A new FIR system identification method based on fourth-order cumulants: Application to blind equalization (Q1349433)

During recent years, a lot of High-Order Statistics (HOS) based algorithms have been proposed for the identification of AR, MA and ARMA processes. Unlike second-order statistics that are phase blind (except for cyclostationary signals), HOS allow for the solution of the phase indetermination problem. Another interesting property of HOS techniques is that they are insensitive to additive colored Gaussian measurement noise. So, HOS based methods are very useful in dealing with non-Gaussian and/or nonminimum phase linear systems, as well as nonlinear systems. That explains why these methods are widely used in many signal processing applications such as channel equalization in data communication, time delay estimation, seismic data deconvolution, pattern recognition, image processing. Recently, numerous Finite Impulse Response (FIR) system identification methods based on High Order Statistics (HOS) have been proposed in the literature. These methods can be classified into three categories: closed-form solutions, linear algebra solutions and nonlinear optimization based solutions. Because of their simplicity, closed-form and linear algebra solutions are the ones most used in practice. In this paper, the authors propose a new explicit solution based on fourth-order cumulants. Compared to existing closed-form solutions, the proposed solution uses more statistics and compared to linear algebra solutions it needs less arithmetic operations. This solution is based on a Cholesky type decomposition of a positive definite Hermitian matrix made up of fourth-order cumulants. As it uses only fourth-order cumulants, this solution is theoretically insensitive to any additive Gaussian noise. An efficient algorithm is given to estimate this matrix. Then, the proposed FIT system identification method is applied to estimate the impulse response coefficients of a communication channel by minimizing the Mean-Square Error (MSE) criterion. The performance of the proposed method is illustrated by some simulation results. In the Appendix, an efficient algorithm is given to estimate the matrix made up of fourth-order cumulants.