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

TL;DR

This paper develops a new analytical framework using stochastic geometry to characterize the distribution of the conditional ROC in radar systems affected by Poisson-distributed interferers and clutters, enabling more robust performance guarantees.

Contribution

It introduces closed-form expressions and bounds for the distribution of false-alarm and detection probabilities in Poisson interference environments, with a beta distribution approximation for detailed performance analysis.

Findings

Derived mean and variance of false-alarm probability

Provided tight upper bounds using Cantelli's inequality

Presented a beta distribution model for the meta-distribution

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.