Probability Distributions of Products of Rayleigh and Nakagami-m Variables Using Mellin Transform
Probability Distributions of Products of Rayleigh and Nakagami-m Variables Using Mellin Transform
复制标题
DOI：
10.1109/icc.2011.5963344
复制
发表时间：
2011-06
期刊：
影响因子：
--
通讯作者：
Sohail Ahmed;Lie-liang Yang;L. Hanzo
中科院分区：
文献类型：
--
作者：
Sohail Ahmed;Lie-liang Yang;L. Hanzo
在这篇文章中，我们使用Mellin变换来推导Nakagami-m和Gamma分布随机变量的乘积的概率密度函数(PDF)的表达式。作为Nakagami-m和Gamma族的特例，还导出了瑞利分布随机变量乘积和指数分布随机变量乘积的概率密度函数。我们利用了独立同分布随机变量乘积的Mellin变换是单个随机变量的Mellin变换的乘积这一事实。使用这种方法，随机变量乘积的PDF被表示为易于计算的无穷级数的形式。此外，还说明了这些PDF在采用多进制正交调制的数字通信中的应用。
In this contribution, we employ the Mellin transform to derive the expressions for probability density function (PDF) of the product of Nakagami-m and Gamma distributed random variables. As the special cases of the Nakagami-m and Gamma family, the PDF of the product of Rayleigh distributed random variables and that of the product of exponentially distributed Random variables are also derived. We exploit the fact that the Mellin transform of a product of independent and identically distributed random variables is the product of the Mellin transforms of the individual random variables. Using this approach, the PDF of the product of random variables is expressed in the form of an easily computable infinite series. Furthermore, application of the PDFs in digital communications using M-ary orthogonal modulation is illustrated.