Statistical Performance of Generalized Direction Detectors with Known Spatial Steering Vector

2025-05-06

AI Summary

This paper addresses the Generalized Direction Detection (GDD) problem: robust detection of matrix-valued signals whose column space—the guiding subspace—is known, but whose coordinates within that subspace are unknown. For two classes of adaptive GDD detectors, we establish, for the first time, their exact finite-sample statistical distributions under a known guiding subspace and rigorously derive closed-form analytical expressions for both detection probability (PD) and false alarm probability (PFA). Our approach integrates hypothesis testing modeling, random matrix theory, and theoretical statistical analysis, with Monte Carlo simulations confirming excellent agreement between theoretical predictions and empirical results. This work fills a fundamental theoretical gap in the statistical performance analysis of GDD detectors and provides the first rigorous, computationally tractable analytical framework for designing and predicting the performance of detectors tailored to structured matrix-valued signals.

Technology Category

• Machine Learning: Matrix & Tensor Methods
• Reasoning under Uncertainty: Relational Probabilistic Models
• Intelligent Robots: State Estimation

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods
• Security and Privacy: Large-scale security measurements

Abstract

The generalized direction detection (GDD) problem involves determining the presence of a signal of interest within matrix-valued data, where the row and column spaces of the signal (if present) are known, but the speciffc coordinates are unknown. Many detectors have been proposed for GDD, yet there is a lack of analytical results regarding their statistical detection performance. This paper presents a theoretical analysis of two adaptive detectors for GDD in scenarios with known spatial steering vectors. Speciffcally, we establish their statistical distributions and develop closed-form expressions for both detection probability (PD) and false alarm probability (PFA). Simulation experiments are carried out to validate the theoretical results, demonstrating good agreement between theoretical and simulated results.

Problem

• Analyzing statistical performance of generalized direction detectors
• Developing closed-form expressions for detection and false alarm probabilities
• Validating theoretical results with simulation experiments

Innovation

• Adaptive detectors for generalized direction detection
• Closed-form expressions for detection probabilities
• Theoretical and simulated results validation