# The Necessity of LED to Ambient Light Ratio Optimization for Vehicular Optical Camera Communication
## 4 Simulation
### Simulation Results  
#### 4.4.1 Effect of L2A Ratio  
This section provides simulation results to illustrate the effect of the L2A ratio. The LED panel images were replicated with the L2A ratio varying from 0.2 to 4. The ambient light is set randomly in the range from 50 to 16,000 lux. The LED luminance is set based on the ambient light and the L2A ratio. The LED surface reflectance is set randomly in the range from 0.3 to 0.5. The ISO is set based on the ambient light. The value of the communication distance and LED interval are fixed at 50 m and 1, respectively. The remaining parameters are set to their fixed values given in Table 1. Figure 12 shows examples of the LED panel frames replicated with L2A ratios of 0.2, 1, 2, and 4, respectively. The figure shows that the extinction ratio changes according to the L2A ratios: At a low L2A ratio, the extinction becomes low because the greyscales of the On and Off LEDs are almost the same. On the other hand, at a high L2A ratio, the extinction becomes high, expressed through the clear difference in the greyscales of the On and Off LEDs.  
Figure 13 shows examples of the distribution of the LED features of typical frames at different L2A ratios. The LED interval in these figures are about the same. In Figure 13a, the L2A ratio is small and the features of each class of LEDs clump together, leading to a small Wvar. However, the clusters of the On and Off LEDs are also close to each other, leading to a small Bvar. In Figure 13b, the L2A ratio is at a mid level and the features of each class of LEDs are spread more, leading to a larger Wvar. However, the clusters of the On and Off LEDs are also apart from each other, leading to a larger Bvar. In Figure 13c, the L2A ratio is high, the clusters of each class of LEDs are spread even more, leading to an even larger Wvar. The Bvar also increases with the distance between the centers of the two clusters.  
Figure 14a shows trend of Bvar and Wvar when the L2A ratio increases. The Wvar of the LED features can be seen to increase all the way as the L2A ratio increases. The Bvar also initially increases with the L2A ratio. However, when the L2A ratio exceeds 2.5, the Bvar barely increases. This is because the maximum greyscale in the image is 255. When the L2A ratio exceeds 2.5, the greyscales of the On LEDs do not increase anymore. However, due to increasing interference, the greyscales of the Off LEDs continue increasing and approach those of the On LEDs. This makes the clusters of the Off LED features become similar to those of the On LED features and reduces the Bvar.  
Figure 12: Replicated LED panel frames at different L2A ratios.  
Figure 14b shows the trend of B2W variance ratios when the L2A ratio changes. It can be seen that when the LED interval is 1 and the communication distance is 50m, the value of the optimal L2A ratio is 2. The distinguishability of the On and Off LEDs would be highest at this L2A ratios. Note that this optimal value of the L2A ratio would change when the LED interval and the communication distance change.  
Figure 14: Variances corresponding to L2A ratios. (**a**) Bvar and Wvar corresponding to L2A ratios. (**b**) Between-class variance to the within-class variance (B2W) ratio corresponding to L2A ratios.  
Figure 13: Distribution of LED features at different L2A ratios. (**a**) Low L2A ratio. (**b**) Mid L2A ratio. (**c**) High L2A ratio.