Deconvolved frequency-difference beamforming for a linear array

Performance comparison of conventional and striation-based beamformers for underwater bearing detection of pulse sources

The multi-path and dispersion properties of shallow water waveguides make conventional beamforming (CBF) face issues such as beam shift, broadening, splitting, output distortion, and array gain reduction. In this paper, the striation-based beamforming (SBF) is investigated to address these issues. SBF differs from CBF by utilizing frequency-shift processing along interference striations. The performance difference between CBF and SBF is compared. It demonstrates that under ideal waveguide modeling with pulse sources, SBF can achieve a beam output response that is close to the plane wave condition. The speed term of SBF's response is approximately independent of modal indexes, which equips SBF to form a unique beam output and guarantee the beam resolution. The processing of consistent signals along the striation maintains the optimal signal correlation, which makes SBF ensure the output fidelity and array gain. To shift the mainlobe of SBF to the source azimuth, the time delay related to the waveform truncation point can be introduced to pre-compensate the array signals. There exist two theoretical accuracy limits to using the truncation. First, truncation time corresponds to the waveform point at r0/c (r0 is the source range), and the mainlobe of SBF is directed to the source azimuth. Second, truncation corresponds to the pulse peak point, and the azimuth estimation accuracy of SBF gets close to CBF. Simulations and experimental results are given as illustrations.

High-resolution frequency-difference beamforming for a short linear array

Conventional beamforming (CBF) is a commonly employed approach for detecting and estimating the direction-of-arrival (DOA) of acoustic signals in underwater environments. However, CBF becomes ambiguous due to spatial aliasing when the received signal's half wavelength is smaller than the array spacing. Frequency-difference beamforming (FDB) allows for processing data in the lower frequency Δf without encountering spatial aliasing by utilizing the product of array data at frequency f with its complex conjugate at frequency f+Δf. However, lower frequency results in a wider mainlobe, which can lead to poorer DOA performance for short arrays. In this paper, a fourth-order cumulants FDB method and a conjugate augmented FDB method are proposed to extend an M-element uniform linear array to 2M-1 and 4M-3 elements. The proposed methods generate narrower beams and lower sidelobe levels than the original FDB for short arrays with large spacing. And by setting the signal subspace dimension reasonably, the proposed methods can improve the weak target detection ability under strong interference compared with FDB. Last, we verify the excellent performance of the proposed methods through simulations and experimental data.

Localization of a remote source in a noisy deep ocean sound channel using phase-only matched autoproduct processing

Long-range passive source localization is possible in the deep ocean using phase-only matched autoproduct processing (POMAP) [Geroski and Dowling (2021). J. Acoust. Soc. Am. 150, 171-182], an algorithm based on matched field processing that is more robust to environmental mismatch. This paper extends these prior POMAP results by analyzing the localization performance of this algorithm in the presence of environmental noise. The noise rejection performance of POMAP is assessed using both simulated and measured signal data, with noise data based on environmental noise measurements. Herein, signal and noise measurements are from the nominally one-year-long PhilSea10 ocean acoustic propagation experiment. All signals were recorded from a single moored source, placed near the ocean sound channel 129.4 km away from a nearly water-column-spanning distributed vertical line array. The source transmitted linear frequency modulated chirps with nominal bandwidth from 200 to 300 Hz. The noise measurements used in this study were collected in the months after this source stopped transmitting, and synthetic samples of noise are calculated based on the characteristics of this measured noise. The effect that noise rejection algorithms have on the source localization performance of POMAP is also evaluated, but only 1 dB of performance improvement is achieved using these.

Deconvolved Fractional Fourier Domain Beamforming for Linear Frequency Modulation Signals

To estimate the direction of arrival (DOA) of a linear frequency modulation (LFM) signal in a low signal-to-noise ratio (SNR) hydroacoustic environment by a small aperture array, a novel deconvolved beamforming method based on fractional Fourier domain delay-and-sum beamforming (FrFB) was proposed. Fractional Fourier transform (FrFT) was used to convert the received signal into the fractional Fourier domain, and delay-and-sum beamforming was subsequently performed. Noise resistance was acquired by focusing the energy of the LFM signal distributed in the time-frequency domain. Then, according to the convolution structure of the FrFB complex output, the influence of the fractional Fourier domain complex beam pattern was removed by deconvolution, and the target spatial distribution was restored. Therefore, an improved spatial resolution of DOA estimation was obtained without increasing the array aperture. The simulation and experimental results show that, with a small aperture array at low SNR, the proposed method possesses higher spatial resolution than FrFB and frequency-domain deconvolved conventional beamforming.

Unambiguous broadband direction of arrival estimation based on improved extended frequency-difference method

In this paper, we consider the problem of bearing ambiguity in the direction of arrival (DOA) estimation due to spatial aliasing when the minimum wavelength of the processing broadband signal is less than the element spacing of a uniform linear array (ULA). First, an extended frequency-difference (FD) method is presented. Unlike the existing FD methods, the extended FD signal is constructed by conjugate multiplying a diagonal matrix consisting of steering vectors at high frequency and pre-processing direction with the array sampled signal matrix at low frequency. Then, this paper establishes a decision criterion for distinguishing the aliasing component that varies linearly with frequency in the extended FD space. Finally, an unambiguous broadband DOA estimation method is achieved by suppressing spatial aliasing in the extended FD space. The simulation results show the effectiveness of the proposed method in low signal-to-noise ratio, low signal-to-interference ratio, and multi-interference conditions. The unambiguous processing ability of the proposed method is further verified in the South China Sea using ship signals in the frequency band of 200 to 700 Hz and a 10-element ULA with a 6.25 m spacing deployed on the seabed.

Aliasing-free broadband direction of arrival estimation using a frequency-difference technique

When the intersensor spacing of a uniform linear array (ULA) is larger than the half-wavelength of an incident narrowband signal, spatial aliasing is generated. For broadband signals, the broadband spatial spectrum is still affected as a result of the spatial aliasing in each frequency bin. In this paper, an aliasing-free broadband direction-of-arrival (DOA) estimation algorithm for ULAs is proposed. First, an array output is constructed with a given Gaussian random sequence from the direction ϑ. Then, a frequency-difference (FD) operation is conducted, which multiplies the array observation in the frequency bin f by the conjugate form of the constructed array output in the frequency bin f+Δf. Thus, an equivalent array output at a desired frequency Δf is obtained, whose wavelength is equal to twice the intersensor spacing. In this manner, an aliasing-free spatial spectrum in the FD domain is achieved. Scanning the direction ϑ, the DOA of signals is finally estimated based on the difference between the peaks in the aliasing-free spatial spectrum and direction ϑ. The proposed method can achieve a satisfactory estimation even in a strong interference environment. The simulations and experimental results are included to demonstrate the superiority of the proposed method.

Robust long-range source localization in the deep ocean using phase-only matched autoproduct processing

Passive source localization in the deep ocean using array signal processing techniques is possible using an algorithm similar to matched field processing (MFP) that interrogates a measured frequency-difference autoproduct instead of a measured pressure field [Geroski and Dowling, J. Acoust. Soc. Am. 146, 4727-4739 (2019)]. These results are extended herein to a new MFP-style algorithm, phase-only matched autoproduct processing, that is more robust at source-array ranges as large as 225 km. This new algorithm is herein described and compared to three existing approaches. The performance of all four techniques is evaluated using measured ocean propagation data from the PhilSea10 experiment. These data nominally span a 12-month period; include six source-array ranges from 129 to 450 km; and involve signals with center frequencies between 172.5 and 275 Hz, and bandwidths of 60 to 100 Hz. In all cases, weight vectors are calculated assuming a range-independent environment using a single sound-speed profile measured near the receiving array. The frequency-differencing techniques considered here are capable of localizing all six sources, with varying levels of consistency, using single-digit-Hz difference frequencies. At source-array ranges up to and including 225 km, the new algorithm requires fewer signal samples for success and is more robust to the choice of difference frequencies.