Positive-definite Toeplitz completion in DOA estimation for nonuniform linear antenna arrays. II. Partially augmentable arrays

Abramovich, Y.I.; Spencer, N.K.; Gorokhov, A.

doi:10.1109/78.765119

Cited by 126 publications

(70 citation statements)

References 30 publications

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“…However, the constructed augmented covariance matrix is not positive semidefinite for finite number of snapshots (and hence violates the condition for being a covariance matrix.) In [5], [6], a transformation of this augmented matrix into a suitable positive definite Toeplitz matrix was suggested and an elaborate algorithm was provided to construct this matrix. However, there are two issues with this approach.…”

Section: Introductionmentioning

confidence: 99%

“…The optimum design of such arrays is not easy and in most cases, they are restricted to computer simulations or complicated algorithms for sensor placement [7], [8], [10]- [12]. Also, the algorithm for finding the suitable covariance matrix corresponding to the longer array is a lengthy and complicated iterative algorithm, which converges only to a local optmimum [5], [6]. In [13], the use of fourth-order cumulants was suggested to completely remove the Gaussian noise term and perform better DOA estimation.…”

Section: Introductionmentioning

confidence: 99%

“…In comparison to aforementioned existing approaches, our proposed method has several advantages. It will be shown in Section IV that the nested array is extremely easy to construct and it is possible to provide exact closed form expressions for the sensor locations and the degrees of freedom for a given number ( ) of sensors, unlike the MRAs used in [3], [5], and [6]. Also, to alleviate the weaknesses of [13] and [17] discussed before, we shall propose a novel spatial smoothing based technique in Section V which utilizes only second-order statistics to exploit the degrees of freedom offered by the array and works well even for stationary sources.…”

Section: Introductionmentioning

confidence: 99%

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Nested Arrays: A Novel Approach to Array Processing With Enhanced Degrees of Freedom

Pal

Vaidyanathan

2010

IEEE Trans. Signal Process.

1,675

1,476

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Abstract-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 ( 2 ) 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.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Nested Arrays: A Novel Approach to Array Processing With Enhanced Degrees of Freedom

Pal

Vaidyanathan

2010

IEEE Trans. Signal Process.

1,675

1,476

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“…In [10], DOA estimation in the superior case has been achieved by constructing the augmented covariance matrix (ACM) and using it for the MUSIC algorithm instead of the direct data covariance matrix. In [9] and [11], DOA estimation algorithms for FAAs and PAAs are presented, respectively. The algorithms in [9] and [11] are based on the maximum entropy, the ACM, and the Maximum Likelihood estimator.…”

Section: Introductionmentioning

confidence: 99%

“…The algorithms in [9] and [11] are based on the maximum entropy, the ACM, and the Maximum Likelihood estimator. The algorithms in [9]- [11] assume uncorrelated sources and their performance has not been evaluated in the presence of correlated sources.…”

Section: Introductionmentioning

confidence: 99%

Gridless compressed sensing for fully augmentable arrays

Suleiman

Sandor

Sorg

et al. 2017

2017 25th European Signal Processing Conference (EUSIPCO)

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Abstract-Direction-of-arrival (DOA) estimation using nonuniform linear arrays is considered. We focus on the so called "fully augmentable arrays" (FAAs) with full set of covariance lags. In FAAs, the number of covariance lags is usually larger than the number of sensors in the array. Thus, with FAAs more sources than the number of sensors can be identified. Existing DOA estimation algorithms for FAAs are based on the assumption of uncorrelated sources. In this paper, based on compressed sensing, we present a DOA estimation algorithm for FAAs without assuming uncorrelated sources. The proposed algorithm is based on the newly introduced gridless SPARse ROW-norm reconstruction (SPARROW) formulation for the joint sparse reconstruction from multiple measurement vectors. By numerical experiments, we show that the proposed algorithm outperforms the existing algorithms in the presence of correlated signals or small number of snapshots. Moreover, using simulations, the behavior of the Cramér-Rao Bound (CRB) for the case of correlated source is demonstrated and it is shown that, when the number of sources is larger than the number of sensors, the CRB for FAAs approaches zero at infinitely large signal-to-noise-ratio (SNR) only if the sources are fully correlated.

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