Optimal Subband Adaptive Filter over Functional Link Neural Network: Algorithms and Applications

Compared with the functional link neural network (FLNN) algorithm, the delayless multi-sampled multiband-structured subband FLNN (DMSFLNN) algorithm provides fast convergence when encountering highly auto-correlated input signals, but there is a compromise between convergence and steady-state performances. Therefore, in order to overcome this flaw, we develop an optimal DMSFLNN (ODMSFLNN) algorithm by minimizing the mean square deviation of the weight vector with respect to the subband gain vectors. Interestingly, a vectorized version is also proposed for the ODMSFLNN algorithm, which aims at reducing computational complexity. Additionally, this paper also presents a stability analysis of this algorithm. Then, considering the impulsive noise environment, we develop two robust variants of ODMSFLNN that are the R-ODMSFLNN-I and R-ODMSFLNN-II algorithms, which are based on the specified robust function and the energy constraint of the weight update increment, respectively. Finally, to resolve that the DMSFLNN algorithm may not exploit cross-terms of input samples in nonlinear active noise control scenarios, we further propose the subband second-order Volterra filter (SSOVF) framework in an analogy way and apply the R-ODMSFLNN-II learning principle to obtain the robust optimal SSOVF algorithm. Simulations in several nonlinear scenarios have shown that the proposed algorithms perform better than their competitors.