Multipath-Aware Hybrid Adaptive Wavelet Thresholding for Denoising Underwater Acoustic BPSK Communication Signals

This paper presents a hybrid adaptive wavelet thresholding method for denoising underwater multipath Binary Phase Shift Keying (BPSK) communication signals corrupted by real ambient noise. A raised-cosine pulse-shaped BPSK signal is transmitted through simulated underwater acoustic channels with varying delay spreads and channel conditions to model realistic underwater propagation. Real ambient underwater noise is added to the transmitted signal at input SNRs of -15, −10, −5, 0, and 5 dB to evaluate the proposed method's robustness under different noise levels. The noisy signal is decomposed using the Continuous Wavelet Transform (CWT) with the Analytic Morlet wavelet. The proposed hybrid method combines adaptive covariance-based weighting with soft thresholding to preserve the transient burst features. Delay-dependent correlation parameters are also incorporated to adapt the thresholding to the severity of multipath propagation. The denoised signal is reconstructed using the inverse Continuous Wavelet Transform, and the performance is evaluated using output Signal-to-Noise Ratio (SNR), Root Mean Square Error (RMSE), Correlation Coefficient (CC), Signal Preservation Index (SPI), computational runtime, and statistical significance analysis. The proposed method is compared with Universal, SURE (Stein's Unbiased Risk Estimate), Minimax, BayesShrink, Empirical Mode Decomposition (EMD)-based, and Variational Mode Decomposition (VMD)-based denoising methods. Monte Carlo simulations show that the proposed hybrid method provides improved denoising performance and better preservation of the transmitted BPSK signal under varying underwater channel conditions.