In satellite-based tactical communication systems, non-cooperative radio frequency (RF) communication signals are widely used, but their detection remains highly challenging in complex electromagnetic environments characterized by low signal-to-noise ratios, multi-signal coexistence, and dynamic interference. This paper focuses on the most widely used non-cooperative communication protocols—Link 11 and Link 4A—and proposes a cross-modal detection approach that maps signals into the image domain through high-resolution time-frequency analysis, enhancing detection robustness and interpretability. Additionally, we construct SC2SM, the first benchmark dataset specifically designed for communication signal detection, comprising 14,791 time-frequency images and over 85,000 annotated bounding boxes, comprehensively covering aliasing, strong interference, and other complex environmental scenarios. Furthermore, we introduce YOLO-Link, the first optimized object detection framework for this task, which enables efficient deployment on Internet of Things (IoT) edge computing platforms. Extensive experimental results demonstrate that, after training on the SC2SM dataset, YOLO-Link achieves state-of-the-art performance in communication signal detection, outperforming existing methods by 4.1% in Recall and achieving real-time inference at 40 FPS on IoT edge computing platforms, striking an optimal balance between detection accuracy and computational efficiency. This study provides technical support for intelligent detection and monitoring of non-cooperative communication signals and promotes the application of cross-modal learning in complex electromagnetic environments. The code and dataset are available at.

Covariance matrix estimation is of great importance in statistical signal processing. This paper considers covariance matrix estimation from correlated complex sub-Gaussian samples via the shrinkage estimator. We establish non-asymptotic error bounds for this estimator in both tail and expectation forms. Our theoretical results demonstrate that the error bounds depend on the signal dimension, the sample size, the shape parameter, and the shrinkage coefficient$\alpha$. These results reveal that the shrinkage estimator can reduce the sample complexity of the standard sample covariance matrix estimator when the target matrix is reliable and$\alpha$is properly chosen.

The Capon method is one of the classical direction-of-arrival (DOA) estimation methods in array signal processing. The standard analysis of the additional bias of this method is asymptotic, which assumes the number of snapshots$K$goes to infinity. This paper provides a non-asymptotic analysis for the additional bias by employing some tools from high-dimensional probability and perturbation analysis of optimization problems. We establish upper bounds for the additional bias in both expectation and tail forms, which reveal that the additional bias has an error rate of$O(K^{-\frac{1}{2}})$when the number of snapshots satisfies a certain condition. We demonstrate our results by some numerical experiments.

Multi-baseline circular synthetic aperture radar (C-SAR) tomography is an important three-dimensional (3-D) radar imaging mode since it allows for omni-directional 3-D reconstruction of targets. Typically, this imaging mode splits the full-aperture data into multiple narrow-apertures to be processed separately due to the sensitivity to elevation angle and imaging height. However, the repeated one-dimensional (1-D) elevation inversion of all imaged pixels for each sub-aperture also leads to more processing time and more parameter estimation uncertainties. In this paper, a new C-SAR tomography framework based on scattering phase correction (SPC) is presented. Our main idea is to use 1-D elevation inversion to estimate the exact height of the distorted scattering points in two-dimensional (2-D) full-aperture image, and derive the imaging height transformation formula. Then these distorted scattering points of different heights are transformed to the proper heights respectively. As a result, the elevation inversion only needs to be done once for the whole framework and does not need to be done for each sub-aperture. Besides, a combination of two separate processing chains (i.e., fast coherent imaging and slices transform imaging) is used to minimize the 3-D reconstruction errors caused by the imaging height transformation and 1-D elevation inversion. Numerical and outdoor measurement results of real-world complex targets are presented to demonstrate the usefulness of the proposed framework.

In this paper, we characterize data-time tradeoffs of the proximal-gradient homotopy method used for solving linear inverse problems under sub-Gaussian measurements. Our results are sharp up to an absolute constant factor. We demonstrate that, in the absence of the strong convexity assumption, the proximal-gradient homotopy update can achieve a linear rate of convergence when the number of measurements is sufficiently large. Numerical simulations are provided to verify our theoretical results.

Compressed sensing (CS) based imaging technique is considered to be an effective solution for high-resolution radar imaging due to the sparse distribution of the scatterers. Nevertheless, the unoptimized CS based synthetic aperture radar (SAR) or inverse SAR (ISAR) imaging approach may suffer from the computationally intensive problem when apply it to wideband radar signatures of electrical large-scale targets. In this paper, a two-dimensional (2-D) superresolution imaging technique based on peak search and compressed sensing (PS-CS) is presented. A peak search strategy is first developed to solve the problem of high computational complexity of CS based method in scattering parameter estimation. Superresolution imaging result is then achieved by extrapolating the estimated parameters of scattering along with the observing angle dimension and frequency dimension. The numerical and measurement data acquired from different man-made targets are presented to demonstrate the feasibility and usefulness of the proposed technique for supperresolution radar imaging.

In this letter, we present a sharp algorithmic analysis for alternating projected gradient descent which is used to solve the covariate adjusted precision matrix estimation problem in high-dimensional settings. By introducing a new analytical tool (the generic chaining), we remove the impractical resampling assumption used in the literature. The new analysis also demonstrates that this algorithm not only enjoys a linear convergence rate in the absence of convexity, but also attains the minimax rate with optimal order of sample complexity. Our results, meanwhile, reveal a time-data tradeoff in this problem. Numerical experiments are provided to verify our theoretical results.

A generalized sum-difference expansion scheme is proposed to construct sparse arrays based on the fourth-order difference co-array with increased degrees of freedom (DOFs). Different from existing structures, both the second-order sum and difference co-arrays are exploited in array construction under this scheme, leading to a large consecutive fourth-order difference co-array with its number of uniform DOFs (uDOFs) derived. To optimize the provided uDOFs, required design properties of the initial prototype arrays are discussed. Three examples are then provided to demonstrate its superior performance over existing structures in both resolution capacity and estimation accuracy.

This paper is concerned with the problem of recovering a structured signal from a relatively small number of corrupted random measurements. Sharp phase transitions have been numerically observed in practice when different convex programming procedures are used to solve this problem. This paper is devoted to presenting theoretical explanations for these phenomena by employing some basic tools from Gaussian process theory. Specifically, we identify the precise locations of the phase transitions for both constrained and penalized recovery procedures. Our theoretical results show that these phase transitions are determined by some geometric measures of structure, e.g., the spherical Gaussian width of a tangent cone and the Gaussian (squared) distance to a scaled subdifferential. By utilizing the established phase transition theory, we further investigate the relationship between these two kinds of recovery procedures, which also reveals an optimal strategy (in the sense of Lagrange theory) for choosing the tradeoff parameter in the penalized recovery procedure. Numerical experiments are provided to verify our theoretical results.

We present extended Cantor arrays based on fourth- order difference co-arrays (E-FO-Cantor). These arrays result from extending the recently proposed fractal arrays to fourth- order difference co-arrays, and lead to fourth-order difference co-arrays that are hole-free. The set of sensor positions of the E-FO-Cantor is expressed in a simple and recursive form. The proposed Cantor arrays lead to O(N2log23) ≈ O(N3.17) degrees of freedom compared to O(N2) that can be achieved by existing sparse arrays with the hole-free property. Compared with other sparse arrays with the hole-free property in their fourth-order co-arrays, the proposed Cantor arrays provide a longer uniform linear array with more virtual sensors, leading to better DOA estimation performance.

This paper is concerned with the problem of recovering a structured signal from a relatively small number of corrupted random measurements. Sharp phase transitions have been numerically observed in practice when different convex programming procedures are used to solve this problem. This paper is devoted to presenting theoretical explanations for these phenomena by employing some basic tools from Gaussian process theory. Specifically, we identify the precise locations of the phase transitions for both constrained and penalized recovery procedures. Our theoretical results show that these phase transitions are determined by some geometric measures of structure, e.g., the spherical Gaussian width of a tangent cone and the Gaussian (squared) distance to a scaled subdifferential. By utilizing the established phase transition theory, we further investigate the relationship between these two kinds of recovery procedures, which also reveals an optimal strategy (in the sense of Lagrange theory) for choosing the tradeoff parameter in the penalized recovery procedure. Numerical experiments are provided to verify our theoretical results.

In this paper, we present non-asymptotic optimization guarantees of gradient descent methods for estimating structured transition matrices in high-dimensional vector autoregressive (VAR) models. We adopt the projected gradient descent (PGD) for single-structured transition matrices and the alternating projected gradient descent (AltPGD) for superposition-structured ones. Our analysis demonstrates that both gradient algorithms converge linearly to the statistical error even though the strong convexity of the objective function is absent under the high-dimensional settings. Moreover our result is sharp (up to a constant factor) in the sense of matching the phase transition theory of the corresponding model with independent samples. To the best of our knowledge, this analysis constitutes first non-asymptotic optimization guarantees of the linear rate for regularized estimation in high-dimensional VAR models. Numerical results are provided to support our theoretical analysis.

The Cramér-Rao bound (CRB) for direction of arrival (DOA) estimation exploiting both auto-correlation and cross-correlation information within multiple frequencies of the received array signals is derived. It provides a tighter bound than the existing CRB for the dual-frequency scenario. For the multiple frequencies, it is much lower than its dual-frequency counterpart, and also exists for a greater number of sources, thereby validating that exploiting multiple frequency pairs can improve both estimation accuracy and target resolvability.

The generalized linear moving sampling scheme (MSS) exploiting the second-order statistics and also the high-order cumulants is studied, where the set of MSS is defined as the shifted distance offsets involved in estimation based on a moving platform. Then, sparse physical arrays (SPAs) with nonuniform linear moving sampling schemes (NL-MSS), referred to as SPA-NL-MSS, are proposed to optimize the consecutive difference co-arrays. For the same number of sensors and data samples, better performance in terms of both the number of degrees of freedom (DOFs) and estimation accuracy can be achieved by SPA-NL-MSS than existing array structures exploiting array motions at the second order level.

A wireless sensing system with n sensors, observing independent and identically distributed continuous random variables with a symmetric probability density function, and one non-collocated estimator acting as a fusion center is considered. The sensors transmit information to the fusion center via a limited capacity communication medium modeled by a collision channel. It is assumed that there is no communication among the sensors prior to transmission, and the collision channel allows at most k < n simultaneous transmissions. Assuming that each sensor uses a symmetric threshold communication strategy, the problem of designing a threshold that minimizes a mean-squared error criterion is considered. Theoretical analysis shows the existence and uniqueness of the optimal threshold for this optimization problem.

Quantized corrupted sensing concerns the problem of estimating structured signals from their quantized corrupted samples. A typical case is that when the measurements y = Φx* + v* + n are corrupted with both structured corruption v* and unstructured noise n, we wish to reconstruct x* and v* from the quantized samples of y. Our work shows that the Generalized Lasso can be applied for the recovery of signal provided that a uniform random dithering is added to the measurements before quantization. The theoretical results illustrate that the influence of quantization behaves as independent unstructured noise. We also confirm our results numerically in several scenarios such as sparse vectors and low-rank matrices.

We consider the joint design of transmit and receive beamforming for multiple-input multiple-output (MIMO) systems in the presence of multiple targets and interferences. The objective is to maximize the minimum receiver output signal-to-interference-plus-noise-ratio (SINR) of the targets with constraints on the total and, respectively, per-antenna transmission power. The problem can be solved by an iterative bisection search (IBS) based method, which is, however, computationally intensive since it requires solving a feasibility problem multiple times for each update of the transmit beamformer. We propose a new method that bypasses the iterative feasibility checking by employing an SINR approximation. An analytical proof, which ensures the convergence of the proposed method, is provided. Numerical results show that the proposed method attains a similar SINR performance as the IBS based method but at a significantly lower computational complexity.

This paper studies the problem of recovering a structured signal from a relatively small number of corrupted non-linear measurements. Assuming that signal and corruption are contained in some structure-promoted set, we suggest an extended Lasso to disentangle signal and corruption. We also provide conditions under which this recovery procedure can successfully reconstruct both signal and corruption.

We consider the joint design of the transmit and receive beamforming in transmit subaperturing multiple-input-multiple-output (TS-MIMO) systems by utilizing the prior knowledge about the locations and power of the target and inherent interferences. The joint design is solved by an iterative algorithm to maximize the output signal-to-interference-plus-noise-ratio (SINR). The proposed approach can benefit from the sum co-array and joint transmit and receive optimization. Simulation results show that the approach provides more directions of freedom (DOFs) and/or directional gain compared to the original TS-MIMO and omni-MIMO, which leads to better output SINR results and interference rejection.

Compressed sensing (CS) with prior information concerns the problem of reconstructing a sparse signal with the aid of a similar signal which is known beforehand. We consider a new approach to integrate the prior information into CS via maximizing the correlation between the prior knowledge and the desired signal. We then present a geometric analysis for the proposed method under sub-Gaussian measurements. Our results reveal that if the prior information is good enough, then the proposed approach can improve the performance of the standard CS. Simulations are provided to verify our results.

Group-sparsity-based method is applied to the 2qth-order difference coarray for underdetermined wideband direction of arrival (DOA) estimation. For complexity reduction, a focused compressive-sensing-based approach is proposed, without sacrificing its performance. Different from the conventional focusing approach, in the proposed one, focusing is applied to the virtual arrays and no preliminary DOA estimation is required. Simulation results are provided to demonstrate the effectiveness of the proposed methods.

To reach a higher number of degrees of freedom by exploiting the fourth-order difference co-array concept, an effective structure extension based on two-level nested arrays is proposed. It increases the number of consecutive lags in the fourth-order difference coarray, and a virtual uniform linear array (ULA) with more sensors and a larger aperture is then generated from the proposed structure, leading to a much higher number of distinguishable sources with a higher accuracy. Compressive sensing based approach is applied for direction-of-arrival (DOA) estimation by vectorizing the fourth-order cumulant matrix of the array, assuming non-Gaussian impinging signals.

An effective sparse array extension method for maximizing the number of consecutive lags in the fourth-order difference co-array is proposed, leading to a novel enhanced sparse array structure based on co-prime arrays (CPAs) with significantly increased number of degrees of freedom (DOFs). One method to exploit the increased DOFs based on nonstationary signals is also proposed, with simulation results provided to demonstrate the effectiveness of the proposed structure.

A class of low-complexity compressive sensing-based direction-of-arrival (DOA) estimation methods for wideband co-prime arrays is proposed. It is based on a recently proposed narrowband estimation method, where a virtual array model is generated by directly vectorizing the covariance matrix and then using a sparse signal recovery method to obtain the estimation result. As there are a large number of redundant entries in both the auto-correlation and cross-correlation matrices of the two sub-arrays, they can be combined together to form a model with a significantly reduced dimension, thereby leading to a solution with much lower computational complexity without sacrificing performance. A further reduction in complexity is achieved by removing noise power estimation from the formulation. Then, the two proposed low-complexity methods are extended to the wideband realm utilizing a group sparsity based signal reconstruction method. A particular advantage of group sparsity is that it allows a much larger unit inter-element spacing than the standard co-prime array and therefore leads to further improved performance.

This letter proposes a novel parameter estimation method based on keystone transform (KT) and Radon-Fourier transform (RFT) for space moving targets with high-speed maneuvering performance. In this method, second-order KT is used to correct the range curvature and part of the range walk for all targets simultaneously. Then, fractional Fourier transform is employed to estimate the targets' radial acceleration, followed by the quadric phase term compensation. Finally, RFT and Clean technique are carried out to correct the residual range walk, and the initial range and radial velocity of moving targets are further obtained. The advantage of the proposed method is that it can overcome the limitation of Doppler frequency ambiguity and correct range curvature for all targets in one processing step, which simplifies the operation procedure. Simulation results are presented to demonstrate the validity of the proposed method.