Phase Error Calibration Research Articles

A 24-Gb/s MIPI C-/D-PHY Receiver Bridge Chip With Phase Error Calibration Supporting FPGA-Based Frame Grabber

A 24-Gb/s MIPI C-/D-PHY Receiver Bridge Chip With Phase Error Calibration Supporting FPGA-Based Frame Grabber

Real-Time Phaseless Microwave Frequency-Diverse Imaging with Deep Prior Generative Neural Network

The millimeter-wave frequency-diverse imaging regime has recently received considerable attention in both the security screening and synthetic aperture radar imaging literature. Considering that the minor systematic errors and alignment errors could still produce heavily corrupted images, these complex-based imaging reconstructions rely heavily on the precise measurement of both phase and amplitude of radiation field patterns and echo signals. In the literature, it is shown that by leveraging phase-retrieval techniques, salient reconstruction images can still be acquired, even in the presence of significant phase errors, which could ease the phase error calibration pressure to a large extent in practical imaging applications. In this paper, in the regime of phaseless frequency-diverse imaging, with the powerful feature inference and generation power of unsupervised generative models, an end-to-end deep prior generative neural network is designed to achieve near real-time imaging. The harsh imaging reconstruction with both the high radiation mode correlations and extremely low scene compression sampling ratio, which are extremely troublesome to tackle for generally applied matched-filter and compressed sensing approach in the current frequency-diverse imaging literature, can still be preferably handled with our reconstruction network. The well-trained reconstruction network is constituted by prior inference and deep generative modules with excellent generative capabilities and significant prior inference abilities. Using simulation experiments with radiation field data, we verify that the integration of phase-free frequency-change imaging with deep learning networks can effectively improve reconstruction capabilities and improve robustness to systematic phase errors. Compared with existing imaging methods, our imaging method has high imaging performance and can even reconstruct targets under low compression ratio conditions, which is somewhat competitive with current state-of-the-art algorithms. Moreover, we find that the proposed method has good anti-noise and stability.

A Fast ISAR Tomography Technique for Fully Polarimetric 3-D Imaging of Man-Made Targets

The 3-D inverse synthetic aperture radar (ISAR) tomography is an enabling technique for applications such as the exact diagnosis of scattering mechanisms for complex targets. Nevertheless, current ISAR tomography solutions still suffer from problems such as the great computational complexity and optimal utilization of the signatures acquired from limited baselines. In this work, we propose a fast ISAR tomography technique for fully polarimetric 3-D imaging of man-made targets. A stack of 2-D complex-valued images with different baselines and polarizations is first obtained through a phase error calibration (PEC) process and graphic processing unit accelerated polarimetric filtered backprojection. A polarimetric state-space decomposition (P-SSD) algorithm is then developed which could provide joint 3-D reconstruction results with low computational complexity. Examples from both numerical multibaseline data for the Sandia laboratories implementation of cylinders (SLICY) benchmark model and the outdoor range dataset collected by the Georgia Tech Research Institute (GTRI) are presented to demonstrate the superior performance and the usefulness of the proposed technique.

Fast phase error calibration through radix-p optimization processing

Optical phased arrays (OPAs) have been a popular option to manipulate the spatial behavior of the free-space optical beams. Inspired by the success of the integrated circuits (IC) industry, photonic IC (PIC) based OPAs have been actively studied in the last decade. Due to the fabrication imperfection, light passing through different paths typically results in random phase errors. The phase errors can seriously deviate the interference pattern of an OPA, and radically change the spatial distribution of the optical field. This phenomenon will significantly degrade the performance for applications like image scanning and optical wireless communication (OWC). Thermally or electrically tunable phase shifters can be applied to compensate the phase errors through dedicated calibration algorithms. However, the complexity of the calibration processes quickly increases with the number of the OPA’s elements. Hence, the whole processing can be time-consuming and this significantly pushes the overall system cost. Besides, considering the potential dynamic factors such as thermal gradient and aging effects, continuous calibration may be necessary. This results in great demand for fast and efficient calibration processing for the practical applications. In this paper, novel and efficient radix-p calibration processing is proposed which can be directly combined with most of the already reported/developed optimization algorithms as a speed-up turbo. It is shown that the computation time of the proposed radix-p processing grows linearly with the number of the OPA’s elements. In comparison to the conventional particle swarm optimization (PSO) algorithm, which exhibits exponential computation time in our numerical results, the radix-p processing shows great efficiency improvement. In the numerical results, speed with more than 12 times faster is shown for the proposed radix-p processing compared to the traditional PSO algorithms.

Direction estimation using a two-level nested array with gain–phase error calibration

Direction estimation using a two-level nested array with gain–phase error calibration

Phase calibration method for microphone array based on multiple sound sources

In the microphone array, the phase error of each microphone causes a deviation in sound source localization. At present, there is a lack of effective methods for phase error calibration of the entire microphone array. In order to solve this problem, a phase mismatch calculation method based on multiple sound sources is proposed. This method requires collecting data from multiple sound sources in turn, and constructing a nonlinear equation setthrough the signal delay and the geometric relationship between the microphones and the sound source positions. The phase mismatch of each microphone can be solved from the nonlinear equation set. Taking the single frequency signal as an example, the feasibility of the method is verified by experiments in a semi-anechoic chamber. The phase mismatches are compared with the calibration results of exchanging microphone. The difference of the phase error values measured by the two methods is small. The experiment also shows that the accuracy of sound source localization by beamforming is improved. The method is efficient for phase error calibration of arrays with a large number of microphones.

A 50 Gb/s PAM-4 Transmitter With Feedforward Equalizer and Background Phase Error Calibration

This brief presents the design of a fully integrated, 50 Gb/s PAM-4 transmitter, which consists of an on-chip pseudorandom word generator (PRWG), a 16:2 quarter-rate serializer with 4-tap FFE, and on-chip duty-cycle calibration (DCC) and quadrature phase error calibration (QEC) loops. The dual-loop DCC and QEC can be operated concurrently on-the-fly to suppress the deterministic data jitter. Incorporating the proposed technique, the eye opening is improved by 30 %. To facilitate built-in-self-test (BIST) under high speed operation, the PRWG provides 16-path parallel test patterns, which correspond to PRBS-13Q after serializer. The output buffer employs inductive shunt-series peaking for broad band impedance matching and bandwidth enhancement. The bandwidth is extended more than twice while the return loss is reduced by more 4dB. The experimental prototype is fabricated in a TSMC 28 nm CMOS process, and the core area is 0.214 mm <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> . The whole transmitter consumes 143.4 mW at 50 Gb/s operation.

Phase measuring deflectometry for obtaining 3D shape of specular surface: a review of the state-of-the-art

Phase measuring deflectometry (PMD) is a superior technique to obtain three-dimensional (3D) shape information of specular surfaces because of its advantages of large dynamic range, noncontact operation, full-field measurement, fast acquisition, high precision, and automatic data processing. We review the recent advances on PMD. The basic principle of PMD is introduced following several PMD methods based on fringe reflection. First, a direct PMD (DPMD) method is reviewed for measuring 3D shape of specular objects having discontinuous surfaces. The DPMD method builds the direct relationship between phase and depth data, without gradient integration procedure. Second, an infrared PMD (IR-PMD) method is reviewed to measure specular objects. Because IR light is used as a light source, the IR-PMD method is insensitive to the effect of ambient light on the measured results and has high measurement accuracy. Third, a proposed method is reviewed to measure the 3D shape of partial reflective objects having discontinuous surfaces by combining fringe projection profilometry and DPMD. Then, the effects of error sources that mainly include phase error and geometric calibration error on the measurement results are analyzed, and the performance of the 3D shape measurement system is also evaluated. Finally, the future research directions of PMD are discussed.

A Novel Channel Phase Error Calibration Method Based on Hybrid AFSA-GSO-GA for Multichannel HRWS-SAR Imaging

The spaceborne high-resolution wide-swath synthetic aperture radar (HRWS-SAR) system generally does not meet the optimal SAR imaging configuration, and thus, it is necessary to apply digital beam-forming filtering technology to restore the nonuniformly sampled signal into the uniform grids. However, in practice, because of the influences of temperature, receiving machine, and other error factors, the channel errors may possibly exist, causing the SAR image to be smeared. To address this issue, this letter proposes a novel algorithm based on the hybrid artificial fish school algorithm–glowworm swarm optimization–genetic algorithm (AFSA-GSO-GA) to address the channel imbalance issue. First, coarse HRWS-SAR imaging processing is performed to obtain the positions of the Doppler ambiguity components. Then, according to the designed cost function, the hybrid AFSA-GSO-GA algorithm is used to realize the channel phase error estimation. Finally, a well-focused SAR image can be obtained after channel balance. The effectiveness of the proposed method is validated by both simulated and real SAR data.

Sparsity-Based DOA Estimation with Gain and Phase Error Calibration of Generalized Nested Array

Sparse arrays, which can localize multiple sources with less physical sensors, have attracted more attention since they were proposed. However, for optimal performance of sparse arrays, it is usually assumed that the circumstances are ideal. But in practice, the performance of sparse arrays will suffer from the model errors like mutual coupling, gain and phase error, and sensor’s location error, which causes severe performance degradation or even failure of the direction of arrival (DOA) estimation algorithms. In this study, we follow with interest and propose a covariance-based sparse representation method in the presence of gain and phase errors, where a generalized nested array is employed. The proposed strategy not only enhances the degrees of freedom (DOFs) to deal with more sources but also obtains more accurate DOA estimations despite gain and phase errors. The Cramer–Rao bound (CRB) derivation is analyzed to demonstrate the robustness of the method. Finally, numerical examples illustrate the effectiveness of the proposed method from DOA estimation.

A Simple Calibration Method for Ratio Error and Phase Error of Electronic Energy Meter

The ratio errors of resistance divider network and current transformer, and the phase error introduced by current transformer, which are the main error sources, greatly affect the measurement accuracy of actual electronic energy metering equipment. Because the fairness of energy metering system has a significant influence on the energy market, a digital calibration method for ratio error and phase error of electronic energy meter is proposed to deal with this problem in this paper. By establishing the equivalent models of the analog front-end circuit of static meter, a simple and high accuracy digital calibration method for reducing ratio error and phase error of static meter is given. Firstly, the DC bias of each channel is subtracted from its corresponding channel. After that, correction coefficients are used to correct the ratio errors of voltage and current channels. Finally, a piecewise Lagrange quadratic interpolation method is used to realize phase error calibration. The proposed approach has the features of simplicity and high efficiency. The experimental results validate the accuracy and effectiveness of the proposed algorithm.

A Quadrature PLL With Phase Mismatch Calibration for 32GS/s Time-Interleaved ADC

This article presents an accurate quadrature phase-locked loop (PLL) with quadrature phase mismatch calibration for 32 GS/s analog-to-digital converter (ADC). Due to the mismatches of clock distribution in layout and variations of the active devices, the quadrature phase of the sampling clock is significantly deteriorated. To solve the problem, a novel quadrature divider with phase calibration is induced in PLL loop. Moreover, a theoretical model of the quadrature divider is proposed to predict the performance and potential ability for phase calibration. Based on the theoretical and model analysis, the proposed PLL can realize accurate quadrature phase for high-speed real-time sampling system. The output frequency of PLL is 8 GHz with quadrature phases for 32 GS/s sampling rate. The proposed clock can realize 8-bit signal to noise ratio requirement with 16 GHz bandwidth. The proposed PLL was fabricated in 65-nm CMOS process with 28 mW dc power consumption under 1.2 V supply voltage. Testing results show that the phase noise of the clock is −127 dBc/Hz @10 MHz-offset frequency when the sampling speed is 27.4 GS/s. With proposed methods, the range of the phase error calibration is around ±20°.

Phase Difference Measurement of Under-Sampled Sinusoidal Signals for InSAR System Phase Error Calibration.

Phase difference measurement of sinusoidal signals can be used for phase error calibration of the spaceborne single-pass interferometric synthetic aperture radar (InSAR) system. However, there are currently very few papers devoted to the discussion of phase difference measurement of high-frequency internal calibration signals of the InSAR system, especially the discussion of sampling frequency selection and the corresponding measuring method when the high-frequency signals are sampled under the under-sampling condition. To solve this problem, a phase difference measurement method for high-frequency sinusoidal signals is proposed, and the corresponding sampling frequency selection criteria under the under-sampling condition is determined. First, according to the selection criteria, the appropriate under-sampling frequency was chosen to sample the two sinusoidal signals with the same frequency. Then, the sampled signals were filtered by limited recursive average filtering (LRAF) and coherently accumulated in the cycle of the baseband signal. Third, the filtered and accumulated signals were used to calculate the phase difference of the two sinusoidal signals using the discrete Fourier transform (DFT), digital correlation (DC), and Hilbert transform (HT)-based methods. Lastly, the measurement accuracy of the three methods were compared respectively by different simulation experiments. Theoretical analysis and experiments verified the effectiveness of the proposed method for the phase error calibration of the InSAR system.

A programmbale 8-channel multiphase clock generator with 360 phases for focus ultrasound applications

An area efficient, programmable multichannel, multiphase clock generator is proposed to improve the phase resolution for focus ultrasound applications. By using the proposed phase-folding method, the cell amount for generating 360 phases are reduced from 360 to 38 cells. The proposed clock generator is able to provide 360 phases in real-time with 1° phase resolution, 1–51.9% 6-bit DPWM for each channel, and which output frequency varies from 0.1 to 1.5 MHz. Due to the proposed multiphase system is a real-time system, many independent multichannel applications such as focus ultrasound could easily adopt the proposed structure. A new phase-error calibration method for PLL is also present in this paper for reducing the static phase-error due to process voltage and temperature variation. It improves the accuracy of the phase difference in the multiphase system. The proposed ASIC was fabricated in a standard 0.18 μm CMOS process. Measured result shows that multiphase clock generator is able to provide 360 selective phases for each channel. The derived DNL is from −0.106 to +0.108 LSB, and the INL is from −0.284 to +0.449 LSB at 1 MHz.

Multichannel Phase Calibration for Linear Array Based on Extended &lt;inline-formula&gt; &lt;tex-math notation="LaTeX"&gt;$\omega K$&lt;/tex-math&gt; &lt;/inline-formula&gt; Algorithm and Minimum-Entropy Method

Millimeter-wave imaging techniques have been used for security inspection at important checkpoints. With the increase of working frequencies of the imaging systems, the precise multichannel phase calibration becomes more and more important. Most of the traditional algorithms are used for the calibration of passive receiving antenna array, based on the signal model of far-field plane wave. However, the near-field spherical wave model should be utilized for the active wideband near-field imaging applications. Consequently, the traditional calibration algorithms cannot be used in wideband near-field imaging systems. The metal plate is usually employed for the calibration of wideband near-field imaging systems, but the precision is very sensitive to the flatness of the surface of the metal plate, which will result in additional phase error after calibration. In this letter, a multichannel phase error estimation and calibration method is proposed for the wideband linear array system. By using an extended $\omega K$ algorithm and the minimum-entropy method, the additional phase error of each channel after preliminary calibration is estimated and calibrated. Simulations and experimental results show the effectiveness of the proposed method.

A Phase Tunable Rotary Traveling Wave Oscillator: Analysis and Calibration

In this paper, a new phase error analysis is introduced for rotary traveling wave oscillators (RTWOs). Two new analytical approaches are used to extract closed-form equations for the RTWOs phase error arising from asymmetric resonator and inequality of negative transconductors. Derived equations show that the phase error can be cancelled and even controlled by adjusting the bias current of negative transconductors without any undesirable changing in oscillation frequency. This characteristic is then used for introducing a new phase error calibration method for RTWOs. This calibration method is not limited by the problems that limit the usage of the prior calibration technique. Our theoretical results are compared with accurate simulations to evaluate the validity of the proposed analysis and accuracy of the closed-form equations. Simulations have been done in 0. 18- $\mu$ m CMOS technology with a 1.8-V supply voltage. The evaluations show good agreement between analytical phase-error equations and simulation results. Also, appropriate simulations confirm the validity of the calibration method that is introduced in this paper.

MIMO Radar Calibration and Imagery for Near-Field Scattering Diagnosis

Multiple-input multiple-output (MIMO) radar is an enabling technique for high-resolution imaging, which is especially useful for near-field electromagnetic scattering diagnosis of complex targets. Among others, high sidelobes and radar cross section (RCS) calibration uncertainty are the major challenges for such applications, due to array nonuniformity, imperfect channels, and antenna pattern tapering. These shortcomings prevent a MIMO radar from obtaining high-quality images with enough dynamic range and RCS accuracy. In this paper, we develop a complete solution for these problems. A novel adaptive weighting technique is proposed, where the complex weights are optimized for exact amplitude and phase error calibration of a MIMO array and for azimuth sidelobe reduction. A MIMO filtered backprojection algorithm is developed for image formation with improved RCS calibration accuracy, where propagation path-loss, antenna pattern tapering, and phase distortion due to the near-field spherical wave front are compensated. Both indoor and outdoor field test results are presented to show the high-quality images obtained using the proposed techniques, demonstrating the applicability of a MIMO radar for diagnostic RCS imaging of complex targets.

Azimuth-Variant Phase Error Calibration Technique for Multichannel SAR Systems

Multiple azimuth channels are usually employed to overcome the inherent limitation between high resolution and wide swath in synthetic aperture radar systems. However, unavoidable channel phase errors will significantly degrade the performance of ambiguity suppression. Conventional calibration methods usually regard these phase errors as constants during the whole observation time and ignore the azimuth-variant phase errors, which may not totally suppress azimuth ambiguities especially for very strong targets. This letter presents an azimuth-variant phase error calibration technique. The proposed technique first selects a strong point-like target as the calibration source. Then, the azimuth-variant phase errors can be estimated by comparing the phase of the calibration source and the corresponding steering vector in the range-compressed signals. Besides, a preprocessing method is presented to improve the calibration accuracy when the selected calibration source is affected by noise or interferences. Theoretical analysis and experiments demonstrate the feasibility of the proposed technique.

Fast channel phase error calibration algorithm for azimuth multichannel high-resolution and wide-swath synthetic aperture radar imaging system

The configuration of multiple uniformly spaced channels in azimuth can achieve high-resolution and wide-swath images for synthetic aperture radar (SAR) systems. The unambiguous Doppler spectrum can be reconstructed via digital beamforming (DBF) techniques in the azimuth multichannel SAR system. However, the performance of DBF deteriorates significantly because of the inevitable channel errors in practical applications. Since the SAR antennas are generally unweighted in azimuth, the power of the SAR signal is symmetrically distributed around the Doppler centroid in the azimuth frequency domain. Based on this observation, the covariance matrix of multichannel output in the range-Doppler domain can be regarded as a real matrix when there is no existence of channel errors and the correction of the baseband Doppler centroid is applied. Consequently, we propose a fast calibration algorithm to calculate channel phase errors. The proposed method can acquire the estimation of phase errors directly from the covariance matrix. Thus, the proposed method has the properties of high robustness and low computation load. Theoretical analysis and experiments validate the performance and the efficiency of the proposed algorithm.

Robust Channel Phase Error Calibration Algorithm for Multichannel High-Resolution and Wide-Swath SAR Imaging

High-resolution and wide-swath synthetic aperture radar (SAR) imaging can be achieved by the azimuth multichannel system. The minimum variance distortionless response (MVDR) beamformer can be utilized to suppress azimuth ambiguities. However, the presence of channel phase errors significantly deteriorates the performance of the azimuth multichannel SAR system. Instead of employing subspace techniques, this letter proposes a robust channel phase error calibration algorithm via maximizing the MVDR beamformer output power. Compared with the conventional subspace-based calibration methods, there is no redundancy of channels required to estimate the subspaces in the proposed algorithm. Also, the proposed algorithm is relatively robust, because it avoids the subspace swap phenomenon, which probably takes place at low signal-to-noise ratios for the subspace techniques. Moreover, the proposed method has the advantage of estimating the channel phase errors without covariance matrix decomposition, which reduces the computation load. The simulation experiments and the real data processing validate the effectiveness of the proposed calibration method.