Signal Detection for Underwater IoT Devices With Long and Sparse Channels

Underwater acoustic communication often suffers from extended channel impulse response (CIR) and large Doppler spread such that signals become difficult to detect and decode. For the underwater Internet-of-Things (IoT) applications, the challenges are even bigger, because the IoT devices usually transmit very short messages due to severe power constraints, and the length of pilots are often shorter than that of CIR. Therefore, conventional pilot-assisted channel estimation and equalization approaches are incapable of detecting the information data. Moreover, the existing blind channel equalization algorithms, which do not require pilots, are not able to detect information data either, because the number of transmitted symbols is too small to approximate the expected loss with empirical loss, where the loss refers to as the error of estimated signal envelopes. In this article, a new equalization and decoding algorithm is proposed for the underwater IoT devices under harsh communication environments. Inspired by the recent blind deconvolution and compressive sensing techniques, we construct an optimization problem with the objective function rewarding sparsity of the estimated CIR using l4-norm and convexify the feasible set of the problem while guarantee the same solution. Then, we develop a pruned tree search initialization method and use gradient descent to find an optimal solution efficiently. The new algorithm is first verified by simulations, which show that the proposed algorithm outperforms conventional methods, such as the linear minimum mean square error (LMMSE) equalizer and a constant modulus algorithm (CMA). The proposed algorithm, along with a practical procedure for compensating large Doppler spread and carrier frequency offset, is further employed to process the real-world underwater IoT data collected in a fish-tag project. It shows that the proposed algorithm can equalize and detect the IoT data which were corrupted by channels whose lengths are longer than that of pilots, but the existing algorithms, such as LMMSE equalizer and CMA-based blind equalizer are not able to accomplish. It also shows that the proposed algorithm can provide a very impressive improvement compared to raw detection (no equalization or decoding) and decoding-only approaches.