# Channel Characteristics and Link Adaption for Visible Light Communication in an Industrial Scenario
## 3 Analysis of Channel Characteristics
### Rms Ds  
Another essential channel characteristic is the RMS DS, which is a metric presenting the temporal dispersion of the multipath transmission. Furthermore, the inter-symbol interference may be caused by large DS. It is defined as:  
\[\tau_{RMS}=\sqrt{\frac{\int_{0}^{\infty}(t-\tau_{0})^{2}h(t)dt}{\int_{0}^{\infty }h(t)dt}}, \tag{6}\]  
where \(\tau_{0}\) denoted the mean delay:  
\[\tau_{0}=\frac{\int_{0}^{\infty}th(t)d(t)}{\int_{0}^{\infty}h(t)d(t)} \tag{7}\]  
The RMS DS has often been reported to increase with distance and to model the RMS DS; the distance-dependent model is selected as one of the candidate models in 3 GPP [7]. The linear model is often used to fit the RMS DS in existing research [31; 32]. Therefore, to model the RMS DS samples when the single LED (S\({}_{8}\)) is only considered as the TX, we can model the RMS DS with the linear model to describe the distance-dependence, as shown in [33], which can be expressed as:  
\[\tau=\alpha_{DS}\cdot d+\beta_{DS}+X_{\sigma}^{DS}, \tag{8}\]  
where \(\alpha_{DS}\) and \(\beta_{DS}\) are the slope and intercept of fitting curves, and \(X_{\sigma}^{DS}\) is the standard deviation between the RMS DS and fitting curve. Figure 4a presents the RMS DS for VLC channels calculated by (6), and the fitting results with the linear model in Road 1 and Road 2. The slopes of the fitting models are 0.61 and 0.65, respectively, for Road 1 and Road 2. Obviously, under the single TX case, the positive slope indicates that the RMS DS increases with the propagation distance. As the RX is farther from the TX, the surrounding reflection environment becomes more complicated, resulting in more MPCs received and greater RMS DS. Furthermore, the RMS DS at \(D_{10}\) is 7.95 ns, which is slightly larger than that at \(E_{10}\) (6.80 ns). As in the previous analysis, the more dense surrounding objects contribute much more MPCs. This explanation can also be demonstrated by the NLOS components of CIRs in Figure 2. CIRs for \(D_{10}\) have more peaks with larger delay (70 ns) than those for \(E_{10}\) (50 ns), which can also be observed at other points in the two roads. Hence, the RMS DS is larger. Moreover, the RMS DS range for VLC channels is larger (6-11 ns) compared to that observed in the underground mining channel (2-8 ns). This can be attributed to the unique characteristics of the IIoT scenario examined in this study, which has a larger scenario size than [34]. Additionally, industrial environments usually have highly reflective surfaces such as metal fixtures and equipment [29]. The simulated environment in this paper with objects deployed is more complex compared to the work areas in [34]. As a result, a larger number of MPCs are generated during the propagation from the TX to the RX, leading to a larger RMS DS in VLC channels. Furthermore, the VLC channel in the paper presents a larger delay fluctuation (70 ns) than that of the VLC channels (30 ns) of the underground mines in the [34], which can also be explained by the complexity of IIoT scenarios. Moreover, the RMS DS can be fitted well by a normal distribution. Under the multiple TXs case, Figure 4b gives the CDF fitting line of the RMS DS samples with different heights' RX in Road 1. The mean value of RMS DS (\(\mu\)) at h = 1.5 m is 13.79 ns, which is smaller than that of 14.78 ns at h = 2.5 m. This can be explained by the blocking effect of objects. As the height of the user is lower than the average height of objects, the light signals are more likely to be obstructed by objects, e.g., manufacturing equipment, assembly lines, and forklifts. The blocking will lead to fewer MPCs for users at h = 1.5 m than 2.5 m, i.e., the RMS DS is reduced. In addition, this paper shows larger RMS DS than that in [13] (6-11 ns) under multiple TXs. This is mainly because the IIoT scenario has a larger physical sizeand much more complicated equipment, while the living room in [13] is small and empty.