Linear Frequency Modulation Signal Research Articles

Azimuth Estimation of Multi-LFM Signals Based on Improved Complex Acoustic Intensity Method

The complex acoustic intensity method is one of the common methods used for the azimuth estimation of single-vector sensors. However, this method establishes a relationship between frequency and azimuth, which limits its practical applicability for multiple linear frequency modulation (LFM) signals with overlapping frequency domains. In this paper, the time–frequency distribution information of the LFM signal is combined with the complex acoustic intensity method, and more signal parameter information is used to expand the application scenario of the single-vector sensor. The proposed method first processes the time–frequency graph of the signal to obtain a stable and clear time–frequency distribution, and then obtains the acoustic intensity distribution of the signal using the time integration of the energy on the ridge of the signal to estimate the target orientation more stably. The simulation results show that the root mean square error of azimuth estimation is less than 1° when the SNR is greater than 0 dB. Furthermore, a pool experiment was carried out to verify the effectiveness of the proposed method.

Parameter estimation method for a linear frequency modulation signal with a Duffing oscillator based on frequency periodicity

In view of the complexity of existing linear frequency modulation (LFM) signal parameter estimation methods and the poor antinoise performance and estimation accuracy under a low signal-to-noise ratio (SNR), a parameter estimation method for LFM signals with a Duffing oscillator based on frequency periodicity is proposed in this paper. This method utilizes the characteristic that the output signal of the Duffing oscillator excited by the LFM signal changes periodically with frequency, and the modulation period of the LFM signal is estimated by autocorrelation processing of the output signal of the Duffing oscillator. On this basis, the corresponding relationship between the reference frequency of the frequency-aligned Duffing oscillator and the frequency range of the LFM signal is analyzed by the periodic power spectrum method, and the frequency information of the LFM signal is determined. Simulation results show that this method can achieve high-accuracy parameter estimation for LFM signals at an SNR of −25 dB.

Airborne Radar Anti-Jamming Waveform Design Based on Deep Reinforcement Learning.

Airborne radars are susceptible to a large number of clutter, noise and variable jamming signals in the real environment, especially when faced with active main lobe jamming, as the waveform shortcut technology in the traditional regime can no longer meet the actual battlefield radar anti-jamming requirements. Therefore, it is necessary to study anti-main-lobe jamming techniques for airborne radars in complex environments to improve their battlefield survivability. In this paper, we propose an airborne radar waveform design method based on a deep reinforcement learning (DRL) algorithm under clutter and jamming conditions, after previous research on reinforcement-learning (RL)-based airborne radar anti-jamming waveform design methods that have improved the anti-jamming performance of airborne radars. The method uses a Markov decision process (MDP) to describe the complex operating environment of airborne radars, calculates the value of the radar anti-jamming waveform strategy under various jamming states using deep neural networks and designs the optimal anti-jamming waveform strategy for airborne radars based on the duelling double deep Q network (D3QN) algorithm. In addition, the method uses an iterative transformation method (ITM) to generate the time domain signals of the optimal waveform strategy. Simulation results show that the airborne radar waveform designed based on the deep reinforcement learning algorithm proposed in this paper improves the signal-to-jamming plus noise ratio (SJNR) by 2.08 dB and 3.03 dB, and target detection probability by 26.79% and 44.25%, respectively, compared with the waveform designed based on the reinforcement learning algorithm and the conventional linear frequency modulation (LFM) signal at a radar transmit power of 5 W. The airborne radar waveform design method proposed in this paper helps airborne radars to enhance anti-jamming performance in complex environments while further improving target detection performance.

Direction of arrival estimation based on slope fitting of wideband array signal in fractional Fourier transform domain

AbstractTraditional direction of arrival (DOA) estimation methods of wideband linear frequency modulated (LFM) signal based on the fractional Fourier transform (FRFT) highly depend on the peak value of LFM signal in the FRFT domain. However, the peak value can be affected by various factors, such as a low signal‐to‐noise ratio (SNR), a small number of snapshots, or the large incident angle of signals, which can lead to a decrease in DOA estimation accuracy. To tackle this problem, based on the energy‐concentrated property of LFM signal in the FRFT domain, the DOA estimation is accomplished by adopting the approach of slope fitting for the wideband array signal in the FRFT domain in this study. The method uses the correspondence between the peak position in the FRFT domain and the delay of the received signal on different uniform linear array elements. The least square method based on threshold outlier detection is used for slope fitting. Compared to conventional methods, the method of this study has high accuracy and relatively low complexity in the case of low SNR or large incident angle of the signal without relying on the peak value. The effectiveness of this method is verified by theoretical analysis and Monte‐Carlo simulations. The proposed method provides a new path for DOA estimation of LFM signal.

Wigner distribution associated with the symplectic coordinates transformation

The celebrated τ-Wigner distribution (τ-WD), a generalization of the ordinary Wigner distribution (WD), has attracted much attention in the literature for its wide use in time-frequency analysis. However, it fails to break through the time-frequency resolution limit of the WD. Due to more degrees of freedom, the matrix Wigner distribution (MWD), a generalization of the τ-WD and a special case of the A-Wigner distribution, seems to be an effective tool to tackle this challenge. In this study, we focus on a specific MWD, i.e., the so-called symplectic Wigner distribution (SWD), through the change of coordinates with the general symplectic matrix. We disclose an equivalence relation between the uncertainty product in SWD domains and that in the classical settings, from which we obtain the optimal symplectic matrix constraint condition under which the SWD achieves higher time-frequency resolution than the WD. We also provide the simulation example associated with linear frequency-modulated signals for verifying the established superresolution theory.

Broadband Signal Digitization Based on Low-Speed Non-Uniform Photonic Sampling

A new non-uniform photonic sampling (NPS) strategy and its special signal reconstruction algorithm are proposed to achieve digital acquisition of broadband periodic signals at a low sampling rate. Compared with the existing schemes, the NPS strategy can largely reduce the sampling number to acquire identical signal information as that obtained by using its equivalent high-speed uniform photonic sampling, which is beneficial for reducing the sampling time and the data volume of the NPS-based analog-to-digital converter (ADC). In addition, the calculation time of the proposed algorithm is millions of times lower than that of the digital alias-free signal processing (DASP) algorithm used before, which benefits from the fast Fourier transform calculation of a one-dimensional data array instead of a two-dimensional data array calculation in the DASP algorithm. A simulation is performed to validate the feasibility of the proposed scheme. In the simulation, a single-channel NPS-based ADC with an average sampling rate of 1 GSa/s is demonstrated by using the proposed NPS strategy and signal reconstruction algorithm. The results indicate the reconstructed signal information for a single-tone microwave signal at 9.9 GHz and a linear frequency modulation signal in the frequency range of 1 GHz to 9 GHz are identical to those obtained by using its equivalent high-speed uniform photonic sampling-based ADC with a sampling rate of 20 GSa/s.

Non-linear Frequency Estimation Based Upon Convolution Neural Network

A frequency estimator is to find the frequency of the received signal distorted by noise, and it has been found in systems such as radar, sonar, etc. In this research, the linear frequency modulation signal(LFM)of the radar system, the detection of the moving target and its frequency estimation were highlighted. The pre-trained convolutional neural network algorithm was used, which proved highly accurate in detecting the target and estimating its frequency, despite the lower level of the signal to the noise ratio(SNR) where it was dealt with. On the basis of the signals received as a two-dimensional image and taking into account the Doppler effect, as the target moves at different speeds and accelerations, the signals have been classified into single-frequency signals and LFM signals

A Novel Interrupted-Sampling Repeater Jamming Suppression Method Based on Time-Frequency Analysis and Target Sparse Reconstruction

Interrupted-sampling repeater jamming (ISRJ) is a new kind of coherent jamming for linear frequency modulation (LFM) signals. Based on digital radio frequency memory (DRFM), ISRJ can generate multiple false target groups by intercepting, storing, and retransmitting radar signal fragments, which significantly affects the postprocessing results of radar systems. Furthermore, due to the fragment interception of ISRJ, ISRJ false targets present a regular and discontinuous time-frequency (TF) distribution in contrast with real targets. Considering this intrinsic property and the coherent nature of ISRJ, this study proposes a new method based on TF analysis and target sparse reconstruction to address the ISRJ suppression issue. In this method, the echo signal is first sparsely represented to obtain both the real and false target positions. Then, according to the acquired target positions, information entropy features of targets are extracted in TF data for subsequent target identification. Finally, guided by the identification result, the real targets can be retained and reconstructed by adaptive filtering in the sparse domain to realize ISRJ suppression. Simulations have validated the effectiveness of the proposed method under various situations.

Vortex-electromagnetic-wave-based ISAR imaging for high-speed maneuvering targets

Vortex electromagnetic wave (VEMW) carrying orbital angular momentum (OAM), which is expected to introduce additional degrees of freedom in inverse synthetic aperture radar(ISAR) imaging. However, the current research about maneuvering targets is based on the "stop go" hypothesis, which does not apply to high-speed motion scenarios due to the intrapulse movement of the target. To improve the imaging quality, this letter proposes a VEMW-based high-speed maneuvering targets imaging method. Firstly, the ISAR imaging scenario of high-speed target is established. According to the spatial geometric relationship between radar and maneuvering target, the vortex echo is deduced and its characteristics are analyzed. Subsequently, a frequency modulation rate estimation method considering both calculation efficiency and high precision is proposed to realize the accurate estimation of target speed. Then, an adaptive azimuth image compensation method based on minimum entropy is proposed. Through the setting of threshold, the number of component signals in linear frequency modulation (LFM) signal is determined and compensated successively. Finally, the range profile and azimuth profile are combined to reconstruct the three-dimensional information. The simulation results demonstrate that this work can effectively eliminate the influence of high-speed motion on range and azimuth profile, also benefit the development of ISAR imaging technique of high-speed maneuvering targets.

Estimation and Classification of NLFM Signals Based on the Time-Chirp Representation.

A new approach to the estimation and classification of nonlinear frequency modulated (NLFM) signals is presented in the paper. These problems are crucial in electronic reconnaissance systems whose role is to indicate what signals are being received and recognized by the intercepting receiver. NLFM signals offer a variety of useful properties not available for signals with linear frequency modulation (LFM). In particular, NLFM signals can ensure the desired reduction of sidelobes of an autocorrelation (AC) function and desired power spectral density (PSD); therefore, such signals are more frequently used in modern radar and echolocation systems. Due to their nonlinear properties, the discussed signals are difficult to recognize and therefore require sophisticated methods of analysis, estimation and classification. NLFM signals with frequency content varying with time are mainly analyzed by time-frequency algorithms. However, the methods presented in the paper belong to time-chirp domain, which is relatively rarely cited in the literature. It is proposed to use polynomial approximations of nonlinear frequency and phase functions describing signals. This allows for applying the cubic phase function (CPF) as an estimator of phase polynomial coefficients. Originally, the CPF involved only third-order nonlinearities of the phase function. The extension of the CPF using nonuniform sampling is used to analyse the higher order polynomial phase. In this paper, a sixth order polynomial is considered. It is proposed to estimate the instantaneous frequency using a polynomial with coefficients calculated from the coefficients of the phase polynomial obtained by CPF. The determined coefficients also constitute the set of distinctive features for a classification task. The proposed CPF-based classification method was examined for three common NLFM signals and one LFM signal. Two types of neural network classifiers: learning vector quantization (LVQ) and multilayer perceptron (MLP) are considered for such defined classification problem. The performance of both the estimation and classification processes was analyzed using Monte Carlo simulation studies for different SNRs. The results of the simulation research revealed good estimation performance and error-free classification for the SNR range encountered in practical applications.

Demonstration of photonics-based flexible integration of sensing and communication with adaptive waveforms for a W-band fiber-wireless integrated network.

The integration of sensing and communication (ISAC) in millimeter-waves (MMW) will play an important role in future 6G applications. Photonics-based radar sensing and communication systems have the advantages of high bandwidth in terms of high-resolution sensing and high-speed data transmission and can be inherently integrated with fiber-optic networks. To support flexible application scenarios, in this paper, we proposed and experimentally demonstrated an MMW photonics-based flexible ISAC system with adaptive signal waveforms for a W-band fiber-wireless integrated network. Photonics-based W-band ISAC signals are generated by heterodyning two free-running external cavity lasers. Microwave photonics-based radar signal processing supports centralized and seamless fiber-wireless communication and sensing networks. In our proposed system, orthogonal frequency-division multiplexing (OFDM) and linear frequency modulation (LFM) signals were combined by frequency-division multiplexing to share this bandwidth. Therefore, we can adaptively allocate bandwidths to OFDM and LFM signals according to the application requirements and realize a flexible ISAC system with high-speed communication and high-resolution radar sensing. As a proof-of-concept, a flexible W-band fiber-wireless ISAC system at 96.5 GHz over 10-km fiber transmission was demonstrated, achieving adaptive access rates from 5.98 to 41.48 Gbit/s after transmission over 1-m free space, and adaptive sensing resolutions from 1.53 to 6.94 cm with the distance error after calibration less than 4 cm. The performance of both communication and sensing under different bandwidth ratios was also studied.

Photonic-Assisted Modulation Format Identification for RF Signals under Low Sampling Rate

A photonic-assisted approach is proposed for modulation format identification (MFI) on radio frequency (RF) signals under low sampling rate. In this approach, a photonic-assisted interferometer (PAI) is designed for computation-free data augmentation by transforming the signal’s phase and frequency variations into modulation format-sensitive amplitude features. A fully connected neural network (FCNN) is used to implement end-to-end MFI. An experiment is conducted on the identification of amplitude-shift keying (ASK), binary phase-shift keying (BPSK), quadrature phase-shift keying (QPSK), frequency-shift keying (FSK), and linear frequency modulation (LFM) signals with signal-to-noise ratios (SNRs) from −10 to 15 dB and carrier frequencies within 5 to 10 GHz. The results show that the proposed photonic-assisted modulation format identifier (PA-MFI) achieves the identification accuracy of 82.44% at 1 GHz sampling rate, which is 10.6% higher than the accuracy of direct modulation format identification (Direct-MFI) without PAI processing.

Interrupted sampling repeater jamming countermeasure technology based on random interpulse frequency coding LFM signal

Interrupted sampling repeater jamming (ISRJ) is an active coherent jamming with the characteristic of suppression and deception, which poses a great threat to modern radars. In this work, a false target identification and suppression method based on random interpulse frequency coding linear frequency modulation (RIFC-LFM) signal processing is proposed. First, we analyze the characteristics of the RIFC-LFM signal and ISRJ using the ambiguity function and cross ambiguity function, respectively. Next, taking advantage of the property that most of the false targets formed by ISRJ will be whitened after range-Doppler processing, a false target range-Doppler (RD) spectrum reconstruction method is proposed. Using the reconstructed false target RD spectrum, we can obtain the positions of the unwhitened false targets in the RD spectrum and distinguish the true and false targets. Finally, we design the suppression matrix based on the reconstructed false target RD spectrum to suppress the false targets. The simulation results demonstrate that the proposed approach can effectively suppress three different ISRJs without estimating the ISRJ parameters.

A target echo simulation method for wideband LFM-PRPC signals based on segmentation processing

ABSTRACT To address the target echo simulation problem for linear frequency-modulated and pseudorandom phase-coded (LFM-PRPC) signals, this letter proposes a target echo reconstruction method based on segmentation processing. We treat the phase mutation points of an LFM-PRPC pulse signal as the basis for segmentation, approximately dividing the time-domain signal into several narrowband, short-term pulse signals, and then calculate the target echo signal corresponding to each pulse. Finally, we reconstruct the full pulse of the wideband target echo signal. This method not only reflects the intrapulse modulation characteristics of a radar signal and the wideband electromagnetic scattering characteristics of the target but also effectively improves the real-time performance of wideband radar target echo signal calculations without reducing the calculation accuracy. Moreover, it is applicable to both uniform and pseudorandom (nonuniform) coded signals. The results prove the reliability and feasibility of the proposed method.

Kernel Function-Based Ambiguity Function and Its Application on DOA Estimation in Impulsive Noise.

To solve the problem that the traditional ambiguity function cannot well reflect the time-frequency distribution characteristics of linear frequency modulated (LFM) signals due to the presence of impulsive noise, two robust ambiguity functions: correntropy-based ambiguity function (CRAF) and fractional lower order correntropy-based ambiguity function (FLOCRAF) are defined based on the feature that correntropy kernel function can effectively suppress impulsive noise. Then these two robust ambiguity functions are used to estimate the direction of arrival (DOA) of narrowband LFM signal under an impulsive noise environment. Instead of the covariance matrix used in the ESPRIT algorithm by the spatial CRAF matrix and FLOCRAF matrix, the CRAF-ESPRIT and FLOCRAF-ESPRIT algorithms are proposed. Computer simulation results show that compared with the algorithms only using ambiguity function and the algorithms only using the correntropy kernel function-based correlation, the proposed algorithms using ambiguity function based on correntropy kernel function have good performance in terms of probability of resolution and estimation accuracy under various circumstances. Especially, the performance of the FLOCRAF-ESPRIT algorithm is better than the CRAF-ESPRIT algorithm in the environment of low generalized signal-to-noise ratio and strong impulsive noise.

Novel windowed linear canonical transform: Definition, properties and application

Linear canonical transform (LCT) has emerged as a powerful tool in nonstationary signal processing. However, it fails to reveal the information of local frequency varying with time due to the global kernel function. In this paper, a novel windowed linear canonical transform (NWLCT) is presented to give a clear time-frequency representation for time-varying signals. Firstly, the definition of NWLCT is proposed by a generalized convolution operator not a sliding window. Some basic properties of NWLCT are derived, such as inverse transform, Parseval theorem and reproducing kernel. Moreover, time-frequency resolution of NWLCT is analyzed theoretically, and the optimal window is derived. Finally, the applications of NWLCT in local spectral analysis for linear frequency modulated (LFM) signals are offered, including mono- and multi-component signals with similar local features. Theoretical and simulation results demonstrate that the proposed NWLCT preserves a crucial physical interpretation similar to classical short-time Fourier transform, which extends low-pass filter banks in the LCT domain. Compared with other time-frequency methods, NWLCT outperforms in improving the energy concentration and being robust to noise in terms of LFM signal processing.

Dynamic intelligent measurement of multiple chirped signals of different types based on the optical computing STFT and the YOLOv3 neural network.

We propose a simultaneous measurement system for multiple signals of different types which combines the optical computing short-time Fourier transform (STFT) and You Only Look Once (YOLOv3) neural network. Through the system, the analytical expressions of multiple broadband signals of different types can be obtained in real time with high-frequency resolution. Experimentally, the accuracy of the signal type in the detection results can almost reach 100%. Additionally, the parameter measurement errors for the bandwidth (BW), pulse width (PW), center frequency (CF), and time of arrival (TOA) of each linear frequency-modulated (LFM) or quadratic frequency-modulated (QFM) signal are within ±30 MHz, ±20 ns, ±15 MHz, and ±20 ns, respectively. The frequency resolution can reach 60 MHz. Factors affecting the performance of the measurement system, such as the quantity of the signal and the number of the category, are discussed.

Comparison between linear frequency-modulated ultrasonic excitation signals and pure tones for concrete applications

Non-destructive testing has supported prognosis and health management in the construction industry for decades. Among them, ultrasonic tests (UT) are increasingly used to assess the structural integrity of the concrete. Typically, the UT uses pure tones as the excitation signal. However, an alternative is to use a linear frequency-modulated pulse (LFMP) followed by compression. This process improves the signal-to-noise ratio, provides broadband frequency responses, and is less susceptible to propagation dispersion. This work compared the ultrasonic transit times (UTT) of LFMP and pure tones. Three nondispersive models for concrete materials were numerically simulated using the k-Wave MATLAB toolbox. Additionally, a sample of reactive powder concrete (RPC) was experimentally tested. The frequencies ranged from 50 kHz to 750 kHz for both simulations and experiments. The simulation results presented LFMP relative errors in UTTs ranging from 0.0 % to 2.7 % compared to the theoretical values, whereas for pure tones, the RE was 2 % to 63 %. Experimentally, as no theoretical value can be considered, the quantitative comparison was the measurement dispersion under repeatability conditions. LFMPs disclosed a standard deviation in transit time of 35 ns, whereas for pure tones, it ranged from 43 to 51 ns. This research reinforces the potential of LFMP excitation compared to traditional pure tones, providing more accurate and precise ultrasonic velocity measurements in heterogeneous environments.

Power-Independent Microwave Instantaneous Frequency Measurement Based on Combination of Brillouin Gain and Loss Spectra

Photonics-assisted microwave instantaneous frequency measurement (IFM) is considered as a promising technique for detecting an unknown radio-frequency (RF) signal, which has advantages of broad frequency measurement range and fast processing speed. Up to date, there is no photonics-assisted IFM system that can essentially measure an unknown RF signal time-frequency information with power fluctuating seriously. Moreover, the measurement accuracy and frequency modulation recognition are not as good as those of traditional electronic methods. Here, we propose an IFM scheme based on the combination of Brillouin gain spectrum (BGS) and Brillouin loss spectrum (BLS), which is RF-power-independent with high measurement efficiency. The combination of BGS and BLS to construct the amplitude comparison function (ACF) can reduce the influence of RF signal power fluctuation within 21.27 dB by single-shot measuring. When an appropriate frequency interval with frequency domain monotonous power of microwave comb signal is modulated on the pump lightwave, the IFM accuracy of the unknown signal reaches about 1 MHz. After the initial calibration of the system, it can recognize the time-frequency variation of single tone signal, linear frequency modulated signal (LFM), nonlinear frequency modulated signal (NLFM), and Costas signal. This scheme will help to promote the application of the IFM in the field of spectrum reconnaissance and reception.

Phase identification with VMD and HT combined method for an active seismic source experiment

We developed a seismic phase identification method for the controlled accurate seismic source (CASS) by combining variational mode decomposition (VMD) and the Hilbert transformation (HT) algorithm. CASS demonstrates significant potential for the study of underground structures with limited destruction and repeated work. However, extracting seismic phase features with high frequency interference is a difficult task. This study aimed to improve seismic phase identification by adopting VMD with HT algorithm using an active seismic source experiment data around Xinfengjiang reservoir. We obtained the main seismic phase included in direct wave Sg and reflected waves PmP and SmS. We evaluated the algorithm by comparing obtained results with theoretical one and found that the proposed algorithm can effectively obtain seismic phase distribution and shows better performance than the matched filtering algorithm. Moreover, the algorithm using the CASS data provides a reference for linear frequency modulation (LFM) signal processing.