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Weibull Fading
Weibull fading, named after Waloddi Weibull, is a simple statistical model of fading used in wireless communications and based on the Weibull distribution. Empirical studies have shown it to be an effective model in both indoor and outdoor environments. In 2005, a theoretical model for a particular class of Weibull distributions was described by Sagias and Karagiannidis, who also analyzed channel capacity Channel capacity, in electrical engineering, computer science, and information theory, is the theoretical maximum rate at which information can be reliably transmitted over a communication channel. Following the terms of the noisy-channel coding ... of a wireless channel in the presence of Weibull fading. References * Radio frequency propagation fading {{wireless-stub ...
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Waloddi Weibull
Ernst Hjalmar Waloddi Weibull (18 June 1887 – 12 October 1979) was a Swedish civil engineer, Materials science, materials scientist, and Mathematician#Applied mathematics, applied mathematician. The Weibull distribution is named after him. Education and career Weibull joined the Swedish Coast Guard in 1905 as a midshipman. He moved up the ranks with promotion to sublieutenant in 1907, Captain (naval), Captain in 1916 and Major (rank), Major in 1940. While in the coast guard he took courses at the Royal Institute of Technology. In 1924 he graduated and became a full professor. He obtained his doctorate from the University of Uppsala in 1932. He was employed in Swedish and Germany, German industry as a consulting engineer. In 1914, while on expeditions to the Mediterranean, the Caribbean and the Pacific Ocean on the research ship ''Albatross'', Weibull wrote his first paper on the propagation of explosive waves. He developed the technique of using explosive charges to determine ...
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Statistical
Statistics (from German language, German: ', "description of a State (polity), state, a country") is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data. In applying statistics to a scientific, industrial, or social problem, it is conventional to begin with a statistical population or a statistical model to be studied. Populations can be diverse groups of people or objects such as "all people living in a country" or "every atom composing a crystal". Statistics deals with every aspect of data, including the planning of data collection in terms of the design of statistical survey, surveys and experimental design, experiments. When census data (comprising every member of the target population) cannot be collected, statisticians collect data by developing specific experiment designs and survey sample (statistics), samples. Representative sampling assures that inferences and conclusions can reasonably extend from the sample ...
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Fading
In wireless communications, fading is the variation of signal attenuation over variables like time, geographical position, and radio frequency. Fading is often modeled as a random process. In wireless systems, fading may either be due to multipath propagation, referred to as multipath-induced fading, weather (particularly rain), or shadowing from obstacles affecting the wave propagation, sometimes referred to as shadow fading. A fading channel is a communication channel that experiences fading. Key concepts The presence of reflectors in the environment surrounding a transmitter and receiver create multiple paths that a transmitted signal can traverse. As a result, the receiver sees the superposition of multiple copies of the transmitted signal, each traversing a different path. Each signal copy will experience differences in attenuation, delay and phase shift while traveling from the source to the receiver. This can result in either constructive or destructive inter ...
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Wireless
Wireless communication (or just wireless, when the context allows) is the transfer of information (''telecommunication'') between two or more points without the use of an electrical conductor, optical fiber or other continuous guided transmission medium, medium for the transfer. The most common wireless technologies use radio waves. With radio waves, intended distances can be short, such as a few meters for Bluetooth, or as far as millions of kilometers for NASA Deep Space Network, deep-space radio communications. It encompasses various types of fixed, mobile, and portable applications, including two-way radios, Mobile phone, cellular telephones, personal digital assistants (PDAs), and wireless networking. Other examples of applications of radio ''wireless technology'' include Global Positioning System, GPS units, garage door openers, wireless Mouse (computing), computer mouse, Keyboard (computing), keyboards and Headset (audio), headsets, headphones, radio receivers, satelli ...
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Weibull Distribution
In probability theory and statistics, the Weibull distribution is a continuous probability distribution. It models a broad range of random variables, largely in the nature of a time to failure or time between events. Examples are maximum one-day rainfalls and the time a user spends on a web page. The distribution is named after Swedish mathematician Waloddi Weibull, who described it in detail in 1939, although it was first identified by René Maurice Fréchet and first applied by to describe a Particle-size distribution, particle size distribution. Definition Standard parameterization The probability density function of a Weibull random variable is : f(x;\lambda,k) = \begin \frac\left(\frac\right)^e^, & x\geq0 ,\\ 0, & x 0 is the ''shape parameter'' and λ > 0 is the ''scale parameter'' of the distribution. Its Cumulative distribution function#Complementary cumulative distribution function (tail distribution), complementary cumulative distribution function is a stretch ...
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Channel Capacity
Channel capacity, in electrical engineering, computer science, and information theory, is the theoretical maximum rate at which information can be reliably transmitted over a communication channel. Following the terms of the noisy-channel coding theorem, the channel capacity of a given Channel (communications), channel is the highest information rate (in units of information entropy, information per unit time) that can be achieved with arbitrarily small error probability. Information theory, developed by Claude E. Shannon in 1948, defines the notion of channel capacity and provides a mathematical model by which it may be computed. The key result states that the capacity of the channel, as defined above, is given by the maximum of the mutual information between the input and output of the channel, where the maximization is with respect to the input distribution. The notion of channel capacity has been central to the development of modern wireline and wireless communication system ...
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