# Experimental Evaluation of the Packet Reception Performance of LoRa
## 5 Results and Analysis
### Parameter Setting of the Transmission Scheme  
Energy is critical for communication networks that require low power consumption. In fact, there has been a lot of work on energy-saving communication protocols and power management strategies, and related work is still ongoing. The time required for successful communication and energy consumption are positively correlated, so we will reduce the energy consumption of nodes from the perspective of reducing the time for successful communication. The previous experiment tells us the significance of each physical parameter for the performance of LoRa, and also gives a detailed Packet Error Ratio \(p_{f}\) report. Assuming that the Packet Error Ratio remains unchanged and the number of possible retransmission attempts is unlimited, the average amount of retransmission required for each packet to be successfully received is shown in Equation (11). \[\mathrm{r}=\sum_{n=1}^{\infty}p_{f}^{n}=\frac{p_{f}}{1-p_{f}} \tag{11}\]  
Figure 11 shows the number of packets that need to be retransmitted under different SNRs and SFs. The \(x\) axis represents different SF values, \(\mathrm{SF}\in[7,12]\); the \(y\) axis represents different SNR values, \(\mathrm{SNR}\in[-24,0]\) dB; and the z axis represents the number of packets that need to be retransmitted. At the same time, we assume that BW is 125 kHz, CR is 4/8, and the packet length is 32 bytes. When the Packet Error Ratio is equal to 1, the LoRa signal is completely covered by the noise signal, and the receiver cannot detect the preamble signal and decoded data. At this time, the number of packets that need to be retransmitted should be infinite, and we use r = 50 to represent it. Figure 10: Measurement results of different LoRa receivers (SX1276 MB1 MAS and RN2483 Note). In order for the receiver to have enough time to receive the LoRa signal completely and to be able to estimate the additional delay caused by the retransmission, we constrain the packet interval to three packet transmission times. Therefore, the time \(t_{r}\) required to retransmit a data packet can be obtained. Moreover, if parameters such as SF, BW, CR, and the packet length are set, the transfer time \(t_{0}\) and Packet Error Ratio \(p_{f}\) are obtained. Since the time \(t_{r}\) required for a packet to be retransmitted is four times the transfer time \(t_{0}\), the time \(t_{r}\) required for a packet to be retransmitted is also obtained. The time t required for the packet to be successfully received can be obtained from Equation (12). \[\text{t}=\ t_{0}+t_{r}\frac{p_{f}}{1-p_{f}} \tag{12}\]  
Assuming the previous conditions and that the number of retransmissions is unlimited, the time t required for the packet to be successfully received is shown in Figure 12. It can be seen from the figure that, although a higher SF has better immunity to interference, it requires a much more successful transmission time than a lower SF under certain SNR conditions. For example, when SNR = \(-13\) dB, BW = \(125\) kHz, CR = \(4/8\), and the packet length is 32 bytes, the successful transmission time t = \(0.3459\) s with SF = \(9\) is much shorter than t = \(1.9814\) s with SF = \(12\). Furthermore, although the transmission time \(t_{0}\) and retransmission time \(t_{r}\) under different parameter settings are different, when the parameters are set, the normal \(t_{0}\) of the packet is a constant without retransmission, and the \(t_{r}\) is also a constant, so the only \(p_{f}\) is related to the total required successful transmission time \(t\). We can reduce the required \(t\) by reducing \(p_{f}\). We know that the size of \(p_{f}\) is related to SF, BW, CR, and the packet length. We can reduce the \(p_{f}\) by adjusting these parameters. However, it should be noted that the \(t_{0}\) and \(t_{r}\) are also related to the above parameters. By adjusting these parameters, \(p_{f}\) is reduced, but \(t_{0}\) and \(t_{r}\) may increase, resulting in an increase in the \(t\).