## 2 Proposed Architecture and Fundamentals of PPFD for Communication
### Design Parameters for Illumination and Communications  
In designing and selecting the LEDs to achieve the required illuminance and the communication performance, the luminous efficacy of the light source should be known. In VLC, the illuminance is a typical constraint limiting the optical power available for communication. Therefore, it is important to choose the optimum luminous efficacy. The luminous efficacy (\(\eta\)) is defined as [21]:  
\[\eta=\frac{\Phi}{P}\ \left[\frac{\text{lm}}{\text{w}}\right] \tag{3}\]  
The luminous efficacy indicated how much luminous flux (\(\Phi\)) is included in a watt of radiant power flux (\(P\)) and has the unit of lm/W. Table 2 shows the calculated luminous efficacy for the commercial REB LEDs used in this work. The Lambertian order (\(m\)) of the  
\begin{table}
\begin{tabular}{c c c c} \hline \hline  & **Red LED** & **Green LED** & **Blue LED** \\ \hline Lux/PPFD & 41.3 & 122.4 & 15.1 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Illuminance-PPFD conversion of tested RGB LEDs.  
light source is also important, which shows the degree of divergence, which is defined as [22]:  
\[m\ =\ \frac{-\ln(2)}{\ln(\cos\Phi_{1/2})} \tag{4}\]  
where \(\Phi_{1/2}\) is the semi-angle for the half intensity. For the perfect Lambertian emission, the order \(m=1\) and the semi angle becomes \(\Phi_{1/2}=60^{\circ}\). The calculation of luminous intensity (\(R(\varphi)\)) can be found by [23; 24]:  
\[R(\varphi)=\Phi\cdot\left[\frac{(m+1)}{2\pi}\right]\cdot\cos^{m}(\varphi)\ \ \left[\frac{\mathrm{Im}}{\mathrm{sr}}\right] \tag{5}\]  
where \(\varphi\) represents the radiation angle. The unit of the angular intensity is \(\mathrm{Im}/\mathrm{sr}\), which is equal to a candela, 1 cd. The conversion of luminous intensity to luminous flux is calculated by [25]:  
\[E=R(\varphi)\cdot\frac{\cos\theta}{r^{2}}\left[\mathrm{lux}\right] \tag{6}\]  
where \(E\) is the luminous intensity defined as the amount of lumen on a unit area. Here, \(\theta\) denotes the angle between the normal direction of the illumination plane and the direction of light propagation. \(r\) means the distance between the light source and the illumination plane. The light intensity is reduced as the distance increases. Most of the vegetables are placed at a distance of 6 to 12 inches (15-30 cm) from the light source [26].  
The PPFD required for the growth of the leafy vegetables is mentioned to be 200 \(\upmu\mathrm{mol}\cdot\mathrm{m}^{-2}\cdot\mathrm{s}^{-1}\) to 300 \(\upmu\mathrm{mol}\cdot\mathrm{m}^{-2}\cdot\mathrm{s}^{-1}\). This range generally depends on the target biomass and productivity [27; 28]. Reference [29] reported that the progressive increase in the biomass of the lettuce is observed up to 250 \(\upmu\mathrm{mol}\cdot\mathrm{m}^{-2}\cdot\mathrm{s}^{-1}\), but no further improvement afterward. Therefore, the PPFD level of 250 \(\upmu\mathrm{mol}\cdot\mathrm{m}^{-2}\cdot\mathrm{s}^{-1}\) is chosen for the following simulations and experiments. Table 3 summarizes the required PPFD for the lettuce. The optimum ratio of PPFD for red, green, blue LEDs is 61%, 24%, and 15%, respectively [17]. The corresponding illuminance and the intensity are derived by the conversion factors shown in Tables 1 and 2.