Demodulation and Detection 2.14 2001/06/07 2004/01/07 09:53:21.940 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 modulation demodulation detection This module serves as an introduction to the problem of demodulation and detection: the decision procedure for deciding which signal of a set of signals was transmitted despite noise and attenuation. Consider the problem where signal set, s 1 s 2 … s M , for t 0 T is used to transmit 2 M bits. The modulated signal X t could be s 1 s 2 … s M during the interval 0 t T .

r t X t N t s m t N t for 0 t T for some m 1 2 … M .

Recall s m t n 1 N s m n ψ n t for m 1 2 … M the signals are decomposed into a set of orthonormal signals, perfectly. Noise process can also be decomposed N t n 1 N η n ψ n t N t ˜ where η n t 0 T N t ψ n t is the projection onto the n th basis signal, N t ˜ is the left over noise. The problem of demodulation and detection is to observe r t for 0 t T and decide which one of the M signals were transmitted. Demodulation is covered here. A discussion about detection can be found here.