4.4 Demodulation

Demodulation

Convert the continuous time received signal into a vector without loss of information (or performance).

The noise projection coefficients ${}_n$ 's are zero mean, Gaussian random variables and are mutually independent if $N_t$ is a white Gaussian process.

The $r_n$ 's, the projection of the received signal $r_t$ onto the orthonormal bases ${}_n(t)$ 's, are independent from the residual noise process $\stackrel{}{N_t}$ .

The residual noise $\stackrel{}{N_t}$ is irrelevant to the decision process on $r_t$ .

Recall $r_n=s_{mn}+{}_n$ , given $s_m(t)$ was transmitted. Therefore,

The conjecture is to ignore $\stackrel{}{N_t}$ and extract information from $\left(\begin{array}{c}{r}_1\\ r_2\\ \\ r_N\end{array}\right)$ . Knowing the vector $r$ we can reconstruct the relevant part of random process $r_t$ for $0\le t\le T$

Once the received signal has been converted to a vector, the correct transmitted signal must be detected based uponobservations of the input vector. Detection is covered elsewhere .