# Interference Modeling for Cellular Networks under Beamforming Transmission

## TL;DR

This paper develops and validates analytical interference models for MIMO beamforming cellular networks in different scattering environments, using heavy tail distributions and mixture models to accurately predict interference power.

## Contribution

It introduces a three-parameter mixture model combining Inverse Gaussian and Inverse Weibull distributions for interference power, with parameter estimation methods and goodness-of-fit validation.

## Key findings

- The mixture model fits simulated interference data remarkably well.
- The model accurately predicts network capacity under beamforming.
- Goodness-of-fit is validated using relative entropy metrics.

## Abstract

We propose analytical models for the interference power distribution in a cellular system employing MIMO beamforming in rich and limited scattering environments, which capture non line-of-sight signal propagation in the microwave and mmWave bands, respectively. Two candidate models are considered: the Inverse Gaussian and the Inverse Weibull, both are two-parameter heavy tail distributions. We further propose a mixture of these two distributions as a model with three parameters. To estimate the parameters of these distributions, three approaches are used: moment matching, individual distribution maximum likelihood estimation (MLE), and mixture distribution MLE with a designed expectation maximization algorithm. We then introduce simple fitted functions for the mixture model parameters as polynomials of the channel path loss exponent and shadowing variance. To measure the goodness of these models, the information-theoretic metric relative entropy is used to capture the distance from the model distribution to a reference one. The interference models are tested against data obtained by simulating a cellular network based on stochastic geometry. The results show that the three-parameter mixture model offers remarkably good fit to simulated interference power. The mixture model is further used to analyze the capacity of a cellular network employing joint transmit and receive beamforming and confirms a good fit with simulation.