# Detection of Weak Radar Return Signals Based on Pseudo-Time Domain Algorithm
## 1 Introduction  
The deployment of radar systems on miniaturized platforms such as drones and satellites confronts a critical technical challenge: the coupling effect between power-constrained transmission systems and strong background noise in complex electromagnetic environments yields received signals with characteristically low signal-to-noise ratios (SNR \(<-10\) dB) [1, 2]. This weak signal characteristic not only substantially elevates false alarm probabilities but also fundamentally undermines the reliability of conventional detection frameworks [3, 4]. In such strong noise environments, the effective identification of weak signals primarily relies on two methodological frameworks: linear and nonlinear analytical approaches. As a core linear analysis technique, time-domain, frequency-domain, and time-frequency joint analysis methods achieve feature extraction by investigating signal characteristics in the time-frequency distribution. Particularly, the time-frequency joint analysis methodology overcomes the limitations of conventional single-domain representations through the construction of time-frequency distribution maps, enabling precisecharacterization of signal transient features. Its principal advantage lies in a multidimensional representation capability that effectively resolves the non-stationary characteristics of complex signals. Among time-frequency joint analysis methods, wavelet transform has emerged as a research focus due to its unique dual-domain filtering capability [5, 6]. Compared with the single-domain frequency representation of the Fourier transform, wavelet decomposition achieves effective noise suppression through multiscale feature extraction while preserving temporal signal details [7, 8, 9]. Current research demonstrates varying performance limits: a modulus maxima detection-based wavelet reconstruction strategy enables lidar echo denoising within the 8 dB to 1 dB [10], while frequency-domain accumulation combined with temporal wavelet transform accomplishes signal recovery at SNR \(=-20\) dB [11]. Recent advancements include multilayer autocorrelation-based detection for weak sinusoidal signals (\(-18\) dB to \(-20\) dB) [12] and range-guided wavelet transform achieving echo denoising at 1.37 dB [13]. A two-step noise reduction strategy has been reported to process \(-19\) dB weak signals [14]. Although these studies have reached a minimum SNR of \(-20\) dB, more effective denoising methods for lower SNR conditions remain imperative. Recent efforts have integrated wavelet denoising with deep learning to reduce computational load and adapt to complex data environments. Representative work includes a completely unsupervised deep learning framework for high-frequency time series monitoring, demonstrating enhanced unsupervised monitoring capabilities [15, 16]. And the method of combining wavelet denoising with long-term and short-term memory (LSTM) network is used to study the denoising effect in the SNR range of \(-6\) dB to \(+24\) dB [17]. Furthermore, wavelet denoising techniques have been specifically applied in hydroacoustic signal processing [18], seismic analysis [19], and target detection [20, 21, 22, 23]. Cross-domain research documented in [24] confirms wavelet transform's capability for defect identification under extreme noise conditions (SNR \(<-40\) dB), suggesting potential applicability to radar signal detection. However, existing wavelet-based denoising studies predominantly focus on temporal waveform analysis. Although some exploratory attempts employ frequency-domain methods such as spectral accumulation [25] and frequency filtering [26], conventional frequency filtering only eliminates out-of-band noise, while in-band noise components persistently degrade useful signal integrity. To address the aforementioned challenges, this paper proposes a radar weak echo signal detection method based on a pseudo-time-domain algorithm.