  In this paper we consider the capacity of the cognitive radio channel in a
fading environment under a "low interference regime". This capacity depends
critically on a power loss parameter, $\alpha$, which governs how much transmit
power the cognitive radio 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 cognitive radio 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 cognitive
radio deployment scenarios.
