On the approximation of the generalized-Κ distribution by a gamma distribution for modeling composite fading channels
ABSTRACT In wireless channels, multipath fading and shadowing occur simultaneously leading to the phenomenon referred to as composite fading. The use of the Nakagami probability density function (PDF) to model multipath fading and the Gamma PDF to model shadowing has led to the generalized-K model for composite fading. However, further derivations using the generalized K PDF are quite involved due to the computational and analytical difficulties associated with the arising special functions. In this paper, the approximation of the generalized-K PDF by a Gamma PDF using the moment matching method is explored. Subsequently, an adjustable form of the expressions obtained by matching the first two positive moments, to overcome the arising numerical and/or analytical limitations of higher order moment matching, is proposed. The optimal values of the adjustment factor for different integer and non-integer values of the multipath fading and shadowing parameters are given. Moreover, the approach introduced in this paper can be used to well-approximate the distribution of the sum of independent generalized-K random variables by a gamma distribution; the need for such results arises in various emerging distributed communication technologies and systems such as coordinated multipoint transmission and reception schemes including distributed antenna systems and cooperative relay networks.
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ABSTRACT: Empirical justifications for the lognormal, Rayleigh and Suzuki (1977) probability density functions in multipath fading channels are examined by quantifying the rates of convergence of the central limit theorem (CLT) for the addition and multiplication of random variables. The accuracy of modeling the distribution of rays which experience multiple reflections/diffractions between transmitter and receiver as lognormal is quantified. In addition, it is shown that the vector sum of lognormal rays, such as in a narrow-band signal envelope, may best be approximated as being either Rayleigh, lognormal or Suzuki distributed depending on the fading channel conditions. These conditions are defined statisticallyIEEE Transactions on Communications 05/1998; · 1.75 Impact Factor
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ABSTRACT: The Rayleigh-lognormal distribution, which has proved useful for modelling fading-shadowing wireless channels, has a complicated integral form. The authors have accurately approximated it by the K distribution. This distribution is simpler and thus more appropriate for analysis and design of wireless communication systemsElectronics Letters 05/1998; · 1.04 Impact Factor
Conference Proceeding: On the utility of gamma PDF in modeling shadow fading (slow fading)[show abstract] [hide abstract]
ABSTRACT: Shadow fading causes random fluctuations of the envelope mean at the mobile. The lognormal distribution is widely accepted for this phenomenon. In this paper we argue that, based on theoretical results and measured data, gamma distribution does the job as well. Then we show that by using the gamma distribution and in contrast with the use of the lognormal distribution, we can obtain easy-to-use and closed-form composite PDFs for fading channels, which in turn extremely simplify analytic calculationsVehicular Technology Conference, 1999 IEEE 49th; 08/1999