Distribution Bounds on the Conditional ROC in a Poisson Field of Interferers and Clutters

2025-05-27

AI Summary

Conventional stochastic geometry methods focus solely on SINR statistics and fail to characterize the statistical variability of radar ROC performance across network realizations. Method: This work establishes, for the first time, an analytical framework for the conditional ROC distribution under Poisson-distributed interference and clutter fields. It derives closed-form expressions for the mean and variance of false-alarm and detection probabilities; employs the Cantelli inequality to obtain tight upper bounds; and approximates the noise-plus-interference power ratio via a Beta-distributed meta-distribution to statistically characterize the conditional ROC. Contribution/Results: Leveraging the higher-order Campbell–Mecke theorem and stochastic geometric analysis, we formulate a quantile-guaranteed robust ROC design paradigm. This provides a rigorous theoretical foundation and novel design principles for detection threshold selection and signal processing in high-reliability radar systems.

Technology Category

• Reasoning under Uncertainty: Stochastic Optimization
• Machine Learning: Calibration & Uncertainty Quantification
• Planning, Routing, and Scheduling: Scheduling under Uncertainty

Application Category

• Security and Privacy: Large-scale security measurements
• Search and Retrieval-Augmented AI: Web evaluation methodologies and metrics
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs

Abstract

We present a novel analytical framework to characterize the distribution of the conditional receiver operating characteristic (ROC) in radar systems operating within a realization of a Poisson field of interferers and clutters. While conventional stochastic geometry based studies focus on the distribution of signal to interference and noise ratio (SINR), they fail to capture the statistical variations in detection and false-alarm performance across different network realizations. By leveraging higher-order versions of the Campbell-Mecke theorem and tools from stochastic geometry, we derive closed-form expressions for the mean and variance of the conditional false-alarm probability, and provide tight upper bounds using Cantelli's inequality. Additionally, we present a beta distribution approximation to capture the meta-distribution of the noise and interference power, enabling fine-grained performance evaluation. The results are extended to analyze the conditional detection probability, albeit with simpler bounds. Our approach reveals a new approach to radar design and robust ROC selection, including percentile-level guarantees, which are essential for emerging high-reliability applications. The insights derived here advocate for designing radar detection thresholds and signal processing algorithms based not merely on mean false-alarm or detection probabilities, but on tail behavior and percentile guarantees.

Problem

• Characterize conditional ROC distribution in radar systems with Poisson field interferers
• Derive closed-form expressions for mean and variance of false-alarm probability
• Analyze conditional detection probability with robust ROC selection guarantees

Innovation

• Novel analytical framework for conditional ROC
• Higher-order Campbell-Mecke theorem and stochastic geometry
• Beta distribution approximation for meta-distribution