# Three-Dimensional Division of Visible Light Communication Irradiation Area
## 4 VLC Experiment Setup and Discussion
### Establishment of 3D Model  
To determine the best receiving area, we established an ideal illumination area model and an experimental data model using the above experimental data, the 3D schematic diagrams of which are shown in Figure 11.  
Figure 10: Lampshade height: 6 cm. Figure 9: Lampshade height: 5 cm. In Figure 11a, \(\phi\) is the FOV at the transmitter. The illumination model at this point is the conventional Lambert radiation model. In Figure 11b, the red solid line area indicates the theoretical signal reception area. When the receiver is located at any position in this area, the optical signal can theoretically be received. In Figure 11c, the red solid line area indicates the actual signal receivable area. Due to the influence of reflected light, the light sensitivity limitation of the sensor at the receiver, and other factors, the optical signal that can be received in the experiment is somewhat different from the theoretical situation. In Figure 11d, \(d_{0}\) is the outer diameter of the lampshade; \(d_{1}\), \(d_{2}\), and \(d_{3}\) are the longitudinal distances of the receiver in area I, area II and area III, respectively; and \(L_{I}\), \(L_{II}\), and \(L_{III}\) are the lateral distances in area I, area II, and area III, respectively. The received optical signal is error-free, as shown in Figure 11d. The interference factor in this area is light intensity attenuation caused by the change in the communication distance. \(L_{I-1}\) represents the longitudinal distance when the lateral receiving distance of the optical signal is increased to the maximum for the first time. Area I is mainly affected by two aspects of interference: (i) the attenuation of the light intensity due to the change in the distance of the reflected light and (ii) the inter-symbol interference caused by the overlapping of the reflected light. Under the effect of two kinds of interference, the receivable area of the signal exhibits an irregular light distribution. From Figure 11d, the longest distance index (LDI) of the VLC system is defined as  
\[LDI=max_{j}\sum L_{i,}(i{=}I,I1,III;j{=}2,3,4,5,6). \tag{3}\]  
The longest lateral distance (LLD) is expressed as  
\[LLD=max_{i,j}d_{i,}(i{=}1,2,3;j{=}2,3,4,5,6). \tag{4}\]  
Table 2 shows the experimental data of different lampshade heights. Figure 11: Experimental model. (**a**) Model of light radiation without lampshade. (**b**) Light reflection model with lampshade. (**c**) Receivable region of the optical signal for the reflection model. (**d**) Optical signal error-free distribution area. We can infer from Table 2 that as the lampshade height increased, the value of \(d_{1}\) changed slightly, indicating that the maximum horizontal receiving distance of the optical signal in area I was not highly correlated with the lampshade height. With the increase in the lampshade height, the value of \(L_{I-1}\) first increased and then stabilized, indicating that the reflected light had a significant impact on optical communication when the receiver and the transmitter were very close. With increasing longitudinal distance, the effects of reflected light gradually diminished and eventually became stable. The values of \(d_{2}\), \(L_{I}\), and \(d_{3}\) increased with increasing lampshade height, indicating that the change in the lampshade height promoted the longitudinal and the horizontal receiving distance of the optical signal in area I. When the lampshade height increased, \(L_{II}\) first increased and then stabilized, indicating that the change in the lampshade height could not further increase the longitudinal distance of area II. At this time, the light intensity attenuation caused by the change in the distance between the transmitter and the receiver had a significant effect on communication. When the lampshade height increased, the value of \(L_{III}\) did not change significantly. The main reason for this is that the light intensity of area III was seriously attenuated, and the effect of external environment was prominent at this time.