Phase Error Compensation Research Articles

Estimation and Compensation of Turbulent Tropospheric Delay in High-Resolution SAR Image

As a typical propagation error, tropospheric delay has been fully considered during synthetic aperture radar (SAR) interferometry and differential interferometry, while the influence on the SAR imaging process is just concerned in advanced configurations, e.g., staring mode, high-resolution, geosynchronous/geostationary (GEO) SAR. In this article, a comprehensive model of turbulent tropospheric delay (TTD), involving atmospheric sciences and fluid mechanics, is introduced, and the influence of which on high-resolution SAR is analyzed. In order to compensate for the influence of TTD in advanced SAR missions, the autofocus method used in motion error compensation is extended, and a 2-D phase error estimation and compensation algorithm is proposed. Subsequently, the simulation experiments of both dot-matrix targets and TerraSAR-X data are performed to validate the effectiveness of the proposed algorithm. Conclusions and prospects are reached in the end.

An Integrated OFDR System Using Combined Swept-Laser Linearization and Phase Error Compensation

This article describes a flexible, compact, semiconductor laser (SCL)-based optical frequency-domain reflectometry (OFDR) design, incorporating swept-laser linearization functions (both passive and active), in situ phase error evaluation function, and phase error compensation function. At the core of the proposed design, a fiber-optic Mach–Zehnder interferometer (MZI) and its electronic digitization components (photodetector and zero-cross circuit) simultaneously perform all the abovementioned functions. Benefitting from the unique digital design, this system combines all functions in a compact fashion without increasing complexity and overhead. Experimental results demonstrate enhanced accuracy using the integrated design compared with prior methods, as well as improved cost-effectiveness, reduced complexity, and optimized form factor.

Two-Dimension Joint Super-Resolution ISAR Imaging With Joint Motion Compensation and Azimuth Scaling

The quality of inverse synthetic aperture radar (ISAR) images suffers seriously from the two-dimension (2-D) resolution and noise. The motion errors arising from translational and rotational motion further aggravate the image defocusing. For the limited bandwidth and short aperture (LB-SA) signal, this letter proposes a novel 2-D joint super-resolution (2D-JSR) ISAR imaging with joint motion compensation and azimuth scaling (JMCAS) algorithm. In this technique, a 2D-JSR signal model is established, enabling the 2-D high-resolution ISAR image to be generated by solving a sparsity-driven optimization problem with a modified quasi-Newton solver. In addition, a new JMCAS algorithm is developed to enhance the focusing performance of image. Not only can this algorithm jointly correct the range shift and phase error caused by translational motion, it can also complete the azimuth scaling and range spatial-variant phase error (RSVPE) compensation simultaneously. Through the iterative processing of 2D-JSR reconstruction and JMCAS, the well-focused and scaled high-resolution ISAR image can be obtained. Both simulated and real data experiments are provided to verify the effectiveness of the proposed algorithm.

Estimation and compensation of phase errors induced by axial bulk motion of a sample in wavelength-sweeping parallel Fourier domain OCT.

We report a new, to the best of our knowledge, approach to correct image blurring due to the axial bulk motion of a sample in wavelength-sweeping Fourier domain parallel optical coherence tomography (OCT). This approach can estimate phase errors changing rapidly in time through direct measurements of the apparent axial shift during the sampling interval using common phase changes in parallel detection without additional hardware. To demonstrate the performance of the proposed algorithm, a single reflection and scattering sample were imaged with wavelength-sweeping parallel OCT implemented by scanning a spectrally dispersed line-field along the line direction. In addition, we quantitatively demonstrated that even a small axial movement of the sample could cause serious image blur at a high nonlinear degree of movement.

Neural network based synthetic aperture ladar imaging through marine atmosphere

The atmospheric turbulence can severely affect the azimuth imaging of the Synthetic Aperture Ladar (SAL). Based on a neural network, this study generates atmospheric phase screens complied with marine atmosphere spectrum. The SAL imaging results with different turbulence intensities and laser wavelengths are calculated, and the changing law of the ratio of real aperture length to atmospheric coherence diameter with turbulence intensity under different slant ranges and laser wavelengths are analyzed in this paper. The results suggest that the SAL imaging becomes worse as the turbulence intensity is stronger, and even the target is not able to be distinguished. A longer laser wavelength can be used to alleviate the defocus effect, and the phase error compensation algorithm based on marine phase screens can effectively improve the SAL imaging quality to guarantee the real–time process of echo signals of SAL in the marine atmosphere.

Wideband Waveform Generation Using MDDS and Phase Compensation for X-Band SAR

This study investigated wideband waveform generation using a field programmable gate array (FPGA) for X-band high-resolution synthetic aperture radar (SAR). Due to the range resolution determined by the bandwidth, we focused on wide bandwidth generation while preserving spectrum quality. The proposed method can generate wide bandwidth using a relatively low system clock. The new approach was designed in Simulink and implemented by very-high-speed-integrated-circuits hardware description language (VHDL). We also proposed a hardware structure in accordance with the proposed method. Signal connections of FPGA and digital analog converter (DAC) are described in the design of the proposed hardware structure. The developed X-band waveform generator using the proposed method output the desired pulse waveform. For the reduction of phase error and improvement of spectrum quality at the X-band, phase error compensation and pre-distortion were applied to the waveform generator. The results of the simulation and the hardware output demonstrate that the variation and standard deviation of the phase error were improved within the frequency spectrum. Accordingly, the proposed method and the developed waveform generator have the potential to produce a high-resolution image of the area of interest.

Compensation of Phase Errors for Spotlight SAR With Discrete Azimuth Beam Steering Based on Entropy Minimization

Spotlight synthetic aperture radar (SAR) achieves very high-resolution (VHR) images by steering the azimuth beam during the formation of the synthetic aperture. In practice, the steering is implemented through discrete azimuth beam switching. Then, phase shifts can occur between the adjacent beams due to the error of the antenna pattern. In addition, the troposphere introduces a beam-angle-dependent delay to the echo. Those undesired phase shifts and delays cause phase errors in the received echo and result in image quality deterioration. In this letter, an algorithm, called the Newton entropy minimization (N-EM), is proposed to estimate and compensate the phase errors caused by the discrete azimuth beam steering for the spotlight SAR data. Combining with the subaperture imaging approach of the spotlight SAR, the algorithm estimates the phase offsets between each couple of the adjacent beams based on the minimum entropy criterion. The analytic expression, which is a nonlinear equation, is developed for the optimal estimation. Then, the Newton's method is employed to solve the equation. The real spaceborne SAR (both the staring and sliding spotlight modes) data processing results demonstrate the efficiency and accuracy of the proposed algorithm.

Relaxation of the Radio-Frequency Linewidth for Coherent-Optical Orthogonal Frequency-Division Multiplexing Schemes by Employing the Improved Extreme Learning Machine

A coherent optical (CO) orthogonal frequency division multiplexing (OFDM) scheme gives a scalable and flexible solution for increasing the transmission rate, being extremely robust to chromatic dispersion as well as polarization mode dispersion. Nevertheless, as any coherent-detection OFDM system, the overall system performance is limited by laser phase noises. On the other hand, extreme learning machines (ELMs) have gained a lot of attention from the machine learning community owing to good generalization performance, negligible learning speed, and minimum human intervention. In this manuscript, a phase-error mitigation method based on the single-hidden layer feedforward network prone to the improved ELM algorithm for CO-OFDM systems is introduced for the first time. In the training step, two steps are distinguished. Firstly, pilots are used, which is very common in OFDM-based systems, to diminish laser phase noises as well as to correct frequency-selective impairments and, therefore, the bandwidth efficiency can be maximized. Secondly, the regularization parameter is included in the ELM to balance the empirical and structural risks, namely to minimize the root mean square error in the test stage and, consequently, the bit error rate (BER) metric. The operational principle of the real-complex (RC) ELM is analytically explained, and then, its sub-parameters (number of hidden neurons, regularization parameter, and activation function) are numerically found in order to enhance the system performance. For binary and quadrature phase-shift keying modulations, the RC-ELM outperforms the benchmark pilot-assisted equalizer as well as the fully-real ELM, and almost matches the common phase error (CPE) compensation and the ELM defined in the complex domain (C-ELM) in terms of the BER over an additive white Gaussian noise channel and different laser oscillators. However, both techniques are characterized by the following disadvantages: the CPE compensator reduces the transmission rate since an additional preamble is mandatory for channel estimation purposes, while the C-ELM requires a bounded and differentiable activation function in the complex domain and can not follow semi-supervised training. In the same context, the novel ELM algorithm can not compete with the CPE compensator and C-ELM for the 16-ary quadrature amplitude modulation. On the other hand, the novel ELM exposes a negligible computational cost with respect to the C-ELM and PAE methods.

Antenna Phase Error Compensation for Terahertz Coded-Aperture Imaging

Coded-aperture antenna plays an important role in terahertz coded-aperture imaging radar system. However, the performance of a system is inevitably affected by the phase errors introduced by the coded-aperture antenna elements. In this paper, we propose a phase error compensation method by deducing a formula to compute all element phase errors accurately. According to the formula, the phase errors can be calibrated by using a calibrator and can be used to compensate the imaging model of the system. Numerical simulations demonstrate that the proposed method can effectively improve the imaging quality when the elemental phase error exceeds 10 ∘ .

A flexible phase error compensation method based on probability distribution functions in phase measuring profilometry

We demonstrate a fast and easy phase-error compensation technique based on statistical analysis of the wrapped phase distributions. The probability distribution functions (PDF) of the wrapped phase will become abnormal when there are nonlinear effects in a phase measuring profilometry. With the known iterative phase compensation algorithm, the most appropriate coefficients will be obtained by smoothing the PDF. The proposed method doesn’t need more fringe images than the choosing three or four step fringe images as well as reference images. It can lead to a fast and easy phase-error compensation. Both computer simulation and experiment are carried out to demonstrate the validity of this technique.

Compensation of Phase Errors in the Frequency Domain for Multi-Carrier LFMCW MIMO Radar

Compensation of Phase Errors in the Frequency Domain for Multi-Carrier LFMCW MIMO Radar

Beyond phase error compensation: pixel mapping-based error correction for high-accuracy 3D surface measurement

In optical-based phase-shifting 3D surface profilometry, phase errors are inevitable and lead to final measurement errors. Error compensation, based on pre-estimated phase errors, is an effective technique to alleviate the phase errors. However, the static and inaccurate nature of the pre-estimated errors lead to an implicit limit to the compensation accuracy. Furthermore, the procedures for error pre-estimation require additional projections, which reduces convenience in practice. In this paper, a novel pixel mapping-based error correction method is proposed. Different from compensation, with the proposed pixel-mapping errors inside each camera pixel can be directly corrected by online replacing with its corresponding ground-truth values input in the projector. This replacement technique is the key idea of our method, which establishes a shortcut to error-free ground-truth values, skipping the traditional laborious and imprecise compensation procedures. To achieve pixel-mapping, an optimization method is proposed and no additional projections are required. A phase error formulation is also introduced in the optimization method to eliminate the phase error distrubance when computing the pixel mapping. Extensive experimental results are shown to demonstrate that the phase accuracy can be obviously improved after utilizing the proposed method.

A Novel Motion Compensation Method Based on Height Term Removing for Spotlight SAR on Circular Trajectories

For spotlight synthetic aperture radar (SAR) on circular trajectories, the phase error caused by motion error is 2-D space-variant. For the conventional motion compensation (MOCO) algorithm, the imaging scene is generally segmented into many sub-regions to compensate for the space-variant phase error. However, the complex phase error results in that fact that it is difficult to obtain the quantitative criterion of scene segmentation. To address this issue, we propose a novel MOCO algorithm. This method contains three steps; the first step is non-space-variant phase error compensation; the second step is to remove the height term; the third step is space-variant phase error compensation. Among these steps, the most critical operation is removing the height term. In the distance equation, the height term is independent of the ground target coordinate. Hence, it can be removed by a serial of operations containing resampling and phase compensation. Through removing height term, it doesn’t only compensate the height error but also makes the residual phase error into 1-D space-variant. Then, the phase error is exclusively related to the radius error and the target abscissa. Hence, after compensating for the space-variant error, it only needs to segment scene along the abscissa direction. Meanwhile, it can gain the quantitative criterion of scene segmentation to guarantee the phase error variation range is less than $\pi /{4}$ in each sub-scene. Eventually, some simulations are conducted to illustrate that the proposed method is valid.

Phase analysis and error compensation of anti-jamming nulling algorithm for satellite navigation array antenna

The traditional adaptive nulling antenna array anti-interference algorithm can cause phase distortion, make the antenna phase unstable, and produce positioning error. Based on the analysis of the adaptive nulling antenna array anti-jamming algorithm, this article deduces the calculation method of its phase centre and the stage of real-time change, determines the phase centre error, and calculates the compensation value which can be used for the repositioning after correction. Simulation and experimental results verify the rationality and effectiveness of the algorithm, which can be used to improve the positioning accuracy of anti-jamming array antenna GNSS receiver.

Phase analysis and error compensation of anti-jamming nulling algorithm for satellite navigation array antenna

Phase analysis and error compensation of anti-jamming nulling algorithm for satellite navigation array antenna

Phase Noise Effect on Millimeter-Wave Pre-5G Systems

The introduction of millimeter waves for 5G wireless communication systems enables the use of more bandwidth and higher carrier frequency, surpassing the capacity of current systems by more than one order of magnitude. The leap of millimeter band results from the development of analog frontends that unfortunately induce relatively large phase noise in phase-locked loop synthesizers. Large phase noise may generate considerable random phase error and residual frequency offset, which in turn produces additional phase error. We evaluate phase error from phase noise on an implemented pre-5G system operating in the millimeter band and through a simulation by modeling the characteristics of a radio frequency integrated circuit. We measure and then compare the residual frequency offset, phase error, and error vector magnitude between the experimental and simulation results. We verify that the phase noise model suitably approximates to the real conditions. Moreover, we show that phase error remains at approximately 4° in the implemented system. By exploiting the implemented phase error compensation, our pre-5G system can overcome a degradation of 1.5 dB in error vector magnitude and achieve an approximate transmission rate of 4 Gbps at gain of 1.49.

Two-dimensional projection histogram assisted with low-overhead pilots for the common phase error compensation in CO-OFDM system

Abstract In this paper, we demonstrate a two-dimensional projection histogram assisted common phase error (CPE) compensation scheme in coherent optical orthogonal frequency division multiplexing (CO-OFDM) system. With the help of the low overhead pilots, the rough estimation can be obtained, and the π/2 deviation problem of projection histogram (PH) assisted scheme can be efficiently solved, which can improve the estimation accuracy of CPE. And, with the processing of the two-dimensional projection histogram mapping, the fine estimation can be achieved. The numerical CO-OFDM system simulations over the single mode fiber (SMF) transmission are conducted. The corresponding results show that, compared to the pilot-aided (PA) estimation method, only less-overhead pilots were employed for our scheme, but more accurate CPE estimation can be achieved, hence improving the system performance. Moreover, to achieve an optimal transmission performance, the overhead of pilots for the PA method should be set to 20%, while the proposed method can reduce to 1.25%.

High Load Fast Startup Sensorless Control of Wheel BLDC Motor with Line-to-Line Back EMF Extraction Using Least Pth-Norm IIR Digital Filter

In this paper, an effective scheme of on-load startup with reduced current has been proposed for BLDC motor and the steady as well as dynamic performance in all four quadrants was verified. Hysteresis band-limited back EMF noise provides the starting pulses, the frequency of which depends on the threshold factor in speed proportional threshold. Scheme is quite fast, comparatively to the state-of-the art schemes of startup and less complex than time-consuming initial position detection (IPD) algorithm. Second-order least [Formula: see text]th-norm infinite impulse response (IIR) digital low pass filter realized in MATLAB/Simulink has been used for extraction of line-to line back EMF from line-to-line terminal voltages measured with two voltage sensors. Proposed filter has wide flexibility of online variation of cut-off frequency, gain and phase without any circuit-based modification due to variability of filter coefficients. This enables the smooth filtering with minimized phase delay in low speed range irrespective of any duty cycle and PWM frequency. Linear compensation of phase error or phase advancement for desired current profile can easily be achieved by the varying the threshold factor. In this experiment, the threshold factor of 1/1460 has been found most suitable for smooth sensorless startup without jerk, vibration and reverse rotation, as the motor operates in advanced mode with this value. First, the performance of Hall sensor-based drive was studied using open loop variable duty cycle speed control. The controller was designed in MATLAB/Simulink platform and implemented using TMS320F28069M DSP control stick with Code composer Studio V5. Later on, a complete controller for proposed sensorless scheme was developed in MATLAB/Simulink environment and was implemented using NI-PCI6221 Controller installed in PC. The proposed sensorless drive has been found capable of operating at very low speed of 50[Formula: see text]rpm in voltage control mode and 85[Formula: see text]rpm in current chopping PWM mode. Approximately 85[Formula: see text]ms less time was taken by sensorless drive to reach the same speed when compared with Hall-based control for identical loading. Also less overshoots during startup was observed. Overlap time of 0.05[Formula: see text]ms between phase currents has been achieved during commutation period.

Real-time motion-induced-error compensation in 3D surface-shape measurement.

Object motion can introduce unknown phase shift and thus measurement error in multi-image phase-shifting methods of fringe projection profilometry. This paper presents a new method to estimate the unknown phase shifts and reduce the motion-induced error by using three phase maps computed over a multiple measurement sequence and calculating the difference between phase maps. The pixel-wise estimation of the motion-induced phase shifts permits phase-error compensation for non-homogeneous surface motion. Experiments demonstrated the ability of the method to reduce motion-induced error in real-time, for shape measurement of surfaces with high depth variation, and moving and deforming surfaces.

Improved weighted least‐squares phase unwrapping method for interferometric SAR processing

Based on the study of existed least-squares and weighted least-squares phase unwrapping methods, an improved weighted least-squares algorithm based on unwrapping phase error compensation is proposed. First, the conventional weighted least-squares method is used to get the initial result of phase unwrapping. Then the unwrapping result is optimised by iterative compensation of phase unwrapping error. In addition, for the reasonable selection of the times of iteration, an iterative mechanism is designed to avoid the redundant or insufficient compensation caused by too many iterative times and too few. Compared with the traditional weighted least-square method, by using the proposed method, the global influence of phase noise is constrained by weighted processing, and meanwhile, the accuracy of phase unwrapping is greatly improved by iterative error compensation. The simulation results confirm the superiority of the proposed method.