## 2 Proposed Architecture and Fundamentals of PPFD for Communication
### PPFD to Illuminance Conversion  
The spectra of LED lights and the absorptance of Chlorophyll A and B that dominate the photosynthesis process are crucial factors. In photosynthesis, the blue and the red spectra are primarily used for growing vegetables. However, an experimental investigation suggested that the addition of 24% green LED light can enhance the growth of the vegetable [17]. This addition of green light has a better penetration in the vegetable canopy and increases vegetable growth by potentially improving the photosynthesis process. Moreover, it solved the problems of complex visual assessment stemming from the red-blue  
Figure 1: Proposed energy-efficient smart-farming architecture.  
combination creating the purplish-gray light. Thus, the additional green light is also taken into account as a grow light and communication source in this work.  
For the growth of the indoor vegetable, a certain energy level required for the process of photosynthesis has to be met. The photosynthetic photon flux density (PPFD) is the most frequently used unit to analyze the required photosynthesis level. The unit of PPFD is \(\upmu\)mol\(\cdot\)m\({}^{-2}\cdot\)s\({}^{-1}\), and it implies the amount of photosynthetically active radiation (PAR) arriving at the vegetable. It can also be thought of as the amount of photons in \(\upmu\)mol falling on a unit area for a second. Illuminance (with the unit of lux) is a more frequently used term in visible light communication. However, PPFD is not a straightforward definition to be converted into illuminance. For instance, an illuminance of 54 lux is equal to is 1 \(\upmu\)mol\(\cdot\)m\({}^{-2}\cdot\)s\({}^{-1}\) when sunlight is considered [18]. However, for artificial lights with various spectral distributions, the relationships have to be carefully derived.  
The calculation of the available photosynthetic energy to vegetables is possible if the spectral power distribution (SPD) of a light source is known across the relevant visible wavelengths (400-700 nm). It is defined that 683 lumens of luminosity flux are equals to 1 watt of radiant power at 555 nm. Using these values and the CIE 1931 luminous efficiency function, the luminous flux (in lumen) can be obtained [19]. Then, the spectral radiant flux \(\Phi(\lambda)\) in \(W\)/nm per lumen can be calculated as:  
\[\frac{\Phi(\lambda)}{\text{lumen}}=\frac{P_{\textit{rel}}\ (\lambda)}{683\cdot \frac{\sum_{\text{400 nm}}^{\text{700 nm}}\ V(\lambda)\cdot P_{\textit{rel}}( \lambda)\cdot\Delta\lambda}} \tag{1}\]  
where \(V(\lambda)\) is the luminous efficiency function at \(\lambda\) wavelength and _Prel_ (\(\lambda\)) is the relative spectral power distribution. The denominator indicates the overall luminous flux. For instance, a light source with a center wavelength closer to 555 nm leads to a higher luminous flux and vice versa. The relative spectral radiant flux is used for PPF-lumen conversion. Then the photosynthetic photon flux per wavelength in \(\upmu\)mol\(\cdot\)s\({}^{-1}\) nm\({}^{-1}\) is calculated as [20]:  
\[\frac{\text{PPF}}{\text{nm}}=\frac{10^{-9}\cdot\lambda\cdot\Phi(\lambda)}{N_{a }\cdot h\cdot c} \tag{2}\]  
where \(\lambda\) is the wavelength (in \(m\)), \(N_{a}\) and \(h\) are the [PERSON]'s constant (6.022 \(\times\) 10\({}^{23}\)) and [PERSON]'s constant (6.626 \(\times\) 10\({}^{-34}\)), respectively, and \(c\) means the speed of light. Therefore, for a given light source, the photosynthetic photon flux (PPF) per lumen can be obtained when its spectral radiant flux (\(\Phi(\lambda)\)) is given. Then, the PPFD of the source can be converted to the illuminance value (lux = lumen/m\({}^{2}\)). Table 1 shows the calculated Lux-PPFD conversion factors for the commercial LED light sources used in this work.