Fast algorithm for finite-length MMSE equalizers with application to discrete multitone systems

This paper presents a new, fast algorithm for finite-length minimum mean square error (MMSE) equalizers. The research exploits asymptotic equivalence of Toeplitz and circulant matrices to estimate Hessian matrix of a quadratic form. Research shows that the Hessian matrix exhibits a specific structure. As a result, when combined with the Rayleigh minimization algorithm, it provides an efficient method to obtain the global minimum of constrained optimization problem. A salient feature of this algorithm is that extreme eigenvector of the Hessian matrix can be obtaind without direct computation of the matrix. In comparison to the previous methods, the algorithm is more computationally efficient and highly parallelizable, which makes the algorithm more attractive for real time applications. The algorithm is applied for equalization of discrete multitone (DMT) systems for asynchronous digital subscriber line (ADSL) applications.