1. A pure ALOHA network transmits 200-bit frames on a
shared channel of 200 kbps . What is the Throughput if the
system (all stations together) produces
a. 1000 frames per second
b. 500 frames per second
c. 250 frames per second
Solution
The frame transmi

In a 7_cell cluster system, we decide to split only one
cell to 7 cells. Draw how to do this splitting.
Determine in each new cell which frequency must be
reused. (First, determine the SIR in each new cell
then find the frequency with minimum SIR)
Solutio

Consider a channel with Rayleigh fading and average received
power Pr=20 dBm . Find the probability that the received power
is below
10 dBm
.
Solution
x
Power distribution p z ( x )=
2
1 p
e ; x 0
pr
r
Received signal pr =20 dBm=100 mw
So
10
P ( Z 2 <10 )

Find the reuse distance D for the channel reuse shown in
the figure for both the diamond and hexagonally shaped
cells as function of cell radius R.
Solution
For Diamond shaped
D=R+2 R+ R=4 R
For hexagonal shaped
D= 3 N R= 21 R=4.58 R

In a 7_cell cluster system, we decide to split only one
cell to 7 cells. Draw how to do this splitting.
Determine in each new cell which frequency must be
reused. (First, determine the SIR in each new cell
then find the frequency with minimum SIR)
Solutio

Find the optimum wavelength and frequency for a halfwave dipole of length 15 m.
Solution
L=15 m
1
half wave dipole : L=
2
=2 L=30 m
c 3 108
f= =
=107=10 MHz
30

Determine the ratio of second and third tier
interference
to
first
tier
interference
for
omnidirectional antennas, 120 degree sectoring
and 60 degree sectoring.
Solution
From above figure, we see
R 2= 3 R 1 = 3 D
R3=2 D
For second tier interference
1
1
SI

Drive Erlang C formula based on Erlang B formula.
So we do not need to have Erlang C Tables.
Solution
lk
k!
ErlangB formula: Pb = k i
i!l
i=0
l
k
l
k !( 1 )
k
ErlangC formula: Pc =
k1 i
k
l
l
+
l
i!
k ! (1 ) i=0
k
lk
lk
lk
l
lk
k ! (1 )
k
k!
Pc =
= k
=
=

Consider a cellular system with a total of 395
traffic channels and a 7-cell frequency reuse.
Suppose the probability of call blocking is to be no
more 1%. Assume that every subscriber makes 1
call per hour and each call lasts 3 minutes on
average.
a. For

Drive Erlang C formula based on Erlang B formula.
So we do not need to have Erlang C Tables.
Solution
lk
k!
ErlangB formula: Pb = k i
i!l
i=0
l
k
l
k !( 1 )
k
ErlangC formula: Pc =
k1 i
k
l
l
+
l
i!
k ! (1 ) i=0
k
lk
lk
lk
l
lk
k ! (1 )
k
k!
Pc =
= k
=
=

Determine the ratio of second and third tier
interference
to
first
tier
interference
for
omnidirectional antennas, 120 degree sectoring
and 60 degree sectoring.
Solution
From above figure, we see
R 2= 3 R 1 = 3 D
R3=2 D
For second tier interference
1
1
SI

(Research) Try to find if there is any ongoing effort in
implementing novel wireless networks (e.g., Mesh Networks,
Wireless Sensor Networks, Cognitive Radio Networks ) in
our country. If you find, briefly explain the main goals of
these networks.
Wireles

Consider a cellular system with a total bandwidth
of 30 MHz . Each full duplex voice or control channel
uses two
(1)
(2)
(3)
25 KHz
simplex channel. It assumes that:
the system uses a 9-cell reuse pattern and
0.75 MHz of total bandwidth is allocated for
c

Consider a receiver with noise power 160 dBm within
the signal bandwidth of interest. Assume a simplified
d 0=1 m
path loss model with
. K obtained from the free
space path loss formula with omnidirectional antennas
and f c =1GHz and =4 . For a transmit p

Consider a receiver with noise power 160 dBm within
the signal bandwidth of interest. Assume a simplified
d 0=1 m
path loss model with
. K obtained from the free
space path loss formula with omnidirectional antennas
and f c =1GHz and =4 . For a transmit p

If the received signal level for a particular digital system is
151 dBW and the receiver system effective noise temperature
is
1500 K
, what is
Eb / N 0
for a link transmitting of
2400 bps
Solution
Eb
S
=
N 0 KTBR
Eb
( dB )=10 log ( S ) 10 log ( K )10 log

Table 1 shows a set of experimental measurements of
Pr
Pt
for an
indoor wireless communication at 900 MHz . Find the path loss
exponent that minimizes the MSE between simplified model (
Pr ( dBm ) =Pt ( dBm ) + K ( dB )10 log (
d
)
d0
)
and
d 0=1 m
measur

A WSSUS channel has a multipath delay spread of
Tm
= 1 s and a Doppler spread of B D = 0.02 Hz. The total
channel bandwidth at bandpass available for signal
transmission is W s = 5 Hz. To reduce the effect of
intersymbol interference, the signal designer

Consider a city of 10 square kilometer. A macro cellular
system design divides the city up into square cells of 1
square kilometer, where each cell can accommodate 100
users. Find the total number of users that can be
accommodated in the system and the le

In this problem we will explore the impact of different lognormal shadowing parameters on outage probability. Consider
a network where the received signal power is distributed
according to a log-normal distribution with mean
standard
dBm
and
deviation
d

Consider a cellular system with hexagonal cells of radius
R=1 Km . Suppose the minimum distance between cell centers
using the same frequency must be
required SINR.
D=6 Km
to maintain the
a. Find the required reuse factor q and the number
of cells per clu