MUSIC-Based Residual Uniform Frequency Offsets Mitigation Method for Underwater Acoustic Differential OFDM Communications

The inherently violent frequency offsets caused by Doppler shifts in underwater acoustic (UWA) channels severely disrupt the orthogonality among subcarriers in differential orthogonal frequency division multiplexing (DOFDM) systems, making precise signal detection quite challenging. Although the passband resampling can efficiently alleviate the non-uniform frequency offsets, it still leaves residual uniform frequency offsets. In this paper, we interestingly find that the residual uniform frequency offsets mitigation is similar to the direction of arrival (DOA) estimation, and thus can be well addressed by the multiple signal classification (MUSIC) algorithm. To meet the two prerequisites of applying the MUSIC, we derive the vectorized form of the resampled signal and propose the uniform null subcarriers insertion to ensure the column full-rank. The verification results based on the realistic UWA channel dataset show that, compared with the channel-adaptive estimation and the fractional fast Fourier transform (F-FFT), our proposed method reduces the mean squared error (MSE) of signal detection by approximately 3 dB and 6 dB (i.e., 50% and 75%) at a Doppler factor of $1 \times 10^{-3}$, a subcarrier number of 1024, and a signal-to-noise ratio (SNR) of 15 dB, respectively.