Underwater Acoustic OTFS With Nonuniform Doppler Shifts: Modeling and Off-Grid Block-Sparse Channel Estimation Algorithm

Orthogonal time frequency space (OTFS) modulation, as a 2-D delay-Doppler (DD) domain technique, shows promising potential for underwater mobile communications. However, a critical challenge emerges in wideband underwater acoustic (UWA) channels where each propagation path exhibits a distinct Doppler factor. These Doppler factors result in frequency-dependent nonuniform shifts across the signal bandwidth, which persist as residual Doppler factors effects even after time-domain resampling compensation. This study investigates the impact of nonuniform Doppler shifts in UWA OTFS systems. A novel systematic derivation of the DD domain input–output relationship for UWA-OTFS systems is presented, incorporating residual Doppler effects. Furthermore, we derive a closed-form mathematical model for Doppler spreading in the DD domain and prove the block-sparse properties of UWA-OTFS. Based on the Doppler spreading model, a channel estimation algorithm combining off-grid block-sparse orthogonal matching pursuit with maximum likelihood estimation is proposed to improve Doppler resolution accuracy. Performance evaluation through comprehensive numerical simulations and experimental trials demonstrates the efficacy of the proposed channel estimation algorithm. The superiority of OTFS over orthogonal frequency-division multiplexing in underwater mobile communications is also demonstrated.