# Experimental Evaluation of the Packet Reception Performance of LoRa
## 3 LoRa  
LoRa is an ultra-long distance wireless transmission scheme based on spread spectrum technology from Semtech. LoRa mainly operates in license-free frequency bands around the world, including 433, 868, 915 MHz, etc. The LoRa structure includes preamble and data parts, as shown in Figure 1. The preamble part consists of several standard consecutive up-chirps, sync, and 2.5 down-chirps. Up-chirps always move in the same direction and with the same slope, until reaching the edge of the frequency band, while down-chirps exhibit the opposite slope. The data part is composed of chirps with different initial positions. We can see that different symbols lead to different initial positions, which indicates that the initial point of each chirp is used for data modulation. The Spreading Factor (SF), Bandwidth (BW), and Coding Rate (CR) are the modulation parameters of LoRa [28]. LoRa uses multiple chips to represent data from payload information. The transmission speed of spreading information is called the symbol rate (Rs), and the ratio of the chip rate to the nominal Rs is the SF, which indicates the number of symbols sent for each information bit. SF can range from 6 to 12. However, because SF6 requires a special configuration, it is generally not used. The number of chips per symbol is calculated as 2 SF. For example, with an SF of 7 (SF7), 128 chips/symbol are used. A lower SF means that more valid data can be sent per second, and a higher SF can only send a small amount of valid data. Compared with a lower SF, when sending the same amount of data, a higher SF requires a longer transmission time, which is called time-on-air. Theoretically, each step up in SF doubles the time required to transmit the same amount of data. More time-on-air means that the modem takes a longer time to launch an RF signal, and consumes more energy. A higher SF is not without advantages. A higher SF has more time-on-air, which means a higher chance of being received, which will increase the receiving sensitivity and thus achieve a longer transmission distance. Because of the orthogonal relationship between different SFs, the SF of the sender and receiver of the link must be known in advance. In addition, the Signal to Noise Ratio (SNR) at the input of the receiver must also be known. Signals can be received normally under negative SNR conditions, which improves the sensitivity, link budget, and coverage of the LoRa receiver. The Bandwidth (BW) refers to the range of the upper-line frequency and lower-limit frequency through which a signal can pass. It can be understood as a channel, and only frequency signals within the signal bandwidth are allowed to pass. \(\text{BW}\in\left[7.8\text{ kHz},500\text{ kHz}\right]\), and the commonly used values are 125, 250, and 500 kHz [24]. In LoRa, the chirp rate only depends on the bandwidth, so increasing the BW can increase the effective data rate, but the sensitivity will also be affected, because the time-on-air is reduced and the probability of being correctly sampled is reduced. The bandwidth (BW) of LoRa is related to the symbol rate (Rs) and the data rate (DR). Rs can be calculated by Equation (1), which means that one chip is sent per Hz per second. We can obtain DR from Equation (2). \[\text{R}_{\text{s}}=\text{BW}/\left(2^{\text{SF}}\right) \tag{1}\]  
\[\text{DR}=\text{SF}*\left(\frac{\text{BW}}{2^{\text{SF}}}\right)*\text{CR} \tag{2}\]  
The reason why channel coding can detect and correct errors in the received bitstream is that some redundant bits are added to spread the information carried in a few bits to more bits. However, the node needs to transmit more bits than it should. To further improve the robustness of the link, the LoRa modem uses cyclic error correction coding for forwarding error detection and error correction. After using such error correction coding, transmission overhead will occur. In the presence of interference, forward error correction  
Figure 1: The LoRa packet structure. (FEC) can effectively improve the reliability of the link.