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Abstract Pyroptosis possesses potent antitumor immune activity, making pyroptosis inducer development a promising direction for tumor immunotherapy. Persistent luminescence nanoparticles (PLNPs) are highly sensitive optical probes extensively employed in tumor diagnosis and therapy. However, a pyroptosis inducer based on PLNPs has not been reported yet. Herein, polyethylene glycol–poly lactic acid‐co‐glycolic acid (PEG–PLGA: PP) modified biodegradable CaS:Eu2+ (CSE@PP) PLNPs are synthesized as a pyroptosis inducer for tumor immunotherapy for the first time. The synthesized CSE@PP possesses biowindow persistent luminescence (PersL) and pH‐responsive degradation properties, allowing it to remain stable under neutral pH but degrade when exposed to weak acid (pH < 6.5). During degradation within the tumor, CSE@PP constantly releases H2S and Ca2+ while its PersL gradually fades away. Thus, the PersL signal can self‐monitor H2S and Ca2+ release. Furthermore, the released H2S and Ca2+ result in mitochondrial dysfunction and the inactivation of reactive oxygen species scavenging enzymes, synergistic facilitating intracellular oxidative stress, which induces caspase‐1/GSDM‐D dependent pyroptosis and subsequent antitumor immune responses. In a word, it is confirmed that CSE@PP can self‐monitor H2S and Ca2+ release and pyroptosis‐mediated tumor Immunotherapy. This work will facilitate biomedical applications of PLNPs and inspire pyroptosis‐induced tumor immunotherapy.

Near-infrared (NIR) persistent luminescence nanoparticles (PLNPs) have inherent advantages for high-sensitivity bioimaging due to the separation of excitation and emission light. However, the single-wavelength emission of NIR PLNPs for bioimaging limits their use in photodynamic therapy (PDT). Herein, a biological window excited up-conversion (UC) PLNPs, Zn3Ga2SnO8:Cr3+,Yb3+,Ho3+ (ZGS), was reported for bioimaging and PDT. ZGS exhibits NIR persistent luminescence (PersL) after red LED excitation and visible UCL under 980 nm excitation. The NIR PersL is designed for in vivo bioimaging; the visible UCL is used to activate photosensitizer (PS) to generate reactive oxygen species (ROS) for PDT. The dual-functional ZGS with UCL and PersL provides an effective method for bioimaging and PDT, which is expected to further promote the application of PLNPs in the integration of efficient diagnosis and treatment.

Abstract Grid theory is rather commonly-used through out the research of integer ambiguity. In order to promote the efficiency of computation, it is of great necessity to reduce the correlations of the grid basis through the reduction. The classical reduction algorithm is known as the LLL (Lenstra–Lenstra–Lovász) algorithm. So as to further enhance the reduction effect, the deep-insertion LLL algorithm can be utilized as an alternative to the basis vector exchange algorithm. In practice, the deep-insertion LLL algorithm can achieve a better reduction effect, but it requires more time for reduction. The PotLLL algorithm replaces the basis vector exchange condition of deep-insertion LLL with an improving in the basis quality, and it can run in polynomial time, but with certain limitations. Therefore, this article proposes a global deep-insertion PLLL algorithm (GS-PLLL) to address the issue of integer ambiguity. GS-PLLL adopts a global strategy for deep-insertion processing, and introduces a rotation sorting method for preconditioning the grid basis. Comparative evaluations were conducted using simulation experiments and real-world measurements on the LLL, DeepLLL, PotLLL, and GS-PLLL algorithms. The experimental results indicate that the GS-PLLL algorithm achieves a better reduction effect than the PotLLL algorithm while improving the efficiency of reduction.

Abstract Near‐infrared (NIR) fluorescence imaging poses significant superiority over traditional medical imaging for tumor resection, thus having attracted widely attention. However, for tiny tumor residues, it requires relative high sensitivity to determine. Here, based on persistent luminescence nanoparticles (PLNPs), an ultrasensitive nanoprobe with extraordinary tumor imaging result is developed to guide surgical removal. Persistent luminescence (PersL) is quenched in normal tissue by the outer layer of MnO2, and is recovered due to the degradation of MnO2 in tumor microenvironment, significantly improving the sensitivity of tumor imaging. Combined with the absence of background fluorescence in imaging of PLNPs, ultrahigh sensitivity is achieved. In orthotopic breast cancer model, the intraoperative tumor‐to‐normal tissue (T/NT) signal ratio of the nanoprobe is 58.8, about 9 times that of downconversion nanoparticles. The T/NT ratio of residual tumor (

Abstract Degrees of freedom and mutual coupling are two important factors to determine the ability of direction of arrival (DOA) estimation. Although coprime planar array (CPPA) has less mutual coupling than hourglass array (HA) and ladder array (LA), its positive and negative covariance corresponding lags are discontinuous, resulting in low degrees of freedom. In this study, we propose a generalized and symmetric coprime planar array (GSCA) by employing the symmetric property of the difference co‐array. By moving one subarray and introducing a supplementary subarray, we construct a connected virtual uniform rectangular array (URA). Through further optimizing the sensor number, the redundant lags are reduced and the array structure is more general. We show that the degrees of freedom are much higher than those of CPPA, HA and LA. Besides, the mutual coupling is close to CPPA, but less than HA and LA. The superiority of GSCA is verified by simulations.

Lead-free ceramic capacitors have the application prospect in the dielectric pulse power system due to the advantages of large dielectric constant, lower dielectric loss and good temperature stability. Nevertheless, most reported dielectric ceramics have limitation of realizing large energy storage density (Wrec) and high energy storage efficiency (η) simultaneously due to the low breakdown electric field (Eb), low maximum polarization and large remanent polarization (Pr). These issues above can be settled by raising the bulk resistivity of dielectric ceramics and optimizing domain structure. Therefore, we designed a new system by doping (Bi0.5Na0.5)0.7Sr0.3TiO3 into 0.9NaNbO3-0.1Bi(Ni0.5Zr0.5)O3 ceramics, which simultaneously obtained a higher bulk resistivity by decreasing the grain size and achieved a smaller Pr by optimizing domain structure, thus the better Eb of 530 kV/cm and Wrec of 6.43 J/cm3 were achieved, η was improved from 34% to 82%. Besides, the 0.4BNST ceramics show excellent temperature, frequency and fatigue stability under the conditions of 20–180 °C, 1–100 Hz and 104 cycles, respectively. Meanwhile, superior power density (PD = 107 MW/cm3), large current density (CD = 1070 A/cm2) and discharge speed (1.025 μs) were achieved in 0.4BNST ceramic. Finally, the charge-discharge performance displayed good temperature stability in the temperature range of 30 °C–180 °C. The above results indicated that the ceramics have potential practical value in the field of energy storage capacitor.

Abstract Rheumatoid arthritis (RA) is a common, chronic, and highly disabling autoimmune disease characterized by difficult treatment, long disease duration, and easy recurrence. The development and application of high‐sensitivity theranostic probes for RA that will facilitate precise monitoring of disease progression and enable effective treatment are currently hotspots in the field of RA theranostics. In this study, mZMI@HA, a dual‐triggered theranostics nanoprobe, is constructed based on near‐infrared persistent luminescence nanoparticles (NIR‐PLNPs) for precise RA treatment and therapeutic evaluation. This is the first reported use of high‐sensitivity autofluorescence‐free imaging based on NIR‐PLNPs for precise RA treatment and therapeutic evaluation. Compared with the NIR fluorescence imaging probe‐indocyanine green, the signal‐to‐background ratio of persistent luminescence (PersL) imaging is improved nearly 14‐fold. Using PersL imaging to guide photothermal therapy and controllable drug release through NIR/pH‐responsiveness, the progress of collagen‐induced RA is relieved. Additionally, the therapeutic evaluation of RA by PersL imaging is consistent with clinical micro‐computed tomography and histological analyses. This study demonstrates the potential of NIR‐PLNPs for high‐sensitivity imaging‐guided RA treatment, providing a new strategy for RA precise theranostics.

Abstract Coprime arrays (CPAs) have been found to be an effective configuration for adaptive beamforming (ABF). However, most ABF methods for CPAs are embedded with the spatial spectrum estimation technique, and therefore they usually deteriorate in the case of low signal‐to‐noise ratio (SNR), especially without prior information of interferences. To address this issue, a robust ABF method for CPAs via atomic‐norm‐based sparse recovery is proposed. This method begins with initialised virtual array interpolation to avoid aperture loss caused by ‘holes’, which is subsequently transformed to a matrix completion and denoising issue via a Toeplitz step. With the matrix’s Hermitian Toeplitz structure and the intrinsic sparsity of interferences, sparse recovery for the interference covariance matrix is introduced by subtracting the target signal and noise from the received signal and implemented by atomic‐norm minimisation. Concretely, this non‐convex process is decomposed into two convex steps and solved iteratively. Unlike previous methods, this method can interpolate the virtual array and estimate the steering vector of the target and the noise power simultaneously; consequently, the interference‐plus‐noise covariance matrix is reconstructed with merely some trivial entry selections without the need for the spatial spectrum. Furthermore, the optimality conditions and boundedness in this method are proven theoretically. Simulation results demonstrate the effectiveness of the proposed method and its advantages over previous methods under those non‐ideal conditions.

Electromagnetic vector sensor (EMVS) arrays bring an epochal opportunity for direction finding, as they enable the estimation of two-dimensional direction of arrival (2D-DOA) and polarization characteristics. In this paper, we revisit the 2D-DOA estimation problem in an EMVS rectangle array under multipath propagation. An improved subspace estimator is proposed, which addresses the rank-deficit problem through matrix arrangement, and the 2D-DOA and polarization parameters are estimated via combining the normalized vector cross-product with the least squares method. Our proposed method is suitable for a single snapshot scenario and offers superior accuracy compared to existing methods. To validate its effectiveness, several numerical simulations have been designed and conducted.

High-performance lead-free dielectric ceramics with simultaneously high energy storage density and power density are in high demanded for pulse power systems. To realize excellent energy-storage characteristics, a strategy to enhance antiferroelectricity and construct a local random field simultaneously was proposed in this study. Based on the above strategy, a series of (1-x)NaNbO3-xBi(Ni1/2Sn1/2)O3 [xBNS, x = 0.05, 0.10, 0.15, 0.20, and 0.22] solid solutions were designed and fabricated. An ultrahigh energy storage density (Utotal) of 7.35 J/cm3, and recoverable energy density (Urec) of 5.00 J/cm3 were achieved in the 0.10BNS ceramics. In addition, an adequate stability of energy storage properties at a range of temperatures (20–140 °C), frequencies (1–100 Hz), and fatigue test durations (1–104 cycles) were realized in 0.10BNS ceramics. 0.10BNS ceramics displayed a high current density of 1005 A/cm2, an ultrahigh power density of 100.5 MW/cm3, and an ultrashort discharge time of 46.5 ns? This remarkable performance not only justified our strategy but also confirmed 0.10BNS ceramics as a promising candidate for energy storage.

Abstract Persistent luminescence nanoparticles (PLNPs) are unique optical materials that emit afterglow luminescence after ceasing excitation. They exhibit unexpected advantages for in vivo optical imaging of tumors, such as autofluorescence-free, high sensitivity, high penetration depth, and multiple excitation sources (UV light, LED, NIR laser, X-ray, and radiopharmaceuticals). Besides, by incorporating other functional molecules, such as photosensitizers, photothermal agents, or therapeutic drugs, PLNPs are also widely used in persistent luminescence (PersL) imaging-guided tumor therapy. In this review, we first summarize the recent developments in the synthesis and surface functionalization of PLNPs, as well as their toxicity studies. We then discuss the in vivo PersL imaging and multimodal imaging from different excitation sources. Furthermore, we highlight PLNPs-based cancer theranostics applications, such as fluorescence-guided surgery, photothermal therapy, photodynamic therapy, drug/gene delivery and combined therapy. Finally, future prospects and challenges of PLNPs in the research of translational medicine are also discussed.

Angle estimation is a hot topic in multiple input multiple output (MIMO) radar. However, most of the existing algorithms are only focus on the scenario of ideal orthogonal transmission waveform. In engineering applications, however, non-orthogonal waveforms scenario is more practical. In this paper, we focus on the Cramer-rao bound (CRB) on angle estimation in MIMO radar with non-orthogonal waveforms. Firstly, the angle estimation model in bistatic MIMO radar with non-orthogonal transmit waveforms is given, and the general expression of CRB is deduced. Thereafter, the CRBs in some special cases are discussed, e.g., monostatic geometry, orthogonal transmit waveforms scenario. In addition, theoretical comparisons between the stochastic CRBs and the deterministic ones are presented. Finally, the computer simulations are carried out to verify the theoretically ones.

In this paper, to address the problem of array sensors failure, we propose a covariance matrix reconstruction method for direction-of-arrival (DOA) estimation. Firstly, we devise a diagnosis method to detect and locate the positions of failure sensors. According to the robustness of the array, the sensor failure scenarios are classified into redundant sensors failure and non-redundant sensors failure. Then, the corresponding DOA estimation method is adopted for two failure scenarios. The former can be solved using the virtual sensors in the difference coarray. As for the latter, the difference coarray has some holes, resulting in the decrease of available continuous virtual sensors or degrees of freedom (DOFs). Based on the matrix completion theory, the covariance matrix is extended to a high-dimensional Toeplitz matrix with missing data, where some elements are zero. We employ the mapping matrix, further use trace norm instead of the rank norm for convex relaxation to reconstruct the covariance matrix, thereby realizing the filling of the virtual sensor holes in difference coarray and restoring the DOFs. Compared with the sparsity-based methods, the proposed method can eliminate the effect of the discretization of the angle domain, and avoid regularization parameter selection. Finally, the root-MUSIC method is given for DOA estimation. Theoretical analysis and simulation results show that the proposed methods can alleviate the effect of array sensors failure and improve the estimation performance.

This article focus on logistics vehicle active localizing using multiple-input multiple output (MIMO) radar, and a fast localizing architecture that integrates edge computing and cloud platform is proposed. The core of the proposed methodology is to measure the angles of logistics vehicle using bistatic MIMO radars, which are configured with coprime electromagnetic vector sensors (EMVS). Unlike the existing localization systems, the proposed localizing architecture provides two-dimensional (2D) angle estimation, i.e., 2D direction-of-departure (DOD) estimation and 2D direction-of-arrival (DOA) estimation, and it offers additional polarization status of the logistics vehicle. A parallel factor (PARAFAC) estimator is developed. Firstly, it estimate the factor matrices via PARAFAC decomposition. Thereafter, the elevation angle estimation is accomplished via least squares (LS) technique, which are ambiguous due to the coprime property of the EMVS. The azimuth angle estimation are followed via vector cross-product. Besides, the polarization information of the targets can be obtained estimated via LS approach. The above process is accomplished at cloud platform. Finally, the localization of the logistics vehicle is achieved with the estimated 2D angles, which is computationally friendly and achieved via edge computing. Detailed analyses concerning degree-of-freedom, identifiability, complexity as well as Cramér-Rao bound (CRB) are provided. To show the effectiveness of the proposed architecture, numerical simulations have been designed.

Virtual reality, driverless cars, and robotics all make extensive use of 3D shape classification. One of the most popular ways to represent 3D data is with polygonal meshes. In particular, triangular mesh is frequently employed. A triangular mesh has more features than 3D data formats such as voxels, multi-views, and point clouds. The current challenge is to fully utilize and extract useful information from mesh data. In this paper, a 3D shape classification network based on triangular mesh and graph convolutional neural networks was suggested. The triangular face of this model was viewed as a unit. By obtaining an adjacency matrix from mesh data, graph convolutional neural networks can be utilized to process mesh data. The studies were performed on the ModelNet40 dataset with an accuracy of 91.0%, demonstrating that the classification network in this research may produce effective results.

Abstract (Ba1-x Bi0.67x Na0.33x )(Ti1-x Bi0.33x Sn0.67x )O3 (abbreviated as BBNTBS, 0.02 ⩽ x ⩽ 0.12) ceramics were fabricated via a traditional solid state reaction method. The phase transition of BBNTBS from tetragonal to pseudo cubic is demonstrated by XRD and Raman spectra. The BBNTBS (x = 0.1) ceramics have decent properties with a high ε r (~2250), small Δε/ε 25°C values of ±15% over a wide temperature range from -58 to 171 °C, and low tanδ ⩽ 0.02 from 10 to 200 °C. The basic mechanisms of conduction and relaxation processes in the high temperature region were thermal activation, and oxygen vacancies might be the ionic charge transport carriers. Meanwhile, BBNTBS (x = 0.1) exhibited decent energy storage density (J d = 0.58 J/cm3) and excellent thermal stability (the variation of J d is less than 3% in the temperature range of 25–120 °C), which could be a potential candidate for high energy density capacitors.

The resource-aware design is of great importance for the distributed multiple-input multiple-output (MIMO) radar in military applications, where multiple missions need to be fully and simultaneously performed constrained by the resource budget. Aiming at the joint of tracking existing targets and detecting new threats, a sensor scheduling integrated with power and bandwidth allocation strategy is put forward. The predicted posterior Cramer-Rao lower bound (PCRLB) in the worst case and the probability of detection are integrated as the optimization metric. Since such a problem is NP-hard, a modified particle swarm optimization (MPSO) for the sensor selection; embed with the greedy idea for the power and bandwidth allocation, is proposed for the solution exploration. The numerical simulations demonstrate that the MPSO is capable of providing close performance to the exhaustive search based method. More importantly, it possesses a lower computational burden and achieves better results compared with multi-start local search (MSLS)-based method.

In this paper, we investigated into the problem of target location in a bistatic multiple-input multiple-output (MIMO), whose transmit antennas and receive antennas are electromagnetic vector sensors (EMVS). Unlike the traditional linear scaler-sensor array, a linear EMVS array can offer two-diemensional (2D) direction estimation, thus a bistatic EMVS-MIMO radar provides (2D) direction-of-arrival and 2D direction-of-departure estimation. Besides, it is able to estimate 2D transmit/receive polarization angles of the targets. An propagator method (PM)-based estimator is proposed. Firstly, it estimate the propagator from the covariance matrix. The parameters are achieved via utilizing the estimation method of signal parameters via rotational invariance technique (ESPRIT) and the vector cross-product technique. The proposed estimator is computationally friendly since it does not involving eigendecomposition of high-dimensional data. Also, it may has similar (or even better) parameter estimation accuracy than the current EPSRIT-Like algorithm. Simulation results verify the effectiveness of the proposed PM estimator.

Target localization is a fundamental task of multiple-input multiple-output (MIMO) radar systems with numerous applications. In this paper, we investigate into the localization problem in a bistatic MIMO radar with electromagnetic vector sensors (EMVS). Unlike the traditional scaler sensors, an EMVS is able to offer two dimensional (2D) direction finding, and it can provide additional polarization characteristics of the source. Therefore, target localization in bistatic EMVS-MIMO radar system involves 2D direction-of-departure (2D-DOD) and 2D direction-of-arrival (2D-DOA) estimation. Besides, we can obtain transmit polarization characteristics as well as polarization characteristics of the targets. To exploit the tensor nature of the array measurement after matched filters, a tensor subspace algorithm is developed, which estimates the target parameters via cross-product technique from tensor subspace. The proposed algorithm, which obtains closed-form solutions for parameters estimation, shows more accurate performance than the existing algorithm. Numerical simulations verify the effectiveness and improvement of the proposed algorithm.

Broomcorn millet is one of the oldest crops cultivated by human that has strong abiotic stress tolerance. To facilitate genome assisted breeding of this and related species, the authors report its genome assembly and conduct comparative genome structure and evolution analyses with foxtail millet.

Direction-of-arrival (DOA) estimation is the preliminary stage of communication, localization, and sensing. Hence, it is a canonical task for next-generation wireless communications, namely beyond 5G (B5G) or 6G communication networks. Both massive multiple-input multiple-output (MIMO) and millimeter wave (mmW) bands are emerging technologies that can be implemented to increase the spectral efficiency of an area, and a number of expectations have been placed on them for future-generation wireless communications. Meanwhile, they also create new challenges for DOA estimation, for instance, through extremely large-scale array data, the coexistence of far-field and near-field sources, mutual coupling effects, and complicated spatial-temporal signal sampling. This article discusses various open issues related to DOA estimation for B5G/6G communication networks. Moreover, some insights on current advances, including arrays, models, sampling, and algorithms, are provided. Finally, directions for future work on the development of DOA estimation are addressed.

Aiming at low degrees of freedom (DOF) and high mutual coupling (MC) of the existing sparse arrays, an enhanced generalized nested array (EGNA) is proposed in this paper. Specifically, the proposed array adds a single antenna on the basis of generalized nested array (GNA), and the difference of coprime factors is employed as the spacing between the second subarray and the additional antenna. Then, the values of the coprime factors are analyzed in detail, which indicates that Yang-NA can be explained as a special case. Compared with the majority of the existing sparse arrays, EGNA not only has the closed-form expressions of the physical antenna locations, consecutive lags, and unique lags, but also significantly increases DOF and reduces MC. In view of the above advantages, EGNA can obtain superior performance in direction of arrival (DOA) estimation. Numerical simulation results verify the rationality and superiority of the proposed nested array.

Ideal transmitting and receiving (Tx/Rx) array response is always desirable in multiple-input multiple-output (MIMO) radar. In practice, nevertheless, Tx/Rx arrays may be susceptible to unknown gain-phase errors (GPE) and yield seriously decreased positioning accuracy. This paper focuses on the direction-of-departure (DOD) and direction-of-arrival (DOA) problem in bistatic MIMO radar with unknown gain-phase errors (GPE). A novel parallel factor (PARAFAC) estimator is proposed. The factor matrices containing DOD and DOA are firstly obtained via PARAFAC decomposition. One DOD-DOA pair estimation is then accomplished from the spectrum searching. Thereafter, the remainder DOD and DOA are achieved by the least squares technique with the previous estimated angle pair. The proposed estimator is analyzed in detail. It only requires one instrumental Tx/Rx sensor, and it outperforms the state-of-the-art algorithms. Numerical simulations verify the theoretical advantages.

This paper addresses a partial spatial-differencing (PSD) approach for the direction of arrival estimation in a low-grazing angle (LGA) condition. By dividing the sample covariance matrix into several column subvectors, we first form the corresponding reconstructed subarray covariance matrices (RSCMs). We then calculate the spatial differencing matrix for the noise parts of RSCMs, while the non-noise parts are kept completely. That is, we build a PSD matrix. Compared with the existing spatial smoothing and full spatial-differencing methods, the PSD approach can use all the data information of the sample covariance matrix and also suppress the effect of additive white or colored noise more effectively. Simulation results show that our method provides a higher estimation accuracy and resolution than the state-of-the-art methods.

The two-level nested array geometry, which systematically nests two uniform linear subarrays, is proved to offer O(N2) degrees of freedom (DOFs) with only N sensors. In this paper, a novel sparse extension array geometry for nested multiple-input multiple-output radar is proposed to provide O(N4) DOFs with N sensors. In the proposed geometry, both the transmitter and receiver are equipped with the two-level nested arrays, where we particularly extend the inter-element spacing of the transmitter with a sparse extension factor, leading to a great increase of DOF. Furthermore, we derive the closed-form expressions for the sensor locations and the available DOFs. Spatial smoothing-based MUSIC algorithm is employed to validate the effectiveness and superiority of the proposed sparse extension array for direction of arrival estimation.

Multipath effect cause serious performance degradation in low-altitude target detection. To overcome the negative multipath effect in a low-altitude environment, a novel weighted detector based on the estimated signal-to-noise ratio (ESNR) is proposed. By introducing the multipath intensity factor, the signal models for different radar systems in the low-altitude environment are established. Then, inspired by the recent development of cognitive theory, the weighted detector based on ESNR is proposed to strengthen the high SNR channels and suppress the low SNR channels. The eigenfunction method is adopted to derive the theoretical detection probability of the proposed detector. Simulation results suggest that, compared with the traditional equal weight detector, the proposed detector can effectively overcome the negative influence of multipath and improve the detection performance in the low-altitude environment. It is also proved that in most cases, with the proposed method, multi-input multi-output (MIMO) radar has better detection performance than that of other radars in the low-SNR region.

Direction finding is a hot research area in radar and sonar systems. In the case of q ≥ 2, the 2qth-order cumulant based direction of arrival (DOA) estimation algorithm for the 2q-level nested array can achieve high resolution performance. A virtual 2qth-order difference co-array, which contains O(N2q) virtual sensors in the form of a uniform linear array (ULA), is yielded and the Gaussian noise is eliminated. However, some virtual elements are separated by the holes among the 2qth-order difference co-array and cannot be fully used. Even though the application of the multi-frequency method for minimum frequency separation (MFMFS) can fill the holes with low computation complexity, it requires that the number of frequencies must increase with the number of holes. In addition, the signal spectra have to be proportional for all frequencies, which is hard to satisfy when the number of holes is large. Aiming at this, we further propose a multi-frequency method for a minimum number of frequencies (MFMNF) and discuss the best frequency choice under two specific situations. Simulation results verify that, compared with the MFMFS method, the proposed MFMNF method can use only one frequency to fill all the holes while achieving a longer virtual array and the DOA estimation performance is, therefore, improved.

This paper proposes an improved spatial differencing (ISD) scheme for two-dimensional direction of arrival (2-D DOA) estimation of coherent signals with uniform rectangular arrays (URAs). We first divide the URA into a number of row rectangular subarrays. Then, by extracting all the data information of each subarray, we only perform difference-operation on the auto-correlations, while the cross-correlations are kept unchanged. Using the reconstructed submatrices, both the forward only ISD (FO-ISD) and forward backward ISD (FB-ISD) methods are developed under the proposed scheme. Compared with the existing spatial smoothing techniques, the proposed scheme can use more data information of the sample covariance matrix and also suppress the effect of additive noise more effectively. Simulation results show that both FO-ISD and FB-ISD can improve the estimation performance largely as compared to the others, in white or colored noise conditions.

In this paper, we propose a computationally efficient spatial differencing matrix set (SDMS) method for two-dimensional direction of arrival (2D DOA) estimation with uniform rectangular arrays (URAs) in a low-grazing angle (LGA) condition. By rearranging the auto-correlation and cross-correlation matrices in turn among different subarrays, the SDMS method can estimate the two parameters independently with one-dimensional (1D) subspace-based estimation techniques, where we only perform difference for auto-correlation matrices and the cross-correlation matrices are kept completely. Then, the pair-matching of two parameters is achieved by extracting the diagonal elements of URA. Thus, the proposed method can decrease the computational complexity, suppress the effect of additive noise and also have little information loss. Simulation results show that, in LGA, compared to other methods, the proposed methods can achieve performance improvement in the white or colored noise conditions.