Fast algorithms for the computation of the finite length decision feedback equalizer

Computationally efficient algorithms are introduced for the real-time calculation of finite impulse response (FIR) equalizers for packet-based data transmission applications. It is found that a minimum mean-square-error decision feedback (MMSE-DFE) with arbitrary (finite) numbers of feedforward and feedback taps can be very efficiently computed from the channel response. The authors combine a recent theory of finite-spectral factorization for the MMSE-DFE with the theory of structured matrices to derive these efficient procedures for computing the equalizer settings. The method introduced is much more computationally efficient than direct computation by matrix inversion or than the use of popular gradient or least-squares algorithms over the duration of the packet