Delay-Doppler Domain Turbo Equalization for Single-Carrier Underwater Acoustic Communications

Single carrier modulation, a commonly used method in high-speed underwater acoustic communications, requires equalization at the receiver. However, its performance remains suboptimal in rapidly time-varying channels. Recently, delay-Doppler (DD) domain modulation, such as the well-known orthogonal time frequency space (OTFS) modulation, has garnered considerable attention for its ability to provide more reliable communication in highly dynamic environments. OTFS is essentially a precoded orthogonal frequency division multiplexing (OFDM) method that implements multicarrier modulation in the DD domain, yet it still has a high peak-to-average power ratio (PAPR). To maintain the low PAPR characteristic of single-carrier systems while enhancing performance in rapidly time-varying channels, this article proposes a DD domain turbo equalizer based on minimum mean square error (DD-MMSE-TEQ) for single-carrier underwater acoustic communications. The proposed equalizer comprises a DD domain equalizer and a time-domain decoder. Specifically, due to the inherent ability of DD domain transformation to convert time-varying channels into quasi-static channels, the proposed method demonstrates increased robustness to high Doppler spread. Moreover, through unitary transformation, the DD domain equalizer and time-domain decoder facilitate cross-domain soft information exchange, thereby reducing the probability of error propagation and enhancing the performance of iterative equalization. Simulation results indicate that the proposed DD-MMSE-TEQ outperforms frequency-domain turbo equalization at the cost of additional computational complexity at the receiver and achieves performance levels comparable to conventional OTFS in terms of bit error rate (BER). The proposed method has been validated using underwater experimental data collected from multiple experiments conducted in the Danjiangkou Reservoir, Henan Province, China, in July 2022. The results confirm that the proposed method surpasses other comparison methods in terms of BER.