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The Cosine GLRT: Comparison of this Scale-Invariant GLRT
with the Kelly GLRT and the AMF

Shawn Kraut and Louis Scharf
University of Colorado at Boulder
Electrical and Computer Engineering / CB 425
Boulder, CO 80309
tel: (303) 492-2759
email: kraut@dsp.colorado.edu

Abstract We examine the problem of "adaptive" detection, wherein the noise covariance structure is unknown, and estimated with training data. We are specifically interested in noise that is not constrained to have the same power level in the test data and training data. For this scenario, we have shown that the "cosine" statistic is the GLRT (Generalized Likelihood Ratio Test) under unknown noise covariance, a companion to the GLRT detector of Kelly. It is invariant to arbitrary scaling of both the training data matrix and the test data. These invariances also make it useful for non-Gaussian noise scenarios, such as radar clutter modeled by a compound-Gaussian noise process with random amplitude scaling, as proposed by Conte et al. We will examine the performance convergence of the cosine GLRT, or CFAR ASD (Constant False Alarm Rate Adaptive Subspace Detector), and compare its performance with the Kelly GLRT and AMF (Adaptive Matched Filter). We have shown that all adaptive detectors of this type have statistically equivalent representations in terms of concise expressions of five statistically independent, scalar random variables, only three of which are needed to completely describe the random fluctuations in the sample covariance. Using these representations, it is observed that the cosine GLRT outperforms the Kelly GLRT when the noise power fluctuates, particularly when the nonadaptive SNR and number of available training samples are small.

Presentation (pdf format)



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