## 2 Methodology
### Methods for Collection and Processing of Respiration Signals
#### 2.1.5 Respiration Signal Processing  
Currently, there are many methods for processing bio-signals based on a millimeter-wave radar, such as the variational mode decomposition (VMD) algorithm [35], the ensemble empirical mode decomposition (EEMD) algorithm, which is an improvement based on the empirical mode decomposition (EMD) algorithm [36], and the improved complete ensemble empirical mode decomposition with adaptive noise (ICEEMDAN) algorithm [37]. The variational mode extraction (VME) algorithm offers advantages over the VMD algorithm in terms of lower time complexity for extracting specific mode signals and the ability to determine the number of modes without prior specification [38]. As shown in Table 1, respiration and heartbeat signals exhibit different frequency characteristics. Heartbeat signal frequencies typically range from 0.8 to 2.0 Hz, while RSP signal frequencies range from 0.1 to 0.5 Hz. Therefore, a Butterworth bandpass filter was used to remove the signal components in different frequency ranges. By filtering the heartbeat signal components from the mixed vital sign signals, we can extract the RSP signals, thereby separating the respiration and heartbeat signals. To select the appropriate signal processing method, the same 1 min data segments were sequentially processed using the EMD, EEMD, ICEEMDAN, VMD, and VME algorithms. The estimated average respiration rates obtained using these methods were compared with the actual values. Additionally, the data were divided into 20 s segments, processed using different methods, and the average processing time required for each method was estimated. The final results are presented in Table 2.  
From Table 2, it can be observed that the EEMD algorithm estimates the RSP rate with a significantly lower accuracy than the ICEEMDAN, VMD, and VME algorithms. The accuracies of the ICEEMDAN, VMD, and VME algorithms were similar, with the ICEEMDAN performing slightly better than the VME, although the differences were minimal. The processing times for the EEMD and ICEEMDAN al \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Signal** & **Frequency (Hz)** & \
\begin{tabular}{c} **Amplitude of** \\ **Anterior Chest (mm)** \\ \end{tabular} &
\begin{tabular}{c} **Amplitude of** \\ **Posterior Chest (mm)** \\ \end{tabular} \\ \hline Respiration & 0.10–0.50 & 1.00–12.00 & 0.10–0.50 \\ Heartbeat & 0.80–2.00 & 0.10–0.50 & 0.01–0.20 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Comparison of respiration and heartbeat signals. data duration, rendering real-time computation infeasible. Although the processing time of the VMD algorithm was less than 20 s, because it was sufficiently close to this limit, it can easily lead to buffer overflow in the actual system, posing a risk to system stability. The specific steps for the final data processing are as Figure 7:  
1. Sample and parse the data acquired from the millimeter-wave radar;
2. Perform three different dimensional analyses on the intermediate frequency signal to obtain target information;
3. Conduct a fast Fourier transform on the received data in the range dimension to obtain the positional information;
4. Eliminate stationary objects in the indoor environment to remove clutter;
5. Extract and analyze the phase to obtain vital signs signals and use bandpass filters for preliminary signal separation;
6. Apply the VME algorithm(see Algorithm 1) to the extracted vital signs signals to isolate the RSP signals.