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2. Consider the baseband binary PAM system shown below. Consider the case when both channel noise and intersymbol interference are present at the same time.
2. Consider the baseband binary PAM system shown below. Consider the case when both channel noise and intersymbol interference are present at the same time. You are expected to design a system where the mean square error of the entire system is minimized. Assume that w(t) is a white noise with power spectral density equal to No/2 and the entire environment is stationary. In such a scenario, show that impulse response of the receive filter must satisfy Q* (f) C($) Sq(f) + No/2 where Q(f) is the combined response of the transmit filter (g(t)) and the channel (h(t)), Sq(f) is the Fourier transform of the temporal autocorrelation function of the sequence {q(kTi)}. = Input binary data lan) x() Channel, *o(1) y(1) y,) Pulse- amplitude modulator Say 1 if y(t;) > Transmit filter g(1) Receive filter c(0) Decision device h(1) Sample at time t; = iTo Say O if y(t;) Transmit filter g(1) Receive filter c(0) Decision device h(1) Sample at time t; = iTo Say O if y(t;)
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