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

  • Muhammad Omer Bin Saeed
  • Waleed Ejaz
  • Saad Rehman
  • Azzedine Zerguine
  • Alagan Anpalagan
  • Houbing Song


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.


Least-mean-square algorithms Mean-square analysis Steady-state analysis Variable step-size Wireless sensor networks 


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Authors and Affiliations

  1. 1.Department of Computer Engineering, College of Electrical and Mechanical EngineeringNational University of Sciences and TechnologyRawalpindiPakistan
  2. 2.Department of Electrical and Computer EngineeringRyerson UniversityTorontoCanada
  3. 3.Department of Electrical EngineeringKing Fahd University of Petroleum and MineralsDhahranSaudi Arabia
  4. 4.Department of Electrical, Computer, Software, and Systems EngineeringEmbry-Riddle Aeronautical UniversityDaytona BeachUSA

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