A unified analytical framework for distributed variable step size LMS algorithms in sensor networks

Internet of Things (IoT) is helping to create a smart world by connecting sensors in a seamless fashion. With the forthcoming fifth generation (5G) wireless communication systems, IoT is becoming increasingly important since 5G will be an important enabler for the IoT. Sensor networks for IoT are increasingly used in diverse areas, e.g., in situational and location awareness, leading to proliferation of sensors at the edge of physical world. There exist several variable step-size strategies in literature to improve the performance of diffusion-based Least Mean Square (LMS) algorithm for estimation in wireless sensor networks. However, a major drawback is the complexity in the theoretical analysis of the resultant algorithms. Researchers use several assumptions to find closed-form analytical solutions. This work presents a unified analytical framework for distributed variable step-size LMS algorithms. This analysis is then extended to the case of diffusion based wireless sensor networks for estimating a compressible system and steady state analysis is carried out. The approach is applied to several variable step-size strategies for compressible systems. Theoretical and simulation results are presented and compared with the existing algorithms to show the superiority of proposed work.