Rao-Blackwellized Coverage Estimation in Poisson Networks: A High-Fidelity Hybrid Framework
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| Main Authors: | , , , , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866908946791399424 |
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| author | Krishnan, Sunder Ram Farooq, Junaid Mishra, Kumar Vijay Liu, Xingchen Pillai, S. Unnikrishna Rappaport, Theodore S. |
| author_facet | Krishnan, Sunder Ram Farooq, Junaid Mishra, Kumar Vijay Liu, Xingchen Pillai, S. Unnikrishna Rappaport, Theodore S. |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2511_19568 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Rao-Blackwellized Coverage Estimation in Poisson Networks: A High-Fidelity Hybrid Framework Krishnan, Sunder Ram Farooq, Junaid Mishra, Kumar Vijay Liu, Xingchen Pillai, S. Unnikrishna Rappaport, Theodore S. Information Theory Signal Processing Probability 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. |
| title | Rao-Blackwellized Coverage Estimation in Poisson Networks: A High-Fidelity Hybrid Framework |
| topic | Information Theory Signal Processing Probability |
| url | https://arxiv.org/abs/2511.19568 |