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

Abstract—In this paper we consider the capacity of the cog-nitive radio (CR) channel in a fading environment under a “low interference regime”. This capacity depends critically on a power loss parameter, α, which governs how much transmit power the CR dedicates to relaying the primary message. We derive a simple, accurate approximation to α which gives considerable insight into system capacity. We also investigate the effects of system parameters and propagation environment on α and the CR capacity. In all cases, the use of the approximation is shown to be extremely accurate. Finally, we derive the probability that the “low interference regime ” holds and demonstrate that this is the dominant case, especially in practical CR deployment scenarios. I