Pulse Amplitude Modulation Through Bandlimited Channel 2.7 2001/06/13 2004/01/07 10:10:16.132 US/Central Behnaam Aazhang aaz@ece.rice.edu Dinesh Rajan dinesh@ece.rice.edu Mohammad Jaber Borran mohammad@ece.rice.edu Behnaam Aazhang aaz@ece.rice.edu Shawn Stewart mrshawn@alumni.rice.edu Roy Ha rha@rice.edu PAM pulse amplitude modulation modulation matched filter intersymbol interference ISI A description of the functionality of a pulse amplitude modulated transmission system in a bandlimited channel. The bandlimited nature of the channel causes it to have memory which causes intersymbol interference, which can be dealt with in a number of ways. Consider a PAM system b -10 ,…, b -1 , b 0 b 1 ,… This implies a n a n M levels of amplitude x t n a n s t n T The received signal is r t τ n a n s t τ n T g τ N t n a n τ s t τ n T g τ N t n a n s ˜ t n T N t Since the signals span a one-dimensional space, one filter matched to s ˜ t s g t is sufficient. The matched filter's impulse response is t h opt t s g T t The matched filter output is y t τ n a n s ˜ t τ n T h opt τ ν t n a n τ s ˜ t τ n T h opt τ ν t n a n u t n T ν t The decision on the k th symbol is obtained by sampling the MF output at k T : y k T n a n u k T n T ν k T The k th symbol is of interest: y k T a k u 0 n a n u k T n T ν k T where n k . Since the channel is bandlimited, it provides memory for the transmission system. The effect of old symbols (possibly even future signals) lingers and affects the performance of the receiver. The effect of ISI can be eliminated or controlled by proper design of modulation signals or precoding filters at the transmitter, or by equalizers or sequence detectors at the receiver.