# LaRaWAN Metering Infrastructure Planning in Smart Cities
## 3 Materials and Methods
### Radio Transmission Range Modeling  
The range of wireless transmission is primarily influenced by three key characteristics of these networks: radio range, data transmission rate, and energy consumption. Each technology aims to strike a balance between these properties. For instance, Wi-Fi and Bluetooth-based devices achieve high transmission speeds at the cost of increased energy consumption and limited range, particularly indoors (typically within several dozen meters or less). In contrast, LoRa technology utilizes lower radio bands and lower data rates, allowing for transmission over significantly longer distances with minimal power consumption. Ensuring optimal coverage involves another crucial factor: direct visibility, which refers to a clear line of sight between the transmitter and the receiver. In radio communication, the radiation area is characterized by Fresnel zones. These zones represent ellipsoids situated between the transmitter and the receiver. The size of each ellipsoid depends on the transmission frequency and the distance separating the two locations. Figure 1: LoRaWAN system architecture [14]. Objects within the Fresnel zone have a detrimental impact on the signal level and can diminish the communication range. LoRa technology possesses a significant advantage by utilizing the 868 MHz, 915 MHz, and 923 MHz ISM bands. These frequencies are considerably lower than the commonly used 2.4 GHz and 5 GHz bands, resulting in reduced transmission losses and improved penetration through obstacles like building walls or trees. Additionally, the interference from devices operating at 2.4 GHz and 5 GHz, such as Wi-Fi and Bluetooth, is increasingly prevalent in densely populated urban environments. The log-distance propagation model, also known as the log-normal shadowing model, is a commonly employed method for predicting radio signal propagation and attenuation across various environments [29]. It assumes that propagation losses follow a logarithmic normal distribution, with the mean varying with distance according to a power relationship. The model is versatile and applicable to both line-of-sight scenarios and scenarios beyond line-of-sight, where the signal may encounter obstacles such as buildings and trees:  
\[P_{r}=P_{t}+G_{t}+G_{r}-10\gamma log_{10}(d)+X_{\sigma}, \tag{1}\]  
where \(P_{r}\) is the received signal power and \(P_{t}\) is the transmit power. Parameters \(G_{t}\) and \(G_{r}\) are antenna gains in transmitting and receiving and \(d\) is the distance between devices. The \(\gamma\) is empirically determined for different environmental conditions. The \(X_{\sigma}\) component refers to the shadow fading of the received signal power. The log-distance propagation model captures the signal attenuation caused by obstacles such as buildings, trees, or terrain. This attenuation is represented by a random variable that follows a log-normal distribution with a mean of zero and a specific standard deviation \(\sigma\). In the literature, various analytical network models for LoRaWAN performance have been described [12; 30]. These models differ in terms of the type of interference from the spreading factor that they consider and whether they incorporate channel fading [31] or other interference from technology [30]. On a different note, the mathematical model for LoRa modulation was introduced in [32]. Analytically, it has been demonstrated that LoRa modulation outperforms FSK modulation in scenarios involving frequency selective fading. The COST-213 Hata model is a radio propagation (that is, path loss) model that extends the Hata model for urban environments. It is based on the Okumura model and designed to cover a wide frequency range up to 2 GHz. It is the most widely cited of the COST-231 models, which were developed as part of a research project funded by the European Union [33].