Asymptotically Exact Approximations to Generalized Fading Sum Statistics

We propose a unified approach to approximate the probability density function and the cumulative distribution function of a sum of independent channel envelopes following generalized, and possibly mixed, fading models. In the proposed approach, the approximate sum distribution can be chosen out of a...

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Bibliographic Details
Published in:IEEE transactions on wireless communications 2020-01, Vol.19 (1), p.205-217
Main Authors: Perim, Victor, Sanchez, Jose David Vega, Filho, Jose Candido Silveira Santos
Format: Article
Language:English
Subjects:
Approximation methods
asymptotic analysis
Asymptotic properties
Closed-form solutions
Convolution
Distribution functions
Diversity reception
Economic models
Fading
Fading channels
generalized fading channels
Matching
Nakagami distribution
Parameters
Probability density function
Probability density functions
Random variables
Signal to noise ratio
Statistical analysis
Statistical models
Sums
sums of random variables
Wireless communication
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Summary:We propose a unified approach to approximate the probability density function and the cumulative distribution function of a sum of independent channel envelopes following generalized, and possibly mixed, fading models. In the proposed approach, the approximate sum distribution can be chosen out of a broad class of statistical models. More fundamentally, given any chosen model, the parameters of the approximate sum distribution are calibrated by matching its asymptotic behavior around zero to that of the exact sum. In a subsidiary fashion, one or more moments of the exact and approximate sums are also matched to one another if the approximate distribution has three or more parameters to be adjusted, respectively. As illustrated through many numerical examples, our approach outperforms existing ones that are solely based on moment matching, by yielding statistical approximations that are remarkably accurate at medium to high signal-to-noise ratio - a paramount operational regime for communications systems. Our results find applicability in several wireless applications where fading sums arise, and can be readily extended to accommodate sums of fading (power) gains and, in a broader context, generic sums of non-negative random variables.
ISSN:1536-1276
1558-2248
DOI:10.1109/TWC.2019.2943336