Equilibrium and Disequilibrium Pricing for Spectrum Trading in Cognitive Radio: A Control-Theoretic Approach

Spectrum trading is a concept used to describe the economics of dynamic spectrum sharing in cognitive radio networks. In this paper, we consider the problem of spectrum trading between primary and secondary services. Multiple markets are established in this trading for the multiple available frequency bands. The primary service is considered as the seller and the secondary service is considered as a buyer in a dynamic spectrum trading market. The spectrum supply from the primary service is derived based on the revenue earned due to spectrum sharing and the cost due to QoS performance degradation of the connections served by the primary service. The spectrum demand of secondary service is obtained based on the utility from spectrum usage. We first obtain the equilibrium pricing which is the point where spectrum supply equals spectrum demand. Then, we consider the case where the spectrum sellers do not offer the equilibrium price. The impact of this disequilibrium pricing is investigated. We model the cases of equilibrium and disequilibrium pricing as feedback control systems in which the spectrum seller and buyer have their own transfer functions. By using classical control theory the stability of the model is analyzed.