Low Probability Of Intercept Research Articles

LPI radar target detection performance optimization based on joint cognitive frequency transmission and power allocation

In the Low Probability of Intercept (LPI) radar system, in order to optimize the radar target detection performance, the energy consumption should be reduced while improving the target detection performance. Based on the Hidden Markov Model (HMM), this paper proposes an optimization algorithm for target detection performance joint cognitive frequency transmission and power allocation combined with the target Radar Cross Section (RCS) frequency response function prediction. The algorithm uses the target RCS's characteristics with different frequency response functions at different frequencies. The radar transmits a set of broadband pulse signals with different frequencies at the current time to irradiate the target and obtain the echo. The passive receiving system processes the echo to obtain the target RCS frequency response measurement value, and determines it as a priori information. The RCS frequency response function of the target at the subsequent time is predicted by the prior information and HMM, and the complete RCS prediction information of the target is obtained. Finally, using the radar equation, the radar transmitting power is calculated through the maximum frequency response function in the predicted values at different times and its corresponding transmitting frequency. The optimized information is then transmitted to the detection radar to complete the joint cognitive frequency transmission and power allocation. The simulation results show that the method used in this paper can lead to more accurate prediction information than the traditional algorithm, efficiently reduce the target detection transmitting power, and improve the radar target detection and LPI performance, which has a high engineering application value.

Co-Design of Transmit-Receive Weights for MIMO System With LPI and Multi-Targets

This letter deals with the co-design of transmit and receive beamforming weights for the multiple-input multiple-output (MIMO) array with a low probability of interception (LPI) in the presence of multiple targets. Based on that, we formulate an optimization model with constraints on the transmit power, aiming to maximize minimum output signal-to-interference-plus-noise-ratio (SINR). To solve the formed optimization problem, we propose the one-step iterative scheme, which generates the transmit weight vector by iteratively solving a series of convex approximate problems. The receive weight of each target is finally formed with the minimum variance distortionless response (MVDR) algorithm. Numerical experiments are completed to show the effectiveness of the proposed method.

Joint Transmit Resource Management and Waveform Selection Strategy for Target Tracking in Distributed Phased Array Radar Network

In this article, a joint transmit resource management and waveform selection (JTRMWS) strategy is put forward for target tracking in distributed phased array radar network. We establish the problem of joint transmit resource and waveform optimization as a dual-objective optimization model. The key idea of the proposed JTRMWS scheme is to utilize the optimization technique to collaboratively coordinate the transmit power, dwell time, waveform bandwidth, and pulse length of each radar node in order to improve the target tracking accuracy and low probability of intercept (LPI) performance of distributed phased array radar network, subject to the illumination resource budgets and waveform library limitation. The analytical expressions for the predicted Bayesian Cramér–Rao lower bound and the probability of intercept are calculated and subsequently adopted as the metric functions to evaluate the target tracking accuracy and LPI performance, respectively. It is shown that the JTRMWS problem is a nonlinear and nonconvex optimization problem, where the above four adaptable parameters are all coupled in the objective functions and constraints. Combined with the particle swarm optimization algorithm, an efficient and fast three-stage-based solution technique is developed to deal with the resulting problem. Simulation results are provided to verify the effectiveness and superiority of the proposed JTRMWS algorithm compared with other state-of-the-art benchmarks.

Power control and beamforming of phased-MIMO radars to achieve a low probability interception

In this paper, the optimum detector of co-located Phased-Mimo Radars (PMRs) with signal diversity is designed and its detection probability and false alarm rate are obtained as performance metrics. Then, the Low Probability Intercept (LPI) optimization of radar is considered while the desired detection performance and power budget limit are preserved. The LPI optimizations design power allocations, beamforming weights deal with the phased array property, and orthogonal signals selection deals with the MIMO property. The complexities arising from the joint optimization of power allocations and beamformings have been handled by some proposed relaxations and lemmas. The proposed solutions' effectiveness is analyzed by numerical simulations. Simulation results verify the superiority of optimized solutions in comparison to the conventional benchmarks in terms of LPI property, detection probability, and power consumption.

Research on the Sequential Difference Histogram Failure Principle Applied to the Signal Design of Radio Frequency Stealth Radar

As electronic warfare becomes the core of modern warfare, radio frequency (RF) stealth radar is becoming the focus of modern electronic warfare. The anti-sorting strategy of RF stealth radar is a new effective method of the anti-enemy electronic reconnaissance system. Hence, research on the failure mechanism of sorting algorithms has become the cornerstone of anti-sorting technology. In this paper, the mechanism of algorithm failure is studied because the SDIF algorithm is widely used in engineering practice throughout the whole workflow of the sequential difference histogram (SDIF) algorithm, from the estimation of pulse repetition interval (PRI) destroyed by the algorithm and algorithm analysis to the staggered signal. Firstly, the working steps of the SDIF histogram sorting algorithm are considered. Key steps of signal sorting by the algorithm are analyzed, and the failure principle of the sorting algorithm is proposed. It is pointed out that if the PRI signal center value of the two groups of radars is within the tolerance range of the sorting algorithm, when the two signal center values are not of the same order of magnitude, the difference is more than 10 times, and the signal variation is less than 30% of the center value, the sorting error of the algorithm for the radar signal is at least 25%. The sorting algorithm fails to sort signals. At the same time, for the sorting failure of the staggered signal, the sub-PRI design formula of the staggered signal is proposed, and the staggered signal satisfying the design formula can make the sorting algorithm invalid. Finally, the correctness of the SDIF failure principle is further verified by formula derivation, signal design simulation and experiment. The principle of sorting failure provides theoretical support and foundation for the design of anti-sorting RF stealth signal. The principle of sorting failure makes up for the shortcomings of random signal design and improves the design efficiency of RF stealth signal.

LPI waveform design for radar system against cyclostationary analysis intercept processing

Low probability of intercept (LPI) property has provided the radar system with superior survivability on the practical battlefield. In this paper, we put forward a waveform design approach to enhance the LPI performance for radar systems by considering the intercept processing of the electronic reconnaissance (ER) systems. Based on this approach, an LPI waveform design problem against the typical cyclostationary analysis (CSA) widely performed by the ER systems is studied and further formulated as an optimization problem. In this problem, the deviation between the cyclic spectrum of the designed waveform and that of the Gaussian white noise is minimized to improve the LPI performance. Meanwhile, the optimal detection signal-to-noise ratio (SNR) restriction is enforced to ensure detection ability. The resulting optimization problem is shown to be a non-convex quartic programming that is intractable in general. To solve the problem efficiently, a structural sequential greedy optimization (S-SGO) algorithm is proposed. The proposed algorithm performs an ingenious reparameterization of the radar waveform vector and solves related problems in a polynomial-time based on the thought of alternation optimization. The convergence of the proposed S-SGO is also investigated. Numerical results verify the effectiveness of the proposed approach for the LPI waveform design as well as the proposed algorithm.

Adaptive Tracking of High-Maneuvering Targets Based on Multi-Feature Fusion Trajectory Clustering: LPI's Purpose.

Since the passive sensor has the property that it does not radiate signals, the use of passive sensors for target tracking is beneficial to improve the low probability of intercept (LPI) performance of the combat platform. However, for the high-maneuvering targets, its motion mode is unknown in advance, so the passive target tracking algorithm using a fixed motion model or interactive multi-model cannot match the actual motion mode of the maneuvering target. In order to solve the problem of low tracking accuracy caused by the unknown motion model of high-maneuvering targets, this paper firstly proposes a state transition matrix update-based extended Kalman filter (STMU-EKF) passive tracking algorithm. In this algorithm, the multi-feature fusion-based trajectory clustering is proposed to estimate the target state, and the state transition matrix is updated according to the estimated value of the motion model and the observation value of multi-station passive sensors. On this basis, considering that only using passive sensors for target tracking cannot often meet the requirements of high target tracking accuracy, this paper introduces active radar for indirect radiation and proposes a multi-sensor collaborative management model based on trajectory clustering. The model performs the optimal allocation of active radar and passive sensors by judging the accumulated errors of the eigenvalue of the error covariance matrix and makes the decision to update the state transition matrix according to the magnitude of the fluctuation parameter of the error difference between the prediction value and the observation value. The simulation results verify that the proposed multi-sensor collaborative target tracking algorithm can effectively improve the high-maneuvering target tracking accuracy to satisfy the radar’s LPI performance.

Dynamic Antenna Selection for Colocated MIMO Radar

Antenna distribution plays an important role for the performance gain in multiple-input–multiple-output (MIMO) radar target tracking. Since to meet the requirements of the low probability of interception, especially in a hostile environment, only a finite number of antennas can be activated at each step. This naturally leads to a performance-driven resource management problem. In this paper, a dynamic antenna selection strategy is proposed for tracking targets in colocated MIMO radar. The derived posterior Cramér–Rao lower bound (PCRLB) of joint direction-of-arrival (DOA) and Doppler estimate were chosen as the optimization criteria. Furthermore, in the deviation, the target radar cross-section (RCS) as the determining variable and the random variable are both discussed. The objective function is related to the antenna allocation and non-convex, and an efficient fast discrete particle swarm optimization (FDPSO) algorithm is proposed for the solution exploration. Additionally, a closed-loop feedback system is established, where the main idea is that the tracking information from the current time epoch is utilized to predict the PCRLB and to guide the antenna adjustment for the next time epoch. The simulation results demonstrate the performance improvement compared with the three fixed-antenna configurations. Moreover, the FDPSO can provide close-to-optimal solutions while satisfying the real-time demand.

Research on the SDIF Failure Principle for RF Stealth Radar Signal Design

Radio frequency (RF) stealth is one of the essential research hotspots in the radar field. The anti-sorting signal is an important direction of the RF stealth signal. Theoretically speaking, the anti-sorting signal design is based on the failure principle of the radar signal sorting algorithm, and the SDIF algorithm is a core sorting algorithm widely used in engineering. Thus, in this paper, the SDIF algorithm is first analyzed in detail. It is pointed out that the threshold function of the SDIF algorithm will fail when the signal pulse repetition interval (PRI) value obeys the interval distribution whose length is 20 times larger than the minimum interval of PRI. Secondly, the correctness of the failure principle of SDIF threshold separation is proved by the formula. Finally, the correctness is further verified by the signal design case. The principle of SDIF sorting threshold failure provides theoretical support for anti-sorting RF stealth signal design. It also complements the shortcoming of the casual design for the anti-sorting signal. Furthermore, the principle of SDIF sorting threshold failure helps improve anti-sorting signal design efficiency. Compared with the Dwell & Switch (D&S) signal and jitter signal, the anti-sorting ability of the signal designed by using the sorting failure principle is notably enhanced through simulation and experimentation.

Joint waveform selection and power allocation algorithm in manned/unmanned aerial vehicle hybrid swarm based on chance-constraint programming

In this paper, we propose a joint waveform selection and power allocation (JWSPA) strategy based on chance-constraint programming (CCP) for manned/unmanned aerial vehicle hybrid swarm (M/UAVHS) tracking a single target. Accordingly, the low probability of intercept (LPI) performance of system can be improved by collaboratively optimizing transmit power and waveform. For target radar cross section (RCS) prediction, we design a random RCS prediction model based on electromagnetic simulation (ES) of target. For waveform selection, we build a waveform library to adaptively manage the frequency modulation slope and pulse width of radar waveform. For power allocation, the CCP is employed to balance tracking accuracy and power resource. The Bayesian Cramér-Rao lower bound (BCRLB) is adopted as a criterion to measure target tracking accuracy. The hybrid intelli gent algorithms, in which the stochastic simulation is integrated into the genetic algorithm (GA), are used to solve the stochastic optimization problem. Simulation results demonstrate that the proposed JWSPA strategy can save more transmit power than the traditional fixed waveform scheme under the same target tracking accuracy.

Ultra-Low Sidelobe Waveforms Design for LPI Radar Based on Joint Complementary Phase-Coding and Optimized Discrete Frequency-Coding

In this paper, in order to reduce the probability of the radar waveform intercepted by the passive detection system, the time-bandwidth product of the radar waveform is increased, and the detection probability of the radar waveform to the target is improved. This paper tackles the holographic RF stealth radar and proposes a joint coding waveform based on the linear frequency modulation (LFM) waveform. Joint coding uses complementary codes to perform phase-coding, and combines the codewords optimized by genetic algorithm in order to perform discrete frequency-coding waveform. The joint coding waveform model is theoretically analyzed, and the ambiguity function, pulse compression and target detection probability of the joint coding waveform are obtained by numerical simulation. In addition, the complexity of the algorithm and the low probability of intercept (LPI) characteristic of the joint coding waveform are analyzed. The results show that the joint coding waveform has an approximate “pushpin” ambiguity function, ultra-low sidelobe characteristics, better RF stealth and target detection performance. Finally, it has good application prospects in the current battlefield environment.

Low probability of intercept‐based cooperative node selection and transmit resource allocation for multi‐target tracking in multiple radars architecture

A low probability of intercept (LPI)-based cooperative node selection and transmit resource allocation (CNS-TRA) strategy is proposed for multi-target tracking in multiple radars architecture (MRA). The key idea of the proposed CNS-TRA strategy is to coordinate the radar node selection and the transmit resource that is, dwell time, transmit power, and effective bandwidth allocation to improve the LPI performance, under the constraints of predefined target tracking accuracy requirement and several resource budgets. By incorporating the above controllable parameters, the Bayesian Cramér-Rao lower bound is calculated and used as the accuracy metric for target tracking. Subsequently, this paper develops a fast and effective two-stage-based solution methodology to solve the resulting non-convex and non-linear optimisation problem. Specifically, the optimisation problem can be decomposed into two sub-problems, that is, the radar node selection sub-problem and the transmit resource allocation sub-problem. The active-set method and the interior point approach are utilised to solve those two sub-problems, respectively. Simulation results demonstrate that the CNS-TRA strategy has superiority over other existing algorithms and can achieve better LPI performance for MRA.

LPI Radar Signal Recognition Based on Dual-Channel CNN and Feature Fusion

The accuracy of low probability of intercept (LPI) radar waveform recognition is an important and challenging problem in electronic warfare. Aiming at the problem of the difficulty in feature extraction and the low recognition rates of the LPI radar signal under a low signal-to-noise ratio, and inspired by the symmetry theory, we propose a new approach for the LPI radar signal recognition method based on a dual-channel convolutional neural network (CNN) and feature fusion. Our new approach contains three main modules: the preprocessing module that converts the LPI radar waveforms into two-dimensional time-frequency images using the Choi–Williams distribution (CWD) transformation and performs image binarization, the feature extraction module that extracts different features obtained from the images, and the recognition module that utilizes a multi-layer perceptron (MLP) network to fuse these features and distinguish the type of LPI radar signals. In the feature extraction module, a two-channel CNN model is proposed that extracts Histogram of Oriented Gradients (HOG) features and deep features from time-frequency images, respectively. Finally, the recognition module recognizes the radar signals using a Softmax classifier based on the fused features from two channels. The experimental results from 12 types of LPI radar signals prove the superiority and robustness of the proposed model. Its overall recognition rate reaches 97% when the signal-to-noise ratio is −6 dB.

Multiple‐input multiple‐output with frequency diverse array radar transmit beamforming design for low‐probability‐of‐intercept in cluttered environments

Multiple-input multiple-output with frequency diverse array (FDA-MIMO) radar has drawn great attention due to providing the range-angle beampattern via designing the transmit beamforming matrix. In this work, the authors investigate the transmit beamforming matrix optimization for Low-Probability-of-Intercept (LPI) of FDA-MIMO radar, which can accurately control the transmit beam energy to meet the LPI requirements and the clutter suppression. The idea of the transmit beamforming matrix design is to minimise the transmit power in a specific direction and simultaneously maximise the signal-to-interference-plus-noise ratio under the power constraint on each array element. To this end, a constrained multiple-ratio fractional programming model with concerning the transmit beam matrix and the receive filter is first constructed, and then, it is transformed into two suboptimisation problems using a circular iterative approach. Moreover, the specific solution of the transmit beamforming matrix is obtained using the quadratic transformation method and the alternating direction method of multipliers algorithm. In addition, the computational complexity is also analysed in this paper. The simulation results demonstrate the correctness and effectiveness of the proposed method.

Instantaneous Frequency Estimation of Nonlinear FM Radar Signal Based on Multi-Scale Chirplet Path

Instantaneous frequency is an important parameter to non-linear frequency modulated (NLFM) signal in low probability intercept (LPI) radar. For electronic intelligence, it is very important to accurately estimate instantaneous frequency of NLFM signal. A multi-scale chirplet path pursuit (MCPP) method and its improved method are proposed for electronic intelligence systems to estimate instantaneous frequency of NLFM radar signal in this paper. Firstly, signal duration is divided into a set of dynamic time interval, multi-scale chirplet basis function is established on each time interval simultaneously. And then, projection coefficient in each dynamic interval is calculated basing on chirplet basis functions. And then, chirplet basis functions which have the largest projection coefficient with the analysis signal in each time interval are connected by path pursuit algorithm. Rough estimation of instantaneous frequency will be achieved by connecting the linear frequency of those chirplet basis functions. At last, to solve the problem that instantaneous frequency curve is not smooth for the impact of noise and chirplet errors, least square fitting method is used to further improve estimation accuracy. Experimental results show that, proposed improved MCPP algorithm is suitable for the instantaneous frequency of the NLFM radar signal at low SNR. Compared with time-frequency analysis method, it has higher estimation accuracy. Proposed method can also be applied to the instantaneous frequencies estimation of other NLFM signal without prior knowledge, such as seismic signals and fault diagnosis signals.

LPI Radar Waveform Recognition Based on Neural Architecture Search.

In order to reach the intelligent recognition, the deep learning classifiers adopted by radar waveform are normally trained with transfer learning, where the pretrained convolutional neural network on an external large-scale classification dataset (e.g., ImageNet) is used as the backbone. Though transfer learning could effectively avoid overfitting, transferred models are usually redundant and might not generalize well. To eliminate the dependence on transfer learning and achieve high generalization ability, this paper introduced neural architecture search (NAS) to search the suitable classifier of radar waveforms for the first time. Firstly, one of the innovative technologies in NAS called differentiable architecture search (DARTS) was used to design the classifier for 15 kinds of low probability intercept radar waveforms automatically. Then, a method with an auxiliary classifier called flexible-DARTS was proposed. By adding an auxiliary classifier in the middle layer, the flexible-DARTS has a better performance in designing well-generalized classifiers than the standard DARTS. Finally, the performance of the classifier in practical application was compared with related work. Simulation proves that the model based on flexible-DARTS has a better performance, and the accuracy rate for 15 kinds of radar waveforms can reach 79.2% under the −9 dB SNR which proved the effectiveness of the method proposed in this paper for the recognition of radar waveforms.

Implementation of a Noise-Shaped Signaling System through Software-Defined Radio

Along with the development of electromagnetic weapons, Electronic Warfare (EW) has been rising as the future form of war. Especially in the area of wireless communications, high security defense systems such as Low Probability of Detection (LPD), Low Probability of Interception (LPI), and Low Probability of Exploitation (LPE) communication algorithms are being studied to prevent military force loss. One LPD, LPI, and LPE communication algorithm, physical-layer security, has been discussed and studied. We propose a noise signaling system, a type of physical-layer security, which modifies conventionally modulated I/Q data into a noise-like shape. To suggest the possibility of realistic implementation, we use Software-Defined Radio (SDR). Since there are certain hardware limitations, we present the limitations, requirements, and preferences of practical implementation of the noise signaling system. The proposed system uses ring-shaped signaling, and we present a ring-shaped signaling system algorithm, SDR implementation methodology, and performance evaluations of the system using the metrics of Bit Error Rate (BER) and Probability of Modulation Identification (PMI), which we obtain by using a Convolutional Neural Network (CNN) algorithm. We conclude that the ring-shaped signaling system can perform high LPI/LPE communication functioning because an eavesdropper cannot obtain the correct modulation scheme information. However, the performance can vary with the configurations of the I/Q data-modifying factors.

Information-Theoretic Optimal Radar Waveform Selection With Multi-Sensor Cooperation for LPI Purpose

For the complex battlefield electromagnetic environment, low probability of interception (LPI) performance has become an indispensable ability for modern radars. Waveform selection is one of the most fundamental and effective technical approaches to achieve the LPI performance of radar. However, the existing LPI waveforms are often optimized by some incomplete or weak performance representation metrics of radar or passive intercept devices (PIDs), which leads to a poor LPI performance of the designed waveform. From the perspective of information flow, this paper reformulated the processes of radar target tracking and the interception and identification of PIDs. For simplifing the LPI waveform selection optimization model, the interception and identification performance optimization criterions of PIDs are well-integrated into a comprehensive metric, which is measured by Kullback-Leibler (KL) divergence. Combining it with the radar tracking performance metric which is measured by the mutual information, an LPI waveform selection optimization model is established, which gives full consideration to both radar and PIDs performance. And, a two-round selection method is proposed to solve the optimization model. In addition, a multi-sensor cooperative tracking mechanism based on the accumulated tracking error constraint is designed for radar radiation control. The optimal waveform selection in the framework of multi-sensor cooperative tracking can improve the LPI performance of radar in both the waveform domain and the energy domain. Simulation results validate the effectiveness of the performance optimization metrics of radar and PIDs, and the superiority and feasibility of the designed waveform selection method in the multi-sensor cooperative target tracking performance and LPI performance.

An Improved LPI Radar Waveform Recognition Framework With LDC-Unet and SSR-Loss

Low probability of intercept (LPI) radar signals have been widely used in modern radars due to the advantages of being hardly intercepted by non-cooperative receivers. Therefore, the waveform recognition of LPI radar signals has recently gained increasing attention. In this letter, an improved LPI radar waveform recognition framework with local dense connection U-net and novel loss function is proposed. Specifically, radar signals are transformed into time-frequency images (TFIs) through time-frequency analysis techniques. Then, the local dense connection U-net is proposed to reduce interference of noise and enhance TFIs features. Finally, the recognition task is implemented through a deep convolutional neural network, which is trained with a noise-robust loss function called SSR-loss. Compared with other existing LPI radar waveform recognition frameworks, our method can obtain a significant improvement in recognition accuracy under noise conditions. When signal-to-noise ratio (SNR) is as low as −10 dB, the overall probability of successful recognition on twelve kinds of typical modulated signals can reach up to 91.17%.

Convex Optimization-Based Power Allocation Strategies for Target Localization in Distributed Hybrid Non-Coherent Active-Passive Radar Networks

To more effectively exploit the omnipresent public non-cooperative illuminators of opportunity (IOs) to improve the low probability of intercept (LPI) performance, a power allocation strategy is developed for target localization in distributed hybrid non-coherent active-passive radar networks. The core of the strategy is to optimize each active radar power allocation to minimize the total intercepted power for the hostile intercept receiver in view of power constraints, while achieving the predetermined collaborative target localization accuracy with the assistance of public non-cooperative IOs. Considering the timing uncertainty of public non-cooperative IOs, the localization performance is determined by joint CramrRao lower bound (CRLB) of the target position and the time-of-arrival (TOA) of the direct-path in a distributed passive radar network. Then, the Bayesian CRLB (BCRLB) is derived to evaluate collaborative target localization accuracy, adopted as the optimization criterion for the power allocation strategy. Furthermore, the optimization problem of the power allocation strategy is strictly proved to be a convex optimization, which implies that the global optimal lower bound can be easily obtained. By introducing a semi-definite matrix, the optimization problem is subsequently converted to semi-definite programming (SDP), resolved by the exiting classical algorithm directly. Finally, the simulation results verify the theoretical analysis and the LPI performance of the proposed strategy which outperforms existing strategies.