# INTRODUCTION 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 [2], [3]. Amplitude model is used in study of propagation by diffracting street corner. 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 [6]. # a) Mobile Computation 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 [9]. 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. ? 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. # Expensive Device for Power Supply 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. # v. Multipath Fading and other Interference 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. # RAYLEIGH DISTRIBUTION 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 [6]. a) Product of independent Rayleigh Random Variables Consider a product of n independent random variables: Y= ? = n i i X 1 (1) Where X i is a Rayleigh distribution [4] random variable with probability density function (pdf) as shown in figure 1. ) 2 exp( ) ( 2 2 2 i i x x x x f i ? ? ? = , x ? 0(2) 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 ], [6] is shown in figure 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) ? Touch Screens: These enable users to easily interact with the units in the field without removing gloves. ? 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. ? Problem in Designing Software: There are many difficulties arises during designing software for moving vehicle. 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 = differ by an integer or a zero. ? The parameter h a and h b are so that no. pole of ( ) s b j ? Î?" , m j ,..., 2 , 1 = 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 [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) Variance is defined by the equation 1 and 3 as: n h n h h v )] 1 2 ( [ ) 2 ( 2 2 + Î?" = ? (6) # III. CONCLUSION 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_Computing b) Meijer G-function [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: 12![Figure 1: Rayleigh Probability Density Function at Different Variance](image-2.png "Figure 1 :Figure 2 :") © 2011 Global Journals Inc. (US) August ## August This page is intentionally left blank n-Rayleigh Distribution in Mobile Computing for Flat-Fading Channel * Mobile channel propagation Parson 2003 Pentech press London * Power distributions revisited JBAndersen IZKovacs presented at the COST273 3rd Management Committee Meeting Guildford, U.K. Jan. 17-18, 2002 * Statistical distributions in mobile communications using multiple scattering JBAndersen Aug. 2002 Maastricht, Netherlands presented at the 27th URSI General Assembly * Probability, random Variables and Stochastic Processes PapoulisAthanasios PillaiSUnnikrishna 2005 Tata McGraw Hill New Delhi 4 th edition * YLLuke Special Functions and Their Approximations Academic Press 1969 1 * The Distribution of the Product of Independent Rayleigh Random Variables JariSalo MHassan PerttiEl-Sallabi Vainikainen IEEE Trans. on Antenna and Propagation 54 2 February 2006 * Generalized Hypergeometric Function with Application in Statistics and Physical Sciences AMMathai RKSaxena 1973 Springer-Verlag Berlin Germany