# Feasibility Analysis of a LoRa-Based WSN Using Public Transport
## 3 Theoretical Analysis of Propagation Performance  
In order to get deeper insight into the maximum distance that could be covered in urban areas at the frequency on which LoRa modules operate in Europe, a theoretical analysis of the propagation performance in term of range and received power was performed. Wireless channel characterization is determined by path loss, shadowing, and multipath fading, where the last two quantities are extremely important in an urban environment and may heavily affect the propagation performance of a radio link. This analysis is also useful to estimate the maximum distance at which end-nodes, gateways, and supergateways can be installed, taking into account different values of transmitted power. In general, \(\left.\mathrm{P_{T}}\right|_{\mathrm{dBm}}\) indicates the power radiated by the transmitter, expressed in dBm, \(\left.\mathrm{G_{T}}\right|_{\mathrm{dB}}\) and \(\left.\mathrm{G_{R}}\right|_{\mathrm{dB}}\) denote the antenna gains, respectively, of the transmitter and receiver expressed in dB, and \(\left.\mathrm{L_{P}}\right|_{\mathrm{dB}}\) denotes the path loss attenuation, expressed in dB, caused by both the distance between transmitter and receiver and the different characteristics of the surrounding environment. The received power \(\left.\mathrm{P_{R}}\right|_{\mathrm{dBm}}\) can be calculated as:  
\[\left.\mathrm{P_{R}}\right|_{\mathrm{dBm}}\ =\ \mathrm{P_{T}}\right|_{\mathrm{dBm}}+ \left.\mathrm{G_{T}}\right|_{\mathrm{dB}}+\left.\mathrm{G_{R}}\right|_{ \mathrm{dB}}-\left.\mathrm{L_{P}}\right|_{\mathrm{dB}} \tag{1}\]  
At present, there is no specific path loss model for the LoRa technology in order to estimate \(\left.\mathrm{L_{P}}\right|_{\mathrm{dB}}\). However, there is a large number of different empirical propagation models which were developed and/or derived from experimental measurements using different standards, different frequencies, and in various propagation conditions. Some of them can be used for the frequency band dedicated to LoRa in Europe. For instance, in [35], the Erceg model [36] is used with promising results comparedwith experimental measurements with a maximum difference 100 m in the useful range. The problem is that the Erceg model tends to overestimate the distances in urban environments due to dampening by buildings and other urban structures. In [32], the authors present an analysis and possible optimizations of the [PERSON] propagation model [37], which can be used for both area-to-area, and point-to-point communications. The model is used to predict the path loss over flat terrain but, according to some arrangements and optimizations, it is possible to adapt it to urban areas. The applicability of [PERSON]'s propagation model is efficient as soon as a proper variant is determined for each specific city but, in the case of Turin, this information is not available. However, by similarity, it could be possible to use the standard parameters defined for urban areas and already applied in some cities (e.g., Newark, USA, [33]), considering the obtained results as indicators of propagation performance. When dealing with transmissions between 100 and 1500 MHz in urban areas, the empirical Okumura-Hata model [38] can be used with good results since it has been specifically developed for wireless communication in urban environments. Equation (2) yields the path loss \(\mathrm{L_{P}}\) by knowing the operating frequency f in MHz, the transmitter and receiver heights \(\mathrm{h_{T}}\) and \(\mathrm{h_{R}}\) expressed in meters, the correction parameter \(\mathrm{a(h_{R})}\), Equation (3), due to the area type (urban area or, even, country area), and the distance d between transmitter and receiver expressed in kilometers.