## 1 Introduction
Measurement procedures and signal processing techniques should be designed to minimize false alarms and maximize the probability of correct detection. Signal processing is vital for detection processes, because analyzing the frequency content of a signal via the Fourier transform (FT) yields deeper insights into its characteristics [28; 29]. Short-time Fourier transform (STFT) and wavelet transform (WT) are particularly advantageous in this regard because they simultaneously provide time and frequency information about the signal [30; 31]. Such time-frequency analysis methods are widely used for respiratory (vital sign) detection, where signals typically exhibit periodic changes within a narrow frequency range of approximately 0.1-0.5 Hz [32; 33]. Different from these methods, the signal can be decomposed into different signal components in the time domain by using empirical mode decomposition (EMD) and variational mode decomposition (VMD) methods. In the literature, STFT analysis was performed on UWB impulse radar signals in [34], and WT and EMD methods were both applied to Doppler radar signals in [35]. In addition, EMD has been used in different studies [36; 37; 38]. EMD was used for Doppler radar signals to identify the arm swinging, breathing, and torso bending movements of humans in debris in [38]. Related studies have performed wavelet analysis of respiratory muscles' EMG signals [39], extracted respiratory information from ECG signals using EMD [40], and employed EMD-based methods for predicting respiratory motion [41]. These works underscore the versatility of advanced signal decomposition techniques in processing physiological signals across various contexts and further enrich the discussion on their applicability for detecting and characterizing respiratory activity. A newer decomposition method, VMD, was also performed on UWB and FMCW radar signals in [42; 43], respectively. To reduce interference and improve the signal-to-noise ratio (SNR) of the signals, state-space methods comprising complex signal demodulation (CSD) and arctangent demodulation (AD) techniques have been developed [44]. A radar-based system, employing a hidden semi-Markov model, highlights the potential of radar technology in capturing heart sounds in the phonocardiograph and radar data [45]. An advanced template matching (ATM) algorithm is utilized for heartbeat detection. Additionally, a hidden Markov model has been employed to detect chest movement due to respiration using impulse radio UWB systems for contactless noninvasive respiratory monitoring [46]. Research also focuses on wireless detection of human respiratory parameters using multi-peak detection of the pulse regulation method with a chest strap sensor [47]. Furthermore, respiratory rate measurement has been conducted using a single wireless continuous wave Doppler radar life signal detection system [48]. In a study on the UWB radar systems, FFT and S-transform were employed to detect and identify human targets through walls [49]. One study [50] carried out human movement detection through walls using a synthetic data set as well as an experimental data set collected with UWB radar. The curvelet transform was developed to eliminate background noise signals, and FFT and the Hilbert-Huang transform were employed to obtain vital sign frequencies. In addition to all of the above-mentioned techniques, artificial intelligence (AI) holds significant promise for advancing the capabilities of respiration and movement detection [51]. An innovative approach using AI-based methods to detect human respiration under debris is presented in [52], which uses a phantom model generated in CST Microwave Studio. By generating simulation-based electromagnetic data and using ANN-based surrogate models, respiratory-related movements are detected. A custom neural network is proposed for detecting diseases using two data sets collected from a breathing belt and a radio sensor [53].