Beat Signal Research Articles

Laser linewidth measurement using beat-note technique

Lasers play a crucial role in quantum and atomic physics experiments. To prepare atoms in a desired quantum state, these lasers must possess specific properties, including tunability and a narrow spectral linewidth. In this study, we construct and employ an external cavity diode laser to prepare cold rubidium atoms. We control the laser’s stability using an electronic system and evaluate its performance by measuring the spectral linewidth through the beat signal technique. The measurement indicates a linewidth narrower than 1 MHz, which makes the laser suitable for subsequent experiments. Finally, we adjust the laser frequency to match the rubidium transition frequency between states 5S 1/2, F = 2 ↔ 5P 3/2, F′ = 2, and successfully utilizing the laser to prepare cold rubidium atoms in a magneto-optical trap.

Mutual Interference Mitigation for Automotive FMCW Radar With Time and Frequency Domain Decomposition

Currently, the frequency-modulated continuous-wave (FMCW) millimeter-wave (MMW) radar is a typical choice for automotive and transportation radar systems. As the number of FMCW radars explodes in the current vehicle market and the working frequency is limited in an open window of 76–81 GHz, FMCW radars on the road easily mutually interfere with each other, especially due to their wide bandwidth. Hence, in this article, we rigorously analyze the target echo, i.e., the beat signal, especially the sparsity of the interference signal in the time domain, and the row sparsity of the useful echo signal in the frequency domain. By taking advantage of this feature, we design an interference mitigation optimization problem to extract the target echoes with a row-sparse constraint. A closed-form solution is given in each iteration with specific derivations. Finally, numerical simulations and multiple practical scenes are provided to demonstrate the effectiveness of the proposed method.

Symmetrical dual-sideband oppositely chirped differential FMCW LiDAR.

A differential FMCW LiDAR for high-precision distance measurements of remote non-stationary targets is proposed and demonstrated experimentally. The required positive and negative symmetrically oppositely chirped laser beams are generated synchronously through a fixed-frequency laser by employing externally unified broadband optical phase modulation and symmetrical dual-sideband optical filtering. After coaxial transmission and reception, orthogonally polarized optical beat signals containing target distance and vector velocity data are de-chirped separately by optical in-phase and quadrature demodulations and then synchronously received by four-channel photoelectric balance detectors. After differential processing of the received beat signals and a fast Fourier transform, it is possible to implement real-time simultaneous range and vector velocity measurements. The inherent symmetrically oppositely chirped optical frequency make it possible to measure the target distance immune to the internal random phase noise introduced by the spectral linewidth of the frequency-swept laser and the external random phase noise introduced by atmospheric turbulence, speckle, and vibration. Meanwhile, the measurement of the target velocity is immune to the nonlinearity of the frequency-swept laser. These results encourage an approach to overcome the barriers of coherence length, nonlinearity, and external noise, and implement simultaneous real-time ranging and velocimetry of long-range, rapid-moving targets.

A Dual-Recursive-Least-Squares Algorithm for Automotive Radar Interference Suppression

Automotive radar sensors are widely used in vehicles so as to allow the “advanced driver assistance systems (ADAS)” to work. As far as we are concerned, no mandatory regulations were established so far for interference control in the cases where multiple vehicles equipped with automotive radars exist in close proximity. Consequently, those inter-vehicle cross-interference easily result in the radar performance degradation, e.g. incapability of target detection and identification. In this paper, an interference suppression algorithm is proposed which utilizes two Recursive-Least-Square (RLS) adaptive filters to estimate, the interference signals caused by the “aggressor” radar and the echo signals from the “ego” radar. The algorithm operates in the iterative mode with its initial input being the originally received beat signals involving interference. In each iteration, the estimates of the interference signals and of the clean signals are calculated sequentially by the two RLS filters, and the beat signal is updated with parts of the fragments substituted with their interference-mitigated counterparts. Such iterative operations stop when the convergence criterion, e.g. none of the fragments in the beat signals are considered being interfered, is achieved or the iteration number reaches the limit predefined due to the practical constraints. Simulation and measurement results demonstrate that the proposed dual-RLS-based algorithm outperforms the existing methods in terms of lower interference-to-signal ratio resultant and superior capability of retrieving the original range-Doppler profile.

Millimeter-wave generation based on a monolithic dual-wavelength DFB laser with four phase-shifted sampled gratings and equivalent chirp technology.

A dual-wavelength DFB laser array based on four phase-shifted grating and equivalent chirp technology is first proposed, fabricated, and experimentally demonstrated. The dual-wavelength emitting is achieved by symmetrically introducing two π phase shifts into a chirped four phase-shifted sampled grating cavity. Meanwhile, the beating signal of the dual-wavelength output is stabilized by applying an electro-absorption modulator integrated at the rear of the cavity. Under different grating chirp rates, a series of RF signals from 66.8 GHz to 73.6 GHz with a linewidth of less than 210 kHz is obtained.

The false beat signal of a high-speed X-ray imaging detector for synchrotron radiation experiments and its elimination with a synchronized CITIUS detector

Recent advances in high-speed X-ray imaging detectors for synchrotron radiation experiments have enabled frame rates to exceed 10 kframes/s. The frame rates are getting closer to the revolution frequencies of the large-scale storage rings, which are of the order of 100 kHz. In such cases, a false asynchronous-operation-induced beat (FAB) may be overlapped with the true signal. In order to eliminate FAB, we have developed a clock and trigger distributor to make the detector operate with frames cycles matching multiples of the revolution of the electron bunches in the storage rings. To experimentally demonstrate the effect, we have conducted a nuclear resonant scattering experiment with the CITIUS detector operating at 17.4 kframes/s. The measured spectra showed a signal-to-noise ratio identical to the Poisson statistics, indicating that the successful elimination of FAB by synchronization. To quantitatively assess the magnitude of FAB, numerical simulations have been carried out. FABs show peak-to-peak intensity variations ranging from 0.04 to 7.5% for SPring-8 bunch patterns. The dependence of the effective frame rates and bunch-filling modes on FABs are also quantitatively reported.

X-RCRNet: An explainable deep-learning network for COVID-19 detection using ECG beat signals

Wearable systems measuring human physiological indicators with integrated sensors and supervised learning-based medical image analysis (e.g. ECG, X-ray, CT or ultrasound images for lung or the chest) have been considered relevant tools for COVID-19 monitoring and diagnosis. However, these two technical roadmaps have their respective advantages and drawbacks. The current wearable systems enable to realize real-time monitoring of COVID-19 but are limited to its basic symptoms only, neither allowing to distinguish it from other diseases nor performing deep analysis. Current medical image analysis can provide accurate decision support for diagnosis but rarely deals with real-time data processing. In this context, we propose a new wearable system by combining the advantages of these two technical roadmaps. Considering that electrocardiogram (ECG) has been proved relevant to evolution of COVID-19 symptoms, the proposed wearable system will integrate an explainable Deep Neural Network to realize online monitoring of COVID-19 gravity by using ECG beat signal. This paper will focus on the Deep Neural Network model named X-RCRNet. The network is based on ResNet18 but with few enhancements: 1) LSTM Layers for regenerating the backpropagation error and further extracting the involved time-varying features; 2) LeakyReLU for increasing the performances of the model. With an accuracy of 96.48% after experiments, ourmodel has not only outperformed the existing methods in terms of accuracy and robustness, but also originally identify the ST interval of the ECG pattern,as the most prominent key features affected by the virus.

Carrier conversion from terahertz wave to dual-wavelength near-infrared light for photonic terahertz detection in wireless communication.

THz waves are promising wireless carriers for next-generation wireless communications, where a seamless connection from wireless to optical communication is required. In this study, we demonstrate carrier conversion from THz waves to dual-wavelength NIR light injection-locking to an optical frequency comb using asynchronous nonpolarimetric electro-optic downconversion with an electro-optic polymer modulator. THz wave in the W band was detected as a stable photonic RF beat signal of 1 GHz with a signal-to-noise ratio of 20 dB via the proposed THz-to-NIR carrier conversion. In addition, the results imply the potential of the photonic detection of THz waves for wireless-to-optical seamless communication.

Simple, low-cost, and well-performing optical phase-locked loop for frequency and phase locking of semiconductor lasers.

We demonstrate a simple, low-cost, and well-performing optical phase-locked loop (OPLL) circuit with ADF4007 as the phase frequency detector chip to achieve frequency and phase locking of two semiconductor lasers in both short and long terms. The measured short term performances, determined by fast feedback, show that the spectral width of the beat signal is low, around 1Hz, and the residual phasing error is 0.04r a d 2. The measured long term performances, determined by slow feedback, show that the drift of the central frequency of the beat signal is within 1.1(1)Hz in 2h, and the derived Allan deviation is less than 0.4Hz within all integration times of up to 1000s. The phase noise measurement shows a suppression of phase noise of the beat signal from free running to closed-loop OPLLs in a Fourier frequency of 10Hz-20kHz. These measurements show that the OPLL circuit we modified can fit most scientific experiments requiring a fixed frequency difference and phase coherence.

Statistical shape modeling-based algorithm for replacing missing beats in blood pressure signals.

In clinical environments, such as the Intensive Care Unit (ICU), continuous and uninterrupted monitoring of vital signs is critical for the early detection of patient deterioration and prompt intervention. Since data collected in these settings are often corrupted by noise, artifacts, or recording gaps, it is important to estimate missing data for a more accurate signal assessment.In this study, we propose an automatic algorithm for reconstructing of arterial blood pressure signal waveforms. The methodological core of the algorithm is based on the idea of statistical shape modeling, which basically estimates the shape variation of beat waveforms in order to reconstruct them in noisy segments. The waveform reconstruction is achieved by combining the average beat template from a 90-second segment of clean signal preceding the gap with the main shape variations of the estimated waveform.The algorithm was validated using arterial blood pressure recordings from 9 subjects admitted in the ICU and collected in the MIMIC-III Waveform Database, each lasting 1 hour and sampled at 125 Hz. For each record, ten fictitious gaps were created, and the reconstructed segments were compared to the original signals with the metrics proposed within the PhysioNet / Computing in Cardiology Challenge 2010. Results demonstrate the excellent performance of the proposed algorithm, with overall averages of both Q1 and Q2 metrics greater than 0.85.

An Operator Theoretic Approach for Analyzing Sequence Neural Networks

Analyzing the inner mechanisms of deep neural networks is a fundamental task in machine learning. Existing work provides limited analysis or it depends on local theories, such as fixed-point analysis. In contrast, we propose to analyze trained neural networks using an operator theoretic approach which is rooted in Koopman theory, the Koopman Analysis of Neural Networks (KANN). Key to our method is the Koopman operator, which is a linear object that globally represents the dominant behavior of the network dynamics. The linearity of the Koopman operator facilitates analysis via its eigenvectors and eigenvalues. Our method reveals that the latter eigendecomposition holds semantic information related to the neural network inner workings. For instance, the eigenvectors highlight positive and negative n-grams in the sentiments analysis task; similarly, the eigenvectors capture the salient features of healthy heart beat signals in the ECG classification problem.

Microfiber evanescent-field photothermal gas detection using acoustic-induced mode-dependent frequency shift

Abstract In this study, we experimentally showcase the microfiber evanescent-field photothermal gas detection by exploiting all-fiber MHz-level frequency shift scheme. Based on the acousto-optic interaction effect, the low-frequency shifts of 0.9 MHz and 1.83 MHz can be obtained through the cyclic conversion between the transverse core modes LP01 and LP11 in the few-mode fiber. Our proposed all-fiber frequency shifters show flexible MHz-level up(down) frequency shifts with superior sideband rejection ratio (over 40 dB) and low insertion loss (less than 1 dB). Furthermore, an all-fiber heterodyne interferometric detection system is implemented by leveraging the above low-frequency shifters, in which around 1-μm-diameter microfiber is investigated for photothermal gas detection. A pump-probe configuration is employed to obtain the photothermal effect induced by the gas absorption of the modulated evanescent field. By demodulating the phase of the beat signal output by the interferometer, an equivalent detection limit (1σ) of 32 ppm and a response time of 22 s are achieved for ammonia, as well as 0.24 % instability within 48 pump cycles. Given its compact all-fiber configuration and high sensitivity with fast response, the experimental results can pave the way for widespread applications like heterodyne detection, fiber optical sensors, and interplanetary coherent communications.

Single-shot Kramers–Kronig complex orbital angular momentum spectrum retrieval

Orbital angular momentum (OAM) spectrum diagnosis is a fundamental building block for diverse OAM-based systems. Among others, the simple on-axis interferometric measurement can retrieve the amplitude and phase information of complex OAM spectra in a few shots. Yet, its single-shot retrieval remains elusive, due to the signal–signal beat interference inherent in the measurement. Here, we introduce the concept of Kramers–Kronig (KK) receiver in coherent communications to the OAM domain, enabling rigorous, single-shot OAM spectrum measurement. We explain in detail the working principle and the requirement of the KK method and then apply the technique to precisely measure various characteristic OAM states. In addition, we discuss the effects of the carrier-to-signal power ratio and the number of sampling points essential for rigorous retrieval and evaluate the performance on a large set of random OAM spectra and high-dimensional spaces. Single-shot KK interferometry shows enormous potential for characterizing complex OAM states in real time.

A Polarimetric Fiber Ring Laser Incorporating a Coupled Optoelectronic Oscillator and Its Application to Magnetic Field Sensing

A novel configuration for a polarimetric fiber ring laser incorporating a coupled optoelectronic oscillator (COEO) is proposed and experimentally demonstrated, and its application to magnetic field sensing is studied. The COEO-based polarimetric fiber ring laser has two mutually coupled loops: the fiber ring laser loop and the OEO loop. In the fiber ring laser loop, longitudinal modes break up into orthogonal polarization modes because of birefringence. The frequency of the polarization mode beat (PMB) signals is determined by the cavity birefringence. In the OEO loop, a microwave signal with its frequency equal to the PMB signal is generated. By feeding the oscillation mode to modulate the optical loop, mode-locking can be achieved, rendering the mode spacing of the laser equal to the frequency of the oscillating OEO mode. We can estimate the birefringence variation by measuring the oscillating frequency of the COEO. To validate the proposed sensing system, a circular birefringence change is introduced in a magneto-optic crystal via the Faraday rotation effect. Then, the magnetic field sensing is implemented. Such configuration can achieve single longitudinal oscillation and realize high-speed and high-precision measurements.

Accuracy of tracking radio altimeters working over a 2D rough surface

Low altitude tracking radio altimeters use periodic frequency modulated continuous signals and the altitude measurement is based on estimation of the mean frequency of the beat signal. To realize the estimation, a closed automatic control loop is organized in radio altimeter. The loop maintains the frequency of the beat signal at a fixed value by adjusting some parameters of the transmitted signal. There is one more way to build up a tracking contour for the altitude estimate, the operation of which is based on the use of a measuring phase locked loop. The circuit adjusts the reference signal ‑ a copy of the beat signal ‑ to maximize the phase structure of the beat signal and the reference signal. When measuring the height over a rough surface, in addition to errors caused by the internal noise in the receiver, the range noise begins to affect the accuracy of the estimate. The range noise is due to the formation of a signal scattered by a rough surface as sum of reflections from stationary points of the surface where the local normal is directed towards the phase center of the radio altimeter antenna. The article aim is a comparative analysis of the accuracy of three types of tracking radio altimeters working over a rough two-dimensional surface: radio altimeter with a phase-locked loop and tracking altimeters with adjustment of the frequency deviation or the modulation period of the transmitted signal. The signal reflected from a two-dimensional rough surface was simulated by the method of stationary points, which is a particular case of the Kirchhoff method. As a result of the simulation, the biases and the root-mean-square errors of height estimates were obtained for the three types of tracking altimeters and different values of the surface roughness parameter. For all altimeters, the estimate bias is small and does not depend on the roughness parameter. The root-mean-square error of height estimation for all considered radio altimeters increases with increase of the roughness parameter. The best results were shown by the radio altimeter with the measuring phase locked loop. Its error is approximately 3 times less than that of the radio altimeters with adjustment of the transmitted signal parameters.

Unidirectional operation criterion in monolithic nonplanar ring oscillators.

Monolithic nonplanar ring oscillators (NPROs) under an applied magnetic field can operate unidirectional single-frequency lasing due to the loss differences among its four eigenpolarizations, where the minimum was empirically estimated to be 0.01%. However, this value has never been verified because the applied magnetic field is not uniformly distributed, making it hard to resolve both theoretically and experimentally. Here, we propose a method to resolve the applied magnetic field through an NPRO by combining finite-element analysis and experimental verification. By introducing the non-uniform magnetic field information to the eigenpolarization theory, the loss differences can be calculated by path integration along the optical path in the NPRO. The critical point, where the bidirectional lasing is emerging, is identified by the relative amplitude noise (RAN) of the laser and by the beating signal between the clockwise (CW) and counterclockwise (CCW) lasing. With this method, we determine that unidirectional operation is possible with loss differences as low as 0.0001% and 0.0003%, corresponding to two different NPRO designs with out-of-plane angles of 90° and 45°, respectively, which increases the precision of the loss differences for unidirectional single-frequency lasing by more than one order of magnitude. Our findings will greatly facilitate NPRO laser design with lowered magnetic field intensity requirements.

A novel approach for biometric recognition based on ECG feature vectors

In the field of biometrics, electrocardiogram (ECG) recognition has the advantages of being live, difficult to replicate, and easy to collect. However, most deep learning methods for biometric recognition use a fixed length of ECG beats and only identify ECGs from a fixed number of people. The fixed input length may lead to information loss and the model needs to be retrained when a new ECG is added to the database, which is inconvenient for real applications. In this paper, we propose a biometric recognition method based on an ECG feature vector that uses a pooling layer to accept variable-length beat signals. The method accepts new classes without requiring model retraining while achieving excellent recognition performance. We verified the robustness of the method in the ECG-ID database, the MITDB arrhythmia database, and a private USSTDB database consisting of the ECG records of 60 volunteers before and after exercise. In addition, this method has good recognition ability in cross-database tests. The proposed method reduces the gap in biometric identification of exercise ECGs and demonstrates robustness and good generalization.

Photonic system for Doppler-frequency-shift and Angle-of-arrival simultaneous measurement using dual-parallel Mach–Zehnder modulator

A simple photonic system is proposed to measure the Doppler frequency shift (DFS) and Angle of arrival (AOA) of microwave signals simultaneously. The echo signals received by the two antennas are fed into two sub-MZM of a dual-parallel Mach–Zehnder modulator (DPMZM) respectively, and the reference signals are sent into one of the sub-MZM. The introduction of reference signals makes it easier to determine the direction of DFS. After the reference signal and echo signal pass through the low-speed PD, the beating signal is obtained. The value and direction of the DFS can be derived from the frequency of the down-converted signal. And the measurement of AOA can be calculated from the power of the output signal. The experimental results show that the echo signal measurement errors of DFS are less than ±0.5 Hz in the operating frequency range of 20 GHz, and the power sensitivity is less than -40 dBm. AOA has measurement errors of less than ±1.5° in the range of 0 to 90°. In addition, by adding only one test branch, the system can achieve the unambiguous measurement of AOA in the range of ±90°.

Pilot optimization for OFDM in the RSSB system

To increase the receiving sensitivity of the reversely single-sideband (RSSB) system with orthogonal frequency division multiplexing (OFDM) signal transmission, we use the improved pilot interval scheme and pilot power scheme in this system. The improved pilot interval scheme uses more pilots in areas where channel conditions are relatively good to avoid signal–signal beat interference (SSBI) issues for sub-carriers. The improved pilot power scheme compensates for frequency-selective fading by increasing the pilot power in areas where channel conditions are relatively poor. According to the simulation, the generated 60 GHz optical millimeter wave with 2.5 G bandwidth OFDM signal is delivered over 100 km standard single-mode fiber (SSMF). The improved pilot interval scheme and pilot power scheme can increase the system’s receiving sensitivity by 2 dB, respectively. These schemes can enhance the system’s performance without increasing the complexity of the algorithm and the costs of the RSSB system.

Phase-sensitive optical time domain reflectometry based on geometric phase measurement

A phase-sensitive optical time domain reflectometer based on coherent heterodyne detection of geometric phase in the beat signal of light, is reported for the first time to our knowledge. The use of the geometric phase to extract strain makes it immune to polarisation diversity fading. This is because a polarisation mismatch between the interfering beams is not a hindrance to its measurement. The geometric phase is calculated using the amplitude of the beat signal and individual beam intensities without any need for phase unwrapping. It is measured per beat period and can be equated with the traditionally measured dynamic phase with appropriate scaling. The results show that the system based on the geometric phase successfully measures strain, free from polarisation mismatch fading and phase unwrapping errors, providing a completely novel solution to these problems.