On the Multivariate \alpha- \mu Distribution: New Exact Analytical Formulations

Correlation among channels is a physical phenomenon that affects the performance of a wireless communication system and that cannot be neglected in a myriad of realistic fading scenarios. Providing computable mathematical means to better characterize the corresponding statistics is certainly of inte...

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Bibliographic Details
Published in:IEEE transactions on vehicular technology 2011-10, Vol.60 (8), p.4063-4070
Main Authors: Rabelo, G. S., Yacoub, M. D., de Souza, R. A. A.
Format: Article
Language:English
Subjects:
alpha - mu distribution
Applied sciences
Approximation
Approximation methods
Convergence
correlated fading
Correlation
Density
Distribution functions
Disturbances. Regulation. Protection
diversity methods
Electrical engineering. Electrical power engineering
Electrical power engineering
Exact sciences and technology
Fading
joint distributions
Joints
Mathematical analysis
Mathematical models
Operation. Load control. Reliability
Power networks and lines
Receivers
Statistics
Wireless communication
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Summary:Correlation among channels is a physical phenomenon that affects the performance of a wireless communication system and that cannot be neglected in a myriad of realistic fading scenarios. Providing computable mathematical means to better characterize the corresponding statistics is certainly of interest to any design engineer. In this context, this paper further extends the statistical correlation investigations of the α-μ fading model, presenting a new, exact, and easily computable series-type formulation for the multivariate α-μ joint cumulative distribution function (JCDF). Along with this general result and capitalizing on practical assumptions, an alternative, simpler formulation for the α -μ multivariate joint density function and its corresponding distribution function are also provided. These formulations are still general and yet compact, assuming arbitrary fading parameters and correlations among the marginal variates. An important feature of the series-type distribution is that any truncation version of it is a valid distribution. As an application example, the truncated series-based outage probability of the selection combining scheme is computed and compared with that obtained by means of numerical methods and simulations. The results show that a small number of terms of the series are sufficient to provide excellent agreement between approximate and exact results.
ISSN:0018-9545
1939-9359
DOI:10.1109/TVT.2011.2163653