The \kappa- \mu Shadowed Fading Model With Integer Fading Parameters

We show that the popular and general κ-μ shadowed fading model with integer fading parameters μ and m can be represented as a mixture of squared Nakagami-m̑ (or Gamma) distributions. Thus, its PDF and CDF can be expressed in a closed form in terms of a finite number of elementary functions (powers a...

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Bibliographic Details
Published in:IEEE transactions on vehicular technology 2017-09, Vol.66 (9), p.7653-7662
Main Authors: Lopez-Martinez, F. Javier, Paris, Jose F., Romero-Jerez, Juan M.
Format: Article
Language:English
Subjects:
<named-content xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:ali="http://www.niso.org/schemas/ali/1.0/" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" content-type="math" xlink:type="simple"> <inline-formula> <tex-math notation="LaTeX"> kappa</tex-math> </inline-formula> -<inline-formula> <tex-math notation="LaTeX"> mu</tex-math> </inline-formula> </named-content> shadowed fading
Channel capacity
Closed form solutions
Communication systems
Cumulative distribution function
Exact solutions
Fading
Fading channels
gamma distribution
Mathematical models
Nakagami distribution
nakagami fading
Parameters
Performance evaluation
Probability density function
Random variables
Shape
Systems analysis
wireless channel modeling
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Summary:We show that the popular and general κ-μ shadowed fading model with integer fading parameters μ and m can be represented as a mixture of squared Nakagami-m̑ (or Gamma) distributions. Thus, its PDF and CDF can be expressed in a closed form in terms of a finite number of elementary functions (powers and exponentials). The main implications arising from such connection are then discussed, which can be summarized as follows. First, the performance evaluation of communication systems operating in κ-μ shadowed fading becomes as simple as if a Nakagami-m̑ fading channel was assumed. Second, the κ-μ shadowed distribution can be used to approximate the κ-μ distribution using a closed-form representation in terms of elementary functions, by choosing a sufficiently large value of m. Finally, restricting the parameters μ and m to take integer values has limited the impact in practice when fitting the κ-μ shadowed fading model to field measurements. As an application example, the average channel capacity of communication systems operating under κ-μ shadowed fading is obtained in closed-form.
ISSN:0018-9545
1939-9359
DOI:10.1109/TVT.2017.2678430