Denoising algorithm of Φ-OTDR systems based on adaptive fractional wavelet transform denoising

An adaptive, and what we believe to be, novel fractional wavelet transform (NFRWT)-based denoising method is proposed for background-noise suppression and signal-to-noise ratio (SNR) enhancement of phase-sensitive optical time-domain reflectometry (Φ-OTDR) signals in long-range sensing and complex engineering scenarios. A time-domain coupled wavelet basis incorporating fractional-order phase modulation and translation phase compensation is constructed, and an adaptive fractional-order selection strategy based on NFRWT-domain energy concentration maximization is introduced. By adjusting the fractional-order phase modulation to the phase characteristics of distributed acoustic sensing (DAS) signals, useful signal components can be clearly distinguished from broadband background noise in the matched NFRWT domain. Combined with multiscale wavelet decomposition and soft-threshold shrinkage, the proposed method suppresses broadband background noise while preserving waveform fidelity. Compared with representative denoising algorithms, NFRWT shows improved performance in both 20.2 km long-range sensing and real-world external intrusion monitoring scenarios. In real-world external intrusion monitoring scenarios, NFRWT achieves an average SNR of 63.38 dB and an average noise floor of -84.32 dB rad²/Hz.