## 3 Results and Discussion
### Experimental Results and Discussion  
Firstly, we evaluated the communication performance at three specific testing points, including points A (25 cm, 25 cm), B (0 cm, 0 cm), and C (\(-\)30 cm, \(-\)30 cm), where each testing point received 1e\({}^{7}\) frames of data (1e\({}^{7}\)\(\times\) 100 = 1e\({}^{9}\) bits). Frames of received waveforms of four LEDs after sampling are shown in Figure 10. We can see that the PD received clear waveforms from each LED at these specific testing points. Based on the  
Figure 8: Surface diagram of positioning error estimated at all testing points of the 8-user VLCP system when the length of spreading code is (**a**)16, (**b**) 32, and (**c**) 64.  
Figure 7: Surface diagram of BER estimated at all testing points of the 8-user VLCP system when the length of spreading code is (**a**)16, (**b**) 32, and (**c**) 64.  
Figure 9: CDF of (**a**) BER and (**b**) positioning error estimated in the whole receiving plane when the 8-user VLCP system adopts spreading codes with different length.  
received waveforms, all of the user data were able to be entirely recovered by using the spreading codes according to Equation (12). Therefore, the PD at these specific testing points was able to achieve error-free communication.  
Figure 10: Frames of received waveforms of LED 1 (**a**) measured at point A, (**b**) measured at point B, and (**c**) measured at point C after sampling; frames of received waveforms of LED 2 (**d**) measured at point A, (**e**) measured at point B, and (**f**) measured at point C after sampling; frames of received waveforms of LED 3 (**g**) measured at point A, (**h**) measured at point B, and (**i**) measured at point C after sampling; and frames of received waveforms of LED 4 (**j**) measured at point A, (**k**) measured at point B, and (**l**) measured at point C after sampling.  
For the positioning performance, we estimated the RSS of each LED at all testing points first. The RSS distributions of four LEDs showed a similar and clear trend, as shown in Figure 11, where the RSS became larger when the PD was closer to the LED. Based on the estimated RSS of each LED, we adopted the fitting method to correct Equation (14). Thus, transmission distance between four LEDs and the PD was able to be calculated from:  
\[\left\{\begin{array}{l}\widetilde{D}_{1}=40.42(\Re_{1})^{-0.2278}+1.47\\ \widetilde{D}_{2}=30.21(\Re_{2})^{-0.2658}+14.06\\ \widetilde{D}_{3}=20.24(\Re_{3})^{-0.3217}+29.08\\ \widetilde{D}_{4}=19.15(\Re_{4})^{-0.3334}+29.81\end{array}\right.. \tag{17}\]  
Then, we defined the absolute value of the difference between estimated transmission distance and real distance as the error of transmission distance (ETD). The ETD distributions of four LEDs are shown in Figure 12, where the closer PD was to the LED, the lower ETD. This is because the area near the LED had the better SNR. Finally, with the measured transmission, we estimated the PD location by using Equation (16). Figure 13 displays the positioning results. We found that the center area of the receiving plane had better positioning performance than the corner area, which was caused by uneven illumination. From Figure 13b, there was an approximate 96% positioning error under 2.0 cm, and the average positioning error was 1.08 cm. Therefore, the proposed VLCP system was able to realize an accurate positioning with a 2 cm positioning accuracy.  
Figure 11: The RSS distributions of (**a**) LED 1, (**b**) LED 2, (**c**) LED 3, and (**d**) LED 4.