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Demodulation and Detection

Module by: Tuan Do-Hong

Consider the problem where signal set, s 1 s 2 … s M s 1 s 2 … s M , for t∈0T t 0 T is used to transmit log2M 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 0≤t≤T 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 0≤t≤T 0 t T for some m∈12…M m 1 2 … M .
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 m∈12…M 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 tdt 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 0≤t≤T 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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