EE 359: Wireless Communications - Fall 2004
SECOND EXAM
This exam is open book and notes, and calculators and your reader are needed. Graded exams and solutions will be available within the next week. Good luck! Problem 1 (35 points): MIMO Channels
Chapter 7
1. Ps = 103
QPSK, Ps = 2Q( s ) 103 , s 0 = 10.8276.
M
Pout (0 ) =
1e
0
i
i=1
1 = 10, 2 = 31.6228, 3 = 100.
M =1
0
Pout = 1 e 1
= 0.6613
M =2
0
Pout = 1 e 1
1e
0
M =3
0
Pout = 1 e 1
1e
0
= 0.1917
2
1e
2
0
3
= 0.0197
M 1
e/
2. p ( ) = M 1 e/
Chapter 10
1. (a)
(AAH )T
= (AH )T .AT
T
= (AT ) AT
= AAH
(AAH )H
For AAH ,
= AAH
= , i.e. eigen-values are real
AAH = QQH
(b) X H AAH X = (X H A)(X H A)H = X H A 0
AAH is positive semidenite.
(c) IM + AAH = IM + QQH = Q(I + )QH
AH positive semidenite
Chapter 11
1. See Fig 1
2B = 100 KHz
fc-B
fc+B
fc = 100 MHz
Figure 1: Band of interest.
B = 50 KHz, fc = 100 MHz
Heq (f ) =
1
=f
H (f )
Noise PSD = N0 W/Hz. Using this we get
fc +B
Noise Power =
=
N0 |Heq (f )|2 df
fc B
fc +B
N0
f 2 df
fc B
3 (fc +B )
= N
Chapter 15
1. City has 10 macro-cells
each cell has 100 users
total number of users = 1000
Cells are of size 1 sqkm
maximumdistance traveled to traverse = 2km
2
time = 30 = 169.7s
In the new setup
number of cells = 105 microcells
total number of users =
Lecture 13 - EE 359: Wireless Communications - Fall 2003
MIDTERM
This exam is open book and notes, and calculators are needed. Graded exams and solutions will be available next week. Good Luck! Problem 1 (40 points): Wireless Channels. This problem
EE 359 - Wireless Communications - Autumn 2015
Course Information
Instructor: Professor Andrea Goldsmith, 371 Packard, 725-6932, email: [email protected] OHs: TTh
after class and by appointment.
Class Time and Location: TTh, 1:30-2:50pm, Thornton 102.
Di
EE359 Final 2014 Solutions
Problem 1
(a) The effective bit rate with CP overhead is
10 1.05 Mbps = 10.5 Mbps.
(3 pts)
64 QAM constellation has 6 bits per symbol. Thus the symboling rate is
10.5
= 1.75 Msps.
6
This is the sampling rate at the A/D converter
EE359 Final 2013 Solutions
December 15, 2013
No points deducted for error propagation
1. (a) Beamforming is capacity optimal when the cutoff value 0 is equal to or greater than 2 . (5 pts)
Lets assume that both p1 and p2 (the fraction of power allocated
EE359, Wireless Communications, Fall 2016
Homework 8 (100 pts)
1. (15 pts) Multicarrier transmission scheme to mitigate ISI (Problem 12-4): Consider a data
signal with a bandwidth of .5 MHz and a data rate of .5 Mbps. The signal is transmitted over a
wire
EE359 Final 2015 Solutions
1. Problem 1 (50 points): Short Answer
(a) Consider an adaptive system with instantaneous SNR at the transmitter that is not necessarily
equal to the true SNR . Assume has the same distribution as , so p( ) = p( ). For the optim
EE359, Wireless Communications, Fall 2016
Homework 7 (100 pts)
1. (15 pts) SNR with Diversity (Problem 10-13*): Consider a MIMO system where the channel gain
matrix H is known at the transmitter and receiver.
(a) (5 pts) Consider a 4x4 MIMO system operati
Chapter 6
1. (a) For sinc pulse, B =
1
2Ts
Ts =
1
2B
= 5 105 s
P
(b) SN R = N0bB = 10
Since 4-QAM is multilevel signalling
P
Es
2s
SN R = N0bB = N0 BTs = NEB
B Ts = 1
2
0
E
SNR per symbol = Ns = 5
0
E
SNR per bit = Nb = 2.5 (a symbol has 2 bits in 4QAM)
Chapter 4
1. C = B log2 1 +
C=
S
N0 B
log2 1+ NSB
1
B
0
As B by LHospitals rule
C=
S1
N0 ln 2
2. B = 50 MHz
P = 10 mW
N0 = 2 109 W/Hz
N = N0 B
C = 6.87 Mbps.
Pnew = 20 mW, C = 13.15 Mbps (for x
1, log(1 + x) x)
B = 100 MHz, Notice that both the bandwidth
Chapter 3
1. d = vt
2
r + r = d + 2h
d
Equivalent low-pass channel impulse response is given by
c(, t) = 0 (t)ej0 (t) ( 0 (t) + 1 (t)ej1 (t) ( 1 (t)
G
0 (t) = 4d l with d = vt
0 (t) = 2fc 0 (t) D0
0 (t) = d/c
D0 = t 2fD0 (t)dt
v
fD0 (t) = cos 0 (t)
0 (t)
EE 359: Wireless Communications - Fall 2005
SECOND EXAM
This exam is open book and notes, and calculators and the textbook are needed. Graded exams and solutions will be available within the next week. Good luck! Problem 1 (25 points): Short Answer.
EE 359 - Wireless Communications - Winter 2008
Finals: Total 100 Points, Duration: 8:30 to 11:30 am
This exam is open book and notes, and calculators are needed. Please state all assumptions used in your calculations. You may use any derivations or
Lecture 13 - EE 359: Wireless Communications - Fall 2004
MIDTERM
This exam is open book and notes, and calculators are needed. Graded exams and solutions will be available next week. Good Luck! Problem 1 (30 points): Wireless Channels. This problem
Lecture 13 - EE 359: Wireless Communications - Fall 2005
MIDTERM
This exam is open book and notes, and calculators are needed. Please state all assumptions used in your calculations. You may use any derivations or statements from the book as long as
EE 359 - Wireless Communications - Winter 2008
Midterm
1. Wireless Channels [30 Points] Consider a wideband channel characterized by the autocorrelation function 1 - Ac (, t) = sinc(W t) e Tm , Tm where W = 50 Hz and Tm = 20 microseconds. (a) [4
EE 359: Wireless Communications - Fall 2003
SECOND EXAM
This exam is open book and notes, and calculators and your reader are needed. Graded exams and solutions will be available within the next week. Good luck! Problem 1 (20 points): Short Problems
EE 359 - Wireless Communications - Fall 2009
Homework 4 Solutions
1. (4-8) (10pts) (a) (4pts) If neither transmitter nor receiver knows when the interferer is on, they must transmit assuming worst case, i.e. as if the interferer was on all the time, ( ) S
Chapter 1
1. In case of an accident, there is a high chance of getting lost. The transportation cost is very high each time. However, if the infrastructure is set once, it will be very easy to use it repeatedly. Time for wireless transmission is negligibl
Chapter 1
1. In case of an accident, there is a high chance of getting lost. The transportation cost is very high each time. However, if the infrastructure is set once, it will be very easy to use it repeatedly. Time for wireless transmission is negligibl
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