Super nested arrays: Sparse arrays with less mutual coupling than nested arrays

Liu, Chun-Lin; Vaidyanathan, P.P.

doi:10.1109/icassp.2016.7472223

Cited by 51 publications

(45 citation statements)

References 22 publications

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“…So it is motivating to design the sensor locations S such that |D| or |U| is large. Several well-known solutions include minimum redundancy arrays (MRA) [61], minimum hole arrays (MHA) [94,103], nested arrays [63], coprime arrays [98], super nested arrays [51,52,54], and many other variants [4,9,[12][13][14]23,38,39,50,66,76,82,83,85,86,106]. All of them have O (N 2 ) distinct lags in the difference coarray, given O (N) physical sensors.…”

Section: Review Of Sparse Array Designmentioning

confidence: 99%

“…For a long time, sparse arrays, such as the minimum redundancy arrays (MRAs) have been known to be able to identify more sources than sensors (D ≥ N) [61]. More recently, the development of sparse arrays such as the nested arrays [63], the coprime arrays [64,98], and their extensions [51,52,54,75,76], have generated a new wave of interest in this topic. These new arrays have simple closedform expressions for array geometry (compared to MRAs which do not have this advantage), which makes them more practical than MRAs.…”

Section: Introductionmentioning

confidence: 99%

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

Liu

Vaidyanathan

2017

Digital Signal Processing

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236

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: Review Of Sparse Array Designmentioning

confidence: 99%

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

Self Cite

236

176

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“…Thus, the objective function is lower bounded by 2 √ N . Equality is obtained in (58) if and only if A = B = √ N . Thus, this choice attains the lower bound and is optimal, which concludes the proof.…”

Section: E Minimal Number Of Elementsmentioning

confidence: 99%

Sparse Convolutional Beamforming for Ultrasound Imaging

Cohen

Eldar

2018

IEEE Trans. Ultrason., Ferroelect., Freq. Contr.

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The standard technique used by commercial medical ultrasound systems to form B-mode images is delay and sum (DAS) beamforming. However, DAS often results in limited image resolution and contrast, which are governed by the center frequency and the aperture size of the ultrasound transducer. A large number of elements leads to improved resolution but at the same time increases the data size and the system cost due to the receive electronics required for each element. Therefore, reducing the number of receiving channels while producing high quality images is of great importance. In this paper, we introduce a nonlinear beamformer called COnvolutional Beamforming Algorithm (COBA), which achieves significant improvement of lateral resolution and contrast. In addition, it can be implemented efficiently using the fast Fourier transform. Based on the COBA concept, we next present two sparse beamformers with closed form expressions for the sensor locations, which result in the same beam pattern as DAS and COBA while using far fewer array elements. Optimization of the number of elements shows that they require a minimal number of elements which is on the order of the square root of the number used by DAS. The performance of the proposed methods is tested and validated using simulated data, phantom scans and in vivo cardiac data. The results demonstrate that COBA outperforms DAS in terms of resolution and contrast and that the suggested beamformers offer a sizable element reduction while generating images with an equivalent or improved quality in comparison to DAS.Index Terms-Medical ultrasound, array processing, beamforming, contrast resolution, sparse arrays, beam pattern.

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“…While the constant numbers represent the number of possible interelement spacing of the remaining subarrays. Following (12), the inter-element spacing for the first subarray is one, so C 3LPA = 2. The first and second subarrays in the 4LPA are left with only one possibility for the spacing based on (13).…”

Section: Ordered Inter-element Spacingmentioning

confidence: 99%

“…A fourth‐level nested array that has

scriptO ()(, N^{4})

DOF using N sensors was proposed in [11]. The authors in [12–14] modified the structure of the nested array and proposed a super nested array. The array has the same features as the conventional nested array but with reduced mutual coupling.…”

Section: Introductionmentioning

confidence: 99%

Multi‐level prime array for sparse sampling

Alawsh

Muqaibel

2018

IET signal process.

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Sensor array configurations such as coprime and nested arrays have attracted many researchers because they increase the degree of freedom (DOF). For example, in the direction of arrival estimation, the number of sources that can be estimated is greater than the total number of sensors. This study proposes a multi-level prime array (MLPA) configuration for sparse sampling that can further increase the DOF. The proposed array uses multiple uniform linear subarrays where the number of sensors in the subarrays is pairwise coprime integers. The inter-element spacing between the sensors is formulated as a scaled multiple of half-wavelength where the subarrays share only their first element. For a fixed number of sensors, multiple MLPA configurations can be constructed by controlling the number of sensors in the subarrays or by adjusting the interelement spacing. For a given number of sensors, the proposed array has a smaller aperture and achieves more number of unique and consecutive lags compared with coprime arrays. The proposed configuration has limited holes in the difference coarray. The analytical expressions of both the difference coarray and the aperture size are derived. Simulation results confirm the advantage of the proposed configurations compared with the two level coprime arrays.

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Super nested arrays: Sparse arrays with less mutual coupling than nested arrays

Cited by 51 publications

References 22 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 Convolutional Beamforming for Ultrasound Imaging

Multi‐level prime array for sparse sampling

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