Residual Phase Error Research Articles

Autofocusing circular synthetic aperture sonar imagery using phase corrections modeled as generalized cones.

Circular synthetic aperture sonar (CSAS) is a coherent aperture synthesis technique that utilizes backscattered acoustic information from an encircled scene to generate information rich, high-resolution imagery. The aperture length required for image synthesis is much longer than in its linear synthetic aperture sonar counterpart and can result in challenging phase delay and navigation estimation constraints. Residual uncorrected phase errors manifest as focus aberrations in reconstructed CSAS imagery. This paper demonstrates that phase error in image patches can be approximated as an aspect variant linear phase shift representable as a generalized cone in wave-number space. If the geometry of the generalized cone is known, it can be applied as the spectral phase of an inverse filter for aberration correction. A method is derived for reconstructing the error cone geometry from independent estimates of its local curvatures, which are found via a series of one-dimensional line searches that maximize the focus of CSAS sub-aperture images. This approach is applied to real and simulated CSAS data containing aperture distortions, and the results successfully demonstrate estimation and correction of the underlying focus aberrations.

Multichannel HRWS SAR Imaging Based on Range-Variant Channel Calibration and Multi-Doppler-Direction Restriction Ambiguity Suppression

In order to obtain high-resolution wide-swath (HRWS) images, the multichannel in azimuth synthetic aperture radar (SAR) system has been adopted to deal with the contradiction problem between high resolution and low pulse repetition frequency (PRF). In this paper, a novel channel-calibration method is proposed for the multichannel in azimuth HRWS SAR imaging system. During the channel calibration, the mismatch between the channels, which results from the gain-phase error and the range sampling time error, is first corrected by the coarse-calibration processing in the range frequency domain. Then, the along azimuth baseline measurement error is estimated. Considering the range variance in the residual phase error, the data are processed in blocks along the range time domain, and the error of every subblock data is estimated. After that, a fitting and filtering is implemented along the range to the estimated values of the phase error of all subblocks. The range-variant phase error is then compensated using their estimated values. After channel calibration, this paper also presents a new Doppler ambiguity suppression algorithm which nulls the ambiguity components in the Doppler domain. The newly proposed algorithm outperforms the post-Doppler ambiguity suppression algorithm. The airborne real measured scan synthetic aperture radar data, which are acquired by a seven-channel in azimuth SAR imaging system with the system working at X-band, are utilized to demonstrate the performance of the newly proposed channel-calibration method and the new Doppler ambiguity suppression algorithm.

GNSS 수신기를 위한 낮은 복잡도를 갖는 새로운 반송파 대 잡음 전력비 추정기법

Abstract: The carrier-to-noise power ratio is a key parameter for determining the reliability of PVT (Position, Velocity, and Time) solutions which are obtained by a GNSS (Global Navigation Satellite System) receiver. It is also used for locking a tracking loop, deciding the re-acquisition process, and processing advanced navigation in the receiver subsystem. The representative carrier-to-noise power ratio estimation schemes are the narrowband-wideband power ratio method (NW), the MM (Moment Method), and Beaulieu’s method (BL). The NW scheme is the most classical one for commercial GNSS receivers. It is often used as an authoritative benchmark for assessing carrier-to-noise power estimation schemes. The MM scheme is the least biased solution among them, and the BL scheme is a simpler scheme than the MM scheme. This paper focuses on the less biased estimation with low complexity when the residual phase noise remains, then proposes a novel carrier-to-noise power ratio estimation scheme with low complexity for GNSS receivers. The asymptotic bias of the proposed scheme is derived and compared with others, and the simulation results demonstrate that the complexity of the proposed scheme is lowest among them, while the estimation performance of the proposed scheme is similar to those of the BL and MM schemes in normal and high gained reception environments.Keywords: GNSS, carrier-to-noise power ratio estimator, complexity, residual phase error, asymptotic bias

A Rotating Synthetic Aperture Radar Imaging Concept for Robot Navigation

This paper introduces a concept for robot navigation based on a rotating synthetic aperture short-range radar scanner. It uses an innovative broadband holographic reconstruction algorithm, which overcomes the typical problem of residual phase errors caused by an imprecisely measured aperture position and moving targets. Thus, it is no longer necessary to know the exact trajectory of the synthetic aperture radar to get a high-resolution image, which is a major advantage over the classical holographic reconstruction algorithm. However, the developed algorithm is not only used to compute a high-resolution 360 ° 2-D image after each turn of the radar platform while the robot is moving, but also to calculate the relative residual radial velocity between the moving radar scanner system and all targets in the environment. This allows us to determine the exact velocity of the robotic system on which the radar scanner is mounted, and thus to obtain the exact radar trajectory, if there are stationary targets like walls in the environment.

Experiments and Perturbative Analysis of Dammann-Grating-Based Aperture Filling in a Passive Coherent Beam Combination

A Dammann-grating-based aperture filling technology is demonstrated in a passive coherent beam combination fiber amplifier array, which is phase-locked using an all-optical feedback loop. The maximum output power is 206 W. The combined efficiency of a three channels aperture filling is discussed and demonstrated to vary with the output power. Perturbative factors leading to the loss of the combined efficiency are theoretically simulated and the key factor is the residual phase error. Theoretical and experimental results show that this technology has good potential to achieve higher brightness in a single beam.

An improved OFDM chirp waveform used for MIMO SAR system

Special attention has been devoted to multi-input multi-output (MIMO) synthetic aperture radar (SAR) systems in recent years. The applications of MIMO SAR systems which involve 3D imaging, highresolution wide-swath remote sensing, and multi-baseline interferometry are seriously limited to the orthogonal waveforms. Although orthogonal frequency division multiplexing (OFDM) chirp waveforms can be used for MIMO SAR systems to avoid intra-pulse interferences, there is a small frequency shift between the transmitted OFDM pulses. This vulnerable shift, which can not only affect the waveform orthogonality, but also introduce residual phase error, renders the OFDM waveforms impractical. In this paper, an improved OFDM chirp waveform which works without the mentioned shift is presented, along with the novel modulation and efficient demodulation procedures. Comparison between the improved and the conventional OFDM chirp waveforms is detailed. The influence of random noise, quantization error, and Doppler shift on the orthogonality of OFDM waveform is also investigated in this paper. Theoretical analysis and simulation results illustrate the feasibility of this waveform scheme.

Multi-step vortex filtering for phase extraction

A quantized version of a continuous spiral phase filter with unitary topological charge, here denominated multi-step spiral phase filter (MSSPF), is proposed to extract phase from rotated spiral interferograms. Spiral interferograms are usually obtained from phase objects by registering the interference of its vortex filtered complex amplitude with a reference complex amplitude. The structure found in this kind of interferograms, depend on the number of steps used in the MSSPF that usually are assumed with an infinite number of steps for the continuous spiral phase filter. Reducing the number of steps of the MSSPF affects the residual phase error obtained after the phase extraction method. This error is therefore analysed here using a numerical simulation of a Mach-Zender interferometer with a MSSPF and a reduced number of steps. It is shown that, for our proposed method of rotated spiral interferograms, a residual error persists as the number of steps is increased approaching the residual error reported for the phase extraction method of single-shot spiral interferograms. Furthermore, it is shown that this novel technique can be applied without further modifications for phase contrast measurement. Experimental results show similar performance of this phase extraction technique, when compared to the results obtained with a commercial interferometer and with the numerical simulations.

High-precision optical phase-locking based on wideband acousto-optical frequency shifting

We present a high-precision optical phase-locking based on wideband acousto-optical frequency shifting. Increasing the modulating bandwidth stabilizes the loop at a high loop gain, thus improving phase correction capability. An optical phase-locked loop with a wide control bandwidth is constructed. The closed-loop residual phase error is only 0.26o or smaller than \lambda/1000. The loop exhibits excellent correction capability for high-frequency noises. The correctable frequency range reaches 35 kHz when the noise amplitude is +(-)\lambda/2, and becomes even wider for smaller noise amplitudes.

Robust Autofocusing Approach for Highly Squinted SAR Imagery Using the Extended Wavenumber Algorithm

For highly squinted synthetic aperture radar (SAR) imaging, the wavenumber domain SAR processing algorithm is commonly accepted as an ideal solution to SAR focusing in the case of an ideal straight sensor trajectory. However, airborne SAR is very sensitive to atmospheric turbulence that causes serious trajectory deviations. In this paper, we propose a robust autofocusing approach for highly squinted airborne SAR imagery using the extended wavenumber algorithm, being capable of estimating the range-dependent phase errors. To apply the proposed autofocusing scheme, a detailed analysis of the motion error model in the conical reference system is presented, where the formulation of range-dependent phase errors for squinted SAR is given. The proposed autofocusing approach is performed by a three-step process: referring to the inevitable residual phase after deramping for highly squinted SAR, a modified squinted phase gradient autofocusing (SPGA) algorithm is put forward to retrieve the range-independent phase errors; based on the established motion error model, the residual range-dependent phase errors are estimated using a local maximum likelihood-weighted SPGA algorithm; and motion compensation is executed by a two-step approach to reach the range-independent and range-dependent corrections, respectively. Experiments based on measured data have shown that the proposed autofocusing approach performs well for highly squinted SAR imaging.

Non-Data-Aided Phase Noise Suppression Scheme for CO-OFDM Systems

We propose a non-data-aided phase noise compensation technique that overcomes the limitation of the zero-overhead decision-directed (DD) phase noise suppression method in high-order constellations for coherent optical orthogonal frequency division multiplexing (CO-OFDM) systems. The proposed technique consists of two equalization stages. First, a blind adaptive phase offset recovery scheme based on high-order statics, called the dispersion minimization de-rotator, is applied to subcarrier symbols to achieve rough correction of the common phase error because of phase noise. Second, the conventional DD phase noise correction scheme is used to remove the residual common phase error. The proposed method effectively compensates phase noise without the help of pilot signals, especially for high-order constellation CO-OFDM systems, as confirmed by our simulation results.

Power Constrained Partially Coherent Distributed Detection Over Fading Multiaccess Channels

In this paper, we consider the problem of power constrained partially coherent distributed detection over fading multiaccess channels. The deflection coefficient maximization is used to optimize the performance of detectors. For a partially coherent distributed detection system, the phase synchronization is imperfect at the fusion center; the residual phase error is modeled by the Tikhonov probability distribution function. Two cases of the channel gain information are considered separately at the fusion center: one case with perfect channel gain [the corresponding method is referred to as partially coherent deflection coefficient maximization (PC-DCM)], the other case with statistical information of channel gain (the corresponding method is referred to as PC-DCM-CS, with CS being the abbreviation for “channel statistics”). We derive the closed-form solutions to the considered problems. Monte Carlo simulations are carried out to verify the performance of the proposed methods. Simulation results show that the newly proposed methods could significantly improve the detection performance of the fusion system under a low signal-to-noise ratio and low false alarm probability.

Phase synchronization processing method for alternating bistatic mode in distributed SAR

In the distributed synthetic aperture radar (SAR), the alternating bistatic mode can perform phase reference without a synchronization link between two satellites compared with the pulsed alternate synchronization method. The key of the phase synchronization processing is to extract the oscillator phase differences from the bistatic echoes. A signal model of phase synchronization in the alternating bistatic mode is presented. The phase synchronization processing method is then studied. To reduce the phase errors introduced by SAR imaging, a sub-aperture processing method is proposed. To generalize the sub-aperture processing method, an echo-domain processing method using correlation of bistatic echoes is proposed. Finally, the residual phase errors of the both proposed processing methods are analyzed. Simulation experiments validate the proposed phase synchronization processing method and its phase error analysis results.

Compensation for the NsRCM and Phase Error After Polar Format Resampling for Airborne Spotlight SAR Raw Data of High Resolution

When the range migration caused by motion error exceeds the range cell resolution, the performance of a conventional phase autofocus approach degrades. In this paper, a new adaptive motion compensation (MoCo) algorithm with the removal of the migration that is nonsystematic has been developed for airborne spotlight synthetic aperture radar (SAR) imagery with high resolution. In the algorithm, the relationship between nonsystematic range cell migration (NsRCM) and phase error was first explicitly revealed after the polar format algorithm resampling. The NsRCM could be readily calculated by coarse but reliable phase error estimation. Subsequently, the NsRCM and the bulk of the azimuth phase error were corrected. After the removal of the NsRCM, degradation of the conventional phase autofocus resulting from sidelobe increase as well as mainlobe broadening was avoided. Finally, a fine MoCo procedure was performed to remove the residual azimuth phase error satisfactorily. Through the analysis of the airborne spotlight SAR raw data with high-resolution and wide-swath illumination, a well-focused imagery was obtained. Quantitative assessment of the image quality was satisfactory. The MoCo algorithm was validated.

Channel Phase Error Estimation and Compensation for Ultrahigh-Resolution Airborne SAR System Based on Echo Data

For a new kind of ultrahigh-resolution airborne synthetic aperture radar system, a novel two-step approach to estimate and compensate channel phase error based on echo data is presented in this letter. According to the relationship between phase error and pulse compression, the residual channel phase error after internal calibration is modeled as frequency-domain polynomials and divided into two parts. By establishing an optimization estimation model, two parts of the channel phase error can be estimated and compensated successively from a small amount of echo data, which result in the advantage of few storage consumption and fast convergence speed while making up for the insufficiency of system calibration method. Actual eight-channel raw data have been processed, the result of which demonstrates the validity of the presented approach.

Phase-locking and coherent power combining of broadband linearly chirped optical waves

We propose, analyze and demonstrate the optoelectronic phase-locking of optical waves whose frequencies are chirped continuously and rapidly with time. The optical waves are derived from a common optoelectronic swept-frequency laser based on a semiconductor laser in a negative feedback loop, with a precisely linear frequency chirp of 400 GHz in 2 ms. In contrast to monochromatic waves, a differential delay between two linearly chirped optical waves results in a mutual frequency difference, and an acoustooptic frequency shifter is therefore used to phase-lock the two waves. We demonstrate and characterize homodyne and heterodyne optical phase-locked loops with rapidly chirped waves, and show the ability to precisely control the phase of the chirped optical waveform using a digital electronic oscillator. A loop bandwidth of ~ 60 kHz, and a residual phase error variance of < 0.01 rad(2) between the chirped waves is obtained. Further, we demonstrate the simultaneous phase-locking of two optical paths to a common master waveform, and the ability to electronically control the resultant two-element optical phased array. The results of this work enable coherent power combining of high-power fiber amplifiers-where a rapidly chirping seed laser reduces stimulated Brillouin scattering-and electronic beam steering of chirped optical waves.

Coherent polarization beam combining of four fiber amplifiers in 100 ns pulsed-regime

We demonstrate the coherent polarization beam combining (CPBC) of four polarization-maintained fiber amplifiers in 100ns-pulse regime using single frequency dithering technique for the first time. Experimental results reveal that phase noise of each amplifier chain can be effectively suppressed. The combining efficiency of the CPBC system is 92% and the residual phase error is less than λ/20. The intensity profile of the coherently polarization combined beam is steady for long time observation without degradation of the beam quality.

Coherent phase lock of a 9 μm quantum cascade laser to a 2 μm thulium optical frequency comb

We demonstrate coherent phase locking of a room-temperature continuous-wave quantum cascade laser (QCL) at 9.1μm to a Tm-fiber laser frequency comb centered at 2μm, with an integrated residual phase error of 0.9rad (30mHz to 1.5MHz). This resulted in a QCL linewidth reduction from 525 to 25kHz at 1ms observation time, limited by the linewidth of the free-running frequency comb.

A digital optical phase-locked loop for diode lasers based on field programmable gate array

We have designed and implemented a highly digital optical phase-locked loop (OPLL) for diode lasers in atom interferometry. The three parts of controlling circuit in this OPLL, including phase and frequency detector (PFD), loop filter and proportional integral derivative (PID) controller, are implemented in a single field programmable gate array chip. A structure type compatible with the model MAX9382∕MCH12140 is chosen for PFD and pipeline and parallelism technology have been adapted in PID controller. Especially, high speed clock and twisted ring counter have been integrated in the most crucial part, the loop filter. This OPLL has the narrow beat note line width below 1 Hz, residual mean-square phase error of 0.14 rad(2) and transition time of 100 μs under 10 MHz frequency step. A main innovation of this design is the completely digitalization of the whole controlling circuit in OPLL for diode lasers.

SAR image reconstruction and autofocus by compressed sensing

A new SAR signal processing technique based on compressed sensing is proposed for autofocused image reconstruction on subsampled raw SAR data. It is shown that, if the residual phase error after INS/GPS corrected platform motion is captured in the signal model, then the optimal autofocused image formation can be formulated as a sparse reconstruction problem. To further improve image quality, the total variation of the reconstruction is used as a penalty term. In order to demonstrate the performance of the proposed technique in wide-band SAR systems, the measurements used in the reconstruction are formed by a new under-sampling pattern that can be easily implemented in practice by using slower rate A/D converters. Under a variety of metrics for the reconstruction quality, it is demonstrated that, even at high under-sampling ratios, the proposed technique provides reconstruction quality comparable to that obtained by the classical techniques which require full-band data without any under-sampling.

Satellite- and Epoch Differenced Precise Point Positioning Based on a Regional Augmentation Network

Precise Point Positioning (PPP) has been demonstrated as a simple and effective approach for user positioning. The key issue in PPP is how to shorten convergence time and improve positioning efficiency. Recent researches mainly focus on the ambiguity resolution by correcting residual phase errors at a single station. The success of this approach (referred to hereafter as NORM-PPP) is subject to how rapidly one can fix wide-lane and narrow-lane ambiguities to achieve the first ambiguity-fixed solution. The convergence time of NORM-PPP is receiver type dependent, and normally takes 15–20 min. Different from the general algorithm and theory by which the float ambiguities are estimated and the integer ambiguities are fixed, we concentrate on a differential PPP approach: the satellite- and epoch differenced (SDED) approach. In general, the SDED approach eliminates receiver clocks and ambiguity parameters and thus avoids the complicated residual phase modeling procedure. As a further development of the SDED approach, we use a regional augmentation network to derive tropospheric delay and remaining un-modeled errors at user sites. By adding these corrections and applying the Robust estimation, the weak mathematic properties due to the ED operation is much improved. Implementing this new approach, we need only two epochs of data to achieve PPP positioning converging to centimeter-positioning accuracy. Using seven days of GPS data at six CORS stations in Shanghai, we demonstrate the success rate, defined as the case when three directions converging to desired positioning accuracy of 10 cm, reaches 100% when the interval between the two epochs is longer than 15 min. Comparing the results of 15 min' interval to that of 10 min', it is observed that the position RMS improves from 2.47, 3.95, 5.78 cm to 2.21, 3.93, 4.90 cm in the North, East and Up directions, respectively. Combining the SDED coordinates at the starting point and the ED relative coordinates thereafter, we demonstrate the performance of RTK PPP with standard deviation of 0.80, 1.34, 0.97 cm in the North, East and Up directions.