# Mixture-based Modeling of Spatially Correlated Interference in a Poisson Field of Interferers

## TL;DR

This paper introduces a mixture-based analytical model for spatially correlated interference in Poisson field wireless networks, simplifying analysis while closely approximating exact PPP results and aiding multi-antenna receiver performance evaluation.

## Contribution

It proposes a novel mixture-based correlation framework that simplifies the analysis of spatially correlated interference in PPP networks, closely matching exact results.

## Key findings

- The mixture-based model accurately approximates PPP interference correlations.
- The model simplifies joint SIR analysis at multiple points.
- Application demonstrated for multi-antenna MRC receiver outage probability.

## Abstract

As the interference in PPP based wireless networks exhibit spatial correlation, any joint analysis involving multiple spatial points either end up with numerical integrations over $\mathbb{R}^2$ or become analytically too intractable. To tackle these issues, we present an alternate approach which not only offers a simpler analytical structure, but also closely mimics the PPP characteristics. This approach at its core models the correlated interferences using a correlation framework constructed using random variable mixtures. Additionally, a correlation framework based on the more standard method of linear combination of random variables is also presented for comparison purpose. The performance of these models is studied by deriving the joint CCDF of SIRs at $N$ arbitrary points. The plots are found to tightly approximate the exact PPP-based results, with the tightness depending on the values of $\lambda p$ (interferer intensity), $\alpha$ (path loss exponent) and $N$. The applicability of the mixture-based model is also shown for a multi-antennae MRC receiver where only major derivation steps that simplifies the outage probability analysis are shown.