The widely-linear complex-valued least-mean-square (WL-CLMS) algorithm exhibits slow convergence in the presence of non-circular and highly correlated filter input signals. To tackle such an issue with reduced computational complexity, this paper introduces adaptive frequency-domain normalized implementations of widely-linear complex-valued filter. Two normalized algorithms are firstly devised based on the circulant matrices of weight coefficients and the regression vector, respectively. In the design, the normalization matrix using the second-order complementary statistical information of the input signal helps increase the algorithm convergence speed. Then, mean-square and complementary mean-square performance of periodic update frequency-domain widely-linear normalized LMS (P-FDWL-NLMS) algorithm for non-circular complex signals is analyzed. In addition, by introducing a variable-periodic (VP) mechanism, we propose the VP-FDWL-NLMS method that provides faster convergence than the P-FDWL-NLMS scheme. Computer simulation results show the superiority of the proposed approach over the fullband widely-linear complex-valued least-mean-square, augmented affine projection algorithm and its variable step-size version, in terms of both complexity and convergence rate.

中文翻译：

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宽线性复值滤波器的自适应频域归一化实现


在存在非圆形且高度相关的滤波器输入信号的情况下，宽线性复值最小均方 (WL-CLMS) 算法表现出缓慢的收敛速度。为了以降低计算复杂度的方式解决这一问题，本文引入了宽线性复值滤波器的自适应频域归一化实现。首先分别基于权系数循环矩阵和回归向量设计了两种归一化算法。在设计中，利用输入信号的二阶互补统计信息的归一化矩阵有助于提高算法收敛速度。然后，分析了非圆复信号周期更新频域宽线性归一化LMS（P-FDWL-NLMS）算法的均方和互补均方性能。此外，通过引入可变周期（VP）机制，我们提出了 VP-FDWL-NLMS 方法，该方法比 P-FDWL-NLMS 方案提供更快的收敛速度。计算机仿真结果表明，该方法在复杂度和收敛速度方面均优于全带宽线性复值最小均方、增强仿射投影算法及其变步长版本。