 
Summary: ReducedComplexity MMSE Decision Feedback
Equalization \Lambda
Naofal AlDhahir y , Member, IEEE, Ali H. Sayed z , Member, IEEE and John M. Cioffi, Senior Member, IEEE
Information Systems Laboratory
Stanford University, Stanford CA 94305
Abstract
The problem of approximating a long FIR filter by a reducedparameter polezero filter is addressed
in this paper. We derive a computationallyefficient algorithm that achieves this task with high accuracy.
Our derivation successfully extends the ``embedding'' approach of [11, 16] to the case of unequal numbers
of poles and zeros.
Our main emphasis is on applying these algorithms to reduce the implementation complexity of the
decision feedback equalizer's long FIR feedforward and feedback filters encountered in highspeed data
transmission on digital subscriber loops.
I. Introduction
In a variety of applications, the engineer is faced with the task of implementing a long finite
impulse response (FIR) filter on a digital signal processor. For example, this long FIR filter could be
the feedforward or the feedback filter of a decision feedback equalizer (DFE), an echo canceller (EC),
a simulator of a channel impulse response (IR), etc. Although in some situations the underlying true
response is of infinite length (IIR), assuming it to be FIR (e.g., by truncating up to the most significant
N samples) has some advantages. Among those advantages are ease of computation (e.g. through
