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An Asymptotically Efficient Weighted Least Squares Estimator for Co-Array-Based DoA Estimation

Published on Jan 1, 2020in IEEE Transactions on Signal Processing5.23
路 DOI :10.1109/TSP.2019.2954506
Saeid Sedighi6
Estimated H-index: 6
(University of Luxembourg),
Bhavani Shankar Mysore Rama Rao8
Estimated H-index: 8
(University of Luxembourg)
+ 0 AuthorsBjorn Ottersten64
Estimated H-index: 64
(University of Luxembourg)
Abstract
Co-array-based Direction of Arrival (DoA) estimation using Sparse Linear Arrays (SLAs) has recently gained considerable interest in array processing thanks to its capability of providing enhanced degrees of freedom. Although the literature presents a variety of estimators in this context, none of them are proven to be statistically efficient. This work introduces a novel estimator for the co-array-based DoA estimation employing the Weighted Least Squares (WLS) method. An analytical expression for the large sample performance of the proposed estimator is derived. Then, an optimal weighting is obtained so that the asymptotic performance of the proposed WLS estimator coincides with the Cram\'{e}r-Rao Bound (CRB), thereby ensuring asymptotic statistical efficiency of resulting WLS estimator. This implies that the proposed WLS estimator has a significantly better performance compared to existing methods. Numerical simulations are provided to validate the analytical derivations and corroborate the improved performance.
  • References (35)
  • Citations (0)
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References35
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#2Yujie Gu (TU: Temple University)H-Index: 16
Last. Yimin D. Zhang (TU: Temple University)H-Index: 34
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Coprime arrays can achieve an increased number of degrees of freedom by deriving the equivalent signals of a virtual array. However, most existing methods fail to utilize all information received by the coprime array due to the non-uniformity of the derived virtual array, resulting in an inevitable estimation performance loss. To address this issue, we propose a novel virtual array interpolation-based algorithm for coprime array direction-of-arrival (DOA) estimation in this paper. The idea of ar...
45 CitationsSource
#1Saeid Sedighi (University of Luxembourg)H-Index: 6
#2M. R. Bhavani Shankar (University of Luxembourg)H-Index: 7
Last. Bjorn Ottersten (University of Luxembourg)H-Index: 64
view all 3 authors...
Source
#1Chengwei Zhou (ZJU: Zhejiang University)H-Index: 10
#2Yujie Gu (TU: Temple University)H-Index: 16
Last. Yimin D. Zhang (TU: Temple University)H-Index: 34
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In this letter, we propose a coprime array interpolation approach to provide an off-grid direction-of-arrival (DOA) estimation. Through array interpolation, a uniform linear array (ULA) with the same aperture is generated from the deterministic non-uniform coprime array. Taking the observed correlations calculated from the signals received at the coprime array, a gridless convex optimization problem is formulated to recover all the rows and columns of the unknown correlation matrix entries corre...
26 CitationsSource
#1Saeid Sedighi (University of Luxembourg)H-Index: 6
#2R Bhavani Shankar Mysore (University of Luxembourg)H-Index: 3
Last. Bjorn Ottersten (University of Luxembourg)H-Index: 64
view all 4 authors...
Sparse linear arrays (SLAs), such as nested and co-prime arrays, have the attractive capability of providing enhanced degrees of freedom by exploiting the co-array model. Accordingly, co-array-based Direction of Arrivals (Doas) estimation has recently gained considerable interest in array processing. The literature has suggested applying MUSIC on an augmented sample covariance matrix for co-array-based Doas estimation. In this paper, we propose a Least Squares (LS) estimator for co-array-based D...
1 CitationsSource
#1Jens SteinwandtH-Index: 8
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In the recent field of co-array signal processing, sparse linear arrays are processed to form a virtual uniform linear array (ULA), termed co-array, that allows to resolve more sources than physical sensors. The extra degrees of freedom (DOFs) are leveraged by the assumption that the signals are uncorrelated, which requires a large sample size. In this paper, we first review the Standard ESPRIT and Unitary ESPRIT algorithms for co-array processing. Secondly, we propose a performance analysis for...
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This paper considers the problem of compressively sampling wide sense stationary random vectors with a low rank Toeplitz covariance matrix. Certain families of structured deterministic samplers are shown to efficiently compress a high-dimensional Toeplitz matrix of size N\times N, producing a compressed sketch of size O(\sqrt{r})\times O(\sqrt{r})The reconstruction problem can be cast as that of line spectrum estimation, whereby, in absence of noise, Toeplitz matrices of any size Ncan b...
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Sparse linear arrays, such as coprime arrays and nested arrays, have the attractive capability of providing enhanced degrees of freedom. By exploiting the coarray structure, an augmented sample covariance matrix can be constructed and MUtiple SIgnal Classification (MUSIC) can be applied to identify more sources than the number of sensors. While such a MUSIC algorithm works quite well, its performance has not been theoretically analyzed. In this paper, we derive a simplified asymptotic mean squar...
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#1Chun-Lin Liu (California Institute of Technology)H-Index: 10
#2P.P. Vaidyanathan (California Institute of Technology)H-Index: 62
The Cramer-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 numbe...
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#2Wei Liu (University of Sheffield)H-Index: 25
Last. Siliang Wu (BIT: Beijing Institute of Technology)H-Index: 11
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Direction of arrival (DOA) estimation from the perspective of sparse signal representation has attracted tremendous attention in past years, where the underlying spatial sparsity reconstruction problem is linked to the compressive sensing (CS) framework. Although this is an area with ongoing intensive research and new methods and results are reported regularly, it is time to have a review about the basic approaches and methods for CS-based DOA estimation, in particular for the underdetermined ca...
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#1Chun-Lin Liu (California Institute of Technology)H-Index: 10
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