In this paper, we present a cognitive radio (CR) based statistical framework for a two-tier (femto-macro) heterogeneous cellular network. In this framework, the coverage probability of an arbitrary femto user is determined. Using tools from stochastic geometry and point process theory (in this paper, the spatial Poisson point process (PPP) theory is used) we model the random locations and topology of both the femto and macro networks. A considerable improvement of system performance can be generally achieved by mitigating interference, as a result of applying the CR idea over the above model. We also study the implication of a Reinforcement Learning (RL) based power control (PC) strategy per femto user in interference-limited networks over the above model to guarantee a certain value of coverage probability for a given signal-to-interference-plus-noise-ratio (SINR) target.
