Sinusoidal Frequency-modulated Signal Research Articles

Frequency response measurement of electro-optic phase modulators using the time-frequency analysis method

We propose a novel method for the frequency response measurement of electro-optic phase modulators by time-frequency analyzing the instantaneous frequency of a sinusoidal frequency-modulated (SFM) signal. The SFM signal is generated by a frequency-shifting loop (FSL) in which the electro-optic phase modulator under test generates a dual-sideband frequency shift per roundtrip. And the bandwidth of the generated SFM signal is dozens of times of the input radio-frequency (RF), which makes it a precise method to measure the frequency response of electro-optic phase modulators at lower cutoff frequencies. Based on the previously proposed time-delayed interference model [H. Yang et al., J. Lightwave Technol. 39, 3112 (2021)10.1109/JLT.2021.3059875], we establish the relationship between the “peak-to-peak” frequency of the SFM waveforms and the modulation index of the phase modulators. And a short-time Fourier transformation (STFT) is adopted to characterize the time-frequency properties of output waveforms. Experimental results are well supported by the simple theoretical model. Finally, the accuracy of the half-wave voltage measurement is discussed.

Parameter Estimation for Sinusoidal Frequency-Modulated Signals Using Phase Modulation

In this letter, we propose a novel estimator for the phase parameters of sinusoidal frequency-modulated (SFM) signals. First, we developed a simple function to perform phase modulation on the original SFM signal to obtain a new modulated signal. Second, we derived the amplitude spectrum (AS) of the modulated signal and proved that the AS exhibited peaks periodically. Third, we obtained the parameter estimation of SFM signals by locating the AS peaks. Finally, the estimates were refined to reduce bias. The simulation results show that the proposed technique has a lower signal-to-noise ratio threshold than the existing methods.

Rotor Blades Micro-Doppler Feature Analysis and Extraction of Small Unmanned Rotorcraft

In this article, the micro-Doppler feature analysis and extraction of small unmanned rotorcraft (SUR) is considered. To be specific, the radar returns from the rotor blades are first modeled as sinusoidal frequency-modulated (SFM) signals. Then, the Gabor transform is utilized to obtain the time-frequency distribution (TFD). In order to solve the problem of limited TF analysis resolutions, high carrier frequency of radar is employed for the sake of separating different sinusoidal curves from TFD. After that, the Hough-Radon transform (HRT) is introduced to detect the sinusoidal curves from the TFD. Finally, based on the relationship between the SFM signal and the rotating blade, the micro-Doppler parameters which can reflect the threat level of the SUR to a large extend are estimated. Compared with other existing methods, the proposed method presents the relationships between the carrier frequency and the rotating blade parameters and it can be employed to extract the micro-Doppler feature of SUR with multiple rotor hubs. Simulation results demonstrate the effectiveness of the proposed micro-Doppler feature extraction method.

Integrated waveform for continuous active sonar detection and communication

A novel integrated waveform (IW) for continuous active sonar detection and communications is proposed in this study based on a generalised sinusoidal frequency-modulated signal. This study first introduces the mixed modulation of the IW and a model for the transmitting signal, and then it analyses the time and frequency resolution and anti-reverberation capability of the proposed IW. The performance of two underwater acoustic (UWA) communication receivers based on the proposed IW are compared and analysed under Gaussian noise and multipath conditions. A UWA communication experiment was carried out in Songhua Lake in December 2019. According to the numerical simulation and experimental results, it was concluded that the IW proposed in this study can meet the requirements of active sonar detection and UWA communications with satisfactory performance.

Method for micro-Doppler separation in ISAR imaging based on discrete sinusoidal frequency-modulated transform

In conventional inverse synthetic aperture radar (ISAR) imaging of complex moving aircrafts, a micro-Doppler effect is generated because of the high-speed rotating parts such as propellers. The rotational parts introduce a sinusoidal frequency-modulated (SFM) signal in the radar echoes, which can significantly affect the quality of the ISAR imaging. To solve this problem, the Doppler frequency forms for the rigid body and rotating parts of an aircraft are analyzed, and a method based on the discrete sinusoidal frequency-modulated transform (DSFMT) is proposed. The SFM signal can be transformed into the DSFMT domain, and the parameters can be estimated by the global maximum. The rigid body is separated after removing the SFM signals using successive elimination technology. This method is not only applicable to targets in uniform motion but also to those in accelerating motion. The results of simulations and a measured data test are given to verify the effectiveness of the proposed method.

A Novel High-Frequency Vibration Error Estimation and Compensation Algorithm for THz-SAR Imaging Based on Local FrFT.

Compared with microwave synthetic aperture radar (SAR), terahertz SAR (THz-SAR) is easier to achieve ultrahigh-resolution image due to its higher frequency and shorter wavelength. However, higher carrier frequency makes THz-SAR image quality very sensitive to high-frequency vibration error of motion platform. Therefore, this paper proposes a novel high-frequency vibration error estimation and compensation algorithm for THz-SAR imaging based on local fractional Fourier transform (LFrFT). Firstly, the high-frequency vibration error of the motion platform is modeled as a simple harmonic motion and THz-SAR echo signal received in each range pixel can be considered as a sinusoidal frequency modulation (SFM) signal. A novel algorithm for the parameter estimation of the SFM signal based on LFrFT is proposed. The instantaneous chirp rate of the SFM signal is estimated by determining the matched order of LFrFT in a sliding small-time window and the vibration acceleration is obtained. Hence, the vibration frequency can be estimated by the spectrum analysis of estimated vibration acceleration. With the estimated vibration acceleration and vibration frequency, the SFM signal is reconstructed. Then, the corresponding THz-SAR imaging algorithm is proposed to estimate and compensate the phase error caused by the high-frequency vibration error of the motion platform and realize high-frequency vibration error estimation and compensation for THz-SAR imaging. Finally, the effectiveness of the novel algorithm proposed in this paper is demonstrated by simulation results.

Estimation of Sinusoidal Frequency-Modulated Signal Parameters by Two Branches and Two Stages

Sinusoidal frequency-modulated (SFM) signal is widely applied in radar, and wireless communication. Therefore, there is significant importance in studying the estimation of SFM signal parameters. However, traditional estimation algorithms have high computational complexity while the corresponding estimation performance degrades when either modulation index or modulation frequency of SFM signals increases. To address these problems of computational complexity as well as the performance degradation, a two-branch two-stage estimation algorithm is proposed in this paper. In the first stage, received signals are passed through two different branches: one for the modulation index not greater than $\pi /2$ , and the other for that larger than $\pi /2$ . This two-branch strategy is derived from the spectrum properties of SFM signals with respect to modulation index, where the first branch utilizes the Jacobi-Anger expansion, and the second one employs an iterative estimation algorithm. In the second stage, precisions of the parameter estimates obtained from the two branches are compared, and the estimates with higher precision correspond to the final estimates of SFM signal parameters. Both theoretical analysis, and numerical results show that the proposed algorithm outperforms the current state-of-the-art algorithms, while yielding significantly lower computational complexities.

Detection and identification technology of rotor unmanned aerial vehicles in 5G scene

In the 5G era, integration between different networks is required to realize a new world of Internet of things, the most typical model is Space–Air–Ground Internet of things. In the Space–Air–Ground Internet of things, unmanned aerial vehicle network is widely used as the representative of air-based networks. Therefore, a lot of unmanned aerial vehicle “black flying” incidents have occurred. UAVs are a kind of “low, slow and small” artificial targets, which face enormous challenges in detecting, identifying, and managing them. In order to identify the “black flying” unmanned aerial vehicle, combined with the advantages of 5G millimeter wave radar and machine learning methods, the following methods are adopted in this article. For a one-rotor unmanned aerial vehicle, the radar echo data are a single-component sinusoidal frequency modulation signal. The echo signal is conjugated first and then is subjected to a short-time Fourier transform, while the micro-Doppler has a double effect. For a multi-rotor unmanned aerial vehicle, the radar echo data are a multi-component sinusoidal frequency modulation signal, the k-order Bessel function base and the signal are used for integral projection processing, which better identifies the micro-Doppler characteristics such as the number of rotors or the rotational speed of each rotor. The noise interference is added to verify that the algorithm has better robustness. The micro-Doppler characteristics of rotor unmanned aerial vehicles are extracted by the above algorithm, and the data sets are built to train the model. Finally, the classification of unmanned aerial vehicle is realized, and the classification results are given. The research in this article provides an effective solution to solve the problem of detecting and identifying unmanned aerial vehicle by 5G millimeter wave radar in the Internet of Things, which has high practical application value.

A Frequency Demodulator Based on Adaptive Sampling Frequency Phase-Locking Scheme for Large Deviation FM Signals

A frequency demodulation scheme based on adaptive sampling frequency phase-locking loop (PLL) is proposed for extracting large deviation message signal from sinusoidal frequency-modulated signals. The proposed scheme has been designed to track the frequency-modulated input signal using a look-up-table and adaptively changing the sampling period. While tracking the carrier signal, the numerically controlled oscillator involved in the PLL structure produces the sampling frequency according to the variation of input frequency. In the PLL, the message signal has been extracted at the output of proportional integral controller. Simulation results prove that the PLL exhibits quick acquisition behavior, wide operating range, negligible steady-state error. Experimental investigation validates the efficacy of the proposed PLL performance in message signal extraction.

Parameter estimation of coupled polynomial phase and sinusoidal FM signals

This paper considers parameter estimation of a new coupled mixture of polynomial phase signal (PPS) and sinusoidal frequency modulated (FM) signal, recently introduced for industrial systems such as linear electromagnatic encoders. Compared with both conventional PPS-only and independent mixture models, the coupled mixture one captures the coupling between the sinusoidal FM frequency and the PPS parameters induced by structural system configurations. In this paper, we are particularly interested in estimating phase parameters of the coupled mixture signal at low signal-to-noise ratios (SNRs). Specifically, we propose a three-stage approach consisting of instantaneous frequency (IF) extraction (e.g., the short-time Fourier transform) and refining steps that reduce the bias introduced by the IF estimation and the mean-squared errors (MSEs) up to the Cramér-Rao bound (CRB). The proposed method is numerically compared with an existing phase-based approach as well as corresponding CRBs in terms of the empirical MSE. The results show that, compared with the phase-based approach, the proposed method can significantly lower the SNR threshold. The convergence of the measured MSEs from the initial stage to the latter refining stages is also numerically evaluated.

Translation compensation and micro-motion parameter estimation of laser micro-Doppler effect

Precise target identification is significant for commanding and identifying enemies. The micro-Doppler effect (MDE) can reflect the subtle movement characteristics of the targets, which provides a new way of detecting and recognizing the target. However, the current research mainly focuses on the micro-motion feature extraction and classification of the targets, which is not capable of identifying the targets of the same type. In fact, by accurately estimating the micro-motion parameters and combining sufficient prior knowledge, the target can be accurately identified. Compared with the microwave radar, the laser detected MDE has high sensitivity and precision in micro-motion parameter estimation. This is more conducive to realizing the accurate classification and fine identification of the targets. In real detection, the MDE always exists in the moving targets. This will generate a mixed echo signal modeled by the polynomial phase signal and sinusoidal frequency modulation (SFM) signal. So far, there have been no effective methods of estimating the micro-motion parameters in such mixed signals. In this regard, a set of translational motion compensation and micro-motion parameter estimation methods is proposed in this paper. A bandwidth searching method based on the fractional Fourier transform (FrFT) is presented to precisely estimate the translation parameters, which will be used to realize the compensation for the translational motion. The advanced particle filtering (PF) method using the static parameter model is designed for the micro-motion parameters in the remaining SFM term. Given the lack of particle diversity in static parameter PF, the Markov chain Monte Carlo sampling is employed, which also helps to improve the algorithm efficiency. Meanwhile, a new likelihood function in calculating the particle weights is designed by using the cumulative residual. With this improvement, the correct convergence under multi-dimensional parameter condition is guaranteed. The proposed method can avoid the influence from error transfer and achieve efficient and accurate estimation. Compared with the typical method that combines the time-frequency analysis and the polynomial fitting through the simulation, the proposed FrFT method is verified to have little computation complexity and high estimation accuracy, where the relative estimation errors of the translational parameters are kept at 0.64% and 0.45%, respectively. The waveform similarity of the SFM signal phase between the compensated signal and the real one indicates that the accuracy fully meets the requirement for accurate estimation of the micro-motion parameters. Further, the simulation result also shows the high efficiency of the improved PF algorithm. The convergence time consumed by the proposed algorithm is 0.353 s, while the traditional method needs 0.844 s. In the end, the comparison with the experimental data from the traditional inverse Radon transform shows the effectiveness and necessity of the proposed method. The research results are conducive to the accurate and rapid estimation of micro-motion parameters, which lays a foundation for the fine target recognition based on the MDE.

Parameter Estimation of Hybrid Linear Frequency Modulation-Sinusoidal Frequency Modulation Signal

In this letter, a novel method which employs the Radon transform (RT) and inverse Radon transform is proposed to estimate the parameters of the hybrid linear frequency modulation (LFM)-sinusoidal frequency modulation (SFM) signal. By adding a parameter called width, we extend the original RT to a three-parameter transform, which we named as extended Radon transform (ERT). Compared with the original RT, the ERT has shown more capacities, such as estimating the parameters of a strip in a plane. As the time–frequency representations (TFRs) of the hybrid LFM-SFM signal is a strip where there is a sinusoidal pattern embedded, the parameters of the signal are related to the strip; herein, we employ the ERT to estimate several parameters of the signal. With the estimated parameters values, the signal can be dechirped to be a SFM signal, whose parameters can be estimated by some existing methods. As it is based on the TFRs, the proposed method has strong robustness under low signal-to-noise ratios. Numerical results and analysis are provided to demonstrate the effectiveness of the proposed method.

Cramér–Rao Bounds for a Coupled Mixture of Polynomial Phase and Sinusoidal FM Signals

This letter introduces a new coupled mixture of polynomial phase signal (PPS) and sinusoidal frequency modulated (FM) signal, motivated by real-world applications, for example, contactless linear encoders. Specifically, the coupling is introduced to express the sinusoidal FM frequency as a function of the PPS-related parameters. Given the coupling mixture, it generalizes two existing models: the pure PPS model and the independent mixture model. Performance bounds of parameter estimation for the coupled mixture model are established in terms of the Cramer–Rao bound (CRB). Unlike the pure PPS case, the derived CRB shows its dependence on the PPS-related and sinusoidal FM-related parameters due to the coupling mixture. On the other hand, the derived CRBs for the PPS-related parameters are lower than their counterparts of the independent mixture model, as the sinusoidal FM frequency provides additional information on the PPS parameters.

The STFT-Based Estimator of Micro-Doppler Parameters

A two-stage technique for estimating micro-Doppler signal parameters has been proposed. In the first stage, rough parameter estimations are performed by regression of instantaneous frequency estimate obtained from the short-time Fourier transform. Afterwards, rough estimates are refined in the second stage. The proposed technique has better performance with respect to current state-of-the-art algorithms, and it reaches the Cramer–Rao lower bound for sinusoidal frequency-modulated signal parameters.

Estimation of sinusoidal frequency-modulated signal parameters in high-noise environment

In this paper, we consider the estimation of the sinusoidal frequency-modulated (FM) signal parameters in high-noise environments. For this purpose, we have combined the Viterbi algorithm for the estimation of the instantaneous frequency with the recently proposed technique for the parametric estimation of the FM signals based on the short-time Fourier transform. The proposed technique gives the accurate parameters estimation of the Cramer–Rao lower bound for signal-to-noise ratio of −2dB.

Serial digital interface video signal jitter generator and its calibration method

Jitter is an important factor for serial digital interface video signal (SDI signal) analysis. In this paper, we present the simulated SDI signal generator with certain amount of jitter using a sinusoidal frequency modulation (FM) signal, and propose a calibration method for the jitter value based on modulation index and relative power of sinusoidal FM signal. An experimental system is set up to generate and calibrate SDI signal with specific jitters. High-definition (HD) SDI signal with bit rate of 1.485Gbit/s is employed to describe the calibration procedure and analyze the uncertainty of measurement.

Parameters estimation of sinusoidal frequency modulation signal with application in synthetic aperture radar imaging

A method for estimating the parameters of the sinusoidal frequency modulation (SFM) signal is presented in this paper. Based on the modified discrete sinusoid frequency modulation transform (DSFMT), the SFM signal can be transformed into the DSFMT domain where it is energy-concentrated and then the parameters can be estimated by the global maximum. To search for the location of the global maximum with less computational load, particle swarm optimization is used in this paper. Then the algorithm is used in the synthetic aperture radar imaging with high frequency vibration of the platform, and the focus performance can be improved significantly. Simulation results demonstrate the effectiveness of the method proposed in this paper.

Moving-Window DFT Based Frequency-Locked Loop for FM Demodulation

A moving-window discrete Fourier transform (MWDFT) based frequency locked loop (FLL) is proposed for retrieving the message signal from sinusoidal frequency modulated signals. The spectra of MWDFT exhibits almost flat amplitude and phase responses when it is placed in a closed-loop with fixed sampling frequency. These flat characteristics for variation in input frequency is utilized for tracking frequency modulated carrier. The small leakage observed in terms of magnitude and phase errors of MWDFT is further corrected by adaptive sampling frequency control. The simulation and experimental investigations demonstrate the capability of proposed FLL in sinusoidal message signal retrieval with good metrics.

Sinusoidal Frequency Modulation Sparse Recovery for Precession Rate Estimation Using Low-Frequency Long-Range Radar

Low-frequency long-range radars (LFLRRs) are assumed to lack the ability of extracting targets micro motion signature, due to their low and nonuniform track update rate, as well as the weak micro Doppler (m-D) owing to their large wave length. The recently proposed sinusoidal frequency modulated (SFM) Fourier transform can achieve a longer integral period gain, and consequently provides a new perspective for extracting weak m-D signature. However, its direct application is unavailable for LFLRRs, since their track update rate is very low and may not even be constant. This paper derives a new approach, named sinusoidal frequency modulation sparse recovery (SFMSR) for m-D analysis with LFLRR, by exploiting the micro motion spectrum sparsity in SFM signal space. SFMSR employs the Fourier modulation dictionary, which is determined only by the frequency in SFM signal space. Unlike other sparse representation-based methods whose dictionary is discretization of a 3-D space parameterized by the micro motion amplitude, frequency, and initial phase, the SFMSR reduces the m-D analysis to 1-D parameter optimization, and therefore can enhance the precision, stability, and computational efficiency simultaneously. The temporally correlated sparse Bayesian learning in SFM signal space is employed to decompose the signal and produce highly sparse solutions. The simulation results indicate that the proposed method outperforms the existing methods in accuracy and robustness, which can provide satisfactory performance even when the carrier frequency is 430 MHz and the average data rate is 0.5 Hz.

An adaptive and computationally efficient algorithm for parameters estimation of superimposed exponential signals with observations missing randomly

In this paper, we consider the parameters estimation of a model of superimposed exponential signals in multiplicative and additive noise when some observations are missing randomly. The least squares estimators (LSEs) and asymptotic Cramer–Rao low bound (ACRLB) for the considered model are studied and the asymptotic distributions of the LSEs for parameters of frequencies, phases and amplitudes of the considered model are also derived and obtained. An adaptive and computationally efficient iterative algorithm is proposed to estimate the frequencies of the considered model. It can be seen that the iterative algorithm works quite well in terms of biases and mean squared errors and the refined estimators by three iterations are observed to be asymptotically unbiased and consistent. The statistics for iteration are designed to change adaptively according to different missing distributions of time points so as to keep the estimators of frequencies to be asymptotically unbiased. Moreover, the proposed estimators attain the same convergence rate and asymptotic distribution as those of LSEs which are used to obtain the confident intervals and coverage probabilities of the frequencies for finite sample. Since the iterative algorithm needs only three iterations to work, it saves much computation time. So the proposed estimators are LSEs equivalent while avoid the heavy computation cost of LSEs. Finally, several simulation experiments are performed to verify the effectiveness of the proposed algorithm. To examine the robustness of the proposed algorithm, we also test the algorithm on the dual tone multi-frequency (DTMF) signal with observations missing in block and symmetric α-stable (SaS) noise condition, as well as on sinusoidal frequency modulated signals.