Chapter 7
Noise Eects in Simple Modulation
Systems
7.1
Problems
Problem 7.1
Degrees kelvin (degrees absolute) are converted to to the Celsius scale by substracting 273
(actually 273.15). Degrees Celsius are converted to degrees Fahrenheit by the familiar
nctuee11s
Principles of Digital Communications
Midterm 2
Solutions
1. (10 3 = 30 points)
Answer the following questions. Please dene appropriate notations by yourself and explain in
details.
(a) See lecture note or textbook.
(b) See lecture note, Topic 3.
Performance of Optimum DPSK Receiver
Let x r (t ) = A cos( wc t + ) + n(t ) n(t) AWGN
T
xk = ( A cos( wc t + ) + n(t ) cos wc t dt
0
T
T
0
0
= A cos( wc t + ) cos wc t dt + n(t ) cos wc t dt
=
AT
cos + nkx
2
Similarly, y k =
AT
sin + nky
2
Design Logic:
Topic 6: Noncoherent FSK
Supplement to page 363 of the textbook
Note:
The materials in this handout are largely from Haykins Communication Systems on
pages 403414.
Consider a binary digital communication system in which the transmitted
signal is
2E
si (t)
Topic 7: Digital Signaling Through Bandlimited Channel
Outline
Statement of the Problem
Inter-Symbol Interference (ISI)
Nyquist Pulse Shaping Criterion
Raised-Cosine Pulses
Statement of the Problem
Motivations
Previous assumptions about channel is ideally
Topic 10: Signal Space Representations of Signals
Outline
Signal Space Representations
Mathematically elegant
Insightful tool for analysis of data transmissions
M-ary PSK
Reading: Textbook Chap. 9.2 and Chap. 9.3
Communications
1
Geometric Concept
In geom
Principles of Communication Systems 2
NCTUEE, S08
Homework 3
Solutions
Total: 100 points
1. (10+20=30 points) Multiple Hypothesis Testing
In class, we have seen the Bayes detection with minimum average cost criterion
for binary hypothesis testing. In this
Principles of Communication Systems 2
NCTUEE, S08
Homework 4
You dont need to turn in this homework!
1. Derive the error probability of optimum noncoherent binary FSK receiver on
page 4 of topic 6.
2. Prob. 7.10 of the textbook.
3. Prob. 7.11 of the textb
Principles of Communication Systems 2
NCTUEE, S08
Homework 5
Due on Friday, 6/13/2008, in class
Total: 100 points
1. (20+20=40%) Consider a standard noncoherent receiver that correlates the receiver input
with cosine and sine signals at the carrier freque
Principles of Communication Systems 2
NCTUEE, S08
Homework 5
Solutions
Total: 100 points
1. (20+20=40%) Consider a standard noncoherent receiver that correlates the receiver input
with cosine and sine signals at the carrier frequency in the corresponding
Topic 0: Introduction
About This Course
Block Diagram of Digital Communication
Why Digital?
Modern Digital Communication Systems
Major Goal
Communications
1
About This Course
Main Theme
Introduction to fundamentals of digital communication
Reliable commun
Principles of Communication Systems
Topic 1
Random Signals and Noise
nctuee08
Summary
In this topic, I will discuss:
Review of Probability
Denition of Random Process
Random Process Examples
Classication of Random Processes
Random Signals in Linear Sy
Principles of Communication Systems
Topic 2
Jointly Gaussian and Gaussian Random Processes
nctuee08
Summary
In this lecture, I will discuss:
Gaussian Random Variables
Moment Generating Function
Central Limit Theorem
Jointly Gaussian Random Variables
Topic 11: Minimum Shift Keying and Bandwidth Efficiency
Outline
Minimum Shift Keying
Bandwidth Efficiency
Reference:
For MSK
1.
Simon Haykin, Communication Systems, 4th edition, 2001, John Wily and Sons Inc. (Page
387~Page 400)
2.
Subbarayan Pasupathy, Mi
nctuee11s
Principles of Digital Communications
Midterm 1
Solutions
1. (6 5 = 30 points)
You can nd answers in the lecture notes.
2. (10 points)
Since X (t) is a Gaussian process, we know X (3) is a Gaussian random variable. So we need
its mean and varianc
Chapter 8
Fundamentals of Basic Binary
Digital Communication Systems
8.1
Problem Solutions
Problem 8.1
a. For PE jdesired = 10
bps, we have
5
we have z jrequired = 9:58 dB (9.08 ratio). For R = B = 5; 000
signal power = A2 = z jrequired N0 R
= 9:08
10
6
5
Chapter 8
Fundamentals of Basic Binary
Digital Communication Systems
8.1
Problem Solutions
Problem 8.1
a. For PE jdesired = 10
bps, we have
5
we have z jrequired = 9:58 dB (9.08 ratio). For R = B = 5; 000
signal power = A2 = z jrequired N0 R
= 9:08
10
6
5
APPENDIX D: FM THRESHOLDING AND RELATED ANALYSES
1
Problem D.1
a. Consider
z (t) = A cos (! 0 + ! d ) t + n (t) ; ! 0 = 2 f0 ; ! d = 2 fd
= A cos (! 0 + ! d ) t + nc (t) cos ! 0 t
with the PSD of n (t) given by Sn (t) = N0 =2 for jf f0 j
also that the PSD
APPENDIX A: NOISE MODELING WITH APPLICATIONS TO COMMUNICATIONS
Problem A.1
All parts of the problem are solved using the relation
p
Vrm s = 4kT RB
where
k
B
1:38 10 23 J/K
30 MHz = 3 107 Hz
=
=
a. For R = 10; 000 ohms and T = T0 = 290 K
p
Vrm s =
4 (1:38
Principles of Digital Communication
Homework 5
Due on Friday, June/17/2011, at 1:30 p.m. in class.
Be noted that late homework will NOT be accepted!
1. (10+20+20=50 points)
Consider coherent QPSK. The modulated signal at the transmitter can be expressed b
Principles of Digital Communication
Homework 4
You dont need to turn in this homework.
I highly encourage you to work all the problems listed. Solutions have been uploaded
previously, although you dont need to turn in. Solutions have been uploaded previou
Principles of Digital Communication
Homework 3
Solutions
1. (10 + 20 = 30 points)
(a) The MAP decision rule is
fY |H (y |0)PH (0)
H =0
H =1
fY |H (y |1)PH (1)
Solving for the inequality gives
999
1000 ,
999
1000 .
Decide H = 1, if Y
Decide H = 0, if Y <
Principles of Digital Communication
Homework 3
Due on Friday, May/6/2011, at 1:30 p.m. in class.
Be noted that late homework will NOT be accepted!
1. (10 + 20 = 30 points) Consider the following model of an home alarm system. The system has
a sensor which
Principles of Digital Communication
Homework 2
Solutions
1. (10 2 = 20 points)
(a) You can show these properties either with the help of a gure for the standard Gaussian PDF,
or with rigorous math. Here I only give the proof that Q is strictly decreasing