Acoustic Signal Detection by Simple Correlators in the Presence of Non-Gaussian Noise. I. Signal-to-Noise Ratios and Canonical Forms

Abstract

The detection of underwater acoustic signals by simple auto- and cross-correlation receivers in the presence of nonnormal, as well as normal background noise is examined on the basis of signal-to-noise ratios calculated from a generalized deflection criterion. Particular attention is devoted to the effects of impulse noise and mixtures of impulse and normal noise on system performance. Comparisons between system behavior vis-à-vis the two types of interference are made. For impulse noise equivalent in spectral distribution and average intensity to a Gaussian noise background it is found that the output signal-to-noise (power) ratios are related by the canonical expression (SN)I2 = (S/N)G21 + (1 − μ)Λ(S/N)G2, 0⩽μ⩽1, where Λ(⩾0) is the “impulse factor” and μ is the fraction (in average intensity) of the total noise background that is attributable to normal noise. Impulse noise always degrades system performance vis-à-vis normal noise in the autocorrelation reception of stochastic signals, characteristic of applications where passive receiving methods must be used. This degradation can be considerable [O(10 dB or more)] if the noise is highly impulsive (large Λ) and if large values of (S/N)out2(>0 dB) are required (for high accuracy of decision). On the other hand, when coherent (i.e., deterministic) signals are employed, so that cross-correlation reception is possible, the degradation may be reduced essentially to zero (i.e., Λ → 0) under realizable conditions of operation. It is observed for impulsive, as well as normal noise backgrounds, that cross-correlation receivers are linear in their dependence on signal-to-noise ratio, i.e., (S/N)out2∼(S/N)in2 if sufficiently strong injected signals are employed. The analysis is carried out largely in canonical form, so that the general results for (S/N)out2 can be applied to other, special types of nonnormal noise backgrounds. Specific relations are included, along with a detailed summary of the principal results, showing the dependence of (S/N)out2 on (S/N)in2, filtering, delay, noise and signal spectra, etc., for weak and strong inputs, little or heavy postcorrelation smoothing and for Gaussian as well as for impulse noise.