| Summary: | To address the problem of the harsh time-varying multi-path interference (TMI) incurred by moving underwater acoustic communications, a joint multiple turbo equalization (JMTE) algorithm is proposed. The superimposed training scheme and the single turbo equalization have been proposed to address the issue of the TMI. To tackle the more challenging fast TMI, the symbol block has been successfully divided into the segments, and the channel correlation between (among) the segments has been established, improving the tracking performance for fast time-varying channels. When the channels sharply change, the channel correlation between (among) the segments is broken, leading to decoding failure. Therefore, we develop the JMTE algorithm with the calculational complexity of the logarithmic order per symbol, where the channel of each segment is separately estimated, so that the establishment of the channel correlation is avoided, and the corresponding separate equalization results of the segments are combined to construct a joint equalization result. Unlike the Gaussian approximate process of the input symbols of the traditional linear minimum mean square error equalization, the discrete independent random variable form of the input symbols of the JMTE algorithm is retained to avoid input information loss. The ‘separate’ channel estimates, the JMTE and decoding are iteratively operated, where based on the low-complexity diagonal-matrix message passing, the information exchange between the JMTE equalizer and the decoder is carried out to dramatically enhance the equalization performance by utilizing the encoding redundant information. Moving underwater communication experiments were done in 2021 (the communication distance was about 5.5 km, and the relative speed was about 0.5 m/s), and the experimental results verify the effectiveness of the proposed algorithm.
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