Adaptive compensating method for Doppler frequency shift using LMS and phase estimation

The novel compensating method directly demodulates the signals without the carrier recovery processes, in which the carrier with original modulation frequency is used as the local coherent carrier. In this way, the phase offsets due to frequency shift are linear. Based on this premise, the compensation processes are： firstly, the phase offsets between the baseband neighbor-symbols after clock recovery is unbiasedly estimated among the reference symbols; then, the receiving signals symbols are adjusted by the phase estimation value; finally, the phase offsets after adjusting are compensated by the least mean squares （LMS） algorithm. In order to express the compensation processes and ability clearly, the quadrature phase shift keying （QPSK） modulation signals are regarded as examples for Matlab simulation. BER simulations are carried out using the Monte-Carlo method. The learning curves are obtained to study the algorithm＇s convergence ability. The constellation figures are also simulated to observe the compensation results directly.

Doppler frequency offset estimation and diversity reception scheme of high-speed railway with multiple antennas on separated carriage

The challenges of severe Doppler effects in high-speed railway are considered. By building a cooperative antenna system; an algorithm of joint channel estimation and Doppler frequency offset （DFO） estimation is proposed based on Ricean channel model. First, a maximum likelihood estimation （MLE） algorithm for DFO is designed, show- ing that the Doppler estimation can be obtained by estimating moving velocity of the train and the path loss with the exploitation of pilots that are placed inside the frame. Then a joint detection algorithm for the receiver is proposed to exploit multi-antenna diversity gains. Last, the theoretical Crammer Rao bound （CRB） for joint channel estimation and DFO estimation is derived. The steady performance of the system is confirmed by numerical simulations. In particular, when the Ricean fading channel parameter equals 5 and the velocities of train are 100 m/s and 150 m/s, the estimation variances of DFO are very close to the theoretical results obtained by using CRB. Meanwhile, the corresponding sig- nal to noise ratio loss is less than 1.5 dB when the bit error rate is 10-5 for 16QAM signals.

Novel Doppler Frequency Extraction Method Based on Time-Frequency Analysis and Morphological Operation

A novel method of Doppler frequency extraction is proposed for Doppler radar scoring systems. The idea is that the time-frequency map can show how the Doppler frequency varies along the time-line, so the Doppler frequency extraction becomes curve detection in the image-view. A set of morphological operations are used to implement curve detection. And a map fusion scheme is presented to eliminate the influence of strong direct current （DC） component of echo signal during curve detection. The radar real-life data are used to illustrate the performance of the new approach. Experimental results show that the proposed method can overcome the shortcomings of piecewise-processing-based FFT method and can improve the measuring precision of miss distance.

Velocity estimation of moving targets with stepped-frequency radar based on Doppler frequency difference

By analyzing the signal model of stepped-frequency waveform, a novel method for velocity measurement is proposed. The method is based on Doppler frequency difference which is achieved by using Hough transform. As the estimated velocity is inversely proportional to the frequency step size instead of the carrier frequency of the transmitted signal as the pulse-Doppler （PD） processing, the new algorithm can achieve much wider unambiguous velocity range. Furthermore, non-coherent integration of the sub-pulses with different carrier frequencies can be implemented by Hough trans- form to improve the anti-noise performance. Besides, field experimental results show that the high range resolution profile （HRRP） of a bullet with high speed can be reconstructed correctly without distortion.

Estimation of DOA and Doppler Frequency on Nonideal UCA

The problem of estimating direction of arrivals (DOA) and Doppler frequency for many sources is considered in the presence of general array errors (such as amplitude and phase error of sensors, setting position error of sensors). Adopting direct array manifold in a uniform circular array (UCA), the estimation of Doppler frequency can be obtained by DOA matrix. Based on analyzing the statistic characters of general array errors, the estimation of DOA can be obtained by Weight Total Least Squares. Numerical results illustrate that the estimator is robust to general array errors and show the capabilities of the estimator.

ESTIMATION OF DOPPLER CENTROID FREQUENCY IN SPACEBORNE SCANSAR

Doppler centroid frequency is an essential parameter in the imaging processing of the Scanning mode Synthetic Aperture Radar (ScanSAR). Inaccurate Doppler centroid frequency will result in ghost images in imaging result. In this letter, the principle and algorithms of Doppler centroid frequency estimation are introduced. Then the echo data of ScanSAR system is analyzed. Based on the algorithms of energy balancing and correlation Doppler estimator in the estimation of Doppler centroid frequency in strip mode SAR, an improved method for Doppler centroid frequency estimation in ScanSAR is proposed. The method has improved the accuracy of Doppler centroid frequency estimation in ScanSAR by zero padding between burst data. Finally, the proposed method is validated with the processing of ENVIronment SATellite Advanced Synthetic Aperture Radar (ENVISAT ASAR) wide swath raw data.

APPROACH OF IMPROVING PRECISION IN ULTRASONIC DOPPLER BLOODSTREAM SPEED MEASUREMENT BY CHAOS-BASED FREQUENCY DETECTING

It is critical for cerebral vascular disease diagnosis through Doppler to detect the maximum and the minimum of the carotid blood flow speed accurately. A kind of Duffing system under an external periodic power with dump is introduced in the letter, numerical analysis is carried out by four-order Runge-Kutta method. An oscillator array is designed according to the frequency of the ultrasonic wave. When the external signals are inputted, computational algorithm is used to scan the array in turn and analyze the result, and the frequency can be determined. Based on the methods above, detecting the carotid blood flow speed accurately is realized. The Signal-to-Noise Ratio (SNR) of-20.23dB is obtained by the result of experiments. In conclusion, the SNR has been improved and the precision of the measured bloodstream speed has been increased, which can be 0.069% to 0.13%.

Computationally Efficient MUSIC-Based Algorithm for Joint Direction of Arrival (DOA) and Doppler Frequency Estimation in Monostatic MIMO Radar

The problem of joint direction of arrival (DOA) and Doppler frequency estimation in monostatic multiple-input multiple-output (MIMO) radar is studied and a computationally efficient multiple signal classification (CE-MUSIC) algorithm is proposed.Conventional MUSIC algorithm for joint DOA and Doppler frequency estimation requires a large computational cost due to the two dimensional (2D) spectral peak searching.Aiming at this shortcoming,the proposed CE-MUSIC algorithm firstly uses a reduced-dimension transformation to reduce the subspace dimension and then obtains the estimates of DOA and Doppler frequency with only one-dimensional (1D) search.The proposed CE-MUSIC algorithm has much lower computational complexity and very close estimation performance when compared to conventional 2D-MUSIC algorithm.Furthermore,it outperforms estimation of signal parameters via rotational invariance technique (ESPRIT) algorithm.Meanwhile,the mean squared error (MSE) and Cramer-Rao bound (CRB) of joint DOA and Doppler frequency estimation are derived.Detailed simulation results illustrate the validity and improvement of the proposed algorithm.

A novel high precision Doppler frequency estimation method based on the third-order phase-locked loop

In deep space exploration,many engineering and scientific requirements require the accuracy of the measured Doppler frequency to be as high as possible.In our paper,we analyze the possible frequency measurement points of the third-order phase-locked loop(PLL)and find a new Doppler measurement strategy.Based on this finding,a Doppler frequency measurement algorithm with significantly higher measurement accuracy is obtained.In the actual data processing,compared with the existing engineering software,the accuracy of frequency of 1 second integration is about 5.5 times higher when using the new algorithm.The improved algorithm is simple and easy to implement.This improvement can be easily combined with other improvement methods of PLL,so that the performance of PLL can be further improved.

Curvelet Transform-Based Denoising Method for Doppler Frequency Extraction

A novel image denoising method based on curvelet transform is proposed in order to improve the performance of Doppler frequency extraction in low signal-noise-ratio (SNR) environment. The echo can be represented as a gray image with spectral intensity as its gray values by time-frequency transform. And the curvelet coefficients of the image are computed. Then an adaptive soft-threshold scheme based on dual-median operation is implemented in curvelet domain. After that, the image is reconstructed by inverse curvelet transform and the Doppler curve is extracted by a curve detection scheme. Experimental results show the proposed method can improve the detection of Doppler frequency in low SNR environment.

Comparison between effects of Doppler broadening on pure and non-pure inversionless gain with frequency up-conversion

A study is made of the effects of Doppler broadening on pure gain without inversion, which means that neither one-photon nor two-photon inversions are allowed, and non-pure gain without inversion, which means that one-photon inversion does not occur but two-photon inversion is present, in a closed A-type three-level system with incoherent pumping. It is shown that when the driving field is resonant but the probe field is not, in a certain range of Doppler width, for the case of the lower degree of frequency up-conversion, generally, pure gain without inversion increases monotonically and non-pure gain without inversion does not monotonically increase or decrease with increasing Doppler width; for the case of the higher degree of frequency up-conversion, pure gain without inversion decreases monotonically but non-pure gain without inversion cannot be produced. In the case of two-photon resonance, in some range of Doppler width, pure gain without inversion does not monotonically increase or decrease while non-pure gain without inversion decreases monotonically with Doppler width increasing. Finally, an experimental scheme for examining our theoretical result is given.

A new Doppler frequency anomaly algorithm for surface current measurement with SAR

Values for Doppler center frequency are calculated from the echo signal at the satellite using the Doppler centroid method and so include the predicted Doppler frequency caused by the relative motion of the satellite and the Earth,which is the main component of Doppler center frequency and must be removed to obtain the Doppler frequency anomaly for ocean current measurement.In this paper,a new Doppler frequency anomaly algorithm was proposed when measuring surface currents with synthetic aperture radar(SAR).The key of the proposed algorithm involved mean filtering method in the range direction and linear fitting in the azimuth direction to remove the radial and the azimuthal component of predicted Doppler frequency from the Doppler center frequency,respectively.The basis is that the theoretical Doppler center frequency model of SAR exhibits an approximately linear characteristic in both the range direction and in the azimuth direction.With the help of the new algorithm for predicted Doppler frequency removal,the estimation error of Doppler frequency anomaly can be reduced by avoiding employing the theoretical antenna pattern and imperfect satellite attitude parameters in the conventional Doppler frequency method.SAR measurement results demonstrated that,compared to the conventional Doppler frequency with/without error correction method,the proposed algorithm allows for a pronounced improvement in the current measuring accuracy in comparison with the global ocean multi-observation(MOB)products.In addition,the eff ectiveness and robustness of the proposed Doppler algorithm has been demonstrated by its application in the high velocity current in the Kuroshio region.

Radial velocity of ocean surface current estimated from SAR Doppler frequency measurements—a case study of Kuroshio in the East China Sea

Ocean currents are a key element in ocean processes and in meteorology,affecting material transport and modulating climate change patterns.The Doppler frequency shift information of the synthetic aperture radar(SAR)echo signal can reflect the dynamic characteristics of the sea surface,and has become an essential sea surface dynamic remote sensing parameter.Studies have verified that the instantaneous Doppler frequency shift can realize the SAR detection of the sea surface current.However,the validation of SAR-derived ocean current data and a thorough analysis of the errors associated with them remain lacking.In this study,we derive high spatial resolution flow measurements for the Kuroshio in the East China Sea from SAR data using a theoretical model of shifts in Doppler frequency driven by ocean surface current.Global ocean multi observation(MOB)products and global surface Lagrangian drifter(GLD)data are used to validate the Kuroshio flow retrieved from the SAR data.Results show that the central flow velocity for the Kuroshio derived from the SAR is 0.4–1.5 m/s.The error distribution between SAR ocean currents and MOB products is an approximate standard normal distribution,with the 90%confidence interval concentrated between–0.1 m/s and 0.1 m/s.Comparative analysis of SAR ocean current and GLD products,the correlation coefficient is 0.803,which shows to be significant at a confidence level of 99%.The cross-validation of different ocean current dataset illustrate that the SAR radial current captures the positions and dynamics of the Kuroshio central flow and the Kuroshio Counter Current,and has the capability to monitor current velocity over a wide range of values.

INSTANTANEOUS DOPPLER FREQUENCY FOR SQUINT SAR IMAGING

Instantaneous Doppler frequency for squint SAR imaging has been found with ChirpScaling Algorithm (CSA). Because the azimuth sample is not perpendicular to the range sample,the range signal must impact on the azimuth signal in the squint SAR data processing, andthe different slant range targets have different Doppler frequencies. From the mathematicalmodel of SAR echo signal, this paper carefully analyzes the instantaneous azimuth frequency, theinstantaneous Doppler frequency component of the azimuth frequency and the impact of rangechirp on azimuth frequency, which explains that Doppler frequency should be properly selected forcorrect SAR imaging in the squint SAR. The results of point target simulation experiments showthat the way is reasonable for the squint SAR and can effectively complete range compressionand azimuth focusing, and improve images' quality.

Deep learning based Doppler frequency offset estimation for 5G-NR downlink in HSR scenario

In the fifth-generation new radio(5G-NR) high-speed railway(HSR) downlink,a deep learning(DL) based Doppler frequency offset(DFO) estimation scheme is proposed by using the back propagation neural network(BPNN).The proposed method mainly includes pre-training,training,and estimation phases,where the pre-training and training belong to the off-line stage,and the estimation is the online stage.To reduce the performance loss caused by the random initialization,the pre-training method is employed to acquire a desirable initialization,which is used as the initial parameters of the training phase.Moreover,the initial DFO estimation is used as input along with the received pilots to further improve the estimation accuracy.Different from the training phase,the initial DFO estimation in pre-training phase is obtained by the data and pilot symbols.Simulation results show that the mean squared error(MSE) performance of the proposed method is better than those of the available algorithms,and it has acceptable computational complexity.

A NEW ESPRIT METHOD FOR BLIND ESTIMATES OF DOA-DOPPLER FREQUENCY WITH UNKNOWN ARRAY MANIFOLD

A novel rotational invariance technique for blind estimates of direction of arrival (I)OA) and Doppler frequency with unknown array manifold due to array sensor uncertainties is proposed, taking Doppler frequency difference between a successive pulses as rotational parameter. The effectiveness of the new method is confirmed by computer simulation. Compared with the existing 2-D DOA-frequeucy estimate techniques, the computation load of the proposed method can be saved greatly.

Thin-film lithium niobate dual-parallel Mach-Zehnder modulator for a simple photonic system measuring Doppler frequency shift

In recent years,thin-film lithium niobate(TFLN)electro-optic(EO)modulators have developed rapidly and are the core solution for the next generation of microwave photonics(MWP)problems.We designed and fabricated a dual-parallel Mach-Zehnder modulator(DPMZM)based on TFLN,achieving a 3 dB electro-electro(EE)bandwidth of 29 GHz and a low drive voltage(Vπ=6 V).The device we manufactured is metal-encapsulated.It is noteworthy that we proposed a single-channel Doppler frequency shift(DFS)measurement system based on this device and conducted verification experiments.We coupled light from an external laser into the chip and passed it through each of the two sub-MZMs of the DPMZM.These lights were modulated by echo signals and reference signals.By measuring the frequency of the output signal,we can obtain a DFS value without directional ambiguity.The success of this experiment marks a key step in the practical application of TFLN modulators in MWP.

Frequency Diversity for OFDM Mobile Communication via Underwater Acoustic Channels

The major constraint on the performance of orthogonal frequency division multiplexing （OFDM） based underwater acoustic （UWA） communication is to keep subcarriers orthogonal. In this paper, Doppler estimation and the respective compensation technique along with various diversity techniques were deliberated for OFDM-based systems best suited for underwater wireless information exchange. In practice, for mobile communication, adjustment and tuning of transducers in order to get spatial diversity is extremely difficult. Considering the relatively low coherence bandwidth in UWA, the frequency diversity design with the Doppler compensation function was elaborated here. The outfield experiments of mobile underwater acoustic communication （UWAC） based on OFDM were carried out with 0.17 bit/（s-Hz） spectral efficiency. The validity and the dependability of the scheme were also analyzed.

Velocity compensation methods for LPRF modulated frequency stepped-frequency(MFSF) radar

In the high speed target environment,there exists serious Doppler effect in the low pulse repetition frequency（LPRF） modulated frequency stepped frequency（MFSF） radar signal.The velocity range of the target is large and the velocity is high ambiguous,so the single method is difficult to satisfy the velocity measurement requirement.For this problem,a novel method is presented,it is a combination of cross-correlation inner frame velocity measurement and range-Doppler coupling velocity measurement.The cross-correlation inner frame method,overcoming the low Doppler tolerance of the cross-correlation between frames,can obtain the coarse velocity of the high speed target,and then the precision velocity can be obtained with the range-Doppler coupling method.The simulation results confirm the method is effective,and also it is well real-time and easy to the project application.

Analysis of the influence of various effects on frequency shifts of the acetylene saturated absorption lines

Frequency shifts of the acetylene saturated absorption lines at 1.5μm with temperature, gas pressure and laser power have been investigated in detail. The second-order Doppler effect, the recoil effect, the Zeeman effect, the pressure shift and the power shift are taken into consideration. The magnitudes of those shifts caused by various effects are evaluated. In order to reproduce the stability of 5.7 × 10^-14 obtained by Edwards, all necessary conditions are given. The results show that when there is a larger external magnetic field, the Zeeman shift could not be neglected, so that the shield should be employed. And the design of a long cavity is advantageous to reduce the influence of the second-order Doppler effect. The results also show that at least 4-2.5℃ temperature control for cavity can effectively prevent several effects and improve the frequency stability.