Rao-Blackwellized Coverage Estimation in Poisson Networks: A High-Fidelity Hybrid Framework

TL;DR

This paper introduces the Rao-Blackwellized Hybrid Estimator (RBHE), a novel method that significantly improves the efficiency of coverage estimation in Poisson cellular networks by analytically handling far-field interference.

Contribution

The paper develops the RBHE framework that combines exact spatial sampling with analytical interference modeling, reducing simulation variance and computational effort.

Findings

RBHE is an unbiased estimator for finite truncations.

Bias decays at rate O(K^{1-η/2}) with increasing K.

Achieves up to 90.75x variance reduction in high-reliability regimes.

Abstract

While stochastic geometry provides a powerful framework for the analysis of cellular networks, standard Monte Carlo simulations often suffer from slow convergence due to the stochasticity of the infinite far-field. This work introduces the \textit{Rao-Blackwellized Hybrid Estimator} (RBHE), which enhances simulation efficiency by analytically marginalizing the residual far-field interference via the conditional Laplace functional. By partitioning the interference field into $K$ dominant interferers and an infinite tail, we derive an estimator that combines exact spatial sampling with a rigorous analytical representation. We prove that the RBHE is an unbiased estimator for any finite truncation, while its systematic bias relative to the infinite-plane benchmark decays at a rate of $\mathcal{O}(K^{1-\eta/2})$. Numerical results demonstrate significant sample parsimony; in the high-reliability regime ($T = -10$ dB) with $K=2$, the RBHE yields a variance reduction gain of $90.75\times$, enabling a $98.90\%$ reduction in the spatial realizations required to reach a target precision. This framework effectively bridges the gap between tractable analytical models and high-fidelity simulations.