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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: In this paper, the probability density function for wave propagation in a straight perfect electrical conductor (PEC) rough wall tunnel is deduced from the mathematical models of the random electromagnetic fields.
Abstract: The probability density function for wave propagating in a straight perfect electrical conductor (PEC) rough wall tunnel is deduced from the mathematical models of the random electromagnetic fields. The field propagating in caves or tunnels is a complex-valued Gaussian random processing by the Central Limit Theorem. The probability density function for single modal field amplitude in such structure is Ricean. Since both expected value and standard deviation of this field depend only on radial position, the probability density function, which gives what is the power distribution, is a radially dependent function. The radio channel places fundamental limitations on the performance of wireless communication systems in tunnels and caves. The transmission path between the transmitter and receiver can vary from a simple direct line of sight to one that is severely obstructed by rough walls and corners. Unlike wired channels that are stationary and predictable, radio channels can be extremely random and difficult to analyze. In fact, modeling the radio channel has historically been one of the more challenging parts of any radio system design; this is often done using statistical methods. In this contribution, we present the most important statistic property, the field probability density function, of wave propagating inmore » a straight PEC rough wall tunnel. This work only studies the simplest case--PEC boundary which is not the real world but the methods and conclusions developed herein are applicable to real world problems which the boundary is dielectric. The mechanisms behind electromagnetic wave propagation in caves or tunnels are diverse, but can generally be attributed to reflection, diffraction, and scattering. Because of the multiple reflections from rough walls, the electromagnetic waves travel along different paths of varying lengths. The interactions between these waves cause multipath fading at any location, and the strengths of the waves decrease as the distance between the transmitter and receiver increases.« less
6 citations
TL;DR: This part I of 2 parts paper investigates carefully a new programmable generator of general ordinary renewal processes in discrete time based on the concept of failure rate and its implementation is completely digital.
6 citations
TL;DR: In this article, the effects of quantum noise in light detection on the modulus and phase measurements are analyzed, and simplified statistical models of normal distributions are derived by using simplified photon-noise models and the so-called log-normal model for atmospheric perturbations.
Abstract: Statistical errors in mutual intensity, measured by a photon-noise-limited, wave-front-folding interferometer, are studied from the viewpoint of high-resolution imaging through the turbulent atmosphere. The effects of quantum noise in light detection on the modulus and phase measurements are analyzed, and simplified statistical models of normal distributions are derived. The errors that are due to both the photon noise and atmospheric phase-front perturbations are clarified by using the simplified photon-noise models and the so-called log-normal model for the atmospheric perturbations. The conditions under which the conventional method for phase-unwrapping preprocessing can be applied to the interferometric data are studied to specify the limitations of wave-front-folding interferometry. The analysis suggests the possible application of such interferometry to a survey of simple objects, such as binary stars, or to a detailed investigation of solar-surface structures.
6 citations
TL;DR: This paper proposes a new semi-parametric approach to build generative embeddings for classification of magnetic resonance images (MRI), and proposes to use Rician mixtures as the underlying generative model, based on which several different generativeembeddings are built.
6 citations
TL;DR: In this article, the authors derived the probability distribution of the largest value attained by a stationary random variable over a period of time, containing many oscillations, is shown to converge to a type 1 extreme value distribution for any value of the spectral width parameter.
Abstract: The probability distribution of the largest value attained by a stationary random variable over a period of time, containing many oscillations, is shown to converge to a type 1 extreme value distribution for any value of the spectral width parameter. This result is derived by using recently presented methods of Galambos [1978] from the general form of the probability that any wave crest exceeds a specified crest height as given by Rice [1944, 1945] and further analyzed by Cartwright and Longuet-Higgins [1956]. A consequence of this generalized derivation is that several asymptotic properties of kth extremes from such distributions, previously obtained by Cartwright [1958], using Rayleigh approximations, may be verified directly. These results illustrate the way in which the spectral width parameter affects the longterm behavior of the system.
6 citations