{"ID":2837677,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2511.19568","arxiv_id":"2511.19568","title":"Rao-Blackwellized Coverage Estimation in Poisson Networks: A High-Fidelity Hybrid Framework","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 $\\mathcal{O}(K^{1-η/2})$. 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.","short_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 ef...","url_abs":"https://arxiv.org/abs/2511.19568","url_pdf":"https://arxiv.org/pdf/2511.19568v2","authors":"[\"Sunder Ram Krishnan\",\"Junaid Farooq\",\"Kumar Vijay Mishra\",\"Xingchen Liu\",\"S. Unnikrishna Pillai\",\"Theodore S. Rappaport\"]","published":"2025-11-24T17:02:20Z","proceeding":"cs.IT","tasks":"[\"cs.IT\",\"eess.SP\",\"math.PR\"]","methods":"[]","has_code":false}