This paper proposes an improved frequency domain turbo equalization (IFDTE) with iterative channel estimation and feedback to achieve both a good performance and low complexity in underwater acoustic communications (UWACs). A selective zero-attracting (SZA) improved proportionate normal least mean square (SZA-IPNLMS) algorithm is adopted by utilizing the sparsity of the UWAC channel to estimate it using a training sequence. Simultaneously, a set-membership (SM) SZA differential IPNLMS (SM SZA-DIPNLMS) with variable step size is adopted to estimate the channel status information (CSI) in the iterative channel estimation with soft feedback. In this way, the computational complexity for iterative channel estimation is reduced effectively with minimal performance loss. Different from traditional schemes in UWACs, an IFDTE with expectation propagation (EP) interference cancellation is adopted to estimate the a posteriori probability of transmitted symbols iteratively. A bidirectional IFDTE with the EP interference cancellation is proposed to further accelerate the convergence. THe simulation results show that the proposed channel estimation obtains 1.9 and 0.5 dB performance gains, when compared with those of the IPNLMS and the l0-IPNLMS at a bit error rate (BER) of 10-3. The proposed channel estimation also effectively reduces the unnecessary updating of the coefficients of the UWAC channel. Compared with traditional time-domain turbo equalization and FDTE in UWACs, the IFDTE obtains 0.5 and 1 dB gains in the environment of SPACE'08 and it obtains 0.5 and 0.4 dB gains in the environment of MACE'04 at a BER of 10-3. Therefore, the proposed scheme obtains a good BER performance and low complexity and it is suitable for efficient use in UWACs.
Keywords: a posteriori soft decision; adaptive sparse channel estimation; expectation propagation; frequency domain turbo equalization; underwater acoustic communication.