In single-input multiple-output (SIMO) underwater acoustic (UWA) communications, the receiver based on passive time reversal (PTR) combined with decision feedback equalizer (DFE) is widely used but has a limited performance. A multi-channel joint estimation algorithm based on sparse Bayesian learning (MJSBL) is proposed in this paper to exploit the diverse gain from multi-channels, where reasonable prior distribution functions are selected for parameters in the probabilistic model. Afterwards, the algorithm is derived by the mean-field variational inference (VI), iteratively updating the estimation of symbols, channels and noise variation. As a result, the maximum likelihood estimation of the dictionary matrix, as well as the maximum posterior estimation of the channel vectors and noise variance, can be approximated. Simulation and experimental results verify that compared to typical single-channel and multi-channel algorithms, the systems always have lower bit error rates (BERs) and symbol error rates (SERs) with the MJSBL algorithm for different communications distances and symbol block lengths.

中文翻译：

---

一种单输入多输出水声通信联合估计算法

在单输入多输出（SIMO）水声（UWA）通信中，基于无源时间反转（PTR）结合判决反馈均衡器（DFE）的接收机被广泛使用，但性能有限。本文提出了一种基于稀疏贝叶斯学习（MJSBL）的多通道联合估计算法，以利用多通道的多样化增益，为概率模型中的参数选择合理的先验分布函数。然后，通过平均场变分推理（VI）导出该算法，迭代更新符号、信道和噪声变化的估计。结果，可以近似字典矩阵的最大似然估计，以及信道向量和噪声方差的最大后验估计。仿真和实验结果表明，与典型的单通道和多通道算法相比，MJSBL算法在不同的通信距离和符号块长度下，系统始终具有较低的误码率（BER）和符号错误率（SER）。