Fast nonlinear Shrinkage LMS Newton equalization algorithm over the satellite nonlinear channel

The adaptive Volterra equalizer is an effective technique for compensating the nonlinearity over satellite channels. However, its adaptive algorithm has a slow convergence speed. To counteract this problem, a new shrinkage least mean square Newton algorithm is devised for the adaptive Volterra equalizer over the satellite nonlinear channel. A noise-free posteriori and priori error signal is obtained by using a known Shrinkage method and L1-L2 minimization formulation. Furthermore, by minimizing the energy of the noise-free posteriori error signal, the SHLMS Newton method is able to provide a variable step size to update the weight vector for the adaptive Volterra equalizer, significantly enhancing the convergence speed. Simulation results indicate that the SHLMS Newton adaptive Volterra equalizer can effectively correct signal amplitude and phase distortions and satellite nonlinear channel distortion.Additionally, the SHLMS Newton algorithm can obtain a faster convergence speed than the traditional algorithms.