On the statistics of cognitive radio capacity in shadowing and fast fading environments

In this paper we consider the capacity of the cognitive radio (CR) channel in different fading environments under a "low interference regime". First we derive the probability that the "low interference regime" holds under shadow fading as well as Rayleigh and Rician fast fading conditions. We demonstrate that this is the dominant case, especially in certain practical CR deployment scenarios. The capacity of the CR channel depends critically on a power loss parameter, ¿, which governs how much transmit power the CR dedicates to relaying the primary message. We derive a simple, accurate approximation to ¿ in Rayleigh and Rician fading environments which gives considerable insight into system capacity. We also investigate the effects of system parameters and propagation environment on ¿ and the CR capacity. In all cases, the use of the approximation is shown to be extremely accurate.