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 except for distributions with infinite variance. 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.

中文翻译：

---

循环平稳白高斯和非高斯输入的扩散最小均方和归一化最小均方算法的随机分析

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随机模型的维数，同时保留了重要的扩散特性。该分析是在循环平稳白节点输入的系统识别框架中完成的。系统参数根据随机游走模型而变化。循环平稳性由节点输入功率的周期性时间变化建模。该分析适用于所有类型的节点输入分布，但具有无限方差的分布除外。派生模型由简单的标量递归组成。这些递归有助于理解网络均值和均方对 1) 节点加权系数的依赖，2) 节点输入峰态和循环平稳性，3) 节点噪声功率，以及 4) 未知系统均方参数增量。研究了节点加权系数的优化。还研究了两种算法对节点输入峰态和加权系数的稳定性依赖性。对于非高斯节点输入，DLMS 和 DNLMS 算法的行为之间存在显着差异。仿真为该理论提供了强有力的支持。对于非高斯节点输入，DLMS 和 DNLMS 算法的行为之间存在显着差异。仿真为该理论提供了强有力的支持。对于非高斯节点输入，DLMS 和 DNLMS 算法的行为之间存在显着差异。仿真为该理论提供了强有力的支持。