Mathematical Problems in Engineering
Volume 2012 (2012), Article ID 284815, 22 pages
Research Article

Nonlinear Blind Identification with Three-Dimensional Tensor Analysis

Unit Research SICISI, High School of Sciences and Techniques of Tunis (ESSTT), 5 Avenue Taha Hussein, Montfleury, 1008 Tunis, Tunisia

Received 15 February 2012; Revised 2 April 2012; Accepted 3 April 2012

Academic Editor: Thomas T. Yang

Copyright © 2012 I. Cherif et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


This paper deals with the analysis of a third-order tensor composed of a fourth-order output cumulants used for blind identification of a second-order Volterra-Hammerstein series. It is demonstrated that this nonlinear identification problem can be converted in a multivariable system with multiequations having the form of 𝐴 𝑥 + 𝐵 𝑦 = 𝑐 . The system may be solved using several methods. Simulation results with the Iterative Alternating Least Squares (IALS) algorithm provide good performances for different signal-to-noise ratio (SNR) levels. Convergence issues using the reversibility analysis of matrices 𝐴 and 𝐵 are addressed. Comparison results with other existing algorithms are carried out to show the efficiency of the proposed algorithm.