On the approximation of the generalized-Kappa distribution by a gamma distribution for modeling composite fading channels (original) (raw)
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IEEE Transactions on Wireless Communications, 2010
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-model for composite fading. However, further derivations using the generalized-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-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-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.
IEEE Transactions on Wireless Communications, 2000
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-model for composite fading. However, further derivations using the generalized-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-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.
GLOBECOM 2009 - 2009 IEEE Global Telecommunications Conference, 2009
Abstrac 1 -Composite fading takes place in several communication channels due to the random variations of the local average power of the received multipath-faded signal. The generalized-K (Gamma-Gamma) probability density function (PDF) has been proposed recently to model composite fading in wireless channels. However, further derivations using the generalized-K PDF have shown to be 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. As expected, matching positive and negative moments leads to a better approximation in the upper and lower tail regions, respectively. However, due to arising limitations for small values of the multipath fading and shadowing parameters, and the higher level of accuracy sought, the use of an adjustable form for the expressions of the approximating Gamma PDF parameters, obtained by matching the first two positive moments, is devised. The optimal values of the adjustment factor for different integer and non-integer values of the fading and shadowing parameters are given. The introduced approximation may simplify performance analysis in distributed antenna systems (DASs), network MIMO, multihop relay networks, radar, and sonar systems.
On the Approximation of the Generalized-K PDF by a Gamma PDF Using the Moment Matching Method
2009 IEEE Wireless Communications and Networking Conference, 2009
Using the Nakagami probability density function (PDF) to model multipath fading and the Gamma PDF to model shadowing, in a wireless channel, has led to a closed-form expression for the composite fading PDF, known as the generalized-K PDF (also called Gamma-Gamma PDF). However, further derivations have shown that the cumulative distribution function (CDF) and the characteristic function of the generalized-K PDF contain special functions that are involved to handle. In this paper, an approximation of the generalized-K PDF by the familiar Gamma PDF is introduced. The parameters of the approximating Gamma PDF are computed using the moment matching method. The accuracy of this approximation in the lower and upper tail regions is enhanced by adjusting the parameters of the approximating Gamma distribution in each region. The CDF and the complementary CDF plots show that this approximation is sufficiently accurate for both integer and non-integer practical values of the multipath fading and shadowing parameters. The region-wise approximation obtained by the adjusted moment matching method is used to wellapproximate the PDF of the sum of identically and independent generalized-K random variables. Applications of the obtained results arise in distributed antenna systems (DASs), cooperative relay networks, radar, and sonar systems.
2001
Capitalizing on the Moschopoulos single gamma series representation of the probability density function (pdf) of the sum of gamma variates, we provide a pdf-based approach for the performance analysis of maximal-ratio combining and postdetection equal-gain combining diversity techniques as well as cochannel interference of cellular mobile radio systems over Nakagami-fading channels with arbitrary parameters. Aside from putting under the same umbrella many of the past results obtained via characteritic function (CF) or moment generating function (MGF)-based approaches, the proposed approach also allows the derivation of additional performance measures, which are harder to analyze via CF or MGF-based approaches.
IEEE Transactions on Communications, 2000
The Gamma-Gamma (GG) distribution has recently attracted the interest within the research community due to its involvement in various communication systems. In the context of RF wireless communications, GG distribution accurately models the power statistics in composite shadowing/fading channels as well as in cascade multipath fading channels, while in optical wireless (OW) systems, it describes the fluctuations of the irradiance of optical signals distorted by atmospheric turbulence. Although GG channel model offers analytical tractability in the analysis of single input single output (SISO) wireless systems, difficulties arise when studying multiple input multiple output (MIMO) systems, where the distribution of the sum of independent GG variates is required. In this paper, we present a novel simple closed-form approximation for the distribution of the sum of independent, but not necessarily identically distributed GG variates. It is shown that the probability density function (PDF) of the GG sum can be efficiently approximated either by the PDF of a single GG distribution, or by a finite weighted sum of PDFs of GG distributions. To reveal the importance of the proposed approximation, the performance of RF wireless systems in the presence of composite fading, as well as MIMO OW systems impaired by atmospheric turbulence, are investigated. Numerical results and simulations illustrate the accuracy of the proposed approach.
IEEE Transactions on Wireless Communications, 2018
In this paper, we perform a systematic investigation of the statistics associated with the product of two independent and non-identically distributed κ-μ random variables. More specifically, we develop novel analytical formulations for many of the fundamental statistics of interest, namely, the probability density function, cumulative distribution function, and moment-generating function. Using these new results, closedform expressions are obtained for the higher order moments, amount of fading and channel quality estimation index, while analytical formulations are obtained for the outage probability, average channel capacity, average symbol error probability, and average bit error probability. These general expressions can be reduced to a number of fading scenarios, such as the double Rayleigh, double Rice, double Nakagami-m, κ-μ/Nakagami-m, and Rice/Nakagami-m, which all occur as special cases. Additionally, as a byproduct of the work performed here, formulations for the κ-μ/κ-μ composite fading model can also be deduced. To illustrate the efficacy of the novel expressions proposed here, we provide useful insights into the outage probability of a dualhop system used in body area networks, and demonstrate the suitability of the κ-μ/κ-μ composite fading for characterizing shadowed fading in device-to-device channels.
IEEE Transactions on Vehicular Technology, 2015
The statistical properties of the multivariate Gamma-Gamma (ΓΓ) distribution with arbitrary correlation have remained unknown. In this paper, we provide analytical expressions for the joint probability density function (PDF), cumulative distribution function (CDF) and moment generation function of the multivariate ΓΓ distribution with arbitrary correlation. Furthermore, we present novel approximating expressions for the PDF and CDF of the sum of ΓΓ random variables with arbitrary correlation. Based on this statistical analysis, we investigate the performance of radio frequency and optical wireless communication systems. It is noteworthy that the presented expressions include several previous results in the literature as special cases.