The Impact of Fading on the Outage Probability in Cognitive Radio Networks

This paper analyzes the outage probability in cognitive radio networks, based on the Poisson point process model of node spatial distribution and the standard propagation path loss model, including Rayleigh and log-normal fading. To make the analysis tractable, all possible scenarios are classified into three cases based on typical outage events. When the average number of nodes in the forbidden region is much smaller than unity, the aggregate interference can be well approximated by the nearest node for both non-fading and fading scenarios (the nearest node dominates the outage performance). When the average number of nodes in the forbidden region is greater than unity, the aggregate interference can be well approximated by a Gaussian random variable for non-fading scenario (many nodes contribute to outage events, rather than a single dominant one). This approximation also applies to the fading scenario, but its accuracy is a bit worse at the transition region. An alternative approximation is proposed, which is accurate for any outage probability. When the average number of nodes in the forbidden region is slightly smaller than unity, neither the nearest node approximation nor the Gaussian one is accurate for the non-fading scenario (since only a few near-by nodes are dominant), and finding an accurate approximation for the outage probability in this case is an open problem. The alternative approximation above is accurate for the fading scenario. All approximations are validated via Monte-Carlo simulations.