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

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, we 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 arithmetical operations. This solution is based on a Cholesky type decomposition of a positive definite Hermitian matrix made up of fourth-order cumulants. An efficient algorithm is given to estimate this matrix. Then, the proposed FIR system identification method is applied to estimate the impulse response (i.r.) coefficients of a radio communication channel in order to “open the eyes” of the channel by minimizing the Mean-Square Error (MSE) criterion. The performance of the proposed method is illustrated by some simulation results.