## 2 System Model
### Energy Supplier Node Architecture  
The ES node has been conceived to act primarily as a WPT device for supplying energy to the WSN IoT devices and as a communication gateway. The proposed architecture is based on a dual frequency eight flat face Switched Beam Antenna (SBA) operating at both 2.45 GHz and 5.8 GHz in circular polarization (CP). CP has been implemented in order to provide robustness in both indoor and outdoor scenarios, since it can contrast multipath (indoor) and Faraday rotation (outdoor). Furthermore, CP is not affected by the terminals relative orientation, this avoiding antenna polarisation mismatching in the power link, that consequently could nullify WPT advantages. However, for our purpose, a single antenna cannot be an effective radiator, since the transmitting node, in order to achieve high power transfer efficiency, should focus the transmitted power to the receiver through a narrow beamwidth. In a dynamic scenario, the relative position of transmitter and receiver are not a priori known. Hence, an adequately narrow beam should be dynamically steered to adaptively direct all the available power towards the target receiver in far or near field. SBAs are cost-effective radiative systems capable to cover an omnidirectional domain as a whole, but able to selectively switch-on the trasmission toward specific directions, hence operating as spatial filter according to the Space Division Multiple Access (SDMA) paradigm. SBAs are typically controlled by means of a multiplexer, thus it is simpler and more cost-effective than electronically steered array. The better solution for both communication and WPT purposes is to adopt a dual band, where each operation is carried out at different frequency. In view of these considerations, we design and simulate a Dual Band Switched Beam Antenna (DBSBA). The basic antenna element considered in this paper is based on an approach already demonstrated in developing a dual band antenna for indoor communication [16]. The latter being designed for dual band WiFi operation working 2.45 GHz and 5.2 GHz [17]. The SBA final arrangement is obtained introducing the octagonal shape, which is sufficient to cover the entire 2D plane considering the performance of the antenna. Figure 2 shows the 3D simulated radiation pattern for the SBA at the considered frequencies. The block diagram of the ES proposed architecture is shown in Figure 3, where it is pointed the presence of both the communication and power transfer chains operating at the two frequencies before introduced. The above presented solution defined for the ES is capable to supply power to RNs and particularly to the root node, as well as to communicate with the cluster. The two chains interact with the SBA through eight parallel double frequencies Diplexer driven by two single-pole eight-trough SP8T switch. These ones are connected, respectively, in the 2.45 GHz communication chain to a half-duplex transceiver, while in the 5.8 GHz one, first to a 27 dB gain Power Amplifier, with an  
Figure 1: High level architecture comprising the Energy Supplier node and the Power Transfer Manager which jointly handle the WPT procedure for an IIoT cluster arranged in a tree-wise topology, in the presence of Rechargeable Nodes. output power of about 47 dBm, then to a 5.8 GHz transceiver used to generate a CW signal with an output power level of 20 dBm. In order to demonstrate the feasibility of such architecture, the performance of each functional block corresponds to a commercially available components, as illustrated in Figure 3, where the characteristics of the block match with its specific datasheet. As a result, ES has the ability to supply power to a target node, as well as communicate with it, while the two SP8T switch both the power and the TX/RX signals to the corresponding active lobe.