International Journal of Emerging Research in Engineering, Science, and Management
Vol. 5, Issue 3, pp. 81-96, Jul-Sep 2026.
https://doi.org/10.58482/ijeresm.v5i3.6

Received: 27 Apr 2026 | Revised: 29 Jul 2026 | Accepted: 12 Aug 2026 | Published: 30 Aug 2026

This work is licensed under a Creative Commons Attribution 4.0 International License.

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

Full Text PDF

B. Shiny

Vijayalakshmi P

M. Monisha

Rajendran V

Department of Electronics and Communication Engineering, Vels Institute of Science, Technology, and Advanced Studies (VISTAS), Chennai, India

Abstract: 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.

Keywords: Underwater acoustic communication, binary phase shift keying (BPSK), hybrid adaptive thresholding, multipath propagation, wavelet denoising, ambient noise suppression.

References
  1. J. Heidemann, W. Ye, J. Wills, A. Syed, and Y. Li, “Research challenges and applications for underwater sensor networking,” IEEE Wireless Communications and Networking Conference, 2006. WCNC 2006., Las Vegas, NV, 2006, pp. 228-235. https://doi.org/10.1109/WCNC.2006.1683469
  2. D. B. Kilfoyle and A. B. Baggeroer, “The state of the art in underwater acoustic telemetry,” IEEE Journal of Oceanic Engineering, vol. 25, no. 1, pp. 4-27, Jan. 2000. https://doi.org/10.1109/48.820733
  3. J. Preisig, “Acoustic propagation considerations for underwater acoustic communications network development,” ACM SIGMOBILE Mobile Computing and Communications Review, vol. 11, no. 4, pp. 2–10, Oct. 2007. https://doi.org/10.1145/1347364.1347370
  4. I. W. Selesnick, “Wavelet Transform with Tunable Q-Factor,” IEEE Transactions on Signal Processing, vol. 59, no. 8, pp. 3560-3575, Aug. 2011. https://doi.org/10.1109/TSP.2011.2143711
  5. J.-L. Starck, F. Murtagh, and J. Fadili, Sparse Image and Signal Processing: Wavelets, Curvelets, Morphological Diversity, Cambridge University Press, 2015. https://doi.org/10.1017/CBO9781316104514
  6. M. Stojanovic, “On the relationship between capacity and distance in an underwater acoustic communication channel,” ACM SIGMOBILE Mobile Computing and Communications Review, vol. 11, no. 4, pp. 34–43, Oct. 2007. https://doi.org/10.1145/1347364.1347373
  7. M. Stojanovic, “Recent advances in high-speed underwater acoustic communications,” IEEE Journal of Oceanic Engineering, vol. 21, no. 2, pp. 125-136, Apr. 1996. https://doi.org/10.1109/48.486787
  8. M. Stojanovic, L. Freitag, and M. Johnson, “Channel-estimation-based adaptive equalization of underwater acoustic signals,” Oceans '99. MTS/IEEE. Riding the Crest into the 21st Century. Conference and Exhibition. Conference Proceedings, Seattle, WA, USA, 1999, vol. 2, pp. 985-990. https://doi.org/10.1109/OCEANS.1999.805007
  9. I. F. Akyildiz, D. Pompili, and T. Melodia, “Underwater acoustic sensor networks: research challenges,” Ad Hoc Networks, vol. 3, no. 3, pp. 257–279, Feb. 2005. https://doi.org/10.1016/j.adhoc.2005.01.004
  10. E. Demirors and T. Melodia, “Chirp-Based LPD/LPI Underwater Acoustic Communications with Code-Time-Frequency Multidimensional Spreading,” Proceedings of the 11th International Conference on Underwater Networks & Systems, Oct. 2016. https://doi.org/10.1145/2999504.3001083
  11. Y. Bai and P.-J. Bouvet, “Orthogonal chirp Division multiplexing for underwater acoustic communication,” Sensors, vol. 18, no. 11, p. 3815, Nov. 2018. https://doi.org/10.3390/s18113815
  12. F. Yuan, Q. Wei, and E. Cheng, “Multiuser chirp modulation for underwater acoustic channel based on VTRM,” International Journal of Naval Architecture and Ocean Engineering, vol. 9, no. 3, pp. 256–265, Oct. 2016. https://doi.org/10.1016/j.ijnaoe.2016.09.004
  13. W. Xie, E. Zhang, L. You, D. Wang, Z. Wang, and F. Liqun, “Combating Multi-Path Interference to Improve Chirp-Based Underwater Acoustic Communication,” ICC 2024 - IEEE International Conference on Communications, Denver, CO, USA, 2024, pp. 5377-5382. https://doi.org/10.1109/ICC51166.2024.10623112
  14. J. Kim, S. Han, B. Seo, Y. Kim, and H. Lee, “Generalized CHIRP spread spectrum for underwater acoustic communications,” Electronics, vol. 14, no. 5, p. 964, Feb. 2025. https://doi.org/10.3390/electronics14050964
  15. S. Mallat, A wavelet tour of signal processing: The sparse way. Academic Press, 2015. https://doi.org/10.1016/B978-0-12-374370-1.X0001-8
  16. D. L. Donoho, “De-noising by soft-thresholding,” IEEE Transactions on Information Theory, vol. 41, no. 3, pp. 613-627, May 1995. https://doi.org/10.1109/18.382009
  17. D. L. Donoho and I. M. Johnstone, “Adapting to Unknown Smoothness via Wavelet Shrinkage,” Journal of the American Statistical Association, vol. 90, no. 432, pp. 1200-1224, 1995. https://doi.org/10.1080/01621459.1995.10476626
  18. S. G. Chang, B. Yu, and M. Vetterli, “Adaptive wavelet thresholding for image denoising and compression,” IEEE Transactions on Image Processing, vol. 9, no. 9, pp. 1532-1546, Sept. 2000. https://doi.org/10.1109/83.862633
  19. L. Sendur and I. W. Selesnick, “Bivariate shrinkage functions for wavelet-based denoising exploiting interscale dependency,” IEEE Transactions on Signal Processing, vol. 50, no. 11, pp. 2744-2756, Nov. 2002. https://doi.org/10.1109/TSP.2002.804091
  20. J. Portilla, V. Strela, M. J. Wainwright, and E. P. Simoncelli, “Image denoising using scale mixtures of Gaussians in the wavelet domain,” IEEE Transactions on Image Processing, vol. 12, no. 11, pp. 1338-1351, Nov. 2003. https://doi.org/10.1109/TIP.2003.818640
  21. R. R. Coifman and D. L. Donoho, “Translation-Invariant De-Noising,” Lecture Notes in Statistics, 1995, pp. 125–150. https://doi.org/10.1007/978-1-4612-2544-7_9
  22. P. Ravisankar, “Underwater acoustic image denoising using stationary wavelet transform and various shrinkage functions,” ELCVIA Electronic Letters on Computer Vision and Image Analysis, vol. 20, no. 2, Sep. 2021. https://doi.org/10.5565/rev/elcvia.1360
  23. H. Yang, M. Lai, and G. Li, “Novel underwater acoustic signal denoising: Combined optimization secondary decomposition coupled with original component processing algorithms,” Chaos, Solitons & Fractals, vol. 193, p. 116098, Feb. 2025. https://doi.org/10.1016/j.chaos.2025.116098
  24. X. Wang and J. Zhao, “Adaptive threshold Wavelet denoising method and hardware implementation for HD Real-Time processing,” Electronics, vol. 14, no. 11, p. 2130, May 2025. https://doi.org/10.3390/electronics14112130
  25. J. Yang, S. Yan, L. Mao, Z. Sui, W. Wang, and D. Zeng, “Underwater acoustic signal denoising based on sparse TQWT and wavelet thresholding,” Digital Signal Processing, vol. 153, p. 104601, Jun. 2024. https://doi.org/10.1016/j.dsp.2024.104601
  26. Y. Zhang, Z. Yang, X. Du, and X. Luo, “A new method for denoising underwater acoustic signals based on EEMD, correlation coefficient, permutation entropy, and Wavelet threshold denoising,” Journal of Marine Science and Application, vol. 23, no. 1, pp. 222–237, Feb. 2024. https://doi.org/10.1007/s11804-024-00386-6
  27. T. Xing, X. Wang, K. Ni, and Q. Zhou, “A novel joint denoising method for hydrophone signal based on improved SGMD and WT,” Sensors, vol. 24, no. 4, p. 1340, Feb. 2024. https://doi.org/10.3390/s24041340
  28. J. Li et al., “WDNET: An underwater acoustic signal denoising algorithm based on Wavelet denoising and deep learning,” Internet Technology Letters, vol. 8, no. 3, May 2025. https://doi.org/10.1002/itl2.70022
Download PDF

This article is part of Volume 5, Issue 3 (Jul–Sep 2026)

×

© 2026 The Author(s). Published by IJERESM. This work is licensed under the Creative Commons Attribution 4.0 International License.

Archiving: All articles are permanently archived in Zenodo IJERESM Community.