Fast computation of channel-estimate based equalizers in packet data transmission

Computationally efficient procedures are introduced for the real-time calculation of finite-impulse-response (FIR) equalizers for packet-based data transmission applications, such as wireless data networks. In such packet data applications, the FIR equalizer filters are computed indirectly by first estimating the channel pulse response from a known training pattern embedded in each packet and then computing the equalizer for use in the recovery of the remaining unknown data in the packet. We find that a minimum mean-square-error decision-feedback equalizer (MMSE-DFE) with a finite-length constraint on its feedforward and feedback filters can be very efficiently computed from this pulse response. We 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 introduced method is much more computationally efficient than direct computation by matrix inversion or the use of popular gradient or least-squares algorithms over the duration of the packet.