 
Summary: TimeVarying versus TimeInvariant FiniteLength MMSEDFE on Stationary
Dispersive Channels
Naofal AlDhahir \Lambda
, Member IEEE
Abstract
A timevarying and a timeinvariant structure for the finitelength MMSEDFE are presented and their
performances are compared on a stationary channel impaired by ISI and additive Gaussian noise. The time
varying structure has an innovations error sequence but incurs a throughput loss on ISI channels because
of its blockprocessing nature. Conditions under which the timeinvariant structure exhibits nearoptimal
performance are described. Both structures converge to the canonical MMSEDFE of [3] as their filters'
lengths become infinite.
I. Introduction
The infinitelength minimummeansquareerror decision feedback equalizer (MMSEDFE) was shown to
be a canonical (information lossless) receiver structure in [3]. In practice, the MMSEDFE is implemented
using finiteimpulseresponse (FIR) filters whose lengths are set by implementational complexity constraints.
These constraints cause the conventional 1 MMSEDFE structure to lose its canonical property since the
error sequence is no longer stationary and hence can not be whitened by the joint action of the finitelength
timeinvariant feedforward and feedback filters, as in the infinitelength case. This nonstationarity was
extensively studied and shown to have a welldefined structure in [1]. To restore the canonical property of the
MMSEDFE under the finitelength constraint, time variance was introduced in the feedforward and feedback
