Frequency-modulated Continuous-wave Signal Research Articles

Increasing SAR Imaging Precision for Burden Surface Profile Jointly Using Low-Rank and Sparsity Priors

The synthetic aperture radar (SAR) imaging technique for a frequency-modulated continuous wave (FMCW) has attracted wide attention in the field of burden surface profile measurement. However, the imaging data are virtually under-sampled due to the severely restricted scan time, which prevents the antenna being exposed to high temperatures and heavy dust in the blast furnace (BF) for an extended period. In traditional SAR imaging algorithm research, the insufficient accumulation of scattered energy in reconstructing the burden surface profile leads to lower imaging precision, and the harsh smelting increases the probability of distortion in shape detection. In this study, to address these challenges, a novel rotating SAR imaging algorithm based on the constructed mechanical swing radar system is proposed. This algorithm is inspired by the low-rank property of the sampled signal matrix and the sparsity of burden surface profile images. First, the sparse FMCW signal is modeled, and the position transform matrix, calculated according to the BF dimensions, is embedded into the dictionary matrix. Then, the low-rank and sparsity priors are considered and reformulated as split variables in order to establish a convex optimization problem. Lastly, the augmented Lagrange multiplier (ALM) is employed to solve this problem under double constraints, and the imaging results are obtained using the alternating direction method of multipliers (ADMM). The experimental results demonstrate that, in the subsequent shape detection, the root mean square error (RMSE) is 15.38% lower than the previous algorithm and 15.63% lower under low signal-to-noise (SNR) conditions. In both enclosed and harsh environments, the proposed algorithm is able to achieve higher imaging precision even under high noise. It will be further optimized for speed and reliability, with plans to extend its application to 3D measurements in the future.

Highly‐Linear and Wavelength‐Tunable Frequency‐Modulated Continuous‐Wave Hybrid‐Integrated Laser

AbstractFrequency‐sweeping laser sources play a critical role in the accurate 3D mapping of frequency‐modulated continuous‐wave (FMCW) LiDAR systems, whose chirp linearity greatly impacts the measurement precision. Although various pre‐distortion algorithms have been proposed to reduce chirp nonlinearity, these open‐loop methods can rapidly suppress the chirp nonlinearity but they are susceptible to environmental variations and often exhibit subpar performance in long‐range detection scenarios. In contrast, the electro–optical phase‐locked loop (EO‐PLL) serves as a real‐time linearizing solution for FMCW LiDAR, enabling high‐precision, high‐resolution, and long‐distance measurement capabilities. In this study, a III/V‐Si3N4 hybrid‐integrated external cavity laser (ECL) is used to generate an FMCW signal over a large wavelength tuning range of 68 nm. The maximum output optical power is 15.8 mW, and the intrinsic linewidth is 0.9 kHz. By modulating the phase shifter, an FMCW signal with a chirp bandwidth of 0.7 GHz is generated at a repetition rate of 1 kHz. The pre‐distortion algorithm is combined with the gain‐tunable EO‐PLL system to suppress the chirp nonlinearity and frequency noise across multiple wavelengths, leading to a remarkable improvement in range precision from 202 to 4.2 cm when targeting a distance of 200 m.

W-Band FMCW MIMO System for 3-D Imaging Based on Sparse Array

Multiple-input multiple-output (MIMO) technology is widely used in the field of security imaging. However, existing imaging systems have shortcomings such as numerous array units, high hardware costs, and low imaging resolutions. In this paper, a sparse array-based frequency modulated continuous wave (FMCW) millimeter wave imaging system, operating in the W-band, is presented. In order to reduce the number of transceiver units of the system and lower the hardware cost, a linear sparse array with a periodic structure was designed using the MIMO technique. The system operates at 70~80 GHz, and the high operating frequency band and 10 GHz bandwidth provide good imaging resolution. The system consists of a one-dimensional linear array, a motion control system, and hardware for signal generation and image reconstruction. The channel calibration technique was used to eliminate inherent errors. The system combines mechanical and electrical scanning, and uses FMCW signals to extract distance information. The three-dimensional (3-D) fast imaging algorithm in the wave number domain was utilized to quickly process the detection data. The 3-D imaging of the target in the near-field was obtained, with an imaging resolution of 2 mm. The imaging ability of the system was verified through simulations and experiments.

Broadband dual-chirp FMCW laser source based on DSB-SC modulation and cascaded FWM.

Based on dual-sideband suppressed-carrier (DSB-SC) modulation and two-stage cascaded four-wave-mixing (FWM), a scheme of broadband dual-chirp frequency-modulated continuous-wave (FMCW) laser source is proposed and experimentally demonstrated. First, via a Mach-Zehnder modulator biased at its null point, an original DSB-SC FMCW signal with 4.0 GHz swept-frequency range and 0.2 GHz/μs sweep rate is generated. Next, the original DSB-SC FMCW signal is sent to a 1 km dispersion compensation fiber for implementing first-stage FWM, a dual-chirp FMCW signal with 12.0 GHz swept-frequency range and 0.6 GHz/μs sweep rate is acquired and used as the pump for second-stage FWM. Finally, via second-stage FWM in a 200 m highly nonlinear fiber, a dual-chirp FMCW signal with a swept-frequency range of 36.0 GHz and sweep rate of 1.8 GHz/μs is generated. Taking the FMCW signal generated at different stages as the emitted signal, we evaluate the ranging resolution through fiber-based distance measurement, and the results demonstrate that the achieved ranging resolutions are 5.31 cm, 2.04 cm, and 1.18 cm, respectively. Through equalizing the optical power of generated FMCW signal over the swept-frequency range, the ranging resolution can be further improved.

Ultralinear 140-GHz FMCW signal generation with optical parametric wideband frequency modulation enabling 1-mm range resolution.

We demonstrate ultralinear and ultrawideband frequency-modulated continuous-wave (FMCW) signal generation using an optical parametric wideband frequency modulation (OPWBFM) method. The OPWBFM method optically expands the bandwidths of FMCW signals beyond the electrical bandwidths of optical modulators via a cascaded four-wave mixing (FWM) process. Compared to the conventional direct modulation approach, the OPWBFM method simultaneously achieves high linearity and a short measurement time of the frequency sweep. On the other hand, it is also known that the OPWBFM method expands the phase noise of idlers as well as their bandwidths if an input conjugate pair has different phase noise. To avoid this phase noise expansion, it is crucial to synchronize the phase of an input complex conjugate pair of an FMCW signal using an optical frequency comb. For demonstration, we successfully generated an ultralinear 140-GHz FMCW signal by using the OPWBFM method. Moreover, we employ a frequency comb in the conjugate pair generation process, leading to the mitigation of phase noise expansion. By using a 140-GHz FMCW signal, we achieve a range resolution of ∼1 mm through fiber-based distance measurement. The results show the feasibility of an ultralinear and ultrawideband FMCW system with a sufficiently short measurement time.

Recognition and Estimation for Frequency-Modulated Continuous-Wave Radars in Unknown and Complex Spectrum Environments

The recognition and estimation of frequency-modulated continuous-wave (FMCW) radar signals is critical for both military electronic countermeasures (ECM) and civilian autonomous driving. However, the increasingly complex radio environment poses two new challenges for detection equipment. First, multiple FMCW radars can share the same frequency band, resulting in overlap of received FMCW signals in the time-frequency domain. Second, unexpected signals in unknown spectrum environments can affect the cognitive performance of FMCW signals. This paper proposes a semantic-based learning network (SLN) that simultaneously learns modulation classification and parameter regression of FMCW signals. By integrating recognition and estimation into a single network, the system can be optimized end-to-end as a whole. Additionally, instance-level semantic learning facilitates the parallel analysis of multiple components in overlapping signals. Finally, contrastive clustering in SLN achieves suppression of unexpected signals. Numerous comparative experimental results demonstrate that SLN has the desirable ability to simultaneously recognize and estimate FMCW signals in real-time, even in unknown spectrum environments.

Characterization of Millimeter-Wave Wideband FMCW Signals Based on a Precisely Synchronized NVNA for Automotive Radar Applications

In this article, a nonlinear vector network analyzer (NVNA) measurement setup is developed to characterize frequency modulated continuous wave (FMCW) signals in the frequency domain. Thanks to the use of precisely synchronized multisine phase reference and pulsed-RF phase calibration standards, such NVNA setup is validated for high-accuracy measurement of wideband FMCW signals at the millimeter-wave test bands. According to the method validation at 24 and 60 GHz with a maximum FMCW bandwidth of 2 GHz, the proposed NVNA setup has lower measurement errors and uncertainties than the commercial real-time oscilloscope (RTO) and vector signal analyzer (VSA), offering a reference standard of test and calibration for automotive radar applications.

Body Motion Artifact Cancellation Technique for Cough Detection Using FMCW Radar

A body motion artifact cancellation (BMAC) technique is proposed to detect human cough signals using a frequency-modulated continuous-wave (FMCW) radar. Human coughs are spontaneously accompanied by large-scale body motions, which overwhelm small-scale vibration signals induced by coughing. To mitigate these effects, motion-induced phase variations are estimated and compensated at respective frequencies of an FMCW signal. The cough signals are extracted from range profiles of the phase-compensated FMCW signals. This allows collecting cough signals at a fixed range bin, which are not so much distorted by range migrations due to the large-scale body motions. It is verified through both simulations and experiments. The experimental result shows that it can clearly detect human cough signals by removing body motion artifacts.

Optical parametric wideband frequency modulation

Various types of photonic applications, such as sensing and communication, require the generation of wideband optical frequency-modulated (FM) signals. However, generating a wideband FM signal beyond the electrical bandwidth limitation of optical modulators is difficult. Here, we propose a method to increase the bandwidths of optical FM signals by using the cascaded four-wave-mixing (FWM) process and show its potential in two applications. We first demonstrate 11-fold bandwidth expansion of frequency-modulated continuous-wave signals (from 5 to 55 GHz), beyond the optical modulator bandwidth. Next, we demonstrate the signal-to-noise ratio (SNR) enhancement for analog communication. The SNR of an analog signal can be increased by ∼12.8 dB using the proposed method. These results show the potential of the proposed method for sensing and communication applications. In addition, the proposed concept opens new possibilities in parametric FWM applications.

Enhanced frequency-modulated continuous-wave generation by injection-locking period-one oscillation in a semiconductor laser with an intensity modulated comb.

We report on an enhanced photonic generation of frequency-modulated continuous-wave (FMCW) signals by injection-locking a semiconductor laser operating in period-one (P1) nonlinear dynamic with an intensity modulated electro-optic frequency comb. When the cavity mode is injection-locked with respect to any of the comb modes, through linearly sweeping the frequency of the injected comb mode while synchronously modulating the injected intensity, the center wavelength of the cavity mode can be tuned following the injected comb mode. This way, it allows maintaining the phase-locking between the cavity mode and comb mode even if beyond the original locking bandwidth of the cavity mode, since it is tuned accordingly. It thus leads to the generation of FMCW signal with efficient phase noise suppression and improved achievable sweep range compared with the limited original injection-locking bandwidth. Such injection enhanced phase-locking is investigated and a demonstration with the injection of -4th order comb mode has realized photonic FMCW generation with enhanced sweep range and suppressed phase noise. Thanks to the flexibility in sweep parameters, this method can also be readily applied for the generation of arbitrary waveforms.

Photonic generation of frequency-modulated continuous-wave signal using sideband amplification injection locking effect based on the integrated mutually injected semiconductor laser

A simple photonic method to generate wideband frequency-modulated continuous-wave (FMCW) signals by taking advantage of the sideband amplification injection locking (SAIL) effect of the monolithic integrated semiconductor laser (MISL) is demonstrated in this paper. Attributing to the naturally mutual injection mechanism, when giving the MISL appropriate control currents, the MISL would enter into the undamped period-one (P1) oscillation. In this case, once one FMCW signal with appropriate power is directly modulated on the MISL with varying frequencies around the subharmonic frequency, the original P1 signal would be constantly locked by SAIL effect and stably output after the photodetector, but with different oscillating frequencies with time. Therefore, one broadband FMCW signal with several-fold central frequency and bandwidth would be realized. In this scheme, attributing to the high-integration MISL, no other additional external modulator or complex optical systems is required, highly simplifying the framework and reducing the power consumption. Furthermore, this simple and compact structure is potential to develop for photonic integration. In the experiment, one FMCW signal with varying frequencies from 16.05 GHz to 19.95 GHz is generated when the original FMCW signal ranging from 5.35 GHz to 6.65 GHz is injected, suggesting three times amplification is successfully realized. Moreover, the regenerated FMCW signal can be arbitrarily adjusted no matter in central frequency, bandwidth, pulse period or in hopping pattern as long as changing the original FMCW signal as well as the P1 frequency, showing huge flexibility and reconfigurability.

Gesture recognition system based on ultrasonic FMCW and ConvLSTM model

Ultrasonic-based technologies could provide light-independent and high-resolution solutions in no-contact human–machine interaction. This paper proposed a gesture recognition system on the basis of ultrasonic frequency modulated continuous wave (FMCW) and ConvLSTM model. It employed a hardware layout of one transmitter and three receivers spatially installed at different directions. An FMCW signal emitted by the transmitter would be detected by the receivers after reflecting from the hand. Then, the range-Doppler maps (RDMs) of the received signal were obtained by processing 2D fast Fourier transform. The spatio-temporal features of the hand were extracted from RDMs by the ConvLSTM model, to facilitate the gesture classification. Experiments showed that a fine resolution of 0.005 m in distance and 0.03 m/s in velocity for hand movement, and an accuracy of 85.7% with a small size of 50 samples training for finger-movement gestures can be achieved, which verified the feasibility of the proposed system.

FMCW SAR Imaging Algorithm of Sliding Spotlight Mode

Under the frequency modulated continuous wave (FMCW) system, the “stop-and-go” echo model of traditional pulse synthetic aperture radar (SAR) is no longer applicable. The range-azimuth coupling term introduced by fast time going term cannot be ignored, or otherwise it will cause degradation in the quality of generated image. This paper proposes a Sliding Spotlight SAR imaging algorithm based on improved two-step method. To address the problems of big interval of FMCW SAR and difference from the pulse SAR echo model triggered by dechirp reception, the proposed algorithm has improved the ωk algorithm and realized great focusing of FMCW signal. Furthermore, this algorithm adopts the method of focusing azimuth deramp in frequency domain to prevent the aliasing problem in image domain encountered by the classic two-step method. The simulation and real data results prove that this method can realize good focusing of FMCW SAR Sliding Spotlight mode.

An Universal Circular Synthetic Aperture Radar

This article presents an universal circular synthetic aperture radar (SAR) (UCSAR) by which the targets to be observed at any radial distance can be imaged, thus making SAR imaging possible in a more general scenario with a circular movement of the radar platform. The UCSAR point spread function (PSF) is firstly analyzed based on the time-domain correlation imaging approach, and thus a three-dimension (3-D) spatial variant PSF of the target can be formulated. The closed-form PSF expressions with single-frequency and frequency-modulated continuous wave (FMCW) transmitted signals are derived respectively to quantify the imaging resolutions, showing that the PSF is a product of a sinc function and a zeroth-order Bessel function when using a wideband FMCW signal. Secondly, a fast UCSAR imaging algorithm and its further simplified version are proposed to reduce the computational cost significantly based on the piecewise constant Doppler (PCD) principle. To quantify the imaging performance, we derive an error function of the slant range approximation for the proposed algorithm, serving as a practical guideline for the UCSAR parameter selection. Finally, the simulation and experimental results are provided to validate the PSF analysis, the fast imaging algorithm, and the implementation of the proposed UCSAR.

Calibration and Operation of a Bistatic Real-Aperture Polarimetric-Interferometric Ku-Band Radar

This article presents the bistatic operation mode and the performance analysis of KAPRI, a terrestrial frequency-modulated continuous-wave (FMCW) Ku-band polarimetric radar interferometer capable of acquiring bistatic full-polarimetric datasets with high spatial and temporal resolution. In the bistatic configuration, the system is composed of two independently operating KAPRI devices, one serving as a primary transmitter and receiver and the other as a secondary receiver. The secondary bistatic dataset is affected by possible offsets between the two devices’ reference clocks, as well as distortions arising from the bistatic geometry. To correct for this, we present a two-chirp bistatic FMCW signal model, which accounts for the distortions, and a reference chirp transmission procedure, which allows correcting the clock offsets in the deramped signal time domain. The second challenge of operation of a bistatic polarimetric system is polarimetric calibration since it is not possible to employ purely monostatic targets such as corner reflectors. For this purpose, we developed a novel active calibration device Variable-Signature Polarimetric Active Radar Calibrator (VSPARC), designed for monostatic and bistatic calibration of all polarimetric channels. VSPARC and its associated novel polarimetric calibration method were then used to achieve full calibration of both KAPRI devices with polarimetric phase calibration accuracy of 20° and 30-dB polarization purity in field conditions. This article thus presents a complete measurement configuration and data processing pipeline necessary for synchronization, coregistration, and polarimetric calibration of bistatic and monostatic datasets acquired by a real-aperture FMCW radar.

Experimental Investigation on the Ranging Resolution of a FMCW Lidar

In some previous reports about frequency-modulated continuous-wave (FMCW) Lidar, observing the longer waveform of a de-chirped signal is considered an effective scheme for further improving the ranging resolution. In this work, the ranging resolution of a FMCW Lidar is experimentally investigated, and the feasibility of such a scheme is tested. During the experiment, a FMCW signal is generated via a Mach–Zehnder modulator in the transmitted port. In the received port, the de-chirped signal is extracted based on a homodyne detection scheme and is analyzed by an electrical spectrum analyzer. Two different methods are adopted to determine the ranging resolution. One is based on a single target, for which the ranging resolution is obtained through inspecting the shift of spectral peak position as the target moves. The other is based on two targets, for which the ranging resolution is acquired through inspecting the variation of spectrum distribution as the spacing of two targets changes. The experimental results demonstrate that extending the observed duration of the de-chirped signal cannot improve the ranging resolution, and the corresponding physical mechanism is revealed.

A 24-GHz Fully Integrated CMOS Transceiver for FMCW Radar Applications

A 24-GHz fully integrated frequency-modulated continuous wave (FMCW) direct conversion transceiver, implemented in a 55-nm low-power CMOS technology with a maximum <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$f_{\mathrm {T}}$ </tex-math></inline-formula> of 190 GHz in typical operating conditions and packaged in a 5-mm <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\times $ </tex-math></inline-formula> 5-mm 32-lead quad-flat no-leads (QFN) package, is presented in this article. The single-chip transceiver uses a single 2.5-V supply while all the core circuits are powered by integrated regulators. The complex low-noise transductor in the receiver uses a quadrature hybrid to generate quadrature signals in the receiving front-end. The analog signal processing circuits including high-pass filters, low-pass filters, and programmable amplifiers are implemented following the receiver front-end circuitry. The FMCW signals are generated by an on-chip 24-GHz fractional-N frequency synthesizer. The synthesizer is completely integrated with the transceiver and provides built-in digital frequency modulation to generate chirping signals for the down-conversion local oscillator (LO) and the transmitted signals. The transmitter is composed of a balanced class-AB power amplifier driven by the FMCW signals from the frequency synthesizer.

Comprehensive mPoint: A Method for 3D Point Cloud Generation of Human Bodies Utilizing FMCW MIMO mm-Wave Radar.

In this paper, comprehensive mPoint, a method for generating 3D (range, azimuth, and elevation) point cloud of human targets using a Frequency-Modulated Continuous Wave (FMCW) signal and Multi-Input Multi-Output (MIMO) millimeter wave radar is proposed. Distinct from the TI-mPoint method proposed by TI technology, a comprehensive mPoint method considering both the static and dynamic characteristics of radar reflected signals is utilized to generate a high precision point cloud, resulting in more comprehensive information of the target being detected. The radar possessing 60–64 GHz FMCW signal with two sets of different dimensional antennas is utilized in order to experimentally verify the results of the methodology. By using the proposed process, the point cloud data of human targets can be obtained based on six different postures of the underlying human body. The human posture cube and point cloud accuracy rates are defined in the paper in order to quantitively and qualitatively evaluate the quality of the generated point cloud. Benefitting from the proposed comprehensive mPoint, evidence shows that the point number and the accuracy rate of the generated point cloud compared with those from the popular TI-mPoint can be largely increased by 86% and 42%, respectively. In addition, the noise level of multipath reflection can be effectively reduced. Moreover, the length of the algorithm running time is only 1.6% longer than that of the previous method as a slight tradeoff.

Time-Varying Vibration Compensation Based on Segmented Interference for Triangular FMCW LiDAR Signals

Frequency modulation continuous wave (FMCW) light detection and ranging (LiDAR) 3D imaging system may suffer from time-varying vibrations which will affect the accuracy of ranging and imaging of a target. The system uses only a single-period FMCW LiDAR signal to measure the range of each spot; however, traditional methods may not work well to compensate for the time-varying vibrations in a single period because they generally assume the vibration velocity is constant. To solve this problem, we propose a time-varying vibration compensation method based on segmented interference. We first derive the impact of time-varying vibrations on the range measurement of the FMCW LiDAR system, in which we divide the time-varying vibration errors into primary errors caused by the vibrations with a constant velocity and quadratic errors. Second, we estimate the coefficients of quadratic vibration errors by using a segmented interference method and build a quadratic compensation filter to eliminate the quadratic vibration errors from the original signals. Finally, we use the symmetrical relations of signals in a triangular FMCW period to estimate the vibration velocity and establish a primary compensation filter to eliminate the primary vibration errors. Numerical tests verify the applicability of this method in eliminating time-varying vibration errors with only a one-period triangular FMCW signal and its superiority over traditional methods.

Utilizing Passive Intermodulation Response of Frequency-Modulated Continuous-Wave Signal for Target Identification and Mapping

In this paper, a passive-intermodulation-based tracking system working with a frequency-modulated continuous-wave (FMCW) is proposed for target identification and localization. Signals in the microwave range are chosen to realize ranging purposes for the benefits of small device size, lightweight, and wide available bandwidth. Depending on whether the nonlinear properties of electrical components, such as diodes, transistors, and mixers, are exploited, the tracking systems can be categorized as linear and nonlinear systems. By nature, the linear tracking methods are vulnerable to surrounding clutter, such as furniture, walls, and other objects, since the reflection signals from clutter are of the same nature as the target. In comparison, the nonlinear detection methods are attractive owning to the fact that the majority of the clutter does not possess nonlinear properties. Hence, the nonlinear detection system does not “see” the linear clutter and only senses the target exhibiting nonlinear responses. Among all the nonlinear technologies, the intermodulation-based tracking and mapping approach has less path loss than the harmonic-based, smaller circuit size than the subharmonic-based, and simpler tag design and fewer signal licenses required than both of its counterparts. Therefore, in this work, the intermodulation-based technology is adopted, and a new nonlinear tracking system is designed to track the distance of the target in a complex indoor scenario crowded with unwanted objects.