Abstract
Properly modeling the shadowing effects during wireless transmissions is crucial to perform the network quality assessment. From a mathematical point of view, using composite distributions allows one to combine both fast fading and slow fading stochastic phenomena. Numerous statistical distributions have been used to account for the fast fading effects. On the other hand, even though several studies indicate the adequacy of the Lognormal distributon (LNd) as a shadowing model, they also reveal this distribution renders some analytic tractability issues. Past works include the combination of Rayleigh and Weibull distributions with LNd. Due to the difficulty inherent to obtaining closed form expressions for the probability density functions involved, other authors approximated LNd as a Gamma distribution, creating Nakagami-m/Gamma and Rayleigh/Gamma composite distributions. In order to better mimic the LNd, approximations using the inverse Gamma and the inverse Nakagami-m distributions have also been considered. Although all these alternatives were discussed, it is still an open question how to effectively use the LNd in the compound models and still get closed-form results. We present a novel understanding on how the α-μ distribution can be reduced to a LNd by a limiting procedure, overcoming the analytic intractability inherent to Lognormal fading processes. Interestingly, new closed-form and series representations for the PDF and CDF of the composite distributions are derived. We build computational codes to evaluate all the expression hereby derived as well as model real field trial results by the equations developed. The accuracy of the codes and of the model are remarkable.
Highlights
In the path from the transmitter to the receiver, besides the propagation loss, the mobileradio signals can be blocked by physical obstructions—shadowing—and suffer multiple reflections, scattering and diffraction—multipath fading
The most common composite models used in the literature are the Rayleighl-Lognormal, composed by the fast fading modeled by Rayleigh distribution and shadowing modeled by Lognormal distribution
Literature presents the results of a series of outdoors field trials which were conducted at the University of Brasília (UnB) and at the University of Campinas (Unicamp), Brazil, in order to obtain the empirical PDFs of the composite multipath/shadowing phenomena [21]
Summary
In the path from the transmitter to the receiver, besides the propagation loss, the mobileradio signals can be blocked by physical obstructions—shadowing—and suffer multiple reflections, scattering and diffraction—multipath fading In this context, a composite fading model, i.e., those describing the combined effects of small fading and fast fading, arises in several opportunities and, is considered to be of great importance [1]. In order to avoid the mathematical difficulties inherent to the Lognormal distribution, authors such as [5] opted for the Gamma distribution as substitute, due to its rather convenient algebraic representation This approach allowed the composition of Nakagamim/Gamma and Rayleigh/Gamma distribution to obtain fading models in closed-form [6].
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