Imperfect Calibration Research Articles

Downlink Pilots for Hybrid Massive MIMO Under Reciprocity Imperfections

In this letter, we study the performance of a time division duplex (TDD) hybrid massive multiple input multiple output (MIMO) system with imperfect calibration of the transmit and receive radio frequency chains. Using deterministic equivalent (DE) analysis, we establish the loss in the achievable rates due to calibration imperfections. We then discuss limited downlink training to estimate the effective downlink channel, and compare the relative merits of this method against frequency division duplexed (FDD) operation. Finally, via detailed numerical simulations, we evaluate the relative performance of no downlink training, limited downlink training, and FDD mode operation in the presence of reciprocity calibration errors.

A Fast and Flexible Projector-Camera Calibration System

Existing projector-camera calibration methods typically warp keypoints from a camera image to a projector image using estimated homographies and often suffer from errors in camera parameters and noises due to imperfect planarity of the calibration target. This article proposes a practical and robust projector-camera calibration system that explicitly deals with these challenges. First, a graph-theory-based correspondence algorithm is built on top of a color-coded spatial structured light (SL) pattern. Such SL correspondences are then used for a coarse projector-camera calibration. To gain more robustness against noises from an imperfect planar calibration board, we develop a bundle adjustment algorithm to jointly optimize the estimated projector-camera parameters and the correspondences’ coordinates. Moreover, our system requires only one shot of an SL pattern for each calibration board pose, which is much more practical than multishot solutions. Comprehensive experimental validation is conducted on both synthetic and real data sets, and our method clearly outperforms the existing methods in all experiments. For the benefit of the society, a practical open-source software with graphical user interface (GUI) of the developed system is publicly available at <monospace xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><uri>https://github.com/bingyaohuang/single-shot-pro-cam-calib</uri></monospace> . <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Note to Practitioners</i> —The proposed method is motivated by two challenges in industrial structured light (SL) system calibration: 1) robustness against imperfect planarity of the calibration target and 2) the number of SL projections per pose. In many industrial SL-based 3-D reconstruction systems, the calibration accuracy greatly affects the reconstruction reliability. Our SL calibration system explicitly deals with calibration target’s imperfect planarity and thus outperforms the existing methods in terms of system accuracy. Another advantage of our SL calibration system is single-shot-per-pose, allowing fast recalibration and reducing the decoding error due to slight pattern misalignment in multishot methods <xref ref-type="bibr" rid="ref37" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">[37]</xref> . In addition, we release the open-source calibration software with a graphical user interface (GUI), with which calibration and sparse 3-D reconstruction can be easily performed without any further instructions. Moreover, considering the complex calibration environment and setup, we make the camera and projector imaging parameters, such as exposure, brightness, and contrast, adjustable through widgets and preview. Finally, a limitation of our color-coded SL system is its sensitivity to environment lighting and target texture. This problem may be solved by projector photometric compensation <xref ref-type="bibr" rid="ref16" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">[16]</xref> , <xref ref-type="bibr" rid="ref18" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">[18]</xref> , <xref ref-type="bibr" rid="ref19" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">[19]</xref> , <xref ref-type="bibr" rid="ref39" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">[39]</xref> .

Evaluation of Iceberg Calving Models Against Observations From Greenland Outlet Glaciers

AbstractFrontal ablation processes at marine‐terminating glaciers are challenging to observe and difficult to represent in numerical ice flow models, yet play critical roles in modulating ice sheet mass balance. Current ice sheet models typically rely on simple iceberg calving models to prescribe either terminus positions or iceberg calving rates, but the relative accuracies and uncertainties of these calving models remain largely unconstrained at the ice sheet scale. Here, we evaluate six published iceberg calving models against spatially and temporally diverse observations from 50 marine‐terminating outlet glaciers in Greenland. We seek the single model that best reproduces observed conditions across all glaciers, at all observation times, and with low sensitivity to calibration uncertainty. Five of six calving models can produce unbiased estimates of calving position or calving rate at the ice sheet scale. However, time series analysis reveals that, when using a single, optimized model parameter, rate‐predicting calving models frequently yield calving rate errors in excess of 10 m d−1. In comparison, terminus position‐predicting calving models more accurately track observed changes in terminus position (remaining within ~1 km of the observed grounded terminus position). Overall, our results indicate that the crevasse depth calving model provides the best balance of high accuracy and low sensitivity to imperfect parameter calibration. While the crevasse depth model appears unlikely to capture the true controls on crevasse penetration, numerically, it reproduces observed terminus dynamics with high fidelity and should be considered a leading candidate for use in models of the Greenland Ice Sheet.

Blind Channel Estimation for Downlink Massive MIMO Systems With Imperfect Channel Reciprocity

We consider the performance of time-division duplex (TDD) massive multiple-input multiple-output (MIMO) with imperfect calibration of the transmit and receive radio frequency chains. By deriving the achievable signal-to-interference-plus-noise ratio (SINR) and the per-user bit error rate (BER) for constant modulus constellations, we establish that, under linear precoding, reciprocity imperfections can result in substantial reduction of the array gain. To mitigate this loss, we propose an algorithm for blind estimation of the effective channel gain at each user. We show that, with sufficiently many downlink data symbols, our blind channel estimation algorithm restores the array gain. In addition, the proposed blind gain estimation algorithm can improve performance compared to standard hardening-based receivers even under perfect reciprocity. Following this, we derive the BERs for non-constant modulus constellations, viz. $M$ -PAM and $M$ -QAM. We corroborate all our derived results using numerical simulations.

Security bound of continuous-variable measurement-device-independent quantum key distribution with imperfect phase reference calibration

Phase reference calibration is a necessary procedure in practical continuous-variable measurement-device-independent quantum key distribution (CV-MDI-QKD) for the need of Bell-State Measurement (BSM). However, the phase reference calibration may become imperfect in practical applications. We explored the practical security of CV-MDI-QKD with imperfect phase reference calibration under realistic conditions of lossy and noisy quantum channel. Specifically, a comprehensive framework is developed to model and characterize the imperfection of practical phase reference calibration operation, which is mainly caused by the non-synchronization of two remote lasers in senders. Security analysis shows that the imperfect phase reference calibration has significant side effects on the performance and security of the CV-MDI-QKD protocol. A tight security bound to excess noise introduced by imperfect phase reference calibration is derived for reverse reconciliation against arbitrary collective attacks in the asymptotic limit, and the tolerance of the CV-MDI-QKD protocol to this excess noise is also obtained. This security analysis framework can eliminate the security hazards caused by imperfect phase reference calibration without changing the existing CV-MDI-QKD system structure.

3D Stereoscopy Video Production: Z-Depth Extraction and Optimized Rendering using Foundry Nuke

This paper proposed an effective and efficient 3D stereo Video production methodology for Stereo conversion of any image or video using the 3D compositing tool Foundry Nuke. For efficient S3D conversion, there are several pipelines uses by video production engineer into the industry. There are several technical issues during the 3D stereo production like spilling, reflection, translucency, occlusion, flickering and noise problems as well due to imperfect calibration. This paper presents a theoretical explanation of the principles of stereo vision systems, followed by a quick review of the state of the art. The research paper concludes with validating the assumption of 3D stereoscopy video conversion with film case studies to execute high-end 3d stereo video production quality with roto-based depth map extraction with optimized render conversion methodology.

GOCE gradiometer data calibration

The GOCE mission provides a unique gravity gradient dataset, which is used by most state-of-the-art global gravity field models. The quality of the gravity gradients of previous data releases degraded during the mission lifetime, which was often attributed to the increasing drag forces towards the end of the mission due to the approaching solar maximum and also, starting in August 2012, a sequence of five orbit lowerings. An imperfect calibration of the gravity gradiometer data was often suspected as root cause for the degradation. We present the novel method for the calibration of the GOCE gravity gradiometer data that was used for the official reprocessing of the GOCE gravity gradients in 2018. It is based on a comprehensive calibration model that includes quadratic factors and angular acceleration couplings as new calibration parameters. The calibration parameters are estimated from star tracker angular rates, gravity gradients calculated from a GRACE gravity field model and the condition that the three gradiometer arms measure the same non-gravitational acceleration. In addition to the GOCE data generated during science mode operations, we also use the data collected during satellite shaking mode operations. We demonstrate that applying the new method removes systematic errors to a large extent and, consequently, yields gravity gradients of superior and constant quality compared to previous data releases.

Comparison of the PPMXL and UCAC5 Catalogs with the Gaia DR2

Abstract Astrometric ground-based catalogs usually suffer from varied systematic errors. These systematic errors were hard to detect because there was no independent reference catalog complete to very faint limiting magnitudes (∼20 mag). This situation has changed since the second data release of the Gaia mission (Gaia DR2). We aim to investigate positions and the proper-motion (PM) system of two ground-based catalogs, the UCAC5 and PPMXL, referring to the Gaia DR2. The individual position in the Gaia DR2 is transferred by its PM to the epoch of other catalogs for comparison. Systematic errors that depend on the magnitude, color, and sky regions in the UCAC5 and PPMXL could be clearly seen. A different behavior between the northern and southern sky is found in the PPMXL, which is possibly inherited from the imperfect calibration of the PM system. Besides, we perform a quantitative analysis of global differences for positions and PMs by the vector spherical harmonics method in terms of 3 rotation angles, 3 glide parameters, and 10 quadrupole parameters. We find a large glide component of ∼8 mas along Z-axis and a rotation angle of ∼5 mas about Z-axis for positional offsets between the PPMXL and Gaia DR2. These terms are found to be insignificant between the UCAC5 and Gaia DR2. We show that the position and PM system of the UCAC5, a new reduction of ground-based observations in the frame of the Gaia reference system, has been largely improved. This indicates that systematic errors in positions and PMs obtained from ground-based observations are mostly impacted by a relatively poor reference catalog. But these observations can be reconstructed in the frame of a space-based reference catalog. In this sense, our results justify the tradition of space-calibrated ground-based astrometric catalogs.

The NANOGrav 11-year Data Set: Pulse Profile Variability

Abstract Access to 50 years of data has led to the discovery of pulsar emission and rotation variability on timescales of months and years. Most of this long-term variability has been seen in long-period pulsars, with relatively little focus on recycled millisecond pulsars. We have analyzed a 38-pulsar subset of the 45 millisecond pulsars in the NANOGrav 11-year data set, in order to review their pulse profile stability. The most variability, on any timescale, is seen in PSRs J1713+0747, B1937+21, and J2145−0750. The strongest evidence for long-timescale pulse profile changes is seen in PSRs B1937+21 and J1643−1224. We have focused our analyses on these four pulsars in an attempt to elucidate the causes of their profile variability. Effects of scintillation seem to be responsible for the profile modifications of PSR J2145−0750. We see evidence that imperfect polarization calibration contributes to the profile variability of PSRs J1713+0747 and B1937+21, along with radio frequency interference around 2 GHz, but find that propagation effects also have an influence. The changes seen in PSR J1643−1224 have been reported previously, yet elude explanation beyond their astrophysical nature. Regardless of cause, unmodeled pulse profile changes are detrimental to the accuracy of pulsar timing and must be incorporated into the timing models where possible.

Energy- and spectral-efficiency of zero-forcing beamforming in massive MIMO systems with imperfect reciprocity calibration: bound and optimization

In a time-division duplex (TDD) system with massive multiple input multiple output (MIMO), channel reciprocity calibration (RC) is generally required in order to cope with the reciprocity mismatch between the uplink and downlink channel state information. Currently, evaluating the achievable spectral efficiency (SE) and energy efficiency (EE) of TDD massive MIMO systems with imperfect RC (IRC) mainly relies on exhausting Monte Carlo simulations and it is infeasible to precisely and concisely quantify the achievable SE and EE with IRC. In this study, a novel method is presented for tightly bounding the achievable SE of massive MIMO systems with zero-forcing beamforming under IRC. On the basis of the analytical results, we demonstrate key insights for practical system design with IRC in three aspects: the scaling rule for interference power, saturation region of the SE, and the bound on the SE loss. Finally, the trade-off between spectral and energy efficiencies in the presence of IRC is determined with algorithms developed to optimize SE (EE) under a constrained EE (SE) value. The loss of optimal total SE and EE due to IRC is also quantified, which shows that the loss of optimal EE is more sensitive to IRC in a typical range of transmit power values.

Calibrating an Ionosonde for Ionospheric Attenuation Measurements.

Vertical ionospheric soundings have been performed at almost all ionospheric observatories with little attention to measuring the attenuation of the signal between transmission and reception. When the absorption has been determined, this has been achieved by comparing the received power after the first and second reflections, but this method has some limitations due to the unknown reflection coefficient of the ground and the non-continuous presence of the second reflection. This paper deals with a different method based on precise calibration of the sounding system, allowing determination of absolute signal attenuation after a single reflection. This approach is affected by a systematic error due to imperfect calibration of the antennas, but when the focus of interest is to measure a trend over a specified period, it is very accurate. The article describes how calibration was implemented, the measurement output formats, and finally it presents some results from a meaningful set of measurements in order to demonstrate what this method can accomplish.

Statistical 21-cm Signal Separation via Gaussian Process Regression Analysis

Detecting and characterizing the Epoch of Reionization and Cosmic Dawn via the redshifted 21-cm hyperfine line of neutral hydrogen will revolutionize the study of the formation of the first stars, galaxies, black holes and intergalactic gas in the infant Universe. The wealth of information encoded in this signal is, however, buried under foregrounds that are many orders of magnitude brighter. These must be removed accurately and precisely in order to reveal the feeble 21-cm signal. This requires not only the modeling of the Galactic and extra-galactic emission, but also of the often stochastic residuals due to imperfect calibration of the data caused by ionospheric and instrumental distortions. To stochastically model these effects, we introduce a new method based on `Gaussian Process Regression' (GPR) which is able to statistically separate the 21-cm signal from most of the foregrounds and other contaminants. Using simulated LOFAR-EoR data that include strong instrumental mode-mixing, we show that this method is capable of recovering the 21-cm signal power spectrum across the entire range $k = 0.07 - 0.3 \ \rm{h\, cMpc^{-1}}$. The GPR method is most optimal, having minimal and controllable impact on the 21-cm signal, when the foregrounds are correlated on frequency scales $\gtrsim 3$\,MHz and the rms of the signal has $\sigma_{\mathrm{21cm}} \gtrsim 0.1\,\sigma_{\mathrm{noise}}$. This signal separation improves the 21-cm power-spectrum sensitivity by a factor $\gtrsim 3$ compared to foreground avoidance strategies and enables the sensitivity of current and future 21-cm instruments such as the {\sl Square Kilometre Array} to be fully exploited.

Robust Foregrounds Removal for 21-cm Experiments

AbstractDirect detection of the Epoch of Reionization via the redshifted 21-cm line will have unprecedented implications on the study of structure formation in the early Universe. To fulfill this promise current and future 21-cm experiments will need to detect the weak 21-cm signal over foregrounds several order of magnitude greater. This requires accurate modeling of the galactic and extragalactic emission and of its contaminants due to instrument chromaticity, ionosphere and imperfect calibration. To solve for this complex modeling, we propose a new method based on Gaussian Process Regression (GPR) which is able to cleanly separate the cosmological signal from most of the foregrounds contaminants. We also propose a new imaging method based on a maximum likelihood framework which solves for the interferometric equation directly on the sphere. Using this method, chromatic effects causing the so-called “wedge” are effectively eliminated (i.e. deconvolved) in the cylindrical (k⊥, k∥) power spectrum.

Robust adaptive beamforming based on sparse representation technique

The problem of robust adaptive beamforming is addressed within the sparse representation framework. The basic idea of the proposed method is to calculate the adaptive beamformer (BF) with the combination of some easily obtained basic BFs, i.e. the conventional data-independent BFs and the loaded sample matrix inversion BFs. Through using the prior information of the spatial angular sector in which the signal of interest is located, a set of basic BFs pointed at this angular sector are calculated firstly. Then based on the observation that an adaptive BF with favourable performance can be obtained by the combination of only several basic BFs, a new sparse representation-based optimisation model is proposed to search for the adaptive BF. However, the initial optimisation model involves a non-convex constraint which makes the problem intractable. The authors show that the non-convex constraint can be relaxed properly and replaced with a convex one, and the resulting problem can be solved effectively with the interior point method. The obtained BF is robust against model mismatch caused by look direction error, imperfect array calibration etc. The effectiveness and robustness of the proposed method are demonstrated through extensive numerical experiments.

Performance Analysis of Multi-User Massive MIMO Downlink Under Channel Non-Reciprocity and Imperfect CSI

This paper analyzes the performance of linearly precoded time division duplex based multi-user massive MIMO downlink system under joint impacts of channel non-reciprocity (NRC) and imperfect channel state information (CSI). We consider a generic and realistic NRC model that accounts for transceiver frequency-response as well as mutual coupling mismatches at both user equipment (UE) and base station (BS) sides. The analysis covers two most prominent forms of linear precoding schemes, namely, zero-forcing (ZF) and maximum-ratio transmission (MRT), and assumes that only the statistical properties of the beamformed channel are used at the UE side to decode the received signal. Under the approximation of i.i.d. Gaussian channels, closed-form analytical expressions are derived for the effective signal to interference and noise ratios (SINRs) and the corresponding capacity lower bounds. The expressions show that, in moderate to high SNR, the additional interference caused by imperfect NRC calibration can degrade the performance of both precoders significantly. Moreover, ZF is shown to be more sensitive to NRC than MRT. Numerical evaluations with practical NRC levels indicate that this performance loss in the spectral efficiency can be as high as 42% for ZF, whereas it is typically less than 13% for MRT. It is also shown that due to the NRC, the asymptotic large-antenna performance of both precoders saturate to an identical finite level. The derived analytical expressions provide useful tools and valuable technical insight, e.g., into calculating the NRC calibration requirements in BSs and UEs for any given specific performance targets in terms of effective SINR or the system capacity bound.

Explicit Permittivity Determination of Medium-Loss Materials From Calibration-Independent Measurements

Calibration-dependent methods, before starting to measurements, require some sort of expensive calibration kits, which could reduce the accuracy of measurements due to the application of imperfect calibration standards. To eliminate such problems and reduce the overall cost of the measurement setup, in this research paper, a novel calibration-independent method has been proposed. Compared with other calibration-independent methods, our method not only extracts the complex permittivity ( $\varepsilon _{r}$ ) uniquely but also removes the need for any numerical method, which generally requires a good initial guess around a global minimum to obtain accurate $\varepsilon _{r}$ results. Non-iterative and unique $\varepsilon _{r}$ is determined by our method using raw (uncalirated) scattering (S-) parameter measurements of four different combinations of two non-reflecting measurement cells (the same length or different lengths) asymmetrically loaded by two identical samples with lengths $L$ and $2L$ (samples are flushed to the terminals of the measurement cells). $X$ -band waveguide measurements of the polyethylene sample ( $L = 3.85$ mm and $2L = 7.70$ mm) were conducted to validate our proposed method and compare its accuracy with other tested methods. An uncertainty analysis was performed to analyze the effect of any inaccurate sample thickness and offset in the position of the shifted sample, which is required by other calibration-independent method, on measured permittivity.

A Causal, Data-driven Approach to Modeling the Kepler Data

Astronomical observations are affected by several kinds of noise, each with its own causal source; there is photon noise, stochastic source variability, and residuals coming from imperfect calibration of the detector or telescope. The precision of NASA Kepler photometry for exoplanet science—the most precise photometric measurements of stars ever made—appears to be limited by unknown or untracked variations in spacecraft pointing and temperature, and unmodeled stellar variability. Here, we present the causal pixel model (CPM) for Kepler data, a data-driven model intended to capture variability but preserve transit signals. The CPM works at the pixel level so that it can capture very fine-grained information about the variation of the spacecraft. The CPM models the systematic effects in the time series of a pixel using the pixels of many other stars and the assumption that any shared signal in these causally disconnected light curves is caused by instrumental effects. In addition, we use the target star’s future and past (autoregression). By appropriately separating, for each data point, the data into training and test sets, we ensure that information about any transit will be perfectly isolated from the model. The method has four tuning parameters—the number of predictor stars or pixels, the autoregressive window size, and two L2-regularization amplitudes for model components, which we set by cross-validation. We determine values for tuning parameters that works well for most of the stars and apply the method to a corresponding set of target stars. We find that CPM can consistently produce low-noise light curves. In this paper, we demonstrate that pixel-level de-trending is possible while retaining transit signals, and we think that methods like CPM are generally applicable and might be useful for K2, TESS, etc., where the data are not clean postage stamps like Kepler.

Performance Analysis of TDD Reciprocity Calibration for Massive MU-MIMO Systems With ZF Beamforming

This study analyzes a two-way signaling method for time division duplex reciprocity calibration (RC) in multiuser beamforming systems. The system model of RC is established, and the estimation error of the RC coefficient is derived. The effect of this error is examined in terms of the user signal-to-interference-plus-noise ratio (SINR) and capacity. Results reveal the relationship between the user SINR and RC errors as well as the number of antennas and users. Moreover, the findings show that the colocated antenna array is less sensitive to calibration errors than the case of distributed antennas even if the calibration signal-to-noise ratio (SNR) is identical. The interference resulting from imperfect calibration becomes the determinant that constrains the performance, particularly when a high user SNR is required.

Modifying MVDR Beamformer for Reducing Direction-of-Arrival Estimation Mismatch

The minimum variance distortionless response (MVDR) beamforming algorithm is used in smart antenna design for wireless communication. The operation of MVDR is based on finding the optimum weight to direct the main lobe beam to the desired user location with a unity gain. MVDR is very sensitive to signature vector mismatch. This mismatch occurs due to waveform deformation, local scattering, imperfect array element calibration and element shape distortion, which leads to errors in finding the direction of arrival (DOA) of the signal. In this paper, a new technique to modify the MVDR is presented, modelled and evaluated. The proposed algorithm is named modified MVDR (MMVDR) and is dependent on reconstructing the signature vector (steering vector) and the covariance matrix to introduce accurate beamformer weight by re-localization the reference element to be in the middle of ULA, rather than at one end side. The new reference position partitions the array’s elements into two groups around this reference, which leads to treat received signals with identical phase along the array’s elements, as well as increasing the degree of freedom to deals with different types of uniform arrays. The evaluation results show that MMVDR outperforms MVDR with respect to beamformer accuracy, system cost, processing time and signal classification to overcome the errors in DOA estimation which occur due to fabrication and calibration errors.

Analysis of circuit imperfections in BosonSampling

BosonSampling is a problem where a quantum computer offers a provable speedup over classical computers. Its main feature is that it can be solved with current linear optics technology, without the need for a full quantum computer. In this work, we investigate whether an experimentally realistic BosonSampler can really solve BosonSampling without any fault-tolerance mechanism. More precisely, we study how the unavoidable errors linked to an imperfect calibration of the optical elements affect the final result of the computation. We show that the fidelity of each optical element must be at least 1 − O(1/n^2 ), where n refers to the number of single photons in the scheme. Such a requirement seems to be achievable with state-of-the-art equipment.