IEEE COMMUNICATIONS LETTERS, VOL. 13, NO. 6, JUNE 2009 393
VoIP Capacity Analysis in Cognitive Radio System
Howon Lee and DongHo Cho
Abstract
—In this letter, we analyze a voice over IP (VoIP)capacity in a cognitive radio system. We formulate the systemas a twodimensional discrete time Markov chain (DTMC).The VoIP traf
ﬁ
c and wireless channel in the cognitive radiosystem are described as a Markov modulated Poisson process(MMPP) model and a Markov channel model, respectively. Wedemonstrate various numerical and simulation results, such aspacket dropping probability and VoIP capacity.
Index Terms
—Cognitive radio, VoIP service, Markov modulated Poisson process, discretetime Markov chain.
I. I
NTRODUCTION
C
OGNITIVE radio is a promising and challengeable technology for maximizing radio resource utilization in afuture wireless communication system because conventionalsystems exploit most available frequency bands for wirelesscommunications and these frequency bands are not alwaysfully utilized in general [1]. In addition, Voice over IP (VoIP)will be an essential service in the future because, throughVoIP technology,wireless users can utilize voice services morecheaply. Therefore, supporting as many voice users as possiblewhile using limited radio resources is a very important issuethat could be a key to the success of the future systems [2][3].In [4], the authors proposed a discretetime Markov chain(DTMC) framework based on a Markov modulated Poissonprocess (MMPP) traf
ﬁ
c model to analyze VoIP performance.However, they did not consider the cognitive radio system.Also, in [5], Q. Bi et al. analyzed the VoIP capacity of 1xEVDO system. In this letter, we analyze VoIP capacity in acognitive radio system through a queuing model based on theMMPP traf
ﬁ
c model and a Markov channel model. Here, VoIPpackets can be transmitted when the wireless channel is notutilized by a primary user. To the best of our knowledge, theVoIP capacity analysis has not been studied yet in the cognitiveradio system.The remainder of this letter is organized as follows. InSection II, we present the VoIP traf
ﬁ
c model based on theMMPP and the Markov channel model for cognitive radiosystem. In Section III, we propose a twodimensional DTMCframework considering multiuser VoIP queuing and wirelesschannel occupancy variations. In Section IV, we demonstratenumerical and simulation results and conclude this letter.II. V
O
IP T
RAFFIC AND
C
HANNEL
M
ODELING
1) VoIP Traf
ﬁ
c Modeling:
In general, we can formulatethe VoIP traf
ﬁ
c of a single user as a simple onoff model.The probability that the status of the users is inactive (=
Manuscript received December 23, 2008. The associate editor coordinatingthe review of this letter and approving it for publication was H.H. Chen.The authors are with KAIST, Republic of Korea (email:hwlee@comis.kaist.ac.kr).Digital Object Identi
ﬁ
er 10.1109/LCOMM.2009.082189
(Unoccupied) (Occupied)
p
01
p
10
p
00
p
11
Fig. 1. Markov channel model for cognitive radio system.
off) in the simple onoff model can be obtained by
p
off
=
β
−
1
/
(
α
−
1
+
β
−
1
)
, and
p
on
= 1
−
p
off
. Here,
1
/α
and
1
/β
arethe mean values of the on and off periods which are distributedexponentially. Furthermore, all the traf
ﬁ
c generated by theVoIP users in the cell can be modeled as a twostate MMPPmodel [6]. This MMPP model is highly suitable for formulating the multiuser VoIP traf
ﬁ
cs because the MMPP capturesthe interframe dependency between consecutive frames. Here,the transition rate matrix (
R
) and the Poisson arrival ratematrix (
Λ
) of the MMPP can be expressed as follows:
R
=
−
r
1
r
1
r
2
−
r
2
,
Λ
=
λ
1
00
λ
2
.
(1)In order to utilize the MMPP model, we should match theMMPP parameters (
r
1
,r
2
,λ
1
and
λ
2
) in Eqn. (1) with the parameters of the simple onoff model (
α
and
β
). We here adoptthe IDC (index of dispersion for counts) matching techniquebecause it yields adequate results for the matching of parameters and has appropriate computation complexity comparedwith other matching techniques [4]. Then,
r
1
,
r
2
,
λ
1
, and
λ
2
inEqn. (1) can be calculated by
r
1
=
2(
λ
2
−
λ
avg
)(
λ
avg
−
λ
1
)
2
(
λ
2
−
λ
1
)
λ
avg
(
IDC
(
∞
)
−
1)
,
r
2
=
2(
λ
2
−
λ
avg
)
2
(
λ
avg
−
λ
1
)(
λ
2
−
λ
1
)
λ
avg
(
IDC
(
∞
)
−
1)
,
λ
1
=
A
·
N act avgi
=0
i
·
π
i
N act avgj
=0
π
j
, and
λ
2
=
A
·
N i
=
N act avg
+1
i
·
π
i
N j
=
N act avg
+1
π
j
. Here,
N
is the total number of VoIP users in the system, and
A
is the emission rate in the onstate (
A
=
1
T
basic
)
.
T
basic
is a frame duration of voice codec,and the average arrival rate is
λ
avg
=
N
×
A
×
p
on
. Also,the average number of active users is
N
act avg
=
N
×
p
on
,and the steadystate probability of an onedimensional Markovchain when considering
N
independent simple onoff voiceusers can be calculated by
π
i
=
N
C
i
·
p
ion
·
(1
−
p
on
)
N
−
i
.Moreover,
IDC
(
∞
)
is given in [6].
2) Channel Modeling in Cognitive Radio System:
In acognitive radio system, a wireless channel can be modeledas a twostate Markov process, as shown in Fig. 1 [7]. Anoccupied state means that the wireless channel is utilized by aprimary user. Given that the channel status is ‘Occupied’, thecognitive user cannot use the channel. In this letter, we assumethat there are ‘
M
’ wireless channels. Then, the transition
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2009 IEEE
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394 IEEE COMMUNICATIONS LETTERS, VOL. 13, NO. 6, JUNE 2009
B
(
i,m
)
,
(
j,n
)
=
M
k
=0
U
·
D
(
j
−
max
(
i
−
k,
0))
·
P
s
(
k

x
c
=
m
)
·
min
(
m,M
−
n
)
x
=
max
(0
,m
−
n
)
mx
p
x
01
p
m
−
x
00
M
−
my
p
y
10
p
M
−
m
−
y
11
.
(5)
probability (
P
m,n
) that there are
m
unoccupied channels (
x
c
)in the current frame, and there will be
n
unoccupied channelsin the next frame can be represented by
P
m,n
=
min
(
m,M
−
n
)
x
=
max
(0
,m
−
n
)
mx
p
x
01
p
m
−
x
00
M
−
my
p
y
10
p
M
−
m
−
y
11
.
(2)Here,
y
=
n
−
m
+
x
, where
x
and
y
denote the numbers of channels whose status are altered from ‘Unoccupied’ to ‘Occupied’ and from ‘Occupied’ to ‘Unoccupied’, respectively.III. S
YSTEM
M
ODELING
1) Assumptions:
Perfect informationfor channel occupancyof primary users is available in the base station (BS), andone VoIP packet can be transmitted through one unoccupiedwireless channel. If all the channels are used by the primaryusers, the VoIP packets cannot be sent. Also, we assume thatthere are no packet retransmissions. That is, unreceived anddestroyed packets are not sent again.
2) System Modeling:
We can formulate a multiuser queuing model for VoIP services in a cognitive radio system asa twodimensional DTMC. In other words, we can analyzethe behavior of queuing packets in the BS with this DTMCmodel. Then, the transition matrix (
P
) can be de
ﬁ
ned as
P
=
A
0
,
0
A
0
,
1
· · ·
A
0
,L
max
............
A
L
max
,
0
A
L
max
,
1
· · ·
A
L
max
,L
max
(3)where
L
max
is maximum queue length and submatrix (
A
i,j
)is expressed as
A
i,j
=
B
(
i,
0)
,
(
j,
0)
B
(
i,
0)
,
(
j,
1)
· · ·
B
(
i,
0)
,
(
j,M
)
............
B
(
i,M
)
,
(
j,
0)
B
(
i,M
)
,
(
j,
1)
· · ·
B
(
i,M
)
,
(
j,M
)
.
(4)In Eqn. (4),
A
i,j
represents the variation of the number of queuing packets. That is, there are
i
packets in the currentframe, and there will be
j
packets in the next frame. In
A
i,j
,each element (
B
(
i,m
)
,
(
j,n
)
) indicates the transitions betweenthe numbers of unoccupied channels when the number of queuing packets is changed from
i
to
j
. Also,
B
(
i,m
)
,
(
j,n
)
is a 2by2 matrix because our MMPP model has two phases,such as underloading and overloading. When the number of queuing packets is
i
, given that
k
packets are scheduled,
(
j
−
max
(
i
−
k,
0))
packets should arrive so that the numberof packets becomes
j
. Hence,
B
(
i,m
)
,
(
j,n
)
can be calculatedby Eqn. (5). Here,
P
s
(
k

x
c
=
m
)
is the probability that theBS serves
k
packets when the number of unoccupied channelsis
m
. In this letter, since we assumed that one VoIP packetcan be transmitted through one unoccupied wireless channel,
P
s
(
m

x
c
=
m
) = 1
. In addition, in Eqn. (5),
U
and
D
(
m
)
are the transition probability matrix and the diagonalprobability matrix of the twostate MMPP model [4]. Eachelement of
D
(
m
)
means the probability that
m
VoIP packetsarrive at the BS during the MAC frame duration (
T
f
) in eachphase of the twostate MMPP.Through the transition matrix (
P
) in Eqn. (3), we canobtain the steadystate probability matrix (
π
p
) for our twodimensional DTMC model, which can be calculated by solvingequations
π
p
·
P
=
π
p
and
π
p
·
1
= 1
. Here,
π
p
is ‘
1
’ by‘
2
×
(
M
+1)
×
(
L
max
+1)
’ matrix. Therefore, the probabilitythat
k
VoIP packets are queued in the BS can be expressed as
π
(
k
) =
2(
M
+1)
−
1
l
=0
π
p
(2
·
(
M
+ 1)
·
k
+
l
)
.
(6)Through Eqn. (6), the ‘
1
’ by ‘
(
L
max
+1)
’ steadystate probability matrix of the DTMC model can be obtained as follows:
π
= [
π
(0)
π
(1)
π
(2)
···
π
(
L
max
)]
. Therefore, by usingthis steadystate probability, we can present various analyticalresults, such as the average number of arrived packets, theaverage queuelength, the average number of serviced VoIPpackets, the average VoIP throughput, and the packet droppingprobability. First, the average queuelength (
L
avg
) and theaverage arrival rate (
ρ
) can be calculated by
L
avg
=
L
max
i
=0
i
·
π
(
k
)
.
(7)
ρ
=
s
·
N
×
A
max
m
=0
m
·
D
(
m
)
·
1
.
(8)In Eqn. (8),
s
is calculated by solving
s
·
U
=
s
, and
1
is acolumn matrix of ones. Also,
A
max
is the maximum numberof packets that can arrive from each VoIP user during
T
f
.Similar to the average arrival rate, the average number of serviced VoIP packets (
κ
avg
) can be expressed as
κ
avg
=
M
i
=0
M
j
=0
L
max
k
=0
min(
j,k
)
·
π
(
k
)
·
P
s
(
j

x
c
=
i
)
·
π
ch
(
i
)
.
(9)Here,
π
ch
(
i
)
is the steadystate probability that the number of unoccupied channels are
i
, and can be expressed as
π
ch
(
i
) =
M i
(
p
10
p
01
+
p
10
)
i
·
(
p
01
p
01
+
p
10
)
M
−
i
.
(10)Moreover, the average throughput is represented by
S
avg
=
κ
avg
×
l
PDU
. Here,
l
PDU
is the size of VoIP PDU. Also,we can calculate the dropping probability of VoIP packets asfollows:
P
drop
= 1
−
κ
avg
/ρ
. Hence, by using
P
drop
, we cande
ﬁ
ne the VoIP capacity as following
C
V oIP
= arg max
N
∈ {
N

1
−
κ
avg
/ρ
≤
P
limit
}
.
(11)Here,
P
limit
is the upper threshold of the packet droppingprobability for VoIP services.IV. N
UMERICAL AND
S
IMULATION
R
ESULTS
We evaluated the VoIP performance of the cognitive radiosystem by using MATLAB. We included all the essential factors required for performance evaluation, such as roundrobin
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LEE and CHO: VOIP CAPACITY ANALYSIS IN COGNITIVE RADIO SYSTEM 395
010203040506070801E30.010.11
P
limit
P a c k e t d r o p p i n g p r o b a b i l i t y
Number of users
sim, p
o
=0.8 sim, p
o
=0.5 sim, p
o
=0.2 anal, p
01
=0.8, p
10
=0.2 anal, p
01
=0.5, p
10
=0.5 anal, p
01
=0.2, p
10
=0.80.02
Fig. 2. Packet dropping probability versus numberof users according to variation of channel occupancy probability when M=10.
01020304050607080050100150200250300350400
A v e r a g e t h r o u g h p u t ( k b p s )
Number of users
sim, p
o
=0.8 sim, p
o
=0.5 sim, p
o
=0.2 anal, p
01
=0.8, p
10
=0.2 anal, p
01
=0.5, p
10
=0.5 anal, p
01
=0.2, p
10
=0.8
Fig. 3. Average throughput (Kbps) versus numberof users according to variation of channel occupancy probability when M=10.
15202530354045500.010.10.02
P
limit
P a c k e t d r o p p i n g p r o b a b i l i t y
Number of users
anal, p
00
=0.2, p
01
=0.8, p
10
=0.8, p
11
=0.2 anal, p
00
=0.5, p
01
=0.5, p
10
=0.5, p
11
=0.5 anal, p
00
=0.8, p
01
=0.2, p
10
=0.2, p
11
=0.8
Fig. 4. Packet dropping probability versus numberof users according to variation of channelstatetransition probability when M=10.TABLE IV
O
IP
CAPACITY ACCORDING TO VARIATION OF
DL/UL
FRAME RATIO
CapacityDL/UL frame ratioDL:UL = 1:1 DL:UL = 2:1Downlink capacity 13 24Uplink capacity 33 21
scheduler, packetsize and packetgeneration period variationsof VoIP codecs, and so on.To obtain results, we assumed that
M
= 10
,
T
f
= 5
ms,
L
max
= 50
, and
A
max
= 200
. We utilized the G.729Bcodec where
T
basic
is
10
ms. This codec has two data rates(
8
kbps and
0
kbps), and voice activity factor is 0.4, in thisletter. We assumed that the size of the RTP/UDP/IPv4 headercompressed by payload header suppression (PHS) is
16
bytes.Also, the size of the MAC header is
6
bytes. In the simulation,we used an onoff source model for each VoIP user.As shown in Fig. 2, we can show
P
drop
versus the numberof users according to variation of channel occupancy probability (
p
o
). In this letter, we assume that
P
limit
= 0
.
02
. Here,
p
o
means the probability that the primary users utilize wirelesschannels, and also denotes the steadystate probability whenchannel status is ‘Occupied’. For a low loading condition, theMMPP based numerical results have lower packet droppingprobabilities than the onoff based simulation results mainlydue to the characteristic of the IDC matching technique [4].In addition, the average throughputgrows linearly accordingto the increment of the number of VoIP users up to thesaturation point, as shown in Fig. 3. Since resource saturationoccurs at this point, the BS cannot assign channels to surplususers beyond the saturation point. Thus, even though thenumber of users increases, the average throughput cannot beenlarged without limit. Given that
p
o
is small, there exist moreunoccupied channels that can be utilized by cognitive users.Thus, the throughput when
p
o
is small could be higher thanthe throughput when
p
o
is large. Also, from Fig. 2 and Fig. 3,it can be seen that the performance of analysis and simulationare almost the same.The VoIP capacity can be varied according to the variationof channelstate transition probability, as shown in Fig.4. Here,the steadystate transition probabilities of the Markov channelmodels for all the cases are the same. However, if the
p
01
and
p
01
are larger, the state transitions occur more frequently.Thus, the VoIP capacity could be smaller. On the other hand,we can apply our formulation to VoIP admission control in thecognitive radio system. If the channel occupancy variations aredynamic, we can adjust the maximum supportable number of users based on the results demonstrated in this letter.Furthermore, given that the total number of channels is
30
,the overhead caused by control signaling is
30
% [8], and
p
o
=0
.
5
, we can obtain both downlink and uplink capacitythrough our analysis method. As shown in Table I, whenDL/UL frame ratio is 1:1, we can show that the VoIP capacityis restricted by the downlink owing to the overhead caused bycontrol signaling. However, when the DL/UL ratio is 2:1, thecapacity is limited by the uplink due to the fact that the sizeof uplink frame is much smaller than that of downlink frame.Therefore, we can conclude that the VoIP capacity is determined by bottlenecklink, which can be different according tosystem parameters such as the DL/UL ratio.R
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