The Coherence of Acoustic Signals in the Ocean and Application to the Design of Very Large Arrays

The most important conclusion to be made from the development of the Multipath Coherence Function MCF is that it demonstrates the existence of coherence without correlation between random channels. The MCF demonstrates the importance of the size of fluctuations compared to their correlation. The existence of partial coherence implies a non-zero mean signal field for fluctuations which are small enough. It was also shown that the MCF is independent of the signal source and depends only on the properties of the medium. The importance of frequency domain processing is readily observed by comparing the coherence function with the normalized cross-correlation function. A broad band signal waveform in a multipath medium may have only one or two discrete frequencies at which coherence is high. The cross-correlation function, however, considers the entire signal waveform and will have a much smaller value than the maximum value of the coherence function. The MCF formulation is a simple, concise mathematical expression, and does not depend on present knowledge of oceanographic fluctuations. The solution is adaptable to future developments in the causes of these fluctuations.