Robust adaptive algorithm for widely-linear Hammerstein system and its application

Abstract

The Hammerstein model is a crucial model frequently employed in the field of signal processing. This paper focuses on the widely-linear (WL) complex-valued adaptive filtering and proposes a WL Hammerstein system model. Firstly, a cost function which minimizes the complex correntropic loss criterion is constructed. Subsequently, by extending the alternate direction method of multipliers (ADMM) optimization and non-convex projection method to the WL model, and leveraging the special structure of the autocorrelation matrix in the WL Hammerstein system, a robust recursive adaptive filtering algorithm for the WL Hammerstein system is proposed, along with its simplified version. More importantly, the performance analysis is studied, in which the convergence performance and the mean-square performance are provided. Simulations about system identification and stereophonic acoustic echo cancelation (SAEC) are carried out to validate the theoretical analysis and demonstrate the superior performance of the algorithms in this paper.