A Unified Approach to the Statistical Convergence Analysis of Frequency-Domain Adaptive Filters
A Unified Approach to the Statistical Convergence Analysis of Frequency-Domain Adaptive Filters
复制标题
频域自适应滤波器统计收敛性分析的统一方法
DOI：
10.1109/tsp.2019.2896133
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发表时间：
2019-04-01
影响因子：
5.4
通讯作者：
Yang, Jun
中科院分区：
文献类型：
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作者：
Yang, Feiran;Enzner, Gerald;Yang, Jun
频域自适应滤波（FDAF）算法以其计算效率高、收敛性能好等优点得到了广泛的应用。过去人们对FDAF的收敛行为进行了大量的研究。然而，先前的分析是基于重叠保存过程的粗略近似或小步长假设，因此对瞬态和稳态性能的预测不准确。此外，到目前为止，还没有给出均方意义上的严格步长界限。为了解决这些问题，我们对一类基于重叠保存结构的fdaf的收敛行为进行了广泛的分析。利用4个fdaf的统一更新方程，在频域严格推导出平均权差向量和权差协方差矩阵的状态递推，并利用该状态递推得到暂态阶段的均方偏差（MSD）和均方误差（MSE）。此外，我们还得到了稳态MSD和MSE的解析结果，以及均值和均方稳定性的步长界。具体地说，这里提出的分析不限制回归数据是高斯或白色。在系统识别场景中的计算机模拟证实了所提出的理论结果比以前的方法更准确。
The frequency-domain adaptive filter (FDAF) algorithms are used in many applications due to their computational efficiency and good convergence performance. Many efforts have been made to analyze the convergence behavior of FDAF in the past. However, the previous analyses are based on coarse approximations of overlap-save procedures or small step-size assumptions and hence came to inaccurate predictions of the transient and steady-state performance. Moreover, the rigorous step-size bound in the mean-square sense has not been provided so far. To address these problems, we carry out an extensive analysis of the convergence behaviors for a family of FDAFs based on the overlap-save structure. Using a unified update equation of four FDAFs, the state recursions of the mean weight-error vector and the weight-error covariance matrix are worked out rigorously in the frequency domain, which are then used to investigate the mean-square deviation (MSD) and mean-square error (MSE) during the transient phase. In addition, we obtain the analytical results on the steady-state MSD and MSE, and the bound on the step size for both the mean and mean-square stabilities. Specifically, the analysis presented here does not restrict the regression data to being Gaussian or white. Computer simulations in a system identification scenario confirmed that the proposed theoretical results are much more accurate than the previous approaches.