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Phase locked results for low SNRs pertaining to phase errors probability, cumulative and variance distribution, including time intervals between cycle-slipping
Automatic tuning of superconducting cavity resonant frequency using optical feedback, discussing phase error processing and frequency deviation
Eigenfunction expansions of reduced nonGaussian phase error transition probability density function for first order tracking loop, analyzing spectral properties of Fokker-Planck equation
A systems evaluation of the 13.3 GHz scatterometer system is presented. The effects of phase error between the scatterometer channels, antenna pattern deviations, aircraft attitude deviations, environmental changes, and other related factors such as processing errors, system repeatability, and propeller modulation, are established. Furthermore, the reduction in system errors and calibration improvement is investigated by taking into account these parameter deviations. Typical scatterometer data samples are presented.
Radar scatterometers have applications in the NASA/MSC Earth Observation Aircraft Program. Over a period of several years, several missions have been flown over both land and ocean. In this paper a system evaluation of the NASA/MSC 13.3-GHz Scatterometer System is presented. The effects of phase error between the Scatterometer channels, antenna pattern deviations, aircraft attitude deviations, environmental changes, and other related factors such as processing errors, system repeatability, and propeller modulation, were established. Furthermore, the reduction in system errors and calibration improvement was investigated by taking into account these parameter deviations. Typical scatterometer data samples are presented.
A digital computer model for Monte-Carlo simulation of an imperfect second-order hybrid phase-locked loop (PLL) operating in radio-frequency interference (RFI) and Gaussian noise backgrounds has been developed. Characterization of hybrid loop performance in terms of cycle slipping statistics and phase error variance, through computer simulation, indicates that the hybrid loop has desirable performance characteristics in RFI backgrounds over the conventional PLL or the costas loop.
A nonlinear analysis of a multifilter phase-lockloop (MPLL) by using the method of harmonic balance is presented. The particular MPLL considered has a low-pass filter and a band-pass filter in parallel. An analytic expression for the relationship between the input signal phase deviation and the phase error is determined for sinusoidal FM in the absence of noise. The expression is used to determine bounds on the proper operating region for the MPLL and to investigate the jump phenomenon previously observed. From these results the proper modulation index, modulating frequency, etc. used for the design of a MPLL are determined. Data for the loop unlock boundary obtained from the theoretical expression are compared to data obtained from analog computer simulations of the MPLL.
An exact mathematical model is developed for a discrete loop of a general order particularly suitable for digital computation. The deterministic response of the loop to the phase step and the frequency step is investigated. The design of the digital filter for the second-order loop is considered. Use is made of the incremental phase plane to study the phase error behavior of the loop. The model of the noisy loop is derived and the optimization of the loop filter for minimum mean-square error is considered.
This paper is concerned with the problem of obtaining time-dependent solutions to a class of Fokker-Planck equations that arise in the analysis and synthesis of a variety of first-order synchronization systems employing the phase-lock principle. These include the classical sinusoidal phase-locked loop, squaring and Costas loops, data-aided loops, hybrid loops, various symbol synchronizer mechanizations, and tunnel-diode oscillators. By analyzing the spectral properties of the associated time-dependent Fokker-Planck boundary value problem, eigenfunction expansions of the reduced modulo-2-pi phase-error-transition probability-density function are developed for a class of first-order synchronization systems.
A simple second-order digital phase-locked loop has been designed for the Viking Orbiter 1975 command system. Excluding analog-to-digital conversion, implementation of the loop requires only an adder/subtractor, two registers, and a correctable counter with control logic. The loop considers only the polarity of phase error and corrects system clocks according to a filtered sequence of this polarity. The loop is insensitive to input gain variation, and therefore offers the advantage of stable performance over long life. Predictable performance is guaranteed by extreme reliability of acquisition, yet in the steady state the loop produces only a slight degradation with respect to analog loop performance.
Astigmatic phase error in large parabolic reflector antennas is discussed. A procedure for focusing an antenna and diagnosing the presence and degree of astigmatism is described. Theoretical analysis is conducted to determine the nature of this error in such antennas.
A multiple phase modulated carrier tracking loop for use in a frequency shift keying system is described in which carrier tracking efficiency is improved by making use of the decision signals made on the data phase transmitted in each T-second interval. The decision signal is used to produce a pair of decision-feedback quadrature signals for enhancing the loop's performance in developing a loop phase error signal.
A simple second-order digital phase-locked loop has been designed to synchronize itself to a square-wave subcarrier. Analysis and experimental performance are given for both acquisition behavior and steady-state phase error performance. In addition, the damping factor and the noise bandwidth are derived analytically. Although all the data are given for the square-wave subcarrier case, the results are applicable to arbitrary subcarriers that are odd symmetric about their transition region.
A FORTRAN IV simulation study of the all-digital phase-processing circuitry is described. A digital phase-lock loop (DPLL) forms the heart of the Omega navigation receiver prototype, and through the DPLL, the phase of the 10.2 KHz Omega signal was estimated when the true signal phase is contaminated with noise. The DPLL uses a frequency synthesizer as the reference oscillator. The synthesizer is composed of synchronous rate multipliers (SRM's) driven by a temperature-compensated crystal oscillator, and the use of the SRM's in this application introduces phase jitter which degrades system performance. Simulation of the frequency synthesizer discussed was to analyze the circuits on a bit-by-bit level in order to evaluate the overall design, to see easily the effects of proposed design changes prior to actual breadboarding, to determine the optimum integration time for the DPLL in an environment typical of general aviation conditions, and to quantify the phase error introduced by the SRM synthesizer and examine its effect on the system.
In order to accommodate a quadrature amplitude-shift-keyed (QASK) signal, Simon and Smith (1974) have modified the decision-feedback loop which tracks a quadrature phase-shift-keyed (QPSK). In the investigation reported approaches are considered to modify the loops in such a way that offset QASK signals can be tracked, giving attention to the special case of an offset QPSK. The development of the stochastic integro-differential equation of operation for a decision-feedback offset QASK loop is discussed along with the probability density function of the phase error process.
The phase correction for a Michelson interferometer with misaligned mirrors in converging light is shown to give rise to a quadratic phase shift. In general, the calculation of a spectrum from the measured interferogram needs phase correction. Phase corrections have been well worked out for the cases of a linear phase shift and a phase that is slowly varying. The standard procedures for correcting calculated spectra need to be modified, however, to remove any phase errors resulting from misaligned mirrors.
A new model for predicting the computational performance of a sequential decoder operating in a noisy carrier reference environment is described. The major difference between this model and previous models is that the new model characterizes the number of computations per frame as the sum of the computations resulting from a number of independent searches. This number of independent searches can then be considered as an effective frame length. When this computational model is averaged over noisy reference phase errors using a medium-rate interpolation scheme, the results are found to agree quite favorably with experimental measurements.
A new model for predicting the computational performance of a sequential decoder operating in a noisy carrier reference environment is described. The major difference between this model and previous models is that the new model characterizes the number of computations per frame as the sum of the computations resulting from a number of independent searches. This number of independent searches can then be considered as an effective frame length. When this computational model is averaged over noisy reference phase errors using a medium-rate interpolation scheme, the results are found to agree quite favorably with experimental measurements.