Nonlinear channel estimation based on robust distributed Hammerstein spline adaptive technique in wireless sensor network

In a wireless sensor network (WSN), channel estimation prior to data communication is an important task. The nonlinear behaviour of the channel makes the estimation procedure challenging. Further, the accuracy of the estimation algorithm deteriorates in the presence of impulsive noise. In such a scenario, the conventional adaptive filtering methods based on the mean square error cost function and its different variants are not suitable for estimating the channel. Hence, this paper proposes a robust Hammerstein spline adaptive filtering based on the inverse square root cost function to mitigate impulsive noise's effect and adapt to the nonlinearity. Further, to fasten the estimation procedure, the robust method is extended to the distributed WSN, where diffusion cooperation among the sensor node is incorporated to estimate the nonlinear channel. The theoretical steady state analysis of the proposed method is carried out and compared with the simulation results, which validates the algorithm performance. The simulation results confirm the robustness of the proposed method compared to other robust strategies based on maximum correntropy criteria, logarithmic hyperbolic cosine cost function, and Geman-McClure cost function.(c) 2022 Elsevier Inc. All rights reserved.