Unformatted text preview: symbols Let us employ the FIR ﬁlter of order ¾Ä · ½ shown in Figure 4.15 as the equalizer. We note that a delay of Ä symbols is incurred at the output of the FIR ﬁlter. Then
¾¼ MSE E
E Á Á ÁÌ Ä Ä ½¾ ¿ Á ¾ (4.27) where Á Á ·Ä Ä
4.14 Á Ä
Ä Ì
Ì (4.28)
(4.29) Wong & Lok: Theory of Digital Communications ~
I z k 4. ISI & Equalization 1 z ... 1 h E,L z 1 hE,L Σ
^
I kL Figure 4.15: FIR ﬁlter as an MMSE equalizer Ä , We want to minimize MSE by suitable choices of Ä . Differentiating with respect to each , and setting the result to zero, we get
EÁ Á ÁÌ ¼ (4.30) Rearranging, we get Ê (4.31) where Ê E Á ÁÌ
E If Ê and (4.32) ÁÁ (4.33) are available, then the MMSE equalizer can be found by solving the linear matrix equation (4.31). It can be shown that the signaltonoise ratio at the output of the MMSE equalizer is better than
that of the zeroforcing equalizer.
The linear MMSE equalizer can also be found iteratively. First, notice that the MSE is a quad...
View
Full
Document
This note was uploaded on 12/13/2012 for the course EEL 6535 taught by Professor Shea during the Spring '08 term at University of Florida.
 Spring '08
 Shea
 Frequency

Click to edit the document details