31 it can be shown that the signal to noise ratio at

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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 Ƽ 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 zero-forcing 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.

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