  LiDAR-based sensors employing optical spectrum signals play a vital role in
providing significant information about the target objects in autonomous
driving vehicle systems. However, the presence of fog in the atmosphere
severely degrades the overall system's performance. This manuscript analyzes
the role of fog particle size distributions in 3D object detection under
adverse weather conditions. We utilise Mie theory and meteorological optical
range (MOR) to calculate the attenuation and backscattering coefficient values
for point cloud generation and analyze the overall system's accuracy in Car,
Cyclist, and Pedestrian case scenarios under easy, medium and hard detection
difficulties. Gamma and Junge (Power-Law) distributions are employed to
mathematically model the fog particle size distribution under strong and
moderate advection fog environments. Subsequently, we modified the KITTI
dataset based on the backscattering coefficient values and trained it on the
PV-RCNN++ deep neural network model for Car, Cyclist, and Pedestrian cases
under different detection difficulties. The result analysis shows a significant
variation in the system's accuracy concerning the changes in target object
dimensionality, the nature of the fog environment and increasing detection
difficulties, with the Car exhibiting the highest accuracy of around 99% and
the Pedestrian showing the lowest accuracy of around 73%.
