Agile Radar Research Articles

A Highly Efficient Compressive Sensing Algorithm Based on Root-Sparse Bayesian Learning for RFPA Radar

Off-grid issues and high computational complexity are two major challenges faced by sparse Bayesian learning (SBL)-based compressive sensing (CS) algorithms used for random frequency pulse interval agile (RFPA) radar. Therefore, this paper proposes an off-grid CS algorithm for RFPA radar based on Root-SBL to address these issues. To effectively cope with off-grid issues, this paper derives a root-solving formula inspired by the Root-SBL algorithm for velocity parameters applicable to RFPA radar, thus enabling the proposed algorithm to directly solve the velocity parameters of targets during the fine search stage. Meanwhile, to ensure computational feasibility, the proposed algorithm utilizes a simple single-level hierarchical prior distribution model and employs the derived root-solving formula to avoid the refinement of velocity grids. Moreover, during the fine search stage, the proposed algorithm combines the fixed-point strategy with the Expectation-Maximization algorithm to update the hyperparameters, further reducing computational complexity. In terms of implementation, the proposed algorithm updates hyperparameters based on the single-level prior distribution to approximate values for the range and velocity parameters during the coarse search stage. Subsequently, in the fine search stage, the proposed algorithm performs a grid search only in the range dimension and uses the derived root-solving formula to directly solve for the target velocity parameters. Simulation results demonstrate that the proposed algorithm maintains low computational complexity while exhibiting stable performance for parameter estimation in various multi-target off-grid scenarios.

AK-MADDPG-Based Antijamming Strategy Design Method for Frequency Agile Radar.

Frequency agility refers to the rapid variation of the carrier frequency of adjacent pulses, which is an effective radar active antijamming method against frequency spot jamming. Variation patterns of traditional pseudo-random frequency hopping methods are susceptible to analysis and decryption, rendering them ineffective against increasingly sophisticated jamming strategies. Although existing reinforcement learning-based methods can adaptively optimize frequency hopping strategies, they are limited in adapting to the diversity and dynamics of jamming strategies, resulting in poor performance in the face of complex unknown jamming strategies. This paper proposes an AK-MADDPG (Adaptive K-th order history-based Multi-Agent Deep Deterministic Policy Gradient) method for designing frequency hopping strategies in frequency agile radar. Signal pulses within a coherent processing interval are treated as agents, learning to optimize their hopping strategies in the case of unknown jamming strategies. Agents dynamically adjust their carrier frequencies to evade jamming and collaborate with others to enhance antijamming efficacy. This approach exploits cooperative relationships among the pulses, providing additional information for optimized frequency hopping strategies. In addition, an adaptive K-th order history method has been introduced into the algorithm to capture long-term dependencies in sequential data. Simulation results demonstrate the superior performance of the proposed method.

Exploring an early warning system for maritime security risks: An approach based on compressed sensing

Piracy has posed intractable challenges to maritime security and the global economy. This study introduces a real-time early warning system designed to monitor piracy activity in the vicinity of merchant vessels, thereby facilitating the assessment and countermeasure of potential attacks. The approach employs frequency agile radar to identify pirate ships characterized by aggregation and jamming behavior. To address the computational difficulties caused by changing frequencies, compressed sensing with a tailored target information processing procedure is applied to reconstruct the radar observation scene. The developed target detection algorithm yields precise information about nearby pirate ships, enabling a comprehensive evaluation of the risk level and the subsequent recommendation of an appropriate security scheme. Extensive experiments have shown that the proposed early warning model can provide best warning performance compared to other benchmark models, with an average accuracy of 0.964, precision of 0.966, recall of 0.955, F1 score of 0.960.

GA-Dueling DQN Jamming Decision-Making Method for Intra-Pulse Frequency Agile Radar.

Optimizing jamming strategies is crucial for enhancing the performance of cognitive jamming systems in dynamic electromagnetic environments. The emergence of frequency-agile radars, capable of changing the carrier frequency within or between pulses, poses significant challenges for the jammer to make intelligent decisions and adapt to the dynamic environment. This paper focuses on researching intelligent jamming decision-making algorithms for Intra-Pulse Frequency Agile Radar using deep reinforcement learning. Intra-Pulse Frequency Agile Radar achieves frequency agility at the sub-pulse level, creating a significant frequency agility space. This presents challenges for traditional jamming decision-making methods to rapidly learn its changing patterns through interactions. By employing Gated Recurrent Units (GRU) to capture long-term dependencies in sequence data, together with the attention mechanism, this paper proposes a GA-Dueling DQN (GRU-Attention-based Dueling Deep Q Network) method for jamming frequency selection. Simulation results indicate that the proposed method outperforms traditional Q-learning, DQN, and Dueling DQN methods in terms of jamming effectiveness. It exhibits the fastest convergence speed and reduced reliance on prior knowledge, highlighting its significant advantages in jamming the subpulse-level frequency-agile radar.

Anti-interrupted sampling repeater jamming based on intra-pulse frequency modulation slope agile radar waveform joint FrFT

Interrupted sampling repeater jamming (ISRJ) is coherent with the radar-transmitted signal, which can form multi-false targets at the radar receiver. Therefore, ISRJ suppression is a compelling task in electronic counter-countermeasure. Intra-pulse frequency coded signals are not well energy-concentrated in the time-frequency (TF) domain, resulting in interference and target overlapping in the TF domain when the number of intermittent samplings and the number of forwarding times is large. To solve this problem, an anti-ISRJ method is proposed based on intra-pulse frequency modulation (FM) slope agile radar waveform joint fractional Fourier transform (FrFT). Firstly, the radar transmits the intra-pulse FM slope agile signal, and the adjacent sub-pulses are modulated with positive and negative FM slopes. Next, the echo signals are divided into multiple slices with the same sub-pulse timing as the transmitted signals. Then, utilizing the characteristics of transceiver time-sharing and energy suppression of the ISRJ, the FrFT is performed on each slice of the echo, and the interfered echo slices can be identified by fractional search and fractional order comparison. Finally, the interference in interfered echo slices is suppressed by fractional filtering. Simulation results show that the proposed method can recognize the interfered echo slice 100 % when the jamming-to-noise ratio and jamming-to-signal ratio (JSR) are both greater than 0 dB and do not generate false alarms when the signal-to-noise ratio is greater than 0 dB and JSR is greater than 10 dB. Fractional filtering reduces the loss of target energy in the process of interference suppression. Simulation results also verify the effectiveness of the proposed method against three typical types of synchronous ISRJ and the compound interferences formed by the combination of different types of synchronous ISRJ.

An Off-Grid Compressive Sensing Algorithm Based on Sparse Bayesian Learning for RFPA Radar

In the application of Compressive Sensing (CS) theory for sidelobe suppression in Random Frequency and Pulse Repetition Interval Agile (RFPA) radar, the off−grid issues affect the performance of target parameter estimation in RFPA radar. Therefore, to address this issue, this paper presents an off−grid CS algorithm named Refinement and Generalized Double Pareto (GDP) distribution based on Sparse Bayesian Learning (RGDP−SBL) for RFPA radar that utilizes a coarse−to−fine grid refinement approach, allowing precise and cost−effective signal recovery while mitigating the impact of off−grid issues on target parameter estimation. To obtain a high-precision signal recovery, especially in scenarios involving closely spaced targets, the RGDP−SBL algorithm makes use of a three−level hierarchical prior model. Furthermore, the RGDP−SBL algorithm efficiently utilizes diagonal elements during the coarse search and exploits the convexity of the grid energy curve during the fine search, therefore significantly reducing computational complexity. Simulation results demonstrate that the RGDP−SBL algorithm significantly improves signal recovery performance while maintaining low computational complexity in multiple scenarios for RFPA radar.

Block Sparse Recovery With Redundant Measurement Matrices and Its Application in Frequency Agile Radar

Block Sparse Recovery With Redundant Measurement Matrices and Its Application in Frequency Agile Radar

Backward and Sequential Inductions for Anti-Jamming Equilibrium Strategy Generation of Frequency Agile Radar

Backward and Sequential Inductions for Anti-Jamming Equilibrium Strategy Generation of Frequency Agile Radar

Anti‐interrupted sampling repeater jamming method for random pulse repetition interval and intra‐pulse frequency agile radar

AbstractInterrupted sampling repeater jamming can produce numerous active false targets with high fidelity, which is a significant challenge for coherent pulse radar. This poses a threat to the effectiveness of anti‐jamming technology, such as time‐frequency analysis and frequency agility for conventional constant pulse repetition interval (PRI) radar, which will render the radar inoperable to detect and track the actual target. A random PRI and intra‐pulse frequency agile radar waveform with low interception properties is proposed, which can effectively restrict the acquisition of radar waveform parameters by the jammer, destroy the coherence of jamming signals, and capture the range‐dimensional centroid feature of the echo. Accordingly, a jamming identification method based on the scale constrained Gaussian mixture model and an entity radar target energe recovery algorithm based on the neighbourhood weighted maximum entropy are proposed for target detection. Theoretical analysis and simulation experiments demonstrate the effectiveness of the proposal.

A gradient set matching pursuit algorithm with anti-base mismatch ability for sparse reconstruction under low SNR

This paper is concerned with designing an effective algorithm for recovering mismatched sparse signals from noise underdetermined measurements. The sparse recovery problem is formulated as the gradient optimization model of the residual cost function in a multidimensional continuous parameter space. The mismatched atoms of the discrete dictionary matrix are recovered as the accurate target sparse coefficient by solving a gradient descent algorithm with a hyperparameters joint adaptive adjustment function. To estimate the target parameters of frequency agile radar, we propose a gradient set matching pursuit algorithm. The algorithm uses the prior knowledge of resolution of the two-dimensional ambiguity function to build a discrete dictionary and obtains the support set according to the orthogonal matching pursuit principle. We divide the gradient set space in the neighborhood of the support set and calculate the mean gradient as the judgment direction and iteration step of the initial optimization process to overcome the residual function distortion and gradient error caused by random noise. The iterative convergence process of the proposed algorithm in the support set vector space is more robust, and the problem of falling into local optimum is avoided. Compared with the conventional sparse recovery algorithm and gradient descent algorithm, the proposed algorithm boosts its reconstruction performance of target parameters in the scenario of low SNR and mismatch of multiple scattering points. Simulation results show the effectiveness of the proposed algorithm.

A Non-Uniform Interrupted-Sampling Repeater Jamming Method for Intra-Pulse Frequency Agile Radar

The existing research proposes an intra-pulse frequency agile radar waveform with “active” anti-jamming characteristics. It uses the discontinuity and periodicity of the interrupted-sampling repeater jamming and combines the anti-jamming algorithm to effectively suppress interrupted-sampling repeater jamming. In order to improve the jamming effectiveness of the interferer for the intra-pulse frequency agile waveform, this paper proposes to jam the intra-pulse frequency agile radar by using a non-uniform interrupted-sampling and forwarding method under parameter constraints. The proposed method first obtains the sub-pulse width of the intra-pulse frequency agile radar waveform by parameter estimation of the intercepted intra-pulse frequency agile radar signal through time–frequency ridge extraction and wavelet transform. Then, we construct non-uniform interrupted-sampling repeater jamming based on sub-pulse width constraint interference parameters. Theoretical analysis and results show that the non-uniform interrupted-sampling forwarding under parameter constraints makes it challenging to suppress interference in multiple domains, such as the time–frequency and pulse compression domain for intra-pulse frequency agile radar, which significantly improves the jamming capability of the jammer for intra-pulse frequency agile radar.

Fractional Fourier Transform Receiver for Modulated Chirp Waveforms

A novel receiver structure for the reception of linearly frequency modulated (LFM) chirps carrying additional narrowband (phase) modulation is proposed. A linear relation between the time delay and the beat frequency shift of the target response in stretch processing is exploited to estimate the target range via correlation of the received signal with the replica in a Fractional Fourier Transform (FrFT) domain. According to numerical simulations, the proposed FrFT receiver demonstrates improved performance and computational efficiency over the state-of-the-art solutions for the moderate-to-large bandwidth of the information-carrying modulation. The receiver was integrated into the waveform-agile radar polarimetric agile radar in S band (PARSAX) and its performance has also been verified experimentally.

Neural Fictitious Self-Play for Radar Antijamming Dynamic Game With Imperfect Information

One emerging issue in modern electronic warfare is the competition between the radar and jammer, which in principle can be viewed as a noncooperative game with two players. In practice, the interaction between the radar and jammer involves multiple rounds as well as partial observation. This makes the competition become a dynamic game with imperfect information. Antijamming strategy design for such kind of a game is still unclear. In this work, the competition between a frequency agile radar and a transmit/receive time-sharing jammer is considered. We utilize an extensive-form game (EFG) with imperfect information to model the multiple rounds interaction between the radar and jammer. For the established EFG, finding Nash equilibrium (NE) strategies is a computationally-intractable task since the number of information states grows exponentially with respect to game stages. Instead, a sampled-based learning method called neural fictitious self play algorithm is used to find approximate NE strategies (ANES). Simulation results show that ANES can be obtained and outperform the common elementary and advanced strategies from the perspective of detection performance.

Reinforcement Learning for Compressed-Sensing Based Frequency Agile Radar in the Presence of Active Interference

Compressed sensing (CS)-based frequency agile radar (FAR) is attractive due to its superior data rate and target measurement performance. However, traditional frequency strategies for CS-based FAR are not cognitive enough to adapt well to the increasingly severe active interference environment. In this paper, we propose a cognitive frequency design method for CS-based FAR using reinforcement learning (RL). Specifically, we formulate the frequency design of CS-based FAR as a model-free partially observable Markov decision process (POMDP) to cope with the non-cooperation of the active interference environment. Then, a recognizer-based belief state computing method is proposed to relieve the storage and computation burdens in solving the model-free POMDP. This method is independent of the environmental knowledge and robust to the sensing scenario. Finally, the double deep Q network-based method using the exploration strategy integrating the CS-based recovery metric into the ϵ-greedy strategy (DDQN-CSR-ϵ-greedy) is proposed to solve the model-free POMDP. This can achieve better target measurement performance while avoiding active interference compared to the existing techniques. A number of examples are presented to demonstrate the effectiveness and advantage of the proposed design.

Newtonalized orthogonal matching pursuit for the linear frequency‐modulated pulse frequency agile radar

The linear frequency-modulated frequency agile radar (FAR) can be used for synthesizing high-range-resolution profiles (HRRP), and also has excellent electronic counter-countermeasures performance. Similar to the Newtonalized orthogonal matching pursuit (NOMP) for line spectral estimation problem, the NOMP for the FAR radar termed as NOMP-FAR is designed to process each coarse range bin to extract the HRRP and velocities of multiple targets, including the guide for determining the oversampling factor and the stopping criterion. In addition, it is shown that the target will cause false alarm in the nearby coarse range bins, and a post-processing algorithm is proposed to suppress the ghost targets. Numerical simulations are conducted to demonstrate the effectiveness of NOMP-FAR.

Joint phase error estimation and sparse scene restoration algorithms for frequency agile radar

Joint phase error estimation and sparse scene restoration algorithms for frequency agile radar

Review on Frequency Agile Radar Seeker

Review on Frequency Agile Radar Seeker

Radar active antagonism through deep reinforcement learning: A Way to address the challenge of mainlobe jamming

Among different jamming techniques, mainlobe jamming is difficult to deal with for the radar and traditional passive anti-jamming methods are less effective because the angular separation between the jammer and the target is almost the same. In contrast to these passive methods, active antagonism requires the radar to take measures in advance to avoid being jammed and this can be achieved via frequency agile (FA) radar. In order to enable the FA radar to combat the jammer and obtain good performance, a deep reinforcement learning (RL) based anti-jamming strategy design method is proposed in which a transmit/receive time-sharing jammer may adopt multiple different jamming strategies. To combat the individual jamming strategy, we propose a specialized strategy learning algorithm that treats probability of detection as the reward signal and uses proximal policy optimization to solve the RL problem of the radar and the jammer. Based on the learned specialized strategies, policy distillation technique is applied to design a unified strategy which enables the FA radar to combat multiple jamming strategies. Simulation results show that the FA radar can avoid being jammed and obtain a high probability of detection whether the jammer adopts individual or multiple jamming strategies through the proposed method.

Phase Transitions in Frequency Agile Radar Using Compressed Sensing

FAR has improved anti-jamming performance over traditional pulse-Doppler radars under complex electromagnetic circumstances. To reconstruct the range-Doppler information in FAR, many compressed sensing (CS) methods including standard and block sparse recovery have been applied. In this paper, we study phase transitions of range-Doppler recovery in FAR using CS. In particular, we derive closed-form phase transition curves associated with block sparse recovery and complex Gaussian matrices, based on prior results of standard sparse recovery under real Gaussian matrices. We further approximate the obtained curves with elementary functions of radar and target parameters, facilitating practical applications of these curves. Our results indicate that block sparse recovery outperforms the standard counterpart when targets occupy more than one range cell, which are often referred to as extended targets. Simulations validate the availability of these curves and their approximations in FAR, which benefit the design of the radar parameters.

Coherent Integration Method Based on Radon-NUFFT for Moving Target Detection Using Frequency Agile Radar.

This paper considers the coherent integration problem for moving target detection using frequency agile (FA) radar, involving range cell migration (RCM) and the nonuniform phase fluctuations among different pulses caused by range-agile frequency (R-AF) coupling and velocity-time-agile frequency (V-T-AF) coupling. After the analysis of the term corresponding to the phase fluctuation caused by V-T-AF coupling, the term can be regarded as related to an equivalent non-uniform slow time, and nonuniform fast Fourier transform (NUFFT) could be the solution. So a fast coherent integration method combining Radon Fourier transform (RFT) and NUFFT based on low-rank approximation, i.e., Radon-NUFFT, is proposed. In this method, the RCM is solved by Radon algorithm via target trajectory searching, the non-uniform phase fluctuation caused by R-AF coupling is compensated by constructing a compensation item corresponding to the range and agile frequency. In addition, the compensation of the non-uniform phase fluctuation caused by V-T-AF coupling is converted into a problem of spectral analysis of non-uniform sampling complex-valued signal, which is solved by the NUFFT based on low rank approximation. Compared with the existing methods, the proposed method can realize the coherent integration for FA radar accurately and quickly. The effectiveness of the proposed method is verified by simulation experiments.