Coverage and Rate Analysis in Downlink ${L}$ -Tier HetNets With Fluctuating Beckmann Fading

The fluctuating Beckmann (FB) fading is a general fading model, and it extends the <inline-formula> <tex-math notation="LaTeX">$\kappa $ </tex-math></inline-formula>-<inline-formula> <tex-math notation="LaTeX">$\mu $ </tex-math></inline-formula> shadowed fading to a power imbalance scenario. However, the FB fading contains a generalized Lauricella confluent hypergeometric function, which makes the performance analysis in downlink stochastic geometry-based heterogeneous cellular networks (HetNets) face a big challenge. In this letter, we first approximate the general and complex FB fading as a Gamma distribution based on the second-order moment matching method. For the application of Laplace trick, we then propose a simple and novel Erlang distribution to approximate the Gamma distribution with non-integer parameters. Using the proposed distribution as well as the Rician approximation for a small parameter, we successfully obtain approximate expressions for the coverage probability and average rate in a downlink <inline-formula> <tex-math notation="LaTeX">${L}$ </tex-math></inline-formula>-tier HetNet with FB fading and validate through simulations.