Synthetic aperture processing for passive co-prime linear sensor arrays

Ramirez, Juan; Krolik, Jeffrey L.

doi:10.1016/j.dsp.2016.07.021

Cited by 45 publications

(13 citation statements)

References 28 publications

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“…Therefore, we consider the array move a short distance, i.e.

d_{m} = v ε = λ / 2

, then the directions of signals can be regarded as unchanged, and the array can operate coherently on data collected. At the time

t + ε

, the steering vector becomes [19]

\begin{matrix} right leftthickmathspace.5em \\ bold-italicb (θ_{k}) & = [\exp (- j π \sin (θ_{k})), \\ \exp (- j 2 π (d_{m} + d_{2}) \sin (θ_{k}) / λ), . . ., \\ {(], \exp ()(, - j 2 π ()(, d_{m} + d_{L}) \sin ()(, θ_{k})) / λ)}^{T} \end{matrix}

By multiplying phase correction factor

\exp ()(, - j 2 π f ε)

X ()(, t + ε)

, the output of received signal vector becomes [18]

\overset{false~}{bold-italicX} ()(, t + ε) = X ()(, t + ε) \exp ()(, - j 2 π f ε) = B s ()(, t) + \overset{false~}{bold-italicn} ()(, t + ε)

where

\overset{false~}{bold-italicn} ()(, t + ε) = \exp ()(, - j 2 π f ε) n ()(, t + ε)

. By combining the array outputs at the time t and

t + ε

, then the synthetic array can be expressed as [20] …”

Section: Data Modelmentioning

confidence: 99%

“…In addition to the aforementioned schemes, DOA estimation exploiting array motion provides another opportunity to increase the number of consecutive lags and improve DOA estimation performance under the same number of physical elements. Considering the situation of array motion, it is pointed out by Ramirez and Krolik [18] that temporal‐coherence‐period (TCP) =

true \frac{N}{2} \cdot \frac{λ}{2}

is the condition of producing a filled co‐array, but it is idealised to assume the source signals are unchanged for a long time. It is proposed by Qin et al [19] that array motion can produce large DCA and more consecutive DCA lags, and the motion of coprime array and sparse uniform linear array (SULA) were studied in detail.…”

Section: Introductionmentioning

confidence: 99%

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Improved unfolded coprime array subject to motion for DOA estimation: augmented consecutive synthetic difference co‐array

Zhang

et al. 2020

IET signal process.

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Direction of arrival (DOA) estimation using the improved unfolded coprime array (IUFCA) subject to array motion isdiscussed in this study. Unfolded coprime array (UFCA) consists of two uniform linear subarrays, and the two subarrays are arranged at different sides of theaxis, which leads to a large number of holes in the difference co‐array (DCA). With array motion and DCA synthesis,part of the holes can be filled, but there are still holes in the center which lead to the virtual arrays separated.By analyzing the hole positions in the synthetic DCA generated by UFCA motion, the authors improve the originalUFCA by relocating some physical elements, then the two dominantconsecutive DCA segments in the positive and negative sides can be connected. The expression of synthetic DCA is analyzed, and the closed‐form expression of theuniform degree of freedom (uDOF) subject to IUFCA motion is studied. Simulation results show that IUFCA motion can obtain a largenumber of uDOFs, which leads to better DOA estimation performance and more identifiable signals compared with existingcoprime array configurations.

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“…Therefore, we consider the array move a short distance, i.e.

d_{m} = v ε = λ / 2

, then the directions of signals can be regarded as unchanged, and the array can operate coherently on data collected. At the time

t + ε

, the steering vector becomes [19]

\begin{matrix} right leftthickmathspace.5em \\ bold-italicb (θ_{k}) & = [\exp (- j π \sin (θ_{k})), \\ \exp (- j 2 π (d_{m} + d_{2}) \sin (θ_{k}) / λ), . . ., \\ {(], \exp ()(, - j 2 π ()(, d_{m} + d_{L}) \sin ()(, θ_{k})) / λ)}^{T} \end{matrix}

By multiplying phase correction factor

\exp ()(, - j 2 π f ε)

X ()(, t + ε)

, the output of received signal vector becomes [18]

\overset{false~}{bold-italicX} ()(, t + ε) = X ()(, t + ε) \exp ()(, - j 2 π f ε) = B s ()(, t) + \overset{false~}{bold-italicn} ()(, t + ε)

where

\overset{false~}{bold-italicn} ()(, t + ε) = \exp ()(, - j 2 π f ε) n ()(, t + ε)

. By combining the array outputs at the time t and

t + ε

, then the synthetic array can be expressed as [20] …”

Section: Data Modelmentioning

confidence: 99%

true \frac{N}{2} \cdot \frac{λ}{2}

Section: Introductionmentioning

confidence: 99%

Improved unfolded coprime array subject to motion for DOA estimation: augmented consecutive synthetic difference co‐array

Zhang

et al. 2020

IET signal process.

View full text Add to dashboard Cite

show abstract

“…Array motions are usually realized by mounting arrays to a moving platform which can be air-borne, vehicleattached or ship-based. In [19], SA processing is applied to CAs with coprime integers M, N . By moving N/2(N > M ) half wavelengths, the CA along with its shifted array can generate a hole-free DcA.…”

Section: Introductionmentioning

confidence: 99%

2D DOA Estimation Exploiting Vertical Synthetic Planar Arrays

2021

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In this paper, vertical motions of sparse linear arrays (SLAs) are utilized to generate equivalent synthetic planar arrays for two-dimensional (2D) direction-of-arrival (DOA) estimation. The proposed array geometry named vertical synthetic planar array (VSPA) consists of an arbitrary SLA on the x-axis and a series of its time-shifted arrays in the vertical orientation. With the original linear array and the moving trail known, the difference coarray of VSPA can be easily obtained. By utilizing both the synthetic aperture processing and the coarray technique, VSPA has the ability to construct a synthetic planar array with only an SLA used. Compared with the traditional sparse planar arrays (SPAs), such as 2D nested array and 2D coprime array, VSPA can achieve higher degree-of-freedom and improved 2D DOA estimation performance with the same number of sensors. Moreover, as different original linear arrays and moving trails can be chosen for different applications, the construction of VSPA is of high flexibility. Numerical simulations are presented to verify the superiority of the proposed VSPA geometry over other typical SPAs.

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“…Though various ingenious designs have been cast into the static NA, the DoFs increase is limited. By adopting the moving platform, the authors in [32] creates the synthetic CA, which can acquire several times higher DoFs than the original CA with the same number of array elements. Unfortunately, synthetic CA must move at least N 1 λ/4 to produce a hole-free difference co-array, where λ is the signal wavelength, N 1 and N 2 (N 1 > N 2 ) are the coprime numbers used to generate CA.…”

Section: Introductionmentioning

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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Synthetic aperture processing for passive co-prime linear sensor arrays

Cited by 45 publications

References 28 publications

Improved unfolded coprime array subject to motion for DOA estimation: augmented consecutive synthetic difference co‐array

Improved unfolded coprime array subject to motion for DOA estimation: augmented consecutive synthetic difference co‐array

2D DOA Estimation Exploiting Vertical Synthetic Planar Arrays

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

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