Nonlinear adaptive system identification with nonlinear discrete Volterra/Wiener models

The objective of this thesis is to present various adaptive algorithms for Volterra system identification application based on discrete-time nonlinear Wiener and Volterra models.; Different from previous works which are mostly based on Volterra model or Gram-Schmidt procedure, this approach represents the truncated Volterra series by its equivalent polynomial functionals. Therefore, the nonlinear Wiener adaptive algorithms can be derived. It greatly improves the performance of adaptive filter especially for the LMS-type algorithms. The major contributions in this thesis include: (1) For white/colored Gaussian input, the LMS-type nonlinear Wiener adaptive algorithm is developed. It does not suffer from the over-parameterization of adaptive coefficients and shrinks the eigen-value spread dramatically. This results in a faster convergence speed and much easier performance analysis. (2) This new approach avoids the dilemma of multiple local minima. Instead, it leads to the typical quadratic MMSE solution. It implies that the global minimum can be found. And, this optimal solution is unique. (3) It can be systematically extended to higher-order without difficulty. And it can also be easily implemented in real-time by DSPs. (4) The RLS-type adaptive algorithms can also be applied to the discrete nonlinear Wiener model. It has very fast convergence speed. However, the computational complexity is higher than the LMS-type methods. The QR-decomposition Volterra adaptive algorithm with subset selection is also developed to identify the most general recursive Volterra system.; Several computer simulations are included to verify the theoretical results. For simplicity, we assume input data real.