Further Results on the Cramér–Rao Bound for Sparse Linear Arrays

Wang, Mianzhi; Zhang, Zhen; Nehorai, Arye

doi:10.1109/tsp.2019.2892021

Cited by 18 publications

(7 citation statements)

References 36 publications

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“…For comparison, the CRB of an M ‐sensors ULA decreases at a rate of O ( M −3 ) . 42,43 This indicates that ULA is more sensitive to the number of sensors than UCA. One of the reasons is that for ULAs, the array aperture increases linearly as M increases.…”

Section: Simulation Resultsmentioning

confidence: 99%

Derivation of multidimensional stochastic Cramer‐Rao bound for mixture of noncoherent and coherent near/far field signals

Molaei

Hoseinzade

2020

Trans Emerging Tel Tech

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The existing Cramer-Rao bound (CRB) expressions in the literature are not applicable to the problem of localization of mixed near-field (NF) and far-field (FF) sources, including noncoherent and coherent signals, using two-dimensional arrays. Given the unique properties of circular arrays, in this article, the mathematical model of received signals in multipath environments, including a mixture of noncoherent and coherent NF/FF signals, is introduced. Then, the stochastic CRBs associated with the above problem are derived. The compact closed-form expression of CRB extracted in this article can be used for the algorithms under the above scenario as a benchmark to evaluate the estimation accuracy of azimuth DOA, elevation DOA, and range parameters as well as fading coefficient parameter. The simulation results show that the CRBs of the azimuth DOAs, elevation DOAs, ranges, and FCs decrease, on average, at a rate of approximately O(M −1.9 ), O(M −1.9 ), O(M −1.2 ), and O(M −1.8 ) as M (number of sensors) goes to infinity, respectively, where O is the notation of the asymptotic growth rate.

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Section: Simulation Resultsmentioning

confidence: 99%

Derivation of multidimensional stochastic Cramer‐Rao bound for mixture of noncoherent and coherent near/far field signals

Molaei

Hoseinzade

2020

Trans Emerging Tel Tech

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“…In this section, the DOA CRB (denoted as CRB(ω)), which gives the low bound on the variance of estimated DOA, on multi-level DNA is focused. In [35]- [37], the authors have investigated some closed-form CRB(ω) expressions for several classical sparse arrays and found their validity even when the number of sources exceeds the number of array elements. Here, CRB(ω) for sparse array is reviewed and some new results will be obtained when CRB(ω) is applied into multi-level DNA.…”

Section: Doa Crb Analysismentioning

confidence: 99%

The Multi-Level Dilated Nested Array for Direction of Arrival Estimation

Zhou

Wen

2020

IEEE Access

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In this paper, a more generalized dilated nested array (DNA) named multi-level dilated nested array (multi-level DNA), which further extends the original DNA to the general situation and improves the direction of arrival (DOA) estimation performance, is proposed. The original DNA, which consists of a nested array and a time-shifted array, possesses the capabilities of handling more sources and achieving improved estimation accuracy compared with the nested array. However, only one time-shifted array is employed in DNA and the performance improvement is quite limited. Here, a new multi-level DNA, which utilizes multiple time-shifted nested arrays, is proposed. The multi-level DNA can provide more degrees of freedom (DoFs), meanwhile its difference co-array is still hole-free. The closed form expression of uniform DoFs in multi-level DNA is derived. The corresponding DOA Cramér-Rao bound, which gives the low bound on the variance of estimated DOA, is deduced in detail and some properties related to it are concluded. In total, for the DOA estimation, multi-level DNA can detect more sources and achieve more accurate estimation performance compared with the original DNA. Numerical simulations are performed to verify the superiority of the proposed multi-level DNA.INDEX TERMS Direction of arrival (DOA), co-array, nested array (NA), dilated nested array (DNA).

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“…The CRB is the lower bound of unbiased parameter estimation and usually used as the performance comparison metrics. According to [24][25][26], the CRB of the WNA can be derived as where Π A ⊥ = I N − A(A H A) −1 A H , A is the direction matrix of WNA, P = 1/J ∑ t = 1 J s(t)s H (t) and D can be presented as…”

Section: Cramer-rao Bound (Crb)mentioning

confidence: 99%

“…can be derived as the following cases: Case 1: if N 1 is even. D WNA + can be expressed asD WNA + = {αn 11 d + βn 2 d, n 2 ∈ [0, N 2 − 1], n 11 = 0, 2, × …, N 1 } ∪ {αn 12 d + βn 2 d, n 2 ∈ [0, N 2 − 1], n 12 = 1, 3, …, N 1 − 1} ∪ {αN 1 d + β(N 2 − 1)d + αn 3 d, n 3 = 1, 3, …, N 1 − 1} (24) Assume that D E + = {αN 1 d + β(N 2 − 1)d + αn 3 d, n 3 = 1, 3, ⋯, N 1 − 1}, by combining(23) and(24), we can conclude that D E + contains N 1 /2 unique lags and satisfies the condition ofD d + βn 2 d, n 2 ∈ [0, N 2 − 1], n 11 = 0, 2, × …, N 1 − 1} ∪ {αn 12 d + βn 2 d, n 2 ∈ [0, N 2 − 1], × n 12 = 1, 3, …, N 1 } ∪ {αN 1 d + β(N 2 − 1)d + αn 3 d, × n 3 = 2, 4, …, N 1 − 1} 1 d + β(N 2 − 1)d + αn 3 d, n 3 = 2, 4, …, N 1 − 1}.It is obvious that D E + has N 1 /2 unique lags and D (according to(23) and(25)). …”

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confidence: 99%

Widened nested array: configuration design, optimal array and DOA estimation algorithm

Xinping

Gong

et al. 2020

IET Microwaves, Antennas & Propagation

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A generalised nested array (GNA) configuration with large minimum inter‐element spacing is attractive to alleviate mutual coupling. In this study, by decomposing and rearranging the sub‐arrays of GNA, the authors propose a new nested array configuration named as widened nested array (WNA). The WNA enables to provide the reduced mutual coupling, enhanced degrees of freedom (DOFs), extended array aperture and improved direction of arrival (DOA) estimation performance compared to GNA. The closed‐form expressions for sensor positions of WNA are given and the optimal array configuration for largest DOFs is derived. Meanwhile, the authors propose a partial angular compressed sensing(CS) based DOA estimation algorithm for WNA. Specifically, discrete Fourier transform method is first derived for consecutive DOFs of WNA to obtain initial DOA estimates. Subsequently, the initial estimates are utilised to compress the angular range of overcomplete dictionary of the CS algorithm, which is exploited to obtain the fine DOA estimates. Extensive simulation results testify that the proposed algorithm has the same estimation accuracy as CS algorithm with lower complexity.

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Further Results on the Cramér–Rao Bound for Sparse Linear Arrays

Cited by 18 publications

References 36 publications

Derivation of multidimensional stochastic Cramer‐Rao bound for mixture of noncoherent and coherent near/far field signals

Derivation of multidimensional stochastic Cramer‐Rao bound for mixture of noncoherent and coherent near/far field signals

The Multi-Level Dilated Nested Array for Direction of Arrival Estimation

Widened nested array: configuration design, optimal array and DOA estimation algorithm

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