter, we model a cognitive radio network as an interference market where each primary user (PU) and secondary user (SU) are price-taking interference offerers and purchasers, respectively. We consider stochastic interference demands of SUs and the existence of random disturbances in PUs' interference observations. Exploiting the fact that the dB value of the uplink inter-cell interference in CDMA networks is modeled as a Gaussian normal distribution, the price-demand decision process in each PU is given by a pair of stochastic differential equations. Then, we investigate an equilibrium of the interference market and its convergence in the context of asymptotic stability in the mean. Numerical results illustrate the convergence of the price-demand decision process to the equilibrium.