Multi-block Sparse Bayesian learning channel estimation for OFDM underwater acoustic communication based on fractional Fourier transform

•According to the sparse characteristics and the correlation of underwater acoustic communication channel, MBSBL is proposed.•Meanwhile, the sparse pilot structure is adopted to reduce the use of 50% pilots on condition of ensuring channel estimation.•The FRFT is introduced to replace FFT. The FRFT has the same complexity with FFT to compensate the Doppler shift and improves the output SNR so as to furtherly improve the channel estimation performance.