Joint message-passing-based accurate bidirectional channel estimation and generalized-approximation-message-passing-based low-complexity perfect equalization with underwater moving transceivers

Abstract

Moving underwater acoustic communications incur the fast time-varying multipath interference (FTMI), leading to a decrease in decoding performance or even decoding failure. In this study, we address the FTMI issue using the superimposed training (ST) scheme and segment strategy with a joint channel estimation and equalization algorithm. The ST scheme refers to the linear superposition of the training sequence with a small power to the symbol sequence; the segment strategy slices a data block into the segments. Thus, the tracking capability of time-varying channels is significantly improved. To realize their full potential, a “novel” joint message-passing-based accurate bidirectional channel estimation and generalized-approximation-message-passing-based low-complexity perfect equalization (BCE-LPE) algorithm is developed. The Gaussian channel estimates of the segments can be parameterized by their means and variances, thereby enabling fusion of the channel estimates. The correlation of the channel estimates for the segments is established through a channel correlation coefficient, so that the whole data block can be used to estimate the channel of each segment, leading to an accurate channel estimation. Unlike the Gaussian approximate process of the input symbol sequence of the traditional linear equalization, the proposed low-complexity perfect equalization maintains the discrete and independent form of the input symbol sequence, avoiding the equalizer’s input information loss. The a priori, a posteriori, extrinsic means and variances of interleaved encoded bits are computed using the low-complexity diagonal-matrix message passing, leading to the low-complexity perfect equalization, with computational complexity in a logarithmic order per symbol. Moreover, channel estimation, equalization, and decoding are jointly performed in an iterative manner to significantly enhance the overall system performance. Additionally, the parallel processing strategy is used to improve the computation speed, in which all the data blocks are separately and parallelly processed. Field experiments with moving transceivers (the communication distance was about 5.5 km, the bandwidth was 4 kHz, and the transmission rate was 3765 bits/s) were performed in Jiaozhou Bay in 2021, with the experimental results verifying the effectiveness of the BCE-LPE algorithm.