###### Abstract  
Life detection is important in earthquake rescue, but weak vital signal is susceptible to interference by clutters. Due to the undesirable characteristics of the hardware, there are two main types of clutter generated by the frequency modulation continuous wave (FMCW) radar when transmitting signals. One is generated by periodic nonlinearity during frequency modulation, and the other is generated by the phase-locked loop spuriousness (PLLS) in frequency division. They cause additional beat frequencies to appear beside those from the target, leading to false alarms. Since the suppression measures for them are different, it is necessary to distinguish the types of clutter and choose appropriate suppression methods. In this paper, the accurate theoretical modeling of the effects of the periodic nonlinearity and phase-locked loop spuriousness on the beat signal is performed to determine distinctions between them. The clutter occurring in the system used is identified as originating from phase-locked loop spuriousness through fiber-optic experiments. A method using long delay lines and cross-correlation is proposed to identify and remove it. In experiments, the false alarm rate is reduced from over 50 percent to nearly 0 percent, providing strong evidence for the effectiveness of the proposed method in through-wall detection. frequency modulation continuous wave (FMCW); periodic nonlinearity; phase-locked loop spuriousness (PLLS); correlation coefficient; through-wall detection +
Footnote †: journal: Applied sciences  
0000-0001-9999-2000]Y.  
frequency of the beat signal. In through-wall detection, the presence of the wall causes a large attenuation of electromagnetic waves. Therefore, for the same detection range, the radar needs to have a higher power than when applied in free space. At this point, the radar with a wideband short pulse requires higher peak power, which is difficult to implement in hardware. However, this is not the case with the FMCW radar because of its large time-width bandwidth product. Moreover, the FMCW radars have a higher degree of device integration, which makes it easy to achieve miniaturization. These make the FMCW radar more suitable for through-wall detection. However, FMCW radar suffers from two types of clutter during transmission due to the undesirable characteristics of the hardware. One is generated by the nonlinear frequency modulation, and the other is generated by the phase-locked loop spuriousness that arises in system frequency division. They cause additional beat frequencies to appear beside those from the target, leading to false alarms. More seriously, they are further complicated by reflections from the wall, the human target, and other objects in through-wall detection [10]. These problems seriously impact the correctness of human target localization [11]. It is necessary to study the solution of removing them before performing target detection. There are different suppression methods for these two types of clutter. For frequency modulation nonlinearities, current research includes both hardware and software correction methods. Hardware techniques include using predistortion technique to compensate for nonlinearity in voltage-controlled oscillator (VCO) response characteristics [12], correcting varactor tuning curves by a tuning voltage converter [13], using direct digital synthesizers (DDSs) [14] and phased-locked loops (PLL) [15]. However, they not only raise the cost but also increase the complexity of the system. Software corrections are divided into two steps: nonlinearity estimation and correction. Using a fixed-range target echo as reference, the estimation methods consist of coherent integration [16], homomorphic deconvolution [17], and high-order ambiguity function [18]. This effect is partially compensated using methods such as residual video phase (RVP) removal [16; 19], time resampling [17; 18], and match Fourier transform [20]. For the phased-locked loop spuriousness, current research focuses on hardware suppression methods.