Parametric spatial post-filtering utilising high-order circular harmonics with applications to underwater sound-field visualisation

Beamforming using a circular array of hydrophones may be employed for the task of two-dimensional (2D) underwater sound-field visualisation. In this article, a parametric spatial post-filtering method is proposed, which is specifically intended for applications involving large circular arrays and aims to improve the spatial selectivity of traditional beamformers. In essence, the proposed method is a reformulation of the cross-pattern coherence (CroPaC) spatial post-filter, which involves calculating the normalised cross-spectral density between two signals originating from coincident beamformers. The resulting parameter may be used to sharpen another beamformer steered in the same look-direction, while attenuating ambient noise and interferers from other directions. However, while the original 2D version of the algorithm has been demonstrated to work well with second-order circular harmonic input, it becomes increasingly less suitable with increasing input order. Therefore, the proposed reformulation extends the applicability of CroPaC for much higher orders of circular harmonic input. The method is evaluated with simulated data of a 96-channel circular hydrophone array in three different passive sonar scenarios, where the proposed post-filter is shown to improve the spatial selectivity of both delay-and-sum and minimum-variance distortionless response beamformers.