Asymptotic analysis of outage probability in cognitive radio networks

The aggregate interference distribution in cognitive radio networks is studied in a rigorous analytical way using the popular Poisson point process model. While a number of results are available for this model of regular (non-cognitive) networks, cognitive ones present an extra level of difficulty for the analysis, mainly due to the exclusion region around the primary receiver, which are typically addressed via various ad-hoc approximations (e.g. based on the interference cumulants) or via the large-deviation analysis. Unlike the previous studies, here we do not use ad-hoc approximations but rather obtain the asymptotic interference distribution in a systematic and rigorous way. This is in contrast to the large deviation analysis, which provides only the (exponential) order of scaling but not the outage probability itself. Unlike the cumulant-based analysis, our approach provides a guaranteed level of accuracy at the distribution tail. Additionally, our analysis also provides a number of novel insights. In particular, we demonstrate that there is a critical transition point below which the outage probability decays only polynomially but above which it decays exponentially. This provides a solid analytical foundation to the earlier empirical observations in the literature and also reveals how typical outage events occur in different regimes. In addition, the proposed asymptotic expressions are also shown to be accurate in the non-asymptotic regimes.