Some Properties and Effects of Reverberation in Acoustic Surveillance

Following the work of Van Trees,[1] the effect of wide-sense stationary clutter on signal detectability with a matched filter is determined. The improvement to be gained by a high time-bandwidth product in the transmitted waveform for the detection of low-velocity targets is clearly shown. The additional noise contributed by the clutter is reduced by a factor equal to the time-bandwidth product. This reducing effect occurs provided that the transmitted waveform is adjusted properly. The optimum transmitted waveform for detection of low-velocity targets turns out to be one whose energy density spectrum is flat over the bandwidth of interest. This derivation is made by a simple application of Schwarz's inequality rather than the application of the calculus of variations that was done by Manasse.[14] Computations were made of the loss encountered by a narrow-band single-frequency waveform and by a wide-band linear FM waveform, each used in a matched-filter detector. The contrast is especially marked for very low target speeds where the narrow-band waveform is very bad. Its loss drops off sharply with target speed while the loss of the wide-band waveform drops off very slowly in comparison. Beyond a certain small target speed, the narrow-band loss is negligible. However, with enough bandwidth, the wide-band waveform can be made to have acceptable loss at all target speeds.