IEEE Workshop on Signal Processing Advances in Wireless
Communications, June 15-18, 2003, Rome, Italy.
Infinite Length Results for Channel Shortening Equalizers
Rick K. Martin (1),
Johnson, Jr. (1),
Ming Ding (2), and
Brian L. Evans (2)
(1) Department of Electrical and Computer Engineering,
Rhodes Hall, Cornell University,
Ithaca, NY 14853 USA
(2) Department of Electrical and Computer Engineering,
Engineering Science Building,
The University of Texas at Austin,
Austin, TX 78712-1084 USA
at Cornell -
at UT Austin
Time-domain equalization is crucial in reducing state dimension
in maximum likelihood sequence estimation, and inter-carrier and
inter-symbol interference in 802.11a and ADSL multicarrier systems.
A time-domain equalizer, or TEQ, which is a finite impulse response
(FIR) filter, placed in cascade with the channel produces an effective
impulse response of v+1 samples that is shorter than the channel
This paper analyzes the two families of TEQ design methods amenable
to cost-effective real-time implementation: minimum mean squared error
(MMSE) and maximum shortening SNR (MSSNR) methods.
For infinite length TEQs, we prove that MMSE target impulse responses
are symmetric and have all v zeros on the unit circle, and MSSNR TEQs
have v of their zeros un the unit circle.
Consequently, finite-length MMSE and MSSNR TEQs will eventually yield
increasing bit error rates (for broadcast systems) or decreasing bit
rates (for point-to-point systems that allow bit allocation) with
increasing filter length.
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