A market-clearing model for spectrum trade in cognitive radio networks

We model cognitive radio networks (CRNs) as a spectrum market where every primary user (PU) offer her subchannels with certain interference bound indicating the interference limit the PU can tolerate, and secondary users (SUs) purchase the right to access the subchannels while observing their budget constraints as well as the inference bound. In this spectrum market model, the utility of SU is defined as the achievable transmission rate in free space, and the utility of PU is given by the net profit the PU can make. Then we develop a market equilibrium in the context of Fisher model, and show that the equilibrium is obtained by solving an optimization problem called Eisenberg-Gale convex program. Furthermore, we develop a distributed algorithm with best response dynamics and price dynamics, and prove that its asymptotic solutions are equivalent to the solutions given by the convex program. Besides, we introduce adaptive step size to the price dynamics for faster convergence. With some numerical examples, we show that it helps to achieve faster convergence.