Detection of an unknown waveform randomly recurring in Gaussian noise

Abstract

Matched filtering is a widely used signal processing technique for detecting a known signal imbedded in noise. In the pulsed sonar case, the medium often distorts the received signal to such an extent that matched filtering is not optimal. This paper deals with the case where a record is obtained of Gaussian noise containing many repetitions of the distorted signal waveform. After obtaining an estimate of the waveform autocorrelation based upon nonoverlapping sections from the first part of the record, a test procedure is developed for determining whether or not the waveform is present in a subsequent section. The test procedure is derived from a Taylor series approximation of the likelihood ratio, where the signal-to-noise ratio is quite low and the probability that two or more waveforms are in the section is negligible. This suboptimal test involves cross correlating the sample autocorrelation with the waveform autocorrelation. An approximation is given to the difference in power between the likelihood-ratio test and its approximation. A comparison is made with the matched filter approach.