Approximation of Meta Distribution and Its Moments for Poisson Cellular Networks

TL;DR

This paper introduces a method to reconstruct the meta distribution of coverage probability in Poisson cellular networks from its moments using Fourier-Jacobi expansion, providing a closed-form approximation and a power scaling law.

Contribution

It presents a novel approach to approximate the meta distribution from moments and derives a power scaling law for cellular networks.

Findings

Reconstructed meta distribution from moments using Fourier-Jacobi expansion.

Provided a closed-form approximation for moments with error analysis.

Derived a power scaling law for downlink Poisson cellular networks.

Abstract

The notion of meta distribution as the distribution of the conditional coverage probability (CCP) was introduced in \cite{Haenggi2015}. In this letter, we show how we can reconstruct the entire meta distribution only from its moments using Fourier-Jacobi expansion. As an example, we specifically consider Poisson cellular networks. We also provide a simple closed-form approximation for its moments, along with its error analysis. Lastly, we apply the approximation to obtain a power scaling law for downlink Poisson cellular networks.