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A Hybrid Dominant-Interferer Approximation for SINR Coverage in Poisson Cellular Networks

Sunder Ram Krishnan, Junaid Farooq, Kumar Vijay Mishra, Xingchen Liu, S. Unnikrishna Pillai, Theodore S. Rappaport

TL;DR

The paper tackles SINR coverage analysis in Poisson cellular networks where base stations form a PPP and interference is difficult to characterize analytically. It introduces a hybrid dominant-plus-tail approximation that treats a small number of nearest interferers exactly and models the far-field tail with a Laplace functional of the PPP, yielding a path-loss-agnostic estimator with error guarantees. The authors derive a conditional coverage expression, establish truncation-error bounds, and validate the method against stochastic geometry benchmarks and Monte Carlo simulations, including fractional path-loss exponents. The work provides a practical, modular tool that bridges stochastic geometry and moment-based interference models, enabling accurate network analysis across noise- and interference-limited regimes.

Abstract

Accurate radio propagation and interference modeling is essential for the design and analysis of modern cellular networks. Stochastic geometry offers a rigorous framework by treating base station locations as a Poisson point process and enabling coverage characterization through spatial averaging, but its expressions often involve nested integrals and special functions that limit general applicability. Probabilistic interference models seek closed-form characterizations through moment-based approximations, yet these expressions remain tractable only for restricted parameter choices and become unwieldy when interference moments lack closed-form representations. This work introduces a hybrid approximation framework that addresses these challenges by combining Monte Carlo sampling of a small set of dominant interferers with a Laplace functional representation of the residual far-field interference. The resulting dominant-plus-tail structure provides a modular, numerically stable, and path-loss-agnostic estimator suitable for both noise-limited and interference-limited regimes. We further derive theoretical error bounds that decrease with the number of dominant interferers and validate the approach against established stochastic geometry and probabilistic modeling benchmarks.

A Hybrid Dominant-Interferer Approximation for SINR Coverage in Poisson Cellular Networks

TL;DR

The paper tackles SINR coverage analysis in Poisson cellular networks where base stations form a PPP and interference is difficult to characterize analytically. It introduces a hybrid dominant-plus-tail approximation that treats a small number of nearest interferers exactly and models the far-field tail with a Laplace functional of the PPP, yielding a path-loss-agnostic estimator with error guarantees. The authors derive a conditional coverage expression, establish truncation-error bounds, and validate the method against stochastic geometry benchmarks and Monte Carlo simulations, including fractional path-loss exponents. The work provides a practical, modular tool that bridges stochastic geometry and moment-based interference models, enabling accurate network analysis across noise- and interference-limited regimes.

Abstract

Accurate radio propagation and interference modeling is essential for the design and analysis of modern cellular networks. Stochastic geometry offers a rigorous framework by treating base station locations as a Poisson point process and enabling coverage characterization through spatial averaging, but its expressions often involve nested integrals and special functions that limit general applicability. Probabilistic interference models seek closed-form characterizations through moment-based approximations, yet these expressions remain tractable only for restricted parameter choices and become unwieldy when interference moments lack closed-form representations. This work introduces a hybrid approximation framework that addresses these challenges by combining Monte Carlo sampling of a small set of dominant interferers with a Laplace functional representation of the residual far-field interference. The resulting dominant-plus-tail structure provides a modular, numerically stable, and path-loss-agnostic estimator suitable for both noise-limited and interference-limited regimes. We further derive theoretical error bounds that decrease with the number of dominant interferers and validate the approach against established stochastic geometry and probabilistic modeling benchmarks.

Paper Structure

This paper contains 9 sections, 1 theorem, 19 equations, 7 figures, 1 algorithm.

Table of Contents

  1. Introduction
  2. System Model and Problem Formulation
  3. Conditional Coverage Probability and Tail Approximation
  4. Analysis of Truncation Error
  5. Expectation-Aware Error Bounds for Specific Path-Loss
  6. Numerical Experiments
  7. Simulation Setup
  8. Results and Discussion
  9. Conclusion

Key Result

Theorem 1

Let $\eta > 2$, and define $s := T r^\eta > 0$, where $r$ is the distance to the serving BS. Then the error incurred by approximating the SG coverage probability using only the $N$ nearest BSs satisfies where the tail error term is given by

Figures (7)

  • Figure : (a) $N = 5$
  • Figure : (a)
  • Figure : (a) $N = 5$
  • Figure : (b) $N = 10$
  • Figure : (c) $N = 20$
  • ...and 2 more figures

Theorems & Definitions (2)

  • Theorem 1: Truncation Error Bound
  • proof