Equilibrium pricing of interference in cognitive radio networks

Dynamically allocating the available spectrum in the cognitive radio networks (CRN) where licensed users allow unlicensed users to make use of part of their allocated spectrum is a complex task. It requires, among others, that the interference generated by the CRN is well controlled. In this paper we address this problem for a particular type of interference constraints, in which the aggregated powers of the interference generated by the unlicensed network are required not to exceed certain thresholds. Traditional distributed water filling based spectrum allocation schemes are not well equipped to enforce such interference constraints. A natural extension to these algorithms involves penalizing each unlicensed user with a set of time-varying prices based upon its contribution to the total interference. In this context, the network is in equilibrium if: i) all interference constraints are satisfied; and ii) no unlicensed user has an incentive to alter its own transmission power levels. In this paper, we propose a distributed algorithm to compute such equilibrium in two distinctive network configurations: 1) the unlicensed users are mobile devices that communicate with a common access point; 2) the unlicensed users are tranceiver pairs. We show that our algorithm converges to a set of equilibria in the first scenario without restriction on the channel gains, and it converges to an equilibrium point in the second scenario under a relatively mild condition related to the channel gains.