Wavelet-Aided OTFS for Doubly Selective Underwater Acoustic Communications

Abstract

Conventional Fourier-based orthogonal time-frequency space (OTFS) modulation performs poorly in doubly selective underwater acoustic (UWA) channels because severe fractional Doppler leakage degrades detection reliability and forces the use of computationally expensive iterative equalizers. The purpose of this work is to remove that dependence on iterative processing by suppressing Doppler leakage directly at the modulation stage rather than compensating for it at the receiver. To this end, we propose a wavelet-aided OTFS (W-OTFS) framework that replaces the Fourier transform with a compactly supported orthonormal wavelet basis. Our central contribution is an analytical proof that compact support renders the effective delay–Doppler channel matrix approximately banded, and a systematic basis-selection study confirming that this banding–not the specific wavelet chosen–is what governs bit error rate (BER); this in turn enables reliable symbol recovery via a lightweight, single-shot linear minimum mean square error (LMMSE) equalizer with no iterative loops. Because BER is invariant to the wavelet family, we further show that the Haar and Daubechies-2 (db2) variants offer a practical deployment trade-off: Haar achieves a near-deterministic peak-to-average power ratio (PAPR) of $\approx 6.1$ dB suited to power-limited nodes, while db2 attains $\approx 8.6$ dB PAPR with superior out-of-band spectral containment. Evaluated under statistical channel models and a highly reverberant 256-tap measured pool channel, both W-OTFS configurations achieve the lowest BER among all evaluated schemes, outperform iterative Fourier-based baselines, and surpass standard OTFS by up to 8 dB under 4-QAM. These findings establish W-OTFS as an energy-efficient, low-complexity physical-layer candidate for emerging Internet of Underwater Things networks.