On generalized signal-to-noise ratios in quadratic detection

The generalized signal-to-noise ratio (GSNR) is a measure of performance often used in evaluating binary hypothesis testing procedures. In this paper, we investigate the properties of the GSNR as applied to the evaluation of quadratic detectors with Gaussian hypotheses. Appealing to reproducing kernel Hilbert space theory, we give a representation for the GSNR that is particularly useful for evaluating extremal properties. Finally, we discuss an alternative performance measure that is both intuitively appealing and superior to the GSNR in some respects.

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