Naturally complex-valued information or those presented in complex domain are effectively processed by an augmented complex least-mean-square (ACLMS) algorithm. In some applications, the ACLMS algorithm may be too computationally- and memory-intensive to implement. In this paper, a new algorithm, termed partial-update ACLMS (PU-ACLMS) algorithm is proposed, where only a fraction of the coefficient set is selected to update at each iteration. Doing so, two types of partial-update schemes are presented referred to as the sequential and stochastic partial-updates, to reduce computational load and power consumption in the corresponding adaptive filter. The computational cost for full-update PU-ACLMS and its partial-update implementations are discussed. Next, the steady-state mean and mean-square performance of PU-ACLMS for non-circular complex signals are analyzed and closed-form expressions of the steady-state excess mean-square error (EMSE) and mean-square deviation (MSD) are given. Then, employing the weighted energy-conservation relation, the EMSE and MSD learning curves are derived. The simulation results are verified and compared with those of theoretical predictions through numerical examples.

中文翻译：

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部分更新增强 CLMS 算法的变体及其性能分析

自然复值信息或那些呈现在复域中的信息可以通过增强复数最小均方 (ACLMS) 算法进行有效处理。在某些应用中，ACLMS 算法可能在计算和内存方面过于密集而无法实现。在本文中，提出了一种新算法，称为部分更新 ACLMS (PU-ACLMS) 算法，其中在每次迭代时只选择系数集的一小部分进行更新。为此，提出了两种类型的部分更新方案，称为顺序部分更新和随机部分更新，以减少相应自适应滤波器的计算负载和功耗。讨论了全更新 PU-ACLMS 及其部分更新实现的计算成本。下一个，分析了PU-ACLMS对非圆形复信号的稳态均值和均方性能，给出了稳态超差均方误差(EMSE)和均方偏差(MSD)的闭式表达式. 然后，利用加权能量守恒关系，推导出EMSE 和MSD 学习曲线。通过数值算例对模拟结果进行了验证，并与理论预测进行了比较。