Fast algorithm for sparse signal reconstruction based on off‐grid model

This paper proposes a direction of arrival estimation based on sparse signal reconstruction in the presence of alpha noise by the off-grid orthogonal matching pursuit algorithm. Assuming Gaussian distribution as the noise model, the previous sparse reconstruction enhances robustness by utilizing the least square criterion-based direction of arrival estimation algorithms. However, they severely degrade, even invalid, when there is thick trailing and large impulse in the noise molded by a stable distribution. In addition, due to the discretization of the potential angle space, the accuracy of these methods will be reduced when the target is not completely on the divided mesh exactly. Increasing the grid density to improve estimation effect will increase the computation burden. The compressed sensing signal model is reconstructed by reshaping the fractional lower order covariance matrix of the sensor array received signal. Based on the reshaped signal model, the novel reshaped orthogonal matching pursuit algorithm and reshaped off-grid orthogonal matching pursuit algorithm are derived. Compared to the least square criterion method with Gaussian distribution assumption, the proposed algorithm obtains high-resolution direction of arrival estimation in a noise. Moreover, the reshaped off-grid orthogonal matching pursuit algorithm improves the direction of arrival estimation accuracy with offgrid target. Numerical simulation results demonstrate the effectiveness of proposed method in direction of arrival estimation with off-grid targets in a noise.

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“…The first-order Taylor series expansion forÃ h ð Þ in formula (16) is performed 22,23 y ¼Ã þB Á Db À Á s…”

Section: R-ogomp Algorithmmentioning

confidence: 99%

“…As long as the sparse structure of the vector s is determined, the mismatch deviation vector b has the same sparse structure. Inspired by Zeng et al 11 and Liu et al 22 , we apply alternating direction iterative method to obtain s p ð Þ and u p ð Þ . The mathematical model is expressed as followsê s p ð Þ ¼ arg min…”

Section: R-ogomp Algorithmmentioning

confidence: 99%

Direction of arrival estimation with off-grid target based on sparse reconstruction in impulsive noise

Liang

Shi

et al. 2020

Journal of Low Frequency Noise, Vibration and Active Control

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“…The number of sparse samples in the slow time domain is 5000, which means the under-sampling rate is M ¼ 2, and the range extension coefficient α is 0.75. Therefore, the maximum unambiguous range can be extended to 41.25 km according to Equation (9), which allows us to detect farther targets.…”

Section: Simulationsmentioning

confidence: 99%

Unambiguous range extension for pulse‐Doppler radar via Poisson disk sampling

Dong

Wang³

et al. 2020

IET Radar Sonar & Navi

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Since the maximum unambiguous range in the traditional single‐channel pulse‐Doppler (PD) radar is restricted by the pulse repetition interval (PRI), there is a trade‐off between the maximum unambiguous range and the maximum unambiguous velocity. As a result, conventional coherent processing used in PD radar systems can hardly provide large unambiguous range and large unambiguous velocity simultaneously. We propose a method of unambiguous range extension for PD radar via Poisson disk sampling. The method enables the PD radar to detect farther targets unambiguously without sacrificing the maximum unambiguous velocity. The Poisson disk sampling is adopted in the slow time domain to ensure the interval length between any two adjacent transmitted pulses to be larger than a desired value, which can be set longer than the Nyquist sampling interval to extend the maximum unambiguous range. Then, the Iterative Soft Thresholding like (IST‐like) algorithm is utilized on the non‐uniformly under‐sampled data to recover the range‐Doppler spectrum accurately. Compared to some of existing methods of unambiguous range extension based on stochastic sampling, the proposed method has better velocity estimation accuracy. Simulations and experiments on real PD radar data demonstrate the effectiveness of the proposed method.

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“…These drawbacks mean that using a random matrix cannot ensure the stability and efficiency of compression sampling, which led to the proposal of using a deterministic measurement matrix [4]. The most popular algorithm for constructing deterministic matrices can be divided into four categories based on different generation methods for the matrix elements: (1) a finite framework, such as the expander graph [5]; (2) encoding, such as chirp codes [6] or the Toeplitz deterministic matrix [7]; (3) the maximum Welch boundary, such as that constructed using a difference set algorithm [8] and numerical searching algorithm [9]; and (4) a training mode by optimizing the restricted isometry property of the initial matrix [10] and implemented by a projection algorithm and gradient-based training algorithm.…”

Section: Introductionmentioning

confidence: 99%

A cooperative construction method for the measurement matrix and sensing dictionary used in compression sensing

Shen

Cheng

Wang

2020

EURASIP J. Adv. Signal Process.

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A measurement matrix and sensing dictionary are the basic tools for signal compression sampling and reconstruction, respectively, which are important aspects in the field of compression sensing. Previous studies which have divided the measurement matrix and sensing dictionary into two separate processes did not make full use of their inherent intercorrelations. In case of which could be fully utilized, the mutual coherence of the atoms of measurement matrix and sensing dictionary can be further reduced under the premise of ensuring that the original signal information is stored, which could improve the accuracy of signal recovery. The present study attempted to reduce the mutual coherence between the sensing dictionary and measurement matrix by proposing the t-average mutual coherence coefficient as an evaluation index for the sensing dictionary. A mathematical model for co-constructing a measurement matrix and sensing dictionary is firstly proposed. Then, the measurement matrix and sensing dictionary cooperative construction(MSCA)algorithm is proposed to solve the model at a faster rate. The simulated results for sparse signal and binary image show that the proposed algorithm has faster computing speed and higher solution precision than the state-of-the-art construction algorithms.

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Fast algorithm for sparse signal reconstruction based on off‐grid model

Cited by 9 publications

References 27 publications

Direction of arrival estimation with off-grid target based on sparse reconstruction in impulsive noise

Direction of arrival estimation with off-grid target based on sparse reconstruction in impulsive noise

Unambiguous range extension for pulse‐Doppler radar via Poisson disk sampling

A cooperative construction method for the measurement matrix and sensing dictionary used in compression sensing

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