This study develops a pseudo-energy-conservation relation to analyze the complementary mean-square performance of a complex-valued normalized least mean-square (CNLMS) algorithm. Based on this relation, we derive a recursion describing the transient complementary mean-square deviation (CMSD) behavior of the CNLMS. Closed-form expressions to predict the steady-state CMSD and complementary excess mean-square error conjugate (CEMSEc) are obtained. Because this method inherits the advantages of the energy-conservation method, our results do not restrict the distribution of input signals. Numerical simulations validate our theoretical analysis results.

中文翻译：

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使用伪能量守恒法的CNLMS算法的互补均方分析

本研究开发了一种伪能量守恒关系来分析复值归一化最小均方 (CNLMS) 算法的互补均方性能。基于这种关系，我们推导出描述 CNLMS 的瞬态互补均方偏差 (CMSD) 行为的递归。获得了用于预测稳态 CMSD 和互补过量均方误差共轭 (CEMSEc) 的封闭式表达式。由于这种方法继承了能量守恒方法的优点，我们的结果不限制输入信号的分布。数值模拟验证了我们的理论分析结果。