1. Capacity Analysis
ofHybrid Wireless
Networks
By: Hakimeh Purmehdi
Advisor: Dr. Farshad Lahouti
Wireless Multimedia Communications Laboratory
Department of Electrical and Computer Engineering
University of Tehran
1
2. Outlines:
Conventional Cellular Network and its Challenges
Probability of Blocking in Hybrid CDMA Networks
◦ System Model
◦ Probability of Blocking for Hybrid Network with
Complete Coverage and Coverage-limited Relays
◦ Numerical Analysis
Probability of Outage in Hybrid CDMA Networks
◦ System Model
◦ Probability of outage for Conventional Cellular and
Hybrid CDMA Networks.
◦ Simulation & Analytical Results
Conclusions
2
4. Conventional Cellular Network and
its Challenges
Congested cells
Load over on the MSC
Poor coverage on the
edge of cells
Hybrid Network
Advantages:
Extend the coverage area
Reduce the interference
level by decrease in the
range of transmissions
Distribute the traffic
homogenously
throughout the network
4
5. Ad Hoc Elements in Hybrid Net.
5
Users of the Network.
Relays as dedicated
elements of the Network.
In-Band Frequency.
Out-of-Band Frequency
7. System Model
Each sector has C channels and traffic
intensity of Ak Erlang.
Each sector can transfer a maximum of XO
calls to, or accept up to XI channels from the
other sector(s).
A fraction of all available channels in each
cell are sharable.
Traffic model: M/G/C/C
Out-of-Band Frequency Relays
BS 1
BS 2
R
3BSCS
BS 3
7
BS 1
BS 2
R
2BSCS
8. Pb for Hybrid Network with with
Coverage-limited Relays
Regarding to the relay coverage ratio, p, if :
◦ New call is located in the coverage area of a relay.
◦ One of the ongoing calls within the coverage area
of the relay which is connected to the base station
is connected to the neighboring base station via the
relay and its channel is allocated to this new call.
active calls in neighboring sectors:
◦ No. of ongoing calls within the coverage area of
the relay:
8
),( 21 ii
),( 21 jj
9. Pb with Coverage-limited in
2BSCS
◦ This call is blocked with probability of 1 if:
or
◦ This call is blocked with probability of if:
and
XCi 1 Cii 221
Cij 11 Ci 1
21
21
,,,
,,21 Υ),,,1(
AAXC
AXCAXC
b
S
AAXCC
P
p1
1
1
,12
1
,2,
1
1
,2,
!)!(
)1(
YY),,,(
N
Mu
buC
CCuua
N
Mt
atCbt
N
Ms
bsCas
CCu
ppae
baNM
XC
Ct
AtCAtAtCAtACACAAXCS
1
,2,,2,,,,,, 12212121
YY
9
,...2,1,0,
!0
0
,,
rdx
r
x
e
r
x
r
s
asar
0,1,2,...r,
!
,
r
ae ra
ar
r
Crs
srsr
a
ar
srs
ppa
e
)!(!
)1(
Y ,
10. 321
321321
,,,,
,,,,2,,,2 'Y
AAAXC
AAAXCXCAXCAXCAXC
b
S
P
p1
Using the same approach as previous case
with a six-dimensional Markov chain, the
call is blocked with probability of 1 if:
or or
This call is blocked with probability of
if: and
Probability of Blocking:
Pb with Coverage-limited in
3BSCS
XCi 21
XCii
XCii
2
2
31
21
Ciii 3321
Cij 11
Ci 1
321321321 ,,,1,,2,,,,,,, AAAXCXCXCAXCAXCAXCAAAXCS
cbaNNMM
bacPNMNacbPNMNcbaPNMN
bacNMcabNMcbaNMcbaPNM
,,,1,,
,,,,,,,,,,,,,,,
,,,,,,,,,,,,,,,,,
K
csbsarcbasr ,,,,,,, T
r
Cs
as
C
XCs
asar
1
,
1
,, YT
]Y[
12
1
,,,,,,,,,,,
XC
XCs
sM
XCt
btasbaNMcrcbaNMr
N
Cs
bsMas
C
XCs
bsMasbaNM
1
,,
1
,,,,, TYT
23
1 1
,,,,,,,, fff
X
r
rN
XCs
srM
Pt
ctbsarcbaPMNK
Cr
Cr
ar
ar
ar
,
,
,
Y
f
cbaMNcbasrNMNMMbcaMNMcbaMNMcbaNM ,,,,,,,,,1,,,,,,,,,,,, K'K'''
]YYYY['
1
,,
1
1
,,,,,,,,,
N
XCr
brMar
XC
Cr
brMar
C
XCr
brMarcrcbaNM
1 1 13
,,1,,,,11,0,,,1
1
,,,, ]ff[
)!(!
)1(
K'
M
Cr
rNM
Ns
srC
Nt
ctbsrNMNbcNrNMcbN
CCrr
cbaMN
CrC
ppa
s
ru
buaKsrbaK ,,,,,, f
10
11. The stationary channel state probability:
Cii
XCii
Csr
s
A
r
A
i
A
i
A
P
XC
r
XC
s
sr
ii
ii
2
,0
2
!!
!!
21
21
0 0
21
,
21
21
Pb with Complete Coverage in
2BSCS
C+X
C-X C+X
i2
i1
BS1
BS2
Ci1,i2
Ci1,i2+1
Ci1+1,i2
Ci1,i2
λδ
λδ
(i2+1)μδ
(i1+1)μδC-X
11
),,(
),,( ,1,
,2
1
0
,
AXCXC
AXCXC
PPP
AXCAXC
XC
XCr
rrC
XC
r
rXCb
M
Ni
AiNMAiANAMANM ,,,1,2),,(
M
Ni
AiNMAiANAMANM ,,,1,),,(
12. Following similar approach, the stationary
channel state probability :
The Probability of Blocking:
Pb with Complete Coverage in
3BSCS
),,(..
),,(..
!!!
!!!
321
0 0 0
321
),,(
321
321
iiiLts
tsrLts
t
A
s
A
r
A
i
A
i
A
i
A
XC
r
XC
s
XC
t
tsr
iii
iiiP
Ciii
XXCiiiiii
XXCiii
iiiL OI
OI
3
),2min(2,,
)2,min(,,
:),,(
321
313221
321
321
12
u
m
d
u
dm
u
m
u
C
r
ddmmmuAr
C
Cr
C
rCCs
AsrCAsAr
C
Cr
dmuArdmAC
b
ACrCrCrCCC
ACrCCACC
P
0
,
1
,3,,
1
,,
,,,minmax,,max
,,,,
13. mu CCii 32
mu CCii 31mu CCii 21
uC
uCuC
mC
mC
mC
dC
dCdC
Ciii 3321
1BS
2BS 3BS
)2,min(
)2,min()2,min(
)2,min(
IOd
OIIOm
OIu
XXCC
XXXXCC
XXCC
13
14. Call Service Time Distribution
Function
For call service time:
◦ Conventional cellular networks (usually voice
calls): Exponential distribution
◦ Multimedia traffic in new wireless networks:
heavy-tail distribution functions such as Pareto
distribution.
For voice and non-voice calls the arrival rate
follows the Poisson distribution function.
m
m
m
X
xx
xx
x
x
xF
0
)(1
)(
is the positive minimum ofmx X21
14
16. Cc=420 channel
A=390 Erlangs
Erlang B:
16
Numerical Analysis for Complete
Coverage
C
r
r
k
C
k
b
rA
CA
P
0
!/
!/
0 5 10 15 20
0
0.005
0.01
0.015
0.02
0.025
0.03
0.035
0.04
0.045
0.05
0.055
Number of shared channels
ProbabilityofBlocking
2BSCS, C = 70 , A = 65
3BSCS, C=140 , A =130
3BSCS, C = 70 , A = 65
Probability of blocking for
traditional cellular network
Asymptotic value for probability of
blocking follows:
0282.0)6/2,6/2( ccb CABP
Asymptotic value for probability of
blocking follows:
0067.0)3/3,3/3( ccb CABP
17. 3BSCS obtains a smaller probability of blocking
in comparison with 2BSCS.
for covering a large cellular network in 2BSCS or
3BSCS scenarios, the number of relays is
respectively, three times or equal to the number of
cells. Therefore, the latter scheme is more
economical and also yields less Pb than the former
scheme.
Sectorization allows for independent sharing of
the channels of each sector without affecting the
neighboring sectors of the same cell. This in turn
allowed for extending the analysis to the whole
network.
Numerical Analysis for Complete
Coverage
17
18. Comparison of Sim. & Analitics for
call service time.
Cc=210.
Ac=195 Erlangs.
Mean time of each call=2min.
0 5 10 15 20
0.01
0.02
0.03
0.04
0.05
0.06
Number of shared channels
ProbabilityofBlocking
3BSCS - Analytic
Exponential Dist. - Simulation
Pareto Dist. - Simulation
18
20. System Model
Relay Sub-Cell
Main Cell
Base Station
Relay
Base Station Sub-Cell
Target Sub-Cell
)1,2(),( hh ji
1hj
2hi
60
)0,0(
1j
1i
60
)1,1(),( ji
No. of available codes
in each cell: n
Traffic modell:
M/G/n/n
Traffic intensity/Cell: A
Traffic intensity/Sub-
Cell: A/4
Threshold on BS:
Perfect Power Control
20
21. System Model
Hard blocking / Code Availability call admission (CA)
The probability of outage together with the probability
of hard blocking, constitute the grade of service (GoS)
in a CDMA cellular network.
Signal to interference ratio call admission (SIR-CA)
Probability of outage for three scenarios will be
investigated:
◦ 1st Scenario: A traditional cellular network with CA call
admission,
◦ 2nd Scenario: A Hybrid network with SIR call admission,
probability of outage for target BS,
◦ 3rd Scenario: A Hybrid network with SIR call admission,
probability of outage for other BS,
CA
OP
SIR
OP
COP
21
22. Interference
The received signal power at the target base
station from the mth user in the cell (i, j):
Total interference: summation of all
interferer located inside and outside the cell.
→
A call request is accepted if a free code is
available.
10
)0,0,(
),,(
)0,0,(
)0,0(,),(,
10)(
mjim
m
jim
m
D
D
X
Euclidian distance from the mth
user to the center of the cell (i, j)path loss exponent
shadowing loss factor for the link
between the user m and the base
station of the cell (i, j) with
normal N(0,σψ
2)
0 1
),(
1
)0,0,()0,0()0,0(
i j
jiu
g
gXuI
The number of active users within
the six symmetric cells identified
by (i, j)The number of active users
connected to the target base
station
)0,0()0,0( uIIout
}Pr{}Pr{ )0,0(
O
out
CA
O IIP
)0,0(uO
22
23. The mean & variance of the individual interferer is:
According Fenton’s method, it is assumed that Iout has
the log-normal where Iout=10-φ/10:
and
Then, the probability of outage is derived as:
This Probability should be averaged over the u(0,0).
x
x
O
O
OO
out
CA
O
dxexQQ
IP
2/10
10
10/
2
2
1
)(,
log10
log10Pr
10PrPr
z
QzuPCA
O
10
)0,0(
log10
Pr
2
2
2
2
1
a
Ln
out
out
I
I
a
aLn outI
22
5.0
A traditional cellular network with CA call
admission
(Our proposed method)
nz
rA
zA
zu n
r
r
z
0,
!/
!/
Pr
0
)0,0(
23
22
)0,0,(
),,(
),(
a
m
jim
ji e
D
D
E 2
),(
4
2
)0,0,(
),,(2
),(
22
ji
a
m
jim
ji e
D
D
E
0 1
2
),(
0 1
2
),(),(
2
6
i j
ji
i j
jijiI Auout
0 1
),(
0 1
),(),( 6
i j
ji
i j
jijiI Auout
24. Assume:
Chernoff Bound achieves the upper bound
for the
),(~10 210/
)0,0,(
NXm
)1()var(
)(
2222
22
222
)0,0,(
2
),(
5.0
)0,0,(),(
aaa
mji
aa
mji
eeX
eXE
)(log10
)0,0,(
),,(
10
m
jim
D
D 222
2 a
A traditional cellular network with CA
call admission0.1×Ln(10)
CA
OP
24
25. Relays with CA call admission:
: the number of active users inside the BS sub-cells.
: the number of active users inside the BS sub-cells.
Mean & variance of interference Iout :
Preposition 1: The average number of active users on the BS sub-
cell, , in a hybrid CDMA network with SIR-CA control for the
BSs is:
0 1
2
)2,2(
2
),(
2
0 1
)2,2(),(
6
6
h h
hhhhout
h h
hhhhout
i j
jirbjirI
i j
jirbjirI
uuu
uuu
A Hybrid network with SIR call
admission for target BS
4/Aur
bu
0
0
!/4/
!/4/
1
4
dx
rA
xA
f
A
u x
r
r
x
Ib out
STEP 1
Given the value of , and
are obtained
bu outI
2
outI
STEP 2
is recomputed in terms of the
mean and variance of
bu
outI
STEP 3
Assuming an initial value for
, the iterative method
is executed until it converges.
bu
25
bu
ru
26. can be described by two distribution functions:
◦ Normal → CLT → ANL-CLT
◦ Log-Normal → Fenton’s method → ANL-FM
Probability of Outage:
Relays with SIR-CA:
Rescaling of conventional cellular network
A Hybrid network with SIR call
admission, Pb for target BS
outIf
0 4/
1Pr)(
A
u
dxxIoutagexfP b
outI
SIR
O out
ε-x
r
r
ε-x
x
rA/
ε-xA/
ε-xtP
0
!/4
!/4
)(
26
rb uu
0 1
),(6
h h
hhout
i j
jibI u
0 1
2
),(
2
6
h h
hhout
i j
jibI u
27. Preposition 2: In the hybrid CDMA system with
SIR-CA over the BSs and CA over the relays, in
the steady state with no outage over any of the
BSs, a newly admitted call in the target BS, the
probability of outage in BSs except the target BS
using Union bound is
where
QoS in Hybrid Networks
0 1
)2,2(
~
6
h h
hh
i j
jiCO PP
0
0
0
)2,2( Pr
!/4/
!/4/
)( dxxkx
rA
kA
xfP
x
k
newx
r
r
k
Iji outhh
dssfskxxkxx Snewnew
0
)(Pr1Pr
sRxx nnew
)(
27
29. Simulation & Analytical Results
Simulation:
◦ 91 cells
◦ Target cell is
in the center
of the area
◦ Monte Carlo
σ=3.5dB, ε= 14dB
ANL-FM is accurate approximation in comparison
with Chernoff bound
10 12 14 16 18 20
10
-2
10
-1
10
0
Traffic Intensity per Cell (Erlangs)
ProbabilityofOutage-PO
CA Cellular Sys. Chernoff Bound
Cellular Sys. ANL-FLT
Cellular Sys. Sim.
Traditional cellular network with CA call admission
29
30. Simulation & Analytical Results
Simulation
Also:
◦ LG-CLT
◦ LG-FM
σ=3.5dB, ε= 15.5dB
ANL-FM is accurate approximation in comparison
with other three methods.
Traditional cellular network with SIR call admission,
Pb for target BS
10 15 20 25 30 35 40 45 50 55
10
-4
10
-3
10
-2
10
-1
Traffic Intensity per Cell (Erlang)
ProbabilityofOutage-PO
SIR
Cellular Sys. Sim. =2.5dB
Cellular Sys. ANL-CLT =2.5dB
Cellular Sys. LG-CLT =2.5dB
Cellular Sys. ANL-FM =2.5dB
Cellular Sys. LG-FM =2.5dB
30
31. Simulation & Analytical Results
A hybrid network with SIR-CA relays and BSs
achieves better performance.
Comparison of relays in both CA call admission and
SIR-CA
15 20 25 30 35 40 45 50 55
10
-2
10
-1
Traffic Intesity per Cell (Erlang)
ProbabilityofOutage
PO
SIR
-Hybrid Sys. w CA Relays, =4dB
PO
SIR
-Hybrid Sys. w SIR-CAC Relays, =4dB
PCO
-Hybrid Sys. w CA Relays, =4dB
PCO
-Hybrid Sys. w SIR-CAC Relays, =4dB
31
32. Simulation & Analytical Results
Capacity Analysis of Conventional Cellular & Hybrid
CDMA Networks
5 10 15 20 25
10
-3
10
-2
10
-1
10
0
Traffic Intensity per Cell (Erlangs)
ProbabilityofOutage(PO
)
PO
SIR
Cell. Sim.
PO
SIR
Cell. ANL-FM
PO
SIR
Hyb. Sim.
PO
SIR
Hyb. ANL-FM
PCO
Cell. Sim.
PCO
Cell. ANL-FM
PCO
Hyb. Sim.
PCO
Hyb. ANL-FM PCO
PCO
Hybrid
Cellular
σ= 3dB, ε=15.5dB
32
33. Simulation & Analytical Results
The average number of active users in hybrid CDMA
network is much more than the amount which is presented
by the conventional CDMA cellular network.
Effect of Shadowing on the Average Number of
Active Users
10 15 20 25 30 35 40 45 50 55
10
15
20
25
30
35
40
45
50
55
60
Traffic Intesity per Cell (Erlang)
AverageNumberofActiveUsers
Cell. Simul. = 0
Cell. Simul. = 2.5dB
Cell. Simul. = 4dB
Cell. ANL-FM = 0
Cell. ANL-FM =2.5dB
Cell. ANL-FM = 4dB
Hyb. ANL-FM =0
Hyb. ANL-FM = 2.5dB
Hyb. ANL-FM = 4dB
Cellular
Hybrid
33
35. Conclusions:
Challenges in Cellular Network.
Advantages of Hybrid Network as a solution.
Hybrid Network overview.
Two hybrid model was introduced.
◦ In load balancing: 2BSCS & 3BSCS
◦ In interference reduction: A hybrid network model
Pb in hybrid networks for 2BSCS & 3BSCS in two scenarios:
◦ Complete coverage of relays.
◦ Coverage limited relays.
Result: Load balancing improves the Capacity of hybrid network
in comparison with conventional cellular networks as:
◦ Both introduced schemes are effective for improving the
grade of service compared to conventional cellular networks.
35
36. ◦ The 3BSCS scheme provides a better performance even
with a smaller number of relays per cell.
◦ 15% of available codes in each sector to dedicate for
channel sharing in complete coverage scheme, or 50%
of a sector area for coverage-limited scheme achieves
the performance improvement.
◦ The presented analysis for the sectorized configurations
is applicable to the whole network.
◦ According to comparisons of simulation vs. analytical
results, the Pb in our analysis is independent of the
distribution function of call service time.
Conclusions:
36
37. Two call admission policies are introduced as CA call admission
& SIR-CA.
Probability of outage according to different call admission
policies in both conventional cellular and hybrid CDMA
networks is investigated.
Results:
◦ A new approximation method named as ANL-FM in addition
to an iterative method for computing the probability of outage
is introduced.
◦ The accuracy of this method compared to Chernoff bound and
other three proposed approximation methods by simulation vs.
analytics.
◦ Hybrid network achieves better performance in terms of
probability of outage & the average No. of active users
compared to the conventional cellular network.
Conclusions:
37
38. ◦ Total probability of blocking is the function of hard
blocking and soft blocking.
Future work: Relays in our system model are Out-of-
Band frequency. It can be assumed that relays work
in In-band frequency. Hence, the issue changes to
Cooperative problem in cellular network. The
Probability of outage according to SIR-CA in this
cooperative network can be investigated.
Conclusions & Future Work:
38
39. Publications:
H. Purmehdi and F. Lahouti, “Channel Sharing in
Hybrid Sectorized Cellular Networks with Coverage-
limited Relays”, IEEE European Modeling
Symposium, EMS’09, Greece, Athens, Nov. 2009.
(Accepted)
H. Purmehdi, A. Behnad and F. Lahouti,
“Performance Analysis of Hybrid CDMA Systems”,
IEEE European Modeling Symposium, EMS’09,
Greece, Athens, Nov. 2009. (Accepted)
H. Purmehdi, A. Behnad and F. Lahouti,“Hybrid
CDMA System with SIR based Call Admission
Control”, (Under Preparation)
39
