Ocean Surface Bias on Doppler System Output

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Usually, the Doppler output of a sonar system is assumed to be monochromatic. The random variation of ocean surface and bottom significantly alter this assumed monochromatic nature of the Doppler signal into a frequeucy band-limited output. The surface heights are assumed to be normally distributed; the facet approach is used to show their effect on the Doppler term. For instance, a transmitted signal: et(t) = sin ωct becomes: ẽr(t) = à sin(ωcf+φ̃d+φ̃a). The random amplitude modulation à and its associated phase-angle modulation φ̃a have been previously shown to be strictly surface-caused effects, whereas φ̃d is the surface-caused randomly varying Doppler term, if one takes out the transmitter beam-modulalation effects. The long time averages of à and φ̃d have been shown to be statistically independent, Rayleigh and uniformly distributed, respectively. Beating of the received signal ẽr(t) with the local oscillator producing the carrier frequency ωc and passing it through the low-pass filter to get rid of 2ωc term results in ēr′ = à sin(φd+φa). Under quite general conditions, the probability density function of ẽr′ was shown to be Gaussian. This result was then verified from experimental data obtained by an underwater Doppler system as well as by its laboratory ultrasonic simulation at the University of Houston in a 20-ft-, 25-ft-deep water tank. Results of the experimental data analysis seem to support the theoretical results discussed earlier. [Work sponsored by the Office of Naval Research (Acoustics Branch).]