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 .
Questions & Answers
what is variations in raman spectra for nanomaterials
Do u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest.
Rafiq
Rafiq
what is differents between GO and RGO?
Mahi
what is simplest way to understand the applications of nano robots used to detect the cancer affected cell of human body.?
How this robot is carried to required site of body cell.?
what will be the carrier material and how can be detected that correct delivery of drug is done
Rafiq
The nanotechnology is as new science, to scale nanometric
brayan
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Damian
Is there any normative that regulates the use of silver nanoparticles?