Beamforming and Source Quantification in Complex Environments Using In-Band and Out-of-Band Methods

Abstract

Acoustic array signal processing in the ocean faces challenges due to multipath propagation, scattering from objects or surfaces, geometric uncertainty, and limitations from array geometry - all of which can harm conventional beamforming outputs. Frequency-difference and frequency-sum beamforming are out-of-band signal processing techniques that exploit signal bandwidth to beamform at below- or above-band frequencies. The work described here evaluates frequency-difference beamforming's ability to reduce the undesirable effects associated with array sparseness, strong random scattering, or geometric uncertainty, and examines the array coherence properties of both techniques. Frequency-difference beamforming has also been used with Synthetic Time Reversal (STR) for blind deconvolution, and is extended to underwater communications here. The performance of frequency-difference beamforming is evaluated using simulations and experiments in a laboratory water tank and a shallow-ocean environment (KAM11 experiment). The method is shown to mitigate the effects of array sparseness, with results comparable to conventional beamforming when the in-band frequency matches the difference frequency, Δf, despite frequency-difference beamforming using a higher frequency signal. Shallow ocean results show agreement when comparing expected directions-of-arrival (DOAs) and the frequency-difference DOAs, with a reduced-chi-squared of 0.91 in experiments, despite notable multipath and array element spacing of 27-80 in-band wavelengths. Horizontal array simulations indicate that frequency-difference beamforming is robust to random variation in ray-path arrival times when Δf*σ = 0.20 (σ = arrival time standard deviation). Additional water tank simulations and experiments show that frequency-difference beamforming mitigates strong scattering effects by utilizing frequencies where Δka is small (k = wavenumber, a = spherical scatterer radius). Here, frequency-difference beamforming localizes a source with a factor of 4 reduction in error and 5 dB peak-to-sidelobe ratio improvement compared to conventional in-band techniques using the same signals. The coherence lengths of frequency-difference and -sum autoproducts are considered using recordings of a bottom-reflected path with an 8 km towed array (COAST 2012 experiment), showing coherence extending below and above the signal band. Here, averaged coherence lengths were 7.0λ for conventional fields from 1-200 Hz, 12.4λ for frequency-difference autoproducts from 1-100 Hz, and 8.6λ for frequency-sum autoproducts from 40-400 Hz (both using a 10-200 Hz signal band). Blind deconvolution of a communication signal (from KAM11 data) is considered using an Overlapping STR (OSTR) technique that provides real-time channel updates. OSTR is shown to be useful for long-duration signals in time-varying environments and is compared to a standard Time Reversal (TR) method. Here, the TR method yields a bit error rate (BER) = 0.34% and an SNR = 8.5 dB (average bit error in the complex plane). For the same signal, OSTR yields BER = 0.0% and SNR = 12.2 dB. An additional experiment considers acoustic measurements of aeroacoustic noise in a wind tunnel. Conventional beamforming and the Spectral Estimation Method with cross spectral density matrix (CSDM) subtraction, and Robust Principal Component Analysis with a subspace denoising technique are considered for noise removal using a reference measurement. In a ≤ -15 dB SNR environment, localization and source level estimation of field changes are possible when the source level is louder than noise resulting from experimental variation. Here, source level increments from 0.05 to 0.15 dB are determined with average error of 0.013 dB or less. This work demonstrates that simple CSDM subtraction is effective when a robust noise reference exists.