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An Improved Propagator-Based Method for DOA Estimation without the Source Number using a nested array

CIRCUITS SYSTEMS AND SIGNAL PROCESSING 2025年 1-16页

作者： Zhang, Mingfeng Gu, Xiaobo Chen, Yitong Fu, Zhe Li, Jianzhong Guangdong Univ Technol Sch Integrated Circuits Guangzhou 510006 Peoples R China Guangdong Univ Technol Sch Automat Guangzhou 510006 Peoples R China Huawei Technol Co Ltd Shenzhen 518129 Peoples R China

Fourth-order cumulants (FOC) are widely adopted in direction of arrival (DOA) estimation due to their capability of mitigating Gaussian noise and constructing virtual arrays. However, the prerequisite of knowing the source number becomes a significant bottleneck when a nested array (NA) is utilized, limiting its practical applications. To address this issue, we propose an improved propagator-based method that eliminates the need for prior knowledge of the source number. By introducing a small-value factor, the proposed method generates an estimator equivalent to the classical multiple signal classification (MUSIC) estimator while retaining the benefits of NA, such as high degrees of freedom and low mutual coupling. Numerical simulations demonstrate the superior performance of the proposed estimator, particularly in scenarios with a large number of signals relative to the number of sensors. Furthermore, experimental results validate the effectiveness of the proposed method in practical situations, showcasing its robustness and accuracy. This approach not only overcomes the limitation of source number estimation but also provides a reliable solution for underdetermined DOA estimation, making it highly applicable in fields such as wireless communications, radar systems, and medical electronics.

关键词： Direction of arrival nested array Improved propagator Source number

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nested array Processing for Distributed Sources

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IEEE SIGNAL PROCESSING LETTERS 2014年第9期21卷 1111-1114页

作者： Han, Keyong Nehorai, Arye Washington Univ Preston M Green Dept Elect & Syst Engn St Louis MO 63130 USA

We consider the problem of using linear nested arrays to estimate the directions of arrival (DOAs) of distributed sources and to detect the source number, where we have more sources than actual physical sensors. Angular spread, caused by the multipath nature of the distributed sources, makes the commonly used point-source assumption challenging. We establish the signal model for distributed sources, using a nested array. Due to the characteristics of distributed sources, the regular spatial smoothing technique, which is used to exploit the increased degrees of freedom provided by the co-array, no longer works. We thus propose a novel spatial smoothing approach to circumvent this problem. Based on the analytical results, we construct the corresponding DOA estimation and source number detection methods. The effectiveness of the proposed methods is verified through numerical examples.

关键词： Direction of arrival estimation distributed source nested array source number detection

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A Velocity-independent DOA Estimator of Underwater Acoustic Signals via an Arbitrary Cross-linear nested array

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CIRCUITS SYSTEMS AND SIGNAL PROCESSING 2023年第2期42卷 996-1010页

作者： Ning, Gengxin Wang, Yu Jing, Guangyu Zhao, Xuejin South China Univ Technol Sch Elect & Informat Engn Guangzhou Peoples R China Guangdong Univ Technol Sch Econ & Commerce Guangzhou Peoples R China

In this paper, an estimator for underwater DOA estimation is proposed by using a cross-linear nested array with an arbitrary cross-angle. The estimator removes the acoustic velocity factor by deriving the geometric relation of the cross-linear array. Compared with conventional DOA estimation algorithms via a linear array, this estimator eliminates systematic errors caused by the uncertainty factor of the acoustic velocity in the underwater environment. In comparison with the conventional acoustic velocity-independent algorithm, this estimator uses the nested array and does not have to estimate the value of the acoustic velocity, which improves the performance of DOA estimation. Moreover, the proposed method is only slightly inferior to some of the conventional algorithms if the acoustic velocity is estimated accurately. Numerical simulations are provided to validate the analytical derivations and corroborate the improved performance in underwater environments where the actual acoustic velocity is not accurate.

关键词： Underwater DOA estimation Velocity-independent Arbitrary Cross-linear array nested array

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Low Complexity DFT Based DOA Estimation for Synthetic nested array Using Single Moving Sensor

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WIRELESS PERSONAL COMMUNICATIONS 2018年第2期101卷 857-874页

作者： Shi, Zhan Xu, Le Zheng, Wang Nanjing Univ Aeronaut & Astronaut Coll Elect & Informat Engn Nanjing 210016 Jiangsu Peoples R China

The issue of direction of arrival (DOA) estimation for synthetic nested array is investigated in this paper. The synthetic nested array (SNA) is formed by one single sensor moving according to the configuration of the physical nested array. With the synthetic array, both high resolution DOA estimation and array aperture miniaturization requirements can be met. To reduce the computationally complexity for SNA, a discrete Fourier transform (DFT) based algorithm is proposed which needs no eigen decomposition. We first reconstruct the data matrix reshaped from the data received by moving senor to obtain the observation vector and then get the initial DOA estimates via DFT of the observation vector. At last the fine estimates can be obtained through searching for peaks corrected by phase rotation matrix over a small sector. The proposed algorithm for SNA can achieve better bearing estimation performance than spatial smoothing (SS) subspace based methods such as SS-MUSIC and SS-ESPRIT, due to the fact that it can fully utilize array aperture while SS-MUSIC and SS-ESPRIT lose a half. Besides, the proposed algorithm involves full degree of freedoms (DOF). Numerical simulations validate the efficiency and superiority of the proposed algorithm.

关键词： Synthetic array nested array Direction of arrival Low complexity DFT

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Product beamforming and nested array in tandem for enhanced sonar performance

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MULTIDIMENSIONAL SYSTEMS AND SIGNAL PROCESSING 2022年第3期33卷 879-898页

作者： Pillai, S. Vijayan Santhanakrishnan, T. Kumar, N. Suresh Rajesh, R. Naval Phys & Oceanog Lab Kochi 682021 Kerala India

High-performance sonar systems mostly combine a large sensor array and an efficient beamformer for enhancing the overall detection capabilities and estimation of Direction of Arrival (DoA) of the acoustic signal released from underwater targets in the ocean. The array geometry and the number of elements have direct influences on the beam width and the signal to noise ratio but increase the complexity in terms of hardware and computational requirement. Even when such hardware complexities are accommodated in complex systems, the performance of such systems is often par below its expected level because of the limitations of the beamformer. The efficacy of the beamforming lies in obtaining a narrow beamwidth for the main lobe with minimum sidelobe levels (SLL) while keeping the element utilization factor as maximum as possible. This in turn demands proper optimization over array parameters and beamforming methods. Several optimization techniques have been established over the years and practised in a variety of sonar systems. Statistical array processing with nested and sparse array concepts with virtual elements offer effective solutions to these challenges. This article proposes an approach comprising a novel product beamforming concept that uses the idea of destructive interference in tandem with the nested array concept to demonstrate that better sonar performance can be achieved. The former helps to minimize the SLL without affecting the veracity of the main lobe, while the latter helps to reduce the requirement of a large number of sensors and thereby reduce the system complexity.

关键词： Direction of arrival estimation nested array Product beamforming Naval ASW applications Shallow ocean Sonar beamforming

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DOA estimation in conformal arrays based on the nested array principles

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DIGITAL SIGNAL PROCESSING 2016年 50卷 191-202页

作者： Alinezhad, Pourya Seydnejad, Saeid R. Abbasi-Moghadam, Dariush Shahid Bahonar Univ Kerman Dept Elect Engn Kerman Iran

The nested array structure has attracted great attention recently due to its ability in reducing the number of sensors in an array and at the same time preserving the array performance. While a uniform linear array (ULA) can detect at most N - 1 sources with N sensors, a nested array can provide O(N-2) degrees of freedom with the same number of sensors;allowing us to detect K sources with K > N sensors. Direction of arrival (DOA) estimation in a conformal array is a challenging task. In this article, by breaking the conformal array into smaller sub-arrays and using an interpolation technique, we employ the nested array principles to detect more number of sources than sensors. This comes at the cost of more snapshots and lower resolution, in the DOA estimation of an arbitrarily-shaped conformal array. Each sub-array in the conformal array is selected such that the "shadow effect" which leads to an incomplete steering vector in the DOA estimation algorithm is eliminated. The selected sub-arrays are then transformed to virtual nested arrays where more degrees of freedom can be obtained by applying the MUSIC algorithm for DOA estimation. The application of our proposed method is highlighted by considering a set of comprehensive examples for cylindrical and spherical arrays. (C) 2015 Elsevier Inc. All rights reserved.

关键词： Conformal array nested array DOA estimation MUSIC

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Solving for Source Parameters Using nested array Data: A Case Study from the Canterbury, New Zealand Earthquake Sequence

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PURE AND APPLIED GEOPHYSICS 2017年第3期174卷 875-893页

作者： Neighbors, Corrie Cochran, E. S. Ryan, K. J. Kaiser, A. E. Univ Calif Riverside CA 92521 USA Western New Mexico Univ Silver City NM 88061 USA US Geol Survey Pasadena CA 91106 USA US Geol Survey Menlo Pk CA 94025 USA GNS Sci Lower Hutt New Zealand

The seismic spectrum can be constructed by assuming a Brune spectral model and estimating the parameters of seismic moment (M-0), corner frequency ( f(c)), and high-frequency site attenuation (k). Using seismic data collected during the 2010-2011 Canterbury, New Zealand, earthquake sequence, we apply the non-linear least-squares Gauss-Newton method, a deterministic downhill optimization technique, to simultaneously determine the M-0, f(c), and k for each event-station pair. We fit the Brune spectral acceleration model to Fourier-transformed S-wave records following application of path and site corrections to the data. For each event, we solve for a single M-0 and f(c), while any remaining residual kappa, k(r), is allowed to differ per station record to reflect varying high-frequency falloff due to path and site attenuation. We use a parametric forward modeling method, calculating initial M-0 and fc values from the local GNS New Zealand catalog M-w, (GNS) magnitudes and measuring an initial k(r) using an automated highfrequency linear regression method. Final solutions for M-0, f(c), and k(r) are iteratively computed through minimization of the residual function, and the Brune model stress drop is then calculated from the final, best-fit f(c). We perform the spectral fitting routine on nested array seismic data that include the permanent GeoNet accelerometer network as well as a dense network of nearly 200 Quake Catcher Network (QCN) MEMs accelerometers, analyzing over 180 aftershocks M-w, (GNS) >= 3.5 that occurred from 9 September 2010 to 31 July 2011. QCN stations were hosted by public volunteers and served to fill spatial gaps between existing GeoNet stations. Moment magnitudes determined using the spectral fitting procedure (Mw, SF) range from 3.5 to 5.7 and agree well with Mw, GNS, with a median difference of 0.09 and 0.17 for GeoNet and QCN records, respectively, and 0.11 when data from both networks are combined. The majority of events are calculated to have

关键词： Canterbury earthquake sequence strong ground motion quake-catcher network MEMs accelerometers nested array Gauss-Newton method Brune model spectral acceleration stress drop

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Robust adaptive beamforming in nested array

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SIGNAL PROCESSING 2015年 114卷 143-149页

作者： Yang, Jie Liao, Guisheng Li, Jun Xidian Univ Natl Lab Radar Signal Proc Xian 710071 Shaanxi Peoples R China

In this communication, we consider the problem of designing robust adaptive beamformer in the newly proposed nested array, where we maintain distortionless response towards the true desired signal and suppress more interferences than the number of actual physical sensors. The essence of our proposed method is to reconstruct the interference-plus-noise covariance matrix and estimate the true desired signal steering vector. The reconstruction process is performed by projecting the spatially smoothed matrix into interference subspace. The estimation process is performed by solving an optimization problem based on minimizing the beamformer sensitivity and enforcing the estimate not to converge to any of the interference steering vectors. We also show that the constructed optimization problem can be efficiently computed at a comparable cost with that of the standard Capon beamformer (SCB). The effectiveness of the proposed method is verified through numerical simulations. (C) 2015 Elsevier B.V. All rights reserved.

关键词： Robust adaptive beamforming nested array Interference-plus-noise covariance matrix reconstruction Steering vector estimation

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An efficient off-grid DOA estimation approach for nested array signal processing by using sparse Bayesian learning strategies

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SIGNAL PROCESSING 2016年 128卷 110-122页

作者： Yang, Jie Liao, Guisheng Li, Jun Xidian Univ Natl Lab Radar Signal Proc Xian 710071 Shaanxi Peoples R China

In this paper, we address the problem of sparsity-inducing direction-of-arrival (DOA) estimation in the context of array covariance vectors when a recently proposed nested array structure is utilized. The proposed approach is based on a Sparse Bayesian learning (SBL) perspective while the off-grid effects inherent in traditional sparse recovery algorithms are taken into account simultaneously. Specifically, the notable advantages of the developed approach can be attributed to two aspects. First, through a linear transformation, the unknown noise variance can be eliminated effectively and the estimation error between the actual and sample covariance matrix can be normalized to an identity matrix, thereby facilitating a noise-free sparse representation. Second, a computationally tractable polynomial rooting procedure is introduced to calculate the discretized sampling grid error one by one based on the reconstructed spatial power spectrum, thus this novel algorithm can maintain high estimation accuracy even under a coarse sampling grid. Extensive simulation results finally demonstrate the superiority of the proposed approach in terms of DOA estimation precision and computational efficiency over off-the-shelves techniques. (C) 2016 Elsevier B.V. All rights reserved.

关键词： Direction-of-arrival (DOA) estimation nested array Sparse Bayesian learning (SBL) Off-grid effects Polynomial rooting

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Block Sparse Recovery Approach for DOA Estimation in nested array with Unknown Mutual Coupling

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CIRCUITS SYSTEMS AND SIGNAL PROCESSING 2023年第8期42卷 5079-5090页

作者： Xu, Yang Zheng, Zhi Wang, Wen-Qin Univ Elect Sci & Technol China Yangtze Delta Reg Inst Huzhou Huzhou 313001 Peoples R China Univ Elect Sci & Technol China Sch Informat & Commun Engn Chengdu 611731 Peoples R China UESTC Inst Elect & Informat Engn Dongguan 523808 Guangdong Peoples R China Univ Elect Sci & Technol China Shenzhen Inst Adv Study Shenzhen 518110 Peoples R China

In this paper, we develop a robust direction-of-arrival (DOA) estimation algorithm with a nested array with unknown mutual coupling. By using the matrix transformation of the product of mutual coupling matrix and steering vector, we firstly derive a coarray signal model including a manifold matrix without mutual coupling effect. Subsequently, we build the block sparse representation of the coarray signal by exploiting the sparsity of the signals. Finally, we estimate the DOAs of sources by formulating a simplified block sparse recovery problem. The proposed algorithm utilizes all coarray outputs and reduces the influence of mutual coupling effect, and thus can resolve more sources than the number of sensors. Numerical results demonstrate the superiority of the proposed algorithm over several existing techniques.

关键词： nested array Mutual coupling DOA estimation Mutual coupling matrix (MCM) Coarray signal Block sparse

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