# Selecting Target Range with Accurate Vital Sign Using Spatial Phase Coherency of FMCW Radar
## 3 Results
### Vital-Sign Accuracy  
The accuracy of the VSs in the range-bins that was selected by the proposed and conventional methods were examined and compared. Figure 5 shows extracted VS signals depending on range-bin selection methods. As shown in Figure 5, the proposed method selected the pair of range-bins for which showed the coherency and correlations between \(P(t,r)\) and referenced VSs were high. However, in the same range-bins, \(M(t,r=0.975,1.000)\) m in Figure 5a and \(M(t,r=1.175,1.120)\) m in Figure 5d do not represent respiration or heartbeat, although \(M(t,r=1.150,1.175)\) m in Figure 5b and \(M(t,r=0.800)\) m in Figure 5c are proportional to referenced heartbeat or respiration. Although \(M(t,r)\) represented vital displacement as in Figure 5b,c, \(M(t,r)\) was not reliable in measuring VS displacement as in Figure 5a,d. Consequently, the accuracy of VSs extracted by method in [37] varied among the subjects. Furthermore, both \(M(t,r)\)  
and \(P(t,r)\) of methods in [38; 39; 40] had inaccurate information about both respiration and heartbeat considering the correlation with the reference. Figure 5: Extracted vital signs. (**a,b**) Extracted respiration and heartbeat signals for subject#1, and (**c,d**) extracted respiration and heartbeat signals for subject#2. Figure 7: Comparison of the extracted heart rate using the proposed method with the referenced ground truth for 20 subjects. For each subject, 105 vital rates were obtained and 2100 vital rates were totally obtained from the all subjects. Figure 8 depicts scatter plots of the estimated vital rates compared to the ground truth. Diagonal patterns are observed in the scatter plots of the proposed method, indicating that estimated vital rates are close to the ground truth. Moreover, we evaluated the accuracy of the estimated vital-sign rates as the mean error \(\epsilon\), correctness \(o\), and correlation coefficient \(\rho\) with ground truth for the various time window, \(t_{0}\) as shown in Figure 9.  
The \(\epsilon\) measures averaged absolute difference between estimated vital rates and ground truth, as in (12):  
\[\epsilon=\frac{1}{K}\sum_{i=1}^{K}|x_{i}-y_{i}|, \tag{12}\]  
where \(K=2100\) is total number of vital rates, \(x\) is estimated vital rates, and \(y\) is referenced vital rates. The \(o\) calculates the proportion of the estimated vital rates of which the error compared to the ground truth is within the boundaries (37; 40), as in (13). \[o=\frac{100}{K}\sum_{i=1}^{K}I(|x_{i}-y_{i}|<thr), \tag{13}\]  
where \(I(statement)=\left\{ \begin{array}{ll}1&\text{if }statement=true\\ 0&\text{if }statement=false^{\prime},thr=2\text{ RPM for respiration and }thr=5\text{ BPM for heartbeat.}\end{array} \right.\)  
The \(\rho\) measures the correlation between the estimated vital rates and ground truth (49), as in (14):  
\[\rho=\frac{\sum_{i=1}^{K}(x_{i}-\mu_{x})(y_{i}-\mu_{y})}{\sigma_{x}\cdot\sigma _{y}}, \tag{14}\]  
where \(\mu_{x}\) and \(\mu_{y}\) are mean of \(x\) and \(y\), and \(\sigma_{x}\) and \(\sigma_{y}\) are standard deviation of \(x\) and \(y\). For both respiration and heartbeat, the vital rates extracted from the proposed method show higher accuracy than conventional methods with respect to \(\epsilon\), \(o\), and \(\rho\) regardless of length of the time window. Figure 8: Comparison of radar based vital rates with reference. (**a**) Respiration rate, and (**b**) heart rate. **Author Contributions:** Conceptualization, H.-IC. and H.S. ; methodology, H.-IC. ; software, H.-IC. ; validation, W.-JS. ; formal analysis, H.-IC. ; investigation, H.S. ; resources, W.-JS. ; data curation, H.-IC. ; writing--original draft preparation, H.-IC. ; writing--review and editing, H.-C.S. ; visualization, H.-IC. and H.-C.S. ; supervision, W.-JS. ; project administration, H.-C.S. ; funding acquisition, H.-C.S. All authors have read and agreed to the published version of the manuscript.