Recursive KRSL based low-complexity adaptive Turbo equalizer for OTFS in underwater acoustic communications

Underwater acoustic communication for mobile unmanned underwater vehicles suffers from severe channel delay spread and Doppler shifts. The orthogonal time-frequency-space (OTFS) modulation improves resistance to multipath fading and Doppler interference via joint delay-Doppler domain modeling, whereas existing adaptive OTFS equalizers cannot balance convergence speed and computational complexity. This paper proposes a dichotomous coordinate descent aided recursive kernel risk-sensitive loss (DCD-RKRSL) algorithm, and further develops a robust low-complexity RKRSL-based Turbo equalization (RKRSL-TEQ) scheme for OTFS systems. Adopting kernel risk-sensitive loss, DCD-RKRSL is robust against non-Gaussian impulsive noise and delivers RLS-comparable convergence speed under Gaussian noise. The DCD iteration replaces matrix inversion by a two-dimensional coordinate search and reduces the computational complexity to 𝑂 ⁡ ( 𝑁 u ⁢ 𝑁 T ) . A reweighted zero-attracting constraint exploits the sparsity of underwater acoustic channels to reduce the estimation error. Equipped with interference reconstruction and two-dimensional decision feedback equalization, RKRSL-TEQ achieves fast and robust equalization. In the lake trial the proposed scheme reaches an uncoded BER of 1 . 7 × 1 ⁢ 0 − 3 at the third Turbo iteration. A towed single-hydrophone sea trial confirms the same ranking, where RKRSL-TEQ enters the 1 ⁢ 0 − 3 level by the third iteration, and the LDPC-coded BER falls to the 1 ⁢ 0 − 4 level by iteration 2.