## 3 Methods
### ICMLD-Cfar  
The CFAR algorithm is designed to automatically detect targets and simultaneously control the false alarm rate [21; 22; 23]. CMLD is a CFAR algorithm and is especially suitablefor multitarget detection environments [24,25]. Unlike the mean-level detector, CMLD-CFAR censors several of the largest samples of the maximum likelihood estimate of the background noise level [26]. If the value of the range point subjected to testing is higher than the estimated background level, the range point is preliminarily determined as the target position. Otherwise, it is considered to be a nontarget signal, namely, noise. Herein, a novel feature is added to enlarge the difference in values between the range points at the target positions and noise positions. Therefore, the targets can be distinguished in an easier and more accurate manner. Figure 3 illustrates the block diagram of the improved CMLD-CFAR algorithm. First, to test whether a range point of \(\widetilde{WE}\) is a target, a sliding window of length \(R\) is determined. It is symmetrically distributed on both sides of the range point \(\widetilde{WE}(x)\). Because of the thickness of the human chest, the trailing effect [27] can lead to signal range points adjacent to \(\widetilde{WE}(x)\) within a certain window, which are similar to the target signal. Therefore, a protective window of length \(Pro\) is designed to avoid the use of these range points to estimate the noise level, and thus decrease the misjudment rate. The remaining \(R-Pro\) range points are then sorted, and larger \(r\) points are censored. The remaining \(R-Pro-r\) range points are then averaged as the estimate of the background noise level as follows:  
\[B_{e}(x)=\frac{1}{R-Pro-r}\sum_{x=1}^{R-Pro-r}\widetilde{WE}(x), \tag{12}\]  
where \(B_{e}(x)\) represents the estimate of background noise level. Subsequently, the threshold factor \(T_{s}\) of ICMLD-CFAR is calculated using the \(R\), \(r\), and \(Pro\), and the false alarm rate \(P_{fa}\) can be estimated as follows:  
\[P_{fa}=\sum_{u=1}^{R-Pro-r}\frac{v_{1}(u)}{T_{s}+v_{2}(u)}, \tag{13}\]  
where \(v_{1}(u)\) and \(v_{2}(u)\) are two intermediate variables defined by  
\[v_{1}(u)=(-1)^{u-1}\bigg{(}\frac{R-Pro}{r}\bigg{)}\bigg{(}\frac{R-Pro-r}{u-1} \bigg{)}\bigg{(}\frac{R-Pro-r-u+1}{r}\bigg{)}^{R-Pro-r-1}. \tag{14}\]  
\[v_{2}(u)=\frac{R-Pro-u+1}{R-Pro-r-u+1}. \tag{15}\]  
Figure 3: Illustration of the censored mean-level detector, constant false-alarm rate. The value of \(P_{fa}\) was set as a fixed constant value. Thus, \(T_{s}\) can be calculated iteratively using Equations (13)-(15). Herein, we set \(P_{fa}=10^{-5}\), \(R=48\), \(r=\frac{3}{SR}\), and \(Pro=8\). To further improve the detection performance of the ICMLD-CFAR, the energy ratio in the reference frequency band (\(E_{r}\)) was designed to enlarge the difference between the target signals and noise. First, ensemble empirical mode decomposition (EEMD) was implemented on the preprocessed radar signal \(R_{AF}(x,\ n)\). A set of intrinsic mode functions (IMFs) can be decomposed from the preprocessed signal at different characteristic scales [28; 29; 30]. By eliminating the unwanted noise IMFs and reconstructing them, the radar signal can become much clearer. This was accomplished according to the following steps:  
While (\(p\leq 50\)) {  
1. Add a series of random white noise signals \(N_{w}(\mathrm{j})\) to \(R_{AF}(x,\ n)\) using  
\[\widetilde{R}_{AF}(x,\ n)=R_{AF}(x,\ n)+N_{w}(p), \tag{16}\]  
where \(p=1,2,\ldots,P\) represents the number of the added white noise signals. 2. Decompose the \(\widetilde{R}_{AF}(x,\ n)\) into a set of \(IMF\)s as \[\widetilde{R}_{AF}(x,\ n)=\sum_{q=1}^{Q_{p}}IMF(q,p)+N_{w}(p),\] (17) where \(Q_{p}\) denotes the decomposed order numbers of \(IMF\)s at trail \(p\). } 3. Regard the \(Q_{min}=\underset{p}{\text{min}}Q_{p}\) as the final order number of \(IMF\)s and then calculate the EEMD results by averaging the IMPs of all \(P\) trails as \[IMF(q)=\frac{1}{P}\sum_{p=1}^{P}IMF(q,p),\] (18) where \(q=1,2,\ \ldots,\ Q_{min}\). 4.