4.3 Demodulation and detection

Consider the problem where signal set, $\{s_1, s_2, , s_M\}$ , for $t\in \left[0 , T\right]$ is used to transmit $\log_{2}M$ bits. The modulated signal $X_t$ could be $\{s_1, s_2, , s_M\}$ during the interval $0\le t\le T$ .

Recall $s_m(t)=\sum_{n=1}^N s_{mn}{}_n(t)$ for $m\in \{1, 2, , M\}$ the signals are decomposed into a set of orthonormal signals, perfectly.

Noise process can also be decomposed

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