1

On the Physical Carrier Sense in Wireless Ad Hoc Networks

Xue Yang and Nitin H. Vaidya
Department of Electrical and Computer Engineering, and
Coordinated Science Laboratory
University of Illinois at Urbana-Champaign
email: xueyang, nhv@uiuc.edu

Technical Report, July 2004

Abstract— The aggregate throughput of a wireless ad

hoc network depends on the channel capacity, channel


overlap in time.). The higher the Signal-to-Interference-
and-Noise-Ratio ( ), the higher rate can packets be
utilization (i.e., the fraction of channel capacity used for transmitted reliably. As a result, the channel capacity be-
generating goodput), and the concurrent transmissions tween a transmitter/receiver pair is a function of channel
allowed in the network. While channel utilization is de-
activities of all stations in the network. On the other
termined by MAC overhead, physical carrier sense has
been used as an effective way to avoid interference and
hand, because of the rapid attenuation of transmitted
exploit spatial reuse. Prior research has attempted to radio signal with distance, concurrent transmissions that
identify the optimal carrier sense range that can maximize reuse the same channel at spatially separated locations
the aggregate throughput. However, the impact of MAC are possible, which leads to co-channel spatial reuse
overhead has been ignored. In this paper, we use both an in wireless networks. The aggregate throughput of a
analytical model and simulation results to show that MAC network depends on both the capacity of each individual
overhead has significant impact on the choice of optimal link and the total amount of concurrent transmissions
carrier sense range. If MAC overhead is not taken into allowed in the network.
account properly in determining the optimal carrier sense
Furthermore, medium access control (MAC) protocols
range, the aggregate throughput can suffer a significant
loss. play an important role in utilizing the link capacity.
In ad hoc networks, which are formed by a group of
Index Terms— System design, Simulations, Wireless ad self-organizing wireless stations without the support of
hoc networks, Physical carrier sense, MAC overhead, access points, stations typically contend for access to
Spatial reuse
the channel in a distributed fashion. Among multiple
stations that contend the channel with each other, when
I. I NTRODUCTION only one makes a transmission attempt, the packet is
delivered successfully; if multiple contending stations
Two fundamental aspects of wireless communication
make transmission attempts simultaneously, collisions
make wireless networks different from wired networks.
may occur. Stations resolve the channel contention ac-
First is the time-variation of the channel strengths due
cording to rules defined by the contention resolution
to the small-scale effect of multipath fading, as well as
algorithm. MAC protocols often introduce overhead that
larger scale effects such as path loss via distance at-
leads to a sub-optimal utilization of the link capacity.
tenuation and shadowing by obstacles. Second, wireless
MAC protocols also govern when concurrent trans-
stations communicate over the air and there is significant
missions may proceed. One representative method is
interference among stations that are spatially close to
based on CSMA (carrier sense multiple access). Carrier
each other.
sense refers to listening to the physical medium to detect
Whether two wireless stations can communicate with
any ongoing transmissions. Only if the radio signal
each other depends on the distance between them, the
strength detected at a station is below a Carrier Sense
terrain, the transmission power used by the transmitter,
etc. Additionally, the quality of the communication link
Threshold, may the attempt of the station to access the


channel proceed. Given a carrier sense threshold  ,

depends on the interference at the receiver caused by
the corresponding Carrier Sense Range  is defined as
other concurrent transmissions in the network (by con-
the minimum distance allowed between two concurrent
current transmissions, we mean the transmissions that
transmitters.
This work is supported in part by the National Science Foundation Prior research has noted the impact of carrier sense
Grant ANI-0125859 and Vodafone Graduate Fellowship. range on the aggregate throughput. That is, the smaller
 2

the carrier sense range, the better the spatial reuse; but method may not work properly in ad hoc networks, as
the interference at a receiver can also increase. Implicitly has been discussed in detail in [4].
assuming a perfect MAC protocol without any overhead, Physical carrier sense can help to avoid the interfer-
Zhu et al. [1] has attempted to identify the optimal ence at a receiver effectively as long as the potential


carrier sense threshold that maximizes the spatial reuse interfering stations are able to sense the radio signal from
given a minimum required for a regular topology. the transmitter. Physical carrier sense can also help to
However, the interactions between carrier sense range control the amount of spatial reuse in the network by
and MAC overhead, as well as their impact on the varying the carrier sense threshold. Zhu et al. [1] has
network aggregate throughput, have not been identified attempted to identify the optimal carrier sense thresh-
by prior research. In this paper, we use both an analytical


old that maximizes the spatial reuse given a minimum
model and simulation results to show that the MAC required for a regular topology. The limitation
overhead has a significant impact on the choice of the of their work lies in that they do not consider the
optimal carrier sense range that maximizes the aggregate MAC overhead as well as the interactions between MAC
throughput. If MAC overhead is not taken into account overhead and the carrier sense range.
properly in determining the optimal carrier sense range, To derive the capacity of wireless networks, Gupta
the aggregate throughput can suffer a significant loss.


and Kumar [5] incorporate the physical channel model
The rest of the paper organized as follows. Section wherein a minimum is necessary for successful
II summarizes the related work. Section III introduces communication. [6] proposes a Honey-grid model to
bandwidth-independent and bandwidth-dependent MAC


calculate the interference level in wireless ad hoc net-
overhead. In Section IV, a analytical model is presented works. The derived expected values of are used to
to explore the impact of MAC overhead on the optimal determine the network capacity and data throughput per
carrier sense range, and associated impact on the ag- node. [7] presents an analytical model to investigate co-
gregate throughput. Section V uses simulation results to channel spatial reuse in dense wireless ad hoc networks
further support our arguments. Finally, conclusions and based on RF propagation models. A common limitation
future work are presented in Section VI. of above works is that they all assume a perfect MAC
protocol with no overhead, which is not practically
II. R ELATED W ORK achievable.
While MAC protocols govern when a station may In this paper, we are interested in exploring the
proceed its transmission attempt, the channel access interactions between MAC and PHY layers, identifying
activities of all stations in the network contribute to the impact of MAC overhead on the choice of optimal
the aggregate interference at a particular receiver, which, carrier sense range, as well as the associated impact on
in turn, determines the performance of MAC protocols. the aggregate throughput.
The inherent interactions between MAC and physical Some research work does consider the impact of phys-
(PHY) layer necessitate considering the MAC and PHY ical layer on MAC layer more explicitly, with a different
characteristics together. However, many prior research objective from this paper. For example, Holland et al. [8]
works have treated MAC and PHY layer characteristics propose a receiver-based rate-adaptive MAC protocol,
separately when discussing the design issues for wireless


in which the link rate between the transmitter/receiver
ad hoc networks. For example, to combat the hidden pair is dynamically chosen based on the level at
terminal problem in ad hoc networks, the earlier work the receiver. Considering the quality variation of wire-
[2] has proposed to use RTS/CTS handshake method, in less links, Sadeghi et al. [9] proposes an opportunistic
which RTS (Request To Send) and CTS (Clear To Send) MAC protocol which sends multiple back-to-back data
frames are exchanged to reserve the channel for subse- packets whenever the channel quality is good to better
quent Data and ACK packets. Stations that overhear the exploit durations of high-quality channel conditions. [10]
RTS/CTS frames defer transmission for a certain period. proposes an enhanced carrier sensing (ECS) scheme to
This method is adopted by IEEE 802.11 DCF [3], and modify the EIFS based deferment in IEEE 802.11 DCF
named as “virtual carrier sense”. RTS/CTS handshake such that the EIFS duration depends on the type of the
works if all stations that may cause interference at a erroneous frame (CTS, Data or ACK). [11] constructs a
receiver are within the transmission range of the receiver. collision model and an interference model to identify the
However, after considering the physical characteristics of optimal transmission power that can yield the maximum
radio signal propagation carefully, it can be shown that throughput and the minimum energy consumption per
many interfering stations can actually locate outside the message. [12] introduces a modeling framework for the
transmission range of the receiver. Therefore, RTS/CTS analytical study of MAC protocols operating in ad hoc
 3

networks. The model explicitly takes into account the bit rate, hence, they also contribute to the bandwidth-
effect of physical-layer parameters on the success of independent overhead.
transmissions. A packet transmission can be corrupted by the
interference at a receiver. In wireless networks, a station
III. BANDWIDTH - INDEPENDENT AND usually can only learn about a transmission failure
BANDWIDTH - DEPENDENT MAC OVERHEAD when the transmission is finished and the expected
MAC overhead can be generally categorized into acknowledgment (in some form) does not come back.
bandwidth-independent overhead and bandwidth- Consequently, a transmission failure will result in
dependent overhead, as pointed out in [13]. Specifically, the loss of entire packet transmission duration, which
if the channel time consumed by an overhead is depends on the packet size and the channel bit rate.
independent of the channel bit rate, the overhead is Therefore, the overhead associated with transmission
defined as bandwidth-independent overhead; otherwise, failures is bandwidth-dependent overhead.
it is bandwidth-dependent overhead1.
Consider one of the standards for wireless networks, One key property of bandwidth-independent overhead
IEEE 802.11 WLAN [3], as an example. Different phys- is that, the larger the channel bit rate, the more the per-
ical layer specifications are defined in IEEE 802.11. Di- centage of wasted channel capacity. Let  (in seconds)
rect sequence spread spectrum (DSSS) system (802.11b) 
represent the duration of channel time occupied by the
provides 1 Mbps, 2 Mbps, 5.5 Mbps and 11 Mbps data bandwidth-independent overhead, be the channel bit
transmission rates, operating in the 2.4 GHz ISM band rate (in bits per second or bps) and   be the payload
[14]. To allow the IEEE 802.11 MAC to operate with  (in bits) associated with the overhead. Accordingly,
size
minimum dependence on the physical layer, a physical  fraction of the channel capacity is wasted in the
layer convergence procedure (PLCP) is defined. PLCP 
bandwidth-independent overhead. Clearly, the smaller
preamble and header aid receivers in demodulation and the , the less the channel wastage.
delivery of transmitted data units from MAC layer. Alternatively, given a modulation scheme, channel bit
For each data unit transmitted by MAC layer, 192   rate is proportional to the channel bandwidth. For a given
additional channel time is consumed by PLCP preamble packet size, the bandwidth-independent overhead can be
and header. Orthogonal frequency division multiplexing reduced by associating it with a channel with a smaller
(OFDM) system (802.11a) operating in the 5 GHz band bandwidth. That is, by splitting a channel into multiple
provides data payload communication rates from 6 Mbps sub-channels, the utilization of each sub-channel may
to 54 Mbps [15], with PLCP preamble and header get improved due to the reduced channel wastage in
overhead of 20   associated with each MAC layer data the bandwidth-independent overhead, which can lead to
unit transmitted. For both DSSS and OFDM systems, an improved aggregate throughput over all sub-channels,
the channel time consumed by PLCP preamble and comparing with using a single channel. An earlier paper
header is independent of the channel bit rate, resulting [16] implicitly applied such an idea to mutli-channel
in bandwidth-independent overhead. wired networks.
In one of the MAC layer sub-functions, IEEE 802.11 In wireless ad hoc networks, motivated by this ob-
DCF (Distributed Coordinated Function), a station want- servation, we can let a wireless link operate at a lower
ing to access the channel has to wait the channel to be bit rate to improve the utilization of the single channel.
idle for an “interframe space (IFS)” duration. After that, Here, channel utilization is defined as the fraction of
a backoff procedure is invoked and a backoff counter channel capacity used for generating goodput. At the
is randomly chosen from the range of [0, CW] (CW 

same time, since a lower bit rate usually requires less
represents the contention window). This backoff counter , more interference can be tolerated at the receiver
corresponds to the number of idle slots this station has given the signal strength of the intended signal. As
to wait before its transmission attempt. Since the slot a result, more concurrent transmissions can proceed
time is determined by the propagation delay and the and more spatial reuse can be exploited. The aggregate
transceiver’s turnaround time2 , the interframe space and throughput can be improved due to the following two
the backoff durations are independent of the channel reasons:
 Despite operating at a lower rate, each wireless link
1
We follow the terms used in [13] here. However, it is probably can be utilized more efficiently because a smaller
more accurate to name them as rate-independent and rate-dependent
overhead under the context we consider in this paper.
fraction of channel capacity is wasted in MAC
2 overhead.
The turnaround time is the delay associated with the transceiver
in switching between transmitting and receiving modes.  More concurrent transmissions are allowed in the
 4

network. As illustrated in Figure 1, three concurrent a tradeoff implies that there exists an optimal carrier
transmissions are allowed in scenario (b), while sense range that maximizes the aggregate throughput.
only two are allowed in scenario (a). The increased
aggregate throughput can result from more concur-
A. Interference Model
rent transmissions, even though the absolute rate of


each individual link is lower. We first derive the worst case interference and
at a receiver station. The radio propagation model used
in this paper is given by:

Low Rate Links
"!$#&% ')(
High Rate Link
High Rate Link
where "!$# is the received signal strength given the
transmission power  , ' is the distance between the
(a) (b) transmitter and receiver, and * is the path loss coefficient,
ranging from 2 (free space) to 4 (indoor) [17].
Fig. 1. More concurrent transmissions +
As shown in Figure 2(a), when a source station
,
is transmitting, a concurrent transmission can happen
only at a station, say , that is distance  away from
By extending above concepts to MAC protocols using +
station , constrained by the carrier sense range of  .
physical carrier sense, we show in the rest of this paper -+ ",
that, not only the bandwidth-independent overhead but Moreover, when stations and are transmitting at
also the bandwidth-dependent overhead can be reduced the same time, the next concurrent transmission can only
come from stations that are distance  away from both
by applying a smaller carrier sense range, which, in + , /.
turn, affects the choice of optimal carrier sense range and , say . Defining the concurrent transmitting
for wireless ad hoc networks. stations that are 01 (where 0 is
-+ 
an integer and 03254 )
as the 0  tier interfering stations
6+
distance away from
for , there are at most six 487 tier interfering stations,
IV. O PTIMAL C ARRIER S ENSE R ANGE
as illustrated in Figure 2(a).
In this section, we develop an analytical model to The spatial reuse in ad hoc networks is very similar
derive the optimal carrier sense range with and without to that in cellular networks. In the cellular system, co-
considering MAC overhead. In the model, a dense net- channel cells in a given coverage area can reuse the same
work is assumed and wireless stations are uniformly and set of frequencies. To reduce the co-channel interference,
independently distributed in an area of  . A common and co-channel cells must be physically separated by a
fixed transmission power  is used by each transmitter. minimum distance to provide sufficient isolation [18].
The minimum received signal strength that invokes the Among the six 4 7 tier interfering stations, it has been


packet receiving procedure at a receiver is defined as

&+
shown in [19] in the context of cell planning in cellular
 

Receiving Signal Threshold, denoted as . Given networks that, with a receiving station, , at the edge

the value of , the Maximum Transmission Range of the transmission range, the worst case interference
, which is defined as the maximum possible distance

comes from the two nearest interfering stations that are
between the transmitter and receiver, can be determined :9 <;)=
away from the receiving station, and four other
<;)=
accordingly based on the radio propagation model. The interfering stations that are exactly 9 ,  , ?>
 ,


link capacity between the transmitter/receiver pair de- @> , respectively, away from the receiving station, as
pends on at the receiver. illustrated in Figure 2(b).
Two concurrent transmissions may occur if and only Both [20] and [21] have observed the fact that the
if the distance between the two transmitters is larger than received power at a receiver station from the nearest
the carrier sense range  . The larger the carrier sense

 neighbor is of the same order as the total interference
range, the less the interference and the better the from  the entire network. As the interference from the
at the receiver. Consequently, the wireless link between 4A7 tier interfering stations dominates,=CB)D we neglect the
the transmitter/receiver pair can operate at a higher rate. remaining interference from the tier or further away
On the other hand, a large carrier sense range may
severely limit the aggregate throughput since each station
&+
interfering stations. As such, the worst case interference
at the receiving station can be expressed as below.
becomes too conservative in initiating a transmission and E8FHGJILKAMNIOKPIOFRQSIUT XZYV1[]W \H^`_Ua XZY[W b c^d_ a Y W e
_ a XfY-ghW b c^d_ a XZY-gRW \H^`_
the number of concurrent transmissions decreases. Such
 5

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S5 . .S4
S5
. .
S4
„ƒ po D nm |{
kOlk
D+R D+R/2

…O†… rOq rq iOji .

S0 D D
S6 . . . S3 R
. . .S3
wx Oy zy
S6
S0
D−R/2 R
D D D

S1
. D
.
S2
D−R
R0
D−R ‡Oˆ ‡ˆ st uv
S1
. .S2
‰Š ‹OŒO‹Œ OŽ

(a) Nearest concurrent transmis- (b) The first tier interfering sta- (c) Multiple concurrent trans-
sions tions missions

Fig. 2. Interference model

 + .
transmitters,  is proportional
As the receiving station (in Figure 2(b)) is po-
 +7 . + to  and we represent
+
sitioned at the edge of the transmission range (i.e.,  7 as  7 %± ¯  , where  ;)is=3² a constant
+² ;)=
depending
on the size of the network ( ® ¬  ¬ ® ¬ ).
+
distance away from the transmitter ), it has the weak-
est receiving signal strength (within


’s transmission As we are interested in the maximum achievable
+
range). The corresponding worst case
 at the aggregate throughput, a busy network is assumed in
receiving station is shown below, where %  which each station is always backlogged and it will
(note that the background noise is ignored here since we initiate a transmission whenever it is allowed. With a per-
mainly concern an interference limited environment). fect MAC scheduling algorithm without any overhead,
each communication link can be fully utilized and the
 network aggregate throughput denoted as ³™ 'O´›µ   can

 .  _
%     be represented as:
‘ “ _ > ‘ bc “ _ > _ > ‘ bc “ _ > ‘ •“ _
U’ U’   ”  ”
. , 4, , ,  
% , “ _ > ‘Z– ,“_ ™ 'O´›µ  ¶% <™Ršœ6œ Až š ¡e¯
‘Z– c “ _ > – _ > f‘ – c “ _ > Z‘ – 
 <7 «
’ ’e— ” —
˜ ” , ¥· ª 4e> .
(1) %  ¯  (2)

where ¸ accounts for the total number of concurrent

B. Optimal Carrier Sense Range without MAC Over- ¸¹ ,
edge effect), and  is a constant
transmissions
, (ignoring . c
defined as  % ½N¾ º¼» ¸  .
head

 »À¿ÂÁ » 1 into Equation 2, we can then
Given a certain , we use Shannon capacity as Substituting Equation
the achievable channel rate, i.e.,
 
<«

identify how the aggregate throughput changes with the
&™›šœ6œ Ÿž š  ¡¢%¤£¦¥¨§C©
. ªU
4 > 
<«
value of carrier sense range. When
ª

is very small,
¥· 4U> 
increases nearly linearly with
 ,
where £ is the channel bandwidth in hertz and an which, in turn, increases fast with . A larger


leads
additive white Gaussian noise channel is assumed [22]. to a higher throughput. On the other hand, when
ª
<«
is very large, the logarithmic increase of ¥· 4U>
Since the minimum separating distance between two


concurrent transmissions is  , each transmitter “con- with respect to

implies that the throughput will
sumes” a certain area  . On one extreme, when there is
7 
begin to decrease with the further increase of . Based
. ;)=
only one transmitter in the network, it is straightforward on Equation 2, the optimal values of that maximize
to see that  ­
% 
¬ ® °
¬ 
¯ 
7 . On the other extreme, the aggregate throughput are solved for various values of
with an infinite number of concurrent transmitters, a * , and are plotted in Figure 3. X axis represents the path
triangle area, as highlighted in Figure 2(c), is shared by loss coefficient * , while y axis represents the optimal X
3 concurrent transmitters and each transmitter shares. six corresponding to each * . The results suggest that, without
;)=
such triangles. Consequently, we have 
7 % ® ¬) . considering the MAC overhead, the optimal carrier sense
In a network with an arbitrary number of concurrent range  should be 3.3 times the maximum transmission
 6

 
when * %Äà , be 3.2 times * %Ŭ 1) With Bandwidth-independent Overhead Only ( šã
range
 = when , and
be 2.7 times when *<% . ß ,ä
Ç %åß ): The first sub-case we consider is that there is
only bandwidth-independent MAC overhead.
3.5
As we discussed in Section III, when multiple stations
3 compete for a common channel, the smaller the channel
bit rate, the smaller fraction of channel capacity is wasted
Optimum value of X

2.5

2 in associated bandwidth-independent overhead and the

1.5
better the channel utilization. At the same time, since


1
a lower bit rate typically requires less , more
interference can be tolerated and more concurrent trans-
0.5
missions are allowed. Even though each communication
0
2 2.5 3
θ
3.5 4 link operates at a lower bit rate, the aggregate throughput
may be improved due to a better channel utilization and
Fig. 3. Optimal X without MAC overhead the improved spatial reuse. Therefore, we expect the
optimal carrier sense range with bandwidth-independent
overhead to be smaller compared with the case where
no MAC overhead is considered.
The same conclusion can be reached by observing
C. Optimal Carrier Sense Range with MAC Overhead Equation 3. With š±ãæß and Çç%èß , we have a non-
zero à¢á , . Comparing Equations 3 and 2, because the item
Now we consider the impact of MAC overhead on the ‘Ùéê ë ì8í Ð
b ò “ increases slower than ¥· ª 4e> 
<«
values of optimal carrier sense range. Let Æ represent the ”
packet pay load size (in bits). To schedule a successful
îS— ïñð
with the— Î)increase of X, the optimal value of X resulting
packet transmission, the associated bandwidth-dependent from Equation 3 is smaller than that obtained from
overhead, denoted by Ç (bits), and the bandwidth- Equation 2. 
independent overhead, denoted by š (seconds), are in- Based on Equation 3, the optimal values of that
troduced by MAC layer. =]õ õ
maximize the aggregate throughput are obtained for the
cases of àâáó% ßNô ßNô÷ö 4 hertz/bps, and are plotted
The aggregate throughput can thus be represented as:
in Figure 4. The curve with no MAC overhead (i.e.,
Æ  à¢áø% ß ) from Figure 3 is also shown here for the
³™ 'O´›µ  È% A

Ë Ë S  ¯
š&> ½ 8B É B)”/Ì Ê   Ì  7
purpose of comparison. To have a sense for what could
be the practical values for à³á , we can do some simple
calculations here for IEEE 802.11a. In 802.11a, the
Ë Ê  PLCP preamble and header consume 20   for each
” Ñ)ÒÀÓÕÔÖÍÔOÎÐ× Ï b ÓJØÙ×
where is the actual throughput obtained
transmitted data packet, and the SIFS is 16   . The
by each transmitter/receiver pair and ¸ reflects the
¸ ¹ Simplifying
total number of concurrent transmissions.
bandwidth occupied by each channel is 16.6 MHz (i.e.,
£ = 16.6 MHz); the slot time is 9   = . Assuming the
the above equation, we have
payload size Æ is 512 bytes, then à³á-%åßNô 4 when there is
no backoff slot, and à á %åßNô÷ùC¬ with eight backoff slots.
, Æ 4 , 802.11b can have larger àâá because of a longer PLCP
³™ 'O´›µ  ¶%  ¯ ¯ ª‘ Ë “ . “ «1
.
Ç>ÚÆ º > ‘, preamble and header, as well as a longer slot time.
É ”/Ê ¿ÂÁ ¿ Á ”6ÛÜLÝ From Figure 4, we can see that, with the increase of
(3) à á , the optimal value of X decreases for various values
, of * . Particularly, when *ú%¦Ã , the optimal X is 3.3,
 is the same constant item defined in Equation 2. 2.9, 2.6, 2.4 for àâá = 0, 0.2, 0.5, 1 hertz/bps, respectively.
Notice that when šÞ%Äß and Ç%Äß , Equation 3 reduces
to Equation 2. Ë 2) With both Bandwidth-independent and Bandwidth-
Let à¢á denote the term ‘ º “ . in Equation 3. dependent Overhead (šÚãûß , Ç?ãüß ): Now we further
The unit of àâá is hertz/bps.É ”/WeÊ ¿ÂÁ can see that àâá consider the sub-case in which both the bandwidth-
reflects the ratio of the wasted channel spectrum in independent and bandwidth-dependent MAC overhead
bandwidth-independent overhead over the sum of the exist. From now on, we strictly differentiate the term
bandwidth-dependent overhead and the payload. concurrent transmissions from the term simultaneous
transmissions. Concurrent transmissions refer to trans-
 7

3.5
In many MAC protocols (e.g., IEEE 802.11 DCF), the
3
probability of simultaneous transmissions (i.e., collision

Optimum Value of X
2.5
probability) increases with the total number of contend-
2
O =0
ing stations. As illustrated in Figure 5, when reducing
i
1.5 O = 0.2
i
Oi = 0.5
the carrier sense range from D to D’, the number of con-
1
Oi = 1
tending stations inside the carrier sense range reduces,
0.5 which leads to the reduced collision probability with S0,
0
thus, less retransmissions and less bandwidth-dependent
2 2.5 3 3.5 4
θ overhead (recall that interference from concurrent trans-
mitters outside the carrier sense range is accounted for
Fig. 4. Optimal X with bandwidth-independent overhead
when choosing the bit rate). The reduced bandwidth-
dependent overhead at a smaller carrier sense range can
further affect the choice of optimal carrier sense range,
missions that overlap in time, while simultaneous trans- making it even smaller compared with the cases that do
missions refer to the transmissions that start within a not consider the bandwidth-dependent overhead.
short period (i.e., the propagation delay and carrier sense As the probability of collision varies with different
delay) before the carrier can be detected. MAC protocols, a MAC protocol needs to be specified
For a receiver, there are mainly two sources of in- in order to have numerical comparisons. In the following,
terference. One interference source is the concurrent we assume a ´ -persistent MAC protocol, in which,
transmissions from transmitters outside the carrier sense at each time slot, a station chooses to transmit with
range. As illustrated in Figure 5, with a carrier sense probability ´ 3 .
range of D, the stations that are outside the outer circle In Equation 3, the bandwidth-dependent overhead Ç
are allowed to transmit at the same time when S0 is depends on the collision probability, which, in turn, de-
transmitting, which causes interference at S0’s receiver. pends on the choice of X. Given M contending stations,
The other interference source results from what we
 ÿ of collisions per transmission cycle,
the average number
usually refer to as collisions, when the simultaneous denoted as ýþ
transmission attempts from transmitters inside the carrier Ê
, is derived in [23] as follows.
«

sense range occur. For example, in Figure 5, if S0 has  ÿ 4ä9 ª 4˜9 ‘ ´
ýþ Ê %  ´ ª 4ä9 ´ «  ú « 9ú4)ô (4)
already begun its transmission, the stations that are inside 9 4
the carrier sense range D can sense the busy channel
and defer their transmissions; but if they start their  .
Assuming that there are k stations per transmission
transmissions simultaneously with S0, S0’s transmission area 

(i.e., the area covered by the maximum trans-
will be interfered by them. mission range ), the number of contending stations M
given the carrier sense range D can be represented as
.
 6 .
  .
%   %  (5)

D
Recall that Æ represents the payload size. As each
S0 collision lasts for the payload transmission duration (we
D’ ignore propagation delay and carrier sense delay here for
simplicity), we have
 ÿ  ÿ «
Ç >øÆ¢%åý þ Ê ¯hÆh>ÚÆä% ª ýþ Ê >ó4 ¯UÆ (6)

Fig. 5. The impact of carrier sense range on bandwidth-dependent

Let šá B  be the bandwidth-independent overhead
overhead associated with each transmission attempt. The total
ª  ÿ 4 overhead
bandwidth-independent
« B š can thus be repre-
sented as š3Ë % ýþ Ë >3 š á à á can be represented
. % Ê ê Ô
º . . à˜á can be regarded as a fixed
, and
as à¢á % ‘ º “
When reducing the carrier sense range, the increased

 É ”/Êvarying
¿ÂÁ Ç ÊAif¿ÂÁ š]á B changes little with Ç , which
interference from concurrent transmissions is taken into
value when
account when we estimate at the receiver and
is the case we consider here.
choose a communication link rate accordingly; but the
interference from simultaneous transmitters inside the 3
[23] shows that IEEE 802.11 DCF can be nicely modeled as a
carrier sense range has not been taken into account.  -persistent protocol.
 8

=
=
By substituting Equations 4, 5, and 6 into Equation 3, ßNô÷öand ±% ß (with both bandwidth-dependent and
letting ´ %ÅßNô ß and àâá = 0.5 hertz/bps, the optimal X bandwidth-independent overhead but different transmit-
ter densities), we plot the aggregate throughput ³™ 'O´›µ  
=
that maximizes the aggregate throughput for the cases of
=
 %@ö and  % ß are plotted in Figure 6, along with the vs. in Figure 7, assuming * % Ã and ´ %ûßNô ß . The
two curves from Figure 4 with à á %:ß and à á % ßNô÷ö , obtained throughput is normalized to the maximum value
where no bandwidth-dependent overhead is considered. in the plot.
As we can see, the optimal X decreases with the From Figure 7, we can see that, if carrier sense
increase of channel contention (when k is increased from threshold is not adjusted according to the MAC overhead,
5 to 20). Particularly, when * %åà , the optimal X is 2.4 the aggregate throughput suffers. Particularly, when ap-
=
for ¼%@ö and 2.1 for  % ß . õ When compared with the plying the optimal carrier sense threshold with no MAC
optimal X = 3.3 when àâá %åß Ç˜%åß , and the optimal X overhead to the case àâá<% ßNô÷ö and ÇÞ%æß , the aggre-
õ
= 2.6 when à á % ßNô÷ö Ç3%ûß , we can also observe that gate throughput degrades about 15% compared with the
the optimal X is even smaller when bandwidth-dependent achievable peak throughput; when it is applied to the
overhead is taken into account. case à¢á?%ÈßNô÷ö and  % ö , the aggregate throughput
degrades as much as 49% compared with the achievable
3.5
peak throughput; the aggregate throughput suffers even
=
3
more when it is applied to the case à³á %åßNô÷ö and  % ß.
Optimum Value of X

2.5

1
2 Oi = 0, b = 0
0.9 O = 0.5, b = 0
i
Oi = 0.5, b > 0, k = 5

Normalized Aggregate Througput

1.5 O = 0, b = 0 0.8 Oi = 0.5, b > 0, k = 20
i
O = 0.5, b = 0
i 0.7
1 Oi = 0.5, b > 0, k = 5
Oi = 0.5, b > 0, k = 20 0.6
0.5
0.5

0 0.4
2 2.5 3 3.5 4
θ 0.3

0.2

Fig. 6. Optimal X with bandwidth-independent and bandwidth- 0.1

dependent overhead 0
−40 −35 −30 −25 −20 −15 −10 −5 0
β (dB)

Fig. 7. Aggregate throughput with bandwidth-independent and

bandwidth-dependent overhead
D. Impact on Aggregate Throughput
Above discussions suggest that the overhead intro-
duced by MAC layer leads to a smaller choice for the V. D ISCRETE M ULTI - RATE W IRELESS N ETWORK
optimal carrier sense range. The carrier sense range is a Some assumptions used by the analysis in Section IV
concept introduced for ease of understanding. In practical may not be feasible in real systems. For example, a very
-

systems, a wireless transceiver determines the channel dense network has been assumed such that a source sta-
status based on the carrier sense threshold  and it tion is always available at any desired place to exploit the
does not know the carrier sense range itself. Therefore, potential spatial reuse. In real networks, source stations
from now on, our discussions will be based on carrier are usually separated by a certain distance. Additionally,
sense threshold instead of carrier sense range. Notice that
a larger carrier sense threshold leads to a smaller carrier


by applying Shannon capacity formula, the link rate is
a continuous function of at the receiver. But,
sense range.
/
 3
  _ ½ ØÙÒ typically, a wireless transceiver in practical use only
,ª Given  % _ and
½ ØÙÒ % , we have  – Û ØÙÒ %
« ( 
– . Defining %  – Û ØfÒ , Equation 3 can be rewritten
 

provides multiple discrete rate levels. Each link rate has

as
a minimum required (i.e.,


threshold). The
higher the rate, the higher the corresponding
threshold.
c
, Æ 4 ,
³™ 'O´›µ _ In this section, we use simulations to further study the
  %± ¯ ¯ ‘, “ « ¯ (7)
Ç>ÚÆ à á > validity of our arguments in discrete multi-rate wireless
¿ÂÁ ”6ÛÜLÝ networks. The simulations are performed using ns-2
For the cases of àâá¢%:ß and Ç % ß (no MAC over- simulator version 2.26. In this version of ns-2, each
head), à¢á %åßNô÷ö and Ç %@ß (with bandwidth-independent individual interfering signal picked up by a receiver is
overhead only), àâá %ûßNô÷ö and  %ûö , as well as à¢áä% treated separately to determine whether it will interrupt
 9

3

Rates (Mbps)  (dB) Modulation Coding Rate

corresponds to the maximum transmission range R
54 24.56 64-QAM 3/4 = 35 meters. Note that symmetric topologies help us to il-
48 24.05 64-QAM 2/3 lustrate the issues discussed earlier. Also, in a symmetric
36 18.80 16-QAM 3/4 topology, it is appropriate to use identical carrier sense
24 17.04 16-QAM 1/2
threshold at all stations. In arbitrary topologies, each
18 10.79 QPSK 3/4
12 9.03 QPSK 1/2 station may have its own optimal carrier sense threshold
9 7.78 BPSK 3/4 depending on its neighborhood.
6 6.02 BPSK 1/2  

 
TABLE I !
!!! 
F OR BER S LESS THAN OR EQUAL TO 1 E -5, THE MINIMUM 350 meters

REQUIRED  CORRESPONDING TO EACH DATA RATE 

 
 

$ % 35 meters
"#" #"#"
# $$%$
 
the receiver’s current reception or not. However, even 
though a single interfering signal may not strong enough
to interfere, collectively, the aggregate interference from Fig. 8. Circular Topology with N = 8
many concurrent transmissions might do. Therefore, we
made the necessary modifications to the related mod- Figure 9 presents the aggregate throughput for the
ules of ns-2 so that the interference from all concur- topologies with N = 3, 8 and 32, respectively. In each


rent/simultaneous transmissions will be accumulated to
½ ØfÒ packet size is 2048 bytes; x axis repre-
plot, the payload
calculate the at a receiver. Two-ray ground radio sents %  – Û ØfÒ in dB (i.e., 4Pß ¥¨§C© ) and is proportional
-

propagation model is used in the simulations. to the value of the carrier sense threshold (  ); y axis
The physical layer characteristics used in the simula- represents the aggregate throughput in the unit of Mbps.


tions follow the specifications of IEEE 802.11a, where As we can observe from Figure 9(a), with only three
the threshold required for each data rate is listed transmitters in the network, the maximum throughput
in Table I [24]. Notice that the same modulation scheme is achieved when operating at the highest data rate 54
(64-QAM) is applied to both data rates of 54 Mbps Mbps with 2 9¢¬Cù'&)( . Interestingly, when the total


and 48 Mbps. The different data rates only result from number of transmitters is increased to 8, the maximum
different coding rates, which explains why the
=C=
throughput is obtained when the link data rate is set to


thresholds of 54 Mbps and 48 Mbps are very close. Due 36 Mbps and 2 9 &*( , as shown in Figure 9(b).
to their close thresholds, the data rates of 54 Further increasing the total number of transmitters to
Mbps and 48 Mbps show similar performance trends for 32, the maximum throughput is then achieved when the
the issues we are interested in. Thus, we only present the link data rate is set to 18 Mbps and % 9&4Pß+&*( , which
results of 54 Mbps for clarity. Similarly, we present the is illustrated in Figure 9(c).
results of 36 Mbps from the pair of 36 and 24 Mbps, 18 Retransmissions lead to the bandwidth-dependent
Mbps from the pair of 18 and 12 Mbps, 9 Mbps from MAC overhead. Increasing the number of transmitters
the pair of 9 and 6 Mbps. from 3 to 8 to 32, the channel contention increases. With
The MAC protocol used follows the specifications of 3 transmitters in the network, there is no retransmis-
IEEE 802.11 DCF. As we are interested in the maxi- sion occurring (i.e., no bandwidth-dependent overhead).
mum achievable aggregate throughput, Constant Bit Rate When it goes to 32 transmitters, many retransmissions
(CBR) traffic is used and the traffic sending rate is ag- occur at each communication link, which leads to a
gressively enough to keep each source station constantly significant amount of bandwidth-dependent overhead.
backlogged. The simulated topology is a symmetric The observations from Figure 9 agree with the analysis
circular topology, in which N transmitters are evenly results we obtained in Section IV-C.2: the optimal carrier
distributed along a circle with a radius of 350 meters. sense threshold increases (i.e., optimal carrier sense
The receiver corresponding to a transmitter locates on the range decreases) when bandwidth-dependent overhead
line from the transmitter to the center of the circle, and is increases.
35 meter away from the transmitter. One example of the Now we examine each simulated topology more care-
simulated topology with N = 8 (i.e., eight transmitters) is fully. Using the topology with only three transmitters
shown in Figure 8. The chosen signal receiving threshold (Figure 9(a)) and choosing % 9â¬Cù'&*( , all three
 10

250 250 250

Rate = 9 Mbps Rate = 9 Mbps Rate = 9 Mbps
Rate = 18 Mbps Rate = 18 Mbps Rate = 18 Mbps
Rate = 36 Mbps Rate = 36 Mbps Rate = 36 Mbps
200 200 200
Aggregate Throughput (Mbps)

Rate = 54 Mbps

Aggregate Throughput (Mbps)

Rate = 54 Mbps

Aggregate Throughput (Mbps)

Rate = 54 Mbps

150 150 150

100 100 100

50 50 50

placements PSfrag replacements PSfrag replacements

0 0 0
-45 -43 -40 -36
,.-0/214-26
-32
3 57698;:
-22-20
3 5 (dB)-17-15 -10 -6 -3 -45 -43 -40 -36
,.-)/<14-26
-32
3 57698;:
-22-20
3 5 (dB)
-17 -15 -10 -6 -3 -45 -43 -40 -36
,.-0/214-26
-32
3 57698;:
-22-20
3 5 (dB)-17-15 -10 -6 -3

(a) N = 3 (b) N = 8 (c) N = 32

Fig. 9. Aggregate throughput vs. = (Packet Size: 2048 bytes)


transmitters can transmit concurrently and at retransmissions experienced by each communication link
each receiver meets the requirements for all data rates. are further illustrated in Figure 10. Figure 10(a) repeats
Increasing further does not change the performance the aggregate throughput presented in Figure 9(c), except
since there are no more transmitters in the network. that the peak throughput positions for link rates of 54, 36,
Hence, the curve remains flat for 2 9¢¬Cù'&)( . With 18 Mbps are marked as Pos A (link rate is 54 Mbps, %
= =C=
three concurrent transmissions, the throughput obtained 9 ù'&)( ), Pos B (link rate is 36 Mbps, ç%Å9 &)( ) and
by each transmitter/receiver pair is 34.3, 25.71, 14.67, Pos C (link rate is 18 Mbps, %Å9&4Pß+&*( ), respectively.
7.89 Mbps, corresponding to the link rate of 54, 36, The average number of retransmissions (per second)
18, 9 Mbps, respectively. The channel utilization of each normalized by the average number of concurrent trans-
communication link is thus 0.635, 0.714, 0.815, 0.977, missions is plotted in Figure 10(b). As we can see, at
corresponding to the link rate of 54, 36, 18, 9 Mbps, a lower link rate, not only the bandwidth-independent
respectively. As there is no retransmission occurring, overhead is smaller (revealed by the better channel
the improved channel utilization at a lower link rate is utilization we calculated for Figure 9(a) where there is
mainly due to the reduced bandwidth-independent over- no retransmissions), but also the bandwidth-dependent
head. However, since the amount of spatial reuse is same overhead associated with retransmissions is smaller. As
for all data rates, and the improved channel utilization we explained in Section IV-C.2, the corruption of the
at the lower link rates is not enough to compensate for transmitted packet is mainly caused by two sources of
the reduction of the absolute link rate, in this particular interference. One is the concurrent transmissions from
topology, the maximum aggregate throughput is achieved transmitters outside the carrier sense range. The other is
when the communication operates at the highest rate 54 the simultaneous transmission attempts from transmitters
Mbps. inside the carrier sense range. When using a smaller
In the topology with eight transmitters (Figure 9(b)), carrier sense range, the interference from concurrent
=
the peak throughput using the data rate of 54 Mbps transmitters outside the carrier sense range will increase,
occurs at the point % 9 ù'&)( , where on average but the probability of being interfered by simultaneous


approximately four concurrent transmissions are allowed transmitters inside the carrier sense range will decrease
to meet the minimum requirement. On the other because of a smaller number of such stations.
hand, using the data rates of 36, 18, 9 Mbps, all eight By operating at a lower link rate, the increased inter-
=C=
transmitters are allowed to transmit concurrently without ference from concurrent transmissions due to the use of
interfering with each other when Ú2Ä9 &)( . Because


a smaller carrier sense range is already priced in, since a
of the improved channel utilization for each individ- lower link rate requires a lower threshold. Bene-
ual communication link, and the increased number of fiting from the reduced probability of being interfered by
concurrent transmissions, the peak aggregate throughput simultaneous transmitters inside the carrier sense range,
using the link rate of 36 Mbps is 1.5 times that obtained the number of retransmissions experienced at Pos C is
using the link rate of 54 Mbps, even though the absolute much smaller than that at both Pos B and Pos A.
link rate is lower (36 Mbps vs. 54 Mbps). The average number of concurrent transmissions oc-
For the topology with 32 transmitters, the average curred is 5.3 at Pos A, 7.1 at Pos B, 14.6 at Pos C,
number of concurrent transmissions and the amount of as shown in Figure 10(c). We can see that increased
 11

250 20

Number of Retransmissions per Communication Link

Pos C
Rate = 9 Mbps Rate = 9 Mbps Rate = 9 Mbps
Rate = 18 Mbps Pos B Rate = 18 Mbps Rate = 18 Mbps

Number of Concurrent Transmissions

Rate = 36 Mbps Pos A Rate = 36 Mbps Rate = 36 Mbps
200
Aggregate Throughput (Mbps)

Rate = 54 Mbps Rate = 54 Mbps Rate = 54 Mbps

1000 15
Pos A

150 Pos C
Pos B
10
Pos C
100
100

5
50 Pos B
Pos A
placements PSfrag replacements PSfrag replacements
0 10 0
-45 -43 -40 -36
,.-0/214-26
-32
3 57698;:
-22-20
3 5 (dB)-17-15 -10 -6 -3 -45-43 -40 -36
,.-)/21>-26
-32
3 57698;:
3 5 (dB)
-22-20 -17-15 -10 -6 -3 -45 -43 -40 -36
,-0/21>-26
-32
3 57698;:
-223 5 -20(dB)-17 -15 -10 -6 -3

(a) Aggregate throughput (Mbps) (b) The average number of retransmissions (c) The average number of concurrent
per communication link (per second) transmissions

Fig. 10. Elaboration on the topology with N = 32

carrier sense threshold largely increases the spatial reuse. ç% 9¢ù'&*( (marked as Pos Z), compared with the peak

Because of the improved spatial reuse, the reduced point %Å9&4Pß+&)( in Figure 10(a) (Pos C).
bandwidth-dependent and bandwidth-independent over- With the decrease of payload sizes, a greater
head at each communication link, the peak throughput throughput gap can also be observed among the peak
achieved at Pos C is 1.14 times that at Pos B and 1.19 points at different rates. In Figure 11(a), the throughput
times that at Pos C, even though the absolute link rate at Pos F is 1.25 times the throughput at Pos E, and
at Pos C (18 Mbps) is only 1/2 of the link rate at Pos B 1.48 times the throughput at Pos D. In Figure 11(b), the
(36 Mbps) and 1/3 of the link rate at Pos A (54 Mbps). throughput at Pos Z is 1.59 times the throughput at Pos
Similar simulations are performed for payload packet Y, and 2.23 times the throughput at Pos X.
sizes of 512 bytes and 20 bytes. By reducing the
payload size, the fraction of the link capacity wasted In summary, when applying a larger carrier sense
in bandwidth-independent overhead (due to physical threshold and operating at a lower link rate, the
preamble and header, interframe space and MAC layer bandwidth-dependent and bandwidth-independent MAC
backoff slots) increases. Figures 11(a) and 11(b) plot the overhead decreases and the channel utilization improves.
aggregate throughput vs. (in dB) for the topology of As long as the source stations in the network can exploit
N = 32, with packet sizes of 512 bytes and 20 bytes, the spatial reuse available in the network, we expect
respectively (recall that Figure 10(a) plots similar results that the optimal carrier sense threshold that maximizes
for packet size of 2048 bytes). Comparing the positions the aggregate throughput is larger (i.e., optimal carrier
having peak throughput in Figures 10(a), 11(a) and sense range is smaller), compared with the case in which
11(b), we can see a gradual trend of the optimal and the MAC overhead is not considered. As we mentioned
therefore, the optimal carrier sense threshold, increasing in Section II, the existing research work does not con-
with the decrease of packet size (i.e., the increase of sider the impact of MAC overhead when discussing the
bandwidth-independent overhead). This observation is optimal carrier sense threshold, which can lead to a
consistent with the analytical results in Section IV- significant throughput loss.
C.1: the optimal carrier sense threshold increases (i.e.,
optimal carrier sense range decreases) when bandwidth- VI. C ONCLUSIONS AND F UTURE W ORK
independent overhead increases.
The difference is more visible by comparing Figures The key observations in this paper are:

10(a) and 11(b). In Figure 11(b), the peak throughput
=C= MAC overhead has a significant impact on the
for the link rate of 54 Mbps is achieved at %Å9 &)( choice of optimal carrier sense threshold. Applying
=
(marked as Pos X in the figure), compared with the peak a larger carrier sense threshold (i.e., a smaller
point :% 9 ù'&)( in Figure 10(a) (Pos A); the peak carrier sense range) can lead to both the reduced
throughput for the link rate of 36 Mbps is achieved at bandwidth-independent MAC overhead and the re-
% 9&4.?&)( =C(marked
= as Pos Y), compared with peak duced bandwidth-dependent MAC overhead, thus,
point :% 9 &)( in Figure 10(a) (Pos B); the peak improve the utilization of each individual wireless
throughput for the link rate of 18 Mbps is achieved at link. Even though the absolute throughput obtained
 12

160
Rate = 9 Mbps Pos F 12 Rate = 9 Mbps
140 Rate = 18 Mbps Rate = 18 Mbps
Rate = 36 Mbps Rate = 36 Mbps
Rate = 54 Mbps Pos Z
Rate = 54 Mbps

Aggregate Throughput (Mbps)

Aggregate Throughput (Mbps)

120 Pos E 10
Pos Y
Pos D
100 8
Pos X
80
6
60
4
40

2
20
PSfrag replacements PSfrag replacements
0 0
-45 -43 -40 -36
,.-)/<14-26
-32
3 57698;:
-223 5 -20(dB)-17-15 -10 -6 -3 -45 -43 -40 -36
,.-0/214-26
-32
3 57698;:
-22-20
3 5 (dB)-17 -15 -10 -6 -3

(a) Packet size: 512 bytes (b) Packet size: 20 bytes

Fig. 11. Aggregate throughput vs. = (N =32)

by each transmitter/receiver pair may decrease be- sense threshold and the communication link rate, which
cause they operate at a lower link rate, the aggregate maximizes the aggregate throughput, is our desired oper-
throughput can be improved as long as there are ating point. However, wireless ad hoc networks are rich
sufficient source stations to exploit the improved in turbulence. We need the optimal operating point to be
spatial reuse. stable such that the system, although perhaps fluctuating,
 The optimal carrier sense threshold depends on tends to move in the direction of the optimal point. The
the degree of channel contention, packet size and exact definition and evaluation of such a dynamic spatial
other factors affecting the bandwidth-dependent and reuse and rate control algorithm is an ongoing activity.
bandwidth-independent overheads. With an inap-
propriate choice of carrier sense threshold, the ag-
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