Performance analysis of third-order nonlinear Wiener adaptive systems

This paper presents a detailed performance analysis of thirdorder nonlinear adaptive systems based on the Wiener model. In earlier work, we proposed the discrete Wiener model for adaptive filtering applications for any order. However, we had focused mainly on first and second-order nonlinear systems in our previous analysis. Now, we present new results on the analysis of third order systems. All the results can be extended to higher-order systems. The Wiener model has many advantages over other models such as the Volterra model. These advantages include less number of coefficients and faster convergence. The Wiener model performs a complete orthogonalization procedure to the truncated Volterra series and this allows us to use linear adaptive filtering algorithms like the LMS to calculate all the coefficients efficiently. Unlike the Gram-Schmidt procedure, this orthogonalization method is based on the nonlinear discrete Wiener model. It contains three sections: a single-input multi-output linear with memory section, a multi-input, multi-output nonlinear no-memory section and a multi-input, single-output amplification and summary section. Computer simulation results are also presented to verify the theoretical performance analysis results.