The LMS cancellation of narrow, extended interferences in sonar

The spatial least mean-square sense cancellation of acoustic interferences, with finite but narrow angular extent, from the output of a primary sensor using reference hydrophones spatially separated from the primary, is considered. This is done by replacing adaptive LMS filters in the canceller structure with continuous Wiener filters. A far-field model for a narrow extended source impinging on a line array of hydrophones is developed and used to determine the canceller output spectrum. Lower bounds on the canceller output spectrum are developed for arbitrary but narrow source distribution. For the special case of a spatially uncorrelated, uniformly distributed narrow interference, the cancellation is evaluated as a function of the number of reference hydrophones, the position of the reference relative to the primary sensor, and the angular extent of the interference. Explicit approximations for the cancellation achieved with such a source are developed and design guidelines described for the selectcion of reference hydrophone position and the number of references. Several significant differences between cancellation of single plane wave and narrow extended sources are demonstrated. Most notably, it is shown that the spatial rejection of an extended source may be bounded significantly above the ambient noise floor if the references are not sufficiently close to the primary sensor, regardless of the number of references.