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Demodulation and Detection

Module by: Behnaam Aazhang. E-mail the author

Summary: 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 s 1 s 2 s M , for t 0 T t 0 T is used to transmit log 2 M 2 M bits. The modulated signal X t X t could be s 1 s 2 s M s 1 s 2 s M during the interval 0tT 0 t T .

Figure 1: r t = X t + N t = s m t+ N t r t X t N t s m t N t for 0tT 0 t T for some m12M m 1 2 M .
Figure 1 (Figure4-12.png)

Recall s m t= n =1N s m n ψ n t s m t n 1 N s m n ψ n t for m12M m 1 2 M the signals are decomposed into a set of orthonormal signals, perfectly.

Noise process can also be decomposed

N t = n =1N η n ψ n t+ N t ˜ N t n 1 N η n ψ n t N t ˜
(1)
where η n =0T N t ψ n td t η n t 0 T N t ψ n t is the projection onto the n th n th basis signal, N t ˜ N t ˜ is the left over noise.

The problem of demodulation and detection is to observe r t r t for 0tT 0 t T and decide which one of the M M signals were transmitted. Demodulation is covered here. A discussion about detection can be found here.

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Definition of a lens

Lenses

A lens is a custom view of the content in the repository. You can think of it as a fancy kind of list that will let you see content through the eyes of organizations and people you trust.

What is in a lens?

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