Extension of Co-Prime Arrays Based on the Fourth-Order Difference Co-Array Concept

Shen, Qing; Liu, Wei; Cui, Wei; Wu, Siliang

doi:10.1109/lsp.2016.2539324

Cited by 94 publications

(75 citation statements)

References 25 publications

(23 reference statements)

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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%

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

Liu

Vaidyanathan

2017

Digital Signal Processing

227

168

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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%

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

Liu

Vaidyanathan

2017

Digital Signal Processing

227

168

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“…Two important array geometries, i.e., nested array [1,2] and co-prime array [3,4,17], have been proposed for systematic sparse array design. Several approaches, including subspace-based methods employing spatial smoothing [1,2,3,4,5,6] and a reshaping process to form a Toeplitz matrix [7] were proposed to exploit the increased number of degrees of freedom (DOFs) offered by co-arrays.…”

Section: Introductionmentioning

confidence: 99%

“…On the other hand, by using compressive sensing (CS) [9,10] based signal reconstruction methods for underdetermined DOA estimation, a higher number of DOFs is achieved by effectively using all consecutive and non-consecutive lags of the resulting difference co-arrays [11,12,13,14,15,16,17]. A performance analysis of the CS-based methods is provided in [18].…”

Section: Introductionmentioning

confidence: 99%

Underdetermined wideband DOA estimation of off-grid sources employing the difference co-array concept

et al. 2017

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A wideband off-grid model is proposed to represent dictionary mismatch under the compressive sensing framework exploiting difference co-arrays. A group sparsity based off-grid method is proposed for underdetermined wideband direction of arrival (DOA) estimation which provides improved performance over the existing group sparsity based method with a same search grid. A two-step approach is then proposed which achieves an even better performance with significantly reduced computational complexity.

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“…In [14], MUSIC algorithm was applied to process fourth-order cumulant matrix to mitigate mutual coupling effects. In [15], 1 -normalization was applied to a fourth-order difference matrix to increase the range of contiguous lags. In this work, we propose a triply primed array (TPA), which is composed of three arrays specified by three mutually primed integers.…”

Section: Introductionmentioning

confidence: 99%

Doa Estimation Using Triply Primed Arrays Based on Fourth-Order Statistics

Hsu¹,

Kiang²

2018

PIER M

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Abstract-A triply primed array (TPA) is configured on three mutually primed integers (N 1 , N 2 and N 3 ), which operates with O(N 1 N 2 N 3 ) degree-of-freedoms to estimate the direction-of-arrivals (DOAs) of multiple incident quasi-stationary signals. The set of unique and contiguous lags of the proposed TPA is searched and verified. Simulation results verify that the proposed TPA can detect more incident signals with higher accuracy than its compatible counterparts.

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Extension of Co-Prime Arrays Based on the Fourth-Order Difference Co-Array Concept

Cited by 94 publications

References 25 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

Underdetermined wideband DOA estimation of off-grid sources employing the difference co-array concept

Doa Estimation Using Triply Primed Arrays Based on Fourth-Order Statistics

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