## 3 Channel Characteristics Comparisons
### Path Loss  
Path loss is the reduction in power density of a radio wave as it propagates [25]. In wireless communication systems, the path loss is of high importance for coverage prediction and interference analysis [26; 27]. For mmWave channels, the path loss is a function of distance and can be written by [14]:  
\[\mathrm{PL}(d)=\mathrm{P_{T}}+\mathrm{G_{T}}+\mathrm{G_{R}}+\mathrm{G_{S}}+20 \mathrm{log}_{10}(\frac{\lambda}{4\pi d})-\mathrm{P_{R}}, \tag{3}\]  
where \(\mathrm{G_{T}},\mathrm{G_{R}}\), and \(\mathrm{G_{S}}\) are the antenna gain of TX, RX, and the system gain, respectively; \(\lambda\) is the wavelength; \(d\) is the spatial distance between TX and RX; \(\mathrm{P_{T}}\) is the transmitter power, and \(\mathrm{P_{R}}=10\mathrm{log}_{10}(\sum_{n=1}^{N}(V^{2}+a_{n}^{2}))\) denotes the received power in our measurements. In each measured position, we can collect 1000 samples of path loss from the first kind of measurements. We can model path loss in this conference room based on these samples with the widely used floating-intercept (FI) [5] and close-in (CI) [28] model. The FI and CI model can be expressed as  
\[\mathrm{PL^{FI}}(d)=\beta+10a\mathrm{log}_{10}(d)+X_{\sigma}{}^{\mathrm{FI}}, \tag{4}\]  
\[\mathrm{PL^{CI}}(f,d)=20\mathrm{log}_{10}(\frac{4\pi d_{0}f}{c})+10n_{CI} \mathrm{log}_{10}(\frac{d}{d_{0}})+X_{\sigma}{}^{\mathrm{CI}}\quad\text{for $d\geq d_{0}$, $d_{0}=1\,m$}, \tag{5}\]  
where \(\beta\) is the intercept, \(\alpha\) and \(n_{CI}\) are the parameters of fit, i.e., path loss exponent (PLE), \(X_{\sigma}\) is a zero-mean Gaussian variable representing the shadowing, and \(d_{0}\) is the reference distance. For VLC channels, the impulse responses of LEDs and PDs have not been standardized as with the antennas in mmWave bands. Therefore, the characteristics of LEDs and PDs are considered in the existing channel models [29; 30; 31] for VLC. The channel path loss coupled with transceivers is defined as OPL, which can be expressed as [18; 32]:  
\[\mathrm{OPL}(d)=-10\mathrm{log}_{10}\left(\int_{0}^{\infty}h_{d}(\tau)d\tau \right), \tag{6}\]  
Figure 6: CIR at the 10 th position. where the \(h_{d}(\tau)\) denotes the CIR for the distance \(d\). The CI model cannot be applied to model the OPL in VLC bands, because this model requires a specific frequency (i.e., \(f\) in (5)), while the LEDs work with mixed wavelengths, as shown in Figure 5c. Therefore, we choose the FI Model (4) to fit the OPL for VLC channels. Figure 7 shows the path loss fitting results in mmWave bands. The PLE in the FI model is 1.31, which is slightly smaller than the PLE (1.57) in the CI model. This difference can also be found by investigating the intercept of these two slopes. The intercept \(\beta\) in the FI model is 63.5 dB, while it is 61.34 dB in the CI model. On the other hand, the standard derivation \(\sigma\) in the CI model is 0.1 dB larger than that in the FI model. Generally, these two models can give good insights into the path loss here, and the FI model appears to fit better with the path loss samples, i.e., smaller standard derivation. We also plot the path loss model defined in the 3 GPP technical report (TR) 38.901 for the indoor office LOS scenario [5]. We can find that the PLE and \(\sigma\) parameters in this model are both larger than the fitted parameters here. This can be explained by the fact that the typical office room in 3 GPP TR 38.901 has more complicated structures than the conference room in Figure 2a, so that the signals are more likely to be obstructed by objects, e.g., the tables, chairs, and plants. Moreover, the path loss model in free space is also presented in Figure 7, and it is apparent that the path loss in free space is larger than the path loss in our measured conference room and the office room. This is within expectation because more reflected signals from walls and ceilings in indoor rooms can be received by the RX. Figure 8a shows the photosensitive area of commercial PDs [33] and \(r\) denotes the RS of PDs. It is clear that the OPL is related to the size of PDs.