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 network topology of both secondary and primary users. 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 some important design factors which their important role in the determination of outage and interference cannot be ignored. We conduct simulations to validate our analytical results and evaluate the proposed schemes in terms of outage probability for different values of signal-to-interference-plus-noise-ratio (SINR) target.
