Joint Channel Estimation and Generalized Approximate Messaging Passing-Based Equalization for Underwater Acoustic Communications

Acquiring channel state information and mitigating multi-path interference are challenging for underwater acoustic communications under time-varying channels. We address the issues using a superimposed training (ST) scheme with a least squares (LS) based channel estimation algorithm. The training sequences with a small power are linearly superimposed with the symbol sequences, and the training signals are transmitted over all time, resulting in enhanced tracking capability to deal with time-varying underwater acoustic channels at the cost of only a small power loss. To realize the full potentials of the ST scheme, we develop a LS based channel estimation algorithm with superimposed training, where the Toeplitz matrix is used, which is formed by the training sequences, enabling channel estimation with superimposed training. In particular, a low-complexity channel equalization algorithm based on generalized approximate messaging passing (GAMP) is proposed, where the a priori, a posteriori, extrinsic means and variances of interleaved coded bits are computed, and then convert them into extrinsic log likelihood ratios for BCJR decoding. Its computational complexity is only in a logarithmic order per symbol. Moreover, the channel estimation, GAMP equalization and decoding are performed jointly in an iterative manner, so that the estimated symbol sequences can also be used as virtual training sequences to improve the channel estimation and tracking performance, thereby remarkably enhance the overall system performance. Moving communication experiments in Jiaozhou Bay (communication frequency 12 kHz, bandwidth 6 kHz, sampling frequency 96 kHz, symbol transmission rate 4 ksym/s) were carried out, and the experimental results verify the effectiveness of the proposed technique.