Effect of Lateral Displacement Distribution on Vehicular Visible Light Communication

The availability of light-emitting diodes (LEDs) in vehicle exteriors (i.e., headlights and taillights) enables visible light communication (VLC) to be used as vehicle-to-vehicle (V2V) wireless access technology. Initial works on vehicular VLC (V-VLC) build upon the assumption that vehicles may have fixed lateral displacement with respect to other vehicles or with respect to the center of the lane. In fact, the vehicles do not stay at a fixed distance from the center of the lane while they are moving. Instead, they move left and right with a distribution known as a lateral displacement distribution (LDD), which is well represented by a Gaussian distribution. In this paper, we consider two vehicles following each other where the LDD of two traveling vehicles are modeled by independent and non-identically distributed (i.n.i.d) Gaussian random variables. We first derive a probability distribution function (PDF) for the relative displacement of one vehicle to another. Utilizing our derived expression, we further drive a closed-form BER expression for two vehicles following each other and investigate the effect of vehicular LDD on the error rate performance. We finally present numerical results to confirm our findings.