A Carrier Frequency Offset Estimation Scheme for Underwater Acoustic MIMO-OFDM Communication Based on Sparse Bayesian Learning-Assisted Tentative Channel Estimation

Carrier frequency offset (CFO) estimation is crucial for underwater acoustic (UWA) multiple-input multiple-output orthogonal frequency-division multiplexing (MIMO-OFDM) systems. By employing pilot symbols, a CFO estimation scheme utilizing least squares (LS)-based tentative channel estimation and equalization can achieve an improved CFO estimation performance. However, it suffers from performance degradation due to inaccurate tentative channel estimation in scenarios with relatively long channels or a relatively large number of transmitting transducers. To address this problem, we propose a sparse Bayesian learning (SBL)-based CFO estimation scheme, which employs the expectation-maximization SBL (EM-SBL) algorithm as the tentative channel estimator. In addition, to reduce computational complexity caused by matrix inversion, a refined scheme employing variational Bayesian inference (VBI) technology is proposed, which achieves comparable performance to the original scheme with lower complexity. Finally, numerical simulations demonstrate that our proposed schemes can achieve a remarkably low root mean square error (below 10−2) and outperform existing methods across diverse system configurations and simulated channels.