Accurate Phase Estimation Research Articles

The method of joint probability distribution functions applied to the one-wavelength anomalous-scattering (OAS) case.

The method of the joint probability distribution function is applied to the case in which the positions of the anomalous scatterers are fully or partially known. The mathematical technique is able to handle errors both in the model structure of the located anomalous scatterers and in measurements. A criterion for ranking the more accurate phase estimates is given.

On the use of amplitude shaping pulses as windows for harmonic analysis

In this paper, we propose the use of shaping pulses as flat top windows for accurate amplitude and phase estimation from periodic signals in power systems. The intention is to eliminate the amplitude correction required to compensate the short-range leakage produced by nonflat-mainlobe windows in case of asynchronous sampling. The performance of the standard rise cosine filter, a generalized raised-cosine filter and a Hanning window, all of them with the same bandwidth, is compared in the simulation results. It is concluded that the accuracy of the estimates provided by the shaping pulses without amplitude compensation in the asynchronous case is relatively better than that of the amplitude compensated estimates obtained with the Hanning window. The generalized raised-cosine filter can achieve lower sidelobe levels but it does not improve the accuracy of the amplitude estimates of the standard raised-cosine filter.

Performance Improvement by Microdiversity for Wideband Signals in Frequency Selective Fading Indoor Channels with Co-Channel Interference

A comprehensive analytical bit-error-rate (BER) model is presented to analyse the performance of antenna-microdiversity for wideband BPSK modulated signals in the frequency selective fading multipath channel, specified by its complex impulse response. The model includes the disturbance by intersymbol interference (ISI) and co-channel interference (CCI), as well as the channels‘ impact on the carrier phase- and clock recovery in the receiver. The channel impulse responses at the antenna elements are determined by taking into account the direction of arrival of the individual paths. Computational BER- and SNIR-gain results (SNIR = signal-to-noise+interference-ratio) show that a substantial performance improvement is achieved with antenna combining for wideband signals which suffer ISI and/or CCI. For the indoor multipath channel with exponentially decaying power delay profile, the performance enhancement is compared for several antenna combining schemes. Quasi-coherent equal gain combining (QCEGC) is proposed as an novel EGC scheme based on a less accurate phase estimation technique. For wideband signals, QCEGC shows a slight performance degradation when compared to maximal ratio combining or minimum mean square error combining (MMSEC), but has a much lower implementation complexity. In the channel with CCI, where the best performance is achieved with MMSEC, QCEGC performs very poor.

Improved procedures for estimating amplitudes and phases of harmonics with application to vibration analysis

In this paper, we propose two procedures for accurate amplitude and phase estimation of multifrequency signals in rotating machinery. The first method reduces the amplitude attenuation and phase shift caused by the nonflat top of the main lobe of the window. The second procedure is able to reduce not only the leakage effects due to windowing but also the distortion that appears when the rotation frequency changes slowly. This second method uses an additional sensor, giving one pulse per revolution, to transform the input (asynchronous) signal into a synchronous signal having a fixed number of samples per revolution. The performance and effectiveness of both procedures are illustrated by means of simulation examples.

REDUCED COMPLEXITY FREQUENCY ESTIMATOR FOR BURST TRANSMISSION

In burst transmission, carrier recovery is a critical point for synchronization systems. With a feedforward carrier phase recovery algorithm, a small frequency offset can significantly increase the cycle slip rate and then the phase error variance. Therefore, in order to obtain an accurate carrier phase estimation, a precise frequency correction is required. For M-states phase shift keying (M-PSK) modulated signals an unbiased feedforward reduced complexity frequency estimator (RCFE), operating in the non-data aided mode (NDA) is derived from the maximum likelihood (ML) principle. A compromise is realized between noise filtering and estimation slip probability by minimizing the estimator variance. It is optimized to operate at a low signal-to-noise ratio and short bursts. Its performance is compared to that of the ML estimator. The estimator is applied to an all-feedforward synchronization structure with QPSK modulated signals. Global performance of the modem synchronization structure is supplied.

The achievable accuracy in estimating the instantaneous phase and frequency of a constant amplitude signal

The approach is based on modeling the signal phase by a polynomial function of time on a finite interval. The phase polynomial is expressed as a linear combination of the Legendre basis polynomials. First, the Cramer-Rao bound (CRB) of the instantaneous phase and frequency of constant-amplitude polynomial-phase signals is derived. Then some properties of the CRBs are used to estimate the order of magnitude of the bounds. The analysis is extended to signals whose phase and frequency are continuous but not polynomial. The CRB can be achieved asymptotically if the estimation of the phase coefficients is done by maximum likelihood. The maximum-likelihood estimates are used to show that the achievable accuracy in phase and frequency estimation is determined by the CRB of the polynomial coefficients and the deviation of true phase and frequency from the polynomial approximations.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Accurate estimation of amplitude, frequency, and phase of harmonic signal components using an FFT

The signal analyzed using an FFT is seldom identical to the true signal. This can result in inaccurate estimates of amplitude, frequency, and phase of harmonic signals. Using an extension of a method described earlier [J. C. Burgess, “On digital spectral analysis of periodic signals,” J. Acoust. Soc. Am. 58, 556–567 (1975)], it is possible to estimate the true amplitude, frequency, and phase of a harmonic signal with good accuracy. For example, acoustic intensity measurements may require determining the phase difference between two harmonic signals of the same amplitude and frequency. Using the method described, this phase difference often can be estimated with an error less than 0.01%. The method requires use of an optimum data window that can be expressed as a Fourier series having only a few nonzero coefficients.

Cramer-Rao Lower Bound On Wavefront Sensor Error

Wavefront sensors that can operate at low light levels, be built from present technology components, and provide accurate wavefront phase estimates in real time are required for use with adaptive optics systems. The use of estimation theory makes possible the evaluation of wavefront sensors without specification of the wavefront phase estimation algorithms. The Cramer-Rao method was used to find a lower bound on integrated rms wavefront sensor estimation error. In addition to an analysis of the general case, the error lower bound was numerically evaluated for the shearing interferometer wavefront sensor. Computer simulations of the atmosphere and wavefront sensor measurements including noise were performed. Using an appropriate algorithm, the phase was estimated and the resulting phase error was compared with the lower bound. The results support the validity of using the Cramer-Rao lower bound to evaluate wavefront sensor performance.

The unimportance of phase in speech enhancement

The importance of Fourier transform phase in speech enhancement is considered. Results indicate that a more accurate estimation of phase is unwarranted in speech enhancement at the S/N ratios where the intelligibility scores of unprocessed speech range from 5 to 95 percent, if the phase estimate is used to reconstruct speech by combining it with an independently estimated magnitude or to reconstruct speech using the phase-only signal reconstruction algorithm.

Adaptive Maximum Likelihood Receiver for Direct-Ranging Applications

Recent interest in direct-ranging navigation methods has prompted new research into practical receiver structures which provide improved signal processing. Maximum likelihood receivers are compared with conventional phase-locked receivers by theoretical and simulation methods as phase estimators based on signal measurements only. Signal-to-noise ratio (SNR) enhancement is examined and filter recommendations made. An adaptive maximum likelihood receiver is then developed which uses both signal measurements and a priori data to improve phase estimation accuracy. Simulation results indicate a 33.3 dB processing gain yielding a ranging error standard deviation of ±15 feet for zero dB received SNR. Nonadaptive and adaptive receivers are fabricated, flight tested, and experimental results reported.