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
(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 k-L 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 signal-to-noise ratio at the output of the MMSE equalizer is better than
that of the zero-forcing equalizer.
The linear MMSE equalizer can also be found iteratively. First, notice that the MSE is a quad...
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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