# IRS-Enabled Ultra-Low-Power Wireless Sensor Networks: Scheduling and Transmission Schemes
## 7 WSN Transmission Power and Range  
The lifetime of a WSN compared to the lifetime of an IRS-equipped WSN boils down to a comparison between a scheduled sensor node with a transmitter unit and a scheduled ISN; the architecture of each is shown in Figure 1a,b. Because these units may be common, it is redundant to compare the energy consumption models of such units. Instead, we compare the energy consumption of the transmitter with the energy consumption of the IRS controller and IRS. Thus, it suffices to compare the power per symbol \(P_{s,t,s}\) for the transmitter under the transmitter-equipped sensor unit with the power per symbol in the ISN. If the power per symbol per IRS element is \(P_{s,ISN}\), then the power per symbol for the whole ISN is \(NP_{s,ISN}\), as all \(N\) elements are changing phase-shift according to the IRS controller in order to modulate the symbol. The transmitter-equipped sensor can be equipped with long-range wide area network (LoRaWAN) technology, which is popular in WSNs and can reach long transmission distances (around 10 km) with \(P_{s,t,s}=100\) mW [22]. On the other hand, existing works [23; 24] have reported a power of \(P_{s,ISN}=5\) mW for controlling an IRS element. For \(N=10\), this amounts to a total of 50 mW, which may well decrease with future development of IRS technologies. Moreover, the range for this IRS-equipped WSN is not restricted by the ISN equipment. Instead, it is determined by the transmitting power of the BS, which is in the order of watts and is not battery-limited. This is compared to the transmitter-equipped sensors nodes, which are battery-limited and have transmitting power in the order of milliwatts. These two aspects combine to make ISNs suitable for scenarios with power and range challenges. Figure 11: Bit error rate versus SNR for a single scheduled ISN transmission with different IRS phase resolutions and different phase configurations. As a proof of concept, we focus on comparing the lifetime and range of an ISN with a LoRa sensor node, with the specifications provided in in Table 4, following the use case in [22]. For simplicity, we highlight the main sensor tasks of sensing, processing, and transmission, as illustrated in Figure 0(a). Figure 12 considers and compares the lifetime of a transmitter-equipped LoRa sensor battery with an ISN with \(N=5,10,15,20\) elements against the measurement period with the battery characteristics described in Table 5. A measurement period describes a period in which the sensor is sensing, processing, and transmitting, and is sleeping for the remaining amount of time. In a measurement period \(T_{m}\), the battery is sleeping for a time \(T_{s}\) and active the rest of the time \(T_{a}\), in which \(T_{a}\) is found as  
\[T_{a}=T_{tr}+T_{sen}+T_{proc}, \tag{47}\]  
where \(T_{tr},T_{sen}\), and \(T_{proc}\) are defined in Table 4 and \(T_{s}=T_{m}-T_{a}\). Furthermore, the lifetime of the battery \(L\) for the sensor node can be calculated as [25]  
\[L=E_{battery}/I_{avg} \tag{48}\]  
in hours, where \(I_{avg}\) is the average current consumption of the sensor node. The energy in the battery is calculated as \(E_{battery}=V_{b}C=3.3\times 950\) mJ and the \(I_{avg}\) for the transmitter-equipped sensor is  
\[I_{avg}=\frac{1}{T_{m}}\big{(}I_{tr}T_{tr}+I_{sen}T_{sen}+I_{proc}T_{proc}+I_{ s}T_{s}\big{)} \tag{49}\]  
where \(I_{tr}=\frac{92.4}{3.3}\) mA, \(I_{sen}=\frac{10.5}{2}\) mA, \(I_{proc}=\frac{1.8}{3.3}\) mA, and \(I_{s}\) is found in Table 5. For the ISN, the average current consumption is calculated as  
\[I_{avg,ISN}=\frac{1}{T_{m}}\big{(}NI_{ISN}T_{tr}+I_{sen}T_{sen}+I_{proc}T_{proc }+I_{s}T_{s}\big{)}, \tag{50}\]  
where \(I_{ISN}=\frac{P_{s,ISN}}{V_{b}}=\frac{5}{3.3}\) mA. Thus, the battery lifetime for the ISN \(L_{ISN}\) is  
\[L_{ISN}=\frac{E_{battery}}{I_{avg,ISN}} \tag{51}\]  
in hours.