## 2 Wireless Sensor Network Technology
### LoRa Wireless Sensor Network Technology  
Due to the use of 2.4 GHz low-power radio modules, the range of wireless communication between ZigBee nodes is limited to a few kilometres. Therefore, more recently, the LoRa (Long Range) communication technology has been introduced for long-range, low-power, low-bit-rate wireless communication, enabling larger WSN coverage with power consumption similar to ZigBee by using chirp spread spectrum (CSS) modulation technology [46]. This modulation technique maintains the same low power characteristics as standard radio modulation but significantly increases the communication range because it is more robust to interference. LoRa consists of the network protocol (LoRaWAN) and the associated hardware components, such as radio module and antennas and is optimized for battery-powered devices [46]. LoRaWAN uses star topologies with three different types of devices: end devices (also called LoRa nodes) that can host a set of environmental sensors, a LoRa gateway, and a LoRa network server [47]. The basic structure of a LoRaWAN wireless network is presented in Figure 4. The LoRa network server is the top of the network tree and stores information about the network, initiates the wireless links within the network, and can connect to a database server (Figure 4). The LoRa gateway acts as a relay station that passes data from the sensor devices to the LoRa server, where it can be processed by the LoRa application software. The LoRa end devices are the environmental sensors, which should have just enough functionality to communicate with the gateway. This allows the LoRa end devices to be asleep a significant amount of the time to save energy. Figure 3: The hybrid wireless underground network topology of SoilNet exemplified for a virtual catchment area (adapted from [PERSON] et al. [14]). Since LoRa networks are specifically designed to be applied to larger areas [39], it is important for the planning and optimization of LoRa networks to know the coverage probabilities depending on the distance between the LoRa transmitting and receiving stations. For this reason, the radio technology of LoRa and the calculation of the potential radio link distance is discussed in more detail in the following. At the heart of LoRa is a proprietary chirp spread spectrum (CSS) modulation technique [48]. For binary chirp modulation, the data passes through a chirp modulator that maps each bit block to 1 of 2 waveforms. The chirped LoRa signal can be described by:  
\[s(t)=\sqrt{\frac{2E_{s}}{T_{s}}}cos\left[2\pi f_{c}t\pm\pi\left(u\left(\frac{t} {T_{s}}\right)-w\left(\frac{t}{T_{s}}\right)^{2}\right)\right] \tag{1}\]  
where \(E_{s}\) is the energy of \(s(t)\) in the symbol duration \(T_{s},f_{c}\) is the carrier frequency, and the parameters \(u\) and \(w\) are the peak-to-peak frequency deviation and the sweep width, respectively, both normalized by the symbol rate. LoRa supports variable data rates, enabling the trade-off between throughput, range, robustness, and power consumption while maintaining bandwidth. The LoRa server manages these aspects by regulating the bandwidth \(BW\) and the so-called spreading factor \(SF\) that determines the length of the chirp symbol. The time-on-air of a transmission increases exponentially with \(SF\), extending the communication range between gateway and end devices. The LoRa protocol has six _SFs_ (7-12, Table 1). The lower _SFs_ provide higher data rates but shorter communication distance, while the higher _SFs_ provide lower data rates but higher transmission stability. A signal failure in the uplink can occur at the gateway if the received signal-to-noise ratio (SNR) is below an \(SF\)-specific threshold value (\(q_{SF}\), Table 1). Figure 4: Principle of the LoRa network topology and its basic system architecture, as well as data communication types demonstrated using the example of the SoilNetLoRa wireless sensor network.