EE 230A
Fall 2012
K. Yao
Homework #3
Due Oct. 24th
Read Chapter 5.7; 5.10; and 6.16.3 of McDonoughWhalen
1. In detection problems dealing with Gaussian r.v. and random process, we always need to evaluate the
complimentary Gaussian distribution function:
EE 230A
Fall 2012
K. Yao
Homework # 4
Due October 31st
Read Chap. 6.16.4; Chap. 9 (pp. 339342).
1. Consider a Bayes Criterion receiver for
cfw_
X=
s0 + N , H0
s1 + N , H1
where s0 = [1, 2, 3]T = s1 and N is a 3 1 realvalued zero mean Gaussian vector wi
Estimation and Detection in Communication and Radar Engineering
EE 230A

Fall 2007
EE 230A
Fall 2007
K. Yao
Midterm Exam (Closed Book)
25 points
1. Consider the random process X(t) = A sin(t + ), < t < , where A is a constant
and and are two independent rvs uniformly distributed with their pdfs given by
p () = (1/(2), 0 2,
p () = (1/0 )
EE230A
Detection and Estimation in
Communication and Radar Engineering
Professor Kung Yao
Electrical Engineering Department
University of California, Los Angeles
Lecture 12
UCLA EE230A
Copyrighted materials@by K. Yao
Outline of Lecture 12
1.
2.
a.
b.
c.
OL EE230A
Homework #9 Solutions
Fall 2015
1. Problem 5.5
In a M ary PAM system where the signal set is given by cfw_A, 3A , . . . , (M/2)A. We assume M is an
even integer, and denote sm = (2m 1)A, m = 1, . . . , M/2 and sm = (2m 1)A, m = 1, . . . , M/2.
OL EE230A
Homework #8 Solutions
Fall 2015
1. Problem 6.6
a. Fig. 4 shows the transfer function of the bandpass lter synthesized from the given FIR lter in terms
of dB unit versus onesided normalized frequency. As can be seen, it has a narrow pass band ab
Estimation and Detection in Communication and Radar Engineering
EE 230A

Fall 2007
EE 230A
Fall 2007
K. Yao
Midterm Exam Solution
1. Since A is a constant, then Ecfw_X 2 (t) A2 < . The mean
Ecfw_X(t) =
2
0
0
0
A
cfw_sin(t) cos() + cos(t) sin()dd = 0,
20
is a constant. The autocorrelation function
R(t, t + ) = Ecfw_A sin(t + )A sin(t + )
Estimation and Detection in Communication and Radar Engineering
EE 230A

Fall 2007
EE 230A
Fall 2009
K. Yao
Midterm Exam
25 points (90 minutes)
1. Answer True or False and give a brief explanation (1 pt for the right answer and 1 pt
for the explanation).
a. A widesense stationary realvalued Gaussian random process
cfw_X(t), < t < , is
Estimation and Detection in Communication and Radar Engineering
EE 230A

Fall 2007
OL EE 230A
Midterm Exam
(90 minutes/25 pts  An 8.5x11 sheet(twosided) is allowed)
Please write your Last Name:
UID:
Fall 2014
K. Yao
; First Name:
;
and handin this sheet as the rst page of your exam.
1. Consider a realvalued widesense stationary Gau
Estimation and Detection in Communication and Radar Engineering
EE 230A

Fall 2007
EE 230A
Midterm Exam Solution
Fall 2013
K. Yao
1. a. True. Let X = [X(t1 ), ., X(tn )]T and X1 = [X(t1 + ), ., X(tn + )]T . Then from ws
stationarity, Ecfw_X = Ecfw_X1 = and Ecfw_(X )(X )T = Ecfw_(X1 )(X1 )T =
. Thus, the pdfs satisfy
T
fX (x; t1 , .,
Estimation and Detection in Communication and Radar Engineering
EE 230A

Fall 2007
EE 230A
Fall 2012
K. Yao
Midterm Solution
1. The mean
2 0
E cfw_X(t) =
0
0
A
cfw_sin(t) cos() + cos(t) sin()dd = 0 .
20
Since
E X 2 (t)
< E A2
= A2 < ,
its second moment is nite.
The autocorrelation function
R(t, t + ) = E cfw_A sin(t + ) A sin(t + ) + )
Estimation and Detection in Communication and Radar Engineering
EE 230A

Fall 2007
EE 230A
Fall 2012
K. Yao
Midterm Solution
1. The mean
E cfw_X(t) =
2 0
0
0
Since
A
cfw_sin(t) cos() + cos(t) sin()dd = 0 .
20
cfw_
E X 2 (t)
cfw_
< E A2
= A2 < ,
its second moment is nite.
The autocorrelation function
R(t, t + ) = E cfw_A sin(t + ) A si
Estimation and Detection in Communication and Radar Engineering
EE 230A

Fall 2007
EE 230A
Fall 2011
K. Yao
Midterm Solution
1. a. False. Since we do not know the mean of X, the rectangular shaped pdf can be shifted
arbitrarily and we do not know the pdf completely.
b. False. We know the onedimensional pdf of X and Y . Only if X and Y
Estimation and Detection in Communication and Radar Engineering
EE 230A

Fall 2007
EE 230A
Fall 2011
K. Yao
Midterm Exam
90 Minutes   25 pts
1. Answer True (i.e., agree with the statement) or False (i.e., not agree) and give a brief explanation for your answer. (1 pt for the right answer and 1 pt for the explanation.)
a. If X is a uni
Estimation and Detection in Communication and Radar Engineering
EE 230A

Fall 2007
EE 230A
Fall 2010
K. Yao
Midterm Exam Solution
1. a. False. While X and Y are Gaussian rvs, both X 2 and Y 2 are not Gaussian rvs.
Thus, their sum is not a Gaussian rv.
b. True. To check for ws stationarity, we need to check three properties. First, we
n
Estimation and Detection in Communication and Radar Engineering
EE 230A

Fall 2007
EE 230A
Fall 2009
K. Yao
Midterm Exam Solution
1. a. True. Let X = [X(t1 ), ., X(tn )]T and X1 = [X(t1 + ), ., X(tn + )]T . Then from
ws stationarity, Ecfw_X = Ecfw_X1 = and Ecfw_(X )(X )T = Ecfw_(X1
)(X1 )T = . Thus, the pdfs satisfy
T
fX (x; t1 , .
OL EE230A
Homework #5 Solutions
Fall 2015
1. Problem 4.10
a. Denonte the (N +1)(N +1) matrix R with parameter N by RN . From the denition of RN in (4), we
know RN is a symmetric matrix (i.e., RN (i, j) = RN (j, i) and Toeplitz (i.e., RN (i, j) = RN (s, t)
EE230A
Detection and Estimation in
Communication and Radar Engineering
Professor Kung Yao
Electrical Engineering Department
University of California, Los Angeles
Lecture 21
UCLA EE230A
Copyrighted materials@by K. Yao
Outline of Lecture 21
1. Review of P
EE230A
Detection and Estimation in
Communication and Radar Engineering
Professor Kung Yao
Electrical Engineering Department
University of California, Los Angeles
Lecture 22
UCLA EE230A
Copyrighted materials@by K. Yao
Outline of Lecture 22
1. Power Spect
EE230A
Detection and Estimation in
Communication and Radar Engineering
Professor Kung Yao
Electrical Engineering Department
University of California, Los Angeles
Lecture 21
UCLA EE230A
Copyrighted materials@by K. Yao
Outline of Lecture 21
1. Review of P
EE230A
Detection and Estimation in
Communication and Radar Engineering
Professor Kung Yao
Electrical Engineering Department
University of California, Los Angeles
Lecture 32
UCLA EE230A
Copyrighted materials@by K. Yao
Outline of Lecture 32
1. Max. A Post
EE230A
Detection and Estimation in
Communication and Radar Engineering
Professor Kung Yao
Electrical Engineering Department
University of California, Los Angeles
Lecture 42
UCLA EE230A
Copyrighted materials@by K. Yao
Outline of Lecture 42
Pages
1. Use o
EE230A
Detection and Estimation in
Communication and Radar Engineering
Professor Kung Yao
Electrical Engineering Department
University of California, Los Angeles
Lecture 51
UCLA EE230A
Copyrighted materials@by K. Yao
IV. Detection of Deterministic Signal
EE230A
Detection and Estimation in
Communication and Radar Engineering
Professor Kung Yao
Electrical Engineering Department
University of California, Los Angeles
Lecture 51
UCLA EE230A
Copyrighted materials@by K. Yao
IV. Detection of Deterministic Signal
EE230A
Detection and Estimation in
Communication and Radar Engineering
Professor Kung Yao
Electrical Engineering Department
University of California, Los Angeles
Lecture 52
UCLA EE230A
Copyrighted materials@by K. Yao
Ex. 1. Now, relate the results on Pe