The Performance Analysis of Diffusion LMS Algorithm in Sensor Networks Based on Quantized Data and Random Topology

We study the performance of diffusion LMS (Least-Mean-Square) algorithm for distributed parameter estimation problem over sensor networks with quantized data and random topology, where the data are quantized before transmission and the links are interrupted at random times. To achieve unbiased estimation of the unknown parameter, we add dither (small noise) to the sensor states before quantization. We first propose a diffusion LMS algorithm with quantized data and random link failures. We further analyze the stability and convergence of the proposed algorithm and derive the closed-form expressions of the MSD (Mean-Square Deviation) and EMSE (Excess Mean-Square Errors), which characterize the steady-state performance of the proposed algorithm. We show that the convergence of the proposed algorithm is independent of quantized data and random topology. Moreover, the analytical results reveal which factors influence the network performance, and we show that the effect of quantization is the main factor in performance degradation of the proposed algorithm. We finally provide computer simulation results that illustrate the performance of the proposed algorithm and verify the results of the theoretical analysis.