An Extended Representation for Generalized Likelihood Ratio Test Detector in Gaussian-Distributed Signals

This paper presents an analysis of Gaussian distribution for radar signals modeling, offering a robust framework for characterizing clutter and target echoes. For radar systems, the generalized likelihood ratio test (GLRT) detectors emerge as versatile tools for navigating diverse statistical conditions through maximum likelihood estimation (MLE). This paper extends the previously available closed-form expressions for the probability of false alarm (P
FA
) and probability of detection (P
D
) for GLRT, considering fluctuating target signals. We show that, despite variations in system models, the same closed-form expressions can be obtained. This extension reaffirms the resilience and applicability of the proposed methodology in enhancing radar signal analysis. Derived expressions are confronted with Monte Carlo simulations, confirming the tightness of the expressions obtained.