Presence Of Phase Errors Research Articles

Channel estimation with Zadoff–Chu sequences in the presence of phase errors

AbstractDue to their perfect periodic autocorrelation property, Zadoff–Chu sequences are often used as stimulus signals in the measurement of radio channel responses. In this letter, the cross‐correlation of a linear shift‐invariant system's response to a Zadoff–Chu sequence is derived for the case that a multiplicative perturbation such as phase noise is present at its output. The perturbation signal is shown to incur a spurious discrete Fourier transform, thus degrading the correlation's peak to sidelobe ratio. The implications for the performance limits of channel measurement systems are discussed.

Reducing phase errors in multimode interference coupler by side grooves formed on its top surface.

The performance of multimode interference (MMI) couplers is limited by the presence of phase errors that represent the deviation of the propagation constants of the modes from the quadratic dependence on their order. In this work, we propose a simple and effective method for reducing the phase errors of spatial modes to a relatively high order by forming rectangular grooves near the side edges of the MMI coupler along its entire length. The influence of the groove dimensions and position on the propagation constants of higher-order modes is analyzed using the perturbation method and strict vector simulations for high- and medium-index contrast material platforms. Through numerical simulations, we demonstrate the effectiveness of the proposed method in improving the performance of air-cladded dual-mode (T E 0 and T E 1) MMI-based 50:50 and 100:0 splitters for 1.31µm wavelength made of medium- and high-contrast materials, T i O 2:S i O 2/S i O 2 and S i/S i O 2, respectively.

BER Reduction Using Partial-Elements Selection in IRS-UAV Communications With Imperfect Phase Compensation

This article considers minimizing the communications bit error rate (BER) of unmanned aerial vehicles when assisted by intelligent reflecting surfaces. By noting that increasing the number of IRS elements in the presence of phase errors does not necessarily improve the system’s BER, it is crucial to use only the elements that contribute to reducing such a parameter. To this end, we propose an efficient algorithm to select the elements that can improve BER. The proposed algorithm has lower complexity and comparable BER to the optimum selection process, which is an NP-hard problem. The accuracy of the estimated phase is evaluated by deriving the probability distribution function (PDF) of the least-square channel estimator, and showing that the PDF can be closely approximated by the von Mises distribution at high signal-to-noise ratios. The obtained analytical and simulation results show that using all the available reflectors can significantly deteriorate the BER, and thus, partial element selection is necessary. It is shown that, in some scenarios, using about 26% of the reflectors provides more than tenfold BER reduction. The number of selected reflectors may drop to only 10% of the total elements. As such, the unassigned 90% of the elements can be allocated to serve other users, and the overhead associated with phase information is significantly reduced.

Phase errors and statistical analysis of silicon-nitride arrayed waveguide gratings.

We present a statistical analysis of arrayed waveguide gratings (AWGs) in the presence of phase errors in the optical waveguides caused by fabrication process variations. Important figures of merit, such as the insertion loss, crosstalk, and non-uniformity, are parameterized as a function of the coherence length, a physical parameter that characterizes the accumulated phase errors in optical waveguides and that can be extracted by measuring variations in the resonant wavelengths of Mach-Zehnder interferometers. A die-level coherence length of 23.7 mm is measured for sub-micrometer-thick silicon nitride (SiN) waveguides fabricated using a 200-mm wafer process. Through Monte Carlo simulations using a semi-analytical model, we examine the impacts of phase errors on the performance of AWGs with 200 GHz and 100 GHz channel spacings. Our results show that the waveguide phase errors cause remarkable excess insertion loss and crosstalk in an AWG, and also increase non-uniformity across channels.

Phase Calibration for Intelligent Reflecting Surfaces Assisted Millimeter Wave Communications

In this paper, wepropose a novel two-stage transmission framework for an intelligent reflecting surface (IRS) assisted millimeter wave (mmWave) system in the presence of phase error caused by hardware impairments. Specifically, in Stage I, we introduce a pilot-based phase calibration task and reformulate it as an alternating optimization program. Building on this formulation, an efficient iterative algorithm is developed to jointly estimate the phase error, which needs to be calibrated, and the channels corresponding to the first user. Stage II consists of two blocks, channel estimation and data transmission. During the channel estimation block, by leveraging on the sparsity of mmWave channels, we propose a fast Fourier transform based scheme to estimate the IRS-BS channel and user-IRS channels. During the data transmission block, based on the estimated channel state information, base station precoders and IRS phase shifts are jointly optimized to maximize the sum signal-to-leakage-plus-noise ratio of all users. To handle this non-convex problem, we further develop a low-complexity joint beamforming algorithm by exploiting fractional programming techniques. Moreover, to examine the performance of the proposed phase calibration scheme, we derive the Cramer-Rao lower bound for the intended phase error estimation. Simulation results validate the effectiveness of our proposed transmission framework and the necessity of IRS phase calibration.

Bit Error Floor Reduction for MQAM Signals in the Presence of Phase Error

Bit Error Floor Reduction for MQAM Signals in the Presence of Phase Error

Compressive Synthetic Aperture Radar Imaging and Autofocusing by Augmented Lagrangian Methods

We consider the problem of synthetic aperture radar (SAR) image reconstruction from undersampled data in the presence of phase errors. We formulate the problem as one of estimating both the phase errors and the underlying image simultaneously through optimization. Within that optimization framework, we use a combination of priors that have proven useful in radar imaging, including strong sparse scattering in the image domain, as well as piecewise smoothness (i.e., gradient sparsity). To solve the resulting optimization problems, we propose an alternating direction method of multipliers (ADMM), an augmented Lagrangian method, for compressive SAR image reconstruction. We use simulated and real data at varying undersampling rates to study the performance of the proposed method and compare it against existing methods in terms of convergence speed and reconstruction quality. Our method provides significant improvements in terms of image reconstruction quality and computation speed, as well as phase error estimation performance.

Three-sided pyramid wavefront sensor, part 1: simulations and analysis for astronomical adaptive optics

The Giant Segmented Mirror Telescopes (GSMTs) including the Giant Magellan Telescope (GMT), the Thirty Meter Telescope (TMT), and the European Extremely Large Telescope (E-ELT), all have extreme adaptive optics (ExAO) instruments planned that will use pyramid wavefront sensors (PWFS). The ExAO instruments all have common features: a high-actuator-count deformable mirror running at extreme speeds (>1 kHz); a high-performance wavefront sensor (WFS); and a high-contrast coronagraph. ExAO WFS performance is currently limited by the need for high spatial sampling of the wavefront which requires large detectors. For ExAO instruments for the next generation of telescopes, alternative architectures of WFS are under consideration because there is a trade-off between detector size, speed, and noise that reduces the performance of GSMT-ExAO wavefront control. One option under consideration for a GSMT-ExAO wavefront sensor is a three-sided PWFS (3PWFS). The 3PWFS creates three copies of the telescope pupil for wavefront sensing, compared to the conventional four-sided PWFS (4PWFS), which uses four pupils. The 3PWFS uses fewer detector pixels than the 4PWFS and should therefore be less sensitive to read noise. Here we develop a mathematical formalism based on the diffraction theory description of the Foucault knife-edge test that predicts the intensity pattern after the PWFS. Our formalism allows us to calculate the intensity in the pupil images formed by the PWFS in the presence of phase errors corresponding to arbitrary Fourier modes. We use these results to motivate how we process signals from a 3PWFS. We compare the raw intensity (RI) method, and derive the Slopes Maps (SM) calculation for the 3PWFS, which combines the three pupil images of the 3PWFS to obtain the X and Y slopes of the wavefront. We then use the Object Oriented MATLAB Adaptive Optics toolbox (OOMAO) to simulate an end-to-end model of an AO system using a PWFS with modulation and compare the performance of the 3PWFS to the 4PWFS. In the case of a low read noise detector, the Strehl ratios of the 3PWFS and 4PWFS are within 0.01. When we included higher read noise in the simulation, we found a Strehl ratio gain of 0.036 for the 3PWFS using RI over the 4PWFS using SM at a stellar magnitude of 10. At the same magnitude, the 4PWFS RI also outperformed the 4PWFS SM, but the gain was only 0.012 Strehl. This is significant because 4PWFS using SM is how the PWFS is conventionally used for AO wavefront sensing. We have found that the 3PWFS is a viable WFS that can fully reconstruct a wavefront and produce a stable closed-loop with correction comparable to that of a 4PWFS, with modestly better performance for high read-noise detectors.

Parameter accuracy analysis of weak-value amplification process in the presence of noise* *Project supported by the National Key Research and Development Program of China (Grant No. 2017YFA0305200), the National Natural Science Foundation of China (Grant Nos. 11674234 and 11605205), the Natural Science Foundation of Chongqing (Grant Nos. cstc2015jcyjA00021 and cstc2018jcyjAX0656), the Innovation Project of Sichuan University (Grant No. 2018SCUH0021), the

We theoretically introduce the statistical uncertainty of photon number and phase error to discuss the precision of parameters to be measured based on weak measurements. When the photon counting scheme is used, we discuss the relative accuracy of the system in the presence of phase error by using the orthogonal and nonorthogonal pre- and post-selected states, respectively. When using the measurement scheme of pointer shift, we discuss the measurement accuracy in the presence of phase error, pointer resolution, and statistical uncertainty. These results give a guide way to get the smallest relative precision and deepen our understanding about weak measurement.

Coherency‐Broken Bragg Filters: Overcoming On‐Chip Rejection Limitations

AbstractSelective optical filters with high rejection levels are of fundamental importance for a wide range of advanced photonic circuits. However, the implementation of high‐rejection on‐chip optical filters is seriously hampered by phase errors arising from fabrication imperfections. Due to coherent interactions, unwanted phase‐shifts result in detrimental destructive interferences that distort the filter response, whatever the chosen strategy (resonators, interferometers, Bragg filters, etc.). State‐of‐the‐art high‐rejection filters partially circumvent the sensitivity to phase errors by means of active tuning, complicating device fabrication and operation. Here, a new approach based on coherency‐broken Bragg filters is proposed to overcome this fundamental limitation. Non‐coherent interaction among modal‐engineered waveguide Bragg gratings separated by single‐mode waveguides is exploited to yield effective cascading, even in the presence of phase errors. This technologically independent approach allows seamless combination of filter stages with moderate performance free of active control, providing a dramatic increase of on‐chip rejection. Based on this concept, on‐chip non‐coherent cascading of Si Bragg filters is experimentally demonstrated, achieving a light rejection exceeding 80 dB, the largest value reported for an all‐passive silicon filter.

The Recombination Landscape in Wild House Mice Inferred Using Population Genomic Data.

Characterizing variation in the rate of recombination across the genome is important for understanding several evolutionary processes. Previous analysis of the recombination landscape in laboratory mice has revealed that the different subspecies have different suites of recombination hotspots. It is unknown, however, whether hotspots identified in laboratory strains reflect the hotspot diversity of natural populations or whether broad-scale variation in the rate of recombination is conserved between subspecies. In this study, we constructed fine-scale recombination rate maps for a natural population of the Eastern house mouse, Mus musculus castaneus. We performed simulations to assess the accuracy of recombination rate inference in the presence of phase errors, and we used a novel approach to quantify phase error. The spatial distribution of recombination events is strongly positively correlated between our castaneus map, and a map constructed using inbred lines derived predominantly from M. m. domesticus. Recombination hotspots in wild castaneus show little overlap, however, with the locations of double-strand breaks in wild-derived house mouse strains. Finally, we also find that genetic diversity in M. m. castaneus is positively correlated with the rate of recombination, consistent with pervasive natural selection operating in the genome. Our study suggests that recombination rate variation is conserved at broad scales between house mouse subspecies, but it is not strongly conserved at fine scales.

Phase Error Correction for Approximated Observation-Based Compressed Sensing Radar Imaging.

Defocus of the reconstructed image of synthetic aperture radar (SAR) occurs in the presence of the phase error. In this work, a phase error correction method is proposed for compressed sensing (CS) radar imaging based on approximated observation. The proposed method has better image focusing ability with much less memory cost, compared to the conventional approaches, due to the inherent low memory requirement of the approximated observation operator. The one-dimensional (1D) phase error correction for approximated observation-based CS-SAR imaging is first carried out and it can be conveniently applied to the cases of random-frequency waveform and linear frequency modulated (LFM) waveform without any a priori knowledge. The approximated observation operators are obtained by calculating the inverse of Omega-K and chirp scaling algorithms for random-frequency and LFM waveforms, respectively. Furthermore, the 1D phase error model is modified by incorporating a priori knowledge and then a weighted 1D phase error model is proposed, which is capable of correcting two-dimensional (2D) phase error in some cases, where the estimation can be simplified to a 1D problem. Simulation and experimental results validate the effectiveness of the proposed method in the presence of 1D phase error or weighted 1D phase error.

Bit Error Floor of MPSK in the Presence of Phase Error

In mobile communication systems, one of the most significant factors of the bit-error-rate (BER) performance degradation of $M$ -ary phase-shift keying (MPSK) is random phase error caused by phase-locked loop (PLL) or imperfect channel estimation. For high-signal-to-noise-power-ratio (SNR) regions, the effect of random phase error on BER performance becomes dominant and results in an irreducible BER called the bit error floor. In this paper, we derive a bit error floor expression of Gray-coded MPSK when random phase error exists and show that the bit error floor in fading channels converges to the bit error floor in additive white Gaussian noise (AWGN) channels. The derived expression is simple and accurate in the error floor region; hence, it can offer a convenient way to calculate the irreducible BER of MPSK in the presence of phase error.

Asynchronous Layered Modulation for High Spectral Efficiency Transmission with Lower Sensitivity to Phase Errors

In this paper, an asynchronous double layered modulation scheme is proposed to achieve high spectral efficiency transmission but has lower sensitivity to phase errors. By intentionally introducing a delay offset to the transmitted signals at each layer, the asynchronous double layered format can use lower level quadrature amplitude modulation (QAM) to achieve the same spectral efficiency as the conventional high level QAM modulation. The error probability performance of the asynchronous double layered format is analyzed in the presence of phase errors and the symbol error rate and the bit error rate are derived in the closed-form expression. Both the theoretical analysis and the simulation results show that the asynchronous layered format can achieve the same spectral efficiency as the conventional high level QAM modulation while has lower sensitivity to the phase errors.

Generalized BER Expression of MPSK in the Presence of Phase Error

In this letter, we derive an exact and general closed-form expression for the bit error rate (BER) of Gray coded M-ary phase shift keying (MPSK) in the presence of a fixed phase error. We also propose a very simple and tight approximate expression from the derived exact expression. To validate the exactness of the proposed exact and general expression and the tightness of the proposed approximation, we compare the results obtained from the proposed expressions with those from computer simulations. We also present the average BER results of MPSK for random phase errors caused by phase-locked loop or imperfect channel estimation by using the derived expressions.

ABEP of EGC Receiver over Composite and Non-homogenous Fading Channels with Phase Error and Co-channel Interference

Average bit error probability (ABEP) performance of a dual branch equal gain combining (EGC) receiver is analyzed in correlated composite fading channels and in independent and identically distributed (i.i.d.) non-homogenous fading channels in the presence of phase error and co-channel interference. Closed form expressions for moments of the combiner output signal to interference plus noise ratio are derived individually for correlated composite fading channels and i.i.d. non-homogenous fading channels. Using the obtained expressions, the ABEP for binary phase shift keying modulation is obtained, applying moment generating function and Padé approximation approach. Numerical and simulation results for different degrees of phase errors and different values of ρ are obtained. The results for special cases were checked with the available results.

Energy efficient collaborative communications in AWGN and Rayleigh fading channel in wireless sensor networks

Collaborative communication produces high power gain and significantly reduces bit error rate BER if both frequency and phase synchronization are achieved. In this paper, a novel collaborative communication system with imperfect phase and frequency synchronization that includes the influence of noise and fading is proposed, modeled, theoretically analyzed, and simulated. Mathematical expressions are derived for the received power as a function of number of collaborative nodes and BER as a function of signal to noise ratio Ebi¾?N0. To analyze the energy efficiency of our proposed collaborative communication system, energy consumption of the system is modeled, simulated, and analyzed by considering the parameters of the off-the-shelf products. Analytical and simulation results showed that the proposed system produces significant power gain and reduction in BER in the presence of phase errors, frequency errors, additive white Gaussian noise, and Rayleigh fading. A detailed theoretical analysis and Monte Carlo simulation revealed that the proposed collaborative communication system is an energy efficient communication system that can be implemented in sensor networks, as approximately N number of collaborative nodes times less total transmitted power is required than for the single input single output communication for a specifies transmission range. Copyright © 2012 John Wiley & Sons, Ltd.

Fourier-Domain Multichannel Autofocus for Synthetic Aperture Radar

Synthetic aperture radar (SAR) imaging suffers from image focus degradation in the presence of phase errors in the received signal due to unknown platform motion or signal propagation delays. We present a new autofocus algorithm, termed Fourier-domain multichannel autofocus (FMCA), that is derived under a linear algebraic framework, allowing the SAR image to be focused in a noniterative fashion. Motivated by the mutichannel autofocus (MCA) approach, the proposed autofocus algorithm invokes the assumption of a low-return region, which generally is provided within the antenna sidelobes. Unlike MCA, FMCA works with the collected polar Fourier data directly and is capable of accommodating wide-angle monostatic SAR and bistatic SAR scenarios. Most previous SAR autofocus algorithms rely on the prior assumption that radar's range of look angles is small so that the phase errors can be modeled as varying along only one dimension in the collected Fourier data. And, in some cases, implicit assumptions are made regarding the SAR scene. Performance of such autofocus algorithms degrades if the assumptions are not satisfied. The proposed algorithm has the advantage that it does not require prior assumptions about the range of look angles, nor characteristics of the scene.

Performance analysis of PSK systems with phase error in fading channels: A survey

Communication system designers need to formulate an accurate and thoroughly reproducible error model for wireless mobile channels in order to assess the quality of communication with different modulation schemes. The task is relatively easy when an ideal situation is assumed, and is covered exhaustively in standard text books. However, the random time-varying nature of radio propagation renders estimation of different channel state information (CSI) very difficult and when these non-idealities (e.g. imperfect phase/frequency/timing information) are considered, the formulation complexity increases manifold. In this paper, we have set our attention on phase shift keying (PSK), which suffers mostly from phase synchronization error when proper CSI is not available at the receiver. The article surveys various error modelling methods for a PSK system operating over a slow flat Nakagami- m distributed wireless fading channel perturbed with additive white Gaussian noise (AWGN) in the presence of phase error. The phase distortions are considered to be random, unbiased, i.e. having zero mean, and may be represented by either Gaussian or Tikhonov distribution. We also provide a novel approach to classify these schemes that are surveyed, and summarize the major contributions of related works. Further, we identify the method that requires lesser mathematical operations and thus proves to be less complex, more stable and accurate than others. Apart from this, simple alternative approaches for calculating analytical bit error rate (BER) through Hermite’s method of integration for Gaussian distributed phase error and through moment generating function (MGF) for Tikhonov distributed phase error have been proposed. Both of these methods have wider applicability, are able to furnish reproducible results, and show significant improvement in accuracy regarding theoretical BER calculation as seen from the graphical comparisons. Extensive Monte Carlo simulations were performed to validate the theoretical results.

Effect of feed phase errors on the crosspolarization of offset reflector antennas

AbstractThe impact of feed phase errors on the crosspolarization of offset reflector antennas is studied.The primary feed is assumed to be linearly polarized, with symmetrical E‐ and H‐plane patterns independent of ϕ. They are modeled by a cosnθ function, along with an extra term to account for the phase errors. Both linear and quadratic phase variations are studied. A broad range of focal length to diameter ratios, f/D from 0.5 to 1.1, are considered to investigate the crosspolarization properties in the presence of phase errors. It is shown that the reflector crosspolarization increases drastically when there is a linear phase error associated with the primary feed pattern. © 2010 Wiley Periodicals, Inc. Microwave Opt Technol Lett 53:231–235, 2011; View this article online at wileyonlinelibrary.com. DOI 10.1002/mop.25643