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.INDEX TERMS Block coordinate descent, group sparse, underwater acoustic communications, impulsive noise.
I. INTRODUCTIONU NDERWATER acoustic (UWA) communications is vital to various commercial and scientific research activities in oceans and has many applications such as military, oceanographic, commercial shipping, offshore oil and gas industry and underwater vehicles [1]. However, due to the propagation characteristics, underwater acoustic channels are considered to be one of the most challenging communication channels. In particular, the low propagation speed and the reflection of acoustic wave from surface and bottom of the ocean, along with the refraction caused by nonuniformity of sound speed in the water, result in significant multipath delay spread, which leads to severe inter-symbol-interference (ISI) especially in high symbol rate single-carrier system. Besides, due to the low speed of sound, coupled with the motion of transceiver platforms as well as the fluctuation of propagation medium, Doppler effect [2] is almost inevitable in UWA communication, which results in time-varying channel. There are different modulation techniques for underwater acoustic communications including direct sequence spread spectrum (DSSS), frquency shift keying (FSK), phase shift keying (PSK) and so on. They all have pros and cons. For example, DSSS and FSK are suitable for low date rate and high reliable communications and coherent modulation like PSK