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
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
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)
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 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 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 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
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
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 - 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
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
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
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
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.
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 =