Robustness Analysis of the Data-Selective Volterra NLMS Algorithm
This work provides theoretical guarantees for an adaptive filtering algorithm, which is incremental as it builds on prior numerical simulations to offer formal robustness analysis for researchers in signal processing.
The paper tackles the lack of theoretical analysis for data-selective adaptive Volterra filters by analyzing the robustness (l2-stability) of the DS-VNLMS algorithm, proving it improves parameter estimation in most update iterations and never degrades estimates if the noise bound is known, with simulation results corroborating its robustness against noise.
Recently, the data-selective adaptive Volterra filters have been proposed; however, up to now, there are not any theoretical analyses on its behavior rather than numerical simulations. Therefore, in this paper, we analyze the robustness (in the sense of l2-stability) of the data-selective Volterra normalized least-mean-square (DS-VNLMS) algorithm. First, we study the local robustness of this algorithm at any iteration, then we propose a global bound for the error/discrepancy in the coefficient vector. Also, we demonstrate that the DS-VNLMS algorithm improves the parameter estimation for the majority of the iterations that an update is implemented. Moreover, we prove that if the noise bound is known, we can set the DS-VNLMS so that it never degrades the estimate. The simulation results corroborate the validity of the executed analysis and demonstrate that the DS-VNLMS algorithm is robust against noise, no matter how its parameters are adopted.