VAMP based Frequency-Domain Turbo Equalization for MIMO Horizontal Underwater Acoustic Communications

Channel equalization plays a crucial role in underwater acoustic (UWA) communications. However, there is a performance gap between conventional equalization methods and the optimal minimum mean square error (MMSE) solution. Recently, a turbo equalization scheme enabled by a soft frequency-domain equalizer (SFDE) based on the Vector Approximate Message Passing (VAMP) algorithm, was introduced for single-carrier UWA communications. The VAMP-SFDE performs selfiterations between an inner soft equalizer (ISE) and an inner soft slicer (ISS), and approaches the performance of an MMSE equalization. Experimental results for single-input single-output deep-sea vertical UWA communications verified the superiority of the VAMP equalizer. In this paper, we extend the investigation to shallow-water multiple-input multiple-output (MIMO) horizontal UWA communications, where the multipath is generally more severe than that in vertical transmissions. As the signal-to-noise ratio (SNR) value is critical to the equalization performance, we incorporate an SNR estimation via the expectation-maximization (EM) algorithm into the VAMP-SFDE, leading to the EM-VAMP-SFDE. Experimental results showed the proposed EM-VAMP-SFDE not only outperformed traditional equalizers but also achieved extra gain over existing VAMP-SFDE with preset SNR value.