Multi-turn instruction following is essential for building intelligent conversational systems that can consistently adhere to instructions across dialogue turns. However, existing approaches to enhancing multi-turn instruction following primarily rely on collecting or generating large-scale multi-turn dialogue datasets to fine-tune large language models (LLMs), which treat each response generation as an isolated task and fail to explicitly incorporate multi-turn instruction following into the optimization objectives. As a result, instruction-tuned LLMs often struggle with complex long-distance constraints. In multi-turn dialogues, relational constraints across turns can be naturally modeled as labeled directed edges, making graph structures particularly suitable for modeling multi-turn instruction following. Despite this potential, leveraging graph structures to enhance the multi-turn instruction following capabilities of LLMs remains unexplored. To bridge this gap, we propose GraphIF, a plug-and-play framework that models multi-turn dialogues as directed relation graphs and leverages graph prompts to enhance the instruction following capabilities of LLMs. GraphIF comprises three key components: (1) an agent-based relation extraction module that captures inter-turn semantic relations via action-triggered mechanisms to construct structured graphs; (2) a relation graph prompt generation module that converts structured graph information into natural language prompts; and (3) a response rewriting module that refines initial LLM outputs using the generated graph prompts. Extensive experiments on two long multi-turn dialogue datasets demonstrate that GraphIF can be seamlessly integrated into instruction-tuned LLMs and leads to significant improvements across all four multi-turn instruction-following evaluation metrics.

Recent years have witnessed increasing interest in few-shot knowledge graph completion (FKGC), which aims to infer novel query triples for few-shot relations from limited references. Despite promising progress, existing methods face two key challenges: (1) They often overlook rich higher-order neighbors, while traditional high-order aggregation methods are prone to introducing noise and lack effective alignment across multi-view neighborhood information. (2) Meta-learning methods over-rely on embeddings, making them susceptible to spurious relational patterns. Meanwhile, LLM-based methods, despite their potential, suffer from hallucinations and input constraints. To this end, we propose a novel framework that combines meta-learning, enhanced via a Local-Global Contrastive network, with LLM-guided Contextual Refinement (LGC-CR). At the data level, we design a local-global contrastive network to jointly aggregate relevant local features and capture stable global representations while filtering high-order noise, then align these two views through a dual contrast module to ensure consistency. At the model level, we employ an LLM refinement module, which retrieves relevant contexts to construct prompts and applies a knowledge selector to identify high-quality facts based on diversity and centrality, enabling efficient fine-tuning of LLMs to refine the preliminary predictions of meta-learning. The experimental results demonstrate that LGC-CR delivers better and more robust performance than state-of-the-art baselines, with Hit@1 improvements of 8.1%, 21.7%, and 20.6% on NELL, Wiki, and FB15K, respectively.

Time series forecasting with exogenous variables is a critical emerging paradigm that presents unique challenges in modeling dependencies between variables. Traditional models often struggle to differentiate between endogenous and exogenous variables, leading to inefficiencies and overfitting. In this paper, we introduce CrossLinear, a novel Linear-based forecasting model that addresses these challenges by incorporating a plug-and-play cross-correlation embedding module. This lightweight module captures the dependencies between variables with minimal computational cost and seamlessly integrates into existing neural networks. Specifically, it captures time-invariant and direct variable dependencies while disregarding time-varying or indirect dependencies, thereby mitigating the risk of overfitting in dependency modeling and contributing to consistent performance improvements. Furthermore, CrossLinear employs patch-wise processing and a global linear head to effectively capture both short-term and long-term temporal dependencies, further improving its forecasting precision. Extensive experiments on 12 real-world datasets demonstrate that CrossLinear achieves superior performance in both short-term and long-term forecasting tasks. The ablation study underscores the effectiveness of the cross-correlation embedding module. Additionally, the generalizability of this module makes it a valuable plug-in for various forecasting tasks across different domains. Codes are available at https://github.com/mumiao2000/CrossLinear.

With the development of dual-function radar communication (DFRC) systems, waveform design has received increasing attention. At the same time, subcarrier superposition can lead to the high peak-to-average power ratio (PAPR) problem in orthogonal frequency division multiplexing (OFDM). To solve the problem, in this paper, we propose an alternating direction method of multipliers (ADMM)-based low-PAPR OFDM waveform design algorithm for DFRC systems, which minimizes the signal PAPR with the constraint of the zero integrated sidelobe level (ISL). Moreover, we compare our algorithm with a recently proposed benchmark algorithm. Simulation results demonstrate that our algorithm has better performance compared to the$l$- norm cyclic algorithm.

Antenna position errors caused by manufacturing accuracy limits lead to a great difference between the real and ideal models of antenna arrays in extremely high frequency (EHF) band MIMO radar with tiny physical elements and spacings. As the real array is a non-uniform array, the conventional window function fails when applied to non-uniform sampling data, which causes angular ambiguities and seriously degrades the performance of DOA estimation. Based on an advanced analysis of spectral distortion in non-uniform sampling, this paper introduces a method to design a specialized window function for non-uniform MIMO arrays, aiming to minimize the equivalent noise bandwidth (ENBW) while sufficiently suppressing the side-lobe-to-peak ratio of the window function's spectrum. The simulation results show the effectiveness of the optimized window function, which reduces angular ambiguities and thereby improves the performance of DOA estimation for non-uniform MIMO arrays.

The omega-K algorithm ($\omega $KA) is an accurate imaging method for squinted synthetic aperture radar (SAR) with linear trajectory. However, for SARs with curved trajectory, since it does not allow the radar velocity to vary with range, the imaging quality would degrade severely. To address this issue, an improved$\omega $KA is proposed in this letter. We design a special Stolt mapping to avoid the complex additional range cell migration (RCM) and the skew of the data support region. Then, the RCM correction (RCMC) and azimuth compression are operated in the range Doppler domain. With these improvements, the radar velocity is allowed to vary with range, which greatly reduces the phase error in the case of large range swaths. Numerical results validate the proposed algorithm.

This letter presents a novel multi-channel improved contrastive predictive coding (CPC) method to extract signals features. Specifically, to extract low pulse width radar signals features and meet the real-time requirements of signals identification, we design a lightweight encoder to realize the CPC features encoding function. Then, we construct a multi-channel CPC features decoder to mine and extract subtle individual signals features from the perspective of multi-domain and multi-channel information input. Simulation results verify the effectiveness of our proposed method, which can achieve state-of-the-art results in both accuracy and running time compared to the existing optimal methods. All our models and code are available at https://github.com/jn-z/MC-CPC.

Air moving target indication (AMTI) is an important task of spaceborne radar. Medium-Earth-orbit (MEO) synthetic aperture radar (SAR) has the characteristics of large coverage, short revisit time, and high orbital altitude, and thus is an attractive tool for AMTI missions. However, due to air moving target’s high-speed maneuvering and MEO SAR’s long synthetic aperture time and significant curvature of trajectory, the signal of air moving target after imaging processing is very complex, which makes the design of AMTI method be challenging. In this article, a study on image-domain signal modeling and refocusing of air moving target for MEO multichannel SAR is presented. The range equation of an air moving target with 3-D velocities and accelerations is established. In addition, the target’s signal models after range migration correction and azimuth compression with the stationary scene parameters are derived. Then, via dividing targets into three types based on their residual range migration and Doppler ambiguity, the image-domain signal models of air moving targets are developed. Furthermore, a refocusing method that can cope with large range migration and Doppler ambiguity is proposed. Finally, numerical experiments are conducted to validate the developed signal models and proposed refocusing method.

With the rapid development of deep learning (DL) in recent years, automatic modulation recognition (AMR) with DL has achieved high accuracy. However, insufficient training signal data in complicated channel environments and large-scale DL models are critical factors that make DL methods difficult to deploy in practice. Aiming to these problems, we propose a novel neural network named convolution-linked signal transformer (ClST) and a novel knowledge distillation method named signal knowledge distillation (SKD). The ClST is accomplished through three primary modifications: a hierarchy of transformer containing convolution, a novel attention mechanism named parallel spatial-channel attention (PSCA) mechanism and a novel convolutional transformer block named convolution-transformer projection (CTP) to leverage a convolutional projection. The SKD is a knowledge distillation method to effectively reduce the parameters and complexity of neural networks. We train two lightweight neural networks using the SKD algorithm, KD-CNN and KD-MobileNet, to meet the demand that neural networks can be used on miniaturized devices. The simulation results demonstrate that the ClST outperforms advanced neural networks on all datasets. Moreover, both KD-CNN and KD-MobileNet obtain higher recognition accuracy with less network complexity, which is very beneficial for the deployment of AMR on miniaturized communication devices.

The performance of ellipse fitting may significantly degrade in the presence of outliers, which can be caused by occlusion of the object, mirror reflection or other objects in the process of edge detection. In this paper, we propose an ellipse fitting method that is robust against the outliers, and thus maintaining stable performance when outliers can be present. We formulate an optimization problem for ellipse fitting based on the maximum entropy criterion (MCC), having the Laplacian as the kernel function from the well-known fact that the ℓ1-norm error measure is robust to outliers. The optimization problem is highly nonlinear and non-convex, and thus is very difficult to solve. To handle this difficulty, we divide it into two subproblems and solve the two subproblems in an alternate manner through iterations. The first subproblem has a closed-form solution and the second one is cast as a convex second-order cone program (SOCP) that can reach the global solution. By so doing, the alternate iterations always converge to an optimal solution, although it can be local instead of global. Furthermore, we propose a procedure to identify failed fitting of the algorithm caused by local convergence to a wrong solution, and thus, it reduces the probability of fitting failure by restarting the algorithm at a different initialization. The proposed robust ellipse fitting method is next extended to the coupled ellipses fitting problem. Both simulated and real data verify the superior performance of the proposed ellipse fitting method over the existing methods.

This paper proposes two methods for robust Capon beamforming. One is for the doubly constrained robust Capon beamforming problem, where the unit modular constraints on the elements of the steering vector of interest are enforced to circumvent the look direction error or phase perturbations of the signal-of-interest; and another addresses robust beamforming in impulsive noise environment, where we consider the lp-norm minimization (0 < p < 2) of the output while constraining the mainlobe response ripple term. We apply the splitting technique to simplify the resultant nonconvex optimization problem and solve it using alternating direction method of multipliers. The performance of the proposed methods is demonstrated via numerical examples.

Due to the freedom degree loss resulted from the unimodular constraints, it is not easy to specify proper and feasible stopband and passband levels for frequency grids of interest in spectrally constrained sequence design problems. In an attempt to avoid this difficulty, we devise a cost function that minimizes the ratio of the maximal stopband level to the minimal passband level. Next, we introduce auxiliary variables to simplify the optimization problem via decoupling the numerator and denominator. Then, the feasible solution is obtained by approximating the nondifferentiable objective function with a smooth function. We also apply an acceleration scheme to increase the algorithm convergence speed. The effectiveness of the proposed approach is demonstrated via numerical examples.

We derive a phase retrieval algorithm using the alternating direction method of multipliers. For the cost function obtained from the maximum likelihood criterion, we introduce auxiliary amplitude and phase variables to avoid the absolute value operator and decouple the determination of the auxiliary phase variables from that of the auxiliary amplitude variables. As a result, a phase retrieval algorithm consisting only of two least-squares steps is derived. The performance of the proposed algorithm is investigated via numerical examples, as well as an application to flat-spectrum periodic unimodular sequence design.

Obtaining high accuracy in orientation assignment for Synthetic Aperture Radar (SAR) image registration is a great challenge because of the serious speckle noise and geometrical distortion. In this letter, a polar scale-invariant feature transform (PSIFT) descriptor is proposed for SAR image registration. The novel descriptor is invariant to rotation, skipping the dominant orientation assignment. In PSIFT, a polar-transformed support region is adopted to calculate the gradient magnitudes and orientations and further sampled in the radial and angular directions with different scales. The final descriptor is then built with the orientation bins covering the omnidirectional space. Furthermore, an improved dual-matching method is proposed to achieve sufficiently correct matches. Extensive experiments confirm that the PSIFT descriptor is suitable for SAR image registration because of its excellent performance.

Traditional tensor decomposition methods, e.g., two dimensional principle component analysis (2DPCA) and two dimensional singular value decomposition (2DSVD), minimize mean square errors (MSE) and are sensitive to outliers. In this paper, we propose a new robust tensor factorization method using maximum correntropy criterion (MCC) to improve the robustness of traditional tensor decomposition methods. A half-quadratic optimization algorithm is adopted to effectively optimize the correntropy objective function in an iterative manner. It can effectively improve the robustness of a tensor decomposition method to outliers without introducing any extra computational cost. Experimental results demonstrated that the proposed method significantly reduces the reconstruction error on face reconstruction and improves the accuracy rate on handwritten digit recognition.

This paper develops a novel decentralized dimensionality reduction algorithm for the distributed tensor data across sensor networks. The main contributions of this paper are as follows. First, conventional centralized methods, which utilize entire data to simultaneously determine all the vectors of the projection matrix along each tensor mode, are not suitable for the network environment. Here, we relax the simultaneous processing manner into the one-vector-by-one-vector (OVBOV) manner, i.e., determining the projection vectors (PVs) related to each tensor mode one by one. Second, we prove that in the OVBOV manner each PV can be determined without modifying any tensor data, which simplifies corresponding computations. Third, we cast the decentralized PV determination problem as a set of subproblems with consensus constraints, so that it can be solved in the network environment only by local computations and information communications among neighboring nodes. Fourth, we introduce the null space and transform the PV determination problem with complex orthogonality constraints into an equivalent hidden convex one without any orthogonality constraint, which can be solved by the Lagrange multiplier method. Finally, experimental results are given to show that the proposed algorithm is an effective dimensionality reduction scheme for the distributed tensor data across the sensor networks.

Secure relay and jammer selection for physical-layer security is studied in a wireless network with multiple intermediate nodes and eavesdroppers, where each intermediate node either helps to forward messages as a relay, or broadcasts noise as a jammer. We derive a closed-form expression for the secrecy outage probability (SOP), and we develop two relay and jammer selection methods for SOP minimization. In both methods a selection vector and a corresponding threshold are designed and broadcast by the destination to ensure each intermediate node knows its own role while knowledge of the relay and jammer set is kept secret from all eavesdroppers. Simulation results show the SOP of the proposed methods are very close to that obtained by an exhaustive search, and that maintaining the privacy of the selection result greatly improves the SOP performance.

Shape fitting, including straight line and ellipse fitting, plays an important role in the (cylinder-) shape control system of silicon single crystal growth, because the straight lines and ellipse in the crystal image contain the important horizontal circle center and diameter information. This information can be used as control variables so that the grown crystal approximates to a perfect cylinder, and thus can be used as high-quality source materials. In this paper, we develop new straight line and ellipse fitting algorithms. The key points are as follows. We formulate the two-dimensional (2-D) binary image into a single-snapshot array signal of a virtual sensor array, and casts the angle estimation problem of straight lines into the direction finding one of virtual incoming sources. Based on the virtual array manifold and potential incoming angles, the relevant over-complete dictionary is constructed, and thus a sparse regression problem is formed. To solve such a regression problem, we introduce the weight vector sparsity term into the conventional linear least-squares support vector regression framework to estimate the angles of these straight lines. Based on the estimated angles and potential offsets, another over-complete dictionary is constructed, and thus the image can be looked upon as the sparse representation of these dictionary atoms. Since the constructed dictionary is of the same size as the image, we use the compressed sensing theory to reduce the relevant dimensionality and then apply the aforementioned sparse regression method to obtain the relevant offsets of these straight lines. We derive a new second-order polynomial of ellipse equation to obtain the ellipse parameters to avoid the trival solution from the conventional polynomial model. Some simulation and experimental examples are given to illustrate the effectiveness of the proposed algorithms.

Ellipse fitting is widely applied in the fields of computer vision and automatic manufacture. However, the introduced edge point errors (especially outliers) from image edge detection will cause severe performance degradation of the subsequent ellipse fitting procedure. To alleviate the influence of outliers, we develop a robust ellipse fitting method in this paper. The main contributions of this paper are as follows. First, to be robust against the outliers, we introduce the maximum correntropy criterion into the constrained least-square (CLS) ellipse fitting method, and apply the half-quadratic optimization algorithm to solve the nonlinear and nonconvex problem in an alternate manner. Second, to ensure that the obtained solution is related to an ellipse, we introduce a special quadratic equality constraint into the aforementioned CLS model, which results in the nonconvex quadratically constrained quadratic programming problem. Finally, we derive the semidefinite relaxation version of the aforementioned problem in terms of the trace operator and thus determine the ellipse parameters using semidefinite programming. Some simulated and experimental examples are presented to illustrate the effectiveness of the proposed ellipse fitting approach.

The steady-state excess mean square error (EMSE) of the adaptive filtering under the maximum correntropy criterion (MCC) has been studied. For Gaussian noise case, we establish a fixed-point equation to solve the exact value of the steady-state EMSE, while for non-Gaussian noise case, we derive an approximate analytical expression for the steady-state EMSE, based on a Taylor expansion approach. Simulation results agree with the theoretical calculations quite well.

This paper develops a distributed dictionary learning algorithm for sparse representation of the data distributed across nodes of sensor networks, where the sensitive or private data are stored or there is no fusion center or there exists a big data application. The main contributions of this paper are: 1) we decouple the combined dictionary atom update and nonzero coefficient revision procedure into two-stage operations to facilitate distributed computations, first updating the dictionary atom in terms of the eigenvalue decomposition of the sum of the residual (correlation) matrices across the nodes then implementing a local projection operation to obtain the related representation coefficients for each node; 2) we cast the aforementioned atom update problem as a set of decentralized optimization subproblems with consensus constraints. Then, we simplify the multiplier update for the symmetry undirected graphs in sensor networks and minimize the separable subproblems to attain the consistent estimates iteratively; and 3) dictionary atoms are typically constrained to be of unit norm in order to avoid the scaling ambiguity. We efficiently solve the resultant hidden convex subproblems by determining the optimal Lagrange multiplier. Some experiments are given to show that the proposed algorithm is an alternative distributed dictionary learning approach, and is suitable for the sensor network environment.

This paper focuses on two signal processing aspects of multistatic active sonar systems, namely enhanced range-Doppler imaging and improved target parameter estimation. The main contributions of this paper are: i) a hybrid dense-sparse method is proposed to generate range-Doppler images with both low sidelobe levels and high accuracy; ii) a generalized K-Means clustering (GKC) method for target association is developed to associate the range measurements from different transmitter-receiver pairs; iii) the extended invariance principle-based weighted least-squares (EXIP-WLS) method is developed for accurate target position and velocity estimation. The effectiveness of the proposed multistatic active sonar system is verified using numerical examples.

Ellipse fitting is widely applied in the fields of computer vision and automatic industry control, in which the procedure of ellipse fitting often follows the preprocessing step of edge detection in the original image. Therefore, the ellipse fitting method also depends on the accuracy of edge detection besides their own performance, especially due to the introduced outliers and edge point errors from edge detection which will cause severe performance degradation. In this paper, we develop a robust ellipse fitting method to alleviate the influence of outliers. The proposed algorithm solves ellipse parameters by linearly combining a subset of ("more accurate") data points (formed from edge points) rather than all data points (which contain possible outliers). In addition, considering that squaring the fitting residuals can magnify the contributions of these extreme data points, our algorithm replaces it with the absolute residuals to reduce this influence. Moreover, the norm of data point errors is bounded, and the worst case performance optimization is formed to be robust against data point errors. The resulting mixed l1-l2 optimization problem is further derived as a second-order cone programming one and solved by the computationally efficient interior-point methods. Note that the fitting approach developed in this paper specifically deals with the overdetermined system, whereas the current sparse representation theory is only applied to underdetermined systems. Therefore, the proposed algorithm can be looked upon as an extended application and development of the sparse representation theory. Some simulated and experimental examples are presented to illustrate the effectiveness of the proposed ellipse fitting approach.

A novel higher order singular value decomposition (HOSVD)-based image fusion algorithm is proposed. The key points are given as follows: 1) Since image fusion depends on local information of source images, the proposed algorithm picks out informative image patches of source images to constitute the fused image by processing the divided subtensors rather than the whole tensor; 2) the sum of absolute values of the coefficients (SAVC) from HOSVD of subtensors is employed for activity-level measurement to evaluate the quality of the related image patch; and 3) a novel sigmoid-function-like coefficient-combining scheme is applied to construct the fused result. Experimental results show that the proposed algorithm is an alternative image fusion approach.

In this paper, a robust adaptive Kalman algorithm for a second-order infinite impulse response (IIR) notch filter to detect the frequency of sinusoid signal in the white Gaussian noise is proposed. Firstly, a general expression for the steady-state sinusoid frequency estimation based on minimum mean square error (MMSE) criterion in terms of state-space equations is derived. Secondly, a robust adaptive Kalman algorithm for the state-space equations with unknown noise statistics is given. Finally, computer simulation results are presented to confirm the effectiveness of the proposed algorithm