Generic stochastic modeling of vehicle-to-vehicle wireless channels

We present a generic statistical characterization of the vehicle-to-vehicle (V-V) wireless channel by adopting a stochastic modeling approach. Our approach is based on the doubly underspread (DU) property of non-wide sense stationary uncorrelated scattering (non-WSSUS) wireless channels, with V-V channels pertaining to this category. DU channels exhibit explicit frequency and time intervals over which they are approximated as WSSUS. We call these intervals restricted time interval (RTI) and restricted bandwidth (RBW), and variations taking place inside them are characterized as small scale variations. Large scale variations take place outside RTI and RBW. In this paper, we focus on small scale variations, thus, our modeling finds its applicability within RTI and RBW. As practical V-V channels exhibit rapid temporal fluctuations due to the inherent mobility of transmitter (Tx), receiver (Rx) and surrounding scatterers (e.g., other vehicles), we analyze the relevant second order statistics characterizing temporal variability, namely, the a) temporal correlation function (CF) (or autocorrelation function (ACF)), b) power spectral density (PSD) (or Doppler spectrum), c) level crossing rate (LCR) and d) average fade duration (AFD). Our analysis considers three-dimensional (3-D) scattering at the Tx and Rx together with random scatterers' mobility. Illustrative examples demonstrate the usefulness and flexibility of our analysis, which is further validated by fitting the theoretical LCR to an empirical, obtained at a US interstate highway. We show that significant Doppler frequencies can arise due to scatterers' mobility exceeding the respective maximum and minimum values when considering only Tx and Rx mobility. Also scatterers' mobility causes more rapid temporal variations when it becomes more intense. The latter is also true when 3-D scattering at the Tx and/or Rx spreads over a greater range of angular sectors and becomes less directional.