The sparse direct adaptive equalization technique recently received many attentions for single-carrier underwater acoustic communications. By taking advantage of the sparse (nonuniform) structure of a direct adaptive equalizer (DAE), one obtains a sparse DAE with improved performance and/or reduced complexity compared with its nonsparse counterpart. In this article, the sparse DAE is revisited with two contributions made: First, a comprehensive comparison is made for existing sparse DAEs designed with the proportionate-updating (PU) or the zero-attracting (ZA) adaptive filtering principles. The comparison concludes that the PU-type DAE outperforms the ZA-type DAE in terms of complexity, performance, and operability, thus shall be favored in practical use. Moreover, it motivates the design of a sparse DAE, named the selective ZA improved proportionate normalized least mean squares DAE (SZA-IPNLMS-DAE), based on the combination of the PU and ZA principles. The SZA-IPNLMS-DAE outperforms existing sparse DAEs armed with only one sparsity-promoting mechanism; second, a partial tap update (PTU) scheme via hard thresholding is introduced to sparse DAEs for reducing their complexity without sacrificing performance. The resulting low-complexity and high-performance sparse PTU-DAE schemes are strong candidates for single-carrier UWA communications. Experimental results of multiple-input multiple-output UWA communications are presented to corroborate all above claims.

中文翻译：

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用于单载波 MIMO 水下声学通信的稀疏直接自适应均衡

稀疏直接自适应均衡技术最近在单载波水声通信中受到了很多关注。通过利用直接自适应均衡器 (DAE) 的稀疏（非均匀）结构，与非稀疏对应物相比，可以获得具有改进性能和/或降低复杂性的稀疏 DAE。在本文中，我们重新审视了稀疏 DAE，并做出了两个贡献：首先，对采用比例更新 (PU) 或零吸引 (ZA) 自适应滤波原则设计的现有稀疏 DAE 进行了全面比较。比较得出PU型DAE在复杂性、性能和可操作性方面均优于ZA型DAE，在实际应用中应受青睐。此外，它激发了稀疏 DAE 的设计，基于 PU 和 ZA 原则的组合，命名为选择性 ZA 改进的比例归一化最小均方 DAE (SZA-IPNLMS-DAE)。SZA-IPNLMS-DAE 优于仅配备一种稀疏促进机制的现有稀疏 DAE；其次，将通过硬阈值的部分抽头更新 (PTU) 方案引入稀疏 DAE，以在不牺牲性能的情况下降低其复杂性。由此产生的低复杂度和高性能稀疏 PTU-DAE 方案是单载波 UWA 通信的有力候选者。多输入多输出 UWA 通信的实验结果证实了上述所有说法。SZA-IPNLMS-DAE 优于仅配备一种稀疏性促进机制的现有稀疏 DAE；其次，将通过硬阈值的部分抽头更新 (PTU) 方案引入稀疏 DAE，以在不牺牲性能的情况下降低其复杂性。由此产生的低复杂度和高性能稀疏 PTU-DAE 方案是单载波 UWA 通信的有力候选者。多输入多输出 UWA 通信的实验结果证实了上述所有说法。SZA-IPNLMS-DAE 优于仅配备一种稀疏促进机制的现有稀疏 DAE；其次，将通过硬阈值的部分抽头更新 (PTU) 方案引入稀疏 DAE，以在不牺牲性能的情况下降低其复杂性。由此产生的低复杂度和高性能稀疏 PTU-DAE 方案是单载波 UWA 通信的有力候选者。多输入多输出 UWA 通信的实验结果证实了上述所有说法。