I. J. Communications, Network and System Sciences, 2008, 4, 285-385
Published Online November 2008 in SciRes (http://www.SciRP.org/journal/ijcns/).
Copyright © 2008 SciRes. I. J. Communications, Network and System Sciences, 2008, 4, 285-385
Collision-Tolerant Transmission with
Narrow-Beam Antennas
Hong-Ning DAI1, Kam-Wing NG1, Min-You WU2, Bo LI3
1Department of Computer Science and Engineering, The Chinese University of Hong Kong, Hong Kong SAR
2Computer Science and Engineering Department, Shanghai Jiao Tong University, Shanghai, P.R.China
3School of Electronic and Information Engineering, South China University of Technology, Guangzhou, P.R.China
Email: {hndai,kwng}@cse.cuhk.edu.hk, wu-my@sjtu.edu.cn, bill.leebo@gmail.com
Received April 29, 2008; revised September 1, 2008; accepted September 23, 2008.
Abstract
The application of directional antennas in wireless ad hoc networks brings numerous benefits, such as
increased spatial reuse and mitigated interference. Most MAC protocols with directional antennas are based
on the RTS/CTS mechanism which works well in wireless ad hoc networks using omni-directional antennas.
However, RTS/CTS frames cannot mitigate the interference completely. Besides, they also contribute a lot
to the performance overhead. This paper studies the problem from a new perspective. We have found that
the transmission success probability under directional transmission and directional reception is quite high
when the antenna beamwidth is quite narrow. Motivated by the analytical results, we design a lightweight
MAC protocol without RTS/CTS frames. The evaluation results demonstrate that this new protocol
performs better than MAC protocols based on the RTS/CTS mechanism. The results also show that a
collision-tolerant transmission is feasible under the narrow beam configuration.
Keywords: Wireless Networks, Directional Antennas, Medium Access Control
1. Introduction
The application of directional antennas to wireless ad
hoc networks has received enormous interest in recent
years. Directional antennas can greatly improve network
performance by increasing network connectivity, expanding
transmission range, enhancing spatial reuse and reducing
interference. Recent studies such as [1–10] focus on
designing new MAC layer protocols to improve network
performance.
Most of these MAC schemes with directional antennas
are based on a four-way handshaking scheme, known as
request-to-send/clear-to-send (RTS/CTS). The RTS/CTS
mechanism has been proposed to resolve the hidden
terminal problem in wireless networks using omni-directional
antennas which can broadcast RTS/CTS frames to inform
neighboring nodes of the oncoming transmission. Those
nodes that have received the RTS/CTS frames can defer
their transmission to avoid collisions. However, using
RTS/CTS cannot eliminate hidden terminals completely
even in wireless networks with omni-directional antennas
[11]. Furthermore, Choudhury et al. [5] have found that
using directional antennas causes new interference such
as new hidden terminals and the deafness problem, which
cannot be solved by using the RTS/CTS mechanism.
Essentially, directional antennas can radiate or receive
signals more effectively in one direction, which can cause
much less interference than omni-directional antennas. So,
does the RTS/CTS mechanism still work well with
directional antennas?
Many novel mechanisms have been proposed to
eliminate the new hidden terminal problem and the
deafness problem, which are caused by directional
antennas. Although Korakis et al. [3] propose a Circular-
DMAC scheme to combat the new hidden terminal
problem and the deafness problem, transmitting multiple
RTS/CTS frames for each data transmission severely
degrades the performance. Other schemes, such as Tone-
based DMAC [7] and BTDMAC [12] can alleviate the
impacts of the hidden terminal and deafness problems by
sending tones over another channel or over the data
channel after data transmission. However, these bulky
and complicated schemes also bring additional cost and
286 H. N. DAI ET AL.
Copyright © 2008 SciRes. I. J. Communications, Network and System Sciences, 2008, 4, 285-385
performance penalty.
How to use directional antennas in wireless networks
more effectively? We address this problem from another
viewpoint. When the beamwidth of a directional antenna
is lessened (a narrower beamwidth), the interference caused
by the antenna will also be reduced. We have found that
when the beamwidth is quite narrow and the network is
not so dense, the collision probability is quite low. It is
the purpose of this paper to study the performance of
wireless networks using narrow-beam antennas. In parti-
cular, we are interested in the following problems:
What will happen when the beamwidth of the
directional antennas is lessened? What is the impact of
other factors on the success transmission probability,
such as the node density?
How effective is the RTS/CTS mechanism in wireless
networks using directional antennas? If RTS/CTS is
turned off, will the network throughput degrade
significantly?
In the next section, we briefly survey the related work
in the literature. Section 3 describes the models used in
this paper and analyzes the success transmission proba-
bility for directional transmission and directional reception.
In Section 4, we present a lightweight MAC protocol
without the RTS/CTS mechanism and compare its per-
formance with a representative MAC protocol using the
RTS/CTS mechanism. Section 5 offers some implications
of our results. Finally, we summarize our paper in
Section 6.
2. Related Work
Many studies [1–10] focus on designing new MAC
protocols with directional antennas. Most of them are
based on the IEEE 802.11MAC [13], which typically
uses RTS/CTS to reduce interference in wireless networks.
Although the RTS/CTS mechanism works well in wireless
networks equipped with omni-directional antennas, it
cannot mitigate interference completely [11]. Besides,
using RTS/CTS in wireless networks with directional
antennas is not as effective as we expected. For example,
ref. [5] shows that RTS/CTS cannot completely mitigate
new interfering nodes caused by directional antennas.
To address the new hidden terminal problem and the
deafness problem, many researchers propose more
complex schemes, such as Circular-DMAC [3], Tone-
based DMAC [7] and BT-DMAC [12]. Although they
can mitigate the impacts of hidden terminals and deafness,
they also bring additional cost on network performance.
For example, Circular-DMAC needs a sender to transmit
multiple RTS frames before each data transmission,
which greatly degrades the network performance. Tone-
based DMAC and BT-DMAC also need to send out-of-
band tone signals to reduce interference.
Other studies [14–17] concentrate on capacity analysis
and performance evaluation on wireless ad hoc networks
using directional antennas. Yi et al. [15] have found that
using directional antenna in arbitrary networks achieves a
capacity gain of 2 /
π αβ
when both transmission and
reception are directional. Here,
α
and
β
are transmitter
and receiver antenna beamwidths, respectively. Under
random networks, the throughput improvement factor is
2
4/ ()
π αβ
for directional transmission directional
reception. Ref. [14] studies the asymptotic bounds on the
amount of capacity gains that directional antennas can
acquire. Wang et al. [16] model and analyze multiple
directional transmission and reception modes coupled
with omni-directional or directional receptions. Carvalho
and Garcia-Luna-Aceves [17] propose a realistic
analytical model which considers the binary exponential
back-off operation of IEEE 802.11.
In this paper, we try to find the relationship between
the interference, the beamwidth of directional antennas
and the density of nodes.
3. Analytical Models
In this section, we analyze the successful transmission
probability with directional antennas. The successful
transmission probability does not only depend on the
activity of the interfering nodes but also on the
transmission/reception mode of directional antennas.
First, we present the antenna model in Section 3.1.
Section 3.2 discusses the interference range for
directional transmission. Finally, we analyze the
successful transmission probability under the directional
transmission and directional reception mode.
3.1. Antenna Model
The radiation pattern of a direction antenna is often
depicted as the gain values in each direction in space. We
can project the radiation pattern of an antenna to an
azimuthal or elevation plane. The projection of the
pattern typically has a main lobe (beam) of the peak gain
and side-/back-lobes of smaller gains.
Since modeling a real antenna with precise values for
main and side-/back-lobes is difficult, we use an approximate
Figure 1. The antenna model.
COLLISION-TOLERANT TRANSMISSION WITH NARROW-BEAM ANTENNAS 287
Copyright © 2008 SciRes. I. J. Communications, Network and System Sciences, 2008, 4, 285-385
antenna pattern [18]. In an azimuthal plane, the main lobe
of antenna can be depicted as a sector with angle
θ
,
which is denoted as the main beamwidth of the antenna.
The side-/back-lobes are aggregated to a circle, as shown
in Figure 1. The narrower the main beamwidth of the
antenna is, the smaller the side-/back-lobes are. Take the
above antenna model as the example. The gain of the
main beam is more than 100 times of the gain of side-
lobes when the main beamwidth is less than 40° [18].
Thus, the side-/back-lobes can be ignored when the main
beam is quite narrow.
Our proposed model assumes that a directional
antenna gain
d
is within a specific angle
θ
, where
θ
is
the beamwidth of the antenna. The gain outside the
beamwidth is assumed to be zero. At any time, the
antenna beam can only be pointed to a certain direction,
as shown in Figure 1, in which the antenna is pointing to
the right. Thus, the probability that the beam is switched
to cover each direction is
/ (2)
θ π
. The antenna gain
pattern is given by:
( )d
G if angle within
g
0 otherwise
θ
θ
=
3.2. Interference Range
Compared with omni-directional antennas, directional
antennas have different transmission properties.
Directional antennas can radiate or receive ratio signals
more effectively in a certain direction than other
directions. Thus, directional antennas have different
transmission range and interference region, compared
with omni-directional antennas. In this subsection, we
investigate the interference region of directional antennas
and the relationship between the transmission range and
the interference range.
When a signal is propagated from the transmitter to
the receiver, whether it is correctly accepted by the
receiver is mainly determined by the receiving power of
the signal at the receiver end. In open space, if the
transmitting power is fixed, the receiving power is mostly
decided by the path loss along the distance between the
transmitter and the receiver. Under this condition, multi-
path and shadowing effects can be ignored since they are
so trivial compared with the large path loss. Therefore, in
this paper, we assume that the signal propagation follows
the two-way ground model which is typically used in
open space.
According to [19], under the assumption of the two-
way ground model, the receiving power of a signal at the
receiver can be calculated by the following equation.
2 2
4
( )
t r
rt tr
h h
PdPG G
d
= (1)
where
( )
r
P d
is the receiving power at the receiver which
is far from the transmitter with the distance
d
,
t
P
is the
Figure 2. The interference model.
transmitter power,
t
G
and
r
G
are the transmitter antenna
gain and the receiver antenna gain, respectively,
and
t
h
and
r
h
are the antenna height of the transmitter and
the antenna height of the receiver, respectively.
Consider a large-scale wireless ad hoc network with
n
static nodes. Without loss of generality, the distribution
of the nodes follows a Poisson distribution with a
parameter
ρ
over the 2-D plane. The probability
( ,)
p iS
of finding
i
nodes in an area of S is given by:
( )
( ,)!
i
S
S
p iSe
i
ρ
ρ
= (2)
We also assume that every node has an identical
antenna and transmits with a fixed power. Thus, each
node has the same transmitting range
t
R
and the same
interference range
i
R
. In the scenario shown in Figure 2,
suppose that node
i
X
transmits to node
j
over a
channel. The receiver
j
locates exactly within the
transmitting range
t
R
of the transmitter
i
X
.
The successful reception of the signal is mainly
decided by the signal-to-interference-plus-noise ratio
(SINR), which is often required to be greater than a
threshold. When their transmission is on-going, an
interfering node
k
at the interference range
i
R
away
from the receiver starts the transmission toward the
receiver at the same time. So, it will have an interfering
signal with the strength
i
P
at the receiver
j
. Since the
thermal noise is negligible compared with interference
signals, similar to [11], we do not count it in our model
as well. Thus, we have4
4
i
r
t t
R
P
SINR PR
σ
= =≥
, where
σ
is
the SINR threshold. In practice,
σ
is usually set to 10.
So, we get the interference range4
i t
R R
σ
=.
3.3. Directional Transmission and Directional
Reception
A directional antenna has two modes: an omni-
directional mode with a gain
o
and a directional mode
with a gain
d
. Since antennas in the directional mode
can radiate or receive radio waves more effectively in
Xj
Rt
Ri
Xi
Xk
θ
288 H. N. DAI ET AL.
Copyright © 2008 SciRes. I. J. Communications, Network and System Sciences, 2008, 4, 285-385
some directions than in others, the directional gain
d
is
generally greater than the omni-directional gain
o
. The
transmitter or the receiver equipped with a directional
antenna can choose any one of the two modes to transmit
or receive frames. Hence, there are four combinations for
the transmission and reception modes of directional
antennas: 1) Omni-directional Transmission and Omni-
directional Reception (OTOR); 2) Directional
Transmission and Omni-directional Reception (DTOR);
3) Omni-directional Transmission and Directional
Reception (OTDR); 4) Directional Transmission and
Directional Reception (DTDR).
According to Equation (1), the larger the antenna
gains both the transmitter and the receiver have, the
higher the receiving power the receiver has. Besides, the
transmission range between the transmitter and the
receiver will be extended if the antenna gains of them are
increased. Thus, when both the receiver and the
transmitter use the directional mode, the communication
range between them is maximized. On the other hand, the
receiver is only susceptible to the interfering signals from
its receiving direction when it is using the directional
mode. So, DTDR also has the smallest interference area
compared with the other three modes. Hence, DTDR is a
preferred method to utilize directional antennas. In this
paper we only discuss the transmission under the DTDR
mode.
Let us consider the scenario shown in Figure 2. When
node
i
X
begins to transmit with node
j
, this packet is
successfully received by node
j
if no node within the
sector region covered by
j
’s antenna beam transmits
toward
j
. First, we need to calculate the probability that
no node can interfere with node
j
. Since the placement
of nodes follows the 2-D Poisson distribution with the
density
ρ
, there are 2
2
i
R
θ
ρπ
π
nodes within the sector
region covered by
j
’s antenna beam. The area of this
region is denoted byS. Among these nodes, the
interfering node
k
can cause interference with node
j
only when it has a frame to send and its antenna beam
is pointed to node
j
. We assume that a node begins to
transmit with a probability
p
.Then, the probability that
node
k
can interfere with node
j
is
2
p
π
. There, the
probability
P
that no nodes within region can cause
collisions with node
j
is given by:
2 2
0
( )
2 2
( )
(1 )
2 !
i
i
i S
i
p SpR
S
P pe
i
e e
ρ
θ θ
ρ ρπ
π π
θ ρ
π
=
− −
= −⋅
= =
(3)
To simplify the calculation, we use
2
t
N R
ρπ
=, which
denotes the average number of nodes within a node’s trans-
Figure 3. The probability of a successful transmission.
mission range. Since4
i t
R R
σ
=, we have 2
i
R N
ρπ σ
=.
Replacing the corresponding part in Equation (3), we have:
2
( )
2
p N
P e
θ
σ
π
= (4)
When
p
=
and
10
σ
=
, we set different
4,8,12,16,20
N
=
respectively and then we get the results
in Figure 3. Figure 3 shows that the successful
transmission probability is high when the beamwidth is
narrow. For example, when
θ
is less than
6
π
, the success
probability is always above 95%. One possible reason is
that using directional mode at the receiver end can
greatly reduce the collision probability.
Results under a narrow beamwidth (
12
π
θ
) are also
tabulated in Table 1, which shows that the transmission
under DTDR is less vulnerable to interference when the
beamwidth is quite narrow.
The analytical results under DTDR show that the
successful transmission probability is quite high when the
beamwidth is lessened enough. For example, when
12
π
θ
(i.e., 15°), the success probability is always
above 98%. A beamwidth of 15° is a feasible angle for
most directional antennas. Thus, intuitively, there is an
Table 1. The probability of a successful transmission under
the very narrow beam.
48
π
θ
=
36
π
θ
=
24
π
θ
=
12
π
θ
=
4
N
=
0.9999 0.9998 0.9995 0.9978
8
N
=
0.9997 0.9995 0.9989 0.9956
12
N
=
0.9996 0.9993 0.9984 0.9934
16
N
=
0.9995 0.999 0.9978 0.9913
20
N
=
0.9993 0.9988 0.9973 0.9891
COLLISION-TOLERANT TRANSMISSION WITH NARROW-BEAM ANTENNAS 289
Copyright © 2008 SciRes. I. J. Communications, Network and System Sciences, 2008, 4, 285-385
interesting question: can the transmission continue even
if there exist few collisions? In other words, when the
beamwidth of antennas is narrow enough and the
collision probability is quite low, can the transmission be
collision-tolerated?
4. Lightweight MAC Protocol
In this section, we propose a lightweight MAC scheme
denoted as Basic Directional Transmission and
Directional Reception (B-DTDR), which turns off the
control frames of request to send (RTS) and clear to send
(CTS). It has a rival termed RTC/CTS Directional
Transmission and Directional Reception (RTS-DTDR).
Then, we compare the performance of B-DTDR with that
of RTS-DTDR and discuss the implications from this
lightweight scheme.
4.1. Quick Review of RTS/CTS Mechanisms
with Directional Antennas
B-DTDR scheme keeps the basic collision avoidance
features, such as the exponential backoff and the control
frame of acknowledge (ACK). Thus, if there is a collision
with data packets, those data packets need to be
retransmitted. In IEEE 802.11 distributed coordination
function (DCF) [13], an exponential backoff scheme can
be used to avoid further collisions of data packets. At
each packet transmission, the backoff time is uniformly
chosen in a range of
( ,)
o w
where
w
is called the
contention window. At the first transmission,
w
is set to
be the minimum value of
min
W
. After each unsuccessful
transmission (no ACK received), the size of w is doubled
until it reaches the maximum value of
max
W. This
mechanism can effectively reduce the collision probability.
Most of current directional MAC schemes are using
another four-way handshaking technique which turns on
RTS/CTS frames. In stead of sending a data packet, a
transmitter sends a short control frame called request to
send (RTS). After the reception of RTS, the receiver
responds the transmitter with the frame called clear to
send (CTS). After shaking hands of RTS and CTS, the
data transmission begins. This mechanism is useful to
reduce the hidden nodes in wireless networks using
omni-directional antennas. However, it cannot mitigate
the hidden terminal problem and the deafness problem
with directional antennas [5]. In this paper, we consider a
general MAC scheme (RTSDTDR) which can be used to
represent the current directional MAC schemes since it
keeps has the main features of them. In both B-DTDR
and RTS-DTDR, RTS, CTS, data packets and ACK are
transmitted directionally.
One of the difficult problems with B-DTDR and
RTSDTDR is to find the location of a node’s neighbors,
or neighbor discovery. This problem can be solved by
using DOA caching [4] or similar mechanisms. A
specific problem with B-DTDR is how to help a receiver
to know that a transmitter is trying to send a frame to it.
Zhang [10] proposes a scheduling mechanism to address
this problem. In this paper, we assume that both B-DTDR
and RTS-DTDR can solve the neighbor discovery
problem.
On the other hand, when a node receives any frames
(RTS, CTS and data frames), it will record the
corresponding information into its DNAV (Directional
Network Allocation Vector), which is a directional
version of NAV of IEEE 802.11, proposed in [4,5].
DNAV excludes the directions and sets the corre-
sponding durations, toward which the node is not allowed
to initiate a transmission to avoid collisions with data or
control frames. When a node receives a frame and the
frame is for this node, it beamforms toward the
transmitter (switch to directional mode) and replies the
frame with a CTS (or ACK) frame. If the frames are not
for itself, it will update the sender’s information and set
the corresponding DNAVs. DNAVs are used in both B-
DTDR and RTS-DTDR.
4.2. Performance Model
In this paper, we adopt a discrete Markov chain model
used in [16, 20] to evaluate the saturation throughput and
the overhead of wireless networks (as shown in Figure 4).
We extend the model to support directional antennas.
Range extension and overhead calculation are also
considered in our model. We also adopt the assumption
that each node operate in time-slotted mode, with a time
slot
τ
. If the time slot
τ
is very small, the performance
of the time-slotted protocol is very close to that one of
the asynchronous version of the protocol [16, 20]. The
period of time during which RTS, CTS, data and ACK
frames are transmitted can be depicted as multiples of
τ
,
i.e.,
rts
t
,
cts
t
,
data
t
and
ack
, respectively.
The throughput is calculated by the proportion of time
that a node spends transmitting data packets successfully
on the average. Let
( )
P S
,
P I
and
( )
P C
denote the
steady-state probability of SUCCESS, IDLENESS and
COLLISION, respectively. From the Markov chain model
Figure 4. The Markov chain model for a node.
290 H. N. DAI ET AL.
Copyright © 2008 SciRes. I. J. Communications, Network and System Sciences, 2008, 4, 285-385
shown in Figure 4, we have the following equation to
calculate the throughput.
( )
()()()
data
CS I
P St
Throughput
P C TPS TPIT
=++ (5)
where
C
T
,
S
T
and
I
T
are the duration of COLLISION,
SUCCESS and IDLENESS, respectively.
The duration of time that a node stays in the
SUCCESS state,
S
T
or the collision state,
C
T
, depend on
the mechanisms of different MAC protocols. Thus, the
detailed calculation will be given in the following
subsections. The duration of a node in IDLENESS state
I
T
is
1
τ
.
Then, we need to calculate the probabilities that the
node stays in different states. From Figure 4, the steady-
state probability of IDLENESS equals:
( )()()()
II
P IP IPP SPC
=⋅ ++ (6)
Note that
()()1( )
PSP CPI
+= −, thus,
()1/ (2)
II
P IP
=− (7)
From Figure 4, the steady-state probability of
SUCCESS can be calculated by()()
IS
P SPIP
= ⋅
. Before
deriving the transition probability
IS
P
from IDLENESS to
SUCCESS, we need to calculate
( )
IS
P r
that node
i
X
successfully shakes hands with node
j
which is a
distance
r
way. The detailed calculation of
( )
IS
P r
will
be stated as follows.
We also derive the MAC overhead by calculating the
portion of time that a node spends transmitting control
frames on the average when data packets are successfully
transmitted.
( )
()()()
ctrl
CS I
P St
Overhead
P C TPS TPIT
=++ (8)
where
ctrl
is depicted as time slots which are used to
transmit control frames such as RTS, CTS and ACK.
In the following subsections, we derive the steady-
state probabilities, transition probabilities and times spent
at different states of the two MAC schemes, respectively.
4.3. RTS/CTS Based Directional Transmission
and Directional Reception (RTS-DTDR)
In this subsection, we calculate the throughput and the
overhead of RTS-DTDR. From the throughput model
presented above, we need to calculate the transition
probability
IS
P
first. Figure 5 indicates that the nodes
within the four regions (named 1, 2, 3, 4) may interfere
Figure 5. The interference region for DTDR.
with node
i
X
and node
j
. The transmission range
between
i
X
and
j
is denoted as
r
. So, the interference
range 4
i
r r
σ
=, which can be easily derived from the
results presented in Section 3.2. Since the number of
nodes depends on the area size, we need to calculate the
four areas of regions 1, 2, 3 and 4, which are denoted
as
1
S
,
2
S
,
3
S
and
4
S
, respectively:
2
1
2 2
2
2 2
3
2 2
4
/ (2)
/ (2)tan(/ 2) / 2
/ (2)/ (2)
/ (2)/ (2)
i
i
S r
S rr
S rr
S rr
π θπ
π θπθ
πθ ππθ π
πθ ππθ π
= ⋅
= ⋅−
=⋅− ⋅
=⋅− ⋅
(9)
( )
IS
P r
equals the probability that
i
X
transmits in a
given time slot, and
j
does not transmit in the same
time slot, and none of the nodes within the four regions
interferes with the handshake between nodes
i
X
and
j
.
Therefore, we have:
1 2 34
( )(1)
IS
PrppP PPP
=−⋅ ⋅⋅ ⋅
(10)
Since RTS-DTDR does not prevent interference from
neighboring nodes in regions 3 and 4, the handshake
might be interrupted at any time. Hence, the COLLISION
period
C
T
lasts from
1
1
rts
T t
= +
till
2
4
rts cts data ack
T tttt
=+ +++
, where one
propagation delay
τ
1is also considered.
C
T
is the mean
value of the truncated geometric distribution. Then, we
obtain the following equation to calculate
C
T
.
2 1
2 1
11
0
(1) / (1)()
T T
T Ti
Ci
Tppp Ti
− +
=
= −−+
(11)
The probability that no nodes in region 1 interferes
with the handshake between nodes
i
X
and
j
is equal
to the probability that no node in this area transmits as
node
i
X
does, which can be depicted as:
1
1
1
10
2
( )
(1 )
2 !
i
S
i
i
p S
S
P pe
i
e
ρ
θ
ρπ
ρ
θ
π
=
= −⋅
=
(12)
1
2
3
4
ri
r
Xi
COLLISION-TOLERANT TRANSMISSION WITH NARROW-BEAM ANTENNAS 291
Copyright © 2008 SciRes. I. J. Communications, Network and System Sciences, 2008, 4, 285-385
The probability
2
P
is equal to the probability that no
node transmits toward node
j
within the duration of
time
rts
t
and no node transmits within the slot when node
i
X
begins to transmit toward node
j
Thus, we have
the following equation to calculate
2
P
.
2 2
( 1)
2 2
2
rts
p Stp S
P ee
θ θ
ρ ρ
π π
−+ −
=⋅ (13)
3
P
is equal to the probability that no node can interfere
with the reception of CTS and ACK frames of node
i
X
.
Hence, we have:
3 3
( 1)(1)
2 2
3
cts ack
pS tpS t
P ee
θ θ
ρ ρ
π π
−+ −+
= ⋅ (14)
In region 4, there is no interference if no node
transmits toward node
j
when node
i
X
is sending a data
frame. Then, we get:
4 4
( 1)
2 2
4
data
pSpS t
P ee
θ θ
ρ ρ
π π
− −+
= ⋅ (15)
Because each transmitter can choose its receiver with
the equal probability and the average number of nodes
within a region of radius
r
is proportional to
2
r
, the
probability density is the function of distance
r
between
nodes
i
X
and
j
, i.e.,
( )2
f rr
=, where 0
t
r R
< <
.
Therefore,
IS
P
is equal to:
0
1 2 3 4
0
( )( )
(1 )2
t
t
R
IS IS
R
PPrfrdr
ppP PPPrdr
=
=−⋅⋅ ⋅⋅ ⋅
(16)
The duration in time slots of a node in the SUCCESS
state is
(1) (1) (1) (1)
4
S rtsctsdataack
rts cts dataack
T tttt
t t tt
=+ ++++ ++
=+ +++ (17)
where rts
t, cts
t, data
t and ack
t are the duration times of
transmitting RTS, CTS, data and ACK frames,
respectively.
After the corresponding parts are replaced in Equation
(5), the throughput of RTS-DTDR is obtained. Following
the similar process, we can calculate the overhead of
RTS-DTDR from Equation (8).
4.4. Basic Directional Transmission and
Directional Reception (B-DTDR)
Since there is no RTS and CTS frames, B-DTDR has a
narrower bound on
C
T
(from 1
1
T
τ
=
to
2
2
data ack
T tt
=+ +
). Then we can calculate
C
T
by using
Equation (11).
And the success period time is
2
Sdata ack
T tt
=+ +
(18)
1
P
keeps the same as RTS-DTDR.
2
P
is equal to the
probability that no node transmits toward node
j
within
data
t
period and does not transmit in the slot when
node
i
X
begins to transmit with node
j
, therefore, we have
2 2
( 1)
2 2
2
data
p Stp S
P ee
θ θ
ρ ρ
π π
−+−
=⋅ (19)
Similarly, we have
3
4 4
( 1)
2
3
( 1)
2 2
4
ack
data
pS t
p Sp St
P e
P ee
θρ
π
θ θ
ρ ρ
π π
− +
− −+
=
= ⋅
(20)
Then after replacing the corresponding parts in
Equation (5), we get the throughput of B-DTDR. Since
2
ctrl ack
t t
= +
in B-DTDR, we can calculate the overhead
of B-DTDR from Equation (8).
4.5. Numerical Results
We compare the performance of the RTS-DTDR and
BDTDR under the different configurations and present
the results in Figure 6 and Figure 7.
Figure 6 shows the saturation throughput and
overhead of RTS-DTDR and B-DTDR under different
node density (
10,20,30,40
N
=
, respectively) when the
beamwidth is less than
6
π
. The results are obtained under
a short data length, i.e.,
40
data
t
τ
=. With the increased
node density, both the throughputs of RTS-DTDR and B-
DTDR begin to degrade although B-DTDR has a much
higher throughput than RTSDTDR protocol. The peak
value of B-DTDR is almost 20% higher than that of
RTS-DTDR. One possible reason is that when the
beamwidth is quite narrow, the number of the interfering
nodes is so small that those nodes cause nearly no
collisions. In this situation, RTS/CTS frames are not
necessary to be used. On the contrary, they only
contribute additional overhead on the throughput.
Then we calculate the throughput and overhead under
the long data length setting (i.e.,
120
data
t
τ
=and the
results are shown in Figure 7. Similarly, both RTS-
DTDR and B-DTDR perform well under a narrow beam
(e.g.,
15
π
). Under this setting, B-DTDR still has a higher
throughput than RTS-DTDR because it gets rid of the
bulky RTS/CTS mechanism. However, when the
beamwidth is increased further, the collisions caused by
292 H. N. DAI ET AL.
Copyright © 2008 SciRes. I. J. Communications, Network and System Sciences, 2008, 4, 285-385
interfering nodes become remarkable, both the
throughput of RTS-DTDR and B-DTDR degrades.
5. Discussions
The results in Figure 6 and Figure 7 show that, when the
beamwidth is decreased, a higher network throughput can
be obtained. The capacity analysis in [15] also proves
that the capacity grows with the lessened beamwidth.
However, the capacity will not grow arbitrarily high
when the beamwidth decreases further and even
approaches to zero. Yi et al. [15] have also observed that
when the beamwidth is too small, the interference has
been fully reduced and there is no further improvement
by decreasing the beamwidth of the antennas.
Actually, when the beamwidth is narrow enough (more
specifically, less than a certain angle) a trans-mission can
yield a high success probability. As shown in Section 3.3,
if the beamwidth is less than
12
π
(i.e., 15°) and both
directional antennas are used at the transmitter and the
receiver, then the probability of a successful transmission
is greater than 99%. The transmission under this situation
can be regarded as a collision-tolerant transmission (the
collision probability is quite small). Hence, DTDR
should be the best way to use directional antennas.
Meanwhile, the angle 15° is feasible in most intelligent
directional antennas. Under this condition, the
complicated collision avoidance mechanisms, such as
RTS/CTS, are not necessary to be used because they only
contribute excessive overhead on the performance. At
that time, using some simple collision avoidance
mechanisms, such as the exponential back-off, might be
enough to reduce the interference.
(a) N=10
(b) N=20
(a) N=30
(b) N=40
Figure 6. Throughput comparison when
0.1,5 ,40
τ τ
== ===
rts cts ackdata
pt t tt(short data frame).
COLLISION-TOLERANT TRANSMISSION WITH NARROW-BEAM ANTENNAS 293
Copyright © 2008 SciRes. I. J. Communications, Network and System Sciences, 2008, 4, 285-385
This collision-tolerant transmission gives us some
important implications on MAC design. Directional
antennas have different properties, e.g., higher spatial
reuse and the smaller interfering region. Although
RTS/CTS schemes work well in wireless networks using
omni-directional antennas, they cannot mitigate
interference caused by directional antennas completely
[5]. Thus, the MAC layer design with directional
antennas should start from another different perspective.
For example, when the beamwidth is narrow enough and
the collision probability is small, we can turn off
RTS/CTS. On the contrary, we should consider other
techniques, such as power control and multi-channel
schemes to reduce interference.
6. Conclusions
This paper studies the performance of wireless networks
using directional antennas with a narrow beam. In
particular, we examine the probability of a successful
transmission under Directional Transmission and
Directional Reception. The numerical results show that
the interference probability is quite low when the antenna
beamwidth is narrow enough. These results encourage us
to design a lightweight MAC protocol which turns off
RTS/CTS. The evaluation results prove that the protocol
has a higher throughput than the typical MAC protocol
based on RTS/CTS. The results also demonstrate that a
collision-tolerant transmission is feasible when the
beamwidth is narrow enough. One of our future works is
to implement the lightweight MAC protocol in simulators
and conduct experiments in real environments.
7. Acknowledgements
This research was partially supported by Natural Science
(a) N=10
(b) N=20
(a) N=30
(b) N=40
Figure 7. Throughput comparison when
0.1,5 ,120
τ τ
== ===
rts cts ackdata
pt t tt(long data frame).
294 H. N. DAI ET AL.
Copyright © 2008 SciRes. I. J. Communications, Network and System Sciences, 2008, 4, 285-385
Foundation of China grant No.60573138 and 60773091,
and the National Grand Fundamental Research 973 Pro-
gram of China under Grant No.2006CB303000.
8. References
[1] Y. B. Ko, V. Shankarkumar, and N. H. Vaidya, “Medium
access control protocols using directional antennas in ad
hoc networks,” in Proceedings IEEE INFOCOM, 2000.
[2] A. Nasipuri, S. Ye, and R. E. Hiromoto, “A MAC
protocol for mobile ad hoc networks using directional
antennas,” in Proceedings IEEE WCNC, 2000.
[3] T. Korakis, G. Jakllari, and L. Tassiulas, “A MAC
protocol for full exploitation of directional antennas in
adhoc wireless networks,” in Proceedings MobiHoc,
2003.
[4] M. Takai, J. Martin, R. Bagrodia, and A. Ren,
“Directional virtual carrier sensing for directional
antennas in mobile ad hoc networks,” in Proceedings
MobiHoc, 2002.
[5] R. R. Choudhury, X. Yang, N. H. Vaidya, and R.
Ramanathan, “Using directional antennas for medium
access control in ad hoc networks,” in Proceedings
MobiCom, 2002.
[6] C. S. Z. Huang, C.-C. Shen, and C. Jaikaeo, “A busytone
based directional MAC protocol for ad hoc networks,” in
Proceedings MILCOM, 2002.
[7] R. R. Choudhury and N. H. Vaidya, “Deafness: a MAC
problem in ad hoc networks when using directional
antennas,” in Proceedings ICNP, 2004.
[8] H. Singh and S. Singh, “Smart-802.11b MAC protocol
for use with smart antennas,” in Proceedings IEEE ICC,
2004.
[9] L. Bao and J. Garcia-Luna-Aceves, “Transmission
scheduling in ad hoc networks with directional antennas,”
in Proceedings MobiCom, 2002.
[10] Z. Zhang, “Pure directional transmission and reception
algorithms in wireless ad hoc networks with directional
antennas,” in Proceedings IEEE ICC, 2005.
[11] K. Xu, M. Gerla, and S. Bae, “How effective is the IEEE
802.11 RTS/CTS handshake in ad hoc networks,” in
Proceedings IEEE GLOBECOM, 2002.
[12] H. N. Dai, K. W. Ng, and M. Y. Wu, “A busy-tone based
MAC scheme for wireless ad hoc networks using
directional antennas,” in Proceedings IEEE Globecom,
2007.
[13] IEEE 802.11, Part 11: Wireless LAN Medium Access
Control (MAC) and Physical Layer (PHY) specifications
- Amendment 4: Further Higher Data Rate Extension in
the 2.4 GHz Band, IEEE Std., 2003.
[14] A. Spyropoulos and C. S. Raghavendra, “Capacity
bounds for ad-hoc networks using directional antennas,”
in Proceedings IEEE ICC, 2003.
[15] S. Yi, Y. Pei, and S. Kalyanaraman, “On the capacity
improvement of ad hoc wireless networks using
directional antennas,” in Proceedings ACM MobiHoc,
2003.
[16] Y. Wang and J. J. Garcia-Luna-Aceves, “Directional
collision avoidance in ad hoc networks,” Performance
Evaluation Journal, Vol. 58, pp. 215–241, 2004.
[17] M. M. Carvalho and J. J. Garcia-Luna-Aceves,
“Modeling wireless ad hoc networks with directional
antennas,” in Proceedings IEEE INFOCOM, 2006.
[18] R. Ramanathan, “On the performance of ad hoc networks
with beamforming antennas,” in Proceedings Mobi-Hoc,
2001.
[19] T. S. Rappaport, “Wireless communications: principles
and practice,” 2nd edition Upper Saddle River, N.J.:
Prentice Hall PTR, 2002.
[20] L. Wu and P. K. Varshney, “Performance analysis of
CSMA and BTMA protocols in multihop networks (i).
single channel case,” Information Sciences, Vol. 120, pp.
159–177, 1999.