循环平稳白高斯和非高斯输入下扩散最小均方和归一化最小均方算法的随机分析
Stochastic Analysis of the Diffusion Least Mean Square and Normalized Least Mean Square Algorithms for Cyclostationary White Gaussian and Non-Gaussian Inputs
摘要：
针对具有融合中心的网络，分析了扩散最小均方（DLMS）和扩散归一化最小均方（DNLMS）算法。这种结构降低了所得到的随机模型的维数，同时保留重要的扩散特性。分析是在循环平稳白节点输入的系统辨识框架中进行的。系统参数根据随机游走模型而变化。循环平稳性模型的节点输入功率的周期性时间变化。该分析适用于所有类型的节点输入分布和节点输入功率变化。导出的模型由简单的标量递归。这些递推公式有助于理解网络平均值和均方值对1）节点加权系数、2）节点输入峰度和循环平稳性、3）节点噪声功率和4）未知系统均方参数增量的依赖性。研究了节点权系数的优化问题。研究了两种算法的稳定性对节点输入峰度和加权系数的依赖关系。显着差异的DLMS和DNLMS算法的行为之间的非高斯节点输入。仿真结果为理论提供了有力的支持。
英文摘要：
The diffusion least mean square (DLMS) and the diffusion normalized least mean square (DNLMS) algorithms are analyzed for a network having a fusion center. This structure reduces the dimensionality of the resulting stochastic models while preserving important diffusion properties. The analysis is done in a system identification framework for cyclostationary white nodal inputs. The system parameters vary according to a random walk model. The cyclostationarity is modeled by periodic time variations of the nodal input powers. The analysis holds for all types of nodal input distributions and nodal input power variations. The derived models consist of simple scalar recursions. These recursions facilitate the understanding of the network mean and mean-square dependence upon the 1) nodal weighting coefficients, 2) nodal input kurtosis and cyclostationarities, 3) nodal noise powers and 4) the unknown system mean-square parameter increments. Optimization of the node weighting coefficients is studied. Also investigated is the stability dependence of the two algorithms upon the nodal input kurtosis and weighting coefficients. Significant differences are found between the behaviors of the DLMS and DNLMS algorithms for non-Gaussian nodal inputs. Simulations provide strong support for the theory.
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