Fixed-point fully adaptive interpolated Volterra filter under recursive maximum correntropy

The second-order Volterra (SOV) filter demonstrates excellent performance for modeling nonlinear systems. The main disadvantage of the adaptive SOV filter is that the number of coefficients increases exponentially with memory length, which hinders its practical applications. To circumvent this problem, the sparse-interpolated Volterra filter has been developed. However, the existing algorithms only investigated the performance of gradient-based interpolators and their performance may degrade for combating impulsive noise. A novel fixed-point fully adaptive interpolated Volterra filter under recursive maximum correntropy (FPFAIV-RMC) algorithm is proposed. In particular, the coefficients of the sparse SOV filter are adapted by the RMC algorithm and the coefficients of the interpolator are updated by the fixed-point algorithm under RMC. Additionally, the convergence of the FPFAIV-RMC algorithm is analyzed. The efficacy of the FPFAIV-RMC algorithm is validated by simulations for nonlinear system identification, nonlinear acoustic echo cancellation (NLAEC), and prediction in impulsive noise.