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This letter investigates the problem of determining the static target in multistatic systems using bistatic range (BR) measurements, which can be obtained by some local sensor signal processing methods. The localization problem is first formulated as a semidefinite programming problem by using the semidefinite relaxation technique. Then, an initial position estimate is given by augmenting the unknown parameter space, which is required for solving the SDP problem. Specifically, this initialization is also a closed-form solution. Compared with existing algorithms, the proposed estimator has the advantage of not relying on the prior knowledge of BR measurement noise power. Simulation results validate the performance of the proposed estimator.

The electrochemical corrosion behavior of the dental Ti50Zr alloy with and without nanocrystalline (TiZr)N coating was comparatively investigated in artificial saliva solutions with different pH values and fluoride ion concentrations. The chemical stability of the passive films on the coated and non-coated Ti50Zr alloy was evaluated by calculating passive film thickness. The chemical compositions and valence structures of the passive films were analyzed by X-ray photoelectron spectroscopy (XPS). The results show that the (TiZr)N-coated alloy displays distinctly decreased corrosion rate and increased impedance compared with Ti50Zr alloy in non-fluoridated and fluoridated acidic solutions. Particularly, in the solution of pH = 3.9 and 0.15% NaF-containing, the corrosion protection efficiency of (TiZr)N coating reaches 90%. The excellent corrosion resistance of the coated alloy is attributed to that the nanocrystallines in (TiZr)N coating decreases micropores and crack defects, which strongly impedes the corrosive ions diffusion and electrode process at Ti substrate/coating interface. Meanwhile, (TiZr)N coating shows good passivation behavior in acidic solution and active–passive transition behavior in fluoridated acidic solution. The coated Ti50Zr alloy with high chemical stability has potential application prospect for dental implants.

Automatic modulation classification (AMC) is an essential part in a cognitive radio receiver. Benefited from the discriminative constellation characteristics among most modulations, AMC methods based on constellation diagrams usually achieve pleasant performance. However, in noncooperation communication systems, constellation diagrams expressing modulations explicitly are difficult to obtain via blind symbol timing synchronization, especially in complicated wireless channels. Therefore, this article proposes a novel constellation diagram-based AMC architecture called attentive Siamese networks (ASNs) by considering multitiming constellation diagrams (MCDs) and selecting the proper symbol timings at the feature level, which is a more robust way than the conventional signal-level symbol timing synchronization. In detail, convolutional neural networks sharing the same parameters first extract deep feature vectors for MCDs. Then, an attention inference module weights all the deep feature vectors. Finally, AMC is realized based on the weighted feature vectors. Moreover, the ASN architecture can be trained end-to-end. Comparing with the state-of-the-art methods that take diverse representations of received baseband signals as input, experimental results based on the RadioML 2018.01A dataset and non-Gaussian noise dataset demonstrate that ASN achieves a remarkable improvement, whose classification accuracy goes over 99% when the signal-to-noise ratio (SNR)10 dB.

The Cramer-Rao bound (CRB) offers insights into the inherent performance benchmark of any unbiased estimator developed for a specific parametric model, which is an important tool to evaluate the performance of direction-of-arrival (DOA) estimation algorithms. In this paper, a closed-form stochastic CRB for a mixture of circular and noncircular uncorrelated Gaussian signals is derived. As a general one, it can be transformed into some existing representative results. The existence condition of the CRB is also analysed based on sparse arrays, which allows the number of signals to be more than the number of physical sensors. Finally, numerical comparisons are conducted in various scenarios to demonstrate the validity of the derived CRB.

By exploiting the relationship between probability density and the differential geometry structure of received data and geodesic distance, the recently proposed information geometry (IG) method can provide higher accuracy and resolution ability for direction of arrival (DOA) estimation than many existing methods. However, its performance is not robust even for high signal-to-noise ratio. To have a deep understanding of its unstable performance, a theoretical analysis of the IG method is presented by deriving the relationship between the cost function and the number of array elements, powers and DOAs of source signals, and noise power. Then, to make better use of the nonlinear and super resolution property of the cost function, a Scaling TRansform based INformation Geometry (STRING) method is proposed, which simply scales the array received data or its covariance matrix by a real number. However, the expression for the optimum value of the scalar is complicated and related to the unknown signal DOAs and powers. Hence, a decision criterion and a simple search based procedure are developed, guaranteeing a robust performance. As demonstrated by computer simulations, the proposed STRING method has the best and robust angle resolution performance compared with many existing high resolution methods and even outperforms the classic Cramer–Rao bound, although at the cost of a bias in the estimation results.

The false scene, which is formed by the false scene deception jamming signal, can cover the real target and scene, confuse synthetic aperture radar (SAR), and mislead the decision-making. If an area is selected to be protected by utilising the false scene deception jamming, the computational burden of the jammer is related to the number of false scatterers. An important problem faced by the SAR deceptive jammer is how to generate the false scene with the low computational burden. To overcome this disadvantage, a mosaic scene deception jamming based on two-dimensional separation is proposed against SAR. The intercepted SAR signal is separated and retransmitted in azimuth and range to enlarge the width of the main lobe and generate the `mosaic scene', which reduces the resolution of the false targets to fill the protected area. Therefore, the number of false scatterers is decreased and the computational burden is also reduced. Moreover, to make a low-resolution false scene similar to the real scene and ensure the jamming effectiveness, the mosaic scene deception jamming template should be highly correlated with the false scene deception jamming template. Finally, the validity of the proposed method is verified by the simulation results.

This paper investigates the moving target localization problem in distributed multiple-input multiple-output (MIMO) radar systems using bistatic range (BR) and bistatic range rate (BRR) measurements, which can be obtained via some local sensor signal processing methods. In the first stage, the cost function of the localization problem is re-formulated by augmenting the unknown vector, and then initial estimates of the target position and velocity are given. In the second stage, the estimation error terms of the first stage are estimated by the weighted least square (WLS) technique. To the end, the target position and velocity are refined by subtracting the estimation errors from the outputs of the first stage. Numerical simulation results corroborate the theoretical developments.

Automatic modulation classification (AMC) based on constellation diagrams that own distinct modulation features performs well in Gaussian channels. However, proper constellation diagrams for AMC are difficult to obtain in non-Gaussian channels due to incorrect estimation of symbol timings, which puts bad effects on AMC greatly. This paper proposes a novel AMC method via two-stage convolutional neural networks (CNN). Specifically, constellation diagrams with respect to all timings of any signal consist of a group of multi-offset constellation diagrams (MCD). Then, the first-stage CNN estimates the signal-to-noise ratio (SNR) for each constellation diagram so that the constellation diagram owning the maximum SNR can be selected out from its MCD. Finally, the second-stage CNN can classify modulations based on the selected constellation diagrams. Comparing with seven conventional methods, experimental results demonstrate the remarkable improvement of the proposed method.

In this paper, a derivative-based MUSIC (DB-MUSIC) algorithm for two-dimensional (2-D) direction-of-arrival (DOA) estimation is proposed using an L-shaped uniform array. It transforms the traditional 2-D search problem into a one-dimensional (1-D) one using a derivative based optimization method, taking into consideration the structure of the steering vector and the associated cost function. As a result, the proposed algorithm has a significantly low computational complexity with the additional benefit of no need for 2-D angle pairing. Simulation results show that the proposed algorithm has better estimation accuracy than some existing representative 2-D DOA estimation algorithms falling into the same category, i.e., low complexity through 1-D search with no need for pairing.

It is well known that the presence of non-circular signals can provide extra degrees of freedom for a sensor array system, which can then be exploited for improved performance. Recently, by exploiting the non-circularity information and the difference and sum co-array concept, a new approach was developed for direction of arrival estimation in the presence of a mixture of circular and noncircular signals. In this paper, the problem is reformulated and a new algorithm is developed for direction finding under the same conditions. As shown by extensive simulation results, the so-called improved MUSIC (IMUSIC) can achieve a better performance than the existing ones.

Conventional direction of arrival (DOA) estimation methods for known waveform sources have often assumed the noise being Gaussian distribution. However, the impulsive noise are frequently encountered in practice, which may severely degrade their estimation performance. To deal with this problem, we firstly construct a hybrid cost function to obtain the matrix related to unknown DOAs and complex amplitudes in the presence of impulsive noise. Then, by incorporating the majorization-minimization (MM) framework, the cost function is optimized iteratively. Finally, the DOAs and complex amplitudes are estimated via using the inherent relationship of the matrix calculated from the MM step. As demonstrated by simulation results, for strongly impulsive noise, the proposed method has a better estimation performance than many existing methods. Moreover, it can handle both weakly and strongly impulsive cases effectively.

Purpose The early predictive values of diagnostic markers for lymph node metastasis (LNM) in endometrial cancer (EC) are still unclear at present. The purpose of this study is to explore the relationship between serum calcium and LNM in EC. Methods We identified all patients with EC who underwent surgery between January 2012 and December 2016. Patient characteristics and various preoperative clinicopathologic data were obtained from medical records and were reviewed retrospectively. These patients were divided into two groups according to the pathology of their lymph node. Logistic regression models analyzed the relationship between the ionized calcium and LNM of EC patients, while adjusting for the potential confounders. Results A total of 448 patients were assessed. Univariate analysis showed that ionized calcium, CA125 level, tumor grade, peritoneal cytology, FIGO stage, histological type, LVSI, and myometrial invasion were positively correlated with LNM (all P

The direction of arrival (DOA) estimation problem for sources with known waveforms in the presence of impulsive noise is studied. To solve the problem, the impulsive noise is decomposed into Gaussian and sparse parts, and a generalized l 2 − l p minimization based cost function is developed by setting generalized Gaussian distribution (GGD) as the prior distribution of sparse part. Then, to solve this nonconvex problem, the generalized l 2 − l p problem is decoupled into multiple independent and dimension reduced simple l 2 − l p optimization problems with respect to the sparse part, and solved under the accelerated proximal gradient framework. Finally, DOAs and complex amplitudes are estimated from the cleaned data. As demonstrated by simulation results, the proposed method has a better performance than existing ones in the presence of Gaussian mixture model (GMM) and GGD noise, while it is comparable for symmetric α stable (S α S) noise.

Bi- and multistatic inverse synthetic aperture radar (ISAR) operate with spatially separated transmitting and receiving antennas. A deception jamming method countering bi- and multistatic ISAR is proposed in this paper based on the study of micro-Doppler effect. The jammer modulates the intercepted ISAR signals with added micro-Doppler information and retransmits them to the real target, which scatters the jamming signals to the radar receivers. Deceptive false-target images with interference bands in the cross-range direction will be induced by the jamming signals through the imaging process of radar receivers. Additionally, real-time movement features of the false-targets can be flexibly adjusted by changing the modulation parameters, which improves the fidelity of the false-targets. The equivalent number of looks (ENL) index is used to evaluate the jamming effects. Simulation results validate our theoretical analysis and show the effectiveness and practicability of our method.

BACKGROUND: Tea (Camellia sinensis (L.) O. Kuntze) is a hyper‐accumulator of fluoride (F). To understand F uptake and distribution in living plants, we visually evaluated the real‐time transport of F absorbed by roots and leaves using a positron‐emitting (¹⁸F) fluoride tracer and a positron‐emitting tracer imaging system. RESULTS: F arrived at an aerial plant part about 1.5 h after absorption by roots, suggesting that tea roots had a retention effect on F, and then was transported upward mainly via the xylem and little via the phloem along the tea stem, but no F was observed in the leaves within the initial 8 h. F absorbed via a cut petiole (leaf 4) was mainly transported downward along the stem within the initial 2 h. Although F was first detected in the top and ipsilateral leaves, it was not detected in tea roots by the end of the monitoring. During the monitoring time, F principally accumulated in the node. CONCLUSION: F uptake by the petiole of excised leaf and root system was realized in different ways. The nodes indicated that they may play pivotal roles in the transport of F in tea plants. © 2020 Society of Chemical Industry

In this paper, a two-dimensional (2-D) direction-of-arrival (DOA) estimation method for a mixture of circular and strictly noncircular signals is presented based on a uniform rectangular array (URA). We first formulate a new 2-D array model for such a mixture of signals, and then utilize the observed data coupled with its conjugate counterparts to construct a new data vector and its associated covariance matrix for DOA estimation. By exploiting the second-order non-circularity of incoming signals, a computationally effective ESPRIT-like method is adopted to estimate the 2-D DOAs of mixed sources which are automatically paired by joint diagonalization of two direction matrices. One particular advantage of the proposed method is that it can solve the angle ambiguity problem when multiple incoming signals have the same angle θ or β. Furthermore, the theoretical error performance of the proposed method is analyzed and a closed-form expression for the deterministic Cramer-Rao bound (CRB) for the considered signal scenario is derived. Simulation results are provided to verify the effectiveness of the proposed method.

To overcome the limitations of radar cross section characteristic, a method using detection probability as an indicator to evaluate plasma stealth effectiveness is proposed in this paper. Based on shift operator finite-difference time-domain method, the distorted waveform of linear frequency modulation radar echo is obtained when the targets coated with plasma. Then, by making a comparison between outputs of pulse compression with and without plasma, the peak instantaneous signal-to-noise ratio (SNR) loss is calculated. According to the signal detection theory, the relationship between plasma parameters and radar detection probability is built up through the SNR loss, in which the attenuation of radar echo and the mismatch loss of pulse compression are both considered. Finally, effects of plasma parameters including electron density, collision frequency, and radar frequency on the probability of detection have been studied systematically. By adopting detection probability $P_{d }\le 0.1$ as a valid criterion, the effective plasma parameters for different radar frequencies are given as a guide when using plasma for stealth application.

A two-dimensional (2-D) direction of arrival estimation method for L-shaped array with automatic pairing is proposed. It exploits the conjugate symmetry property of the array manifold matrix to increase the effective array aperture and the number of virtual snapshots simultaneously, and then applies the principle of MUSIC to construct an angle cost function and transforms the conventional 2-D search into 1-D via a Rayleigh quotient, which can greatly reduce the computation complexity. Finally, the azimuth and elevation angles are estimated without pair matching. Simulation results show that the proposed method has a better performance and can resolve more sources than some existing computationally efficient methods.

Based on the resonance absorption effect of plasma, the mechanism of plasma jamming technology is studied and verified in this letter. Different from the power perspective, the effects of plasma on the radar echo waveform and the radar signal detection are studied. It is found that the radar echo waveform is distorted and the performance of pulse compression is degraded. Moreover, the phenomenon of radar false targets appears with several meters apart. Thus, plasma could not only act as electromagnetic wave absorbers, but also a kind of passive jammer. Finally, many optimal plasma parameters are presented to achieve desired jamming effects for different radar frequencies. These data provide some useful references to plasma jamming technology.

Non-uniform L-shaped array consisting of two nested arrays and its computationally efficient two-dimensional direction-of-arrival (DOA) estimation method are developed in this study. The basic idea of the proposed method is to utilise the property of nested arrays and the conjugate symmetry property of the signal auto-correlation function for different time lags to construct a conjugate augmented spatial–temporal cross-correlation matrix (CAST-CCM) and form joint diagonalisation structure from the signal subspace corresponding to the CAST-CCM. Hence, the DOAs are estimated and paired automatically via signal subspace joint diagonalisation technique. The proposed method can handle underdetermined DOA estimation with automatic matching and deal with the angle ambiguity problem when multiple sources have the same azimuth or elevation angles. Meanwhile, the proposed method is computationally efficient without multidimensional search. The effectiveness of the proposed method is verified through computer simulations.

Transient Receptor Potential Melastatin 4 (TRPM4) is a nonselective channel conducting monovalent ions and indirectly regulates intracellular Ca(2+). Aberrant expression has been reported in a number of cancers. However, the biological function of TRPM4 in endometrial carcinoma (EC) is still unknown. We find that decreased TRPM4 expression is significantly correlated with a poor prognosis, overall survival (OS, P

This paper addresses the harmonic problem in one-bit linear frequency modulation (LFM) signal recovery. We develop a novel quantization strategy with random thresholds to mitigate the annoying harmonic effect caused by one-bit sampling. The proposed quantization strategy changes the probability distribution of harmonic amplitude. In this case, the average amplitude of each order harmonic is dominated by the probability density function of random thresholds. Therefore, we employ the flexible Beta distribution to approximate various distribution types and then explore the potential optimal distribution of random thresholds. Furthermore, the quantization strategy with the possible optimal random thresholds is introduced into the classical one-bit recovery algorithm to improve the performance. Numerical simulation results demonstrate the effectiveness of our proposed strategy.

As L-shaped array can provide good angle estimation performance and is easy to implement, many two-dimensional (2-D) direction-of-arrival (DOA) estimation algorithms have been developed. In this letter, we present a low-computation-complexity DOA estimation method for L-shaped array that exploits the conjugate symmetry property of the array manifold matrix to increase the effective array aperture and improve the angle estimation performance. Hence, the DOA estimation is obtained via combining propagator method (PM) with ESPRIT algorithm, which does not need spectrum peak search or additional angle pair matching procedure. Simulation results demonstrate the effectiveness of the proposed method.

A novel DOA estimation method for known waveform sources with different unknown time delays and Doppler shifts is proposed. Based on the idea of maximum likelihood and the matrix projection theory, a decoupled cost function is first constructed and then the problem of estimating time delay and Doppler shift is transformed into a nonlinear least squares (NLS) problem. To solve the NLS problem efficiently without multidimensional search, a Toeplitz dominant rule is established to perform initial estimates with a reduced dimension. Finally, with the aid of time delay and Doppler shift estimates, DOAs and complex amplitudes of the incoming signals are obtained. Simulation results show that the proposed method can achieve a performance close to CRB at high SNR and with a large number of snapshots.

A low-cost and highly efficient biosorbent for the removal of fluoride from drinking water from spent mushroom compost (SMC) that was carbonized (spent mushroom compost biochar, SMCB) coated by aluminum hydroxide. Adsorption studies were performed to investigate the influence of adsorbent dosage, initial fluoride concentration, contact time, pH, and coexisting ions on fluoride adsorption. The fluoride adsorption capacity of the coated SMCB was greater than that of uncoated SMCB. Fluoride adsorption by coated SMCB followed the Langmuir isotherm model, and the maximum adsorption capacity was 36.5 mg/g. The fluoride concentration could be reduced to below 1 mg/L from an initial fluoride concentration of 10 mg/L. While the pH of the solution did play an important role in the fluoride removal capacity, with the SMCB performed well under a wide pH range, from 6.0 to 8.0. These findings indicate that fluoride can effectively be removed from drinking water using modified mushroom cultivation waste biomass.

A low-cost and highly efficient biosorbent was prepared by loading Al/Fe oxides onto tea waste and was tested for the ability to remove fluoride from drinking water. Key factors, including adsorbent dosage, initial fluoride concentration, contact time and initial pH of the biosorbent, were investigated. It was found that the solution pH played an important role in the removal of fluoride. The biosorbent combinations Tea–Al or Tea–Al–Fe could reduce the fluoride concentration to below 1.5 mg/L in the drinking water, a level which meets the drinking water standard recommended by the World Health Organization (WHO). In addition, the residual concentrations of Al and Fe in the drinking water after Tea–Al–Fe treatment were below the standards set by WHO when treatment was conducted at pH values ranging from 5.0 to 10.0. The experimental data were analyzed using two-parameter theoretical models. The maximum fluoride adsorption capacities for the original tea, Tea–Fe, Tea–Al and Tea–Al–Fe biosorbents were 3.83, 10.47, 13.79 and 18.52 mg/g, respectively. These findings demonstrate the suitability of a prepared biosorbent based on tea waste for the removal of fluoride from drinking water.

Direction of arrival (DOA) estimation is a crucial problem in electronic reconnaissance. A novel broadband DOA estimation method utilizing nested arrays is devised in this paper, which is capable of estimating the frequencies and DOAs of multiple narrowband signals in broadbands, even though they may have different carrier frequencies. The proposed method converts the DOA estimation of multiple signals with different frequencies into the spatial frequency estimation. Then, the DOAs and frequencies are pair matched by sparse recovery. It is possible to significantly increase the degrees of freedom (DOF) with the nested arrays and the number of sources can be more than that of sensor array. In addition, the method can achieve high estimation precision without the two-dimensional search process in frequency and angle domain. The validity of the proposed method is verified by theoretic analysis and simulation results.

A novel and low-cost biosorbent of tea waste supported hydrous aluminium oxide (Tea–APAM–Al) was prepared with help of anionic polyacrylamide (APAM) for highly efficient defluoridation of drinking water. Batch adsorption studies were carried out by varying the adsorbent dosage, initial fluoride concentration, contact time, initial pH, and presence of co-existing ions to evaluate the efficiency of fluoride removal. It was found that Tea–APAM–Al performed well over a considerably wide pH range, from 4.0–9.0. With the exception of bicarbonate, other co-existing ions (nitrate, chloride and sulphate) did not have a significant effect on the defluoridation process. The adsorption process could be described by the Lagergren pseudo-second-order kinetic model. Adsorption data could be fitted by the Langmuir isotherm model and the maximum fluoride adsorption capacity for Tea–APAM–Al was 42.14 mg g−1. The results from SEM, EDS, XRD, FTIR and XPS studies showed that the fluoride adsorption mechanism likely involved hydroxyl and sulfate ion exchange with fluoride. Moreover, fluoride anion exchange with sulfate ions was the main mechanism for fluoride adsorption at low initial fluoride concentration.

To solve the angle ambiguity problem when multiple sources have the same azimuth or elevation angles, a novel two-dimensional direction of arrival (2-D DOA) estimation method with L-shaped array based on conjugate augmented spatial temporal technique is developed in this letter. The basic idea of the proposed method is to utilize the conjugate symmetry property of the signal auto-correlation function with different delays to construct a conjugate augmented spatial-temporal cross-correlation matrix (CAST-CCM) and form joint diagonalization structure from the signal subspace corresponding to the CAST-CCM. Hence, the DOAs are estimated and paired automatically via joint diagonalization technique. The proposed method can handle the angle ambiguity problem efficiently and can also work in the underdetermined case. The effectiveness of the proposed method is verified through computer simulations.

Frutescones H–R (1–11), new sesqui- or monoterpene-based meroterpenoids, were isolated from the aerial parts of Baeckea frutescens. Their structures and absolute configurations were established by means of spectroscopic analyses (HRESIMS, 1D and 2D NMR, and ECD), as well as single-crystal X-ray crystallography of 1, (−)-7, and 9. The anti-inflammatory activities of all isolates were evaluated by measuring their inhibitory effects on NO production in LPS-stimulated RAW 264.7 macrophages, and the structure–activity relationships of 1–11 are also discussed. Compound 8 exhibited anti-inflammatory activity with an IC50 value of 0.36 μM, which might be related to the regulation of the NF-κB signaling pathway via the suppression of p65 nuclear translocation and the consequent decrease of IL-6 and TNF-α.

In this paper, a two-dimensional (2-D) direction-of-arrival (DOA) estimation method for a mixture of circular and strictly noncircular signals is presented based on a uniform rectangular array (URA). By exploiting the second-order non-circularity of incoming signals, a computationally effective ESPRIT-like method is developed to estimate the 2-D DOAs of mixed sources. The proposed method can automatically pair the estimated DOAs by joint diagonalization of two direction matrices. It can also solve the angle ambiguity problem when multiple incoming signals have the same angle θ or β. Simulation results are provided to verify the effectiveness of the proposed method.

Tea (Camellia sinensis (L.) O. Kuntze) hyper-accumulates fluoride (F), mainly in the leaves. To understand how tea copes with the stress caused by F, we tracked photosynthesis, antioxidant defense, and cell ultrastructure under different F concentrations (0–50 mg L−1). High F (≥5 mg L−1) caused decreases in photosynthetic and chlorophyll fluorescence parameters. Activated oxygen metabolism was altered by F, as manifested in increasing lipid peroxidation, electrolyte leakage (EL), and accumulation of H2O2. The activities of ascorbate peroxidase (APX, EC 1.11.1.1) and catalase (CAT, EC 1.11.1.6) increased at 0–5 mg L−1 F, but sharply decreased less than 10–50 mg L−1 F. The activity of manganese superoxide dismutase (Mn-SOD, EC 1.15.1.1) decreased with increasing F concentration. Expression of genes encoding antioxidant enzymes were in accordance with their measured activities. The results suggest that the antioxidant enzymes in the tea plant can eliminate reactive oxygen species (ROS) at

For the problem of two dimensional direction of arrival (2-D DOA) estimation of Liner Frequency Modulated (LFM) signals, a novel 2-D DOA estimation method is proposed based on sparse representation in fractional Fourier domain. First, utilizing the energy-concentrated characteristic of fractional Fourier transform for LFM signals, the redundant dictionaries based on the space angles are established in fractional Fourier domain. Then the space angles can be estimated by sparse recovery algorithm respectively. Finally, the azimuth and elevation angles are calculated through the estimated space angles. The proposed method has a better estimation precision, high-resolution performance and lower SNR threshold without multidimensional search process. The validity of the proposed method is verified by theoretic analysis and simulation results. Keywords—LFM signal; DOA estimation; fractional Fourier transform; sparse recovery