Homework set 6 of ELEC 430, Rice University, Department of Electrical and
Computer Engineering
Problem 1
Consider the following modulation system
${s}_{0}(t)=A{P}_{T}(t)-1$
and
${s}_{1}(t)=-(A{P}_{T}(t))-1$
for
$0\le t\le T$ where
${P}_{T}(t)=\begin{cases}1 & \text{if $0\le t\le T$}\\ 0 & \text{otherwise}\end{cases}$
The channel is ideal with Gaussian noise which is
${}_{N}(t)=1$ for all
$t$ ,
wide sense stationary with
${R}_{N}()=b^{2}e^{-\left|\right|}$ for all
$\in \mathbb{R}$ .
Consider the following receiver structure
${r}_{t}={s}_{m}(t)+{N}_{t}$
a) Find the optimum value of the threshold for the
system (
e.g. ,
$$ that minimizes the
${P}_{e}$ ).
Assume that
${}_{0}={}_{1}$
b) Find the error probability when this threshold is used.
Problem 2
Consider a PAM system where symbols
${a}_{1}$ ,
${a}_{2}$ ,
${a}_{3}$ ,
${a}_{4}$ are transmitted where
${a}_{\mathrm{n}}\in \{2A, A, -A, -(2A)\}$ .
The transmitted signal is
${X}_{t}=\sum_{n=1}^{4} {a}_{n}s(t-nT)$
where
$s(t)$ is a rectangular pulse of duration
$T$ and height of 1. Assume that
we have a channel with impulse response
$g(t)$ which is a rectangular pulse of duration
$T$ and height 1, with white
Gaussian noise with
${S}_{N}(f)=\frac{{N}_{0}}{2}$ for all
$f$ .
a) Draw a typical sample path (realization) of
${X}_{t}$ and of the received signal
${r}_{t}$ (do not forget to add a bit of noise!)
b) Assume that the receiver knows
$g(t)$ .
Design a matched filter for this transmission system.
c) Draw a typical sample path of
${Y}_{t}$ ,
the output of the matched filter (do not forget to add a bit ofnoise!)
d) Find an expression (or draw)
$u(nT)$ where
$u(t)=(s, g, {h}^{\mathrm{opt}}(t))$ .
Problem 3
Proakis and Salehi, problem 7.35
Problem 4
Proakis and Salehi, problem 7.39
Questions & Answers
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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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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
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Is there any normative that regulates the use of silver nanoparticles?