Partial Diffusion LMS for Distributed Estimation over Fading Wireless Channels

In this paper, we present a study on partial-diffusion least mean-square (PDLMS) strategy in distributed wireless sensor networks (WSNs) in presence of wireless channel impairments, such as path loss, fading, and additive noise. Our main focus is to demonstrate the stability of the PDLMS algorithm in both the mean and mean-square sense, even in the presence of channel distortion. Additionally, we analyze the convergence behavior of the algorithm under these challenging conditions. To further enhance the performance of PDLMS over fading channels, we propose an optimal combination matrix obtained by minimizing the steady-state mean-square deviation (MSD). This matrix allows us to mitigate the performance degradation resulting from wireless channel distortions.The efficacy of our proposed optimal PDLMS method is validated through extensive simulations, which provide substantial evidence supporting the theoretical findings of this study.