University of Illinois
Spring 2013
ECE 361: Problem Set 4: Solutions
Linear Equalization, Precoding
1. [Matched Filter]
(a) By denition, cMF = 1, cMF =
1
2
1
2
and cMF = 1 .
3
3
(b) Since:
y [1] = x[1] + w[1],
we have:
y [2] =
1
x[1] + x[2] + w[2],
2
y [3
University of Illinois
Spring 2013
ECE 361: Problem Set 2: Solutions
Energy-Ecient and Rate-Ecient Reliable Communication, Error Control
Coding, Hamming Code, Erasure Channel, Fountain Code
1. [Position Modulation with Sign]
We can encode the index j of t
University of Illinois
Spring 2013
ECE 361: Problem Set 1: Problems and Solutions
Additive noise channel, Optimum receiver, Sequential and block
communication
Due:
Reading:
Tuesday January 29 in class
361 Course Notes Lectures 1-4
1. [Variance of sum of r
University of Illinois
Spring 2011
ECE 361: Problem Set 0: Solutions
Linear Systems and Probability Review
Note: In this course, we use Fourier transforms with respect to the frequency variable f (measured in Hertz)
rather than the radian frequency variab
ECE398 Spring 2008
Solutions to Midterm 1
1. (a) We decide that x = +1 whenever
n
yk > 0
(1)
m=1
and -1 otherwise.
(b) The probability of error is
Q
(c) For small 2 , we can approximate
n
Q
n
.
1
n
exp 2 .
2
2
(2)
(3)
Thus doubling the number of antennas
University of Illinois
Spring 2013
ECE 361: Problem Set 3: Problems and Solutions
Pulse Shaping and Sampling, Continuous-time AWGN capacity, Wireline
Channel and ISI, Matched Filter
Due:
Reading:
Tuesday February 26 in class
361 Course Notes Lectures 9-12
University of Illinois
Spring 2011
ECE 361: Final Examination
Friday May 6, 2011, 1:30 p.m. 4:30 p.m.
This is a closed-book closed-notes examination except that three 8.5 11 sheets of notes are
permitted: both sides may be used.
1. [45 points] Consider a
University of Illinois
Spring 2013
ECE 361: Problem Set 6: Solutions
Complex Baseband, Wireless Channel, Rayleigh Fading
1. [Implementing a complex baseband lter]
Q
I
yb (t) = yb (t) + jyb (t),
and
Q
I
gb (t) = gb (t) + jgb (t).
Therefore
Q
Q
I
I
zb (t) =
University of Illinois
Spring 2013
ECE 361: Midterm Exam I
Wednesday, February 27, 2013
7:00 p.m. 8:15 p.m.
MEB 153
1. (a) The ML decision rule is given by:
2
ML = arg min v j y
j
2
j
=
= arg max
j
y [m]vj (m)
m=1
1 if y [1] y [2] y [2] y [1]
=
0 if y [1]
University of Illinois
Spring 2011
ECE 361: Problem Set 2: Solutions
Matched and Unmatched Filtering, and Signal Design
Throughout this Problem Set, assume that the bits being transmitted are equally likely to be 0 or 1.
1. [Matched Filtering]
T /2
(a) E0
University of Illinois
Spring 2013
ECE 361: Practice Midterm Exam II
1. [17 points] [Equalization] Consider the 2-tap ISI channel with
1
y [m] = x[m] + x[m 1] + w[m]
2
Only two symbols x[1] and x[2] are sent on this channel, i.e., you can assume that x[m]
University of Illinois
Spring 2015
ECE 361: First Exam
Tuesday, 3 March 2015, 9:30 am 10:50 am
Name: (in BLOCK CAPITALS)
Signature:
Instructions
This is a closed-book closed-notes examination except that one side of one 8.5 11 sheet
of notes is permitted.
University of Illinois
Spring 2017
ECE 361: Problem Set 3
Released:
Due:
Reading:
Friday, February 10
Friday, February 24, by 4pm
361 Course Notes Lectures 6-10.
1. [Position Modulation with Sign]
Consider the following modification to the position modula
University of Illinois
Spring 2017
ECE 361: Problem Set 2: Problems and Solutions
Decisions and Reliable Communication
Released:
Due:
Reading:
Friday, January 27
Friday, February 10 by 4pm
361 Course Notes Lectures 3-5.
1. [Repeated uses of binary symmetr
University of Illinois
Spring 2013
ECE 361: Midterm Exam I
Wednesday, February 27, 2013
7:00 p.m. 8:15 p.m.
MEB 153
1. [15 points] [Vector ML] Consider the following communication scheme for sending one bit
on a discrete-time AWGN channel using 2 time ins
ECE 461 Fall 2007
Midterm I Solutions
1. The noise n is composed of 10 independent subnoises n1 , n2 , , n10 . n is sum of many
independent noises with the same variance. We know from the central limit theorem
that a good statistical model for n will be G
ECE 361: Digital Communications
Spring 2015
Lecturer:
Prof. Lav R. Varshney, varshney@illinois.edu
Office Hours: T 2-3pm, 123 CSL and by appointment
Teaching Assistant:
Ihab Nahlus, nahlus2@illinois.edu
Office Hours: W 4-5pm, 411 CSL and by appointment
Le
University of Illinois
Spring 2010
ECE 361: Second MidSemester Exam: Solutions
1. Let x, y, and z denote three binary vectors of length n. The Hamming distance dH (x, y)
between x and y is the number of coordinates in which x and y differ. The Hamming wei
University of Illinois
Spring 2016
ECE 361: Problem Set 6: Problems and Solutions
Precoding and OFDM
Released:
Due:
Reading:
Tuesday, April 5
Tuesday, April 19 (in class)
361 Course Notes Lectures 1720.
1. [Tomlinson-Harashima Precoding in 2-D]
Suppose we
University of Illinois
Spring 2016
ECE 361: Problem Set 7: Problems and Solutions
Wireless
Released:
Due:
Reading:
Tuesday, April 19
Thursday, April 28 (in class)
361 Course Notes Lectures 2124.
1. [Inscribed Matter]
Many people are interested in communic
University of Illinois
Spring 2016
ECE 361: Problem Set 5: Problems and Solutions
Intersymbol Interference
Released:
Due:
Reading:
Tuesday, March 15
Thursday, March 31 (in class)
361 Course Notes Lectures 1416.
1. [Matched Filter]
Consider the 3-tap ISI c
University of Illinois
Spring 2016
ECE 361: Problem Set 4: Problems and Solutions
Capacity and Sampling
Released:
Due:
Reading:
Tuesday, February 16
Thursday, February 25 (in class)
361 Course Notes Lectures 11-13.
1. [BEC with Feedback]
Suppose we are co
University of Illinois
Spring 2017
ECE 361: Problem Set 1: Problems and Solutions
Probability review
Released:
Due:
Reading:
Tuesday, January 17
Friday, January 27 (by 4pm)
361 Course Notes Lectures 1-2, and probability review.
1. [Variance of sum of rand
ECE461 Fall 2007
Midterm 1
Midterm Instructions:
All information bits are equally likely to be 0 or 1 and statistically independent of each
other.
No calculators or electronic devices are allowed.
The test is in class and is closed book and closed note
LEARNING OBJECTIVES - Lecture 4 (Sequential and Block Communication)
After lecture, you should be able to:
1. State reasons for needing to transmit more than one bit of information
2. Discuss the advantages and disadvantages of expanding the signaling con
LEARNING OBJECTIVES - Lecture 3 (Histogram to Optimum Receiver)
After lecture, you should be able to:
1. State our notion of error in communication
2. Define and derive a maximum a posteriori (MAP) detector for arbitrary distributions
3. Derive the neares
LEARNING OBJECTIVES - Lecture 2 (Statistical Channel Model)
After lecture, you should be able to:
1. Discuss where noise statistics come from: experiment, physical/mathematical considerations, etc.
2. State why knowing noise statistics is useful to improv
University of Illinois
Spring 2017
ECE 361: Problem Set 2
Decisions and Reliable Communication
Released:
Due:
Reading:
Friday, January 27
Friday, February 10 by 4pm
361 Course Notes Lectures 3-5.
1. [Repeated uses of binary symmetric channel.]
Suppose we
University of Illinois
Spring 2017
ECE 361: Problem Set 1
Probability review
Released:
Due:
Reading:
Tuesday, January 17
Friday, January 27 (by 4pm)
361 Course Notes Lectures 1-2, and probability review.
1. [Variance of sum of random variables]
Let W1 , W
LEARNING OBJECTIVES - Lecture 9 (Pulse Shaping and Sampling)
After lecture, you should be able to:
1. Describe a modular architecture for separating modulation/demodulation from
interpolation/sampling
2. Discuss the use of pulse-shaping for interpolation
LEARNING OBJECTIVES - Lecture 10 (Capacity of the Continuous-Time AWGN Channel)
After lecture, you should be able to:
1. Convert a continuous-time AWGN channel into a discrete-time AWGN channel, by connecting
everything one by one.
LEARNING OBJECTIVES - Lecture 11 (Modeling the Wireline Channel: Intersymbol Interference)
After lecture, you should be able to:
1. Describe the physical properties of signal propagation over wires, such as linearity, time-invariance,
causality, and dispe
LEARNING OBJECTIVES - Lecture 12 (Intersymbol Interference Management: Low SNR Regime)
After lecture, you should be able to:
1. Define the effective signal to interference and noise ratio (SINR).
2. Describe how interleaving leads to independence between
LEARNING OBJECTIVES - Lecture 7 (Reliable Communication with Erasures)
After lecture, you should be able to:
1. Discuss erasures demodulation
2. Argue the rank condition of linear codes for decoding erasures
3. Implement message-passing decoding over bina