# Performance Evaluation of LoRa Communications in Harsh Industrial Environments
## 3 LoRa, Channel and Noise
### LoRa: Modulator and Demodulator
#### 3.1.1 Modulator  
During LoRa transmission, the message is transformed into a series of bits. These bits are then grouped together to form symbols. Each symbol is then modulated using a chirp waveform that is specifically designed to match the symbol in question by encoding its value in its starting frequency. This waveform is created by varying the carrier frequency along a linear path between \(-\)B/2 and B/2, where B represents the bandwidth, producing a ramp-like waveform. The length of each symbol is controlled by the spreading factor (SF). This represents \(M=2^{SF}\) symbol values, the duration of each of which is given by the following formula: \(T_{s}=M/B\). Symbols are transmitted in the form of frames, which are structured data packets. Each frame consists of a header, payload data, and an error correction section and can be written as follows:  
\[x(t)=\sum_{n=1}^{N}S_{n}(t-nT_{s}), \tag{1}\]  
where \(N\) and \(S_{n}\) represent the total number of symbols per frame and the symbol of index \(n\), respectively.  
The modulated signal is expressed mathematically by the following equation:  
\[s(t)=e^{\jmath\pi[(\frac{B}{T_{s}}t^{2}-\frac{m_{n}}{T_{s}}t)_{mdB}-\frac{B}{2 }t]}, \tag{2}\]  
where, \(B\) represents the bandwidth, \(n\) represents the symbol index, and \(m_{n}\) and \(T_{s}\) represent the symbol value and duration, respectively, as illustrated in Figure 1.  
\begin{table}
\begin{tabular}{c c c c c} \hline
**Reference** & **Objectives** & **Architecture** & **Scenarios** & **Tools** & **Results** \\ \hline \multirow{8}{*}{[21]} & The study at Mie University in & \multirow{8}{*}{Point to Point} & \multirow{8}{*}{NLOS} & LoRa module & \multirow{8}{*}{The results showed that the harsh environment leads to a reduction in the communication range.} \\  & Japan measured LoRa & & & \\  & communication performance & & & \\  & using a Python-developed & & & \\  & system to evaluate received & & & \\  & signal strength and geographic & & & \\  & coordinates and identified & & & \\  & points outside the & & & \\  & communication range. & & & \\ \hline \multirow{8}{*}{[24]} & The experiment at Ulsan & \multirow{8}{*}{Many to one} & \multirow{8}{*}{NLOS} & Tests on a platform with a gateway and fifteen nodes demonstrated a transmission success rate \\  & University compared packet & & & \\  & transmission success rates of & & & \\  & LoRaWAN, Slotted Aloha, and & & & \\  & RT-LoRa protocols using a & & & \\  & gateway and 15 nodes on three & & & \\  & floors, considering two & & & \\  & interference scenarios. & & & \\ \hline \end{tabular}
\end{table}
Table 1: _Cont._In LoRa communications, the spreading factor is a parameter that plays an important role in the quality of data transmission. When the spreading factor is high, transmission is more robust and less sensitive to interference and noise, which increases the transmission range and improves communication reliability. However, one consequence of using a high spreading factor is that data transmission time is longer, which reduces data throughput. In other words, a higher spreading factor enables data to be transmitted over a greater distance with better signal quality, but at the cost of a slower data rate and higher energy consumption.