Nonlinear Frequency Modulation Research Articles

Estimation of intrapulse modulation parameters of LPI radar under noisy conditions

AbstractLow probability of intercept (LPI) radars utilize specially designed waveforms for intra-pulse modulation and hence LPI radars cannot be easily intercepted by passive receivers. The waveforms include linear frequency modulation, nonlinear frequency modulation, polyphase, and polytime codes. The advantages of LPI radar are wide bandwidth, frequency variability, low power, and the ability to hide their emissions. On the other hand, the main purpose of intercept receiver is to classify and estimate the parameters of the waveforms even when the signals are contaminated with noise. Precise measurement of the parameters will provide necessary information about a threat to the radar so that the electronic attack or electronic warfare support system could take instantaneous counter action against the enemy. In this work, noisy polyphase and polytime coded waveforms are analyzed using cyclostationary (CS) algorithm. To improve the signal quality, the noisy signal is pre-processed using two types of denoising filters. The denoised signal is analyzed using CS techniques and the coefficients of spectral correlation density are computed. With this method, modulation parameters of nine types of waveforms up to −12 dB signal-to-noise ratio with an accuracy of better than 95% are extracted. When compared with literature values, it is found that the results are superior.

Low Correlation Interference OFDM-NLFM Waveform Design for MIMO Radar Based on Alternating Optimization.

The OFDM chirp signal is suitable for MIMO radar applications due to its large time-bandwidth product, constant time-domain, and almost constant frequency-domain modulus. Particularly, by introducing the time-frequency structure of the non-linear frequency modulation (NLFM) signal into the design of an OFDM chirp waveform, a new OFDM-NLFM waveform with low peak auto-correlation sidelobe ratio (PASR) and peak cross-correlation ratio (PCCR) is obtained. IN-OFDM is the OFDM-NLFM waveform set currently with the lowest PASR and PCCR. Here we construct the optimization model of the OFDM-NLFM waveform set with the objective function being the maximum of the PASR and PCCR. Further, this paper proposes an OFDM-NLFM waveform set design algorithm inspired by alternating optimization. We implement the proposed algorithm by the alternate execution of two sub-algorithms. First, we keep both the sub-chirp sequence code matrix and sub-chirp rate plus and minus (PM) code matrix unchanged and use the particle swarm optimization (PSO) algorithm to obtain the optimal parameters of the NLFM signal’s time-frequency structure (NLFM parameters). Next, we keep current optimal NLFM parameters unchanged, and optimize the sub-chirp sequence code matrix and sub-chirp rate PM code matrix using the block coordinate descent (BCD) algorithm. The above two sub-algorithms are alternately executed until the objective function converges to the optimal solution. The results show that the PASR and PCCR of the obtained OFDM-NLFM waveform set are about 5 dB lower than that of the IN-OFDM.

Millimeter-level resolution through-the-wall radar imaging enabled by an optically injected semiconductor laser.

Millimeter-level resolution through-the-wall radar (TWR) imaging is demonstrated using a broadband nonlinear frequency-modulated (NLFM) signal that is generated by an optically injected semiconductor laser. The proposed system uses period-one dynamics of a semiconductor laser, together with an optical frequency downconversion technique to generate NLFM signals, which addresses the problem of traditional period-one oscillation not being able to generate broadband signals in the low-frequency region. In the experiment, an NLFM signal having a broad bandwidth of 18.5 GHz (1.5-20 GHz) is generated with a corresponding radar range resolution of 8.1 mm. Using this signal, TWR imaging is demonstrated, in which the use of the NLFM signal achieves good side-lobe suppression during pulse compression, and a modified back projection imaging algorithm with sub-aperture weighting is proposed to improve the imaging quality.

Experimental Results of Underwater Acoustic Communication with Nonlinear Frequency Modulation Waveform.

In this paper, we propose underwater acoustic (UWA) communications using a generalized sinusoidal frequency modulation (GSFM) waveform, which has a distinct ambiguity function (AF) and correlation function characteristic. For these reasons, it is more robust in multipath channels than the conventional chirp spread spectrum (CSS) with a linear frequency modulation (LFM) waveform. Four types of GSFM waveforms that are orthogonal to each other are applied for each symbol in the proposed method. To evaluate the performance of the proposed method, we compared the performances of the proposed method and conventional method by conducting diverse experiments: simulations, lake trials and sea trials. In the simulation results, the proposed method shows better performance than the conventional method. The lake trial was conducted with a distance of 300~400 m between the transmitter and receiver. As a result of the experiment, the average bit error rate (BER) of the proposed method is and that of the conventional method is , which shows that the proposed method is superior to the conventional method. The sea trial was conducted at a distance of approximately 20 km between the transmitter and receiver at a depth of 1500 m, and the receiver was composed of 16 vertical line arrays (VLAs) with a hydrophone. The proposed method had a BER of in one channel and was error free in the other.

Compensation of target signal migration in the multichannel matched filter

The study proposes a method of target range signal compensation within different pulse burst periods during in-period matched filtering. The proposed method allows to reduce losses in case of long-term signal integration. This is especially important for signals highly sensitive to Doppler frequency shift. In terms of this parameter, a multichannel configuration of the compression filter is a probable solution for such signals. Based on the example of a signal with non-linear frequency modulation and the results of simulation modelling, we analyse the effectiveness of migration compensation and give recommendations on channel multiplexing for the compression filter with an integrated migration compensator.

Pulse Coding in Distributed Optical Fiber Vibration Sensor: A Review

Distributed optical fiber vibration sensor (DOFVS) is suitable for remote monitoring of vibration signals generated by external perturbations. In order to improve the sensing performance, various pulse coding techniques are applied in DOFVS, which have attracted an increasing amount of research attention. In this paper, recent advances of pulse coding methods used in DOFVS are reviewed, from pulse compression, including linear frequency modulation (LFM) and nonlinear frequency modulation (NLFM), pulse coding modulation based on the linear combination and correlation operation, such as Simplex code, Golay code and random code, as well as pulse sequence modulation (PSM), such as phase-shift pulses, differential frequency pulses, etc. Characteristics, working principles and the latest research results of pulse coding methods are discussed. Furthermore, some application progresses of pulse coding for performance enhancement in DOFVS are also introduced. By combining these technologies, the sensing performance could be improved in aspects of sensing distance, spatial resolution (SR), and frequency response, which show considerable potential applications in perimeter security, oil and gas monitoring, pipeline leakage, and structural health monitoring.

Staring Spotlight SAR with Nonlinear Frequency Modulation Signal and Azimuth Non-Uniform Sampling for Low Sidelobe Imaging

In synthetic aperture radar (SAR) imaging, geometric resolution, sidelobe level (SLL) and signal-to-noise ratio (SNR) are the most important parameters for measuring the SAR image quality. The staring spotlight mode continuously transmits signals to a fixed area by steering the azimuth beam to acquire azimuth high geometric resolution, and its two-dimensional (2D) impulse response with the low SLL is usually obtained from the 2D weighted power spectral density (PSD) by the selected weighting window function. However, this results in the SNR reduction due to 2D amplitude window weighting. In this paper, the staring spotlight SAR with nonlinear frequency modulation (NLFM) signal and azimuth non-uniform sampling (ANUS) is proposed to obtain high geometric resolution SAR images with the low SLL and almost without any SNR reduction. The NLFM signal obtains non-equal interval frequency sampling points under uniform time sampling by adjusting the instantaneous chirp rate. Its corresponding PSD is similar to the weighting window function, and its pulse compression result without amplitude window weighting has low sidelobes. To obtain a similar Doppler frequency distribution for low sidelobe imaging in azimuth, the received SAR echoes are designed to be non-uniformly sampled in azimuth, in which the sampling sequence is dense in middle and sparse in both ends, and azimuth compression result with window weighting would also have low sidelobes. According to the echo model of the proposed imaging mode, both the back projection algorithm (BPA) and range migration algorithm (RMA) are modified and presented to handle the raw data of the proposed imaging mode. Both imaging results on simulated targets and experimental real SAR data processing results of a ground-based radar validate the proposed low sidelobe imaging mode.

Underwater acoustic communication using nonlinear frequency modulation waveform with low side-lobe characteristics

In fluctuating underwater acoustic (UWA) communication, reducing the interference caused by multi-path propagation is important to get better performance. For this reason, Chirp Spread Spectrum (CSS), which has insensitive Doppler effect and having effective bandwidth, using Linear Frequency Modulation (LFM) waveform was used in UWA communication before. But LFM waveform has high auto-correlation function sidelobes it becomes interference and gets worse performance in reverberation environment. This presentation proposes an UWA communication using Generalized Sinusoidal Frequency Modulation (GSFM) waveform which is generalized form of sinusoidal FM. GSFM waveform usually attains much higher spectral efficiency and lower peak-to-average power ratio than LFM while maintaining same bandwidth and pulse duration. GSFM waveform has various types and we use two GSFM pulses that is a Forward type in time-frequency domain and a time reversing type of Forward type in this presentation. Each type represents binary values '0' and '1', respectively. Each of pulses occupy same band of frequency and each of GSFM pulses have nearly orthogonality. Simulation results in various underwater channel environments with noise will be presented. A Bellhop-based underwater channel model is used for simulation. The proposed method will be analyzed compared to the conventional CSS method with LFM waveform.

CESAM-Coded excitation scanning acoustic microscope.

Scanning acoustic microscopy (SAM) finds use across many disciplines, e.g., biology, industrial quality control, and materials science, thanks to its unique ability to quantify mechanical sample properties combined with its high resolution. However, such imaging is often slow, especially if averaging is necessary. We present a Coded Excitation Scanning Acoustic Microscope (CESAM) that employs coded signals and show that it produces images of higher signal-to-noise ratios (SNRs) than the classical SAM in a comparable measurement time. The CESAM employs coded signals instead of the short bursts used in traditional SAMs, and we employ both linear and non-linear frequency modulation. Our results show that compared to the SAM approach, this modulation increases the SNR by 16.3 dB (from 39.9 to 56.2 dB) and reduces the echo duration by 26.7% when we employ a linear chirp to the transducer with a nominal bandwidth of 130-370MHz. Driving the transducer with a broader bandwidth signal using non-linear chirps (100-450MHz), we obtained a SNR increase of 10.3 dB and a reduced echo duration of 70.5%. The shorter echo duration increases z-resolution, whereas the lateral resolution remains limited by the wavelength. Finally, we show that by using these coded signals, one can obtain enhanced image quality relative to the standard actuation of the same measurement time. Our results have potential to invigorate the field of acoustic microscopy, especially with samples where the enhanced SNR and/or contrast-to-noise ratio is crucial for image quality.

Roll angular rate extraction based on modified spline-kernelled chirplet transform

The roll angular rate is much crucial for the guidance and control of the projectile. Yet the high-speed rotation of the projectile brings severe challenges to the direct measurement of the roll angular rate. Nevertheless, the radial magnetometer signal is modulated by the high-speed rotation, thus the roll angular rate can be achieved by extracting the instantaneous frequency of the radial magnetometer signal. The objective of this study is to find out a precise instantaneous frequency extraction method to obtain an accurate roll angular rate. To reach this goal, a modified spline-kernelled chirplet transform (MSCT) algorithm is proposed in this paper. Due to the nonlinear frequency modulation characteristics of the radial magnetometer signal, the existing time-frequency analysis methods in literature cannot obtain an excellent energy concentration in the time-frequency plane, thereby leading to a terrible instantaneous frequency extraction accuracy. However, the MSCT can overcome the problem of bad energy concentration by replacing the short-time Fourier transform operator with the Chirp Z-transform operator based on the original spline-kernelled chirplet transform. The introduction of Chirp Z-transform can improve the construction accuracy of the transform kernel. Since the construction accuracy of the transform kernel determines the concentration of time-frequency distribution, the MSCT can obtain a more precise instantaneous frequency. The performance of the MSCT was evaluated by a series of numerical simulations, high-speed turntable experiments, and real flight tests. The evaluation results show that the MSCT has an excellent ability to process the nonlinear frequency modulation signal, and can accurately extract the roll angular rate for the high spinning projectiles.

Simultaneous Time-Varying Vibration and Nonlinearity Compensation for One-Period Triangular-FMCW Lidar Signal

Frequency modulation continuous wave (FMCW) Lidar inevitably suffers from vibration and nonlinear frequency modulation, which influences the ranging and imaging results. In this paper, we analyze the impact of vibration error coupled with nonlinearity error on ranging for FMCW Lidar, and propose a purely theoretical approach that simultaneously compensates for time-varying vibration and nonlinearity in one-period triangular FMCW (T-FMCW) signals. We first extract the localized characteristics of dechirp signals in time-frequency domain by using a second-order synchro-squeezing transform (second-order SST), and establish an instantaneous ranging model based on second-order SST which can characterize the local distributions of time-varying errors. Second, we estimate the nonlinearity error by using time-frequency information of an auxiliary channel and then preliminarily eliminate the error from the instantaneous measurement range. Finally, we construct a particle filtering (PF) model for T-FMCW using the instantaneous ranging model to compensate for the time-varying vibration error and the residual nonlinearity error, and calculate the range of target by using triangular symmetry relations of T-FMCW. Experimental tests prove that the proposed method can accurately estimate the range of target by compensating for the time-varying vibration and the nonlinearity errors simultaneously in one-period T-FMCW signal.

Enhanced Noise Tolerance Levels for Digital Receiver using Non-Linear Frequency Modulation

One of the critical issues concerning the industries of aerospace and Defence is the accuracy and precision levels of the possible range resolution. And equally important is the detection of the signal in the presence of noisy environments. Signal-to-Noise ratio is one such measure that ensures enhancement of target detection in tough environments. Besides this, high range resolution is also essential for the digital receiver to identify closely spaced multiple targets. The projected digital receiver design primarily highlights the possibility of pulse compression techniques combined with linear frequency modulation and non-linear frequency modulation waveforms for refining the range resolution of targets compared to their counterpsrts, the traditional waveforms. The range resolution and detection enhancement using the advanced signal processing techniques in the presence of noisy environments have been presented with evidence from the simulations accomplished in MATLAB. The ability of the pulse compression waveform to perform in the presence of noise has been tested. Further, this paper presents the minimum signal to noise ratio of the received echo signal for achieving the required range resolution with MATLAB simulations. The paper also includes further plan of work to make this design more robust as an adaptable receiver for industrial applications.

A Waveform Design Method Based on Nonlinear Frequency Modulation and Space-coding for Coherent Frequency Diverse Array Radar

A Frequency Diverse Array (FDA) radar achieves the uniform coverage of a large-scale airspace within a pulse duration by introducing a designed carrier frequency increment between adjacent transmitting elements. Unfortunately, the beam scanning property of an FDA radar leads to a reduction in dwell time at certain azimuth direction, which results in the deterioration of the range resolution. To solve this problem, we propose a novel coherent FDA radar waveform in the space–time domain, in which spatial phase encoding is introduced between transmitting elements to significantly improve the range resolution of a coherent FDA radar. A nonlinear frequency modulation signal is also used in the time domain to obtain a low-range Peak to SideLobe Ratio (PSLR). Simulation results verify that the proposed FDA radar waveform design realizes both a low PSLR and high range resolution. Finally, we analyze the Doppler sensitivity of our proposed method for the observation of high-speed moving targets.

Quasi-Orthogonal Waveforms for Ambiguity Suppression in Spaceborne Quad-Pol SAR

This article deals with the synthesis and analysis of quasi-orthogonal nonlinear frequency modulation (NLFM) waveforms to mitigate the impairments of ambiguous returns in quadrature-polarimetric (quad-pol) synthetic aperture radars (SARs). To this end, focusing on signals with a continuous piecewise linear instantaneous frequency, the design of a waveform pair exhibiting both a low cross correlation energy (CCE) and low peak to sidelobe ratios (PSLRs), is considered. To handle the resulting nondeterministic polynomial (NP) hard problem, a coordinate descent (CD) method is employed, where, at each step, the marginal minimization is tackled via a MATLAB optimization toolbox. Hence, transmission/reception schemes jointly capitalizing quasi-orthogonal NLFM waveforms and azimuth phase coding (APC) techniques are proposed to suppress ambiguity interference. Moreover, a systematic framework for the evaluation of the resulting azimuth ambiguity-to-signal ratio (AASR) and range ambiguity-to-signal ratio (RASR) is provided. Finally, detailed simulation experiments based on the LuTan (LT-1) parameters are carried out to verify the practicability and effectiveness of the newly proposed transceiver schemes.

Optimal Signal Design for a New Physically Motivated Clutter Model With Applications to Ultrasonic Testing.

In this article, we will explore the optimal signal design problem for a new physically motivated clutter model. The reason to pursue the optimal signal design is that the model, even though it was simple, led to a robust detector that worked well on real ultrasonic data. Moreover, by using the model, an analytical solution for the optimal signal is obtained. In addition, the optimal waveform gives a new insight into the signal design problem that can be valuable for many applications. New proof has been provided for a finite data record that is lacking in the literature. We have found that the optimal signal is an impulse, and as a result, it has an impulsive autocorrelation sequence (ACS). Since an impulsive ACS signal is not realizable, in practice, a study for an alternative waveform is conducted. Waveforms from four different categories have been explored: linear frequency-modulated (LFM), nonlinear frequency-modulated (NLFM), phase-coded modulated (PCM) signals, and, finally, what we called other signals. Comparison analysis between these waveforms themselves and the most commonly used transmitted pulse in practice, which is the Gaussian amplitude-modulated sinusoid (GAMS) pulse, has been implemented. We show that the LFM pulse has a large advantage over the GAMS pulse in terms of detectability. In addition, a comparison between the LFM and the GAMS signals under a deviation from the single scatterer assumption, indicating a more complex target, using simulated noise is performed.

FPGA based Identification of Frequency and Phase Modulated Signals by Time Domain Digital Techniques for ELINT Systems

In this paper, a decision tree algorithm based on time-domain digital technique is developed for the identification and classification of diverse radar intra-pulse modulated signals for the electronic intelligence system in real-time. This includes linear frequency modulation, non-linear frequency modulation, stepped frequency modulation and bi-phase modulation. The received signal is digitised and the instantaneous phase and high accuracy instantaneous frequency are estimated. The instantaneous amplitude is also estimated to get the start and stop of the pulse. Instantaneous parameters are estimated using a moving autocorrelation technique. The proposed algorithm is employed on the instantaneous frequency and the modulation is identified. The modulation type and modulation parameter are important for unique radar identification when similar radars are operating in a dense environment. Simulations are carried out at various SNR conditions and results are presented. The model for algorithm is developed using a system generator and implemented in FPGA. These results are compared when the proposed algorithm is used with the existing digital in-phase and quadrature-phase (DIQ) technique of instantaneous frequency and amplitude estimation.

Adaptive stochastic resonance in bistable system driven by noisy NLFM signal: phenomenon and application.

The stochastic resonance (SR) in a bistable system driven by nonlinear frequency modulation (NLFM) signal and strong noise is studied. Combined with empirical mode decomposition (EMD) and piecewise idea, an adaptive piecewise re-scaled SR method based on the optimal intrinsic mode function (IMF), is proposed to enhance the weak NLFM signal. At first, considering the advantages of EMD for dealing with non-stationary signals, the segmented NLFM signal is processed by EMD. Meanwhile, the cross-correlation coefficient is used as the measure to select the optimal IMF that contains the NLFM signal feature. Then, the spectral amplification gain indicator is proposed to realize the adaptive SR of the optimal IMF of each sub-segment signal and reconstruct the enhanced NLFM signal. Finally, the effectiveness of the proposed method is highlighted with the analysis of the short-time Fourier transform spectrum of the simulation results. As an application example, the proposed method is verified adaptability in bearing fault diagnosis under the speed-varying condition that represents a typical and complicated NLFM signal in mechanical engineering. The research provides a new way for the enhancement of weak non-stationary signals. This article is part of the theme issue 'Vibrational and stochastic resonance in driven nonlinear systems (part 1)'.

Optimization of two-stage NLFM signal using Heuristic approach

Background/Objectives: The design of appropriate Non-Linear Frequency Modulation (NLFM) signals continues to be the focus of research in radar pulse compression theory for sidelobe reduction. This study focuses on a heuristic design and optimization algorithm to optimize the side lobe values of the NLFM signal designed using two-piece wise linear frequency modulation (LFM) functions. Methods: 1) Heuristic search identifies the optimum B1, T1, and B2, T2, which yield the lowest sidelobe value of the designed function.2) Compute all the side lobe values of the designed NLFM signal using an algorithm developed in Python scripting language. To plot a complete contour map for all the calculated side lobe values, which helps identify the associated variations in the range of side lobe values. Finally, optimize the side lobe values keeping the main lobe width and time-bandwidth (BT) product unchanged by designing a dynamic optimization algorithm. Findings: The algorithm developed considered all side lobe levels after the main lobe for optimization. The focus is mainly on the peak sidelobe ratio (PSLR) value without affecting the other parameters. The results demonstrate that the achieved side lobes exhibit their desired levels. Novelty: The method is useful in all types of hardware associated with weather radar applications to military solutions. The technique can be extended to other multistage signals consisting of piecewise linear Segments. Keywords: Contour; LFM; NLFM; optimization; PSLR

A variable chirp rate stepped frequency linear frequency modulation waveform designed to approximate wideband non-linear radar waveforms

The non-linear frequency modulation (NLFM) waveform is one of the existing waveforms that can be used in high range resolution radar applications. However, a high sampling frequency and consequently an expensive ADC are required. To overcome this drawback while taking advantage of the features of the NLFM waveform, we suggest approximating the wideband NLFM waveform by a piecewise linear waveform and using it in a stepped frequency (SF) framework. Thus, a variable chirp rate SF-LFM waveform is proposed where SF is combined with a train of LFM pulses having different chirp rates, durations, and bandwidths. In this paper, these parameters are derived from a tangent-based NLFM waveform. At the receiver, a generalized version of the time domain (TD) algorithm is proposed to process the received echoes. Our purpose is to obtain the high range resolution profile (HRRP) whose properties are of the same magnitude orders as those obtained using a tangent-based NLFM waveform. These properties are the peak sidelobe ratio, the integrated sidelobe, and the range resolution. Toward this goal, a multi-objective optimization issue is addressed to deduce the parameters of the proposed waveform by using two types of approaches based on evolutionary algorithms. Their relevance is compared. Our analysis and simulations show that the proposed approaches attain the targeted performance goals with a smaller sampling frequency at the receiver.

NLFM pulse radar for drone detection using predistortion technique

The development of radar technology for the detection of small drones is getting attention of researchers. In this work, the detection of drones using Ku-band radar system has been discussed. We have utilized the advantage of nonlinear frequency modulation (NLFM) waveform for the suppression of range sidelobes. The performance and sensitivity of a radar system can be related with the linearity of system response. Here, we have made an effort to minimize non-linearity in the radar system response by using digital predistortion method. In this method, amplitude weighting coefficients have been calculated based on the received data. We have used FPGA-based transceiver for intermediate frequency (IF) signal generation and data acquisition, along with Ku-band up-down converters. The radar system was first calibrated for desired frequency band using amplitude predistortion method. In this article, experiment results for the detection of single drone and two drones using NLFM pulse signal are presented.