Search Results (20)

Accurate estimation of Interrupted Sampling Repeater Jamming (ISRJ) sampling duration is essential for effective radar anti-jamming. However, in complex electromagnetic environments, the simultaneous presence of suppressive and deceptive jamming, coupled with significant signal overlap in the time–frequency domain, renders ISRJ separation and parameter estimation considerably challenging. To address this challenge, this paper proposes a method utilizing the Fractional Fourier Transform (FRFT) and a Hybrid Modality Fusion Network (HMFN) for ISRJ signal separation and sampling-duration estimation. The proposed method first employs FRFT and a time–frequency mask to separate the ISRJ and target echo from the mixed signal. This process effectively suppresses interference and extracts the ISRJ signal. Subsequently, an HMFN is employed for high-precision estimation of the ISRJ sampling duration, offering crucial parameter support for active electromagnetic countermeasures. Simulation results validate the performance of the proposed method. Specifically, even under strong interference conditions with a Signal-to-Jamming Ratio (SJR) of −5 dB for deceptive jamming and as low as −10 dB for suppressive jamming, the regression model’s coefficient of determination still reaches 0.91. This result clearly demonstrates the method’s robustness and effectiveness in complex electromagnetic environments. Full article

To effectively utilize the rich spectral information of hyperspectral remote sensing images (HRSIs), the fractional Fourier transform (FRFT) feature of HRSIs is proposed to reflect the time-domain and frequency-domain characteristics of a spectral pixel simultaneously, and an FRFT order selection criterion is also proposed based on maximizing separability. Firstly, FRFT is applied to the spectral pixels, and the amplitude spectrum is taken as the FRFT feature of HRSIs. The FRFT feature is mixed with the pixel spectral to form the presented spectral and fractional Fourier transform mixed feature (SF²MF), which contains time–frequency mixing information and spectral information of pixels. K-nearest neighbor, logistic regression, and random forest classifiers are used to verify the superiority of the proposed feature. A 1-dimensional convolutional neural network (1D-CNN) and a two-branch CNN network (Two-CNN_SF²MF-Spa) are designed to extract the depth SF²MF feature and the SF²MF-spatial joint feature, respectively. Moreover, to compensate for the defect that CNN cannot effectively capture the long-range features of spectral pixels, a long short-term memory (LSTM) network is introduced to be combined with CNN to form a two-branch network C-CLSTM_SF²MF for extracting deeper and more efficient fusion features. A 3D-CNN_SF²MF model is designed, which firstly performs the principal component analysis on the spa-SF²MF cube containing spatial information and then feeds it into the 3-dimensional convolutional neural network 3D-CNN_SF²MF to extract the SF²MF-spatial joint feature effectively. The experimental results of three real HRSIs show that the presented mixed feature SF²MF can effectively improve classification accuracy. Full article

Faced with increasingly complex electronic jamming environments, intra-pulse agility has become a primary method of anti-interrupted-sampling repeater jamming (ISRJ) for radar systems. However, existing intra-pulse agile signals suffer from high autocorrelation sidelobe levels and limited jamming suppression capabilities. These issues restrict the performance of intra-pulse agile signals in complex electromagnetic environments.This paper proposes an anti-interrupted-sampling repeater jamming method based on Simulated Annealing–2-optimization (SA-2opt) parallel optimization of waveforms and fractional domain extraction. Firstly, the proposed method employs the SA-2opt parallel optimization algorithm to optimize the joint frequency and chirp rate encoding waveform. Then, the received signal is subjected to the fractional Fourier transform (FrFT) and inverse transform to extract the target signal. Finally, jamming detection is conducted based on the multi-dimensional features of the pulse-compressed signal. After this detection, a time-domain filter is constructed to achieve jamming suppression. The optimized waveform exhibits the following advantages: the sub-pulses are orthogonal to each other, and autocorrelation sidelobe levels are as low as -20.7dB. The method proposed in this paper can achieve anti-ISRJ in the case of a high jamming-to-signal ratio (JSR). Simulation experiments validate both the effectiveness of the optimized waveform in achieving low autocorrelation sidelobes and the anti-ISRJ performance of the proposed method. Full article

This study investigated the integration of detection and communication techniques. First, the fractional-order Fourier transform (FRFT) is introduced, and the golden section method, parabolic interpolation, and Brent method are applied to search for the optimal fractional-order domain to accurately estimate the parameters of the linear frequency modulation (LFM) signal. Second, the three search algorithms and the performance of the integrated sensing and communication waveform are simulated. The Brent method improves the parameter searching efficiency by approximately 30% compared with the golden section method; the bit error ratio (BER) of the integrated LFM signal can reach 10⁻⁴ with a signal-to-noise ratio (SNR) of 3 dB. The results show that the integrated waveform can realize the detection function with guaranteed communication performance. An anti-frequency sweeping interference method based on the fractional domain matching order was also carried out to optimize the detection performance of the integrated waveform. Through the analysis of the difference-frequency signal under frequency sweeping interference, two methods, direct filtering, and pairwise cancellation filtering, are used to suppress the interference signal and detect the target distance. The simulation evaluated the detection performance of the two methods under different signal-to-interference ratios (SIR) and filter widths. The simulation results show that the pairwise cancellation filtering suppresses the frequency sweeping interference by 4–6 dB more than the direct filtering with an SIR ≤ −15 dB. Both filtering methods can correctly extract the target position information under frequency sweeping interference with a low signal-to-interference ratio (SIR). In conclusion, this study provides an effective solution for parameter estimation optimization and frequency-sweeping interference suppression for FRFT-based sensing communication systems. Full article

Synthetic aperture radar (SAR) operating mode recognition plays a crucial role in SAR countermeasures and serves as the foundation for effective SAR interference. To address the limitations of current SAR operating mode recognition algorithms, such as low recognition rates, poor generalization, and limited engineering applicability under low signal-to-noise ratio (SNR) conditions, an enhanced algorithm named dual-input feature fusion ShuffleNet (DIFF-ShuffleNet) based on intercepted SAR signal data is proposed. First, the SAR signal is processed by combining pulse compression and time–frequency analysis technology to enhance anti-noise robustness. Then, an improved lightweight ShuffleNet architecture is designed to fuse range pulse compression (RPC) maps and azimuth time–frequency features, significantly improving recognition accuracy in low-SNR environments while maintaining practical deployability. Moreover, an improved coarse-to-fine search fractional Fourier transform (CFS-FRFT) algorithm is proposed to address the chirp rate estimation required for RPC. Simulations demonstrate that the proposed SAR operating mode recognition algorithm achieves over 95.00% recognition accuracy for SAR operating modes (stripmap, spotlight, sliding spotlight, and scan) at an SNR greater than −8 dB. Finally, four sets of measured SAR data are used to validate the algorithm’s effectiveness, with all recognition results being correct, demonstrating the algorithm’s practical applicability. Full article

In indoor visible light communication (VLC) and visible light positioning (VLP) systems, the performance of conventional orthogonal frequency-division multiplexing (OFDM) schemes is often compromised due to the nonlinear characteristics and limited modulation bandwidth of light-emitting diodes, the multipath effect in enclosed indoor environments, and the relative positions of transmitters and receivers. This paper proposes an OFDM scheme based on the fractional Fourier transform (FRFT) to address these issues, demonstrating promising results when applied to indoor VLC and VLP systems. The FRFT, a generalization of the conventional Fourier transform (FT) in the fractional domain, captures information in both the time and frequency domains, offering greater flexibility than the FT. In this paper, we first introduce the computation method of the reality-preserving FRFT for an intensity modulation/direct detection VLC system and integrate it with OFDM to optimize system performance. By adopting FRFT-OFDM under the optimal fractional order, we enhance both the bit error ratio (BER) performance and positioning accuracy. Simulation results reveal that the FRFT-OFDM scheme with an optimized fractional order significantly improves the BER and positioning accuracy compared to the FT-OFDM scheme across most receiver positions within the indoor observation plane. For communication, the FRFT-OFDM scheme achieves over 6 dB $E_b/N_0$ gain compared to the FT-OFDM scheme at a BER of $3\times {10}^{-4}$ when the receiver is positioned at most locations in the room. For positioning, the FRFT-OFDM scheme enhances positioning accuracy by more than 1 cm relative to the FT-OFDM scheme at most locations in the room. Notably, both systems maintain the same computational complexity and spectral efficiency. Full article

This paper proposes a new hybrid model for classifying stress states using EEG signals, combining multi-domain transfer entropy (TrEn) with a two-dimensional PCANet (2D-PCANet) approach. The aim is to create an automated system for identifying stress levels, which is crucial for early intervention and mental health management. A major challenge in this field lies in extracting meaningful emotional information from the complex patterns observed in EEG. Our model addresses this by initially applying independent component analysis (ICA) to purify the EEG signals, enhancing the clarity for further analysis. We then leverage the adaptability of the fractional Fourier transform (FrFT) to represent the EEG data in time, frequency, and time–frequency domains. This multi-domain representation allows for a more nuanced understanding of the brain’s activity in response to stress. The subsequent stage involves the deployment of a two-layer 2D-PCANet network designed to autonomously distill EEG features associated with stress. These features are then classified by a support vector machine (SVM) to determine the stress state. Moreover, stress induction and data acquisition experiments are designed. We employed two distinct tasks known to trigger stress responses. Other stress-inducing elements that enhance the stress response were included in the experimental design, such as time limits and performance feedback. The EEG data collected from 15 participants were retained. The proposed algorithm achieves an average accuracy of over 92% on this self-collected dataset, enabling stress state detection under different task-induced conditions. Full article

The double random phase encoding (DRPE) image encryption method has garnered significant attention in color image processing and optical encryption thanks to its R, G, and B parallel encryption. However, DRPE-based color image encryption faces two challenges. Firstly, it disregards the correlation of R, G, and B, compromising the encrypted image’s robustness. Secondly, DRPE schemes relying on Discrete Fourier Transform (DFT) and Discrete Fractional Fourier Transform (DFRFT) are vulnerable to linear attacks, such as Known Plaintext Attack (KPA) and Chosen Plaintext Attack (CPA). Quantum walk is a powerful tool for modern cryptography, offering robust resistance to classical and quantum attacks. Therefore, this study presents an optical color image encryption algorithm that combines two-dimensional quantum walking (TDQW) with 24-bit plane permutation, dubbed OCT. This approach employs pseudo-random numbers generated by TDQW for phase modulation in DRPE and scrambles the encrypted image’s real and imaginary parts using the generalized Arnold transform. The 24-bit plane permutation helps reduce the R, G, and B correlation, while the generalized Arnold transform bolsters DRPE’s resistance to linear attacks. By incorporating TDQW, the key space is significantly expanded. The experimental results validate the effectiveness and security of the proposed method. Full article

In this paper, a one-dimensional (1-D) range profile of the hypersonic target enveloped by a plasma sheath is investigated. Firstly, the non-uniform property of the plasma sheath is studied and its impact on the wideband electromagnetic (EM) wave is analyzed. A wideband radar echo model for the plasma-sheath-enveloped hypersonic target is constructed. Then, by exploiting the relationship among the incident depth, reflection intensity, and plasma velocity, it reveals that distinct scatter points in various areas of the target will suffer from varying reflection intensity and coupled velocity, leading to severe defocusing in the range profile. To tackle this issue, a novel focusing algorithm combing the Fractional Fourier Transform (FRFT) with the CLEAN technique is developed, which independently calculates the coupled plasma velocity and compensates for the phase error via a series of iterative procedures. Finally, the influence of the plasma sheath on the 1-D range profile and the effectiveness of the proposed focusing algorithm are validated through simulations. Full article

In this paper, we first use the quantum Fourier transform (QFT) and quantum phase estimation (QPE) to realize the quantum fractional Fourier transform (QFrFT). As diverse definitions of the discrete fractional Fourier transform (DFrFT) exist, the relationship between the QFrFT and a classical algorithm is then established; that is, we determine the classical algorithm corresponding to the QFrFT. Second, we observe that many definitions of the multi-fractional Fourier transform (mFrFT) are flawed: when we attempt to propose a design scheme for the quantum mFrFT, we find that there are many invalid weighting terms in the definition of the mFrFT. This flaw may have very significant impacts on relevant algorithms for signal processing and image encryption. Finally, we analyze the circuit of the QFrFT and the reasons for the observed defects. Full article

Synthetic aperture radar (SAR) is an essential tool for maritime surveillance in all weather conditions and at night. Ships are often affected by sea breezes and waves, generating a three-dimensional (3D) swinging motion. The 3D swing ship can thereby become severely defocused in SAR images, making it extremely difficult to recognize them. However, refocusing 3D swing ships in SAR imagery is challenging with traditional approaches due to different phase errors at each scattering point on the ship. In order to solve this problem, a novel method for refocusing swing ships in SAR imagery based on the spatial-variant defocusing property is proposed in this paper. Firstly, the spatial-variant defocusing property of a 3D swing ship is derived according to the SAR imaging mechanism. Secondly, considering the spatial-variant defocusing property, each azimuth line of the SAR 3D swing ship image is modeled as a multi-component linear frequency modulation (MC-LFM) signal. Thirdly, Fractional Autocorrelation (FrAc) is implemented in order to quickly calculate the optimal rotation order set for each azimuth line. Thereafter, Fractional Fourier Transform (FrFT) is performed on the azimuth lines to refocus their linear frequency modulation (LFM) components one by one. Finally, the original azimuth lines are replaced in the SAR image with their focused signals to generate the refocused SAR image. The experimental results from a large amount of simulated data and real Gaofen-3 data show that the proposed algorithm can overcome the spatial-variant defocusing of 3D swing ships. Compared with state-of-the-art algorithms, our approach reduces the image entropy by an order of magnitude, leading to a visible improvement in image quality, which makes it possible to recognize swing ships in SAR images. Full article

The concept of the phase space plays a key role in the analysis of oscillating signals. For a 1-D signal, the coordinates of the 2-D phase space are the observation time and the instant frequency. For measurements of propagating wave fields, the time and instant frequency are linked to the spatial location and wave normal, defining a ray. In this case, the phase space is also termed the ray space. Distributions in the ray space find important applications in the analysis of radio occultation (RO) data because they allow the separation of interfering rays in multipath zones. Examples of such distributions are the spectrogram, Wigner distribution function (WDF), and Kirkwood distribution function (KDF). In this study, we analyze the application of the fractional Fourier transform (FrFT) to the construction of distributions in the ray space. The FrFT implements the phase space rotation. We consider the KDF averaged over the rotation group and demonstrate that it equals the WDF convolved with a smoothing kernel. We give examples of processing simple test signals, for which we evaluate the FrFT, KDF, WDF, and smoothed WDF (SWDF). We analyze the advantages of the SWDF and show examples of its application to the analysis of real RO observations. Full article

The definition of the discrete fractional Fourier transform (DFRFT) varies, and the multiweighted-type fractional Fourier transform (M-WFRFT) is its extended definition. It is not easy to prove its unitarity. We use the weighted-type fractional Fourier transform, fractional-order matrix and eigendecomposition-type fractional Fourier transform as basic functions to prove and discuss the unitarity. Thanks to the growing body of research, we found that the effective weighting term of the M-WFRFT is only four terms, none of which are extended to M terms, as described in the definition. Furthermore, the program code is analyzed, and the result shows that the previous work (Digit Signal Process 2020: 104: 18) based on MATLAB for unitary verification is inaccurate. Full article

The parametric decomposition of full-waveform Lidar data is challenging when faced with heavy noise scenarios. In this paper, we report a fractional Fourier transform (FRFT)-based approach for accurate parametric decomposition of pulsed Lidar signals with noise corruption. In comparison with other joint time-frequency analysis (JTFA) techniques, FRFT is found to present a one-dimensional Lidar signal by a particular two-dimensional spectrum, which can exhibit the mathematical distribution of the multiple components in Lidar signals even with a heavy noise interference. A FRFT spectrum-processing solution with histogram clustering and moving LSM fitting is designed to extract the amplitude, time offset, and pulse width contained in the mathematical distribution. Extensive experimental results demonstrate that the proposed FRFT spectrum analysis method can remarkably outperform the conventional Levenberg–Marquardt-based method. In particular, it can accurately decompose the amplitudes, time offsets, and pulse widths of the pulsed Lidar signal with a −10-dB signal-to-noise-ratio by mean deviation ratios of 4.885%, 0.531%, and 7.802%, respectively. Full article

In this paper, a method for automatically separating the mixed circular fringe patterns based on the fractional Fourier transform (FrFT) analysis is proposed. Considering the mixed two-dimensional (2-D) Gaussian-based circular fringe patterns, detected by using an image sensor, we propose a method that can efficiently determine the number and parameters of each separated fringe patterns by using the FrFT due to the observed higher sparsity in the frequency domain than that in the spatial domain. First, we review the theory of FrFT and the properties of the 2-D circular fringe patterns. By searching the spectral intensities of the various fractional orders in the FrFT projected along both the frequency axes, the proposed method can automatically determine the total fringe number, the central position, binary phase, and the maximum fringe width of each 2-D circular fringe pattern. In the experimental results, both the computer-simulated and optically mixed fringe patterns are used to verify the proposed method. In addition, the additive Gaussian noise effects on the proposed method are investigated. The proposed method can still successfully separate the mixed fringe pattern when the signal-to-noise ratio is higher than 7 dB. Full article