Statistical Performance of Generalized Direction Detectors with Known Spatial Steering Vector

TL;DR

This paper provides a theoretical analysis of two adaptive detectors for generalized direction detection with known spatial steering vectors, deriving their statistical distributions and detection performance metrics.

Contribution

It offers the first analytical derivation of detection and false alarm probabilities for these detectors in GDD scenarios with known steering vectors.

Findings

Theoretical detection probability and false alarm probability expressions are derived.

Simulation results validate the accuracy of the theoretical analysis.

Good agreement between theoretical and simulated detection performance.

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.