Time- and Frequency-Varying <inline-formula> <tex-math notation="TeX">$K$</tex-math> </inline-formula>-Factor of Non-Stationary Vehicular Channels for Safety-Relevant Scenarios

Abstract

Vehicular communication channels are characterized by a non-stationary time- and frequency-selective fading process due to fast changes in the environment. We characterize the distribution of the envelope of the first delay bin in vehicle-to-vehicle channels by means of its Rician <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="TeX">$K$</tex-math></inline-formula> -factor. We analyze the time–frequency variability of this channel parameter using vehicular channel measurements at 5.6 GHz with a bandwidth of 240 MHz for safety-relevant scenarios in intelligent transportation systems (ITS) . This data enables a frequency-variability analysis from an IEEE 802.11p system point of view, which uses 10 MHz channels. We show that the small-scale fading of the envelope of the first delay bin is Rician distributed with a varying <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="TeX">$K$</tex-math></inline-formula> -factor. The later delay bins are Rayleigh distributed. We demonstrate that the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="TeX">$K$</tex-math></inline-formula> -factor cannot be assumed to be constant in time and frequency. The causes of these variations are the frequency-varying antenna radiation patterns, as well as the time-varying number of active scatterers, and the effects of vegetation. We also present a simple but accurate bimodal Gaussian mixture model, which allows to capture the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="TeX">$K$</tex-math></inline-formula> -factor variability in time for safety-relevant ITS scenarios.