# Optical Camera Communication as an Enabling Technology for Microalgae Cultivation +
## 3 Communications Modelling
### Plant Distribution  
The distribution of the photobioreactor nodes across the room plays an essential role in communications. To establish a link, the receiver should visualise each node, and consequently, it is necessary to reserve some space free of obstructive interference between the transmitters and the camera. This reveals the importance of analysing different possible solutions for placing the nodes until finding the one that best suits the project's initial requirements, either in terms of better link quality, higher capacity or more efficient space exploitation. In a previous work [22], a metric was proposed to compare the performance of different solutions. Nevertheless, the complex nature of this problem, which involves several variables and a wide range of possible initial requirements, highlighted the need to modify this classification strategy. This work proposes replacing the original metric based on a single value with a modified multidimensional metric, Equation (18), allowing a more flexible classification of the arrangements. This new metric offers a comparison tool in which it is left to the designer's discretion to select a specific application design's priorities. \[F:\{N,Q,SUR\} \tag{18}\] \[\text{where}:\quad\text{SUR}=\frac{\text{V}_{\text{cont}}}{\text{ V}_{\text{room}}} \tag{19}\]  
It consists of three independent variables: the number of simultaneous photobioreactors monitored by a single camera, \(N\), a communications performance metric, \(Q\), and the space utilisation ratio (SUR). The first two variables account for the overall achievable data rate of the setup. The last term relates the total equivalent volume of the containers bound to biomass harvesting, \(\text{V}_{\text{cont}}\), and the minimum room volume needed, \(\text{V}_{\text{room}}\). The optimisation of this term has direct implications in the reduction of production costs and, therefore, the viability and competitiveness of cultivation plants based on artificial lightning and vertical racks. The proposed \(Q\) metric is derived from the well-known [PERSON]'s equation [30] for estimating the channel capacity for each container (Equation (20)). \[C=BW\cdot log_{2}(1+S/N) \tag{20}\]  
where \(C\) is the capacity in bits per second, \(BW\) is the bandwidth of the channel in Hertz and \(S/N\) is the SNR, expressed as a linear power ratio. As was previously mentioned, communications happen in a windowed manner. In other words, the transmission effectively takes place during a fraction of the time to acquire a frame, \(t_{\text{frame}}\). This fraction of time, or channel availability, \(\tau_{\text{rx}}\), depends on the geometrical configuration, \(t_{\text{geo}}\), and on the elapsed time between when the camera finishes capturing one frame and starts with the next one \(t_{\text{inter}}\) (Equation (22)). However, this last term is considerably lower than \(t_{\text{frame}}\) and can be neglected. Adding this factor to Equation (20), the effective capacity is obtained for each container, as Equation (21) shows. \[C=BW\cdot log_{2}(1+S/N)\cdot\tau_{\text{rx}} \tag{21}\] \[\text{where}:\quad\tau_{\text{rx}}=\frac{t_{\text{geo}}}{t_{ \text{frame}}+t_{\text{inter}}}\approx\frac{t_{\text{roi}}}{h_{\text{res}}} \tag{22}\]  
The proposed metric \(Q\) is then defined as the relationship between the channel's capacity for a particular arrangement and container, \(C\), and the ideal capacity, \(C_{ideal}\), Equation (23). \[Q=\frac{C}{C_{\text{ideal}}}=\frac{BW}{BW_{\text{ideal}}}\cdot\frac{log_{2}(1+ S/N)}{log_{2}(1+(S/N)_{\text{ideal}})}\cdot\frac{\tau_{\text{rx}}}{\tau_{ \text{rx,ideal}}} \tag{23}\]The vast number of parameters involved in this metric's computation makes this metric unreasonable for a practical analysis of different plant distributions, even more so if there are plenty of configurations to be compared. Hence, for this metric to be a useful tool for this purpose, it is necessary to assume a series of coarse approximations.