Frequency-difference beamforming [Abadi, Song, and Dowling (2012b). J. Acoust. Soc. Am. 132, 3018-3029] is an unconventional beamforming method for use with sparse receiver arrays. It involves beamforming a quadratic product of complex field amplitudes, P(ω)P(ω), at the difference frequency, ω-ω, instead of beamforming the complex field amplitude P(ω) at frequencies ω within the signal bandwidth. Frequency-difference beamforming is readily implemented with ordinary transducer array recordings of non-zero bandwidth signals. Results for, and comparisons of, frequency-difference beamforming from simulations and experiments are reported herein. In particular, spherical-wave beamforming is investigated using 15 and 165 kHz pulse signals in a 1.07-m-diameter water tank with a linear array having 14 elements spaced 5.08 cm apart. Here, frequency-difference beamforming using the high-frequency pulses provides comparable results to conventional beamforming at 15 kHz. Plane-wave beamforming is investigated using 11.2-32.8 kHz frequency-sweep signals broadcast 3 km through a 106-m-deep ocean sound channel to a vertical array having 16 elements spaced 3.75 m apart. Here, frequency difference beamforming in the 1.7-2.3 kHz difference frequency band provides results comparable to conventional beamforming in this band.
Frequency-difference beamforming [Abadi, Song, and Dowling (2012). J. Acoust. Soc. Am. 132, 3018–3029] is a nonlinear, out-of-band signal processing technique used to beamform non-zero bandwidth signals at below-band frequencies. This is accomplished with the frequency-difference autoproduct AP(Δω)=P(ω2)P*(ω1), a quadratic product of complex field amplitudes that mimics a genuine field at the difference frequency, Δω=ω2−ω1. For frequency-difference beamforming, AP(Δω) replaces the in-band complex field in the conventional beamforming algorithm. Here, the near-field performance of frequency-difference beamforming is evaluated in the presence of 1 to 30 high-contrast spherical scatterers with radius a placed between, and in the plane defined by the source and a 12-element linear receiving array with element spacing d. Based on the center frequency wave number, k, of the 150–200 kHz frequency sweep source signal, the scatterers are large, ka ≈ 15; the array is sparse, kd = 37; and the average source-to-receiver distance is up to 4.3 mean-free-path lengths. Beamforming results from simulations and experiments show that in-band beamforming loses peak-to-sidelobe ratio and fails to reliably locate the source as the scatterer count increases. Using the same signals, frequency-difference beamforming with difference frequencies from 5 to 25 kHz localizes sources reliably with higher peak-to-side-lobe ratios, though with reduced resolution.
Compressive beamforming methods have shown promise for use in high resolution direction finding and source localization. However, these methods often fail in scenarios with low SNR, particularly if only a few snapshots are available. The Spectral Estimation Method (SEM) (Blacodon and Elias, 2004, J. Aircraft 41 (6), 1360–1369) provides a means of source localization and source power estimation by minimizing the mean squares error between cross-spectral-density matrices of a measured signal and modeled signals at each location of interest. SEM With Additive Noise (SEMWAN) (Blacodon, 2011, Applied Acoustics, 72, 11–21) does the same but also utilizes the cross-spectral-density matrix of one or more noise references. In this presentation, the performance of a compressive version of SEMWAN is assessed for use in low SNR scenarios when the solution is sparse and a noise reference is available. Compressive SEMWAN is analyzed first using far-field, free-space simulations with varying SNR and multiple sources. Compressive SEMWAN is then applied to laboratory measurements taken with real noise sources at varying SNR and including some multipath propagation. The performance in each scenario is compared directly to conventional beamforming, a standard compressive beamforming method, and traditional SEMWAN. [Sponsored by NAVSEA through the NEEC.]
Distributed Acoustic Sensing (DAS) is a technology in which a fiber-optic cable is turned into an acoustic sensor by measuring backscatter of light caused by changes in strain from the surrounding acoustic field. In October 2022, 9 days of DAS and colocated hydrophone data were collected in Puget Sound near Seattle, WA. Passive data was continuously recorded for the duration and a broadband source was fired from several locations and depths on the first and last days. This dataset provides direct comparisons between DAS and hydrophone measurements, and demonstrates the ability of DAS to measure acoustics signals up to ~500Hz.
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