Fast techniques for computing finite-length MMSE decision feedback equalizers

Existing computationally efficient methods for computing the finite length minimum mean-square-error decision feedback equalizers (MMSE-DFE) rely on fast methods for Cholesky decomposition, which may face several implementation difficulties. As the demand for broadband communications increases, developing less complex methods is highly motivated. We propose new techniques for computing the MMSE-DFE coefficients. The new algorithms are obtained by identifying the relationship between the feedforward equalizer computation and well known fast recursive least squares (RLS) adaptive algorithms, and the feedback equalizer as a convolution of the feedforward equalizer with the channel. The proposed algorithms are less complex, more structured, and more stable in finite precision than known methods encountered in the literature.