With this sequence detection approach we can employ

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Unformatted text preview: back, i.e., Á Á . Then · ÁÌ ÁÌ Á (4.47) where Á Á ·Ä½ Á ·Ä½ ½ Á Á ½ Á ¾ Ľ ½ Á Ì (4.48) Á ľ Ì (4.49) Ľ·½ ¾ ¼ ľ Ì (4.50) Ì (4.51) Further assume that the data symbols Á are zero-mean unit-variance iid random variables. We seek the filters and that minimize the MSE given by E ´Á Á µ¾ Differentiating with respect to and E and ¼ and E Á ÁÌ ´Á ÁÌ ÁÌ µ¾ (4.52) , we get ´Á ÁÌ Á ´Á ÁÌ EÁ Notice that E Á Á E ÁÌ ÁÌ µ µ ¼ (4.53) ¼ (4.54) Áľ ¢Ä¾ , i.e., the identity matrix. The equations for optimal reduce to E Á ÁÌ · E Á ÁÌ E Á ÁÌ · 4.18 EÁ Á (4.55) ¼ (4.56) Wong & Lok: Theory of Digital Communications 4. ISI & Equalization Solving these equations, we have E Á ÁÌ E Á EÁ ½ ÁÌ E Á ÁÌ EÁ Á ÁÌ (4.57) (4.58) Similar to the case of the MMSE equalizer, we can also solve for the feedforward and feedback filters using the steepest descent approach. If we do not know the expectations of the...
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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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