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This paper evaluates the comparative performance of adaptive and conventional square law detectors for inputs consisting of finite bandwidth signals in white Gaussian noise. The comparative performance of two distinct ALE augmented detector implementations will be provided. Performance is determined on the basis of ROC curves for a range of signal bandwidths, ALE bulk delays, ALE time constants, ALE frequency resolutions, and postdetection integration times for the ALE augmented detectors. These curves are evaluated to determine the best choice of ALE parameters for various input signal conditions, the sensitivity in performance to that choice, and the comparative performance of the conventional and ALE augmented detectors. Monte Carlo simulation is used to generate the ROC curves on which the performance analysis is based.