Bearing Estimation in the Presence of Surface Noise Using a 2D Array

We consider a rectangular grid of <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$m_{\mathrm{h}}$</tex> horizontal by <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$m_{\mathrm{v}}$</tex> vertical hydrophones (in total <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$m=m_{\mathrm{h}}m_{\mathrm{v}}$</tex> elements). The array is mounted on a rigid structure in a plane perpendicular to the sea surface. The array is used to estimate the bearings of sources located in the far field. We analyze the performance gain over a horizontal line array (i.e. an array with <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$m_{\mathrm{v}}=1$</tex> ) where the surface sea noise is the limiting factor. To achieve the directional properties of the noise, a sea surface noise model is proposed. The performance is analyzed for both conventional delay-and-sum (DAS) and Capon (a.k.a minimum variance distortionless response (MVDR)) beamforming. The results show that the output SNR improvement (as a function of <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$m_{\mathrm{v}}$</tex> ) is larger than that achieved with spatially white noise (i.e. noise which is uncorrelated betwen the hydrophones) and that Capon performs better than DAS in the considered scenario. For sample-level simulations, including detection and estimation, the performance of DAS and Capon are similar. A small but significant per-formance advantage of DAS over Capon is observed when the bottom material is highly absorbent and the beamforming is aimed slightly below the target. In that case the downtilt of the DAS beams reduce the impact of the surface noise more than the signal loss is from target off-pointing. However, only a single source is simulated and the improved resolution capabilities of Capon could make it the better solution when several sources are considered.