# Channel Characteristics and Link Adaption for Visible Light Communication in an Industrial Scenario
## 3 Analysis of Channel Characteristics
### Angular Spread  
Studying the spatial angular properties of the channel helps to understand the distribution of objects in the scenarios' propagation mechanism of the signal. The angular spread is a key parameter to describe the directions of MPCs [35]. The AS of arrival (ASA) can be calculated by [36]:  
\[\sigma_{ASA}=\sqrt{-2(|\frac{\sum_{r=1}^{R}exp(j\phi_{r}P_{r})}{\sum_{r=1}^{R} P_{r}}|)}, \tag{9}\]  
where \(\phi_{r}\) and \(P_{r}\) are the angle in radians and power of the \(r\)-the path. The distance dependence of ASA in the office and corridor is fitted by the linear model [31]:  
\[ASA(\log_{10}(ASA/1^{\circ}))=\alpha_{ASA}\cdot d+\beta_{ASA}+X_{e}^{ASA}, \tag{10}\]  
where \(\alpha_{ASA}\) and \(\beta_{ASA}\) are the slope and intercept of fitting curves, and \(X_{e}^{ASA}\) is the standard deviation between the AS and fitting curve. Figure 4a presents the real number results for ASA data calculated by (9) and (10), and the fitting results with the linear model in Road 1 and Road 2. The positive slopes of the fitting models (0.04 and 0.05) indicate that the ASA is proportional to the propagation distance under the single TX case. At short propagation distances, the LOS component occupies an absolute power ratio, and the proportion of NLOS components is small. Hence, the received components mainly come from the LED source. However, the LOS component occupies an absolute power ratio, and the proportion of NLOS components is pretty small. However, as the propagation distance increases, the proportion of NLOS components also increases and cannot be overlooked. The distributed signal with power amplitude fluctuations from all directions leads to a larger ASA. Furthermore, the ASA at \(D_{10}\) is 0.3\({}^{\circ}\) larger than that at \(E_{10}\). The RX surrounded by the denser complicated objects will receive more MPCs, leading to more NLOS components. Hence, the ASA is larger. Furthermore, the ASA can be fitted well by a normal distribution. Under the multiple TXs' case, Figure 5b gives the CDF fitting line of the ASA samples with different heights' RX in Road 1. To confirm our results for the fitting of actual and normal graphs, the statistical test function in the Matlab, i.e., the Kolmogorov-Smirnov test (KS-test), is used to decide whether the ASA data follow the  
Figure 4: (**a**) The distance dependence of RMS DS samples under single TX case; (**b**) the CDF of RMS DS under the multiple TXs’ case in Road 1.  
Normal distribution. The result obtained is zero, indicating that VLC cluster numbers follow the Normal distribution. The mean value of ASA (\(\mu\)) at h = 1.5 m is 2.04, which is smaller than that of 2.08 ns at h = 2.5 m. This can also be explained by the blocking effect of objects. Some MPCs received at the RX with a 1.5 m height will be blocked by the surrounding objects, which are set to be higher than 1.5 m, i.e., the NLOS components are reduced. Hence, the mean value of the ASA in the 2.5 m is larger. Furthermore, the fitted mean value of the ASA at 1.5 m is 2.08, which shows a larger value compared to the measured ASA in [37] (1.46). It is mainly because the IIoT scenario is larger and more complicated than the conference room in [37]. The reflecting and scattering multipath can be received in this paper, which makes the ASA larger.  
According to the above analysis, it can be found that the degree of the time domain and spatial domain dispersion (RMS DS and ASA) for VLC channels in this paper is higher than that in the typical rooms of the related works. These differences can be explained by the specificity of the IIoT scenarios, including the large physical size and the abundance of metal scatterers deployed. The complex VLC channel characteristics caused by the features of IIoT scenarios make the VLC system require a good robustness with optimization algorithms for overcoming inter-code interference.