Frequency Modulation Signal Research Articles

Synthetic Aperture Ladar Motion Compensation Method Based on Symmetric Triangle Linear Frequency Modulation Continuous Wave Segmented Interference

Synthetic Aperture Ladar (SAL) is a sensor that combines laser detection technology with synthetic aperture technology to achieve ultra-high-resolution imaging. Due to its extremely short wavelength, SAL is more sensitive to motion errors. The micrometer-level motion will affect the target’s azimuth focus. This article proposes an SAL motion compensation method based on Symmetric Triangular Linear Frequency Modulation Continuous Wave (STLFMCW) segmented interference, utilizing the characteristics of a triangular wave, to solve the problem of target azimuth defocusing. This article first establishes an STLFMCW echo signal model based on the SAL system under the influence of motion errors. Secondly, the radial velocity gradient along the azimuth direction is extracted using the triangular-wave-positive and -negative frequency modulation signals segmented interference method. Then, for the initial phase wrapping problem, the frequency spectral cross-correlation method is used to accurately estimate the initial radial velocity error. The radial velocity gradient is integrated along the azimuth to obtain the platform motion trajectory. Finally, the compensation functions are constructed to complete the echo Range Cell Migration (RCM) correction and residual phase compensation, resulting in a focused SAL image. This article verifies the practical effect of this method in eliminating motion errors using only one-period STLFMCW signal through simulation and real experiments. The quantitative results show that compared with the traditional method, the proposed method reduces the azimuth Peak Sidelobe Ratio (PSLR) by 8dB and the Integrated Sidelobe Ratio (ISLR) by 9 dB. This method has significant improvements and is of great significance for high-resolution FMCW SAL imaging.

Separation of signal and harmonics in non-explosive seismic prospecting with amplitude and nonlinear frequency-modulated signals

When vibroseis oscillations are excited, along with the main signal, harmonics are generated. They travel into the Earth and, like the main signal, interact with the target reflectors. Harmonics have a wider than that of the main signal frequency band, so they can be used to increase the resolution of the seismic data. To do this, the signal-related data should be separated from the harmonic-related data. This problem can be successfully solved by the previously proposed optimization recursive filtering algorithm, which, however, was developed only for linearly frequency-modulated signals. In this work, the algorithm is generalized to the case of amplitude modulation and nonlinear frequency modulation. Examples of application of the technique to increase the resolution of real vibroseis data are given.

Modeling of harmonics of amplitude and nonlinear frequency-modulated signals

In vibroseismic data, nonlinear signal distortions called harmonics are usually present. The previously proposed method of separating the signal and its harmonics makes it possible to improve the quality of the initial data, as well as to obtain additional information about the geological structure of the earth interior. One of the limitations of the proposed methodology is its initial development for linear frequency-modulated signals. A new method of prediction of harmonics that allows non-linear frequency modulation as well as amplitude variation is proposed.

Photonic Approach to Multi-band Dual-chirp Microwave Waveform Generation with Quadruple Bandwidth

We propose a scheme for generating a microwave waveform with dual-band, dual-chirp, linearly chirped characteristics and quadruple chirp bandwidth. In this scheme, we employ two cascaded Mach-Zehnder modulators (MZMs), with each modulated by a microwave signal and a linearly frequency modulated (LFM) signal. This modulation technique extends the LFM signal to multiple frequency bands and enhances its bandwidth. By properly adjusting the microwave signal's frequency and the LFM's carrier frequency, we can intelligently combine the up-chirp and down-chirp signals obtained after heterodyne beating in the photodetector (PD). This combination results in the creation of multi-band dual-chirp signals with quadruple chirp bandwidth. Our simulation demonstrates the simultaneous generation of dual-chirp microwave waveforms in the X, Ka, U, and V bands, with central frequency-bandwidth ranges of 10GHz-4GHz, 30GHz-4GHz, 50GHz-4GHz, and 70GHz-4GHz respectively. These dual-chirp signals possess a bandwidth four times that of the driving chirp signal, leading to a Time Bandwidth Product (TBWP) four times greater than that of the driving chirp signal. Consequently, the proposed scheme has the potential to significantly improve range Doppler resolution in modern radar systems. Additionally, the high-frequency and large-bandwidth dual-band dual-chirp LFM signals generated by this approach are anticipated to enhance range resolution and detection range in multitarget radar systems.

Doppler and Channel Estimation Using Superimposed Linear Frequency Modulation Preamble Signal for Underwater Acoustic Communication

Due to the relative motion between transmitters and receivers and the multipath characteristic of wideband underwater acoustic channels, Doppler and channel estimations are of great significance for an underwater acoustic (UWA) communication system. In this paper, a preamble signal based on superimposed linear frequency modulation (LFM) signals is first designed. Based on the designed preamble signal, a real-time Doppler factor estimation algorithm is proposed. The relative correlation peak shift of two LFM signals in the designed preamble signal is utilized to estimate the Doppler factor. Moreover, an enhanced channel estimation algorithm, the correlation-peak-search-based improved orthogonal matching pursuit (CPS-IOMP) algorithm, is also proposed. In the CPS-IOMP algorithm, the excellent autocorrelation characteristic of the designed preamble signal is used to estimate the channel sparsity and multipath delays, which are utilized to construct the simplified dictionary matrix. The simulation and sea trial data analysis results validated the designed preamble, the proposed Doppler estimation algorithm, and the channel estimation algorithm. The performance of the proposed Doppler factor estimation is better than that of the block estimation algorithm. Compared with the original OMP algorithm with known channel sparsity, the proposed CPS-IOMP algorithm achieves a similar estimation accuracy with a smaller computational complexity, as well as requiring no prior knowledge about the channel sparsity.

Range and Velocity Resolution of Linear- Frequency-Modulated Signals on Subarray-Mimo Radar

The most important radar system performance is determining the range-velocity of the detected target. This performance is obtained from processing an ambiguity-function (AF) between signals from target reflections and radar radiation signals. Selection of the appropriate waveform transmitted by the radar is a key factor in supporting high resolution radar performance in the AF. There are many waveforms that have been studied in radar systems, especially for multi-antenna radars, i.e., subarray-MIMO (SMIMO) radar which can form phased array (PA) and MIMO radars simultaneously, in the form of linear-frequency-modulated (LFM) signals. In this paper, we examine the use of LFM waveforms combined with SMIMO radar to produce plots of three-dimensional AF as a function of time delay and Doppler shift. The results of the comparison with the Hadamard signal determine the effectiveness of the observed AF performance on parameters such as magnitude, range-velocity resolution, peak sidelobe level ratio, and integrated sidelobe ratio by taking into account the factors of the number of Tx antennas on the PA radar and the number of Tx subarrays on the MIMO radar. The evaluation results of the SMIMO radar configuration (M = 6) with the number of Tx-Rx antenna elements the being 8 provide the best mainlobe magnitude, sidelobe magnitude, range resolution, velocity resolution, PSLR, and ISLR of AF LFM signals compared to conventional radars are 235.2dB, 7.54dB, 37.5m, 75km/s, 29.89dB, and 29.8dB, respectively. Meanwhile, the LFM signal is far superior to the Hadamard signal which has PSLR and ISLR 1.16dB and -3.36dB, respectively.

Sine Approximation-Based Comparison Method for Determining the Phase–Frequency Characteristic of Analog-to-Digital Converters

The analog-to-digital converters (ADCs) have been widely used in the applications of such as precision metrology, motion control, position and pose estimation, whose phase-frequency characteristic usually brings in an inevitable influence. In order to ensure the performance of these applications, the phase-frequency characteristic of ADCs has to be definitely determined before they are used. In this study, a new sine approximation-based comparison measurement method is presented, which accurately deter- mines this characteristic by utilizing the linear frequency modulation signal with high carrier frequency and narrow bandwidth instead of the sinusoidal signal. Experimental results demonstrate that the presented method is able to obtain the satisfactory accuracy for the phase-frequency characteristic of general ADCs and promote the improve- ment of their applications.

Frequency properties of channeled spectropolarimetry: an information theory perspective.

Channeled spectropolarimetry (CSP) has emerged as a notable technique due to its unique capacity to instantaneously measure either the polarization state of light or the Mueller matrix of a sample over a broad spectral range. Leveraging the quasi-linear relation between phase retardances of thick birefringent retarders and wavenumber, the target signal undergoes wavelength encoding. For the first time, we present a theoretical framework for the general CSP from a perspective of information theory. This framework comprehensively addresses the frequency properties of CSP, encompassing signal bandwidth, modulation frequency, sampling relationships, and filter window width during the demodulation process. Drawing from the frequency properties of CSP, we establish a theoretical foundation that informs the design of versatile CSPs and evaluates their measurement capabilities. Simulations for both Stokes CSP and Mueller CSP validate the efficacy of the proposed approach.

Simultaneous detection of multi-channel signals in MHz bandwidth using nitrogen-vacancy centers in a diamond.

In this paper, we propose a method for simultaneously recovering multiple radio wave signals based on nitrogen-vacancy (NV) centers in diamond combining optically detected magnetic resonance (ODMR) spectrum. A controlled magnetic field gradient applied to the laser excitation area on the surface of diamond widens the detectable ODMR bandwidth to 200 MHz. Three different frequency-modulated (FM) signals with distinct carrier frequencies falling within the resonance frequency range are received and demodulated in real-time. Subsequently, the FM signal reception capability of this system is further investigated by measuring baseband signal frequencies ranging from 0.1 Hz to 200 Hz and adjusting the carrier power within a dynamic range from -10 dBm to 30 dBm. This proposal, which accomplishes multi-channel demodulation using a compact and single device, has potential applications in fields such as wireless communication, radar and navigation.

Evaluation of the Success of Simulation of the Unmanned Aerial Vehicle Precision Landing Provided by a Newly Designed System for Precision Landing in a Mountainous Area

Unmanned aerial vehicle technology is the most advanced and helpful in almost every area of interest in human work. These devices become autonomous and can fulfil a variety of tasks, from simple imaging and obtaining data to search and rescue operations. The most challenging environment for search and rescue operations is the mountainous area. This article is devoted to the theoretical description and simulation tests of a prototype method of landing the light and the medium-weight UAVs used as supplementary devices for SAR (search and rescue) and HEMS (helicopter emergency medical service) in hard-to-reach mountainous terrains. The autonomous flight of a UAV in mountainous terrain has many specifics, and it is usually performed according to predetermined map points (pins) uploaded directly into the control software of the UAV. It is necessary to characterise each point flown on the chosen flight route line in advance and therefore to know its exact geographical coordinates (longitude, latitude and height of the point above the terrain), and the control system of UAV must react to the change in the weather and other conditions in real time. Usually, it is difficult to make this forecast with sufficient time in advance, mainly when UAVs are used as supplementary devices for the needs of HEMS or MRS (mountain rescue service). The most challenging phase is the final approach and landing of the UAV, especially if a loss of GNSS (global navigation satellite system) signal occurs, like in the determined area of the Little Cold Valley in the Slovak High Tatras—which is infamous for the widespread loss of GNSS signals or communication/controlling connection between the UAV and the pilot-operator at the operational station. To solve the loss of guidance, a new method for guiding and controlling the UAV in its final approach and landing in a determined area is tested. An alternative landing navigation system for UAVs in a specific mountainous environment—the authors’ designed frequency Doppler landing system (FDLS)—is briefly described but thoroughly tested with the help of artificial intelligence. An estimation of dynamic stability is used based on the time recording of the current position of the UAV, with the help of a frequency-modulated or amplitude-modulated signal based on the author’s prototype of a precision landing system designed for mountainous terrain. This solution could overcome the problems of GNSS signal loss. The presented research primarily evaluates the success of the simulation flights for the supplementary UAV. The success of navigating the UAV to land in the mountainous environment at an exact landing point using the navigation signals from the FDLS was evaluated at more than 95%.

PHS: A Pulse Sequence Method Based on Hyperbolic Frequency Modulation for Speed Measurement

The channel in the marine environment is a time-varying and space-varying channel. Pulse-truncated continuous wave (PCW) speed measurement is often used in sonar, but the instability effect of PCW signal in the channel limits the effectiveness of speed measurement. Hyperbolic frequency modulation (HFM) signal is insensitive to Doppler; therefore, HFM signals are widely used in ranging and velocity measurement of sonar and radar. However, due to the filtering effect of the marine environment, the HFM signal of a single frequency band may cause excessive transmission loss, and the echo energy may be too weak to detect the target. Based on the analysis of the influence of speed on the distance measurement of HFM signal, a pulse sequence method based on HFM for speed measurement (PHS) is proposed, which uses HFM signals of different frequency bands and pulse widths in the pulse sequence to perform speed measurement. Extensive simulation results show that PHS method not only guarantees the speed measurement but also makes full use of the energy of the HFM sequence to improve the accuracy of the distance measurement. And PHS method is valuable to the practical application of engineering.

Fast 3D positioning based on a simplified THz photonic stereo ISAR system.

In this work, a THz stereo inverse synthetic aperture radar scheme based on photonics is proposed, and proof-of-concept experimentally demonstrated, achieving high resolution and fast three-dimensional (3D) positioning of multiple targets. An optical frequency comb and a uni-traveling carrier photodiode are employed to photonically generate a linear frequency-modulation signal at 300-320GHz. By two incoherent measurements at different angles with one pair of antennas, 3D positioning of plane reflectors over a distance of 0.6m is successfully accomplished, achieving a resolution of 7.5mm for both range and azimuth dimensions, and a maximum experimental height error of 4mm.

Improved Lv’s Distribution for Noisy Multicomponent LFM Signals Analysis

This paper presents the improved Lv’s distribution (ImLVD) for noisy multicomponent linear frequency-modulated (LFM) signals analysis, which is of significant importance in radar signal processing. Two goals of this paper are (i) to overcome drawbacks of the Lv’s distribution (LVD), and (ii) to study mechanisms of the constant delay introduction. Theoretical comparisons in cross-term suppression, resolution, peak-to-sidelobe level, anti-noise performance and implementation are performed for the maximum likelihood (ML) method, Wigner–Hough transform (WHT), LVD, parameterized centroid frequency–chirp rate distribution (PCFCRD) and ImLVD. Based on theoretical comparisons and illustrative examples, superiorities of the ImLVD are demonstrated and several unclear mechanisms of the introduced constant delay are interpreted. Finally, three numerical examples are given to illustrate that, because of the high cross-term suppression, resolution, peak-to-sidelobe level and anti-noise performance without the non-uniform integration variable, the ImLVD is more suitable for noisy multicomponent LFM signals analysis.

Progress in Photonics-Based Linear Frequency-Modulated Microwave Signal Generation Technology (Invited)

Progress in Photonics-Based Linear Frequency-Modulated Microwave Signal Generation Technology (Invited)

Extending the Multi-Tone Sinusoidal Frequency Modulation Signal Model by Fourier Expansions With Arbitrary Periods

Extending the Multi-Tone Sinusoidal Frequency Modulation Signal Model by Fourier Expansions With Arbitrary Periods

Studies on High-Resolution Airborne Synthetic Aperture Radar Image Formation with Pseudo-Random Agility of Interpulse Waveform Parameters

By means of alteration of the transmitted linear frequency modulation (LFM) signal waveform parameters, such as pulse width or chirp rate, initial phase, pulse repetition interval (PRI), and chirp rate polarity at every position of synthetic apertures, the pseudo-random agility technology of interpulse waveform parameters in airborne Synthetic Aperture Radar (SAR) actively increases the complexity and uncertainty of radar waveforms. This technology confuses jamming interception receivers, thus improving its anti-interference ability for active coherent jamming, which is one of the main research interests of airborne SAR technology. But the pseudo-random agility technology for interpulse waveform parameters faces certain challenges of large computation and complex system design, which need to be further studied and solved. To address these issues, a processing scheme of high-resolution SAR image formation which is appropriate for agile interpulse waveform parameters is proposed in this paper. This method can deal with multiple agile parameters, not only single ones as in most existing literature. Its computation load is nearly comparable to that of traditional SAR image formation with constant waveform parameters. The high-resolution SAR imaging results obtained by processing SAR raw data with agile interpulse waveform parameters demonstrate the effectiveness of the proposed method. In addition, real SAR images with resolutions of 0.5 m and 0.15 m, which are rarely found in the public literature, are shown under the circumstance of randomly changing the transmitted wideband LFM signal pulse parameters one by one.

A Novel Chaotic-NLFM Signal under Low Oversampling Factors for Deception Jamming Suppression

Synthetic aperture radar (SAR) is a high-resolution imaging radar. With the deteriorating electromagnetic environment, SAR systems are susceptible to various forms of electromagnetic interference, including deception jamming. This jamming notably impacts SAR signal processing and subsequently worsens the quality of acquired images. Chaotic frequency modulation (CFM) signals could effectively counteract deception jamming. Nevertheless, due to the inadequate band-limited performance of CFM signals, higher oversampling factors are needed for achieving optimal low sidelobe levels, leading to increased system costs and excessively high data rates. Additionally, not all chaotic sentences meet the CFM signal requirements. In response, this paper proposes a novel signal modulation method called chaotic-nonlinear frequency modulation (C-NLFM) that enhances band-limited performance. The optimum parameters for C-NLFM signals are selected using the particle swarm optimization (PSO) algorithm. In this way, C-NLFM signals attain ideal low sidelobe levels even when faced with reduced oversampling factors. Meanwhile, this chaotic coding mode retains its capability to effectively suppress deception jamming. Moreover, C-NLFM signals demonstrate versatility in adapting to various chaotic sequences, thereby enhancing their flexibility to modify the signals as required. Through comprehensive simulations, data analysis, and a semi-physical experiment, the effectiveness and superiority of this proposed method have been confirmed.

Wigner-Ville distribution and ambiguity function of QPFT signals

The quadratic phase Fourier transform(QPFT) has received my attention in recent years because of its applications in signal processing. At the same time the applications of Wigner-Ville distribution (WVD) and ambiguity function (AF) in signal analysis and image processing can not be excluded. In this paper we investigated the Wigner-Ville Distribution (WVD) and ambiguity function (AF) associated with quadratic phase Fourier transform (WVD-QPFT/AF-QPFT). Firstly, we propose the definition of the WVD-QPFT, and then several important properties of newly defined WVD-QPFT, such as nonlinearity, boundedness, reconstruction formula, orthogonality relation and Plancherel formula are derived. Secondly, we propose the definition of the AF-QPFT, and its with classical AF, then several important properties of newly defined AF-QPFT, such as non-linearity, the reconstruction formula, the time-delay marginal property, the quadratic-phase marginal property and orthogonal relation are studied. Further, a novel quadratic convolution operator and a related correlation operator for WVD-QPFT are proposed. Based on the proposed operators, the corresponding generalized convolution, correlation theorems are studied. Finally, a novel algorithm for the detection of linear frequency-modulated(LFM) signal is presented by using the proposed WVD-QPFT and AF-QPFT.

Chirp Rate Estimation of LFM Signals Based on Second-Order Synchrosqueezing Transform

For the problem of low time-frequency aggregation of the short-time Fourier transform (STFT), which causes the parameter estimation performance degradation of linear frequency modulation (LFM) signals at low signal-to-noise ratio (SNR), second-order synchrosqueezing transform (SSST) is proposed based on the square of STFT amplitude. The time-frequency resolution and energy aggregation are improved by means of squeezing and reassigning the time-frequency spectrum. Meanwhile, in order to decrease the calculation of classical parameter estimation methods, the Hough transform is used for rough estimation, and then the fractional Fourier transform (FRFT) is used for accuracy estimation based on the Renyi entropy. The simulation result shows that higher estimation accuracy is obtained at low SNR, and it has better robustness.

High-purity linearly frequency-modulated signal generation based on the integrated semiconductor laser subject to the dynamical optoelectrical feedback.

A novel photonic method of linearly frequency-modulated (LFM) signal generation with high purity based on the monolithically integrated semiconductor laser (MISL) subject to the dynamical optoelectrical feedback is proposed and demonstrated in this paper. In this approach, the MISL is firstly operated in period-one state. By introducing the dynamical optoelectrical feedback to modulate the MISL, the generated LFM signals would be constantly optimized as long as the delay of the feedback loop is matched with the repetition period of the LFM signal. In this system, no additional high-speed external modulator, high-frequency electrical LFM oscillator are required, highly simplifying the framework and reducing the power consumption. In the current proof-of-concept experiment, one LFM signal with the bandwidth as large as 5.6 GHz is generated and the corresponding frequency comb contrast can be drastically improved by 51 dB. Furthermore, the effect of the delay mismatch is also discussed in this paper.