It is based on the mean square error mse criterion

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Unformatted text preview: ¼ ½ ¬ ¬ ¾Ì Ò ½ ¬ÀÌ Ò Ì À Ò Ì ¬¾ ¬ ¬ ¬ (4.21) Hence, the noise-whitening filter ÀÏ ´Þ µ can be chosen as ÀÏ ¾Ì Õ and then the PSD of the whitened-noise samples filter ´Þµ in Figure 4.14 is ¾Ì À Now, we choose the zero-forcing filter À À ¾Ì ½ À´ ¾ (4.22) ̵ Ò is simply Ƽ ¾. As a result, the overall digital ¾ÌÀ Ï ¾Ì Õ À´ ¾ ̵ (4.23) ´Þµ as ´ ½ ¾ ̵ Õ ½ À´ ¾ ̵ (4.24) Since the zero-forcing filter simply inverts the effect of the channel on the original information symbols Á , the signal component at its output should be exactly Á . If we model the Á as iid random variables with zero mean and unit variance, then the PSD of the signal component is 4.13 ½ and hence the signal Wong & Lok: Theory of Digital Communications 4. ISI & Equalization Ê ½ ¾Ì ½ Ì . On the other hand, the PSD of the noise energy at the output of the equalizer is just ½ ¾Ì component at the output of the equalizer is Ê ½ ¾Ì output is ½ ¾Ì Ƽ ¾ ¬ ¬ ¬ À ¬ ¾ Ì ¬¾ ¬ ¬ Ƽ ¬ ¾¬ ¬ ¾ Ì ¬¾ ....
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