## 5 Calculus Analysis
### Calculation Results and Analyses
#### 5.2.4 Effect of SNR on System Reliability  
In order to analyze the impact of different SNRs on system reliability indicators, the following five scenarios were set up for comparison. In these five scenarios, we set three transmit powers and frequencies. Scenario 1: The wireless transmit power \(P_{0}\) is 250 dB and the frequency \(f\) is 230 MHz. Scenario 2: The wireless transmit power \(P_{0}\) is 250 dB and the frequency \(f\) is 2.6 GHz. Scenario 3: The wireless transmit power \(P_{0}\) is 250 dB and the frequency \(f\) is 4.9 GHz. Scenario 4: The wireless transmit power \(P_{0}\) is 230 dB and the frequency \(f\) is 4.9 GHz. Scenario 5: The wireless transmit power \(P_{0}\) is 200 dB and the frequency \(f\) is 4.9 GHz. The variation of system reliability indexes under different noise powers is shown in Figure 6.  
As can be seen from Figure 6, for the above five scenarios, the higher the system transmitting power and the lower the operating frequency, the higher the noise power required to cause an increase in the average outage time of the system, and the lower the probability of the occurrence of BER (bit error rate) in data transmission. Taking scenario 5 as an example for detailed analysis, when the noise power received by the base station was less than 26 dB, the system reliability index remained almost unchanged with the increase in noise power. This was because at this stage, the system error rate did not exceed the threshold. The information link was effective and the controllable devices of the physical system were still reliably controlled by the information system. When the noise power was greater than 26 dB and less than 48 dB, the system reliability index increased accordingly. At this time, the error rate of information data during transmission exceeded the controllable range of the system. This resulted in information link failure and uncontrolled physical system equipment. When the noise power was greater than 48 dB, the system reliability index no longer changed. This was because when the physical system failed, the information link corresponding to the controllable action switch failed. The fault could only be repaired manually. Comparing the five scenarios, it can be seen that scenario 1 required the highest noise power and the lowest probability of data transmission errors to increase the reliability index. A high system transmission power requires good equipment quality, and a low  
Figure 6: Variation of system reliability index at different noise power levels. operating frequency can carry less information. Therefore, in practice, it is necessary to set the system transmission power and frequency reasonably while ensuring error-free data transmission, which is beneficial for cost savings. In other words, the higher the system generating power, the higher the quality requirements of the equipment, and the lower the operating frequency, the lower the amount of information that can be carried. Therefore, under the condition of ensuring the accuracy of data transmission, the reasonable setting of system transmit power and operating frequency can improve the transmission efficiency and reduce the cost of equipment. In order to study the effect of weather on system reliability in wireless mode, this study selected a wireless transmit power of 250 dB and frequency of 2.6 GHz and set four kinds of weather, namely, sunny, rainy, snowy, and foggy, for analysis. The changes in system reliability indexes under different weather conditions and different time delays are shown in Figure 7.  
From Figure 7, it can be seen that the system reliability index was smaller under adverse weather conditions than on sunny days. This was because wireless signals are more prone to scattering, diffraction, and absorption during propagation in adverse weather conditions, thereby reducing signal strength. This reduces the power of the signal-receiving end, thereby lowering the SNR.