Unformatted text preview: Hence the noise energy at the equalizer
¬ À . Deﬁning the SNR as the ratio of the signal energy to the noise energy, we have
SNR ½ Æ¼ Ì ¾ ½ ¾Ì ¾ ½ ¾Ì Ò ½ ¬
¬
¬
¬ Ò ¬¾ ½ Ì ¬¬¬ Ò Ì À ÀÌ ½
(4.25) Notice that the SNR depends on the folded spectrum of the signal component at the input of the
receiver. If there is a certain region in the folded spectrum with very small magnitude, then the SNR
can be very poor. 4.3.3 MMSE equalizer
The zeroforcing equalizer, although removes ISI, may not give the best error performance for the
communication system because it does not take into account noises in the system. A different equalizer
that takes noises into account is the minimum mean square error (MMSE) equalizer. It is based on the
mean square error (MSE) criterion. Á beforehand, we model each symbol
Á as a random variable. Assume that the information sequence Á is WSS. We choose a linear
equalizer À ´Þ µ to minimize the MSE between the original information symbols Á and the output of
the equalizer Á :
MSE E ¾
E ´Á Á µ¾
(4.26)
Without knowing the values of the information...
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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
 Shea
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