Frequency and angle spreads of acoustic signals reflecting from a fixed rough boundary

Abstract

A simple geometric-acoustic model (used previously to predict time spreads of reflecting signals) is slightly modified and extended to predict frequency and angle spreads, which can be used to predict coherence losses to sonar systems. In that model, the expected energy received from a boundary facet (via reflection) is computed as a function of the x and y coordinates of the facet. A ray arriving from any facet has a well-defined travel time, relative-frequency shift (for a given source and receiver motion), polar arrival angle, and azimuthal arrival angle. The frequency-spread function is defined as the histogram of expected received energies as a function of Q=( f−f0)/ f0, where f0 and f are, respectively, sent and received frequencies of a transmitted cw signal. The angle-spread function is similarly defined for the polar and azimuthal angles. The angle-spread function shows the well-known ‘‘shifting toward the horizon’’ of the reflected image of a source as the reflecting surface gets rougher. An analogous effect occurs for frequency spread. Because the horizon limits Doppler and angle spread, increased roughness sometimes narrows the spread functions instead of broadening them. Coherence-loss computations are performed using a plane-wave approximation local to the receiver.