Performance comparisons of frequency-difference and conventional beamforming

Abstract

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.

Spatial Coherence Comparisons between the Acoustic Field and Its Frequency-Difference and Frequency-Sum Autoproducts in the Ocean

“…Interestingly, recent work has considered surrogate fields, the frequency-difference and frequencysum autoproducts, as possible replacements for genuine acoustic fields at frequencies not broadcast by the source [20,21]. Use of the autoproducts has been successful for beamforming [22][23][24][25] and matched-field processing [26][27][28] at frequencies outside the broadcast signal's bandwidth. However, the coherence of autoproducts has yet to be directly examined, despite its importance in signal processing applications.…”

Direction-of-Arrival Estimation Based on Frequency Difference–Wavenumber Analysis for Sparse Vertical Array Configuration

“…Abadi et al proposed a beamforming approach based on the concept of frequency difference, known as frequency-difference (FD) beamforming [ 11 ]. FD beamforming is a method of beamforming a difference-frequency component that is equal to the difference between two frequencies extracted by the product of two relatively high-frequency components [ 11 , 12 , 13 ]. Xenaki et al applied the concept of compression sensing (CS) to beamforming in 2014 [ 14 , 15 , 16 , 17 , 18 ].…”

In-Depth Exploration of Signal Self-Cancellation Phenomenon to Achieve DOA Estimation of Underwater Acoustic Sources

“…Conventional beamforming (or delay-and-sum beamforming) is also one of the common DOA estimation methods [4][5][6]. Based on the ray-path approximation for the sound channel's impulse response, the frequency-difference beamforming method for the sparse hydrophone array is proposed in [7,8], which can estimate the signal phase difference by using the conventional delay-and-sum beamforming of the field product at the difference frequency. In contrast, by determining the array weight coefficients in a nonlinear manner, the minimum variance distortionless response (MVDR) method can achieve higher angular resolution than conventional beamforming [4].…”