The noise projection coefficients
${\eta}_{n}$ 's are zero mean, Gaussian random variables and
are mutually independent if
${N}_{t}$ is a white Gaussian process.
${\eta}_{k}$ 's are uncorrelated and since they are Gaussian they are
also independent. Therefore,
${\eta}_{k}\approx \mathrm{Gaussian}(0, \frac{{N}_{0}}{2})$ and
${R}_{\eta}(k, n)=\frac{{N}_{0}}{2}{\delta}_{kn}$
The
${r}_{n}$ 's, the projection of the received signal
${r}_{t}$ onto the orthonormal bases
${\psi}_{n}(t)$ 's, are independent from the residual noise
process
$\tilde{{N}_{t}}$ .
The residual noise
$\tilde{{N}_{t}}$ is irrelevant to the decision process on
${r}_{t}$ .
Recall
${r}_{n}={s}_{mn}+{\eta}_{n}$ , given
${s}_{m}(t)$ was transmitted. Therefore,
Since both
$\tilde{{N}_{t}}$ and
${r}_{n}$ are Gaussian then
$\tilde{{N}_{t}}$ and
${r}_{n}$ are also independent.
The conjecture is to ignore
$\tilde{{N}_{t}}$ and extract information from
$\left(\begin{array}{c}{r}_{1}\\ {r}_{2}\\ \dots \\ {r}_{N}\end{array}\right)$ .
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 .
Do u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest.
Rafiq
Rafiq
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Rafiq
Rafiq
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Anam
analytical skills graphene is prepared to kill any type viruses .
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brayan
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Damian
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