Fresnel-Corrected Second-Order Interfrequency Correlations for a Surface-Scatter Channel

The correlation of the transfer function taken simultaneously at two different frequencies is computed for a random surfacescatter channel. The analysis is limited to transmission in the specular direction but uses a Fresnel-corrected model. It is therefore applicable to channels excited by a wide beam transmitter. Using this model it is possible to explain why in certain circumstances channel activity at two closely spaced frequencies is uncorrelated while in other cases correlation may be observed at widely spaced frequencies. Some guidelines for predicting various modes of channel behavior are derived. The Fresnel-corrected model is also used to explore the duration of the reverberant impulse response of the channel. The results are presented in a broad-band Sonar context but they can easily be generalized. Comparisons with the Fraunhofer limit are made in order to establish what advantages are offered by the Fresnel model.