In modern warfare, low-altitude unmanned aerial vehicle (UAV) swarms have emerged as a dominant operational paradigm, posing significant challenges to radar detection systems. The UAV swarms typically exhibit low radar cross section (RCS), high density, and low-altitude flight characteristics, leading to three key challenges for radar systems: (i) low signal-to-noise ratio (SNR) of radar echoes, (ii) unresolvable targets within the same range-Doppler-angle cell, and (iii) elevation-dimension multipath interference. To address these challenges, this study proposes a detection and localization strategy that integrates long-time coherent integration (LTCI) with an enhanced reweighted atomic norm minimization (RAM) method, simultaneously enhancing both echo SNR and radar resolution. First, we establish a multipath signal model based on multi-reflection-center that better conforms to real-world terrain environments. Based on this sophisticated model, we employ the Keystone transform coupled with exhaustive acceleration compensation (KT-EAC) to eliminate range cell migration (RCM) and Doppler frequency cell migration (DFCM) during the long-time integration process. To decouple the direction-of-arrival (DOA) estimation problem for spatially adjacent mixed coherent and non-coherent sources, caused by the high-density characteristics of UAV swarms and multipath interference, we employ a larger signal bandwidth to achieve higher range resolution. This enables range-domain separation of intra-swarm target echoes, thereby transforming the problem into multiple DOA estimation subproblems for coherent source groups. To achieve enhanced discrimination between coherent direct-path and multipath echoes, we propose a Hankel-Toeplitz block matrix-based RAM (HT-RAM) method for super-resolution angle estimation, with extension to multiple snapshots. Unlike the RAM method with high computational complexity, the proposed approach achieves both reduced computational burden and enhanced estimation performance. Furthermore, we derive the Cramér-Rao Lower Bound (CRLB) for multi-reflection-center model. Finally, both simulated and field-measured data processing results demonstrate the higher accuracy, stronger robustness and moderate computational efficiency of the proposed methods compared with the benchmark approaches.

Accurate recognition of radar jamming is the foundation for mastering the battlefield electromagnetic situation and implementing effective jamming countermeasures. Existing radar jamming recognition models are limited to predefined categories and can only identify fixed types of jamming, which fails to meet the requirements of diversified and dynamic jamming recognition in actual battlefield scenarios. Drawing inspiration from Contrastive Language-Image Pre-training (CLIP), a classic multimodal work, this paper proposes text-guided radar jamming recognition, a radar jamming recognition paradigm dubbed RaJa-CLIP. Unlike conventional jamming recognition models that leverage semantic-free digital IDs as supervision signals, the proposed approach adopts jamming description texts with abundant semantic information for supervised learning. This mechanism guides the recognition model to capture category and attribute information embedded in the texts, thereby enabling a jamming recognition paradigm based on custom text labels. Furthermore, this paper constructs a comprehensive “jamming signal-text description” dataset to facilitate the feature-aligned training of jamming and text. An attribute-supervised contrastive learning method is also proposed to explicitly guide the model in learning jamming attributes, which enhances the model's recognition performance for specific attributes. Experimental results demonstrate that the recognition model trained with the proposed method exhibits flexible jamming recognition capabilities. It can simultaneously support multiple tasks, including signal type recognition, jamming type recognition, zero-shot jamming recognition, and jamming recognition for unknown signal types, while maintaining high recognition accuracy.

Aiming at the issues where traditional direction-of-arrival (DOA) estimation algorithms experience substantial performance degradation in low signal-to-noise ratio environments, and deep learning-based DOA estimation methods rely on massive training data with prolonged model training cycles, this paper proposes two efficient and high-precision DOA estimation methods based on ensemble learning. By formulating DOA estimation as a multi-label classification problem and leveraging the classification chain paradigm, data-driven models, classification chain-random forest (CC-RF) and classification chain-eXtreme gradient boosting (CC-XGBoost), are constructed, which are capable of handling multi-label classification tasks. To verify the effectiveness of the proposed methods, a multi-dimensional comparative experiment is designed to benchmark their performance against the traditional multiple signal classification (MUSIC) algorithm and a convolutional neural network (CNN) model. Experimental results indicate that in both single-source and multi-source scenarios, the proposed CC-RF algorithm exhibits excellent performance, achieving DOA estimation accuracy comparable to the MUSIC algorithm; in multi-source estimation scenarios, both proposed models demonstrate strong noise adaptability. Compared with the traditional MUSIC and CNN algorithms, the estimation error of the CC-XGBoost and CC-RF models is reduced by up to nearly 30 times while maintaining low time complexity, with the single estimation time reduced by approximately 90% compared to traditional methods. This study provides a technical pathway for DOA estimation in complex environments and holds significant applicationvalue in fields such as radar detection and wireless communication.

Programmable metasurfaces enable two-dimensional direction-of-arrival (DOA) estimation using reconfigurable coding instead of fully digital element-wise sampling. However, coding obscures the shift-invariant structure of the underlying uniform rectangular array (URA), while colored noise distorts the covariance eigenspace and source coherence causes rank deficiency. This paper proposes a covariance-reconstruction framework for gridless 2-D DOA estimation under colored noise and coherent sources. Signal-free noise samples are first extracted by projecting the measurements onto the left null space of the coding matrix. A Hermitian Toeplitz model is then used to estimate and remove the colored-noise covariance. Subsequently, a regularized covariance-domain inverse reconstructs the equivalent uncoded URA covariance. Forward-backward spatial smoothing restores the signal rank, and total least-squares ESPRIT provides automatically paired azimuth and elevation estimates without angular grid search. The identifiability of the noise reconstruction and the stability of covariance recovery are characterized by the rank of the Toeplitz regression matrix and the conditioning of the coding matrix, respectively. Numerical results demonstrate that the proposed method achieves lower RMSE and higher detection probabilities than coded-domain MUSIC, OMP, SBL, and ANM, particularly with limited snapshots, strong colored noise, and highly coherent sources.

To address the limitations of traditional coherent sources direction-of-arrival (DOA) estimation methods, which rely on rank recovery of covariance matrices and fail to perform effectively in complex environments, and the instability of neural network models caused by insufficient spatiotemporal feature extraction during coherent DOA estimation, this paper proposes a hybrid neural network combining convolutional neural network (CNN) and Transformer to jointly extract spatiotemporal features from array-received signals. The proposed model treats DOA estimation as a regression problem, directly modeling the mapping relationship between received signals and DOA. By using array-received signals as input, the model employs CNN to extract spatial features firstly. The resulting feature maps are restructured and fed into a multi-head attention mechanism to capture spatial relationships between array elements. Finally, the learned features are input into a Transformer model to capture long-range dependencies in received signals across different snapshots from the same array element, thereby suppressing temporal coherence. By combining CNN�s local feature extraction and Transformer's global dependency modeling, this approach overcomes the limitation of single-model architectures in simultaneously capturing local and global features, significantly improving the representation capability for complex coherent signals. Experimental results demonstrate that the proposed method exhibits strong robustness and reliability under challenging conditions such as low signal-to-noise ratio, limited snapshots, and multiple sources.

The coherent source can cause the rank deficiency of the receiving covariance matrix of the radar signal, which degrades the performance of conventional MUSIC-based Direction of Arrival (DOA) estimation. Existing Toeplitz reconstruction methods can alleviate this problem, but they remain sensitive to noise and suffer from reduced accuracy under low signal-to-noise ratio (SNR) and limited-snapshot conditions. To address these limitations, this paper proposes a coherent-source DOA estimation method based on snapshot cross-correlation matrix, Schur decomposition, and Toeplitz reconstruction. The method first introduces a time-delay parameter τ to compute the cross-correlation matrix of received signals across different snapshots, thereby suppressing noise and enhancing the distinguishability of signal features. Next, to accommodate the non-Hermitian property of the cross-correlation matrix, Schur decomposition is employed in place of conventional eigenvalue decomposition, and a representative signal matrix is constructed to preserve the directional information of the sources. Finally, Toeplitz reconstruction is performed on the signal matrix to effectively decorrelate coherent sources, and DOA estimation is accomplished via spatial spectrum construction and peak search. Simulation results show that the proposed method outperforms MUSIC, spatial smoothing, and Toeplitz reconstruction in terms of accuracy and stability under low-SNR and limited-snapshot conditions.

In this letter, we propose a deep learning-based off-grid Direction of Arrival (DOA) estimation method for low Signal-to-Noise Ratio (SNR) scenarios. Specifically, we develop a dual-branch neural network with residual connections that processes frequency-domain features, consisting of a coarse classification branch and a fine regression branch. The classification branch employs a multi-label approach to obtain on-grid results, while the regression branch predicts the residual between the classification outputs and ground-truth angles. This structural design effectively leverages classification results to avoid convergence difficulties associated with direct off grid angle prediction, thereby enhancing DOA estimation accuracy. Simulation results demonstrate that under low SNR conditions, the proposed method outperforms existing approaches, including both classical model-based and other deep learning-based methods.

This paper proposes a Direction-of-Arrival (DOA) estimation method based on Deep Convolutional Autoencoder (DCAE). This method constructs a DCAE to map the covariance matrix of the received signals of a sparse array into a feature space and then reconstructs it into the covariance matrix of the received signals of a uniform linear array. Subsequently, the DOA estimation is performed in combination with the MUSIC algorithm, which effectively increases the degrees of freedom of the sparse array and better solves the DOA estimation problem under the underdetermined condition of the sparse array. To address the issues of low estimation accuracy and poor angular resolution in traditional algorithms for sparse arrays, a DOA estimation method based on Deep Convolutional Neural Network (DCNN) is proposed. This method extracts the mapping from the covariance matrix of the received signals of the physical elements of the sparse array to the angles of arrival, achieving higher accuracy and higher resolution DOA estimation.

Direction of arrival (DOA) estimation is an important research focus, with applications in many fields such as wireless communication and radar localization. Particularly, maximum likelihood-based DOA estimation methods have drawn significant attention from researchers owing to the strong robustness, versatility, and practical applicability, but suffer from high complexity. To address these issues, under the deterministic maximum likelihood (DML) criterion, DOA estimation is transformed into a convex constrained optimization problem that can be solved via semidefinite programming (SDP), yielding a gridless method named DML-SDP. Then, combining the alternating direction method of multipliers (ADMM), another more efficient and gridless method named DML-ADMM is proposed. In simulations or real-world radar localization with multipath interference, both DML-SDP and DML-ADMM exhibit highly accurate estimation of targets.

To address the severe performance degradation of Direction of Arrival (DOA) estimation under few-snapshot conditions, we propose a Space-Time Cross-Modal Attention Network, ST-CMANet. The method formulates DOA estimation as a multi-label classification task. It uses a two-branch architecture: a spatial branch that a residual network with embedded Convolutional Block Attention Module (CBAM) to extract multi-level spatial information from the covariance matrix; and a temporal branch that combines 1D convolutions with a Vision Transformer (ViT) encoder to capture local and global temporal dependencies from the raw I/Q signals. We then introduce a cross-modal bidirectional attention mechanism to enable deep interaction between spatial and temporal features. Finally, an attention-based pooling mechanism aggregates sequence features into global representations; after feature fusion, the network outputs the DOA estimates. Simulation results show that under few-snapshot scenarios ST-CMANet outperforms traditional algorithms and existing deep-learning methods.

Small-sized and high-precision velocity receiving sensors offer significant potential for direction-of-arrival (DOA) estimation in multiple-input multiple-output (MIMO) radar systems. This paper addresses the challenge of twodimensional (2D) angle estimation in a conformal MIMO radar architecture that employs a scalar transmitting array and a velocity-based receiving array. To this end, we propose a novel coarse-to-refined estimation strategy for 2D-DOA estimation. In the first stage, a coarse estimate is obtained by leveraging an enhanced rotational invariance technique that exploits the velocity diversity inherent in the receiving sensors. In the second stage, the initial estimates are refined using the spatial diversity of the full array configuration. Unlike existing methods, the proposed strategy supports arbitrary array geometries, provides closed-form solutions, and inherently resolves the pairing problem between azimuth and elevation angles. Extensive simulations validate the effectiveness and robustness of the proposed algorithm, achieving a favorable trade-off between complexity and accuracy compared to state-of-the-art methods.

Resource management technologies offer significant potential for enhancing system performance. This paper proposed an efficient joint node selection and power allocation (JNSPA) strategy to improve the detection performance of a multisite multiple input multiple output (MIMO) Radar System operating in multi-beam modes under multi-airspace multi-target scenarios. Our approach derives explicit expressions for detection probability based on the Neyman-Pearson criterion, distinctively incorporating the detection probability of fluctuating targets in dynamic multi-airspace environments. Employing the Max-min criterion, we optimize the detection performance of the most challenging targets, aiming to elevate the lower bound of the system's overall performance. Considering the practical resource constraints, the proposed JNSPA is formulated as a discontinuous, non-convex mixed-integer nonlinear problem. To solve this NP-hard problem, a three-stage algorithm is proposed: initial model preprocessing to approximate the problem via the squeeze theorem and continuous relaxation of Boolean parameters, followed by convex optimization in two steps to achieve an approximate optimal solution for node selection, culminating in power allocation through convex optimization to yield the final joint resource optimization solution. Simulation results confirm that our JNSPA strategy offers excellent effectiveness and efficiency with reduced computational burden, achieving near-optimal solutions. Additionally, a sensitivity analysis of the parameters influencing detection performance is presented.

In recent years, sparse arrays have made considerable strides in resolving uncorrelated sources. However, the ubiquitous coherent sources across various emerging applications pose unique challenges for direction-of-arrival (DOA) estimation with sparse arrays. In this work, based on insight into the structure of the source covariance matrix, we first propose an effective strategy to achieve decorrelation by partitioning the diagonal and off-diagonal elements in the source covariance matrix. Then, we introduce two Toeplitz matrix reconstruction programs tailored for DOA estimation with sparse arrays. On one hand, we directly implement the decorrelation operation on the covariance matrix of sparse arrays, and further construct a Toeplitz matrix reconstruction program via virtual array interpolation for enhanced DOA estimation. On the other hand, we relate the sparse array to the hypothetical uniform linear array (ULA) through the compressed matrix, and perform decorrelation operation on the covariance matrix of the hypothetical ULA. Following this, a Toeplitz matrix reconstruction program via physical array interpolation is formulated for DOA estimation. Unlike the prevailing decorrelation techniques, the proposed algorithms can precisely estimate coherent sources without losing degrees of freedom and array aperture. Moreover, the Cram & eacute;r-Rao bound pertinent to this problem is derived. Numerical simulations demonstrate that the proposed algorithms outperform their competitors in estimating coherent sources.

Integrated Sensing and Communication (ISAC)-enabled Roadside Units (RSUs) encounter significant performance trade-offs between target sensing and multi-user communication in complex urban environments, where conventional optimization methods are prone to converging to local optima and joint optimization methods often yield sub-optimal results due to conflicting objectives. To address the challenge of trade-off between sensing and communication performance, this paper proposes a hierarchical beamforming optimization solution designed to tackle joint sensing–communication problems in such scenarios. The overall optimization problem is decomposed into a two-level “leader-follower” structure. In the leader layer, we introduce a max–min strategy based on the bisection method to transform the non-convex Signal-to-Interference-plus-Noise Ratio (SINR) optimization problem into a second-order cone constraint problem and solve the communication beamforming vector. In the follower layer, the Signal-to-Clutter-plus-Noise Ratio (SCNR) maximization problem is converted into a Semi-Definite Programming (SDP) problem solved via the CVX toolbox. Additionally, we introduce a “spatiotemporal resource isolation” mechanism to project the sensing beam onto the null space of the communication channel. The hierarchical optimization solution jointly optimizes communication SINR and sensing SCNR, enabling an effective balance between sensing accuracy and communication reliability. Simulation results demonstrate the proposed method’s effectiveness in simultaneously improving sensing accuracy and communication reliability.

This study explores a novel radar single-target detection method that relies on Convolutional Neural Networks (CNNs). This method not only determines the existence of a target but also effectively estimates target parameters. Initially, this study preprocesses radar echo data to obtain a one-dimensional fast-time range profile of the target. Subsequently, we appropriately convert these data into an image format and utilize all-zero and zero-one vectors as output labels for classification training. The CNN undergoes training with fine-tuned hyperparameters to ensure the error between input and output falls within an acceptable range, thereby determining the training network parameters. Ultimately, these trained network parameters are employed for target detection and distance parameter estimation in actual received data. Compared to traditional radar target detection methods, simulation results demonstrate that the proposed approach exhibits significant advantages in terms of detection accuracy.

DOA estimation is one of the core tasks in radar signal processing and of great significance in communication, military, and other daily activities. The traditional DOA estimation algorithms has a high time cost for angle estimation, while most available data-driven estimation methods cannot achieve high-precision estimation since converting DOA estimation into multi-label classification task. Based on this, this paper has proposed a dual layer DOA estimation model based on Support Vector Machine(SVM) classification and Random Forest (RF) regression (SVM-RF) for exactly and rapidly estimating the angle of signal sources received from the Radar antenna array system, which transforms the DOA estimation problem into regression task. This method extracts triangular data on the signal covariance matrix as feature input, first divides the dataset into several small sample sets using SVM, and then it conducts RF regression training separately. Six experiments were conducted to verify the validity, reliability and robustness in different SNRs and snapshots for single and multi-targets. Simulation results indicate that the SVM-RF proposed in this paper has implemented the super-resolution DOA Estimation with the estimation accuracy comparable to the classical algorithm MUSIC and CNN. Moreover, SVM-RF has low computational cost and can perform real-time DOA estimation.

In the domain of vehicular engineering, multipath detection plays a critical role in the accurate assessment of the environment. This paper introduces a Shapley value-based power resource allocation (SVPRA) method developed for low-grazing angle detection in distributed multiple-input multiple-output (D-MIMO) radar sensor networks (RSN). The SVPRA leverages multipath echoes for improved detection performance through coordinated power resource allocation (PRA). A systematic multipath scattering model with uncertainty identifies four independent spatial paths, highlighting the impact of multipath effects (ME) fluctuations on detection. The PRA is then formulated as a non-convex Max-min optimization problem, incorporating the signal-to-interference plus noise ratio (SINR) indicator and modeling cognitive collaboration detection as a cooperative game. The application of the PRA rule has been mathematically proven to consistently enhance the detection performance. To address convergence challenges in multi-target scenarios, a fine-tuning method is introduced, providing a provisional iteration outcome, succeeded by a greedy selection process to achieve a feasible solution. Simulation results validate that the SVPRA method effectively enhances detection performance while reducing the system's timeliness load.

To address the issue of low-elevation target height measurement in the Multiple Input Multiple Output (MIMO) radar, this paper proposes a height measurement method for meter-wave MIMO radar based on transmitted signals and receive filter design, integrating beamforming technology and cognitive processing methods. According to the characteristics of beamforming technology forming nulls at interference locations, we assume that the direct wave and reflected wave act as interference signals and hypothesize a direction for a hypothetical target. Then, the data received are processed to obtain the height of low-elevation-angle targets using a cognitive approach that jointly optimizes the transmitted signal and receive filter. Firstly, a signal model for the meter-wave MIMO radar based on the transmit weight matrix is established under low-elevation scenarios. Secondly, the signal model is analyzed and transformed. Thirdly, the beamforming algorithm that jointly optimizes the transmitted signals and receive filter is derived and analyzed. The algorithm maximizes the output Signal-to-Interference-plus-Noise ratio (SINR) of the receiver by designing the transmit weight matrix and receive filter. The optimization problem based on the SINR criterion is non-convex and difficult to solve. We transformed it into two sub-optimization problems and approximated the optimal solution through an alternating iteration algorithm. Finally, the proposed height measurement algorithm is compared with the Generalized Multiple Signal Classification (GMUSIC) and Maximum Likelihood (ML) height measurement algorithms. Simulation results show that the proposed algorithm can realize the height measurement of low-elevation targets. Compared to the GMUSIC and ML algorithms, it demonstrates superior performance in terms of computational complexity and multi-target elevation estimation.

The emerging sparse arrays achieve enhanced direction of arrival (DOA) estimation by flexibly deploying sensors and fully extracting the structural information contained in the incident sources. However, the existing DOA estimation algorithms for sparse arrays typically yield satisfactory performance only in ideal or single nonideal scenarios. In this work, we address the issue of DOA estimation for sparse arrays under the coexistence of gain-phase errors and nonuniform noise. The analysis of the negative impact of these two types of nonidealities on virtual array processing motivates us to develop new algorithm. Specifically, with the perturbation of gain-phase errors, a least squares optimization program is first constructed to solve the nonuniform noise power. Then, based on the initial gain errors obtained by exploiting the diagonal entries in the denoised covariance matrix, we implement the iterative estimation of DOAs and gain-phase errors with the aid of the eigenstructure-based subspace approach. To improve the DOA estimation accuracy, we formulate the difference coarray interpolation problem and introduce the truncated nuclear norm minimization to recover the missing information. The developed algorithm can overcome the effects of gain-phase errors and nonuniform noise simultaneously. Numerical simulations demonstrate that the developed algorithm outperforms its competitors.

Low-grazing angle detection (LGAD) is a critical challenge in radar systems due to the complex propagation environment and the high probability of signal cancellation. Multisite multiple input multiple output radar systems offer a solution by forming multiple orthogonal beams, each illuminating targets from different angles, thereby enhancing detection capabilities. This article proposes a novel power allocation strategy, LGAD-based power allocation (LGAD-PA), to optimize system efficiency in detecting multiple targets under low-grazing angle conditions. The strategy is based on a Neyman-Pearson detection model that accounts for multipath effects, imperfect waveforms, and measurement uncertainties. The signal-to-interference-plus-noise ratio is derived as the optimization metric, with the multipath distance difference incorporated to enhance the robustness of the max-min optimization model. The LGAD-PA problem is shown to be nonconvex, nonlinear, and nondifferentiable with respect to power variable constraints. To address this, an efficient two-stage technique, the smoothed proximal inexact augmented Lagrange multiplier method, is proposed. This method uses a smooth approximation to ensure a continuously differentiable utility function, enabling near-optimal power allocation with guaranteed convergence. Extensive simulations demonstrate the effectiveness and efficiency of the proposed LGAD-PA strategy in detection performance improvement.