## 2 Drone Visible Light Communications with Differentiated LED Beams
### Drone Visible Light Communications with Non-Lambertian LED Beam  
Without loss of generality, for the following discussion of non-Lambertian drone VLC, the beam models from the Z-Power LED and the NSPW345 CS Nichia LED are chosen carefully. In particular, the emission intensity of Z-Power LED beam can be described by the following equation [33; 34]:  
\[R_{\text{Z-Power}}(\phi)=\sum\limits_{k=1}^{K}g_{1k}^{\text{Z-Power}}\exp[-\ln 2 (\frac{|\phi|-g_{2k}^{\text{Z-Power}}}{g_{3k}^{\text{Z-Power}}})^{2}], \tag{13}\]  
where \(K=3\). Additionally, the setting of coefficients \(g_{11}^{\text{Z-Power}}\), \(g_{21}^{\text{Z-Power}}\), \(g_{31}^{\text{Z-Power}}\), \(g_{12}^{\text{Z-Power}}\), \(g_{32}^{\text{Z-Power}}\), \(g_{32}^{\text{Z-Power}}\), \(g_{13}^{\text{Z-Power}}\), \(g_{23}^{\text{Z-Power}}\), and \(g_{33}^{\text{Z-Power}}\) are consistent with the work of [33]. And the application scenario of 6G drone VLC based on non-Lambertian Z-Power light beam for terrestrial user and aerial user is shown in Figures 2a and 2b separately. For drone A2T VLC, the Z-Power channel gain can be presented as:  
\[H_{\text{A2T}}^{\text{Z-Power}} = \tag{14}\] \[= \left\{ \begin{aligned} &\left(\sum\limits_{k=1}^{K}g_{1k}\exp[- \ln 2(\frac{|\phi_{\text{A2T}}|-g_{2k}^{\text{Z-Power}}}{g_{3k}^{\text{Z-Power}}}) ^{2}]\right)\\ &\times\frac{A_{\text{PD}}T_{s}(\theta_{\text{A2T}})}{P_{\text{ normZ-Power}}d_{\text{A2T}}^{2}}\biggl{(}\frac{n^{2}}{\sin^{2}(\theta_{\text{FOV}})} \biggr{)}\left(\frac{H}{\sqrt{r_{\text{A2T}}^{2}+H^{2}}}\right),& 0\leq\theta_{\text{A2T}}\leq \theta_{\text{FOV}}\\ & 0,&\theta_{\text{A2T}}>\theta_{\text{FOV}}\\ \end{aligned} \right.,\]  
where \(P_{\text{normZ-Power}}\) is the power normalization factor for Z-Power LED beam. Similar to (8), the non-Lambertian Z-Power optical channel gain for A2A VLC with upward orientation receiver could be presented as:  
\[H_{\text{A2A,up}}^{\text{Z-Power}} = \left\{ \begin{aligned} &\frac{A_{\text{PD}}}{P_{\text{normZ-Power}}d_{\text{ A2A}}^{2}}R_{\text{Z-Power}}(\phi_{\text{A2A}})T_{s}\bigl{(}\theta_{\text{A2A,up}} \bigr{)}g\bigl{(}\theta_{\text{A2A,up}}\bigr{)}\cos\bigl{(}\theta_{\text{A2A,up}}\bigr{)},& 0\leq\theta_{\text{A2A,up}}\leq\theta_{\text{FOV}}\\ & 0,&\theta_{\text{A2A,up}}>\theta_{\text{FOV}}\\ &\left(\sum\limits_{k=1}^{K}g_{1k}\exp[-\ln 2(\frac{|\phi_{\text{A2A}}|-g_{ 2k}^{\text{Z-Power}}}{g_{3k}^{\text{Z-Power}}})^{2}]\right)\\ &\times\frac{A_{\text{PD}}T_{s}\bigl{(}\theta_{\text{A2A,up}} \bigr{)}}{P_{\text{normZ-Power}}d_{\text{A2A}}^{2}}\biggl{(}\frac{n^{2}}{\sin ^{2}(\theta_{\text{FOV}})}\biggr{)}\left(\frac{H-h_{\text{alt}}}{\sqrt{r_{ \text{A2A}}^{2}+(H-h_{\text{alt}})^{2}}}\right),& 0\leq\theta_{\text{A2A,up}}\leq\theta_{\text{FOV}}\\ & 0,&\theta_{\text{A2A,up}}>\theta_{\text{FOV}}\\ \end{aligned} \right., \tag{15}\]Similar to (10), the non-Lambertian Z-Power optical channel gain for A2A VLC with horizontal orientation receiver could be presented as:  
Figure 2: Schematic of 6G drone VLC based on non-Lambertian Z-Power light beam for 6G aerial vehicular networks: (**a**) the respective application scenario of terrestrial user, (**b**) the respective application scenario of aerial user. \[H_{\rm A2A,hor}^{\rm Z-Power} = \begin{cases}\dfrac{A_{\rm PD}}{P_{\rm normZ-Power}d_{\rm A2A}^{2}}R_ {\rm Z-Power}(\phi_{\rm A2A})T_{s}(\theta_{\rm A2A,hor})g(\theta_{\rm A2A,hor}) \cos(\theta_{\rm A2A,hor}),&0\leq\theta_{\rm A2A,hor}\leq\theta_{\rm FOV}\\ 0,&\theta_{\rm A2A,hor}>\theta_{\rm FOV}\\ \left(\sum\limits_{k=1}^{K}g_{1k}\exp[-\ln 2(\dfrac{|\phi_{\rm A2A}|-g_{2k}^{ \rm Z-Power}}{g_{3k}^{\rm Z-Power}})^{2}]\right)\\ \times\dfrac{A_{\rm PD}T_{s}(\theta_{\rm A2A,hor})}{P_{\rm normZ-Power}d_{\rm A2 A}^{2}}\bigg{(}\dfrac{n^{2}}{\sin^{2}(\theta_{\rm FOV})}\bigg{)}\left(\dfrac{r_{ \rm A2A}}{\sqrt{r_{\rm A2A}^{2}+(H-h_{\rm alt})^{2}}}\right),&0\leq\theta_{ \rm A2A,hor}\leq\theta_{\rm FOV}\\ 0,&\theta_{\rm A2A,hor}>\theta_{\rm FOV}\end{cases}