notes14 - ECE 562 Fall 2010 Equalization If we cannot...

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Unformatted text preview: ECE 562 Fall 2010 Equalization If we cannot eliminate ISI by satisfying the Nyquist condition, we are left with the following model for the received samples after filtering Z k = L- 1 X ` =0 h ` s m k- ` + W k , k = 1 , 2 ,... (1) where { h ` } represent the effective channel coefficients taking into account the combined effects of the transmit filter, channel, and receive filter. We make the following assumptions: The noise terms { W k } can be assumed to be i.i.d. CN (0 ,N ), if we assume that we sample at the receiver in such a way that the impulse response equals 1 at t = 0, and equals 0 at other multiples of T s . The transmitted signal is linearly modulated so that s m n = p E m n e j mn . We will further usually assume that symbols are equally likely so that E [ | s m n | 2 ] = 1 M M X m =1 E m = E s We normalize the channel so that L- 1 ` =0 | h ` | 2 = 1. Thus the average received symbol energy equals E s and the received symbol SNR equals s = E s /N . We assume that....
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notes14 - ECE 562 Fall 2010 Equalization If we cannot...

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