Bayesian Optimization-Based Bit-Correlation Doppler Estimation for Underwater Acoustic OFDM Communications

Underwater sensor networks (USNs) constitute the fundamental infrastructure for marine monitoring and oceanographic data collection. The reliable transmission links are essential for the operation of these sensor nodes. Acoustic transmission provides an effective solution to meet this demand in the complex underwater environment. In particular, orthogonal frequency division multiplexing (OFDM) has attracted considerableattention in USNs due to its high data rate transmission and multi-user and multi-access capability. However, Doppler-induced time-scaling distortions in the practical marine environment severely degrade the performance of underwater acoustic (UWA) OFDM systems. Conventional cross-ambiguity function (CAF) methods generally necessitate long training sequences to ensure estimation accuracy, resulting in excessive signal-frame overhead. To address this issue, we propose a novel Bayesian optimization-based bit-correlation (BOBC) Doppler estimation algorithm that exploits the M-sequences to perform the bit-correlation with only two OFDM symbols. To avoid the computationally expensive fine-grid search typically used for the bit-correlation peak localization, we formulate the Doppler estimation as a black-box optimization problem and solve it via Bayesian optimization, which efficiently searches for the Doppler candidate associated with a high bit-correlation value without exhaustive fine-grid searches. Numerical simulations demonstrate that, under the same two-OFDM-symbol observation interval, the proposed BOBC algorithm reduces the root mean square error (RMSE) from approximately 1.2–1.5 Hz for the CAF and block estimation methods to approximately 0.35 Hz at a 10 Hz Doppler shift. When the CAF observation interval is extended to six OFDM symbols, its estimation accuracy becomes comparable to that of BOBC. In addition, the proposed BO strategy reduces the number of objective-function evaluations from 2001 to approximately 75 compared with the exhaustive bit-correlation search. This framework alleviates signal-frame overhead and computational burden and may offer potential gains for resource-constrained USNs.