Diffusion LMS algorithms for sensor networks over non-ideal inter-sensor wireless channels

In this paper, we propose diffusion-based least mean square (LMS) algorithms that are robust against fading phenomena in wireless channels. The proposed algorithms, developed by combining diffusion LMS and classical estimation approaches, are able to estimate and update the underlying system parameters at each node by exploiting the sensor measurements and the fused data obtained from the neighboring nodes. The fusion of the information at each node takes place based on a convex combination strategy whose coefficients are determined according to the channel state information, the noise statistics and the output error of the local adaptive filter. In this work, we assume the broadcast data from the sensors experience Rayleigh fading and are further contaminated by the additive noise. Numerical results demonstrate the efficiency of the proposed algorithms and show their satisfactory performance compared with the costly centralized adaptive techniques.