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EE 179 Introduction to Communications
Winter 2011
Homework 5
Due Thursday, Feb 10 4pm
(Total: 100 pts.)
1. Random Cosine Signals [15 pts] Given a random process
x(t) = a cos(c t + )
where c is a constant and a and are independent RVs uniformly distributed
EE 7615
Problem Set # 1
Due: 9,10,10
1) Please attempt each problem on a new page and write on one side only.
2) Show all your work clearly.
1. Problem 2.18 of the textbook on page 85.
2. Problem 2.20 of the textbook on page 86.
3. Problem 2.22 of the tex
1
EE 7615
1)
Solutions to Problem Set # 6
11,22,10
a) K = 3, L = 4. The code rate is Rc = K/L = 3/4.
NW(t)
Binary
source
Z1 Z 2 Z 3
Channel
encoder
s1 s2 s 3 s 4
Binary
ASK mod.
t=T
L
f(TL -t)
Vector
Decision rule
r1 r r 4
r
23
s(t)
+
s1 s2 s 3 s 4
r(t)
I
1
EE 7620
Solutions to Problem Set # 5
Nov. 10
1) Since the frequency band is (2500, 3000), the system must be a bandpass sytem.
a) We have Rb = 500, W = 1000. Thus Rb /W = .5. Also
P Tb
P
P
Eb
=
=
=
= 100P
N0
N0
Rb N0
500 2 105
i) Any PSK system satises
EE 7615
1. Let (t) =
Solutions to Problem Set # 4
2
T
10/26/2010
cos(2f0 t) for 0 t T . Then we get the following signal vectors.
si (t) = d i +
1q
2
(t),
1q
2
si = d i +
(a) For q = 4,
s0
s1
s
s2
0
3
t=T
r(t)
g(r)
hr (t)
where hr (t) =
V^
r
2
T
cos(2f0
EE 7615
Solutions to Problem Set # 3
4.3 We need that R1 be sucient statistic for decisions about S cfw_s1 , s2 =
cfw_ E, E based on (R1 , R2 ). For this we need
pR2 |R1 ,S (r2 |r1 , s) = pR2 |R1 (r2 |r1 ) s cfw_s1 , s2 , r2 , r1
The event that S = s an
EE 7615
Solutions Problem Set # 2
2010
Sept.
1. The following fact regarding Gaussian random variables is used in the
solution.
Fact: If X1 , X2 , X3 and X4 are four Gaussian random variables, then
E [X1 X2 X3 X4 ] = E [X1 X2 ]E [X3 X4 ]+E [X1 X3 ]E [X2 X
1
EE 7615 Digital Communication
Solutions to Exam II
11/9/2010
Problem 1
1) Let
ai =
1 Z i = 0
+1 Zi = 1
Then
p1 (t) = a1
E
E
cos(2f0 t) + a3
sin(2f0 t)
T
T
where T = 4Tb = 4/Rb , where Rb is the source rate. Also
p2 (t) = a2
E
E
cos(2f0 t) + a4
sin(2f0 t
Massachusetts Institute of Technology
Department of Electrical Engineering and Computer Science
6.011: Introduction to Communication, Control and Signal Processing
QUIZ 2 , April 21, 2010
ANSWER BOOKLET
SOLUTIONS
Your Full Name:
Recitation Time :
oclock
ECE302 Spring 2006
HW12 Solutions
April 27, 2006
1
Solutions to HW12
Note: These solutions are D. J. Goodman, the authors of our textbook. I have annotated and corrected them as necessary. Text in italics is mine.
Problem 10.10.2
Let A be a nonnegative r
Residential Solar Systems:
Technology, Net-metering, and Financial payback
Kourosh Sedghisigarchi
Electrical and Computer Engineering Department
West Virginia University Institute of Technology, Montgomery, WV, USA
Abstract The objective is to address bot
THE IMPACT OF NET METERING ON THE
RESIDENTIAL ROOFTOP PV MARKET
Adam M. Payne, Richard D. Duke, Robert H. Williams
Princeton University, Princeton, NJ 08540
ABSTRACT
Federal net metering legislation could have and
enormous impact on the demand for rooftop
n=3;
s=0;
y=3;
x(1)=2;x(2)=2.75;x(3)=4;
for i=1:1:n
j=1;
for k=1:1:n
if (k=i)
continue
else
j=j*(y-x(k)/(x(i)-x(k);
end
end
z(i)=j;
end
0or i=1:1:n
% j=1;
% for k=1:1:(i-1)
%
j=j*(y-x(k)/(x(i)-x(k);
%
% end
% for k=(i+1):1:n
% j=j*(y-x(k)/(x(i)-x(k);
%
%
EE 7615, Homework 1: Due in class on 09/14/2012
1. Denote X N (0, 1), and Q(x) = Pr (cfw_X x). Answer the following questions
using Q(x) to express your nal answer.
(a) when Y N (, 2 ), nd Pr (a < Y b).
(b) Denote the correlation coefcient between random
Low complexity MMSE interference cancellation
for LTE uplink MIMO receiver
Bei Yin and Joseph R. Cavallaro
ECE Department, Rice University, 6100 Main St., Houston, TX 77005
Email: cfw_by2, [email protected]
AbstractIn this paper, we propose a novel low co
ECE 461
Fall 2006 August 31, 2006
Complex Baseband Representation
Channel Model for Point-to-Point Communications Point-to-point communications systems are well modeled using a bandpass additive noise channel model of the form shown in Figure 1. |S(f )| f
EE 7625 (Digital Communications II), Homework 2
Assigned on 02/8/2013, Due on 02/15/2013
1. Consider a baseband PAM system using the raised-cosine pulse:
sin(t/T ) cos(t/T )
t/T 1 (2t/T )2
gT (t) =
Assume the symbol sequence Ik is white and has unit varia
EE 511 Problem Set 5
Due on 17 October 2007 1. An experiment has four equally likely outcomes 0, 1, 2, and 3, i. e., S = cfw_0, 1, 2, 3. If a random process Xt is dened as Xt = cos (2st) for all s S , then (a) Sketch all the possible sample functions. (b)
1
EE 7615 Digital Communication
Problem 1
1)
Solutions to Exam I
Y (t) =
Nw (t )h( ) d =
2)
E [Y (T )] =
1
T
Oct. 2010
T
0
Nw (t ) d
T
1
T
0
E [Nw (t )] d = 0
var[(Y (T )] = E [Y 2 (T )]
1TT
=
E [Nw (t 1 )Nw (t 1 )] d1 d2
T2 0 0
N0 T T
=
(1 2 ) d1 d2
2T
EE 7620
Solutions to Problem Set # 1
2.18. In general for Y = aX 3 + b, a > 0, the answer is given by:
pY (y ) =
1
yb
p
2/3 X
3a[(y b)/a]
a
1/3
X is a Gaussian r.v. with zero mean and unit variance, i.e., pX (x) =
2
1 ex /2 . Hence
2
pY (y ) =
1 y b 2/3
1
EE 7615
Problem 2.17
Problem 2.18
Solutions to Problem Set #1
Sept. 2011
1
Problem 2.16
1) Let T and R denote input and output respectively. Having received A we calculate
P (T = 0)P (R = A|T = 0) = .4 (1/4) = .1 and P (T = 1)P (R = A|T = 1) =
.6 (1/3) =
1
EE 7615
Solutions to Exam II
Nov. 2011
Problem 1
1) By inspection we can see that the rst three signals are orthogonal and normalized. Also
all the other signals can be written as a linear combination of these three signals. Thus
our orthonormal basis i
1
EE 7615
Solutions to Exam I
1) We have
Oct. 2011
106 |f | < 1
0
otherwise.
SN (f ) = SNW (f )|H (f )|2 =
a) We have E [N (0)] = 0 and
E [N (0)2 ] = RN (0) =
Thus var(N (0) = 2 = 2 106 . We have
fN (0) (x) =
SN (f ) df = 2 106
x2
1
e 22
2
b) E [N (.5)]
1
EE 7620
Solutions to Problem Set # 5
11,4,11
1) Since the frequency band is (2500, 3000), the system must be a bandpass sytem.
a) We have Rb = 500, W = 1000. Thus Rb /W = .5. Also
P Tb
P
P
Eb
= 100P
=
=
=
N0
N0
Rb N 0
500 2 105
i) Any PSK system satises
1
EE 7615
Problem Set # 6
Due: 11,18,11
1) A communication system uses the signal set shown below in order to transmit equiprobable
binary messages across an AWGN channel.
2E
cos(2f0 t),
0tT
T
2E
t
cos(2f0 t + 2h ),
0tT
T
T
s0 (t) =
s1 (t) =
Assume that f
1
EE 7615
Problem Set # 5
Due: 11,4,11
1) Please attempt each problem on a new page.
2) Show all your work clearly.
1) Binary Data of rate Rb = 500 bits/sec. is to be transmitted across an AWGN channel
with noise power spectral density SNW (f ) = 105 watt