Statistical Models for Fading and Shadowed Fading Channels in Wireless Systems: A Pedagogical Perspective

Abstract

A unified analysis of statistical models for describing fading, shadowing, and shadowed fading channels is presented from a pedagogical viewpoint. The different probability density functions such the Rayleigh, Nakagami, gamma, generalized gamma, Weibull, lognormal, Nakagami-lognormal, K distribution, generalized K distribution, and Nakagami inverse Gaussian distribution are presented and the relationships among them are detailed. These density functions are compared in terms of two quantitative measures, namely the amount of fading and outage probability. A general approach to fading and shadowed fading channels using a cluster based approach is also presented to link several of the distributions. It is expected that this overview will be very helpful to students and educators who are engaged in the study of wireless systems and the adverse impact of fading and shadowing in wireless data transmission.

Statistical models for battery recharging time in RF energy harvesting systems

“…Parameterized by m representing the effect of fading, the Nakagami-m channel model is an approximation of the Rician channel and the generalized form of the Rayleigh channel (for m = 1). The PDF of the instantaneous received power in presence of Nakagami-m fading is [12] …”

Estimation of the Composite Fast Fading and Shadowing Distribution Using the Log-Moments in Wireless Communications

“…4 we have plotted a graph with the values of permitted α and µ for m = 0.5 to 3.5 and σ s = 0 to 12 dB using (45) and (46). The region shaded in grey corresponds to the possible values of α and µ using the log-moments estimators which is limited for the four curves.…”

“…For both µ = 1 and α = 2 the α-µ is equivalent to a Rayleigh distribution [28]. Recently, in [46] Shankar obtained boundaries for α values in shadowed channels. This restriction assumes that the multipath physical model proposed by Yacoub in [29, (10)] is satisfied.…”

“…This optimal size of the window assures that the received signal samples contained in this window are not substantially affected by shadowing. For window sizes larger than this optimal size, the received signal samples also suffer shadowing and the standard deviation increases until σ c given by (46). Nevertheless, the performance of this method depends strongly on the choice of the window center.…”

The Complexα-μFading Channel with OFDM Application

“…Wireless communication channels are subject to fading, with the received signal varying in a random manner [1,2]. Because signal variation deteriorates the performance of the communication systems, the correct characterization of the phenomenon is of paramount importance.…”