Adaptive detection of signals with linear feature mappings and representations

In a previous paper, Reed (1993) developed a new test function for detecting a 2-D signal with limited prior information about the signal waveform and the statistical properties of clutter. This was accomplished by substituting a maximum likelihood estimate (MLE) of the unknown clutter covariance matrix and the MLE´s of the amplitudes of the selected signal-feature components into a maximum invariant ratio test. However, performance analyses of this detector were not obtained. In this paper, the test statistic in Reed´s previous paper is extended to the complex domain for application to synthetic aperture radar (SAR) imagery. The performance of the detector is studied analytically. Closed-form expressions for the performance of the detector, under both hypotheses H₀ and H₁ are obtained. The theoretical results show that the detectability of the test is strongly effected by the feature mapping and selection techniques used to represent a signal. Here the effectiveness of a feature representation is evaluated in terms of the number of features needed to represent a signal and the separability of those features from the clutter background. The dependence of the detection probability on the effectiveness of the features is quantitatively shown by a set of performance curves. The resulting analyses indicate that the detector has the property of a constant false alarm rate (CFAR). To make the results of the detection performance analysis more applicable to real problems, the loss due to a “mismatched feature” representation is also studied analytically