# Vehicular Visible Light Communication for Intersection Management +
## 4 V2X Cooperative System Evaluation
### The Cooperative VLC System  
In Figure 2, a traffic scenario was simulated using VLC cooperative communication. In the lab, as PoC, it was tested by moving the receiver along known paths. The worst-case scenario was modeled. Here, vehicles \(a\), \(b\), \(c\) and \(d\), oncoming both intersections have a conflicting trajectory. When they reach the request distance (see Figure 4), they send a request to the traffic light controller (V2I) that faces the lane, asking permission to cross the intersection. If they receive permission (I2V), they go forward or turn left depending on the occupied lane, otherwise stop at the respective stop lines within the message distance. Four crossing different instants are considered: the request (\(t\)) and the response (\(t^{\prime}\)) times, and also the crossroad enter (\(t^{\prime\prime}\)) and the exit (\(t^{\prime\prime\prime}\)) times. All the requests comprise vehicle positions and approach speeds. If a follower exists (vehicle \(d\)), the request message from its leader, \(c\), includes the position and speed previously received by V2V. This information alerts the controller to a later request message (V2I), confirmed by the follow vehicle. We have assumed that, in the four-legged intersection \(t_{a}<t_{b}<t_{c}<t_{d}<t_{f}\). In the split, for Intersection 1: \(t_{a}<t_{c}<t_{d}=t_{b}<t_{f}\); and for Intersection 2: \(t_{a}=t_{b}<t_{e}\). In Figure 7, the movement of the cars, in the successive moments, with their colorful poses (color arrows) and \(q_{i,j}\) spatial relative poses (dot lines), is displayed for a four-legged intersection (a) and for a split one (b). In coordinating traffic signals (Figure 7b), we assume that a vehicle's movement along a main street (W > E) can be predictable, and the two intersections referred to as one entity, the interchange. Thus, any reference to signal timing includes not only the joint set of phasing patterns at the two intersections, but also the cycle length and the offset relationship between the two intersections. The option of usi  
Figure 7: Movement of the cars, in the successive moments, with their colorful poses (color arrows) and \(q_{i,j}\) spatial relative poses (dot lines). (**a**) Four-legged intersection. (**b**) Split intersection. provides the maximum flexibility because it allows the use of all phasing patterns for the pair of intersections. We denote \(q\), \(q^{\prime}\), \(q^{\prime\prime}\), \(q^{\prime\prime\prime}\) as the vehicle pose estimation at the time \(t\), \(t^{\prime}\), \(t^{\prime\prime}\), \(t^{\prime\prime\prime}\) (request, response, enter and exit times), respectively. To estimate these variables, it is possible to take advantage of what is defined as control inputs, and which represent an estimation of the motion along the time. The vehicle speed can be calculated by measuring the actual travelled distance overtime, using the ID's transmitter tracking. Two measurements are required: distance and elapsed time. The distance is fixed while the lapsed time is obtained using the times where the footprint region changes. There is a fixed spacing between reference points (Figure 2), but the correspondent time integrated by the receiver varies depending on how fast the vehicle is going. The receivers compute the geographical position in the successive instants (path) and infer the vehicle's speed. When there are two neighboring vehicles in different lanes, the geometric relationship between them (\(q_{i,j}\); dotted lines in Figure 7) can be inferred through local SLAM fusing their self-localizations via a chain of geometric relationships among the vehicles poses and the local maps. For a vehicle with several neighboring vehicles, the mesh node (Figure 4) uses the indirect V2V relative pose estimations method taking advantage of the data of each neighboring vehicle. As an example, for vehicle \(d\), two instants can be considered, \(t\) and \(t^{\prime}\). To help control the flow of vehicle \(b\), the request the vehicle \(c\) leader, has to include its position and speed, earlier received by the V2V.