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Communications Theory

Homework#3

1) The channel given in homework#1 and #2 , i.e.,

p(t) =  -  sin c + 1 + sin c -  sin c  ,

is used for QAM transmission with Ex   = 1 and SNR MFB  = 10dB .

Find WMMSE -DFE (D), B(D), GM(2)MSE -DFE , and SNR MMSE -DFE .

2) Binary PAM data is transmitted through a multi-path channel with impulse response h(t) = 6(t)+1.86(t - 1)+ 0.816(t - 2)).

The modulator uses basis function  Q(t) =   1  sin c(| t )| with T = 1 . Assume  N0   = 0.01 .

a) Find the channel pulse response p(t) ,  p(t) 2 ,  SNR MFB and the function Q(D) which characterises the ISI.

b) Find the MMSE-LE and corresponding SNR.

c) Find the MMSE-DFE and compute the corresponding SNR.

d) Find the ZF-DFE and the corresponding SNR and loss with respect to SNR MFB .