Sinusoidal Frequency Modulation Research Articles

Parameter Estimation of SAR Signal Based on SVD for the Nyquist Folding Receiver.

The Nyquist Folding Receiver (NYFR) is a novel ultra-wideband (UWB) receiver structure that can realize wideband signal monitoring with fewer components. The NYFR induces a Nyquist zone (NZ)-dependent sinusoidal frequency modulation (SFM) by a modulated local oscillator (LOS), and the intercepted linear frequency modulated (LFM) synthetic aperture radar (SAR) signal will be converted into an LFM/SFM hybrid modulated signal. In this paper, a parameter estimation algorithm is proposed for the complicated NYFR output signal. According to the NYFR prior information, a chirp singular value ratio (CSVR) spectrum method based on singular value decomposition (SVD) is proposed to estimate the chirp rate directly before estimating the NZ index. Then, a fast search algorithm based on golden section method for the CSVR spectrum is analyzed, which can obviously reduce the computational complexity. The simulation shows that the presented algorithm can accurately estimate the parameters of the LFM/SFM hybrid modulated output signal by the NYFR.

Overlapping Laser Micro-Doppler Feature Extraction and Separation of Weak Vibration Targets

The laser-detected micro-Doppler (MD) effect is more likely to achieve precision target identification and recognition because of its high-accuracy estimation ability. MD features overlapping in the time–frequency (TF) are encountered in targets with similar micromotion parameters, which cannot be solved with one-channel detection. In this letter, a novel separation method based on a constrained particle filter (PF) in a time-varying autoregressive (TVAR) model is developed to solve this extremely underdetermined problem. First, the TVAR model for a multicomponent MD signal is established, and the connection between the interested instantaneous frequency (IF) and model poles is analyzed. Then, the continuity characteristic of the IF law is used to design a constraint condition for a PF assuming that the laser MD effect obeys the sinusoidal frequency modulation form. By fusing the constraint into the process of particle update and weight computation, the IF curve for each component is correctly separated through the well-tracked pole trajectories. Finally, the performances of the presented method and traditional method are compared for a TF overlapping scenario. The simulation results verify the validity and necessity of the new method; meanwhile, the low-level computational complexity makes it possible for real-time processing.

Parameter estimation of LFM signal intercepted by improved dual‐channel Nyquist folding receiver

A Nyquist folding receiver (NYFR) is a novel ultra-wideband (UWB) receiver architecture, which can realise a wideband receiving with fewer components. Intercepted by the NYFR with a sinusoidal frequency modulation (SFM) local oscillator, a linear frequency modulation (LFM) signal will be converted into a LFM/SFM hybrid modulated signal. To simplify the processing of this kind of complicated signal, the authors propose improved dual-channel NYFR architecture with an efficient parameter estimation algorithm. Compared with the existing parameter estimation methods for the NYFR, the proposed architecture offers better estimation performance, higher signal type adaptability, and simpler operation.

Iodine-frequency-stabilized laser diode and displacement-measuring interferometer based on sinusoidal phase modulation

We propose a sinusoidal phase modulation method to achieve both the frequency stabilization of an external-cavity laser diode (ECLD) to an 127I2 saturated absorption transition near 633 nm and displacement measurement using a Mach–Zehnder interferometer. First, the frequency of the ECLD is stabilized to the b21 hyperfine component of the P(33) 6-3 transition of 127I2 by combining sinusoidal phase modulation by an electro-optic modulator and frequency modulation spectroscopy by chopping the pump beam using an acousto-optic modulator. Even though a small modulation index of m = 3.768 rad is utilized, a relative frequency stability of 10−11 order is obtained over a sampling time of 400 s. Secondly, the frequency-stabilized ECLD is applied as a light source to a Mach–Zehnder interferometer. From the two consecutive modulation harmonics (second and third orders) involved in the interferometer signal, the displacement of the moving mirror is determined for four optical path differences (L0 = 100, 200, 500, and 1000 mm). The measured modulation indexes for the four optical path differences coincide with the designated value (3.768 rad) within 0.5%. Compared with the sinusoidal frequency modulation Michelson interferometer (Vu et al 2016 Meas. Sci. Technol. 27 105201) which was demonstrated by some of the same authors of this paper, the phase modulation Mach–Zhender interferometer could fix the modulation index to a constant value for the four optical path differences. In this report, we discuss the measurement principle, experimental system, and results.

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.

Mathematical properties of generalized Bessel functions and application to multi-tone sinusoidal frequency modulation

The generalized Bessel function (GBF) is a multi-dimensional extension of the standard Bessel function. Two dimensional GBFs have been studied extensively in the literature and have found application in laser physics, crystallography, and electromagnetics. However, a more rigorous treatment of higher-dimensional GBFs is lacking. The GBF exhibits a rich array mathematical structure in regards to its partial differential equation representation, its asymptotic characterization, and its level sets. In this talk/paper, we explore these properties and connect spectral and ambiguity function optimization of a multi-tone SFM signal to finding the location of the roots of these generalized Bessel functions.

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.

ANALYSIS OF PHASE NOISE INFLUENCE ON MICRO-DOPPLER FEATURE EXTRACTION OF VIBRATING TARGET

It is generally considered that increasing the carrier frequency of radar is an important way to improve the precision of micro-motion measurement. However, the increase of the radar frequency may raise the phase noise intensity of the radar transmitting signal and make the extraction more difficult, therefore it is particularly necessary to study the influence of phase noise on the extraction of micro-motion characteristics. In this study, specific studying about the effect of phase noise on the extraction of micro-Doppler (m-D) features is carried out. The effect of phase noise on the extraction performance of the m-D features is evaluated based on a parameter micro-motion signal-to-clutter ratio and an empirical formula is put forward based on the experiments. The results of simulation experiments indicate that increasing the carrier frequency cannot improve the extraction performance of micro-motion features in the case of using both time–frequency analysis method and the new developed sinusoidal frequency modulation Fourier transform (SFMFT) method. Meanwhile, increasing the frequency of target's micro-motion has an improvement effect through time–frequency method due to the increase of Doppler frequency.

Signals of Autodyne Sensors with Sinusoidal Frequency Modulation

Signals of Autodyne Sensors with Sinusoidal Frequency Modulation

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.

Time-frequency bandwidth product estimation of Sinusoidal Non-linear Chirp Keying scheme

Sine Non-linear Chirp Keying (SNCK) is a kind of high-efficient modulation scheme, which provides a potential new beamforming method in communication and radar systems. It has been proved to have advantages in some parameter estimation issues over conventional modulation schemes. In this paper, a novel transform termed as Discrete Sinusoidal Frequency Modulation transform (DSFMT) is proposed. Then, the DSFMT of SNCK signal is deduced and classified into three types, based on which, the time-bandwidth product is estimated by the proposed algorithm. Simulation results show that the noise has a significant impact on the localization of the peak value and the time-bandwidth product can be estimated by using local ratio values when 5 NR > 5dB.

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.

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.

Sinusoidal Frequency Modulation Fourier-Bessel Series for Multicomponent SFM Signal Estimation and Separation

Multicomponent sinusoidal frequency modulated (SFM) signals are widely used in radar, acoustics, and biomedicine. The instantaneous frequency (IF) characterizes important physical parameters of the real applications. In this paper, a sinusoidal frequency modulation Fourier-Bessel (SFMFB) series is defined for IF estimation. It provides the signal decomposition on the Bessel function basis with a finer resolution, which proposes an extension of the performance and the applicability of the classic Fourier-Bessel transform (FBT). Based on the property analysis of the SFMFB series, an algorithm of IF estimation and signal separation is introduced. Unlike the existing estimation methods which apply sliding windows to make an instantaneous approximation, the proposed method uses the global data, which provides a longer period gain, therefore achieving a better estimation performance. Moreover, considering that most estimation methods are invalid in multicomponent separation, the individual signals are well separated by the proposed algorithm, which facilitates the further monocomponent analysis. A performance comparison between the proposed method, the FBT, and another recently proposed sinusoidal frequency modulation Fourier transform (SFMFT) is also provided. Simulation results indicate that the proposed method outperforms the existing methods in estimation precision and computation load, and it is free of interference which exists in SFMFT.

A chaos-oriented prediction and suppression model to enhance the security for cyber physical power systems

Smart grid has become a fully automated system with common use of electronic equipments to control, compute and communicate. This can be modeled as cyber physical power systems (CPPS) to analyze connections and interactions, and security is one of the key factors to find the inner unmanaged vulnerabilities. In some cases, voltage source inverters (VSI) with pulse width modulation (PWM) are sensitive to initial conditions, and this is a typical chaotic state. In this paper, we present a CPPS model with the improved chaos prediction and suppression methods to enhance the security with the abilities to avoid and eliminate chaos. The main process is “prediction–quantization–control”. First, an improved maximum velocity criterion method is used to predict the possibility of chaos in the parameter space of CPPS. Second, when a possibility of chaos is predicted, a sinusoidal wave frequency modulation is used to suppress chaos. To analyze the connections of the inner entities’ transmission, a security coefficient is introduced to obtain hazard perception and to express measurements quantitatively. Third, it has proposed a chaotic control algorithm based on a fuzzy model with closed-loop dynamic mechanism to solve the security coefficient effectively. The experiments prove the predicted result has a margin of error of plus or minus 10%, and the sinusoidal wave frequency modulation can avoid chaos on CPPS. Also, the results show that security coefficient increases by 13.89%, which means it is useful with sensitive parameters and other related disturbances. Overall, this CPPS model can eliminate potential chaos phenomena caused by inversion processes, and it can be used into smart grids to improve the security effectively.

A Cyclic Frequency Tracking Loop for Wideband Spectrum Sensing and FM Demodulation

A cyclostationary feature-based wideband spectrum sensing is proposed in which cyclic frequency offset is considered. The received signal passes through a rough and flexible filter which its effective band tuned to a specific part of the received signal spectrum. It belongs to a target signal, which possibly exists in the received signal. Some cyclic frequencies of the target are employed to derive the normalized least mean square algorithm that estimates the filter output from its frequency shifted samples. Based on the weight estimate’s norm, the algorithm is tuned to find the accurate cyclic frequencies. If it succeeded, it means that the target signal is present. On the other hand, a complete search without major weights estimate means that the target signal is absent. In addition, the overall system, named cyclic frequency lock loop can be reformed as a demodulator for sinusoidal frequency modulation signals. The method is very easy to implement and has less computational complexity comparing with its other spectrum sensing counterparts. Simulation results validate the efficiency of the proposed method.

Amplitude modulation masking for frequency modulation detection

It is generally assumed that frequency modulation (FM) is detected as amplitude modulation (AM) for fast FM rates with low carrier frequencies, and for all FM rates with high carrier frequencies. If this is the case, then FM detection in the presence of an AM masker should exhibit the main features of AM masking: tuning, dependency on AM masker depth, negative masking, beating effects and phase effects. We explored the masking effects produced by sinusoidal AM on detection thresholds of sinusoidal FM for normal-hearing listeners. FM rates ranged between 2 and 64 Hz. The carrier was either a 500-Hz or a 5000-Hz pure tone that was either unmodulated in amplitude or modulated in amplitude at 2 or 16 Hz. The masker AM depth was fixed to either 50% or 25%, and stimulus duration was set to either 500 ms or 1 sec. Additionally, detection thresholds were tested as a function of the phase relationship between a 2-Hz FM target and a 2- or 4-Hz AM masker, and between a 16-Hz FM target and an 8-, 16-, or 32-Hz AM masker. The data will be discussed in light of previous studies on AM masking and the modulation filter-bank concept.

Sinusoidal frequency modulation for frequency stabilization of laser diode to an I2 saturated absorption line and a displacement measuring interferometer

Sinusoidal frequency modulation for frequency stabilization of laser diode to an I2 saturated absorption line and a displacement measuring interferometer

Accurate displacement-measuring interferometer with wide range using an I2 frequency-stabilized laser diode based on sinusoidal frequency modulation

We propose the use of the sinusoidal frequency modulation technique to improve both the frequency stability of an external cavity laser diode (ECLD) and the measurement accuracy and range of a displacement-measuring interferometer. The frequency of the ECLD was modulated at 300 kHz by modulating the injection current, and it was locked to the b21 hyperfine component of the transition 6-3, P(33), 127I2 (633 nm) by the null method. A relative frequency stability of 6.5 × 10−11 was achieved at 100 s sampling time. The stabilized ECLD was then utilized as a light source for an unbalanced Michelson interferometer. In the interferometer, the displacement and direction of the target mirror can be determined using a Lissajous diagram based on two consecutive and quadrant-phase harmonics of the interference signal. Generally, the measurement range of the interferometer by the proposed method is limited by the modulation index and the signal-to-noise ratio of the harmonics. To overcome this drawback, suitable consecutive harmonic pairs were selected for the specific measurement ranges to measure the displacement. The displacements determined in the specific ranges by the proposed method were compared with those observed by a commercial capacitive sensor. From the comparison, the proposed method has high precision to determine the displacement. The measurement range was also extended up to 10 m by selecting a suitable modulation index and suitable consecutive pairs of harmonics.

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.