# Design of Indoor Visible Light Communication PAM4 System
## 4 Modulation Characteristic Analysis
### Multiplicative Noise  
We use the low-frequency multiplicative noise data tested in the outdoor actual environment to research and analyze the lognormal noise model and test the noise data in light rain, moderate rain, heavy rain, wet snow, dry snow, mist, and thick fog weather. The noise mean has been normalized, and the variance after noise fitting is 0.092, 0.053, 0.057, 0.114, 0.156, 0.133, and 0.215, respectively. Through numerical calculation and the BER formula of Equation (13), the BER performance results are obtained, as shown in Figure 13a. As can be seen from Figure 13a, for the BER of \(10^{-5}\), light rain, moderate rain, and heavy rain, respectively, need 39.2 dB, 35.1 dB, and 37.3 dB. The SNR difference is 4.1 dB and 2.2 dB in the case of the same SNR, and the BER of light rain is greater than the BER of heavy rain and moderate rain because the backscattering of rain particles is large in light rain weather. At this time, the signal attenuation is more serious, with the increase in rain, the radius of rain particles increases, but the number remains almost unchanged, the forward scattering will increase with the increase in rain particles; at this time, the signal attenuation is small, resulting in the variance in the case of light rain is greater than the variance in the case of moderate rain and heavy rain, so the BER in the case of light rain is large.  
Comparing Figure 10 can be seen to achieve the BER of \(10^{-5}\), white Gaussian noise requires a SNR of 13.8 dB, the GMM noise model requires a SNR of 16.6 dB and 18.9 dB, and  
Figure 12: The relationship between BER and SNR (**a**) Set 9 and Set 10 (**b**) Set 11 and Set 12.  
Figure 13: The relationship between BER and SNR: (**a**) rainy days, (**b**) snowy days, and (**c**) foggy days.  
in such a SNR, light rain, moderate rain, and heavy rain are greater than \(10^{-1}\). Even in the case of 20 dB SNR, the BER is also very large; therefore, the influence of the lognormal noise model on the BER of PAM4 is much greater than that of the GMM noise model. The reason for this huge difference is that the influence of the lognormal noise belongs to multiplicative noise, the reaction channel state information, and CMM noise belongs to additive noise, the fluctuation of the multiplicative noise is more violent, has low uniformity, and a greater impact on BER performance.  
The BER performance results in the case of snowy days are shown in Figure 13b. As can be seen from Figure 13b, under the same SNR, the BER of dry snow is greater than that of wet snow. For the BER of \(10^{-5}\), the SNR difference in the two weather conditions is 2.9 dB. Comparing Figure 13a,b, the BER performance on snowy days is generally greater than on rainy days. This can be seen from the variance after fitting the noise data. The noise variance on snowy days is greater than on rainy days, and the attenuation of the signal is greater than on rainy days, resulting in the BER performance being worse overall than on rainy days.  
The BER performance results in the case of foggy days are shown in Figure 13c. As shown in Figure 13c, under the same SNR, the BER of thick fog is greater than that of mist. For the BER of \(10^{-5}\), the mist needs a SNR of 38.5 dB, while when the thick fog is 40 dB SNR, the BER is of the order of \(10^{-4}\), so the BER performance in thick fog weather is worse, which can be seen from the variance after fitting the noise data. Compared with Figure 13a,c, the BER performance on foggy days is greater than that on rainy days, the noise variance on foggy days is greater than that on rainy days, and the attenuation of the signal is greater than that on rainy days, resulting in the BER performance being worse than that on rainy days.