Computation of an Equilibrium in Spectrum Markets for Cognitive Radio Networks

In this paper, we investigate a market equilibrium in multichannel sharing cognitive radio networks (CRNs): it is assumed that every subchannel is orthogonally licensed to a single primary user (PU), and can be shared with multiple secondary users (SUs). We model this sharing as a spectrum market where PUs offer SUs their subchannels with limiting the interference from SUs; the SUs purchase the right to transmit over the subchannels while observing the inference limits set by the PUs and their budget constraints. Moreover, we consider each SU limits the total interference that can be invoked from all other SUs, and assume that every transmitting SU marks the interference charges to other transmitting SUs. The utility function of SU is defined as least achievable transmission rate, and that of PU is given by the net profit. We define a market equilibrium in the context of extended Fisher model, and show that the equilibrium is yielded by solving an optimization problem, Eisenberg-Gale convex program. To make the solutions of the convex program meet the market equilibrium, we apply monotone-transformation to the utility function of each SU. Furthermore, we develop a distributed algorithm that yields the stationary solutions asymptotically equivalent to the solutions given by the convex program.