## 3 Overview of LoRa  
Long-range (LoRa) is initiated in 2012, it can perform the communication with a high link budget with low power consumption [29]. LoRa is developed for supporting the LPWAN (Low Power Wide Area Network) that utilizes the ISM (Industrial, Scientific, Medical) bands of 433 MHz (Asia), 915 MHz (North America), and 868 MHz (Europe) [13]. LoRa modulation is formed from the CSS (Chirp Spread Spectrum) that provides robustness in case of multipath propagation interferences [30]. LoRa modulation is customized on distinct parameters, like spreading factor (SF), code rate (CR), and bandwidth (BW). * SF is the number of chirps generated by each symbol, and its range is between 7 and 12. The higher the SF value, the better the receiver will eliminate the noise from the signal. The more time it takes to deliver a packet, the greater the amount it takes to transmit the packet. * CF is the frequency of a carrier wave that is modulated to transmit signals; SX 1278 transceiver works on a carrier frequency of 433 MHz. * BW depicts the frequency in the spectrum band, and it is chosen from these three bands: 500 kHz, 250 kHz, or 125 kHz. Large bandwidth represents speed transmission and the small bandwidth presents long-range transmission. The main parameter of the LoRa modulation is BW. The 2 SF chirps that covers the entire frequency band is represented as LoRa symbol. Initially, it begins with a sequence of upward chirps, if the highest frequency band is achieved then frequency is wrapped and there will be a rise in the frequency again from the lowest frequency. As LoRa is established on chirp spread spectrum modulation and the transmitted data is represented as chirp signal from a frequency range from min to fmax. Here, there is an opportunity of configuring the symbol by varying the SF and BW parameters. According to Reference [31], one symbol will take TS of second to transmit, which is a function of SF and BW are presented in the equation below:  
\[\text{TS}=\frac{2^{\text{SF}}}{\text{BW}}. \tag{1}\]  
CR is implemented in communication for assuring short interference during transmission. In any data transmission, LoRa modulation includes a forward error correction (FEC). Thisis achieved by encoding 4-bit data with 5-bit, 6-bit, 7-bit, and even 8-bit redundancies. The LoRa signal can sustain small interferences with this redundancy. CR is expressed as  
\[\text{CR}=\frac{4}{4+\text{n}}, \tag{2}\]  
where n has values in the range between 1 and 4. CR is proportional to transmission speed and inversely proportional to the time on-air (ToA) during the transmission of data. HigherCR represents high transmission speed and low ToA. _LoRa packet structure_ comprises a preamble, optional header, payload, and Cyclic Redundancy Check (CRC), as shown in Figure 1. A preamble is employed for communication between the receiver and the transmitter. The header contains the payload size and information of LoRa configuration, and it is encoded with CR = 4/8. The payload is determined with CR and CRC is transmitted at the end of the frame. ToA is defined as the duration of time that is consumed before a receiver receives this signal. ToA of a packet is calculated with the combination of CR, SF, and BW. LoRa packet duration is defined as the combination of transmitted packet and preamble. The preamble length is expressed as follows. \[T_{\text{preamble}}=(n_{\text{preamble}}+4.25)T_{\text{sym}}, \tag{3}\]  
where npreamble indicates programmed preamble length. The payload is based upon the enabled header mode, and the number of payload symbol is calculated with this Equation (4). \[n_{\text{payload}}=8+max\bigg{(}cirel\bigg{[}\frac{(8\text{PL}-4\text{SF}+28+1 6\text{RC}-20\text{IH})}{4(\text{SF}-2\text{DE})}\bigg{]}(\text{CR}+4),0\bigg{)}, \tag{4}\]  
where PL indicates number of payload bytes, SF indicates spreading factor from 7 to 12, if IH = 0, it indicates header is enabled, if IH = 1, it indicates, if DE = 1, then Low Data Rate Optimize = 1, DE = 0; otherwise, CR is the coding rate (1 equivalent to 4/5, 4 to 4/8).