Abstract
The characterization of multipath fading and shadowing in wireless communication systems is essential towards the evaluation of various performance measures. It is well known that the statistical characterization of shadowing phenomena is captured by distributions viz., log-normal distribution, gamma distribution and other mixture distributions. However, it is observed that the log-normal distribution fails to characterize the outliers in the fading signal. The extreme fluctuations in the fading signal needs to be characterized efficiently for error free computation of the various performance metrics. In this context, this paper portrays an adaptive generalized Tsallis’ non-extensive q-Lognormal model towards the characterization of various fading channels. This model operates well with the synthesized fading signals and captures the wide range of tail fluctuations to adapt different fading scenarios. The significance and applicability of the proposed novel q-lognormal model in capturing the slow fading channels is validated using different statistical tests viz., chi-square test and symmetric JS measure. Furthermore, essential performance measures viz., the average channel capacity, closed form expression of cumulative distribution function (CDF) in terms of Gauss-Hypergeometric function \({}_2{F_1}\left[ {\mathrm{{a, b, c; z}}} \right] \), moment generating function, higher order moments corresponding to q-Lognormal channel capacity and coefficient of variation is evaluated corresponding to the proposed q-lognormal model performing extensive Monte-Carlo simulation techniques up to \(O(10^7)\).
Highlights
In pragmatic wireless propagation environments, the channels gets impaired by shadowing phenomena
The log-normal distribution is often averaged with several other distributions viz., the Rayleigh distribution, the Weibull distribution to contemplate the concurrent effects of fading and shadowing [23, 18, 27]
It is observed that the log-normal distribution has an ascendancy over other slow fading channel models viz., gamma distribution, inverse gaussian distribution [4, 16] in capturing the long range fading signals
Summary
In pragmatic wireless propagation environments, the channels gets impaired by shadowing phenomena. The outliers are the regions in the signal where the extreme fluctuations are observed due to various obstructions between the transmitter and the receiver, and this should be analyzed effectively for error free signal transmission and evaluation of performance measures In this context, a framework incorporating maximum entropy principle based on non-extensive parameter ‘q’ defined by Tsallis’ is portrayed to explain the extreme tail fluctuations of the fading signals [10, 9, 14, 28, 7]. It is observed that the proposed q-Lognormal distribution based on Tsallis’ entropy widely captures the extreme fluctuations in the tail regions of the fading signals. In this setting, the presented model signified an excellent agreement to the outliers of the synthesized fading signals in the continuous range, 1 < q < 3.
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