 
Summary: Fast Computation of ChannelEstimate Based Equalizers in
Packet Data Transmission
Naofal M. W. AlDhahir \Lambda , Member, IEEE, and John M. Cioffi, Senior Member, IEEE
Information Systems Laboratory
Stanford University, Stanford CA 94305 y
Abstract
Computationallyefficient procedures are introduced for the realtime calculation of Finite Impulse
Response (FIR) equalizers for packetbased data transmission applications, such as wireless data net
works. 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 meansquareerror decision feedback equalizer (MMSEDFE) with a finitelength
constraint on its feedforward and feedback filters can be very efficiently computed from this pulse re
sponse. We combine a recent theory of finitespectral factorization for the MMSEDFE 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 than the use of popular gradient or leastsquares algorithms over the duration of the packet.
1 Introduction
In an increasing number of data transmission applications, including many of the new wireless data trans
mission networks [1, 2], data is organized, transmitted, and received in finitelength packets.
