Saturation Throughput Analysis of IEEE 802.11b
DCF Considering Capture Effects
Haihua Han
School of Information Science and
Engineering Shandong University
Jinan Shangdong 250100, P.R.China
hanhaihua204@126.com
Weihong Zhu
Na Li
School of Information Science and
Engineering Shandong University
Jinan Shangdong 250100, P.R.China
zhuwh@sdu.edu.cn
School of Information Science and
Engineering Shandong University
Jinan Shandong 250100, P.R.China
nazheng708@126.com
Abstract—The performance of the distributed coordination
function (DCF) has been discussed in the past years. This paper
provides a simple and accurate analysis by Markov chain
modeling to evaluate the IEEE 802.11 DCF performance in the
presence of capture effect. We extend the Bianchi’s
multidimensional Markov chain analytical model of IEEE 802.11
DCF to characterize the behavior of DCF considering capture
effect and packet retransmission limits. We compare the NS-2
simulation results with the derived analysis. Numerical results
and simulations are provided to validate the accuracy of our
model.
Keywords- IEEE 802.11 DCF; NS-2; Markov chain; capture
effect; packet retry limits
I.
INTRODUCTION
The IEEE802.11 protocol is widely used in today’s
wireless local area networks (WLANs) and multi-hop mesh
networks. The 802.11 standard for wireless networks
incorporates two kinds of medium access methods, which are
the distributed coordination function (DCF) and the point
coordination function (PCF). PCF is a centralized and optional
protocol, which uses the pooling mechanism for gaining the
access of channel. The DCF is a mandatory protocol, which is
based on the carrier sense multiple access with collision
avoidance (CSMA/CA) algorithm.
In 802.11, The DCF defines two medium access schemes
for packet transmission, the basic access mechanism and the
request-to-send /clear-to -send (RTS/CTS) mechanism. The
basic scheme is a default mechanism and uses DATA/ACK, a
two-way handshaking technique, to confirm whether the
DATA packet is successfully transmitted in the channel. The
other optional RTS/CTS mechanism is a four-way
handshaking access method, which uses smaller control
packets (RTS and CTS) to reserve the channel before data
transmission.
Many researchers have been studied the performance of
802.11 DCF based on two dimensional Markov chain
analytical model. As far as know, G. Bianchi[1] first proposed
a two-dimensional Markov chain model to analyze the
saturation throughput of the DCF, in the assumption of a
limited number of terminals and ideal channel conditions (no
errors). In contrast, Wu et al. [2] extended the Bianchi’s model
with consideration of finite packet retry limits specified by the
IEEE 802.11 standards. In Wu’s model, the station discards
the packet after m back-off stages, while in Bianchi’s model,
the station keeps iterating in the m-th back-off stage until the
packet is successfully transmitted. The result is the throughput
of 802.11 can be predicted more accurately. In [3], the authors
introduced another state (idle) in which the station buffer is
waiting for a new packet after a successful completion of a
packet transmission to investigate the performance of DCF
considering packet retry limits in the unsaturated traffic
conditions. When two or more stations simultaneously
transmit to an Access Point (AP), the station whose power is
sufficiently stronger than the other stations captures the
channel, and thus, the actual throughput increases. This
phenomenon is known as capture effect. Thus, the capture
effect widely exists in the IEEE 802.11 WLANs. The authors
[4, 5, 6, 7] presented a derived Markov model to analyze the
throughput of IEEE 802.11 taking into account transmission
errors and capture effects over Rayleigh fading channel in
saturated and non-saturated traffic conditions. Moreover,
paper [8] analyzed the saturation throughput of the basic
802.11 protocol by including the capture effect in Rayleigh
fading environment. In this paper, we present a simple
analytical model to characterize the performance of
IEEE802.11 DCF, which takes into account packet retry limits
and capture effect in saturated traffic conditions. The key
difference between our model with the others which the above
papers presented is that the Markov chain models are
different, where our model considers the effects of frame
retransmitting limit.
The rest of the paper is organized as follows. Section II
briefly overviews the DCF procedure of the IEEE802.11 MAC
protocol which includes both basic access and RTS/CTS
mechanism. Our analysis model for the basic access
mechanism under saturated traffic condition is described in
Sections III, Section IV presents numerical and simulation
results where typical MAC layer parameters for IEEE802.11b
are used. Finally, Section V concludes the paper.
II.
IEEE 802.11 DISTRIBUTED COORDINATION
FUNCTION(DCF) PROCEDURE
The DCF, a basic MAC layer mechanism of IEEE 802.11
is based on CSMA/CA protocol to share medium between
multiple stations. The DCF protocol in IEEE802.11 includes
two access techniques for a packet transmission: the basic
access mechanism and an optional RTS/CTS mechanism as
shown in Fig.1 and Fig.2, respectively.
A. The basic access method
Before transmitting a new data packet, the station (STA)
must gain access to the medium, which is a radio channel that
all stations share. If the channel is idle for a period of duration
equal to a distributed inter-frame space (DIFS), the STA will
transmit its packet. If the channel is sensed to be busy, the
STA will delay a DIFS and then generate a random back-off
interval before transmitting the new packet. The back-off
interval counter is decremented by one as long as the medium
is idle, or it is frozen when the channel is sensed to be busy,
and resumes after the channel is sensed to be idle again for a
DIFS time. When the back-off timer reaches zero and the
channel is idle, the station will send its data packet. Once the
transmitting packet is received correctly, the destination STA
will send an acknowledgment (ACK) frame to the source STA
after a short inter-frame space (SIFS) interval. If the source
STA does not receive the ACK, the data packet is assumed to
be lost and a retransmission is scheduled.
The random back-off interval is uniformly chosen in the
interval [0, Wi -1] , where Wi is the current Contention Window
(CW) and i is the station back-off stage. The value of
Wi depends on the frame retransmissions and is an integer in
the range W0  Wi  Wm' . At the first transmission attempt of
a packet, this value is set to be W0  CWmin , which is called the
minimum contention window size. After each unsuccessful
transmission, it is doubled, up to a maximum value
Wm'  CWmax  2m W0 , where m' represents the back-off stage
'
Figure 2.
III.
RTS/CTS mechanism
ANALYY ICAL MODEL AND THROUGHPUT
ANALYSIS FOR DCF
We use the two-dimensional random process s(t ), b(t ) to
represent the sate of the two-dimensional Markov chain at a
slot time t , therein, b(t ) is the back-off timer for a station, s (t )
is the back-off stage [0,......,m] for the station, where m
represents the maximum back-off stage or the station short
retry count (SSRC)[9], which is the maximum number of
retransmissions for the RTS frame or the DATA frame when
the RTS/CTS is not used. When the SSRC limits is reached,
retry attempts will cease and the frame will be discarded. In
this model, we suppose m is equal to 7, and each station
always has a packet available for transmission. The key
assumption in our model is that the collision probability Pcol
and capture probability Pcap is constant and independent for
each transmitted packet.
For the sake of simplicity, we adopt the same notation
P{i1 , k1 | i0 , k0 }  P{s(t  1)  i1 , b(t  1)  k1 | s(t )  i0 , b(t )  k0 } as used
in reference [1]. Our Markov chain is shown in fig. 3.
at which the CW size reaches the maximum value. When Wi is
equal to CWmax , it will be remain at the value of CWmax until
it is reset. Therefore, if the station is in the i back-off stage,
the CW size can be given as:
i

i  m'
 Wi  2  W
(1)
'

m

i  m'
Wi  2  W
B. RTS/CTS mechanism
The RTS/CTS mechanism tries to reserve the channel by
smaller control packets (RTS and CTS) before the DATA
transmission. When the back-off interval counter is zero and
the medium is idle, the source STA sends a RTS frame to the
destination STA and it will receive a CTS frame in response
after a SISF time interval. If the source STA receives a CTS
frame, the source STA starts transmitting its data. If the CTS is
not received by the source STA, it is assumed that a collision
occurred and a RTS retransmission is scheduled. Other
procedures are same as the basic one.
Figure 3. A Markov chain model for a station
The state transition diagram for the Markov chain model
has the following non-null one-step transition probabilities
P{i, k | i, k  1}  1,
k  0, wi  2,
i  0, m
P 0, k | i, 0   1  Pcol   Pcol Pcap  / W0
P{i, k | i  1, 0}  Pcol (1  Pcap ) / Wi
k  0,Wi  1 ,
k  [0,Wi  1]
i  [0, m)
i  [1, m]
(2)
P{0, k | m,0}  1/ W0
Let bi , k  lim t   P{s(t )  i, b(t )  k}, i （0，m), k  (0, Wi  1)
Figure 1. basic access mechanism
be the stationary distribution of the Markov chain. According
to the one-step transition probabilities, the following relations
can be established:
bi ,0  bi 1,0 ( Pcol (1  Pcap ))
0  i m
(3)
bi ,0  b0,0 ( Pcol (1  Pcap )) i
0im
(4)
Because the chain is regular, for each k  [0, Wi  1] , we have
m 1

Wi  k   1  Pcol   Pcol Pcap   b j ,0  bm ,0 ,
j 0
bi , k 

Wi 
 Pcol 1  Pcap  bi 1,0 ,
i0
(5)
1 i  m
Substituting (4) in (5), (5) can be rewritten as:
W k
bi ,k  i
 bi ,0
, 0im
(6)
Wi
Then, when the normalization condition for stationary
distribution is applied, we have
1
Wi 1 m
 b
i, k
k 0 i 0
W 1i
m

b 
i ,0
i 0
k 0
Wi  k

Wi
W 1
bi ,0  i
2
i 0
m
From the normalization equation, the expression of b0,0 can
be given as (7).
,
m  m'
,
m  m'
where we assume
Pt  Pcol (1  Pcap )
2(1  2Pcol )(1  Pcol )

, m  m'

m1
m1
 W (1  (2Pcol ) )(1  Pcol )  1  2Pcol (1  Pcol )
b0,0  
2(1  Pt )(1  Pt )

, m  m'
'
'
'
'
m

1
W (1  (2Pcol ) )(1  Pcol )  1  2Pcol  1  Pcolm1  W  2m  Pcolm 1 (1  2Pcol )(1  Pcolmm )

(8)
Which is similar to the one found in [2] under saturated load
conditions.
Now the probability τ, a randomly chosen slot time in which a
station attempt transmission, can be expressed as,
m

i 0
m
bi,0 

Pt  b0,0  b0,0 
i 0
1  Pt m1
1  Pt
(9)
where b0,0 value can be attained from (7).
The probability  generally depends on the conditional
collision probability Pcol and capture probability Pcap . In our
model, we assume that capture effect is a subset of the
collision events. Thus the conditional collision probability
Pcol that packet collides with other packet transmission in a
given time slot can be expressed as
Pcol  1  (1   )n 1  Pcap
(10)
Our model considers power loss and multi-path fast fading
of the transmitted signal. Suppose the signal is transmitted in
Rayleigh fading channel, then, the received instantaneous
signal power is exponentially distributed as:
f  x 
x
1  P0
e ,
P0
x0
 i
i
here, the value of   Pu /  Pk is the ratio of the power,
k 1
of i interfering frames, denoted by Pk . z0 is the capture ratio
(the signal-to-interference power ratio identifying the capture
threshold at the receiver), and g ( S f ) is the processing gain of
inversely proportional to the spreading factor S f . For Direct
Sequence Spread Spectrum (DSSS) modulation using a fixed
11-chip spreading factor ( S f  11 ), the g ( S f ) can be
expressed as
When Pcap  0 , then (7) can be rewritten as (8).


 
Pcap（  z0 g S f / i)  1 / 1  z0 g S f
the correlation receiver. In fact, the processing gain introduces
a reduction of interference power by factor g (S f ) , which is
(7)

n
A  ri p is the deterministic path loss.
When two or more stations transmit simultaneously, the
capture probability conditioned on i interfering frames can be
defined as follows:
denoted by Pu , of the detected frame to the sum of the power

2(1  2 Pt )(1  Pt )

W (1  (2 P ) m 1 )(1  P )  1  2 P (1  P m 1 )

t
t
t 
t

b0,0  
2(1  2 Pt )(1  Pt )

'
'
'
m' 1
 W (1  (2 Pt )
)(1  Pt )  1  2 Pt  1  Pt m 1   W  2m  Pt m 1 (1  2 Pt )(1  Pt m  m )

where P0 denotes the local mean power determined by the
equation:
n
P0  A  ri p  Pt
n p is the path loss exponent, Pt is the transmitted power, and
g (S f ) 
2
3S f
Probability  also impacts the probability of the frame capture
probability, Pcap can be obtained as following:
n 1
Pcap (z0 , n)   Ri Pcap（  z0 g  S f  / i )
i 1
where, Ri is the probability of i interfering frames of
n contending stations being generated in the observed time
slot, according to
 n  i 1
 (1   ) n 1 i
Ri  
i

1


Let Ptr be the probability that there is
transmission occurs in a randomly chosen slot
denote the successful transmission probability,
sum of the conditional probability that the
occurring on the channel is successful without
with capture effect. Then we have
Ptr  1  (1  )n
n 1   
n 1
Ps 
at least one
time. Let Ps
which is the
transmission
collision and
(11)
 Pcap
1  (1   ) n
(12)
Now we are able to express the normalized system
throughput S of the DCF as the ratio,
Ptr Ps E[ P]
S
(13)
(1  Ptr )  Ptr (1  Ps )Tc  Ptr PsTs
0.7
Pcol ,z0=5dB
Pcol ,z0=10dB
0.6
Pcol ,z0
τ,z0=5dB
0.5
Pcol ,z0
col
,τ
0.4
0.3
0.2
0.1
MODEL VALIDATION AND PERFORMANCE
EVALUATION
5
10
15
20
25
30
number of stations
35
40
45
50
Figure 4. Theoretical behvior of the probability Pcol , 
1
0.9
0.8
normalized throughput
To validate this model, we have compared the theoretical
results with that of obtained NS-2 simulation results. In this
paper, we assume the NS-2 simulator considers a Basic
Service Set (BSS) with an Access Point (AP) scenario in
which n contending stations, which communicates only with
the AP, are randomly distributed in a circular area of radius R
(10 m) and the common access point is placed in the center of
the transmitting area. The network parameters of IEEE
802.11b used in our simulations is summarized in table.1.
Moreover, we assume C min  32 , C max  1024 and m  7 . In
this section, we focus on presenting some simulation and
theoretical results that show the impact of capture effect on the
system capacity.
τ,z0=10dB
τ,z0=30dB
0
0.7
0.6
0.5
0.4
0.3
0.2
TABLE I.
NETWORK PARAMETERS
MAC header
PHY header
ACK
ACK timeout
τd
Slot time 
SIFS
DIFS
Basic rate
Data rate
24 bytes
16 bytes
14 bytes
300μs
1μs
20μs
10μs
50μs
1Mbps
1Mbps
theo-no capture
theo-z 0=6db
0.1
0
5
10
15
20
25
30
number of stations
35
40
45
50
Figure 5. normalized system throughput vs. numbers of contending stations
1
0.9
0.8
n1=5 no capture
normalized throughput
IV.
Pcol ,z0=30dB
P
where Tc and Ts are the average time which the channel is
sensed busy due to a packet collision and a successful packet
transmission, respectively, and E[P] is the average packet
length. For simplicity, the size of all packets is assumed to be
same and fixed, and  is the duration of an idle slot time. Let
us now consider a system that each packet is transmitted by
way
of
the
basic
access
mechanism.
Let
H  PHYhdr  MAChdr indicate packet header, and  d be the
propagation delay.
Then we can have the following expression.
Tc  PHYhdr  MAChdr  E[ P]  ACK timeout

 Ts  PHYhdr  MAChdr  E[ P]  SIFS  ACK  DIFS  2 d
0.7
n2=20 no capture
0.6
n3=50 no capture
0.5
0.4
0.3
0.2
n1=5
0.1
n2=20
n3=50
0
0
5
10
15
20
capture thrshold z 0(dB)
25
30
Figure 6. normalized system throughput vs. capture thresholds
The theoretical behavior of the probabilities Pcol ,  are
depicted in Fig.4 for the basic access mechanism as a function
of the number of contending stations, for four different capture
thresholds z0 .The result shows that the transmission
probability τ decreases as the value of capture thrshold and the
contending stations increase, while the probability of collision
Pcol increases. The curves of collision probability Pcol and
transmission probability τ at z 0  30dB are very closed to the
ones at z0   , this also means that when the capture
threshold is greater than z 0  30dB , the collision
probability Pcol and transmission probability τ will not change
so much. In Fig.5, we can obtain the behavior of the saturation
throughput for the 2-way mechnisam as a function of the
number of contending stations, for the capture theshold
z 0  6dB and without capture effect ( z0   ). Simulation
results are marked by five-pointed star. Through comparing
the curves shown in Fig.5, we easily find that the system
throughput significantly increases under condition of capture
effect, and with the number of contending stations increase,
the throughput decreases. In order to further observe the
impact of capture effect into different contending stations, we
compare the throughput under three values of the number of
contending stations, n1  5 , n 2  20 and n3  50 . Fig.6 shows
the behavior of the saturation throughput as a function of
capture thresholds z0 . From Fig.6 we can see that as the value
of capture thresholds increases, the throughput for the three
numbers of contending stations decreases, but it is greater than
the throughput without capture effect.
V.
CONCLUSION
In this paper, we have presented an analytical model to
evaluate the performance of the IEEE802.11 DCF considering
Rayleigh fading channel induced capture effect and packet
retry limits under saturated conditions. Simulation and
analysis results show that our analytical model can accurately
predict the throughput performance of IEEE 802.11 DCF.
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