## 2 Hybrid PLC and VLC Channel Based on Distinct Optical Beam Configurations
### Hybrid Channel Based on Distinct Non-Lambertian Optical Beam Configuration
\right.. \tag{14}\]  
Overall, the final hybrid PLC and VLC channel, based on LUXEON non-Lambertian optical beam configuration for one certain receiver, is represented by the superposed effects of all the LUXEON non-Lambertian LED optical sources and can be given by the following:  
\[H_{\text{Rebel}}(f)=\sum\limits_{i=1}^{N_{\text{LED}}}H_{i,\text{PLC}}(f)H_{i, \text{VLC}}^{\text{Rebel}}(f), \tag{15}\]  
where \(H_{i,\text{PLC}}(f)\) denotes the PLC channel between the PLC modulator and the \(i\)-th LED optical source, \(H_{i,\text{VLC}}^{\text{Rebel}}(f)\) represents the VLC channel between the \(i\)-th LUXEON non-Lambertian LED optical source and the optical receiver, and \(N_{\text{LED}}\) represents the number of the LED sources that the optical receiver can detect. Figure 2: Schematic of hybrid PLC and VLC based on LUXEON Rebel optical emission beam for the coming 6G IoT network: (**a**) the respective application scenario, (**b**) the respective 3D illustration of beam pattern. As a matter of fact, unlike the Lambertian emission beam and the LUXEON Rebel optical beam, the radiation pattern of the NSPW345 CS Nichia LED (Nichia, Tokushima, Japan) is not rotationally symmetric anymore. Thanks to this novel beam asymmetry, the non-Lambertian NSPW345 CS Nichia LED was adopted for the following exploration of a hybrid channel based on the non-Lambertian emission beam in this subsection. Obviously, the NSPW emission beam can provide a much more novel spatial radiation characteristic when compared with the baseline Lambertian emission beam, and this asymmetric emission beam, from a representative commercially available LED, can assure that the following work is applicable for future implementation as well. In one typical indoor hybrid PLC and VLC scenario, when the radiation characteristics of the optical source follow the NSPW non-Lambertian beam, the channel gain of the NSPW non-Lambertian VLC at the receiver could be given as follows:  
\[H_{\rm VLC}^{\rm NSPW}(f)=\eta_{\rm LOS}^{\rm NSPW}e^{-\beta\pi f \Delta I_{\rm LOS}}+\eta_{\rm DIFF}\frac{e^{-2\pi/\Delta I_{\rm DIFF}}}{1+jf/f_ {\rm C}}, \tag{16}\]  
where \(\eta_{\rm LOS}^{\rm NSPW}\) denotes the optical wireless channel gain of the NSPW LOS signal. Under this NSPW emission beam configuration, the LOS channel gain should be specifically represented by the following:  
\[\eta_{\rm LOS}^{\rm NSPW}=\left\{ \begin{array}{cc}\frac{A_{R}}{P_{\rm nonNSPW }d^{2}}I_{\rm NSPW}(\phi,\alpha)\cos(\theta),&0\leq\theta\leq\theta_{\rm FOV }\\ 0,&\theta_{0}>\theta_{\rm FOV}\end{array} \right., \tag{17}\]  
where \(P_{\rm normNSPW}\) denotes the normalization factor of the asymmetric NSPW emission beam, which ensures that the power radiated across the whole of the spatial directions is \(1\) W, and \(I_{\rm NSPW}(\phi,\alpha)\) is the spatial radiation intensity of the asymmetric NSPW emission beam, which is profiled by the following equation as one sum of multiple Gaussian functions [23; 24]:  
\[I_{\rm NSPW}(\phi,\alpha)=\sum\limits_{m=1}^{2}g1_{m}\exp\left[-( \mathrm{In2})(|\phi|-g2_{m})^{2}\left(\frac{\cos^{2}\alpha}{\left(g3_{m}\right) ^{2}}+\frac{\sin^{2}\alpha}{\left(g4_{m}\right)^{2}}\right)\right], \tag{18}\]  
where \(\alpha\) is the azimuth angle, and the coefficient values in the Gaussian functions are written as \(g_{11}^{\rm NSPW}=0.13\), \(g_{21}^{\rm NSPW}=45^{\circ}\), \(g_{31}^{\rm NSPW}=g_{41}^{\rm NSPW}=18^{\circ}\), \(g_{12}^{\rm NSPW}=1\), \(g_{22}^{\rm NSPW}=0\), \(g_{32}^{\rm NSPW}=38^{\circ}\), and \(g_{42}^{\rm NSPW}=22^{\circ}\). Similarly, the 3D display of the NSPW345 CS UB light beam is illustrated in Figure 3. By substituting (16) into (15), the asymmetric NSPW optical wireless channel gain for this hybrid PLC and VLC could be renewed as follows:  
\[\eta_{\rm LOS}^{\rm NSPW}=\left\{