Exact SINR Statistics in the Presence of Heterogeneous Interferers

We derive new results for the higher order moments of signal-to-interference-plus-noise ratio (SINR) in the presence of an arbitrary Poisson point process (PPP)-based heterogeneous interference field. The analysis leverages on a moment-generating-function (MGF) methodology, which only requires the statistics of intended signal and aggregate interference, thus eliminating the need for the exact distribution of SINR. We extend the existing results on interference statistics by deriving a generalized closed-form expression of the interference MGF considering Nakagami-m fading channels with exclusion region. In certain special cases, explicit expressions for the averages of different functions of SINR are found, which also lead to closed-form solutions for the probability distributions of aggregate interference reciprocal and signal-to-interference ratio. We prove that in such cases the effect of total PPP-based interference power on useful transmission is mathematically equivalent to the severe fluctuations from a one-sided Gaussian fading channel. As an application example, the proposed methodology is used together with stochastic geometry theory to characterize the average SINR and rate in heterogeneous cellular networks. The validity of our analytical derivations is confirmed via Monte Carlo simulations for various system settings. We show that with cellular network densification there exists a tradeoff between the average SINR and rate performance.