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In dual-channel synthetic aperture radar (SAR) systems, the estimation of the four-dimensional motion parameters of the ground maneuvering target is a critical challenge. In particular, when spatial degrees of freedom are used to enhance the target’s output signal-to-clutter-plus-noise ratio (SCNR), it is possible to have multiple solutions in the parameter estimation of the target. To deal with this issue, a novel algorithm for estimating the motion parameters of ground moving targets in dual-channel SAR systems is proposed in this paper. First, the random sample consensus (RANSAC) and modified adaptive 2D calibration (MA2DC) are used to prevent the target’s phase from being distorted as a result of channel balancing. To address range migration, the RFRT algorithm is introduced to achieve arbitrary-order range migration correction for moving targets, and the generalized scaled Fourier transform (GSCFT) algorithm is applied to estimate the polynomial coefficients of the target. Subsequently, we propose using the synthetic aperture length (SAL) of the target as an independent equation to solve for the four-dimensional parameter information and introduce a windowed maximum SNR method to estimate the SAL. Finally, a closed-form solution for the four-dimensional parameters of ground maneuvering targets is derived. Simulations and real data validate the effectiveness of the proposed algorithm.

This paper proposes an unambiguous method for joint angle and range estimation in colocated multiple-input multiple-output (MIMO) radar using the nested frequency diverse array (NFDA). Unlike a conventional phased array (PA), the transmission beampattern of FDA-MIMO radar depends not only on angle but also on range, which enables the precise identification of ambiguous regions in the two-dimensional frequency space. As a result, we can simultaneously estimate the angle and range of targets using FDA-MIMO radar, even when range ambiguity exists. By employing a nested array configuration, the degrees of freedom (DOFs) of the FDA are expanded. This expansion leads to improved accuracy in parameter estimation and enables a greater number of identifiable targets. In addition, the Cramér–Rao lower bound (CRLB) and the algorithm complexity are obtained to facilitate performance analysis. The simulation outcomes are presented to showcase the superior performance of the suggested approach.

A Frequency Diverse Array (FDA), developed innovatively based on phased array radar, can obtain an angle-range-time-dependent multidimensional transmit beampattern by modulating frequencies across different transmit antenna elements, which considerably increases the beam control ability and signal processing dimension. After joint transmit-receive processing, an FDA can be applied to various areas, such as multidimensional parameter joint estimation, mainlobe deceptive jammer suppression, ambiguous clutter suppression, and high-resolution and wide-swath imaging. This study investigates the waveform design and signal processing method of a multifunctional integrated system based on an FDA from the system level, with emphasis on new signal processing methods for integrated detection and estimation, integrated ambiguity resolution and jammer suppression, as well as integrated Synthetic Aperture Radar (SAR) imaging and moving target detection. Moreover, the application prospects of FDA multifunctional integrated systems are provided.

Non-side-looking airborne radar provides important applications on account of its all-round multi-angle airspace coverage. However, it suffers clutter range dependence that makes the samples fail to satisfy the condition of being independent and identically distributed (IID), and it severely degrades traditional approaches to clutter suppression and target detection. In this paper, a novel reweighted extreme learning machine (ELM)-based clutter suppression and range compensation algorithm is proposed for non-side-looking airborne radar. The proposed method involves first designing the pre-processing stage, the special reweighted complex-valued activation function containing an unknown range compensation matrix, and two new objective outputs for constructing an initial reweighted ELM-based network with its training. Then, two other objective outputs, a new loss function, and a reverse feedback framework driven by the specifically designed objectives are proposed for the unknown range compensation matrix. Finally, aiming to estimate and reconstruct the unknown compensation matrix, special processes of the complex-valued structures and the theoretical derivations are designed and analyzed in detail. Consequently, with the updated and compensated samples, further processing including space–time adaptive processing (STAP) can be performed for clutter suppression and target detection. Compared with the classic relevant methods, the proposed algorithm achieves significantly superior performance with reasonable computation time. It provides an obviously higher detection probability and better improvement factor (IF). The simulation results verify that the proposed algorithm is effective and has many advantages.

It is difficult for the traditional radar to suppress deceptive mainlobe interference and separate the range ambiguous clutter. The proposal of a waveform diverse array changes the way of obtaining information through utilizing degrees-of-freedom in the transmit dimension. Through flexible system design and signal processing methods, this array enhances the ability of information extraction and improves the anti-jamming and detection performance, compared with the traditional phased array and Multiple-Input Multiple-Output (MIMO) radar. This paper summarizes the research progress of waveform diverse array radars in China and overseas and provides the basic concepts of the array diversity system regarding frequency, time, and phase modulation. Furthermore, the research trend of waveform diverse array radars has been discussed. Based on the existing basic theory and key technology research, the advantages of a waveform diverse array in providing new information about targets and increasing the additional controllable degrees-of-freedom of the system are verified, thereby improving the multidimensional detection capability of the new radar system.

In the present complex electromagnetic environment, radar target detection is threatened by different kinds of interferences, especially mainlobe deceptive interference, which occupies the same energy distributions of targets spatially, meaning that targets and interferences cannot be discriminated. To make matters worse, the number of suppressible interferences is limited by the number of physical array elements, leading to the degradation of the suppression performance of traditional radar. In this work, we propose a frequency-increment-based interference suppression method for minimum redundancy frequency diverse array multiple-input multiple-output (MR-FDA-MIMO) radar, which effectively solves the aforementioned two problems. The interference suppression method consists of two steps: (i) in the sidelobe barrage interference suppression stage, the interference-plus-noise covariance matrix is reconstructed to overcome the influence of the true targets and mainlobe deceptive interference on the performance of the beamformer; (ii) in the mainlobe deceptive interference suppression stage, a nonadaptive beamforming method is employed to suppress mainlobe deceptive interference and overcome the impact of insufficient virtual samples on interference suppression performance. Additionally, we design a frequency-increment-based MR-FDA-MIMO radar, fully utilizing the advantages of the virtual array to enhance interference suppression performance and increase the number of interferences. Numerical experiments undertaken demonstrate the effectiveness of the algorithm under different scenarios.

To achieve high-resolution and wide-swath (HRWS) synthetic aperture radar (SAR) images, this paper focuses on resolving the problem of separating range-ambiguous echoes with the space–time coding (STC) array. At the modeling stage, the transmit elements and pulses of the STC array are configured with time delay and phase coding modulation, which introduces extra degrees of freedom (DOFs) in the transmit domain. To separate the echoes corresponding to different range-ambiguity regions, the equivalent transmit beamforming is performed in the two-dimensional space–frequency domain. Moreover, in order to compensate for the loss of range resolution during the beamforming progress, the frequency splicing method is proposed. At the analysis stage, the distributed target simulation is provided to demonstrate the effectiveness of obtaining HRWS SAR images in the STC radar. Additionally, the performance of resolving range ambiguity is compared with the traditional radar in terms of the range-ambiguity-to-signal ratio (RASR).

Aimingat non-side-looking airborne radar, we propose a novel unsupervised affinity propagation (AP) clustering radar detection algorithm to suppress clutter and detect targets. The proposed method first uses selected power points as well as space-time adaptive processing (STAP) weight vector, and designs matrix-transformation-based weighted input data, with which the first unsupervised weighted AP clustering is proposed by means of their similarity matrix, responsibility values and availability values. Then, new reconstructed weighted power inputs are designed, and the second weighted AP clustering is proposed. Finally, with their cluster results, a detection-discriminant criterion is designed for the judgment of target detection, and simultaneously, the clutter is suppressed. Compared with the conventional and important STAP, ADC and JDL algorithms, and several SO-based, GO-based and OS-based CFAR algorithms, the proposed unsupervised algorithm achieves much higher probability of detection and provides distinctly superior target-detection performance. With reasonable computation time, it can better conquer the range dependence in characteristic of clutter and better process non-independent identically distributed (non-IID) samples of non-side-looking radar. Sufficient simulations are performed, and they demonstrate that the proposed unsupervised algorithm is preferable and advantageous.

This paper proposes a cooperated range ambiguous clutter suppression method for moving target detection in the background of range-ambiguous clutter with a phased array (PA)–frequency diverse array (FDA) dual-mode radar. With the FDA mode, the range-ambiguous clutters are discriminated in the transmit spatial frequency domain, and thus the clutter covariance matrixes (CCMs) corresponding to unambiguous and ambiguous regions can be independently estimated. Therefore, the enhanced CCM can be reconstructed by using a linear combination of these distinguished CCMs from different range regions. With the PA mode, the enhanced CCM is applied, thus taking advantages of its high beampattern gain as well as alleviating the range ambiguous clutter suppression problem. Simulation results are presented to verify the effectiveness of the proposed method in range-ambiguous clutter scenarios.

In this article, we propose a novel phase unwrapping method termed the square-root cubature Kalman filter phase unwrapping (SCKFPU) method. Specifically, as the system model of the interferometric synthetic aperture (InSAR) phase unwrapping can be formulated as the discrete Markovian jump system for tracking a maneuvering target, a phase unwrapping method is proposed by combining the SCKF algorithm with a phase gradient estimator. Moreover, we design a phase quality estimate function, and present an optimal path-following strategy. The strategy ensures that the SCKFPU method simultaneously performs noise suppression and unwraps InSAR images along the pixels with high-reliance to the pixels with low-reliance. Simulation results based on synthetic data, true InSAR data, and measured (real) InSAR data show that the proposed InSAR phase unwrapping method can achieve better performance compared with other existing phase unwrapping methods.

Clutter suppression is a key problem for airborne radar, and space-time adaptive processing (STAP) is a core technology for clutter suppression and moving target detection. However, in practical applications, the non-uniform time-varying environments including clutter range dependence for non-side-looking radar lead to the training samples being unable to satisfy the sample requirements of STAP that they should be independent identical distributed (IID) and that their number should be greater than twice the system’s degree of freedom (DOF). The lack of sufficient IID training samples causes difficulty in the convergence of STAP and further results in a serious degeneration of performance. To overcome this problem, this paper proposes a novel autoencoder neural network for clutter suppression with a unique matrix designed to be decoded and encoded. The main challenges are improving the accuracy of the estimation of the clutter-plus-noise covariance matrix (CNCM) for STAP convergence, designing the form of the data input to the network, and making the network successfully explored to the improvement of CNCM. For these challenges, the main proposed solutions include designing a unique matrix with a certain dimension and a series of covariance data selections and matrix transformations. Consequently, the proposed method compresses and retains the characteristics of the covariances, and abandons the deviations caused by the non-uniformity and the deficiency of training samples. Specifically, the proposed method firstly develops a unique matrix whose dimension is less than half of the DOF, meanwhile, it is based on a processing of the selected clutter-plus-noise covariances. Then, an autoencoder neural network with l2 regularization and the sparsity regularization is proposed for the unique matrix to be decoded and encoded. The training of the proposed autoencoder can be achieved by reducing the total loss function with the gradient descent iterations. Finally, an inverted processing for the autoencoder output is designed for the reconstruct ion of the clutter-plus-noise covariances. Simulation results are used to verify the effectiveness and advantages of the proposed method. It performs obviously superior clutter suppression for both side-looking and non-side-looking radars with strong clutter, and can deal with the insufficient and the non-uniform training samples. For these conditions, the proposed method provides the relatively narrowest and deepest IF notch. Furthermore, on average it improves the improvement factor (IF) by 10 dB more than the ADC, DW, JDL, and original STAP methods.

Range-ambiguous clutter is an inevitable issue for airborne forward-looking array radars, especially with the high pulse repetition frequency (PRF). In this paper, a method to suppress the range-ambiguous clutter is proposed in an FDA-MIMO radar with a forward-looking planar array. Compressed sensing FDA technology is used to suppress the range-ambiguous clutter and the forward-looking non-uniformity short-range clutter of radar. Specifically, first, the range ambiguous clutter in different regions is separated by the characteristics of the planar array radar elevation dimension and FDA radar range coupling. Meanwhile, regarding the issue of the FDA radar main lobe moving between coherent pulses, a main lobe correction (MLC) algorithm proposes a solution for the issue, where the FDA radar cannot coherently accumulate signals in the case of non-full angle illumination. Finally, compressed sensing technology and elevation dimension filtering are utilized to suppress the range ambiguous clutter at the receiver, with the approach alleviating the range dependence of clutter in the observation region. A small number of clutter snapshots can obtain an approximately ideal clutter covariance matrix through compressed sensing sparse recovery. The method not only reduces the number of training samples, but also overcomes the problem of clutter non-uniformity in the forward-looking array. Therefore, the clutter suppression problems faced by the high repetition frequency airborne radar forward-looking array structure are solved. At the analysis stage, a comparison among the conventional MIMO and FDA methods is carried on by analyzing the improvement factor (IF) curves. Numerical results verify the effectiveness of the proposed method in range-ambiguous clutter suppression.

Hypersonic vehicles (HSV) have attracted much attention in recent years because of its military value. The radar system will face more serious clutter problem due to the increasing altitude and velocity. Thus, clutter characteristics analysis of hypersonic vehicles radar (HSV-R) is essential to clutter suppression. In this study, clutter model for HSV-R is proposed and the selection of pulse repetition frequency (PRF) is discussed. Finally, the results of simulation and the analysis of clutter characteristics under different PRFs are given.

The multi-target tracking filter under the Bayesian framework has strict requirements on the prior information of the target, such as detection probability density, clutter density, and target initial position information. This paper proposes a novel robust measurement-driven cardinality balance multi-target multi-Bernoulli filter (RMD-CBMeMBer) for solving the multiple targets tracking problem when the detection probability density is unknown, the background clutter density is unknown, and the target’s prior position information is lacking. In RMD-CBMeMBer filtering, the target state is first extended, so that the extended target state includes detection probability, kernel state, and indicators of target and clutter. Secondly, the detection probability is modeled as a Beta distribution, and the clutter is modeled as a clutter generator that is independent of each other and obeys the Poisson distribution. Then, the detection probability, kernel state, and clutter density are jointly estimated through filtering. In addition, the correlation function (CF) is proposed for creating new Bernoulli component (BC) by using the measurement information at the previous moment. Numerical experiments have verified that the RMD-CBMeMBer filter can solve the multi-target tracking problem under the condition of unknown target detection probability, unknown background clutter density and inadequate prior position information of the target. It can effectively estimate the target detection probability and the clutter density.

The target detection of the passive multiple-input multiple-output (MIMO) radar that is comprised of multiple illuminators of opportunity and multiple receivers is investigated in this paper. In the passive MIMO radar, the transmitted signals of illuminators of opportunity are totally unknown, and the received signals are contaminated by the colored Gaussian noise with an unknown covariance matrix. The generalized likelihood ratio test (GLRT) is explored for the passive MIMO radar when the channel coefficients are also unknown, and the closed-form GLRT is derived. Compared with the GLRT with unknown transmitted signals and channel coefficients but a known covariance matrix, the proposed method is applicable for a more practical case whenthe covariance matrix of colored noise is unknown, although it has higher computational complexity. Moreover, the proposed GLRT can achieve similar performance as the GLRT with the known covariance matrix when the number of training samples is large enough. Finally, the effectiveness of the proposed GLRT is verified by several numerical examples.

Spatial spectrum estimation, also known as direction of arrival (DOA) detection, is a popular issue in many fields, including remote sensing, radar, communication, sonar, seismic exploration, radio astronomy, and biomedical engineering. MUltiple SIgnal Classification (MUSIC) and Estimation Signal Parameter via Rotational Invariance Technique (ESPRIT), which are well-known for their high-resolution capability for detecting DOA, are two examples of an eigen-subspace algorithm. However, missed detection and estimation accuracy reduction often occur due to the low signal-to-noise ratio (SNR) and snapshot deficiency (small time-domain samples of the observed signal), especially for sources with different SNRs. To avoid the above problems, in this study, we develop a DOA detection approach through signal subspace reconstruction using Quantum-Behaved Particle Swarm Optimization (QPSO). In the developed scheme, according to received data, a noise subspace is established through performing an eigen-decomposition operation on a sampling covariance matrix. Then, a collection of angles randomly selected from the observation space are used to build a potential signal subspace on the basis of the steering matrix of the array. Afterwards, making use of the fact that the signal space is orthogonal to the noise subspace, a cost function, which contains the desired DOA information, is designed. Thus, the problem of capturing the DOA information can be transformed into the optimization of the already constructed cost function. In this respect, the DOA finding of multiple signal sources—that is, the multi-objective optimization problem—can be regarded as a single objective optimization problem, which can effectively reduce the probability of missed detection of the signals. Subsequently, the QPSO is employed to determine an optimal signal subspace by minimizing the orthogonality error so as to obtain the DOA. Ultimately, the performance of DOA detection is improved. An explicit analysis and derivation of the developed scheme are provided. The results of computer simulation show that the proposed scheme has superior estimation performance when detecting signals with very different SNR levels and small snapshots.

The image of ground maneuvering targets may be defocused due to the Doppler ambiguity, high-order range migration (RM), and Doppler frequency migration (DFM) caused by the target’s complex motions in a synthetic aperture radar (SAR) system. To settle these problems, an efficient algorithm based on discrete polynomial-phase transform (DPT), keystone transform (KT), and matched filtering processing (MFP) is presented for ground maneuvering target refocusing and motion parameter estimation in this paper. Firstly, the DPT is applied to transform the cubic phase into the quadratic phase and simultaneously eliminate the quadratic RM, cubic RM, and quadratic DFM. Furthermore, the Doppler ambiguity containing Doppler center blur and Doppler spectrum ambiguity is also dealt with effectively by introducing a very small fixed lay time after DPT operation. Then, the KT is performed to correct the linear RM. After that, the matched filtering function related to the target’s equivalent third-order coefficient is constructed to compensate for the residual linear DFM in the range-time and slow-time domain. Lastly, a well-refocused image of the maneuvering target can be acquired, and the target’s motion parameters can be estimated effectively. The proposed algorithm has high computational efficiency and possesses favorable refocusing performance and motion parameter estimation precision. Simulation and real data processing results prove the effectiveness of the presented algorithm.

It is a challenge to realize wide swath imaging due to the conflict between Doppler ambiguity and range ambiguity for hypersonic vehicle (HSV) radar. In addition, there are many conditions requiring the forward-looking imaging. In a forward-looking synthetic aperture radar (SAR) system, left−right ambiguity arises, since two symmetrical targets have the same Doppler frequency magnitude. After selecting an appropriate pulse repetition frequency (PRF) to avoid Doppler ambiguity, we only need to solve the range ambiguity and left−right ambiguity. To handle these issues, this paper proposes an approach to resolve the range ambiguity and left−right ambiguity using the frequency diverse array (FDA). With the range-angle-dependent property of the transmit steering vector, FDA can distinguish the range ambiguous echoes in the spatial frequency domain. By performing transmit beamforming after range compensation, the echo from the desired range region can be extracted from ambiguous echoes. Then, the back projection (BP) algorithm is used to achieve imaging. Next, the echoes of all channels are processed by two receive beamformers, which are designed for the right and left sides, respectively. With the aforementioned procedures, an unambiguous image can be obtained. Simulation results have verified the effectiveness of the proposed approach.

As a special type of coherent collocated Multiple-Input Multiple-Output (MIMO) radar, a circulating space-time coding array (CSTCA) transmits an identical waveform with a tiny time shift. It provides a simple way to achieve a full angular coverage with a stable gain and a low sidelobe level (SLL) in the range domain. In this paper, we address the problem of direction-of-arrival (DOA) estimation in CSTCA. Firstly, we design a novel two-dimensional space-time matched filter on receiver. It jointly performs equivalent transmit beamforming in the angle domain and waveform matching in the fast time domain. Multi-beams can be formed to acquire controllable transmit freedoms. Then, we propose a beamspace multiple signal classification (MUSIC) algorithm applicable in case of small training samples. Next, since targets at the same range cell show characteristics of coherence, we devise a transformation matrix to restore the rotational invariance property (RIP) of the receive array. Afterwards, we perform spatial smoothing in element domain based on the transformation. In addition, the closed-form expression of Cramer-Rao lower bound (CRLB) for angle estimation is derived. Theoretical performance analysis and numerical simulations are presented to demonstrate the effectiveness of proposed approaches.

Multiple-input multiple-output (MIMO) radar imaging can provide higher resolution and better sensitivity and thus can be applied to targets detection, recognition, and tracking. Missile-borne forward-looking SAR (MFL-SAR) is a new and special MIMO radar mode. It has advantage of two-dimensional (2D) imaging capability in forward direction over monostatic missile-borne SAR and airborne SAR. However, it is difficult to obtain accurate 2D frequency spectrum of the target echo signal due to the high velocity and descending height of this platform, which brings a lot of obstacles to imaging algorithm design. Therefore, a new imaging algorithm for MFL-SAR configuration based on the method of series reversion is proposed in this paper. This imaging method can implement range compression, secondary range compression (SRC), and range cell migration correction (RCMC) effectively. Finally, some simulations of point targets and comparison results confirm the efficiency of our proposed algorithm.

As a special multiple-input multiple-output (MIMO) radar networking mode, missile-borne forward-looking synthetic aperture radar (MFL-SAR) has many potential applications. This paper describes and analyzes properties of this new configuration. Range history and Doppler history are analyzed and derived using the designed geometric configuration. Then the expressions of range and Doppler resolution are determined based on the validity of two-dimensional (2D) resolution imaging capability. To help to design the proper system and motion parameters of this configuration, key parameters affecting the imaging ability are found out. Due to high velocities and accelerations of both transmitter and receiver, high-order terms in the slant range equation should be kept to reduce the approximation error. The range resolution and Doppler resolution of MFL-SAR are both space-variant and time-variant owing to the complexity of this configuration. The tiny changes of 2D resolution during the synthetic aperture time should be considered when designing the imaging algorithm of MFL-SAR.

A sparse recovery based transmit-receive angle imaging scheme is proposed for bistatic multiple-input multiple-output (MIMO) radar. The redundancy of the transmit and receive angles in the same range cell is exploited to construct the sparse model. The imaging is then performed by compressive sensing method with consideration of both the transmit and receive array gain uncertainties. An additional constraint is imposed on the inverse of the transmit and receive array gain errors matrices to make the optimization problem of the CS solvable. The image of the targets can be reconstructed using small number of snapshots in the case of large array gain uncertainties. Simulation results confirm the effectiveness of the proposed scheme.