## 4 System Architecture and Design Procedures
### RF Energy Harvesting System
The Schottky diode's current-voltage relationship (1) describes the current flowing through the diode (\(I_{D}\)) to the applied voltage (\(V_{D}\)). Understanding this behaviour is fundamental for effective rectification. The diode voltage, \(V_{D}\), is provided in (2). \[I_{D}=I_{s}\cdot(e^{(V_{D}/\eta\cdot V_{T})}-1), \tag{1}\]  
\[V_{D}=\eta\cdot V_{T}\cdot ln((\frac{I_{o}}{I_{s}})+1), \tag{2}\]  
where the reverse saturation current is (\(I_{s}\)), \(\eta\) is the ideality factor, i.e., the deviation of an actual diode's behaviour from the ideal diode model, and \(V_{T}\) is thermal voltage provided by \(kT/q\). The input RF signal to the rectifier, represented as \(V_{ac}\), varies with frequency. The average output current of the rectifier, \(I_{o}\), can be expressed using (3). \[I_{o}=\frac{1}{T}\cdot\int_{0}^{T}I_{D}\cdot dt. \tag{3}\]  
The output current, \(I_{o}\), can be analysed for two key energy harvesting scenarios: optimising device efficiency and maximising energy storage [48]. The maximum energy storage of the system occurs at the no-load output voltage, \(I_{o}=0\), which is determined by (4). \[E_{RF}=\frac{(C_{out}\cdot V_{dc}^{2})}{2}. \tag{4}\]  
The proposed rectifier functions during a complete cycle, transferring an average power (\(V_{ac}\cdot I_{IN}\)) from the RF source. The maximum power available to the rectifier is \((V_{ac}\cdot I_{IN})/2\) when optimal impedance matching is applied. The corresponding PCE of the rectifier is defined as the ratio of input RF power (\(P_{IN}\)) to output DC power (\(P_{O}\)) and is provided by (5). \[PCE=\frac{P_{O}}{P_{IN}}, \tag{5}\]  
where  
\[P_{IN}=\frac{V_{ac}\cdot I_{IN}}{2}\quad\text{and}\quad P_{O}=\frac{V_{dc}^{2 }}{R_{L}}. \tag{6}\]The efficiency of an RF-EH system relies on the antenna's performance, impedance matching, and rectifier efficiency. Thus, the energy harvesting efficiency of a single-input single-output (SISO) RF-EH system (\(\eta_{{}_{SISO}}\)) is defined by (7). \[\eta_{{}_{SISO}}=(PEE_{\mathit{Ant}}\times PCE_{\mathit{MN}}\times PCE), \tag{7}\]  
where,  
\[PEE_{\mathit{Ant}}=\frac{P_{\mathit{input}.\mathit{MN}}}{P_{\mathit{ received}.\mathit{antenna}}}\quad\mathit{and}\quad PCE_{\mathit{MN}}=\frac{P_{\mathit{input}. \mathit{ rectifier}}}{P_{\mathit{input}.\mathit{MN}}}. \tag{8}\]  
The PCE of the rectifier is provided in (5). The power extraction efficiency of the receiving antenna \(PEE_{\mathit{Ant}}\) and the power conversion efficiency of the impedance matching network \(PCE_{\mathit{MN}}\) can be calculated using (8). MIMO configurations in RF-EH provide benefits like spatial diversity, adaptability to varying environments, increased robustness, and potentially greater efficiency compared to standard antenna arrays [50]. This investigation evaluates MIMO technology by employing multiple RF power sources as antennas, focusing on configurations with 1, 2, 4, 8, and 16 antennas for IoT applications. Each MIMO subsystem comprises an SISO RF-EH setup, including an antenna, matching network, and rectifier, with their output powers combined using a power combiner tool in ADS. Efficiency is assessed using probability theory, with each subsystem's efficiency, \(\eta_{{}_{SISO}}\), representing the probability of successful energy harvesting. The overall MIMO RF-EH efficiency, \(\eta_{{}_{RF}}\), is determined as one minus the product of the complementary probabilities \((1-\eta_{{}_{SISO}})\). \[\eta_{{}_{RF}}=1-\prod_{N=1}^{2^{a}}(1-(\eta_{{}_{SISO}})_{N}). \tag{9}\]  
In this context, \((\eta_{{}_{SISO}})_{N}\) represents the efficiency of the \(N\)-th antenna in the RF-EH system. The variable \(N\) ranges from 1 to 2\({}^{a}\), where \(a\) varies from 0 to 4, corresponding to MIMO RF-EH with 1, 2, 4, 8, and 16 antennas, respectively. Several optimisation techniques can be implemented on the antenna front-end of the RF energy harvesting subsystems to further enhance the performance of the MIMO RF energy harvesting system.