Extending coprime sensor arrays to achieve the peak side lobe height of a full uniform linear array

Adhikari, Kaushallya; Buck, John R.; Wage, Kathleen E.

doi:10.1186/1687-6180-2014-148

Cited by 95 publications

(52 citation statements)

References 18 publications

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“…The most essential property of these successful sparse arrays is that, given N sensors, the difference coarrays of these arrays have O (N 2 ) elements, which allows them to identify D = O (N 2 ) sources using N sensors. In particular, therefore, D N is possible as demonstrated amply in [1][2][3][16][17][18][19]21,[28][29][30][31][32]36,40,53,57,58,61,63,64,67,68,70,71,[74][75][76][77]93,94,96,98,107,108].…”

Section: Introductionmentioning

confidence: 99%

Cramér–Rao bounds for coprime and other sparse arrays, which find more sources than sensors

Liu

Vaidyanathan

2017

Digital Signal Processing

248

176

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a r t i c l e i n f o a b s t r a c tArticle history: Available online xxxx Keywords: Cramér-Rao bounds Fisher information matrix Sparse arrays Coprime arrays Difference coarraysThe Cramér-Rao bound (CRB) offers a lower bound on the variances of unbiased estimates of parameters, e.g., directions of arrival (DOA) in array processing. While there exist landmark papers on the study of the CRB in the context of array processing, the closed-form expressions available in the literature are not easy to use in the context of sparse arrays (such as minimum redundancy arrays (MRAs), nested arrays, or coprime arrays) for which the number of identifiable sources D exceeds the number of sensors N. Under such situations, the existing literature does not spell out the conditions under which the Fisher information matrix is nonsingular, or the condition under which specific closed-form expressions for the CRB remain valid. This paper derives a new expression for the CRB to fill this gap. The conditions for validity of this expression are expressed as the rank condition of a matrix defined based on the difference coarray. The rank condition and the closed-form expression lead to a number of new insights. For example, it is possible to prove the previously known experimental observation that, when there are more sources than sensors, the CRB stagnates to a constant value as the SNR tends to infinity. It is also possible to precisely specify the relation between the number of sensors and the number of uncorrelated sources such that these conditions are valid. In particular, for nested arrays, coprime arrays, and MRAs, the new expressions remain valid for D = O (N 2 ), the precise detail depending on the specific array geometry.

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Section: Introductionmentioning

confidence: 99%

Cramér–Rao bounds for coprime and other sparse arrays, which find more sources than sensors

Liu

Vaidyanathan

2017

Digital Signal Processing

248

176

View full text Add to dashboard Cite

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“…The DOF determine e.g. the achievable point spread function in array imaging [3], the number of resolvable sources in direction-of-arrival (DOA) estimation [4], [5], or the beamforming capabilities of the array [6]. Mutual coupling may also be reduced due to the larger interelement distances in sparse arrays [7], [8].…”

Section: Introductionmentioning

confidence: 99%

Sparse linear nested array for active sensing

Rajamäki

Koivunen

2017

2017 25th European Signal Processing Conference (EUSIPCO)

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Abstract-Sparse sensor arrays can match the performance of fully populated arrays using substantially fewer elements. However, finding the array configuration with the smallest number of elements is generally a computationally difficult problem. Consequently, simple to generate array configurations that may be suboptimal are of high practical interest. This paper presents a novel closed-form sparse linear array configuration designed for active sensing, called the Concatenated Nested Array (CNA). The key parameters of the CNA are derived. The CNA is also compared to the optimal Minimum-Redundancy Array (MRA) in numerical simulations. The CNA is shown to require only about 10% more elements than the MRA in the limit of large apertures.

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“…[6][7][8][9][10][11] This includes the authors' investigations into expanding the coprime theory to include alternate operating frequencies. 12 The results showed that coprime arrays provide useful results at any frequency lower than the design frequency implied by the length and two coprime factors of the standard CSA.…”

Section: Introductionmentioning

confidence: 99%

n-tuple coprime sensor arrays

Bush

Xiang

2017

The Journal of the Acoustical Society of America

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Until now, coprime sensor arrays have used two sparsely spaced subarrays to emulate the performance of a single uniform array with many more sensors (generally on the order of the product of each subarrays' number of sensors). This allows for similar results with fewer sensors, or the observation of higher frequencies (above the Nyquist limit) with a similar number of sensors. The theory rests on the cross-referencing (using directional filter banks) or cancellation (using product processing) of the M grating lobes in one subarray's beampattern and N grating lobes in the other, where M and N are coprime integers. Sets of coprime integers can consist of more than two integers, however, and introducing another coprime factor theoretically multiplies observable frequency (or further decreases the number of array elements needed for the same frequency). Any amount, n, of coprime integers and corresponding subarrays may be used. In this work, “n-tuple coprime sensor array” theory is expounded and implemented. Experimentally measured beampattern results of a triple coprime sensor array (with three subarrays) are shown, using an extension of the authors' previously established product processing. Results also confirm that the usable range of an n-tuple coprime array extends below its design frequency.

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Extending coprime sensor arrays to achieve the peak side lobe height of a full uniform linear array

Cited by 95 publications

References 18 publications

Cramér–Rao bounds for coprime and other sparse arrays, which find more sources than sensors

Cramér–Rao bounds for coprime and other sparse arrays, which find more sources than sensors

Sparse linear nested array for active sensing

n-tuple coprime sensor arrays

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