Second-Order Statistics of $\kappa-\mu$ Shadowed Fading Channels

Simon L Cotton

doi:10.1109/tvt.2015.2506260

Abstract

In this paper, novel closed-form expressions for the level crossing rate and average fade duration of $\kappa-\mu$ shadowed fading channels are derived. The new equations provide the capability of modeling the correlation between the time derivative of the shadowed dominant and multipath components of the $\kappa-\mu$ shadowed fading envelope. Verification of the new equations is performed by reduction to a number of known special cases. It is shown that as the shadowing of the resultant dominant component decreases, the signal crosses lower threshold levels at a reduced rate. Furthermore, the impact of increasing correlation between the slope of the shadowed dominant and multipath components similarly acts to reduce crossings at lower signal levels. The new expressions for the second-order statistics are also compared with field measurements obtained for cellular device-to-device and body-centric communication channels, which are known to be susceptible to shadowed fading.

Highlights

The κ − μ shadowed fading model first appeared in the literature in [1] and immediately after this in [2]
Both papers have developed important statistics related to the κ − μ shadowed fading model such as the pdf and the momentgenerating function
To illustrate the utility of the new equations for modeling shadowed fading channels, they were compared with data obtained from two different sets of field measurements, which considered channels that are known to be susceptible to shadowed fading

Summary

INTRODUCTION

The κ − μ shadowed fading model first appeared in the literature in [1] and immediately after this in [2]. In [1], a rigorous mathematical development of the model was performed, whereas in [2], the model was the result of channel measurements conducted to characterize the shadowed fading observed in D2D communication channels Both papers have developed important statistics related to the κ − μ shadowed fading model such as the pdf and the momentgenerating function. Pi and qi are the mean values of the inphase and quadrature phase components of multipath cluster i, and d2 = In this model, all of the dominant components are subject to the same common shadowing fluctuation, i.e., ξ, which is a Nakagami-m random variable with the shaping parameter m used to control the amount of shadowing experienced by the dominant components, and E[ξ2] = 1.

LEVEL CROSSING RATE

AVERAGE FADE DURATION

COMPARISON WITH MEASURED SHADOWED FADING CHANNELS

CONCLUSION