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The Gaussian noise assumption is usually made for slowly time-varying underwater acoustic communication (UWAC) systems, which is entirely adequate for most cases. However, certain human activities such as geophysical surveys, multi-beam echosounders and iceberg breakup generate impulsive noise. Consequently, the impulsive noise degrades the designed receiver based on the Gaussian noise model significantly. An optimization formulation which takes the slowly time-varying channel impulse response (CIR), the group-sparse impulsive noise and the encoder structure of the data symbol into account is proposed. To tackle the optimization problem, we propose a joint channel estimation, data decoding and impulsive noise estimation (JCDI) algorithm consisting of two modules named module A and module B, where module A performs the joint channel estimation, data estimation and impulsive noise estimation, while module B uses the low density parity check (LDPC) decoder to decode the encoded data symbols. In particular, the block coordinate descent (BCD) algorithm is proposed, and a smoothed fast iterative threshold soft algorithm (FISTA) is proposed to estimate the group-sparse impulsive noise. Substantial numerical simulations and real experiments are conducted to show the effectiveness of JCDI under impulsive noise, i.e., JCDI achieves lower coded BER than conventional receivers.

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Joint Channel Estimation, Data Decoding and Group-Sparse Impulsive Noise Estimation for Slowly Time-varying Single Carrier Underwater Acoustic Communications