Intervehicle Communication: Cox-Fox Modeling

Safety message dissemination in a vehicular ad-hoc network (VANET) requires vehicle-to-vehicle (V2V) communication with low latency and high reliability. The dynamics of vehicle passing and queueing as well as high mobility create distinctive propagation characteristics of wireless medium and inevitable uncertainty in space-time patterns of the vehicle density on a road. It is therefore of great importance to account for random vehicle locations in V2V communication. In this paper, we characterize intervehicle communication in a random field of vehicles, where a beacon or head vehicle (transmitter) broadcasts safety or warning messages to neighboring client vehicles (receivers) randomly located in a cluster on the road. To account for a doubly stochastic property of the VANET, we first model vehicle´s random locations as a stationary Cox process with Fox´s H-distributed random intensity (vehicle concentration) and derive the distributional functions of the lth nearest client´s distance from the beacon in such a Fox Cox field of vehicles. We then consolidate this spatial randomness of receiving vehicles into a path loss model and develop a triply-composite Fox channel model that combines key wireless propagation effects such as the distance-dependent path loss, large-scale fading (shadowing), and small-scale fading (multipath fading). In Fox channel modeling, each constituent propagation effect is described as Fox´s H-variate, culminating again in Fox´s H-variate for the received power or equivalently the instantaneous signal-to-noise ratio at the lth nearest client vehicle. Due to versatility of Fox´s H-functions, this stochastic channel model can encompass a variety of well-established or generalized statistical propagation models used in wireless communication; be well-fitted to measurement data in diverse propagation environments by varying parameters; and facilitate a unifying analysis for fundamental physical-layer performances, such as error probability- and channel capacity, using again the language of Fox´s H-functions. This work serves to develop a unifying framework to characterize V2V communication in a doubly stochastic VANET by averaging both the small- and large-scale fading effects as well as the (random) distance-dependent path losses.