Journal Article•
Mathematical Analysis of Random Noise-Conclusion
About: This article is published in Bell System Technical Journal.The article was published on 1945-01-01 and is currently open access. It has received 807 citations till now.
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TL;DR: Estimates of the distribution of the fade lengths for various depths of fades are given, and relations which may be useful in analyzing fading data are derived.
Abstract: The fluctuations of a received radio signal due to fading are assumed to behave like the envelope of narrow-band Gaussian noise. Estimates of the distribution of the fade lengths for various depths of fades are given, and relations which may be useful in analyzing fading data are derived. A similar problem involving the separation of the intercepts of the noise current itself, instead of its envelope, is also discussed.
295 citations
TL;DR: A review of the operational methods that have been developed for analyzing stochastic data in time and scale can be found in this paper, where a basic ingredient of the approach to the analysis of fluctuating data is the presence of a Markovian property, which can be detected in real systems above a certain time or length scale.
284 citations
TL;DR: The simulation model's amplitude and phase probability density function (PDF) is investigated, but also higher order statistics [e.g., level-crossing rate (LCR) and average duration of fades (ADFs] are investigated].
Abstract: Rice's (9144, 1945) sum of sinusoids can be used for an efficient approximation of colored Gaussian noise processes and is therefore of great importance to the software and hardware realization of mobile fading channel models. Although several methods can be found in the literature for the computation of the parameters characterizing a proper set of sinusoids, less is reported about the statistical properties of the resulting (deterministic) simulation model. In this paper, not only is the simulation model's amplitude and phase probability density function (PDF) investigated, but also higher order statistics [e.g., level-crossing rate (LCR) and average duration of fades (ADFs)]. It is shown that due to the deterministic nature of the simulation model, analytical expressions for the PDF of the amplitude and phase, autocorrelation function (ACF), crosscorrelation function (CCF), LCR, and ADFs can be derived. We also propose a new procedure for the determination of an optimal set of sinusoids, i.e., the method results for a given number of sinusoids in an optimal approximation of Gaussian, Rayleigh, and Rice processes with given Doppler power spectral density (PSD) properties. It is shown that the new method can easily be applied to the approximation of various other kinds of distribution functions, such as the Nakagami (1960) and Weibull distributions. Moreover, a quasi-optimal parameter computation method is presented.
281 citations
TL;DR: In this paper, an analytical study of the failure region of the first excursion reliability problem for linear dynamical systems subjected to Gaussian white noise excitation is carried out with a view to constructing a suitable importance sampling density for computing the failure probability.
255 citations
TL;DR: In this article, a Doppler reflectometry technique was used to measure Er fluctuations directly, and measurements of Geodesic acoustic modes (GAMs) and ZF properties in ohmic, L-mode and H-mode ASDEX Upgrade tokamak discharges were performed.
Abstract: Zonal flows (ZFs) and associated geodesic oscillations are turbulence-generated time-varying Er × BT rigid poloidal plasma flows with finite radial extent. They are of major interest for tokamak confinement since they are thought to moderate drift-wave turbulence and hence edge transport. However, detection of ZFs (believed to be driven by Reynolds stress) and Geodesic acoustic modes (GAMs) (linked with poloidal pressure asymmetries) is challenging since they appear predominantly as low frequency (few kilohertz) potential or radial electric field Er fluctuations. Presented here are measurements of GAM/ZF properties in ohmic, L-mode and H-mode ASDEX Upgrade tokamak discharges using a new Doppler reflectometry technique to measure Er fluctuations directly.
252 citations