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 a fading environment under a ldquolow interference regimerdquo. This capacity depends critically on a power loss parameter, alpha, which governs how much transmit power the CR dedicates to relaying the primary message. We derive a simple, accurate approximation to alpha which gives considerable insight into system capacity. We also investigate the effects of system parameters and propagation environment on alpha 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 ldquolow interference regimerdquo holds and demonstrate that this is the dominant case, especially in practical CR deployment scenarios.