Rao-Blackwellized Coverage Estimation in Poisson Networks: A High-Fidelity Hybrid Framework
This work addresses efficiency issues in stochastic geometry simulations for cellular networks, offering a significant but incremental improvement over existing methods.
The paper tackles the slow convergence of Monte Carlo simulations in cellular network analysis by introducing the Rao-Blackwellized Hybrid Estimator (RBHE), which reduces variance by 90.75 times and cuts required spatial realizations by 98.90% in high-reliability scenarios.
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 $\mathcal{O}(K^{1-η/2})$. 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.