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Report presents comparative theoretical analysis of four conceptual techniques for initial estimation of carrier frequency of suppressed-carrier, binary-phase-shift-keyed radio signal. Each technique effected by open-loop analog/digital signal-processing subsystem part of Costas-loop phase-error detector functioning in closed-loop manner overall.
Since diffraction-limited imaging with a single aperture yields angular resolution approx. lambda/D, the attainment of high angular resolution with single apertures requires the construction of correspondingly large monolithic apertures, the whole surface of which must be figured to much less than a wavelength. At the longer wavelengths, it is impossible to build a sufficiently large single aperture: for example, at lambda 21 cm, arcsec resolution requires an aperture of diameter approx. 50 km. At the shorter wavelengths, the atmosphere imposes a natural limit in resolution of about one arcsec. However, another route is possible; that is, using synthetic apertures to image the sky. Synthetic apertures are now in use in many fields, e.g., radio interferometry, radar imaging, and magnetic-resonance imaging. Radio-interferometric techniques developed in radio astronomy over the past 40 years are now being applied to optical and IR astronomical imaging by a number of groups. Furthermore, the problem of figuring synthetic apertures is considerably simpler, and can be implemented in a computer: new 'self-calibration' techniques allow imaging even in the presence of phase errors due to the atmosphere.
Recent development using compact difference schemes to solve the Navier-Stokes equations show spectral-like accuracy. A study was made of the numerical characteristics of various combinations of the Runge-Kutta (RK) methods and compact difference schemes to calculate the unsteady Euler equations. The accuracy of finite difference schemes is assessed based on the evaluations of dissipative error. The objectives are reducing the numerical damping and, at the same time, preserving numerical stability. While this approach has tremendous success solving steady flows, numerical characteristics of unsteady calculations remain largely unclear. For unsteady flows, in addition to the dissipative errors, phase velocity and harmonic content of the numerical results are of concern. As a result of the discretization procedure, the simulated unsteady flow motions actually propagate in a dispersive numerical medium. Consequently, the dispersion characteristics of the numerical schemes which relate the phase velocity and wave number may greatly impact the numerical accuracy. The aim is to assess the numerical accuracy of the simulated results. To this end, the Fourier analysis is to provide the dispersive correlations of various numerical schemes. First, a detailed investigation of the existing RK methods is carried out. A generalized form of an N-step RK method is derived. With this generalized form, the criteria are derived for the three and four-step RK methods to be third and fourth-order time accurate for the non-linear equations, e.g., flow equations. These criteria are then applied to commonly used RK methods such as Jameson's 3-step and 4-step schemes and Wray's algorithm to identify the accuracy of the methods. For the spatial discretization, compact difference schemes are presented. The schemes are formulated in the operator-type to render themselves suitable for the Fourier analyses. The performance of the numerical methods is shown by numerical examples. These examples are detailed. described. The third case is a two-dimensional simulation of a Lamb vortex in an uniform flow. This calculation provides a realistic assessment of various finite difference schemes in terms of the conservation of the vortex strength and the harmonic content after travelling a substantial distance. The numerical implementation of Giles' non-refelctive equations coupled with the characteristic equations as the boundary condition is discussed in detail. Finally, the single vortex calculation is extended to simulate vortex pairing. For the distance between two vortices less than a threshold value, numerical results show crisp resolution of the vortex merging.
Phase retrieval algorithms, including the iterative transform algorithm and gradient search algorithms, were generalized to include the effects of propagation through a complicated optical system and to discount the effects of bad CCD pixels. For the gradient search algorithms, analytic gradients were derived that greatly speed up the computation over finite difference methods. For the Hubble Space Telescope (HST), the aperture function was reconstructed and the phase errors were retrieved. This information is useful to design correction optics for the telescope and for the deconvolution of blurred images from the HST.
A technique for Fourier processing of images larger than the space-bandwidth products of conventional or smart spatial light modulators and two-dimensional detector arrays is described. The technique involves a spatial combination of subimages displayed on individual spatial light modulators to form a phase-coherent image, which is subsequently processed with Fourier optical techniques. Because of the technique's similarity with the mosaic technique used in art, the processor used is termed an optical MOSAIC processor. The phase accuracy requirements of this system were studied by computer simulation. It was found that phase errors of less than lambda/8 did not degrade the performance of the system and that the system was relatively insensitive to amplitude nonuniformities. Several schemes for implementing the subimage combination are described. Initial experimental results demonstrating the validity of the mosaic concept are also presented.
This report addresses modulation and synchronization techniques for a multi-frequency time division multiple access (MF-TDMA) system with onboard baseband processing. The types of synchronization techniques analyzed are asynchronous (conventional) TDMA, preambleless asynchronous TDMA, bit synchronous timing with a preamble, and preambleless bit synchronous timing. Among these alternatives, preambleless bit synchronous timing simplifies onboard multicarrier demultiplexer/demodulator designs (about 2:1 reduction in mass and power), requires smaller onboard buffers (10:1 to approximately 3:1 reduction in size), and provides better frame efficiency as well as lower onboard processing delay. Analysis and computer simulation illustrate that this technique can support a bit rate of up to 10 Mbit/s (or higher) with proper selection of design parameters. High bit rate transmission may require Doppler compensation and multiple phase error measurements. The recommended modulation technique for bit synchronous timing is coherent QPSK with differential encoding for the uplink and coherent QPSK for the downlink.
This article reexamines the notion of closed-loop carrier phase synchronization motivated by the theory of maximum a posteriori phase estimation with emphasis on the development of new structures based on both maximum-likelihood and average-likelihood functions. The criterion of performance used for comparison of all the closed-loop structures discussed is the mean-squared phase error for a fixed-loop bandwidth.
We have recently conducted a controlled comparison of a number of approximations for gravitational clustering against the same n-body simulations. These include ordinary linear perturbation theory (Eulerian), the adhesion approximation, the frozen-flow approximation, the Zel'dovich approximation (describable as first-order Lagrangian perturbation theory), and its second-order generalization. In the last two cases we also created new versions of approximation by truncation, i.e., smoothing the initial conditions by various smoothing window shapes and varying their sizes. The primary tool for comparing simulations to approximation schemes was crosscorrelation of the evolved mass density fields, testing the extent to which mass was moved to the right place. The Zel'dovich approximation, with initial convolution with a Gaussian e(exp -k(exp 2)/k(exp 2, sub G)) where k(sub G) is adjusted to be just into the nonlinear regime of the evolved model (details in text) worked extremely well. Its second-order generalization worked slightly better. All other schemes, including those proposed as generalizations of the Zel'dovich approximation created by adding forces, were in fact generally worse by this measure. By explicitly checking, we verified that the success of our best-choice was a result of the best treatment of the phases of nonlinear Fourier components. Of all schemes tested, the adhesion approximation produced the most accurate nonlinear power spectrum and density distribution, but its phase errors suggest mass condensations were moved to slightly the wrong location. Due to its better reproduction of the mass density distribution function and power spectrum, it might be preferred for some uses. We recommend either n-body simulations or our modified versions of the Zel'dovich approximation, depending upon the purpose. The theoretical implication is that pancaking is implicit in all cosmological gravitational clustering, at least from Gaussian initial conditions, even when subcondensations are present.
A prototype adaptive secondary mirror has been developed on a 2.3-m telescope to stabilize rapid motion caused by atmospheric turbulence. The instantaneous position of an image's centroid, or brightest speckle, is measured by a near-infrared camera system which enables the tip-tilt mirror to recenter the image. Correction is accomplished at closed-loop frequencies of less than or = 100 Hz on guide stars with K (2.2 micrometers) magnitudes less than or = 8. Image motion is reduced to less than 0.1 sec rms, removing over 90% of low-frequency (f less than or = 5 Hz) tilt power, leaving less than or = 1 rad exp 2 mean square wave front tilt phase error. In seeing conditions where D/r sub o approximately = 4, long exposures in the H band (1.6 micrometers) exhibit a nearly diffraction-limited resolution of 0.19 sec full width at half maximum (FWHM) (Strehl ratio aprroximately = 0.14)-a factor of 4 improvement over uncorrected images. Reduction of the present static optical errors will improve the Strehl ratio another factor of 2, leading to approximately 70% of the maximum possible Strehl ratio.
Depending on the basis used for comparison, it is possible to predict different gains when applying carrier arraying to a conventional coherent receiver. In the past, the specific performance comparisons were made between the arrayed and nonarrayed cases assuming a fixed carrier-tracking closed-loop bandwidth. While the notion of loop bandwidth for the nonarrayed loop with a single input is well defined and meaningful, the comparable notion for an arrayed loop with multiple inputs is not uniquely defined since it depends on the knowledge of the statistical relation, e.g., degree of correlation, among the various antenna inputs. To circumvent the need for such knowledge, which is often not completely available, we suggest in this article an alternate criterion for comparing arrayed and nonarrayed loops, namely, fixed steady-state phase error, which, in the arrayed case, is independent of the statistical relation among the antenna inputs. We show that, in this case, the gain derived from carrier arraying is quite different from that obtained under the assumption of fixed-loop bandwidth, which suggests that one should exercise care when comparing arrayed and unarrayed loops in that the criterion used for comparison should be directly applicable to the situation at hand.
This paper discusses the theory and early experimental results related to an optical phasing sensor created at Marshall Space Flight Center. The sensor is a combination of a Young's double slit experiment and a Hartmann sensor used to measure intersegment phase error of a segmented telescope or other optic. The techniques used are proven interferometric techniques and require simple mathematics. Speed and efficiency are goals of the device as well as measurement of the important central area of the segments. Early results are encouraging and show that it is likely that this technique is feasible in the lab and possibly in space.
The quality of volume-localized magnetic resonance spectroscopy is affected by eddy currents caused by gradient switching. Eddy currents can be reduced with improved gradient systems; however, it has been suggested that the distortion due to eddy currents can be compensated for during postprocessing with a single-frequency reference signal. The authors propose modifying current techniques for acquiring the single-frequency reference signal by using relaxation weighting to reduce interference from components that cannot be eliminated by digital filtering alone. Additional sequences with T1 or T2 weighting for reference signal acquisition are shown to have the same eddy current characteristics as the original signal without relaxation weighting. The authors also studied a new eddy current correction method that does not require a single-frequency reference signal. This method uses two free induction decays (FIDs) collected from the same volume with two sequences with opposite gradients. Phase errors caused by eddy currents are opposite in these two FIDs and can be canceled completely by combining the FIDs. These methods were tested in a phantom. Eddy current distortions were corrected, allowing quantitative measurement of structures such as the -CH = CH- component, which is otherwise undetectable.
We present an auto-calibration and metrology system concept to correct for phase errors and mechanical deformation during the misssion.
Coalescing binary black hole mergers are expected to be the strongest gravitational wave sources for ground-based interferometers, such as the LIGO, VIRGO, and GEO600, as well as the spacebased interferometer LISA. Until recently it has been impossible to reliably derive the predictions of General Relativity for the final merger stage, which takes place in the strong-field regime. Recent progress in numerical relativity simulations is, however, revolutionizing our understanding of these systems. We examine here the specific case of merging equal-mass Schwarzschild black holes in detail, presenting new simulations in which the black holes start in the late inspiral stage on orbits with very low eccentricity and evolve for approximately 1200M through approximately 7 orbits before merging. We study the accuracy and consistency of our simulations and the resulting gravitational waveforms, which encompass approximately 14 cycles before merger, and highlight the importance of using frequency (rather than time) to set the physical reference when comparing models. Matching our results to PN calculations for the earlier parts of the inspiral provides a combined waveform with less than half a cycle of accumulated phase error through the entire coalescence. Using this waveform, we calculate signal-to-noise ratios (SNRs) for iLIGO, adLIGO, and LISA, highlighting the contributions from the late-inspiral and merger-ringdown parts of the waveform which can now be simulated numerically. Contour plots of SNR as a function of z and M show that adLIGO can achieve SNR 2 10 for some IMBBHs out to z approximately equals 1, and that LISA can see MBBHs in the range 3 x 10(exp 4) approximately < M/Mo approximately < 10(exp 7) at SNR > 100 out to the earliest epochs of structure formation at z > 15.
While there are a myriad of applications for microwave phase shifters in instrumentation and metrology, power combining, amplifier linearization, and so on, the most prevalent use is in scanning phased-array antennas. And while this market continues to be dominated by military radar and tracking platforms, many commercial applications have emerged in the past decade or so. These new and potential applications span low-Earth-orbit (LEO) communications satellite constellations and collision warning radar, an aspect of the Intelligent Vehicle Highway System or Automated Highway System. In any case, the phase shifters represent a considerable portion of the overall antenna cost, with some estimates approaching 40 percent for receive arrays. Ferrite phase shifters continue to be the workhorse in military-phased arrays, and while there have been advances in thin film ferrite devices, the review of this device technology in the previous edition of this book is still highly relevant. This chapter will focus on three types of phase shifters that have matured in the past decade: GaAs MESFET monolithic microwave integrated circuit (MMIC), micro-electromechanical systems (MEMS), and thin film ferroelectric-based devices. A brief review of some novel devices including thin film ferrite phase shifters and superconducting switches for phase shifter applications will be provided. Finally, the effects of modulo 2 phase shift limitations, phase errors, and transient response on bit error rate degradation will be considered.
A phase locked loop utilizing digital techniques to control the closed loop bandwidth of the RF carrier phase locked loop in a receiver provides high sensitivity and a wide dynamic range for signal reception. After analog to digital conversion, a digital phase locked loop bandwidth controller provides phase error detection with automatic RF carrier closed loop tracking bandwidth control to accommodate several modes of transmission.
The CESE development is driven by a belief that a solver should (i) enforce conservation laws in both space and time, and (ii) be built from a non-dissipative (i.e., neutrally stable) core scheme so that the numerical dissipation can be controlled effectively. To initiate a systematic CESE development of high order schemes, in this paper we provide a thorough discussion on the structure, consistency, stability, phase error, and accuracy of a new 4th-order space-time flux-conserving and neutrally stable CESE solver of an 1D scalar advection equation. The space-time stencil of this two-level explicit scheme is formed by one point at the upper time level and three points at the lower time level. Because it is associated with three independent mesh variables (the numerical analogues of the dependent variable and its 1st-order and 2ndorder spatial derivatives, respectively) and three equations per mesh point, the new scheme is referred to as the a(3) scheme. Through the von Neumann analysis, it is shown that the a(3) scheme is stable if and only if the Courant number is less than 0.5. Moreover, it is established numerically that the a(3) scheme is 4th-order accurate.
We report progress on a nulling coronagraph intended for direct imaging of extrasolar planets. White light is suppressed in an interferometer, and phase errors are measured by a second interferometer. A 1020-pixel MEMS deformable mirror in the first interferometer adjusts the path length across the pupil. A feedback control system reduces deflections of the deformable mirror to order of 1 nm rms.