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nested arrays in Two Dimensions, Part I: Geometrical Considerations

IEEE TRANSACTIONS ON SIGNAL PROCESSING 2012年第9期60卷 4694-4705页

作者： Pal, Piya Vaidyanathan, P. P. CALTECH Pasadena CA 91125 USA

A new class of two dimensional arrays with sensors on lattice(s) is proposed, whose difference co-array can give rise to a virtual two dimensional array with much larger number of elements on a "dense" lattice. This structure is obtained by systematically nesting two arrays, one with sensors on a sparse lattice and the other on a dense lattice where the lattices bear a certain relation with each other. The difference co-array of such an array with and elements respectively on the two lattices, is a two dimensional array with elements present contiguously (without holes) on the dense lattice. The difference co-array can be realized on any arbitrary lattice by choosing the dense and sparse lattices appropriately. The generator matrices of the sparse and the dense lattices are related by an integer matrix. The Smith form of this integer matrix is shown to provide a very insightful perspective which is exploited heavily in the construction of nested arrays. The design of the two dimensional nested array gives rise to several interesting geometrical orientations of the co-array which are addressed in detail, and it is shown how the orientations can be manipulated to yield more virtual sensors in a continuum on the dense lattice. The increased number of elements in the virtual difference co-array can be exploited to perform two dimensional direction of arrival (DOA) estimation of many more sources than what traditional methods can achieve. A novel algorithm for application of the nested array in two dimensional direction of arrival estimation is reported in the accompanying part II of the paper.

关键词： Co-array Khatri Rao product lattice nested arrays reciprocal lattice Smith form sparse arrays two-dimensional arrays

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nested arrays: A Novel Approach to Array Processing With Enhanced Degrees of Freedom (vol 58, pg 4167, 2010)

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IEEE TRANSACTIONS ON SIGNAL PROCESSING 2010年第9期58卷 4973-4973页

作者： Pal, P. Vaidyanathan, P. P. Student Member IEEE California Institute of Technology Pasadena CA 91125 USA Fellow IEEE

A new array geometry, which is capable of significantly increasing the degrees of freedom of linear arrays, is proposed. This structure is obtained by systematically nesting two or more uniform linear arrays and can provide O (N²) degrees of freedom using only physical sensors when the second-order statistics of the received data is used. The concept of nesting is shown to be easily extensible to multiple stages and the structure of the optimally nested array is found analytically. It is possible to provide closed form expressions for the sensor locations and the exact degrees of freedom obtainable from the proposed array as a function of the total number of sensors. This cannot be done for existing classes of arrays like minimum redundancy arrays which have been used earlier for detecting more sources than the number of physical sensors. In minimum-input--minimum-output (MIMO) radar, the degrees of freedom are increased by constructing a longer virtual array through active sensing. The method proposed here, however, does not require active sensing and is capable of providing increased degrees of freedom in a completely passive setting. To utilize the degrees of freedom of the nested co-array, a novel spatial smoothing based approach to DOA estimation is also proposed, which does not require the inherent assumptions of the traditional techniques based on fourth-order cumulants or quasi stationary signals. As another potential application of the nested array, a new approach to beamforming based on a nonlinear preprocessing is also introduced, which can effectively utilize the degrees of freedom offered by the nested arrays. The usefulness of all the proposed methods is verified through extensive computer simulations. [ABSTRACT FROM AUTHOR]

关键词： Beamforming co-array direction-of-arrival (DOA) estimation Khatri Rao product minimum redundancy array nested arrays spatial smoothing

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Sparse Doppler Sensing Based on nested arrays

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IEEE TRANSACTIONS ON ULTRASONICS FERROELECTRICS AND FREQUENCY CONTROL 2018年第12期65卷 2349-2364页

作者： Cohen, Regev Eldar, Yonina C. Technion Israel Inst Technol Dept Elect Engn IL-3200003 Haifa Israel

Spectral Doppler ultrasound imaging allows visualizing blood flow by estimating its velocity distribution over time. Duplex ultrasound is a modality in which an ultrasound system is used for displaying simultaneously both B-mode images and spectral Doppler data. In B-mode imaging, short wideband pulses are used to achieve sufficient spatial image resolution. In contrast, for Doppler imaging, narrowband pulses are preferred in order to attain increased spectral resolution. Thus, the acquisition time must be shared between the two sequences. In this work, we propose a nonuniform slow-time transmission scheme for spectral Doppler, based on nested arrays, which reduces the number of pulses needed for accurate spectrum recovery. We derive the minimal number of Doppler emissions needed, using this approach, for perfect reconstruction of the blood spectrum in a noise-free environment. Next, we provide two spectrum recovery techniques which achieve this minimal number. The first method performs efficient recovery based on the fast Fourier transform. The second allows for continuous recovery of the Doppler frequencies, thus avoiding off-grid error leakage, at the expense of increased complexity. The performance of the techniques is evaluated using realistic Field II simulations as well as in vivo measurements, producing accurate spectrograms of the blood velocities using a significantly reduced number of transmissions. The time gained, where no Doppler pulses are sent, can be used to enable the display of both blood velocities and high quality B-mode images at a high frame rate.

关键词： Blood doppler blood velocity estimation medical ultrasound nested arrays spectral estimation

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Super nested arrays: Linear Sparse arrays With Reduced Mutual Coupling-Part II: High-Order Extensions

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IEEE TRANSACTIONS ON SIGNAL PROCESSING 2016年第16期64卷 4203-4217页

作者： Liu, Chun-Lin Vaidyanathan, P. P. CALTECH Pasadena CA 91125 USA

In array processing, mutual coupling between sensors has an adverse effect on the estimation of parameters (e.g., DOA). Sparse arrays such as nested arrays, coprime arrays, and minimum redundancy arrays (MRA) have reduced mutual coupling compared to uniform linear arrays (ULAs). These arrays also have a difference coarray with O (N-2) virtual elements, where N is the number of physical sensors, and can therefore resolve O (N-2) uncorrelated source directions. But these well-known sparse arrays have disadvantages: MRAs do not have simple closed-form expressions for the array geometry;coprime arrays have holes in the coarray;and nested arrays contain a dense ULA in the physical array, resulting in significantly higher mutual coupling than coprime arrays and MRAs. In a companion paper, a sparse array configuration called the (second-order) super nested array was introduced, which has many of the advantages of these sparse arrays, while removing most of the disadvantages. Namely, the sensor locations are readily computed for any N (unlike MRAs), and the difference coarray is exactly that of a nested array, and therefore hole-free. At the same time, the mutual coupling is reduced significantly (unlike nested arrays). In this paper, a generalization of super nested arrays is introduced, called the Qth-order super nested array. This has all the properties of the second-order super nested array with the additional advantage that mutual coupling effects are further reduced for Q > 2. Many theoretical properties are proved and simulations are included to demonstrate the superior performance of these arrays.

关键词： Sparse arrays nested arrays coprime arrays super nested arrays mutual coupling DOA estimation

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NON-ITERATIVE BLIND CALIBRATION OF nested arrays WITH ASYMPTOTICALLY OPTIMAL WEIGHTING

NON-ITERATIVE BLIND CALIBRATION OF NESTED ARRAYS WITH ASYMPT...

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IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)

作者： Weiss, Amir Yeredor, Arie Weizmann Inst Sci Dept Comp Sci & Appl Math Rehovot Israel Tel Aviv Univ Sch Elect Engn Tel Aviv Israel

ISBN: (纸本)9781728176055

Blind calibration of sensors arrays (without using calibration signals) is an important, yet challenging problem in array processing. While many methods have been proposed for "classical" array structures, such as uniform linear arrays, not as many are found in the context of the more "modern" sparse arrays. In this paper, we present a novel blind calibration method for 2-level nested arrays. Specifically, and despite recent contradicting claims in the literature, we show that the Least-Squares (LS) approach can in fact be used for this purpose with such arrays. Moreover, the LS approach gives rise to optimally-weighted LS joint estimation of the sensors' gains and phases offsets, which leads to more accurate calibration, and in turn, to higher accuracy in subsequent estimation tasks (e.g., direction-of-arrival). Our method, which can be extended to K-level arrays (K > 2), is superior to the current state of the art both in terms of accuracy and computational efficiency, as we demonstrate in simulation.

关键词： nested arrays sparse arrays blind calibration maximum likelihood optimally-weighted least squares

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Joint Doppler and Channel Estimation with nested arrays for Millimeter Wave Communications

Joint Doppler and Channel Estimation with Nested Arrays for ...

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IEEE Global Conference on Communications (GLOBECOM) / Workshop on Wireless Networking and Control for UAV

作者： Wu, Xiaohuan Zhu, Wei-Ping Lin, Min Yan, Jun Nanjing Univ Posts & Telecommun Key Lab Minist Educ Broadband Wireless Commun & Sensor Ne Nanjing Jiangsu Peoples R China Concordia Univ Dept Elect & Comp Engn Montreal PQ Canada

ISBN: (纸本)9781538647271

Channel estimation is essential for precoding/combining in millimeter wave (mmWave) communications. However, accurate estimation is usually difficult because the receiver can only observe the low-dimensional projection of the received signals due to the hybrid architecture. We take the high speed scenario into consideration where the Doppler effect caused by fast-moving users can seriously deteriorate the channel estimation accuracy. In this paper, we propose to incorporate the nested array into analog array architecture by using RF switch networks with an objective of reducing the complexity and power consumption of the system. Based on the covariance fitting criterion, a joint Doppler and channel estimation method is proposed without need of discretizing the angle space, and thus the model mismatch effect can be totally eliminated. We also present an algorithmic implementation by solving the dual problem of the original one in order to reduce the computational complexity. Numerical simulations are provided to demonstrate the effectiveness and superiority of our proposed method.

关键词： Channel estimation millimeter wave (mmWave) nested arrays covariance fitting criterion

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Broadband DOA Estimation Based on nested arrays 2018

Broadband DOA Estimation Based on Nested Arrays

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2nd International Conference on Telecommunications and Communication Engineering (ICTCE)

作者： Wang Dan Li Yan Xiong Shujie Shanghai Engn Ctr Microsatellites Shanghai Peoples R China Chinese Acad Sci Acad Optoelect Beijing Peoples R China

ISBN: (纸本)9781450365857

Using the structure of nested arrays, a broadband direction of arrival ( DOA) estimation algorithm is presented. The algorithm combines different sensors data to construct a covariance matrix, which is equivalent to that of the uniform linear array whose aperture is same as the nested arrays, and then the DOAs of broadband sources can be estimated by the incoherent MUSIC algorithm. Compared to the traditional coherent subspace algorithms, the proposed algorithm does not need to pre-estimate the azimuths of sources. When the number of sources is greater than the number of sensors, it can still perform well. Under the condition of same array aperture, the number of the sensors is reduced considerably by using nested arrays, and the good localizing performance and spatial resolution can be obtained. Finally, computer simulations show the performance of the proposed algorithm.

关键词： Array processing DOA estimation broadband signal nested arrays

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SUPER nested arrays: SPARSE arrays WITH LESS MUTUAL COUPLING THAN nested arrays 41

SUPER NESTED ARRAYS: SPARSE ARRAYS WITH LESS MUTUAL COUPLING...

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41st IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)

作者： Liu, Chun-Lin Vaidyanathan, P. P. CALTECH Dept Elect Engn Pasadena CA 91125 USA

ISBN: (纸本)9781479999880

In array processing, mutual coupling between sensors has an adverse effect on the estimation of parameters (e.g., DOA). Sparse arrays, such as nested arrays, coprime arrays, and minimum redundancy arrays (MRAs), have reduced mutual coupling compared to uniform linear arrays (ULAs). With N denoting the number of sensors, these sparse arrays offer O(N-2) freedoms for source estimation because their difference coarrays have O(N-2)- long ULA segments. These arrays have different shortcomings: coprime arrays have holes in the coarray, MRAs have no closed-form expressions, and nested arrays have relatively large mutual coupling. This paper introduces a new array called the super nested array, which has all the good properties of the nested array, and at the same time reduces mutual coupling significantly. For fixed N, the super nested array has the same physical aperture, and the same hole-free coarray as does the nested array. But the number of sensor pairs with separation lambda/2 is significantly reduced. Many theoretical properties are proved and simulations are included to demonstrate the superior performance of these arrays.

关键词： nested arrays coprime arrays super nested arrays mutual coupling DOA estimation

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Broadband Beamforming Using 2D Trapezoidal Filters and nested arrays

Broadband Beamforming Using 2D Trapezoidal Filters and Neste...

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IEEE Pacific Rim Conference on Communications, Computers and Signal Processing (PACRIM)

作者： Moazzen, Iman Agathoklis, Panajotis Univ Victoria Dept ECE Victoria BC Canada

ISBN: (纸本)9781457702518

A broadband beamforming technique using 2D trapezoidal filters (TFs) and nested arrays is proposed. Each subarray feeds into a subband beamformer processing an octave frequency band. Using subsampling in space and time all frequency subbands are transformed into the same frequency range in the 2D frequency domain. This allows using the same 2D trapezoidal filter design for all subbands. The advantage of using nested arrays is that the effective aperture for low temporal frequencies is larger than in the case of using a Uniform Linear Array (ULA) with the same number of array elements. This leads to a better spatial selectivity at low frequencies than using ULAs. The performance of the proposed beamformer is illustrated and evaluated using simulations.

关键词： 2D frequency domain 2D trapezoidal filters Array signal processing Broadband communication Equalizers Filter banks Finite impulse response filter Passband array signal processing broadband beamforming technique filtering theory nested arrays octave frequency band uniform linear array

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Symmetry-Imposed Rectangular Coprime and nested arrays for Direction of Arrival Estimation With Multiple Signal Classification

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IEEE ACCESS 2019年 7卷 153217-153229页

作者： Adhikari, Kaushallya Drozdenko, Benjamin Louisiana Tech Univ Elect Engn Dept Ruston LA 71272 USA Louisiana Tech Univ Cyber Engn Dept Ruston LA 71272 USA

Linear sparse arrays (coprime and nested arrays) have been studied extensively as a means of performing direction of arrival (DoA) estimation while bypassing Nyquist sampling theorem. However, rectangular sparse arrays have few studies, most of which are based in lattice theory. Although the multiple signal classification (MUSIC) alogrithm can be applied to lattice theory-based sparse arrays, fewer DoAs can be estimated for these arrays than for a full array with the same aperture. One contribution of this paper is the formulation of symmetry-imposed rectangular coprime and nested array designs that have wider contiguous lags than lattice-based arrays. Also, existing algorithms for rectangular arrays employ the direct sample covariance matrix estimate, which has low accuracy. Another contribution of this paper is an alternate method for estimating the covariance matrix that ensures the matrix is block-Toeplitz. Using the proposed covariance matrix estimate, we integrate a MUSIC-based DoA estimation method that applies to both full arrays and sparse arrays. The results show that the covariance estimates produced by the proposed method have higher accuracy than the traditional sample covariance estimates. The results also demonstrate that symmetry-imposed sparse arrays have higher resolution than full rectangular arrays with the same number of sensors.

关键词： Covariance matrices Sensor arrays Direction-of-arrival estimation Multiple signal classification Estimation Apertures Coarray coprime arrays DoA estimation MUSIC nested arrays planar arrays rectangular arrays sparse arrays

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