The paper studies the behavior of the diffusion least mean square (DLMS) algorithm in the presence of delays in probing the unknown system by the nodes. The types of input distribution and the probing delays can be different for different nodes. The analysis is done for a network having a central combiner. This structure reduces the dimensionality of the resulting stochastic models while preserving important diffusion properties. Communication delays between the nodes and the central combiner are also considered in the analysis. The analysis is done for system identification for cyclostationary white nodal inputs. Mean and mean-square behaviors of the algorithm are analyzed. The derived models consist of simple scalar recursions. These recursions facilitate the understanding of the algorithm mean and mean-square dependence upon the 1) nodal input kurtosis, 2) nodal probing delays, 3) communication delays between the nodes and the central combiner, 4) nodal noise powers, and 5) nodal weighting coefficients. Significant differences are found between the algorithm behavior for equal probing delays and that for unequal probing delays. Results for unequal probing delays are surprising. Simulations are in excellent agreement with the theory.

中文翻译：

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循环平稳白高斯和非高斯输入的具有探测延迟的扩散 LMS 算法分析

本文研究了扩散最小均方 (DLMS) 算法在节点探测未知系统存在延迟的情况下的行为。对于不同的节点，输入分布的类型和探测延迟可以不同。该分析是针对具有中央组合器的网络进行的。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。分析中还考虑了节点和中央组合器之间的通信延迟。分析是为了循环平稳白节点输入的系统识别。分析了算法的均值和均方行为。派生模型由简单的标量递归组成。这些递归有助于理解算法均值和均方依赖于 1) 节点输入峰度、2) 节点探测延迟、3) 节点与中央组合器之间的通信延迟、4) 节点噪声功率和 5) 节点加权系数。在相等探测延迟和不相等探测延迟的算法行为之间发现了显着差异。不平等的探测延迟的结果令人惊讶。模拟与理论非常吻合。