In this paper, we present a cognitive radio (CR) based statistical framework for a two-tier heterogeneous cellular network (femto-macro network) to model the outage probability at any arbitrary secondary (femto) and primary (macro) user. A system model based on stochastic geometry (utilizing the spatial Poisson point process (PPP) theory) is applied to model the random locations and topology of both secondary and primary networks. A considerable performance improvement can be generally achieved by mitigating interference, in result of applying the CR idea over the above model. Novel closed form expressions are derived for the outage probability of any typical femto and macro user considering the Nakagami-m fading for each desired and interference links. We also study the effect of some important design factors which play vital roles and are usually ignored in determination of outage and interference. We conduct simulations to evaluate the performance of our proposed schemes in terms of outage probability for different values of signal-to-interference-plus-noise-ratio (SINR) target.
