## 3 PAI-Rife Algorithm
### PAI-Rife Algorithm
Because the two frequency domain estimation algorithms of HAQSE and T-PP do not judge the correction direction, we only compared the misjudgment situation of PAI-Rife with Rife, ASIQ-Rife, An-Rife, and CQRE algorithms under different SNRs. From the previous analysis of the frequency estimation algorithm, it can be seen that when the frequency point is close to the quantized frequency, the correction direction misjudgment rate of the Rife algorithm is relatively large, increasing the frequency error after frequency deviation correction. For the ASIQ-Rife algorithm, it judged the correction direction again after the signal frequency shift and reduced the misjudgment rate. Due to the improvement of the correction direction judgment method of the Quinn algorithm, the

Figure 8: Mean of PAI\(-\)Rife and other frequency domain estimation algorithms at different SNRs. Figure 9: Standard deviation of PAI\(-\)Rife and other frequency\(-\)domain estimation algorithms at different SNRs. correction ability of the An-Rife algorithm has been optimized. The misjudgment rate of the CQRE and PAI-Rife algorithms are almost the same, and both have been significantly reduced. The reason is that the two methods of judging and correcting the direction are combined, which makes up for the shortcomings of the CQRE algorithm. For the PAI-Rife algorithm, we shifted the signal frequency to the best estimate range and used a phase angle less susceptible to noise to determine the direction of correction. Therefore, in the low signal-to-noise ratio environment, the accuracy of the correction direction judgment of the CQRE and PAI-Rife algorithms has been improved. After the analysis, it is concluded that under the condition of strong noise, the misjudgment rate of the correction direction of the PAI-Rife algorithm is very close to zero, which is much lower than that of the Rife, ASIQ-Rife, and An-Rife algorithms (Figure 10). ### Analysis of Actual Measurement Data

We used an FMCW (Frequency Modulation Continuous Wave) radar sensor to obtain actual data of five different distances and further verified the estimation accuracy of the PAI-Rife algorithm. In addition, we estimated the frequency of the echo signal using the PAI-Rife algorithm. The estimated value of the distance is obtained by

\[R=\frac{cTf_{e}}{2B}, \tag{17}\]

where, \(T=N/f_{s}\) is the sampling period, \(c=299,792,458\) m/s is the speed of electromagnetic waves, \(B\) is the signal bandwidth. The measurement environment is a closed room. The radar is placed horizontally with the launch panel facing the roof. The distance data between the radar and the roof is obtained, and the data are sent to the terminal through serial communication. Before the measurement, the sampling frequency of the FMCW radar is set to \(f_{s}=92.7835\) KHz, the signal bandwidth \(B=999.47\) MHz, and the sampling number \(N=1024\). The actual distances measured by the radar are 2097 mm, 2378 mm, 2420 mm, 2561 mm, and 2653 mm. Above all, the frequency estimation algorithm is used to estimate the beat frequency of the radar, and then the distance value is calculated. The results obtained by different Rife algorithms are shown in Figure 3:0 From the bias in the table, it can be concluded that for these five different distance data, the Rife algorithm has the worst estimation ability. Compared with the other four algorithms, the results obtained using the PAI-Rife algorithm are closer to the actual distance. In terms of distance estimation accuracy, the error rate of PAI-Rife is only 0.2%. Figure 3:1 Correction misjudgment rates of several Rife algorithms under different SNRs. ## 5 Conclusions

The signal input of IoT wireless sensors is often affected by noise, resulting in data loss from the original signal and the inability to access and correctly estimate the signal frequency. Spectral leakage and fence effects are issues that must be addressed when estimating frequency using a single-sensor approach based on signal processing.