Approximation of Meta Distribution and its Moments for Poisson Cellular Networks

The notion of meta distribution as the distribution of the conditional coverage probability was introduced in the literature before. 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.