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Most research regarding passive radar exploiting `illuminators of opportunity', such as FM radio, has focused on detecting and tracking targets. This study explores adding automatic target recognition (ATR) capabilities to such systems. The ATR algorithms described here use the radar cross-section (RCS) of potential targets, collected over a short period of time. The received signal model accounts for aircraft position and orientation, propagation losses, and antenna gain patterns. One proposed algorithm uses a coordinated flight model to estimate aircraft orientations, while a more sophisticated algorithm uses an extended Kalman filter to estimate the target orientations along with measures of uncertainty in those estimates. In both cases, the orientations are estimated using velocity measurements obtained from a tracking algorithm. The radar return of each aircraft in the target library is simulated as though each is executing the same manoeuvre as the target detected by the system. To improve the robustness of the result, the more sophisticated algorithm jointly optimises over feasible orientation profiles and target types via dynamic programming.

The ionosphere causes serious phase error in P-band inverse synthetic aperture radar (ISAR) systems, which makes it difficult to obtain a high-quality image. Recently, the convolutional neural network (CNN) has gained much attention in signal processing, and it can automatically extract features to realise an image super-resolution reconstruction. As a popular CNN-based network, U-net can work with less training samples. Hence, the authors are interested in exploiting and modifying the U-net to enhance the P-band ISAR imaging. In this study, in light of the analysis of the effect of the ionospheric total electron content on the ground-based P-band radar echo signal, a novel ISAR imaging method is proposed for the ionospheric effect correction based on the modified U-net and polar formatting algorithm (PFA). The PFA is performed for the phase error coarse compensation. Then, the phase error fine compensation is exploited by the trained U-net. The proposed method can adapt the ionosphere disturbances and show high performance in imaging quality and computational efficiency. The simulation results show the effectiveness of the proposed method.

Automatic modulation classification of radar signals, which plays a significant role in both civilian and military applications, is researched in this study through a deep learning network. In this study, a novel network combined a shallow convolution neural network (CNN), long short-term memory (LSTM) network and deep neural network (DNN) is proposed to recognise six types of radar signals with different signal-to-noise ratio (SNR) levels from -14 to 20 dB. First, raw signal sequences in the time domain, frequency domain and autocorrelation domain are as input for a shallow CNN. Then the features extracted by CNN will be the input of LSTM network. Finally, DNNs will output the signal modulation types directly. The simulation results demonstrate that the accuracies in autocorrelation domain are all more than 90% at -6 dB and close to 100% when SNR > -2 dB. The recognition performances of the three domains are compared. Compared with other recognition methods, the proposed method has higher average accuracy and better performance under low SNR condition. The measured results show that the proposed method has achieved high accuracies of common four kinds of measured radar signals.

In this study, the problem of the low probability of intercept (LPI) performance optimisation for a joint radar-communications system (JRCS) is investigated, which can simultaneously estimate surveillance channel parameters from the target returns and decode the received communications signals. The primary purpose of the proposed LPI performance optimisation strategy is to improve the LPI performance of a JRCS by optimising the energy spectral density of radar waveform design and the communications power allocation while maintaining a predetermined mutual information threshold for parameter estimation and a certain communications data rate for information delivery. The traditional isolated sub-band (TISB) situation, radar isolated sub-band (RISB) situation, and communications isolated sub-band (CISB) situation are analysed. Subsequently, the technique of Lagrange multipliers and the Karush-Kuhn-Tuckers optimality conditions are employed to solve the resulting optimisation problems. Moreover, the successive interference cancellation method is adopted to process the received radar-communications compound signal. Finally, several numerical simulations are conducted to demonstrate the theoretical calculations and to validate the effectiveness of the proposed LPI performance optimisation strategy. It is also shown that the achievable LPI performance in RISB and CISB situations is much better than that in TISB situation.

Collocated multiple-input multiple-output radar can track multiple targets simultaneously by transmitting multiple orthogonal beams and adopting the digital beamforming technology. In this scenario, the authors propose a joint power and time width allocation approach, which combines a cognitive tracking model based on the posterior Cramer-Rao lower bound (PCRLB) and the square-root cubature Kalman filter. The aim of the optimisation model is to improve the velocity estimation accuracy by minimising the sum of the PCRLBs of the velocity of multiple targets, which are predicted based on the feedback information from the cognitive tracking model. However, there are two finite working resources in the optimisation model: the total transmit power of multiple beams and the total effective time width of each corresponding signal. The resource allocation problem can be transformed into a non-convex optimisation problem, which can be converted into a standard convex optimisation problem by the linear relationship between the optimal power and the optimal time width. In this way, the joint power and time width allocation scheme is established as an adaptive closed-loop system. Numerical results demonstrate that the velocity tracking accuracy can be improved efficiently by the proposed algorithm.

The authors present a non-traditional, parametric method for velocity, angle, and range estimation in a frequency diverse array radar. Unlike the traditional beamforming techniques, the proposed scheme transmits an omni-directional sinusoid regardless of the target locations. They propose a simple sampling strategy, which eliminates the need for employing a bank of bandpass filters at the receiver. Under the proposed sampling scheme the received data follows a convenient low rank model. They exploit this model to design a fast and accurate parametric estimation algorithm. Their velocity and range estimation steps employ known spectral analysis techniques. For angle estimation, they propose a new grid-less sparse recovery algorithm. The resulting methods are applicable to any arbitrary array geometry. Furthermore, they propose an efficient method to mitigate jamming. They also provide necessary guidelines to avoid ambiguity and achieve the desired resolution performance. The Cramer-Rao lower bound for the estimation problem is derived. The utility of the proposed method is demonstrated via numerical simulation results.

To deal with problems of uncertain modulations and multiple pulse widths in pulse waveforms (PWs) during the identifying procedure, a novel specific emitter identification (SEI) method based on PW images (PWIs) and convolutional neural network is proposed. In the method, a more accurate signal model is built with considering the rising, steady and falling part of the whole PW based on actual radar pulse signals. PWI achieves transforming time-domain waveforms to 2D binary images as an SEI analysis feature. To match the PWI feature, a convolutional neural network with the small convolutional kernel is designed to extract the subtle features and finish the supervised training. By tuning the parameters of the convolutional neural network, it completes a balance of consuming time and identifying accuracy. Simulations and experiments indicate that the proposed method outperforms the existed methods on identifying radar individuals with uncertain modulations and multiple pulse widths in the intercepted pulse signals.

Funding: UK Science and Technology Facilities Council ST/N006569/1 (DR). This study presents a convolutional neural network (CNN) based drone classification method. The primary criterion for a high-fidelity neural network based classification is a real dataset of large size and diversity for training. The first goal of the study was to create a large database of micro-Doppler spectrogram images of in-flight drones and birds. Two separate datasets with the same images have been created, one with RGB images and other with grayscale images. The RGB dataset was used for GoogLeNet architecture-based training. The grayscale dataset was used for training with a series architecture developed during this study. Each dataset was further divided into two categories, one with four classes (drone, bird, clutter and noise) and the other with two classes (drone and non-drone). During training, 20% of the dataset has been used as a validation set. After the completion of training, the models were tested with previously unseen and unlabelled sets of data. The validation and testing accuracy for the developed series network have been found to be 99.6% and 94.4% respectively for four classes and 99.3% and 98.3% respectively for two classes. The GoogLenet based model showed both validation and testing accuracies to be around 99% for all the cases. Postprint

In this study, by employing the intra-pulse cross-correlation (IPCC) operation, an unambiguous velocity estimation method is proposed for narrow-band long-range radars with high carrier frequency and low pulse repetition frequency. This estimation algorithm is simple and could be easily implemented in existing radar systems without changing the radar hardware or the pulse transmitting scheme. Comparing with the slow time dimension correlation algorithm, the accuracy of the proposed intra-pulse frequency domain method is greatly improved, and the brute-force search for the unknown motion parameters is also unnecessary. By first setting a small frequency offset of the IPCC operation, the unambiguous velocity region could be significantly enlarged. Using the relatively coarse but unambiguous estimates and increasing the frequency offset step by step, the IPCC is repeatedly applied to obtain more accurate estimates. Note that the estimation results of the IPCC algorithm could be used in the maximum-likelihood estimator for ambiguity resolution. The Cramer-Rao bound for the proposed algorithm is derived, and the optimal frequency offset in the sense of estimation accuracy is also analysed. Through numerical simulations for both synthetic and real radar data, the effectiveness of the proposed estimation algorithm is verified.

To apply the Ramanujan filter bank based on the compressed sensing theory to the period estimation of multiple sets of radar pulses, alternatives to period data and the Ramanujan Subspace are proposed in this study. First, the rationality of alternatives to the TOA (time of arrival) model is illustrated by comparing the advantages and disadvantages of the time-point model and the TOA model. Next, by clarifying the zero-sum energy property of the Ramanujan Subspace, the possibility of finding an alternative to the discrete Fourier transform sequence with smaller data is proved. On this basis, a new algorithm for estimating the stagger period of mixed pulses is proposed, which introduces the initial phase of the stagger pulses. The results of the experiments show that the algorithm can accurately estimate the hidden stagger periods of mixed pulses, and it is adept at dealing with false and missing mixed pulses.

Simulation of radar cross-sections of pedestrians at automotive radar frequencies forms a key tool for software verification test beds for advanced driver assistance systems. Two commonly used simulation methods are the computationally simple scattering centre model of dynamic humans and the shooting and bouncing ray technique based on geometric optics. The latter technique is more accurate but computationally complex. Hence, it is usually used only for modelling scattered returns of still human poses. In this work, the authors combine the two methods in a linear regression framework to accurately estimate the scattering coefficients or reflectivities of point scatterers in a realistic automotive radar signal model which they subsequently use to simulate range-time, Doppler-time and range-Doppler radar signatures. The simulated signatures show a normalised mean square error 81% with respect to measurement results generated with an automotive radar at 77 GHz.

The frequency diverse array multiple-input multiple-output (FDA-MIMO) radar provides range estimation capability by exploiting a small frequency offset across the transmit sensors, which has been utilised in numerous applications. However, the estimation performance is basically limited by the array geometry and signal bandwidth. In this study, the authors propose a new FDA-MIMO framework, i.e. the unfolded coprime array with `unfolded' coprime frequency offsets (UCA-UCFO) framework, for joint angle and range estimation without ambiguity. The array aperture and signal bandwidth are obviously expanded by employing UCA in the spatial domain and frequency domain, which results in significantly enhanced estimation accuracy and resolution. In addition, we construct the joint angle and range estimation problem as a two-dimensional (2D)-multiple signal classification spatial spectrum and transform 2D total spectrum search into a 1D local spectrum search by introducing a successive iteration (SUIT) algorithm. The SUIT algorithm can significantly relieve the computational burden but without performance degradation. The Cramer-Rao bounds of angle and range are provided as a performance benchmark. The analysis and simulations have validated the superiority and advantages of the UCA-UCFO framework and SUIT algorithm with respect to location accuracy, resolution, and computational complexity.

High-frequency surface-wave radar (HFSWR) is widely used in vessel and aircraft detection, sea-state sensing and wind-field mapping. Target detection suffers from the ionospheric clutter, which is reflected by the ionosphere. Adaptive beamforming (ABF) has been used for ionospheric clutter mitigation. However, the performance of ABF is limited by the heterogeneous ionospheric clutter and degrees of freedom (DOF) of the antennas array. In order to improve the performance, here, the one-dimensional ABF is expanded to two-dimensional fast-time space–time adaptive processing (STAP), which combines beam and range domains to obtain more DOFs than that in the ABF. In addition, the blind sources separation (BSS) method is also used to improve the spatial covariance matrix estimation accuracy of STAP in the heterogeneous ionospheric clutter background. The simulation and real data results demonstrate the effectiveness of the proposed BSS-STAP method in HFSWR.

The prevalent imaging method in inverse synthetic aperture radar (ISAR) system is range-Doppler (RD) method, which is implemented by the fast Fourier transformation (FFT). FFT is computationally efficient, but it comes with a price – the problems of wide main-lobes and high side-lobes, especially under the sparse apertures condition. In addition, the resolution of RD method is determined by the radar parameters, which poses limitation to super-resolution imaging, multi-tasking and cognitive reconfigurable applications. In this study, the authors propose a novel super-resolution ISAR imaging method based on the total least squares-estimation of signal parameters via rotational invariance technique (TLS-ESPRIT). The locations and intensities of the scatterers are obtained by employing the ESPRIT algorithm and the least squares technique. Then the ISAR image is formulated, having circumvented all of the above-mentioned limitations. Experiments based on simulated and real measured data validate the effectiveness of the proposed method.

The characteristics of the radar returns for unmanned aerial vehicle (UAV) are useful for radar detection and classification of the UAV. In this study, the authors carried out an experiment in an anechoic chamber to measure the fully polarimetric echoes of a fixed-wing UAV in X-band. With the measured data, they analysed the distribution of the radar cross-section of the UAV. They also analysed the distributions of the phases and polarisation ratios of the UAV returns in various polarisation modes. They found that the radar cross-sections of the fixed-wing UAV in HH and VV polarisation modes obey lognormal distribution. The radar cross-sections of the UAV in VH and HV polarisation modes obey Weibull distribution. The means of the radar cross-section in co-polarisation modes are 8–10 dBsm higher than those in cross-polarisation modes. The phases of the UAV echo in HH, HV, VH and VV polarisation modes are uniformly distributed within 0 and 2π. The amplitudes of the polarisation ratios of the UAV echo are well fitted by lognormal distribution.

Low-observable manoeuvring target detection is a challenging problem for radar signal processing, due to the complex environment, target manoeuvrability, limited observation time etc. The study proposed a novel long-time coherent integration (LTCI) method for radar manoeuvring target, especially for low-observable unmanned aerial vehicle targets. The fast non-parametric searching LTCI via a non-uniform (NU) resampling and scale processing (SP) technique is proposed, where the high-order signal phase is reduced to linear term using NU resampling. After that, the SP method is applied to realise the range migration compensation. The sparse Fourier transform (FT) and inverse FT are performed for the final integration. The manoeuvring target would appear as peaks in the non-uniformly resampling and SP-sparse LTCI domain. Experiments using two sets of real radar data indicate that the proposed method can achieve a good balance between computational cost and integration gain. In addition, detailed detection performances are compared with the traditional methods, e.g., moving target detection, fractional FT, fractional ambiguity function, Radon-based LTCIs, and sparse fractional FT.

In the past few years, the commercial use of drones has exploded, since they are a safe and cost-effective solution for many kinds of problems. However, this fact also opens the door for malicious use. This work presents a novel system able to detect and recognise drones from other targets, allowing the police and security agencies to deal with this new aerial thread. The proposed system only uses a persistent range-Doppler radar, avoiding the restrictions of the optical sensors, usually required for the recognition part. The processing is based on constant false alarm rate detection stage, followed by a convolutional neural network that performs the recognition. This network takes as input raw range-Doppler radar data and predicts their class (car, person, or drone). For this purpose, an extensive controlled trial test campaign has been performed, resulting in a novel dataset with more than 17,000 samples of drones, cars, and people, acquired in real outdoor scenarios. As far as authors' knowledge, this is the first range-Doppler radar database for the recognition of drones and other targets. The high-accuracy results (99.48%) suggest that this system could be successfully used in security and defence applications to discriminate between drones and other entities.

A numerical method based on the recursive convolution finite difference time domain was used to calculate the radar cross-section (RCS) of a square target under different conditions. The results indicate that for electron number density below 10 16 m − 3 , unmagnetised plasma provides better RCS reduction compared to magnetised plasma. For this range of electron density, the wave bending plays an important role and its effect is stronger than the resonant and non-resonant absorption. For densities higher than 2 × 10 16 m − 3 , and for collision frequencies less than plasma frequency, magnetised plasma causes greater RCS reduction compared to unmagnetised plasma due to strong resonant absorption. In this situation, the inhomogeneous magnetic field is preferred because of its broader bandwidth. The enhanced bandwidth is due to multi-resonance absorption of the inhomogeneous magnetic field. For collision frequencies above the plasma frequency, resonance absorption weakens and non-resonance absorption prevails. Then in this range of plasma parameters, the unmagnetised plasma is the proper choice for optimum RCS reduction.

An out-of-band (OoB) emission modelling of high-power pulse linear frequency modulation (PLFM) radar is proposed in this study. Aiming at the frequency-domain characteristic of the OoB emission, the analytical expression of the frequency-domain model by simplifying the Fresnel integral is presented. And in consideration of the time-domain characteristic of the OoB emission, the bandpass time-domain analytical model is presented. Furthermore, the frequency-domain model is improved by introducing the characteristic of transition time appeared at the rising and falling edges, and the time-domain model is improved by introducing the characteristic of frequency transition band appeared at the junction of the pass-band and stop-band of the bandpass filter. The simulation and experimental results confirm that the proposed model can accurately describe the time- and frequency-domain characteristics of the OoB emission of PLFM radar. It can be used for the time- and frequency-domain interference mechanism analysis, and guide the analysis on interference suppression demand and research on interference suppression method of the time and frequency domains.

Both waveforms of the frequency diverse array radar and the orthogonal frequency division multiplexing multiple-input–multiple-output radar are range coupled, so they provide an inherent advantage of angle–range joint imaging. The derivation of the signal models shows that the ranging principles are the same and the main differences lie in the spectrum structures and the demodulation schemes. Space–range adaptive processing (SRAP) is proposed for the two kinds of radar systems. Numerical simulations show that super-resolution angle–range images with extra-low sidelobes can be obtained via SRAP. The super-resolution performances of the range-coupled radars are evaluated and analysed.

In this study, a transmit waveform design method based on spatial-temporal optimisation for multiple-input multiple-output (MIMO) radar is proposed. The goal is not only to design the waveforms for beampattern matching, but also to minimise the autocorrelation sidelobes of the spatial synthesis signals of interested direction. Especially, to synthesise the constant envelope waveform directly, an improved sequential convex algorithm is proposed to tackle the non-convex problem in spatial optimisation. Then the autocorrelation sidelobes are reduced by using the steepest descent algorithm in temporal optimisation. Finally, the authors assess the effectiveness of the proposed technique through numerical simulations in comparison with the traditional and the alternating direction method of multipliers method.

In this work, the authors study the problem of detecting and tracking small targets using high-resolution maritime radar, where sea clutter is correlated in range, and its amplitude fluctuations are characterised by occasional spikes. To tackle this problem, they develop a Bernoulli track-before-detect filter, as the optimal recursive Bayesian detector/estimator of target state and its presence in noise. A realistic clutter model, in the form of the K -distribution with unknown distribution parameters, is adopted. Target amplitude fluctuations are also included in the model. The detection and tracking improvement are demonstrated by simulations and compared against a conventional point target tracking algorithm.

A method for evaluating the share of scattering component related to structural components of unmanned air vehicle (UAV) in the field scattered by the UAV is proposed. The method takes into account the scattering interaction of the UAV's dielectric hull with perfectly conducting elements under the hull as well as the scattering contribution of its dielectric components into the scattered field. The latter contributions are evaluated based on the methods of short-wave diffraction. The model of UAV has been designed that includes both metallic elements and dielectric hull. Scattering simulation results are obtained and the UAV model's scattering characteristics are analysed.

This study examines moving target detection for airborne radar in heterogeneous environments. The non-homogeneity of the clutter may lead to a shortage of training samples in practice. In contrast to detectors assuming rich training data, the authors consider a knowledge-aided treatment for training data-limited scenarios by incorporating a priori knowledge of the clutter subspace. The proposed detector is developed within the generalised likelihood ratio test framework, based on the sparsity of the clutter response in the space-time domain. It does not require training samples and allows the usage of uncertain a priori knowledge of the clutter subspace, which may be erroneous. The maximum likelihood estimate of the target amplitude is obtained via oblique projection, which provides more accurate estimates compared with the conventional orthogonal projection. Moreover, they jointly exploit the sparsity of the clutter signal, the block-Toeplitz nature of the clutter covariance matrix, and the a priori knowledge about the clutter subspace, and develop an atomic norm minimisation approach to achieve super-resolution estimation of the clutter response. The simulation results indicate that the proposed detector outperforms several state-of-the-art methods.

In order to address the off-grid angular estimation of direction of departure and direction of arrival of a target for bistatic multiple-input multiple-output radar, a novel method involving the combined effect of compressive sensing theory and an optimal estimation algorithm is proposed. The proposed method, named as simultaneous orthogonal matching pursuit with Kalman filtering (SOMP-KF) first exploit the sparsity of the target in the spatial domain by discretising the area of detection to formulate a dictionary matrix. Sparse sampling created during the discretisation of the off-grid space leads to a remodelling of the problem where a linearisation technique that inculcates a grid-varying position vector is applied to the Kalman filtering method. The modified Kalman filtering method resolves the off-grid offset, which hence results in achieving the off-grid angle estimation objective. Additionally, the Cramer-Rao lower bounds are derived theoretically for all parameters to explain the estimation performance. Experimental analysis against existing methods indicates the proposed SOMP-KF effectiveness in improving the angle estimation of target whiles, maintaining a minimal computational cost than its competitors.

The coexistence of radar and communication system is a crucial task owing to the shortage of spectrum resources. In this study, the authors consider a multiple manoeuvring targets tracking problem via a radar network in the presence of several non-cooperative, spatially random, and spectral overlapped communication areas (CAs). Instead of costly inner pattern optimisation, a communication awareness joint beam and power allocation (CJBPA) scheme of radar network is proposed to achieve high flexibility in coexistence. In CJBPA, radars and CAs treat the signals from each other as interference, which are formulated and discussed from the perspective of spectrum and space. The CJBPA optimises the overall tracking performance, which is characterised by the posterior Cramer-Rao lower bound under the consideration of coexistence. The resultant non-convex problem is relaxed and decoupled as an integrated two-staged optimisation. To accelerate the numerical procedures of the optimisations, custom-built primal dual interior point methods are derived by the structure information of the problems. The effectiveness of the proposed CJBPA scheme is assessed through simulations, showing that by using spatial and spectral information of undesired signals, the tracking performance can be optimised while the impacts of interference on both radars and CAs are restricted.

In the introduction, the topic of passive radar jamming and the possibilities of using dipole reflectors (Chaff) to provide radar camouflage are described. This study further describes the two-dimensional and three-dimensional mathematical and physical simulations and rows of Chaff in free space. It then concentrates on the rotation and distances of Chaff with regard to electric field and radar cross-section (RCS) of simulating Chaff puffs in limited space. The theoretical analysis is supplemented by complex computer based simulation. Finally, the required amount of Chaff for protecting aircraft in airspace is determined. This study provides a detailed overview of the physical processes occurring in a limited number of Chaff in open space by the use of a modern simulation software tool.

The study utilises two shape factors as the radar feature set for the recognition of a mid-sized aircraft target in the high-frequency (HF) band. The two shape factors are the dihedral and tilt features of the aircraft parts. The determination of the two shape factors is feasible through the optimum polarisation states of the target's complex natural resonances in the HF band. The identification algorithm applies a resonance-weighted measure to the feature set in a supervised learning approach to discriminate between two targets of the same class that slightly differ in shape. The rate of correct recognition within a sector of the target aspect exceeded 80% for receiver sensitivity above −10 dB.

Accurate antenna motion-measurement is an essential pre-condition for synthetic aperture radar (SAR) to produce well-focused images. The measurement accuracy at high and low frequencies affects the quality of images and the geolocation error. Hence, motion compensation and focusing techniques require a minimum degree of accuracy in the radar motion measurements. The Inertial Measurement Unit (IMU) sensor selection process is done based on the SAR parametric requirements. The IMU instruments have inherent limited precision and accuracy, which are significantly related to the technology and the cost. The navigation algorithm may improve the precision and accuracy to overcome the limitations of the IMU sensor. This study intends to improve motion measurement accuracy using frequency-weighted state estimation. The proposed algorithm shows an error reduction in state estimation and an improvement in some parameter indices which are in relation to SAR image quality and geolocation. Two innovative algorithms are proposed in this study. The first one is the frequency-weighted Kalman filter which is an improved form of the Kalman filter. Another one is multi-resolution decomposition which is an approach to evaluate the SAR motion measurement system.

Cubic phase (CP) signal is widely used in radar and sonar signal processing and the CP signal received by the radar or sonar sensors may miss part of discrete samples and be corrupted by noise. In this study, a novel end-to-end CP signal recovery method is proposed to recover the CP signal that experiences data missing and noise corruption based on deep convolutional neural network (DCNN). Two key techniques are used in the structure design of the proposed network. The first is dilated convolution, which has a larger receptive field than the standard convolution operation and can extract information more efficiently in the CP signal recovery problem. The second is denseNet, which connects all layers directly and can alleviate the vanishing-gradient problem. Experiment results show that the proposed DCNN-based method achieves superior performance to the traditional compressed sensing-based method both from the perspective of recovery error and time consumption.

Clutter suppression for non-side-looking airborne radar operating at high pulse repetition frequency is an intractable problem because the clutter statistical properties vary with the range, especially in the near range. In addition, the near-range clutter is always coupled with the far-range clutter. Elevation prefiltering is recognised as an effective method to suppress the range-dependent near-range clutter, but the elevation training samples required must be independent and identically distributed (IID) and not contaminated by the far-range clutter. Here, an elevation-compensation-prefiltering space-time adaptive processing (STAP) algorithm is developed. In the proposed algorithm, the elevation training samples are selected from the elevation snapshots corresponding to the first pulse, which are not contaminated by the far-range clutter. An elevation compensation method is presented to alleviate the range dependence, and then there are adequate IID training samples to estimate the elevation covariance matrix. The performance of the near-range clutter suppression is improved. As for the residual range-independent far-range clutter, it can be suppressed by the cascaded azimuth-Doppler STAP. Numerical examples demonstrate the effectiveness of the proposed algorithm.

In sky-wave over-the-horizon radar (OTHR), there are some difficulties to efficiently detect targets in the non-homogeneous sea clutter by using conventional constant false alarm rate detectors. The amplitude of the clutter is supposed to follow the Weibull distribution in OTHR. Moreover, the characteristic of the clutter with a continuous region distribution in the range-Doppler (RD) map suggests that there exist the spatial relationship between neighbouring cells. The authors propose a rigorous algorithm to incorporate these relationships and the regularisation of interferences into the estimation of the shape parameter and scale parameter for every cell under test. This algorithm is mainly based on the consideration that the improvement of detection performance could be carried out by properly utilising the spatial information between neighbouring cells in the non-homogeneous Weibull clutter. Then, the adaptive detection threshold is calculated by the estimated parameters. The validity and effectiveness of the proposed algorithm are verified by simulations and the experiments in the real RD maps collected from an experimental sky-wave OTHR system.

Recently, the authors have built and evaluated a prototype quantum radar in the laboratory which operates at microwave frequencies. This radar, which they call a quantum two-mode squeezing radar (QTMS radar), generates a pair of entangled microwave signals and transmits one of them through free space, using the other signal as a reference to perform matched filtering. The specific type of entanglement is called a two-mode squeezed vacuum, a type of continuous-variable entanglement between two frequencies. Motivated by the success of these experiments, they try to better understand the entangled QTMS radar signals in this study. They do so by comparing it to a simpler, more conventional radar system, which they call a two-mode noise radar (TMN radar). They also show how both types of radars are related to standard noise radars as described in the literature. They find that the signals for QTMS radar signals and TMN radar signals have the same mathematical form and that they are related to noise radar by a simple mathematical transformation. This shows that QTMS radar signals can be emulated by a fictional, idealised TMN radar and that it is possible to apply results from the noise radar literature to QTMS radar.

In the context of white complex Gaussian noise, this study presents one constant false-alarm rate mono-pulse detector for both the narrowband and wideband pulse-Doppler (PD) radars. To this end, coherent-like integration is proposed to improve the signal-to-noise ratios of one radar echo. The PD radar returned signals are first performed by stretch processing. Stretched signals are analysed by short-time Fourier transform (STFT) in the time-frequency representation. Coherent-like integration is then utilised to operate the two-dimensional (2D) STFT matrix and the new 2D matrices after coherent-like integration are decomposed to obtain singular values. Finally, the largest singular value, which is assumed to be corresponding to an isolated scatterer for narrowband PD radars (dominate scatterer for wideband PD radars) is selected as the test static to be compared with the detection threshold. Since the new detector is not highly sensitive to the target motion, it can solve the detection problem of the high-speed manoeuvring target. Furthermore, the experiments based on raw data are conducted to illustrate the performance of the proposed detector.

Owing to covariance matrix estimation error, desired signal steering vector mismatch, and the existence of target signal in training samples, most of adaptive beamforming algorithms suffer from a great performance degradation. Aim at this, this study proposes a robust adaptive beamforming algorithm for multiple-input-multiple-output radar. To be specific, the sample covariance matrix is replaced by the reconstructed covariance matrix, to narrow the difference between the maximum and minimum noise eigenvalues. In addition, the diagonal loading technique is applied to correct the mismatched desired signal steering vector by maximising the output signal-to-interference-plus-noise ratio of adaptive beamformer, and a simple closed-form solution to loading factor can be further obtained. Computer simulation results demonstrate that the proposed algorithm can efficiently improve the robustness of adaptive beamformer against both covariance matrix estimation error and desired signal steering vector mismatch.

The vortex electromagnetic (EM) wave carrying orbital angular momentum (OAM) has attracted much attention in radar applications. Aimed at the moving target detection application of vortex EM waves, the Doppler effect and the micro-Doppler (m-D) effect, both including the linear Doppler shift and the angular Doppler shift, are investigated. The theoretical analyses demonstrate that the Doppler effect and the m-D effect in vortex-EM-wave-based radar are significantly more complicated than those in traditional non-vortex-EM-wave-based radar, and can provide additional features for target identification and recognition. Simulations are given to validate the proposed theoretical analyses.

Feature extraction for radar high-resolution range profiles (HRRPs) is an essential procedure for robust target recognition based on radar HRRPs. It is almost always better to utilise multiple HRRPs from the target than a single HRRP. The commonly used recognition techniques are not robust enough to extract features from HRRP sequences, especially when there is not enough training data. In this study, the authors present a compact model named the infinite conditional restricted Boltzmann machine (iCRBM) for jointly feature learning and recognition of radar HRRPs. The model is developed from the conditional restricted Boltzmann machine, which is a powerful model for representing high-dimensional and multi-modal conditional distributions. Unlike ordinary RBMs, iCRBM can automatically select the model complexity according to the data, which especially suits for the case of large data dimensionality and small training dataset. A multi-scale structure is also proposed for learning multiple scales of temporal/spatial dependencies. Two types of radar HRRP recognition experiments were conducted to validate the efficiency and robustness of iCRBM: the multi-view HRRP recognition and the small aperture HRRP recognition. The results indicate that, the proposed model can be more adaptive at learning the feature of HRRPs than other common methods. The multi-scale structure is helpful for better recovering missing HRRP samples from non-consecutive sequences.

Distributed scattering centre (DSC) is a particular type of scattering centres which has the strongest scattering amplitude among all scattering centres. Furthermore, their distributed signatures in radar images have directly shown geometries of targets. Therefore, DSCs play an important role in target recognition. DSCs are currently described by the attributed scattering centre (ASC) model, which is developed out of the asymptotic expansion solutions to canonical geometries. However, rather than canonical geometries, real radar targets have various geometric structures, which show different signatures in radar images. In order to characterise these various signatures, the parametric model is modified. Scattered fields from planar and single-curved surfaces with arbitrary shapes are studied in this study and motivated by which, the parametric models of DSCs for more general structures are presented. To validate these models, the scattered waves and the post-imaging results simulated by these models are compared with those obtained by a rigorous full-wave numerical method, and those obtained by the conventional ASC model. The comparison results demonstrate these models have a higher accuracy over the conventional model in simulations of scattered waves, as well as inverse synthetic aperture radar image signatures of different geometric structures.

A solid-state, very high frequency (VHF) band, moving target detection air surveillance radar requires a complex pulse burst waveform to mitigate the visibility issues originating from the blind Doppler intervals and range eclipsing. The waveform employs multiple pulse repetition frequencies to mitigate the effects of the blind Doppler intervals and interleaves short and long pulses to mitigate range eclipsing. In the authors’ previous works, they pointed out that the waveform design is a multi-objective optimisation problem and defined the mathematical model of the waveform optimisation problem. They also presented how the exact Pareto optimal (PO) set can be determined by means of exhaustive search. In this paper, they improve the mathematical model of the waveform optimisation problem by altering the way in which one of the objective functions is calculated and adding a new constraint, which eliminates meaningless solutions. Finally, they propose a solution method based on a multi-objective evolutionary algorithm. The performance evaluation test indicates that compared to the exhaustive search, the proposed method provides a solution that is insignificantly different. However, the proposed method is more scalable and requires over three orders of magnitude smaller number of comparisons to determine the PO set, which makes it more viable for the online waveform adaptation.

Direction-of-arrival and polarisation estimation is an important issue in array signal processing. Among various polarisation sensitive arrays (PSAs), arrays with only measurements of the electric field are most extensively applied in practice. In this study, the manifold ambiguity of such electric-measurement-only PSA is investigated to evaluate the uniqueness of parameter estimation. For co-centred PSAs and spatially-spread PSAs, the necessary and sufficient conditions of linearly dependent steering vectors are established based on the cosine similarity. Furthermore, for various arrays, the explicit parameter sets corresponding to trivial manifold ambiguity are provided. Moreover, for the noisy case, the closed-form Cramer-Rao bounds for arbitrary PSAs are also presented to evaluate the performance bound of parameter estimation with the considered arrays. Simulations and experimental results of high-frequency radar further reveal the influences of array configurations on the identifiability and performance bound of PSAs, and verify the corresponding theoretical results. The presented results can be easily generalised to other PSAs containing magnetic measurements, which provide guidelines for designing the spatial and polarimetric configuration of PSAs to ensure unambiguous and accurate parameter estimation.

In this study, the authors propose an energy-efficient adaptive transmit beamspace design for cognitive frequency diverse array (FDA) radar to efficiently detect and track the target in a cognitive way, particularly, for the case when the target is lost in one scan. Additionally, an algorithm is presented for a selection of the illumination range-angle sector to recover a lost target. Moreover, an algorithm is proposed to discriminate the target from interferers, while an FDA beampattern time-variance that is normally ignored in the literature is also considered. Finally, the transmit beamspace is adaptively updated to illuminate the predicted range-angle-based area of interest in each cognitive scanning cycle. The proposed design generates a single maximum beam pattern by using a set of non-uniform frequency offsets along an FDA. Numerical results show that the proposed method achieves improved target detection and tracking performance as compared to the standard frequency diverse and phased-array radars due to its increased output signal-to-interference-plus-noise ratio, while improved energy efficiency is achieved due to an adaptive range-angle sector selection algorithm.

In modern radars, the problem of estimating elevation angle at low grazing angles is typically solved using super-resolution techniques. These techniques often require one to provide an estimate of the number of waveforms impinging the array, which one can accomplish using model selection techniques. In this study, the authors investigate the performance of an alternative approach, based on the Bayesian-like model averaging. The Bayesian approach exploits the fact that the parameters of the model related to multipath signals are nuisance ones, which allows one to avoid the estimation of the number of waveforms and improves estimation performance. The method is introduced for the classical conditional maximum-likelihood estimator and extended to its, recently proposed, robustified version. The authors find, however, that the robustified estimator includes its own soft-decision mechanism and benefits from the averaging only for low levels of model uncertainty.

Jet engine modulation (JEM) are micro-Doppler features obtained from the radar data of aircraft, including jet aircraft and helicopters, and generally viewed as unique phenomenon suitable for identifying aerial targets. The authors demonstrate however, that JEM are not unique, and that the rotating wheel spokes on the wheels of ground vehicles produce a modulation similar to the rotating rotor blades of jet engines and helicopter rotor blades. They also develop a mathematical model to analyse the radar signal scattering mechanism of wheel spokes, and also employ a Ku-band Doppler radar system to collect radar echoes from a wheeled vehicle and a helicopter. Both the theoretical and experimental results verify the existence of rotor blade modulation (RBM) phenomena from helicopters and wheel spoke modulation (WSM) phenomena from vehicles. Both RBM and WSM are similar to JEM features. This fact indicates that JEM is a necessary but insufficient condition for the identification of aerial targets, and additional recognition features inherent in surface surveillance radar are needed to distinguish the JEM spectra arising from aerial targets and ground vehicles.

In order to reduce the uncertainty of radar manoeuvring target tracking (RMTT) in cluttered background, a joint detection and tracking algorithm based on cognitive radar is proposed. First, a prism structure resolution cell of time-delay, Doppler and azimuth is designed. Then, an approximate expression of measurement error covariance including waveform and detection threshold parameters is given. Then, based on the idea of human brain perception-action cycle, a joint waveform and detection threshold adaptive tracking algorithm based on minimum information entropy criterion is proposed. Finally, a cognitive structure adaptive particle filter (CSAPF) algorithm, based on parallel structure of extended Kalman filter (EKF) and particle filter, are used with Probabilistic Data Association (PDA) algorithm for RMTT. During the process, CSAPF-PDA can always obtain the best tracking performance with the minimum number of particle samples, thus effectively taking into account the tracking accuracy and efficiency. The effectiveness of the proposed algorithm is verified by simulation experiments.

The study presents a direction-finding method that is not limited to the main lobe zones of antenna patterns. The technique allows for the angular sector of interest to be divided by few channels, pursuing low size, weight, costs, and computational power in radar detection. Experiments done on a building rooftop have shown that, with a minimum of 150 processed pulses, the distributions of estimates of direction of arrival are well behaved, with a relationship between standard deviation and signal-to-noise ratio. As a result, information is provided that may soften the deinterleaving of radar pulses.

This study proposes a low-band scheme utilising the polarisation dominance of the target's resonance regions in the frequency domain to recognise a fighter-sized aircraft. The methodology implements a binary decision tree based on three polarisation power terms, namely Stokes variables, to determine the polarisation dominance of six directions, and subsequently, predict the canonical shape of the target substructures. The decision tree comprises three inequalities of the Stokes variables subject to an orthogonality threshold to reflect the dominant polarisation directions as a function of the target resonance region. The simulation data for two fighter-sized aircraft illustrate the feasibility of the method by comparing the differences (or similarity) in the target decision outcomes. The results indicate that resonance-scattering region lies within the frequency band of 9–200 MHz where thin-wedge scattering is prominent within the frequency band of 9–30 MHz, whereas the corner (dihedral) scattering becomes dominant within the band of 110–170 MHz, mainly when the radar illuminates the target sides aspect. The method was robust to the noise and target aspect change using the paradigms of the MIG29 and F16 aircraft models.

Ionospheric clutter is detrimental to target detection in high-frequency surface-wave radar (HFSWR). Adaptive beamforming (ABF) has been adopted to suppress the ionospheric clutter in recent years. Unfortunately, the performance of ABF degrades due to the heterogeneity of the ionospheric clutter. In this study, a new approach is proposed to suppress the ionospheric clutter. A novel heterogeneous ionospheric clutter model based on the mixture of mutually independent ionospheric clutter sources is established. The blind source separation (BSS) approach is used to separate the clutter sources first. Then the separated components are exploited to estimate the spatial covariance matrix (SCM) of the cell under test. The SCM estimation based on BSS is more accurate than the classical sample matrix inversion method under the heterogeneous ionospheric clutter. Therefore, the ABF performance improves due to the better SCM estimation. The simulation and real data results demonstrated the effectiveness of the new BSS-based ABF method in HFSWR. The signal-to-clutter-plus-noise ratio of the new method improved compared with the traditional ABF based on the SMI method. The new method can help to detect targets under the heterogeneous ionospheric clutter. It may also be a promising methodology in other ABF applications.

The authors address the performance analysis of the least squares (LS) Prony method for estimating the natural frequencies of radar target in the study. Based on the perturbation theory and the Taylor series expansion, the authors get explicit expressions of the mean square error (MSE) of the LS solution, the MSE of the z-plane natural frequencies and the MSE of the s-plane natural frequencies. The validity of the derived expressions is demonstrated by comparing the analytic results with simulation results. For further validation of the results, simulation results of the GPOF method have been used for comparison.

The azimuthal imaging can be acquired by the orbital angular momentum (OAM) wave. In addition, a large-scale OAM mode number is necessarily required for high azimuthal resolution. To reduce the required OAM mode number, an azimuthal imaging method based on compressed sensing and OAM mode selection is presented. To be specific, the system architecture and the mathematical model of the OAM imaging radar are established. Meanwhile, an efficient OAM generation method with rotational antenna is proposed. Moreover, experiments show that different radar cross sections (RCSs) of a specific complex target can be obtained by different OAM waves, which are generated by the proposed method. It is a delight to find that the signal-to-noise ratio gain can be achieved due to the appropriate OAM mode selection in the experiment. Since different OAM waves lead to different RCSs of complex target, the OAM modes corresponding to high RCSs are selected to measure the azimuth for low complexity. Furthermore, simulations are conducted to evaluate the performance of the proposed azimuthal imaging method for the general complex target. Using Monte Carlo simulations, it is found that the accuracy of azimuthal imaging can be guaranteed by the proposed azimuthal imaging method with only approximately 6% selected OAM modes.

In this study, mutual information (MI)-based waveform design methods for the coexistence between orthogonal frequency division multiplexing (OFDM) radar system and communication system corrupted by Gaussian mixture interference are investigated for the first time. Firstly, the received signal is formulated as a Bayesian linear model. Subsequently, from a statistical perspective, the approximate differential entropy of received signal is derived, followed by three different approximate MIs and corresponding theoretic upper bounds. After that, two adaptive waveform design methods are proposed by maximising MI and minimising radar transmitted power, respectively. The numerical results show that exploiting the reflected communication signals helps to obtain higher MI value and reduce radar transmitted power. Besides, by maximising the MIs, the optimised radar waveforms remarkably outperform the fixed ones, which benefits the estimation performance.