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\title{N-Rayleigh Distribution in Mobile Computing for Flat-Fading Channel}
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\begin{document}

             \author[1]{Dr. Amit  Kumar}

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\date{\small \em Received: 23 June 2011 Accepted: 18 July 2011 Published: 28 July 2011}

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\begin{abstract}
        


In wireless communication, the presence of reflectors, obstacles etc, the signal experiences variation in characteristics like amplitude and frequency is known as fading channel [1]. This paper, explain the importance of Rayleigh distributed random variables in mobile computing field. At present time in emerging wireless technology, n-Rayleigh distribution has played an important role. The concept of random process in communication is expansion of cdf and pdf which are mostly used in application of physical science, statistics, and experimental data collection in wireless environment, random modeling and estimation of fading channel.

\end{abstract}


\keywords{Fading Channel, Radio Propagation, Rayleigh Distribution.}

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\let\tabcellsep& 	 	 		 
\section[{INTRODUCTION}]{INTRODUCTION}\par
or radio wave propagation through wireless communication channel, the n-Rayleigh distribution has been found to explain precisely amplitude behaviour. A series of statistically random Rayleigh fading process connected by narrow pipes just like n-Rayleigh model which agree well with measurement in forest environment \hyperref[b1]{[2]}, \hyperref[b2]{[3]}. Amplitude model is used in study of propagation by diffracting street corner.\par
The probability density function and distribution function for n=1,2 is generally studied but more general form the n-Rayleigh distribution function appears to be absent in studies. Mostly Monte Carlo simulation has been used in studies. Here used an inverse Mellin transform technique from statistics and in terms of Meijer G-function for probability density and distribution function which provides cascade form of distribution function. The additional advantage of this result may be used where distribution of product of Rayleigh independent variables were studied using Monte Carlo simulation. This may be used for proposed n-scattering model. Analytical expression of signal amplitude is needed in study of performance of wireless radio wave propagation \hyperref[b5]{[6]}. 
\section[{a) Mobile Computation}]{a) Mobile Computation}\par
Mobile Computation requires wireless network to support outdoor mobility and handoff from one network to the next. The term Mobile Computation deals with mobility of hardware, data and software. The access to computing is necessary not only from local one, but also while the user is moving from one place to another  {\ref [9]}.\par
There are many types of computers and phones which have been familiar from last two decades include: ii. Radiation is Injurious to Health Mobile computation device used electromagnetic radiation. The radiation from mobile phone and BTS are potential health hazards. The cellular radio frequency radiation can cause the heating of tissue that leads to an increase in body temperature. Some harmful effects are given below.\par
? Thermal effect ? Non-thermal effect iii. Secrecy Purpose Secrecy is a major concern so far as the secure and confidential communication is required. The main schemes for secure communication include:? Authentication Schemes ? Encryption Schemes iv. 
\section[{Expensive Device for Power Supply}]{Expensive Device for Power Supply}\par
Since the power consumption is always a factor of major concern but the mobile computers must depend entirely on battery power. Combined with compact size, this means unusually expensive batteries used. 
\section[{v. Multipath Fading and other Interference}]{v. Multipath Fading and other Interference}\par
The interference in a Mobile Computation are due to multipath fading, co-channel interference weather and terrain problems as well as distance-limited connection exist with some technologies. Reception of signal in tunnels and some buildings is poor.  
\section[{RAYLEIGH DISTRIBUTION}]{RAYLEIGH DISTRIBUTION}\par
Here the distribution function of n-Rayleigh random variables is represented. The Mellin transform technique is used in advanced statistics. The main idea may also be useful in other similar distribution problems \hyperref[b5]{[6]}. a) Product of independent Rayleigh Random Variables Consider a product of n independent random variables:Y= ? = n i i X 1 (1)\par
Where X i is a Rayleigh distribution \hyperref[b3]{[4]} random variable with probability density function (pdf) as shown in figure  {\ref 1}.) 2 exp( ) ( 2 2 2 i i x x x x f i ? ? ? = , x ? 0\textbf{(2)}\par
In this way Y is defined and can be called an "n-Rayleigh" random variable. The n th moment of X i.e. E[X i h ], \hyperref[b5]{[6]} is shown in figure  {\ref 2}.  ? Invisibility of Screen Due to Sun: Visibility of standard screens becomes an issue in bright sunlight.h i ] = dx x x i i h ) 2 exp( 2 2 0 2 1 ? ? ? ? ? + ( ) ? ? ? ? ? ? + Î?" = 1 2 2 2 2 h h i ? (3)\par
? Touch Screens: These enable users to easily interact with the units in the field without removing gloves.\par
? Sensitive to High-Temperature: Lithium Ion batteries are sensitive to high temperature conditions for charging. A computer for the mobile environment should be designed with a high-temperature charging function that limits the charge to 85\% or less of capacity.\par
? Problem in Designing Software: There are many difficulties arises during designing software for moving vehicle.\par
The function is defined under following hypothesis [8]:? , 0 q m ? ? p n ? ? 0 and 1 ? ? q p ? 0 ? z ? No. pair of k b , ( ) m k ,..., 2 , 1 =\par
differ by an integer or a zero.\par
? The parameter h a and h b are so that no. pole of ( )s b j ? Î?" , m j ,..., 2 , 1 =\par
coincide with any pole of ( ) Here the probability density functions of the inverse Mellin transform using contour integral. In figure 3, is derived using distinct value of variance Mellin transform defined with respect to order of moment. In application of advanced statistics, definite integral is done by Mellin transform technique. In this way the result may be expressed in terms of Meijer Gfunction.One can find the pdf of as the inverse Mellin transform of v h = E[Y h ], defined by the contour integral \hyperref[b6]{[7]}.s a k + ? Î?" 1 , n k ,..., 2 , 1 = ? ,... 2 , 1 ? ? k j b a for n j ,..., 2 , 1 = and m k ,..., 2 , 1 = ? if q p = ,? + ? = l h h Y dh y v j y f ) 1 ( 2 1 ) ( ? (5)\par
Variance is defined by the equation 1 and 3 as:n h n h h v )] 1 2 ( [ ) 2 ( 2 2 + Î?" = ? (6) 
\section[{III. CONCLUSION}]{III. CONCLUSION}\par
In application of Mobile Computation like data management and transaction method, the wireless path has a multipath profile. Practically there is scattering environment so signal propagation through wireless media is complicated phenomenon due to some effect like shadowing and multipath but n-Rayleigh method may also be helpful in modeling and evaluation for upcoming wireless and Mobile Computation technology. 8. Meijer G-function -Wikipedia, the free encyclopedia. 9. http://www.en.wikipedia.org/wiki/Mobile\textunderscore Computing b) Meijer G-function \hyperref[b4]{[5]} In the result, the density and distribution functions will be given in terms of the Meijer G-function, which is a generalization of the generalized hypergeometric function and can be defined using the contour integral representation as: \begin{figure}[htbp]
\noindent\textbf{12}\includegraphics[]{image-2.png}
\caption{\label{fig_0}Figure 1 :Figure 2 :}\end{figure}
   			\footnote{© 2011 Global Journals Inc. (US)} 			\footnote{August} 		 		\backmatter  			 
\subsection[{August}]{August}\par
This page is intentionally left blank n-Rayleigh Distribution in Mobile Computing for Flat-Fading Channel			 			  				\begin{bibitemlist}{1}
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\bibitem[Luke ()]{b4}\label{b4} 	 		 			Y L Luke 		.  		\textit{Special Functions and Their Approximations},  				1969. Academic Press. 1.  	 
\bibitem[Parson ()]{b0}\label{b0} 	 		\textit{Mobile channel propagation},  		 			Parson 		.  		2003. London: Pentech press.  	 
\bibitem[Andersen and Kovacs ()]{b1}\label{b1} 	 		‘Power distributions revisited’.  		 			J B Andersen 		,  		 			I Z Kovacs 		.  	 	 		\textit{presented at the COST273 3rd Management Committee Meeting},  				 (Guildford, U.K.)  		Jan. 17-18, 2002.  	 
\bibitem[Athanasios and Unnikrishna ()]{b3}\label{b3} 	 		\textit{Probability, random Variables and Stochastic Processes},  		 			Papoulis Athanasios 		,  		 			Pillai S Unnikrishna 		.  		2005. New Delhi: Tata McGraw Hill.  	 	 (4 th edition) 
\bibitem[Andersen (2002)]{b2}\label{b2} 	 		\textit{Statistical distributions in mobile communications using multiple scattering},  		 			J B Andersen 		.  		Aug. 2002. Maastricht, Netherlands.  	 	 (presented at the 27th URSI General Assembly) 
\bibitem[Salo et al. (2006)]{b5}\label{b5} 	 		‘The Distribution of the Product of Independent Rayleigh Random Variables’.  		 			Jari Salo 		,  		 			M Hassan 		,  		 			Pertti El-Sallabi 		,  		 			Vainikainen 		.  	 	 		\textit{IEEE Trans. on Antenna and Propagation}  		February 2006. 54  (2) .  	 
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\end{document}
