Notes for EE5139R Overview of a Communication System
T. J. Lim
July 15, 2011
1
Course Overview
This course tells the story of communication systems, starting with why it is important to
understand the mechanisms underpinning communication systems today, t
EE5139R Communication Systems Problem Set 2, 2011/12
1. The Fourier transform of a continuoustime signal x(t) is X (j ), where
X (j ) =
x(t)ejt dt
x(t) =
1
2
X (j )ejt d.
Prove the following Fourier transform properties:
(a) Complex conjugation: x (t) X
No
Date
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We
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=
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 r <Co]
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EE5139R Communication Systems Problem Set 3, 2011/12
1. Consider an ISI channel modelled by the discretetime symbolrate impulse response
h[n] = [n] + 0.5 [n 1] + 0.25 [n 2]
and assume that thermal noise at the receiver is nonexistent.
(a) Find the chan
EE5139R Communication Systems Problem Set 4, 2011/12
1. A random variable Y is related to another X through Y = X + a, where a is a
deterministic value. If the density of X is fX (x), nd the density of Y .
2. Let X and N be two independent random variable
No
Date
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 ( (X/ l ln)  r ? (Xtt
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 Lql
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EE5139R Communication Systems Problem Set 5, 2011/12
1. Consider a scalar AWGN channel
Y =X +N
where X cfw_1, +1, and N N (0, 2 ). The receiver has no prior information
about X .
(a) Find the conditional probability mass function (PMF) of X , given Y = y
EE 4640 Communication Systems II
Fall 2013
Chichao Chao
Homework Assignment No. 1 (Rev. 1)
Due 10:10am, October 16, 2013
Reading: Haykin, Chapter 1, Appendix 1, A.2.3A.2.4.
Problems for Solution:
1. Suppose X and Y are jointly Gaussian random variables,
No
Date
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ze
GP)
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v6
7 = tt
o
No
Date
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EE5139R Communication Systems Problem Set 1, 2011/12
1. Consider the design of a communication system that enables a speech signal to
be transmitted directly (without any intermediate nodes) from the source to the
receiver.
(a) Identify the advantages and
Protocol Layering & Cross
Layer Design
Mehul Motani
Electrical & Computer Engineering
National University of Singapore
[email protected]
EE5139R Communication Systems
Outline
A look inside the Network
What is Layering?
The OSI model and its seven layer
Notes for EE5139R Transmitters and Channels
T. J. Lim
August 2011
In this chapter, we will discuss the processing of bits into signals at the transmitter, and
the eects of various channels on the transmitted signal. In the next instalment of these
notes,
Notes for EE5139R Basic Detection Theory
T. J. Lim
August 2011
1
Introduction
The signal that arrives at the receiver through the channel is corrupted by various
eects, as described previously. The main task of the receiver is to recover the message
trans
Notes for EE5139R Key Concepts in Detection Theory
Applied to Communication Systems
T. J. Lim
September 2011
1
Detection as Applied Probability
As we have already seen, the output Y of a communication channel is normally a stochastic function of its input
N
for
fhapter Five: OptimumReceivers the Additive White Gaussian oise Channel
S
rrr a ny k >1, w heret ruu/No i s t he a verage NR p er b it. T he p robability o f a
S
p lotted i n F igure 5. 216 a s a f unction o f t he a verage NR p er b it.
,rmbol e
EE5139R Communication Systems, Quiz
Name:
9 November 2011 / Page 1 of 2
Matric. # :
Instructions: Please answer questions in the spaces provided. Each part is worth ve marks.
Q1. Source Coding.
Q1.a. Prex Codes: Prex codes are one which satisfy the prex c
EE5139R Communication Systems, Part 2, Problem Sets
Page 1 of 7
EE5139R, Part 2, Problem Set 1
Q1. A useful inequality  Prove that ln(x) x 1. Also plot ln(x) and x 1 on the
same graph.
Solution: Letf (x) = x 1 ln(x). The rst and second derivatives of f (
EE5139R Communication Systems, Part 2, Problem Sets
Page 1 of 4
EE5139R, Part 2, Problem Set 1
Q1. A useful inequality  Prove that ln(x) x 1. Also plot ln(x) and x 1 on
the same graph.
Q2. The output of a discrete source consists of the possible letters