A Convex Combination Least Mean Square Algorithm Based on the Distributed Diffusion Strategy for Sensor Networks

In this paper, we propose a novel convex combination algorithm based on the distributed diffusion strategy, utilizing the least mean square (LMS) approach to enhance the performance of sensor networks. By enabling communication among nodes, the algorithm achieves decentralization and improves the robustness of the network. To address the limitations of slow convergence speed and large static error associated with fixed step size errors, we introduce a convex combination strategy that integrates two filters with variable step sizes. The LMS algorithm with the convex combination variable step size assigns a higher weight to the filter with a larger step size when the error is significant, ensuring rapid convergence. Conversely, the convex combination small step size filter is assigned a higher weight when the error is small, reducing the error in the stable state. The convergence behavior of the proposed algorithm is analyzed through theoretical analysis, and its complexity is compared with that of the distributed diffusion LMS algorithm through extensive experimental simulations. The results demonstrate that the combination of the LMS algorithm with the distributed diffusion strategy offers advantages in challenging external environments, including improved convergence speed and reduced stability error. This study makes significant contributions to the existing research field by introducing a novel convex combination algorithm that addresses the shortcomings of fixed step size errors and expands the range of available algorithms. By leveraging the distributed diffusion strategy, our approach enhances the robustness of sensor networks and achieves improved performance. The findings of this study provide valuable insights for researchers working on decentralized algorithms and highlight the potential of combining the LMS algorithm with the distributed diffusion strategy in challenging environmental conditions.