Approximation of Meta Distribution and Its Moments for Poisson Cellular Networks

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.