## 2 Drone Visible Light Communications with Differentiated LED Beams
### Drone Visible Light Communications with Non-Lambertian LED Beam
, \tag{16}\]  
Accordingly, similar to (11), the achievable rate of non-Lambertian Z-Power drone VLC could be approximately by [19]:  
\[C^{\rm Z-Power}=\dfrac{1}{2}\log_{2}\bigg{(}1+\dfrac{e}{2\pi}\bigg{(}\dfrac{ \eta PH^{\rm Z-Power}}{\sigma_{w}}\bigg{)}^{2}\bigg{)}, \tag{17}\]  
where \(H^{\rm Z-Power}\) could be explicitly given by (14)-(16) for the non-Lambertian Z-Power A2T user link, the non-Lambertian Z-Power A2A user link with upward orientation receiver and the non-Lambertian Z-Power A2A user link with horizontal orientation receiver, respectively. Thus, the relevant energy efficiency of the non-Lambertian Z-Power drone VLC:  
\[\eta^{\rm Z-Power}=\dfrac{C^{\rm Z-Power}}{P}=\dfrac{1}{2P}\log_{2}\bigg{(}1+ \dfrac{e}{2\pi}\bigg{(}\dfrac{\eta PH^{\rm Z-Power}}{\sigma_{w}}\bigg{)}^{2} \bigg{)}, \tag{18}\]  
where \(P\) refer to the emitted optical signal power as well. Moreover, as for the case of 6G drone VLC based on asymmetric NSPW light beam, the relevant emission intensity expression can be given [25; 26]:  
\[R_{\rm NSPW}(\phi,\alpha)=\sum\limits_{j=1}^{N_{2}}g_{j}\exp\Bigg{[}-(\ln 2) (|\phi|-g_{2})^{2}\bigg{(}\dfrac{\cos^{2}\alpha}{\left(g_{3}\right)^{2}}+ \dfrac{\sin^{2}\alpha}{\left(g_{4}\right)^{2}}\bigg{)}\Bigg{]}, \tag{19}\]  
where \(\alpha\) denotes the azimuth angle from the optical source to the receiver, the coefficient values of Gaussian functions are given 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 \(g_{42}^{\rm NSPW}=22^{\circ}\)[33]. Similarly, the respective 3D radiation pattern for the drone VLC application scenario of terrestrial user and aerial user is shown in Figures 2(a) and 2(b) separately. Accordingly, the channel gain for non-Lambertian NSPW drone A2T VLC can be written as:  
\[H_{\rm A2T}^{\rm NSPW} = \begin{cases}\dfrac{A_{R}}{P_{\rm normNSPW}d_{\rm A2T}^{2}}R_{ \rm NSPW}(\phi_{\rm A2T},\alpha_{\rm A2T})T_{s}(\theta_{\rm A2T})g(\theta_{ \rm A2T})\cos(\theta_{\rm A2T}),&0\leq\theta_{\rm A2T}\leq\theta_{\rm FOV}\\ 0,&\theta_{\rm A2T}>\theta_{\rm FOV}\\ \end{cases}  \tag{20}\] \[= \begin{cases}\dfrac{A_{R}T_{s}(\theta_{\rm A2T})}{P_{\rm normNSPW }d_{\rm A2T}^{2}}\Bigg{\{}\sum\limits_{j=1}^{N_{2}}g_{1j}\exp\Bigg{[}-(\ln 2)(| \phi_{\rm A2T}|-g_{2j})^{2}\Bigg{(}\dfrac{\cos^{2}\alpha_{\rm A2T}}{\left(g_{3} \right)^{2}}+\dfrac{\sin^{2}\alpha_{\rm A2T}}{\left(g_{4}\right)^{2}}\bigg{)} \Bigg{]}\Bigg{\}}\\ \times\bigg{(}\dfrac{n^{2}}{\sin^{2}(\theta_{\rm FOV})}\bigg{)}\Bigg{(}\dfrac{ H}{\sqrt{r_{\rm A2T}^{2}+H^{2}}}\bigg{)},&0\leq\theta_{\rm A2T}\leq\theta_{\rm FOV}\\ 0,&\theta_{\rm A2T}>\theta_{\rm FOV}\end{cases} \]where \(\alpha_{\rm AZT}\) is the azimuth angle of the terrestrial receiver with respect to the NSPW LED source, \(P_{\rm normNSPW}\) is the power normalization factor of the NSPW beam. Figure 3: Schematic of 6G drone VLC based on asymmetric NSPW light beam for 6G aerial vehicular networks: (**a**) the respective application scenario of terrestrial user, (**b**) the respective application scenario of aerial user. For A2A VLC, the non-Lambertian NSPW LED beam-based channel gain with an upward orientation receiver could be presented as:  
\[H_{\text{A2A,up}}^{\text{NSPW}} = \left\{\begin{aligned} &\frac{A_{R}}{P_{\text{normNSPW}}d_{\text{A2A}}^{2}}R_{ \text{NSPW}}(\phi_{\text{A2A}},\alpha_{\text{A2A}})T_{s}(\theta_{\text{A2A,up} })g(\theta_{\text{A2A,up}})\cos(\theta_{\text{A2A,up}}),\ \ \ 0\leq\theta_{\text{A2A,up}}\leq\  
[PERSON] model's accuracy and reliability in this article are solid and supported by sufficient experimental data in ref. [33]. To demonstrate the accuracy of reconstruction, the difference between experimental data and the modeled equation must be compared by computing both the root mean square (RMS) error and the normalized cross correlation (NCC) [33; 36; 37].