## 3 Overview of LoRa
The payload duration is the number of payload symbols multiplied by the symbol period, and it is expressed as:  
\[T_{\text{payload}}=n_{\text{payload}}*Ts. \tag{5}\]  
The time of the air or packet is the summation of the preamble and the payload duration, and it is expressed as:  
\[T_{packet}=T_{\text{preamble}}+T_{\text{payload}}. \tag{6}\]  
Bit Rate/data rate is defined as the rate at which bits are transferred from one location to another location. The bit rate (Rbit) of LoRa is expressed as:  
\[R_{bit}=\frac{\text{SF}*\text{BW}}{2^{\text{SF}}*\text{CR}}. \tag{7}\]  
Sensitivity is the inherent property of a system's ability to extract information from signals. It can also be quantified as the lowest possible signal strength that can trigger the system to its packet resolution. The first term is due to thermal noise in 1 Hz of bandwidth and can only be influenced by changing the temperature of the receiver. The second term, BW, is the receiver bandwidth. NF Is the receiver noise figure and is fixed for a given hardware implementation. Finally, SNR represents the signal to noise ratio required by  
Figure 1: Long-range (LoRa) packet structure. the underling modulation scheme. It is the signal to noise ratio and bandwidth that are available as design variables to the LoRa designer. LoRa receiver sensitivity (S) is calculated with this expression as:  
\[\text{S}=-174+10\text{log}_{10}\text{BW}+\text{NF}+\text{SNR}, \tag{8}\]  
where S = receiver sensitivity in dB, BW = Bandwidth in KHz, NF = Noise fig. of a receiver in dB, and SNR = Signal to Noise Ratio. _Signal-to-Noise Ratio (SNR)_ is the measure of received power signal and the noise floor power level. Generally, the range of SNR is between \(-20\) dB and \(+10\) dB. If the range is around the \(+10\) dB, then the received signal is less corrupted. The SNR range of LoRa is between \(-7.5\) dB to \(-20\) dB. A _link budget or received power_ is the summation of all the losses and gains from the transmitter, over free space to the receiver [32]. Using a simple model, the link budget can be calculated by adding transmitter power (\(P_{Tx}\)), receiver sensitivity (Rx), antenna gain, and free space path loss (FSPL). The link budget is expressed as:  
\[\text{CR}=\frac{4}{4+\text{n}}, \tag{2}\]0  
where \(P_{Rx}\) indicates received power or link budget (dBm), \(P_{Tx}\) denotes transmitter power (dBm), \(G_{Tx}\) denotes transmitting antenna gain (dB), \(G_{Rx}\) denotes es receiver antenna gain (dB), and FSPL denotes free space path loss (dB). Free space path loss (FSPL) is defined as the amount of energy that is lost in free space during a communication between the transmitter (Tx) and receiver end (Rx). FSPL expression derives from fris transmission equation and fris transmission equation [33] is expressed as follows:  
\[\text{CR}=\frac{4}{4+\text{n}}, \tag{2}\]1  
where \(p_{r}\) and \(p_{t}\) denotes power receiver and power transmitted, \(\lambda\) indicates wave length, and \(G_{0t}G_{0r}\) directivity of the transmitting and receiving antenna. Concerning the definition of FSPL and the expression of FSPL is represented as follows:  
\[\text{CR}=\frac{4}{4+\text{n}}, \tag{2}\]2  
where d denotes a distance between Tx and Rx (Meters), Tx indicates transmitter, Rx indicates receiver, f indicates the frequency in Hertz, and \(\lambda\) indicates wavelength. \[\text{CR}=\frac{4}{4+\text{n}}, \tag{2}\]3