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Published in IET Communications
Received on 1st February 2009
Revised on 7th September 2009
doi: 10.1049/iet-com.2009.0071
In Special Issue on Vehicular Ad Hoc and Sensor Networks
ISSN 1751-8628
Saturation throughput analysis of WAVE
networks in Doppler spread scenarios
T. Luo
1
Z. Wen
1
J. Li
1
H.-H. Chen
2
1
Key Laboratory of Universal Wireless Communications, Ministry of Education; School of Information and Telecommunication
Engineering, Beijing University of Posts and Telecommunications, Beijing 100876, People’s Republic of China
2
Department of Engineering Science, National Cheng Kung University, 1 Da-Hsueh Road, Tainan City 70101, Taiwan
E-mail: tluo@bupt.edu.cn
Abstract: IEEE 802.11p, also known as wireless access in vehicular environment (WAVE), extends the applications of IEEE
802.11 to a fast fading vehicular communication environment. In WAVE systems, Doppler effect should not be ignored
because of the high velocity of vehicles. Hence, in this paper the authors study the characteristics of physical layer WAVE
system in the presence of the Doppler spectrum, such as symbol error rate performance and inter-subcarrier
interference power. The throughput performance expression of a WAVE system is derived theoretically, which is the
function of the frame size, number of the nodes, transmission probability, frame error rate and Doppler spread.
Based on the obtained expressions, the optimal frame size, transmission probability and the number of nodes
supportable in the WAVE system are derived to evaluate the maximum throughput performance. Finally, to validate
the analytical results, simulations have been conducted to show the effectiveness of the proposed scheme.
1 Introduction
As an amendment to the existing IEEE 802.11 standard, IEEE
802.11p, which is also known as dedicated short-range
communications standard of North America, has been
proposed and has attracted a lot of attention recently [1– 6].
IEEE 802.11p, also called wireless access in vehicular
environment (WAVE), works to provide many applications in
vehicle-to-vehicle communication networks. Because of the
high mobility of the vehicles, which may yield an inconstant
topology of a WAVE network, it is extremely difficult to
deploy a MAC scheme with a centralised controller, such as
the ones working on time division multiple access (TDMA)
and frequency division multiple access (FDMA). It is well
knownthatcarriersensemultipleaccesswithcollision
avoidance (CSMA/CA) is a MAC scheme that does not
require a central controller, in which each node works by
detecting the wireless channel first and transmitting only if
the channel is free. An enhanced distributed channel access
(EDCA) scheme, which also uses CSMA/CA,willbeused
as one of the MAC protocols for 802.11p systems. Many
previous works on CSMA/CA schemes reported in the
literature were based mainly on IEEE 802.11b protocol over
slow fading channels, such as the works given in [7, 8] for a
lossless channel, and those in [9– 12] for a lossy channel,
respectively. The works reported in [9, 10] considered a
constant frame error probability only for data frames and
ignored the errors of control frames. The study carried out in
[11] calculated the average probability of transmission errors
without considering the use of two-dimensional Markov
chain. Based on the concept of virtual slots defined in [11],
the authors in [12] extended the analysis done in [7, 8] to
study the saturation throughput for a lossy channel.
However, in a WLAN system based on multicarrier
modulation, such as IEEE 802.11a/g/p, Doppler effect should
not be ignored because of their sensitivity to the frequency
synchronisation [4, 13– 16]. For example, in [4], based on the
parameters of IEEE 802.11a, the maximum Doppler spread
fdinsuburban,highway,andruralis0.583,1.53and
1.11 kHz, and the corresponding minimum 90% coherence
time tcis 1, 0.3 and 0.4 ms, respectively. Particularly, Doppler
effect is more serious in IEEE 802.11p systems because of the
high velocity of vehicles. In a 802.11p system, when 10 MHz
bandwidth is adopted, the Doppler spectrum with 10.8 km/h
and 216 km/h is about 59 Hz and 1.18 kHz, respectively.
Although it is much less than the bandwidth of the subcarriers
(156.25 kHz), the performance deterioration caused by the
Doppler spread should not be ignored. This is because the
time variations of the channel destroy the orthogonality of
IET Commun., 2010, Vol. 4, Iss. 7, pp. 817– 825 817
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the different subcarriers and generate power leakage among the
subcarriers, known as inter-carrier interference (ICI). Wang
et al. [13] and Stantchev et al. [14] studied performance
distortions because of Doppler spreading in orthogonal
frequency division multiplexing (OFDM) systems such as
802.11a and digital video broadcasting (DVB) systems. For
example, in [13], when the system is operating at a signal to
noise ratio (SNR) of 40 dB in a vehicle travelling at a speed
of 200 km/h and with uncoded 16-QAM modulation, the
average symbol error rates (SERs) of IEEE 802.11a system
with/without Doppler spread are 3.5 ×10
24
and
1.8 ×10
24
, respectively, increasing by 1.94 times, whereas
the SERs of a DVB system operating in the CS2 mode are
2.78 ×10
22
and 1.8 ×10
24
, respectively, increasing by 500
times. Moreover, there is an error floor because of Doppler
spread [13]. Therefore in order to evaluate the distortions to
a WAVE system, in this paper, the ICI power, SER
performance and throughput performance are studied jointly
in the presence of the Doppler spectrum, and their
expressions are theoretically derived.
The rest of the paper is outlined as follows. In Section 2, the
ICI power and SER performance of WAVE systems are
derived theoretically in the presence of Doppler spectrum.
Then, in Section 3, the saturation throughput performance
of WAVE systems is analysed in Doppler spread scenarios.
Finally, in Section 4, numerical results will be presented,
followed by the conclusions drawn in Section 5.
2 ICI and SER analysis in Doppler
channels
It is well known that WAVE systems use binary phase-shift keying
(BPSK)/quadrature phase shift keying (QPSK)/quadrature
amplitude modulation (QAM) based OFDM modulation
schemes. Hence, for analysis convenience, M-PSK-based
OFDM is considered in this paper. Let us consider an OFDM
system with Nsubcarriers.Thesamplingrateandtheduration
of OFDM symbol are denoted by Tbans T, respectively.
Obviously, we have T=NTb. The impulse response of the
time-variant channel, h(n,l), denotes the tap gain of the lth tap
at time n. Then, in this paper, with the assumption of the
perfect sampling and symbol timing synchronisation, the kth
(0 ≤k≤N−1) output of the FFT demodulator at the
receiver, R(k), can be written as follows
R(k)=1
N
N−1
n=0
N−1
m=0
d(m)Hm(n)ej2
p
n(m−k)/N+
v
(k) (1)
where d(m), the mth input pin of the IFFT operation, is an
M-PSK modulated symbol,
v
(n) is the additive white Gaussian
noise with zero mean and variance
s
2
v
and Hm(n)istheFourier
transform of the channel impulse response at time n,whichis
defined as
Hm(n)=
L0−1
l=0
h(n,l)ej[2
p
n1/N+
f
(n)]e−j2
p
lm/N(2)
where L0is the number of the multipath returns, 1=DfT and
f
(n) are defined as the normalised carrier frequency offset and
phase noise, respectively, which can be caused by either Doppler
spread or unstable crystal oscillator or both. In a land mobile
fading channel, Doppler effect is considered, and h(n,l)is
assumedtobesatisfiedwithacomplexwhiteGaussianprocess
with zero mean, variance
s
2
hand autocorrelation function as [15]
r
WE{h(n1,l1)h∗(n2,l2)}
=cJ0
2
p
fdT(n1−n2)
N
e−l1/L0
d
(l1−l2) (3)
where J0(∗) is the zeroth order Bessel function of the first kind
[17]. Particularly, in a slow fading channel, we have
r
¼1.
For analysis convenience, in a time-variant channel, R(k)
in (1) can be separated to three parts: a desired item d(k),
ICI I(k) and the noise item
v
(k). Thus, (1) can be
rewritten as
R(k)=d(k)
N
N−1
n=0
Hk(n)+1
N
N−1
m=0,m=k
d(m)
×
N−1
n=0
Hm(n)ej2
p
n(m−k)/N+
v
(k)
=d(k)
N
N−1
n=0
Hk(n)+1
NI(k)+
v
(k) (4)
For an M-PSK symbol, we have E[|d(k)|2]=1. Hence, from
(4), the instant SNR
g
(k) and the normalised ICI power
PICI(k) of the kth subcarrier can be deduced (the detail
derivation can be found in the appendix) as (see (5))
where E(∗) denotes the expectation operation. Fig. 1
illustrates the normalised ICI power against Doppler spread
fdTwith different frequency offsets 1¼0, 0.01, 0.1,
g
(k)=|N−1
n=0Hk(n)|2
|I(k)|2+N2
s
2
v
PICI(k)=E[|I(k)|2]
E[|N−1
n=0Hk(n)|2]
=N−1
m=0,m=kN−1
n1=0N−1
n2=0J0{2
p
fdT(n1−n2)/N}ej[(2
p
(n1−n2)(m−k+1)/N)+
f
(n1)−
f
(n2)]
N−1
n1=0N−1
n2=0J0{2
p
fdT(n1−n2)/N}ej[(2
p
(n1−n2)1/N)+
f
(n1)−
f
(n2)]
⎧
⎪
⎪
⎪
⎪
⎪
⎪
⎪
⎪
⎪
⎨
⎪
⎪
⎪
⎪
⎪
⎪
⎪
⎪
⎪
⎩
(5)
818 IET Commun., 2010, Vol. 4, Iss. 7, pp. 817– 825
&The Institution of Engineering and Technology 2010 doi: 10.1049/iet-com.2009.0071
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respectively. It is shown from (5) and Fig. 1 that the ICI power
caused by Doppler spread and frequency offset increases with
fdTand 1, and thus the performance is degraded. Hence, the
Doppler effect and its resultant frequency offset have a negative
influence on the system performance, and need to be
eliminated in the time-variant channel.
In fact, if it is a time-invariant channel with 1=0,
f
(n)=const, (4) and (2) then become
R(k)=H(k)d(k)+
v
(k)
H(k)=
L0−1
l=0
h(l)e−j2
p
lk/N
⎧
⎨
⎩
(6)
From (6), there is no ICI in this case, and only frequency-
selective fading exists. As we know, when BPSK or QPSK
modulation is adopted, the instant SER of the kth subcarrier
over additive white gaussian noise (AWGN) channel is [17]
Pb(
g
)=
P2=Q
2
g
(k)
, for BPSK
P4=2Q
g
(k)
−Q2
g
(k)
,forQPSK
⎧
⎨
⎩(7)
respectively. Hence, based on (5) and (7), the average SER in
the Rayleigh fading channel can be obtained by Ps=E[Pb(
g
)]
[17],whereh(n,l) is assumed to be a complex white Gaussian
process with zero mean, variance
s
2
hand the autocorrelation
function defined in (3). Obviously, it is hard to obtain its
closed form. Consequently, the numerical calculation and
computer simulation are used in the following section of the
paper. Then, it follows that the average frame error rate
(FER) in a fading channel is
Pe=1−(1 −Ps)L(8)
where Lis the number of symbols in a data frame.
3 Saturation throughput of IEEE
802.11P
The draft IEEE 802.11p standard will make use of the
physical layer architecture of IEEE 802.11a and the MAC
layer QoS amendments from IEEE 802.11e [1–3].In
IEEE 802.11p draft, four different QoS classes are defined
by prioritising the data traffic within each node. It implies
that each node maintains four different queues, which have
different arbitration interframe spaces (AIFS) and different
backoff parameters, In other words, the higher priority, the
shorter AIFS will be. In IEEE 802.11p draft, EDCA
scheme is used as MAC protocol. It is well known that
EDCA works based on CSMA/CA, meaning that the
node starts by listening to the channel first, and if it is free
for an AIFS, the node may start transmission immediately.
If the channel is busy or becomes busy during the AIFS,
the node must perform a backoff. The backoff procedure in
IEEE 802.11 works according to a procedure described as
follows [2, 3]:
1. generate an integer from a uniform distribution [0,W];
2. multiply this integer with the slot time derived from the
physical layer in use to obtain a backoff value;
3. decrement the backoff value only when the channel is idle;
4. when reaching a backoff value of zero, send packet
immediately.
The MAC protocol of IEEE 802.11 is a stop-and-
wait protocol and therefore the sender awaits an
acknowledgment (ACK). If no ACK is received as a result
from any of the events defined as follows: the transmitted
packet never reaching the recipient, the packet being
incorrectly received, or the ACK being lost or corrupted, a
backoff procedure is invoked before a retransmission is
allowed. For every attempt to send a specific packet, the
size of the contention window (W) will be doubled from
its initial value (W
start
) until a maximum value (W
end
)is
reached. This is important because of the fact that during
high utilisation periods, it is vital to spread in time the
nodes that want to transmit. After a successful transmission
or when a packet has to be thrown away because the
maximum number of channel access attempts is reached,
the contention window will be set to its initial value again.
Hence, we can directly extend the discrete Markov chain
model from [7, 9], which was proposed for its applications
in 802.11b to 802.11p systems by taking the Doppler effect
into account. That is, the unsuccessful transmission packets
may be caused by either collision and/or transmission bit
errors in a wireless fading channel. Additionally, we also
assume the finite number of retransmission attempts,
(m+f+1), after which the frame is discarded from the
transmit queue and a new frame is admitted in the queue.
Figure 1 Normalised ICI power against Doppler spread f
d
T
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3.1 Throughput analysis
For analysis convenience in studying the MAC protocol of
IEEE 802.11p, we might as well consider a vehicular
communication network with a finite number of nodes, or
N. Assume that
t
denotes the transmission probability
of each node at a randomly given slot, and thus Pc=1−
(1 −
t
)N−1denotes the FER because of collisions with
other nodes. Hence, the probability of an unsuccessful
(re)transmission attempt seen by a tag node as its frame is
being transmitted in the channel is
Pf=1−(1 −Pc)(1 −Pe)
which is also the transition probability from one state to
another in the Markov model as defined in [7, 9].
Obviously,
t
and Pfdepend on each other according to a
non-linear function. However, they can be resolved by
using numerical techniques and there is a single solution of
t
=f(N,W,m,f,Pe)
for each given N,W,m,fand Pe[9, 10].
Consequently, the saturation throughput of an IEEE
802.11p network in an error-prone channel can be
calculated as follows [9]
ST =PsPtr(1 −Pe)E[L]
(1 −Ptr)
s
+PtrPs(1 −Pe)Ts+Ptr(1 −Ps)Tc+Ptr PsPeTe
(9)
where E[L] is the average frame payload size, Ptr is the
probability of at least one node in transmission in the
observed time slot
s
and Psis the probability of a single
successful transmission given that at least one node (out of
all Nnodes) is transmitting. After
t
is given, Ptr and Pscan
be deduced by
Ptr =1−(1 −
t
)N
Ps=N
t
(1 −
t
)N−1/Ptr
(10)
where Ts,Tcand Testand for the average time that the channel
is sensed busy by each node because of a successful
transmission, that it is sensed busy during a collision, and
that it is sensed busy from a frame which suffered
transmission errors, respectively. In CSMA protocol, it is
clear that we always have Te=Ts. Assume that the
preamble/header of a frame is always received successfully by
all nodes, and the frame errors can occur only in the
remaining part of the frame [9]. Then, in an IEEE 802.11p
system, Tsand Tccan be defined as follows (see (11))
where
CWPHYpre/hdr +MAChdr +AIFS
BWSIFS +ACK
are all constants, Rbis the bit rate in transmission, ‘pre’ and
‘hdr’ denote the preamble and header, respectively, and
SIFS refers to short interframe space. Moreover, we have
AIFS ¼AIFSN ×
s
+SIFS [1, 2]. For convenience, let
AIFSN ¼2,
s
¼20 ms and then AIFS ¼50 ms.
Substituting (8), (10) and (11) into (9), and we assume that
the sizes of all frames are equal to L, that is, E[L]¼L. The
saturation throughput of a WAVE system then becomes
(see (12))
3.2 Relationship between throughput
and system parameters
The relationship between saturation throughput and the
system parameters, for example, frame size L, number of
nodes N, transmission probability
t
, SER Ps, and Doppler
spread fd, will be discussed in this section.
1. ST L relationship: From (12), we can see that the
throughput is approximately proportional to the frame size
when Lis small. That is, the throughput performance
increases from zero with L. Moreover, because of Ps,1, we
always have limL1(1 −Ps)L=0 and thus limL1
ST =0. Therefore there may be an optimal value for L
Ts=(PHYpre/hdr +MAChdr +L+SIFS +ACK +AIFS)
Rb
=(B+C+L)
Rb
Tc=(PHYpre/hdr +MAChdr +L+AIFS)
Rb
=(C+L)
Rb
⎧
⎪
⎪
⎪
⎨
⎪
⎪
⎪
⎩
(11)
ST =N
t
(1 −Pe)E[L]
(1 −
t
)
s
+N
t
(1 −Pe)Ts+[(1 −
t
)−N+1−(1 −
t
)−N
t
]Tc+N
t
PeTe
=N
t
(1 −Ps)LL
(1 −
t
)
s
+N
t
Ts+[(1 −
t
)−N+1−(1 −
t
)−N
t
]Tc
=N
t
(1 −Ps)LLRb
(1 −
t
)
s
Rb+N
t
(B+C+L)+[(1 −
t
)−N+1−(1 −
t
)−N
t
](C+L)(12)
820 IET Commun., 2010, Vol. 4, Iss. 7, pp. 817– 825
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corresponding to the maximum value of the saturation
throughput. In fact, letting ∂ST/∂L=0, we have
A2L2+A1L+1
ln(1 −Ps)=0 (13)
where
A2W(1 −
t
)−N+1−(1 −
t
)
A1W(1 −
t
)
s
Rb+N
t
(B+C)
+[(1 −
t
)−N+1−(1 −
t
)−N
t
]C
and certainly we have A=A1+A2L, which is the denominator
of the last equation in (12). Therefore the solution to the
quadratic equation (13), or
Lopt =
−A1+
A2
1−[4A2/ln(1 −Ps)]
2A2
is the optimal frame size corresponding to the maximum
throughput performance.
2. ST N relationship: Similarly to the analysis of the
relationship between throughput and L, there may also be
an optimal Ncorresponding to the maximum value of the
saturation throughput. Letting ∂ST/∂N=0, we have
(1 −
t
)N(C+L−
s
)=N(C+L) ln(1 −
t
)+C+L
(14)
The solution of (14) is the optimal number of nodes. Obviously,
it is difficult to resolve the non-linear function (14), and we can
obtain the solution by using numerical analysis for sure.
3. ST
t
relationship: Intuitively, the collision probability
depends mainly on the transmission probability of each
node at a chosen slot and the number of nodes. In fact,
from (12) and letting ∂ST/∂
t
=0, we have
(1 −
t
)N=C+L
C+L−
s
Rb
(1 −N
t
) (15)
Similarly, the solution of (15) is the optimal transmission
probability for each node. Obviously, it is also very hard to
resolve it and the solution can be found by using numerical
analysis. Hence, in the design of a WAVE system, we can
set the transmission probability according to the given
parameters, such as frame size, number of nodes and so on.
4. ST P
s
relationship and ST P
d
relationship: From (12),
it is seen that the throughput is proportional approximately to
(1 −Ps)L. Therefore the throughput decreases smoothly with
the increase of Pswhen Psis small; while it sharply reduces to
zero when Psis large. It is well known that in a fast fading
channel, Doppler spread is the main contributor of SER.
For example, in [17], the closed SER form of binary
differential phase-shift keying (DPSK) over Rayleigh fading
channel is given as
Ps=1+
g
(1 −
r
)
2(1 +
g
)(16)
where
g
WVEb/N0is the average fading SNR, Vis the
channel gain and
r
is the fading correlation coefficient
defined in (3). Then, for binary DPSK, substituting (16) to
(12), we have the relationship between the throughput
performance and Doppler spread as follows (see (17))
Obviously, when
r
=J0(2
p
fdTb)=1, (17) degenerates into
the throughput expression over a slow fading channel.
Additionally, as a major physical layer technique in WAVE
systems, multicarrier modulation such as OFDM is more
sensitive to frequency offset because of its orthogonality of
subcarriers in the frequency domain. In an OFDM-based
WAVE system, a large Doppler spread caused by a high
vehicular velocity can result in serious intercarrier
interference, and thus the SER performance decreases
sharply as discussed in Section 2. Hence, in a fast fading
channel, Doppler spread is a major factor affecting the
saturation throughput significantly.
Based on the aforementioned discussions, we can
summarise that the throughput performance is determined
jointly by the frame size, number of the nodes,
transmission probability, the FER and Doppler spread. In
particular, the Doppler spread poses a serious threat to the
performance of an OFDM-based WAVE system.
Consequently, in order to improve the throughput
performance in a fast fading channel, we suggest that it is
very important to use the optimal frame size and
transmission probability, to accommodate the suitable
number of nodes in a WAVE network, to use some
Doppler resilient technologies to improve the SER
performance in physical layer. Apparently, a novel MAC
protocol is in particular important for WAVE systems,
which should be able to mitigate the Doppler effect
effectively.
4 Simulation results
In order to validate the analytical results, computer
simulation and numerical calculation have been conducted
to show the effectiveness of the aforementioned analytical
results on Doppler effect and throughput performance.
ST =N
t
{1 −(1 +
g
[1 −J0(2
p
fdTb)]/2(1 +
g
))}LLRb
(1 −
t
)
s
Rb+N
t
(B+C+L)+[(1 −
t
)−N+1−(1 −
t
)−N
t
](C+L)(17)
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4.1 Results of Doppler spread
In the simulations, parameters and environment were set up
as follows: the channel model A (with 18 paths, 390 ns
maximum delay spread and 50 ns average rms delay spread)
of HIPERLAN II and QPSK modulation were adopted,
data rate was set to 9 Mbps, the double sliding window
packet detection algorithm [16] was used for physical layer
convergence procedure (PLCP) frame synchronisation, and
the linear minimum mean-squared error algorithm-based
pilots were used for channel estimation. In the simulations,
we only evaluated the channel once in each PLCP frame.
Figs. 2–4illustrate the BER against SNR with the different
lengths of PLCP frame LPLCP =35, 60, 225 OFDM symbols,
respectively, in which Doppler spectrum is fd=0, 59, 590,
1180 Hz (the corresponding velocity is 0, 10.8, 108 and
216 km/h), respectively. As we know, the coherence time is
approximately defined as Dt≃(0.423/fd)≃1 ms. When the
Doppler spread is fd=59, 590, 1180 Hz, the corresponding
coherence time is Dt≃7.2, 0.72, 0.36 ms, respectively. That
is to say, the channel is almost time invariant in about 900,
90, 45 OFDM symbols with fd=59, 590, 1180 Hz when
Ts=8ms (with 10 MHz bandwidth in IEEE 802.11p),
respectively. Hence, in Fig. 2,withLPLCP =35 OFDM
symbols, it is less than the smallest coherence time or 45
OFDM symbols, and thus all BER curves are almost the
same. With the increasing LPLCP =60 OFDM symbols in
Fig. 3, the BER curve with fd=1180 Hz degenerated
quickly, while both curves with fd=1180 and 590 Hz are
reduced sharply in Fig. 4 with LPLCP =225 OFDM symbols.
In summary, it can be concluded that BER performance
with different Doppler spreads is dependent definitely on
the length of PLCP frame. Furthermore, from Fig. 3,
when BER is about 10
22
, there is about 6 dB loss with
fd=590 Hz. Moreover, BER is worse when fdis larger.
Similarly to [13], it can be concluded from Figs. 3 and 4
that there is an error floor of BER because of Doppler spread.
4.2 Results of throughput
According to [2], the network parameters used in the simulations
are listed as follows (similar to [9]): m¼5; W¼8; f¼10;
s
¼20 ms; physical layer preamble and header are 12 symbols
(ten short and two long symbols, 32 ms) and one OFDM
symbols (signal field, 8 ms), respectively; MAC header is 36
octets; ACK is 14 octets plus physical layer preamble and
header; SIFS and AIFS are set to 10 and 50 ms, respectively.
Therefore we can obtain Ts≃2210.2msandTc≃2187.8ms
when L¼2324 octets and Rb=9Mbps.
The throughput performances against frame size, number of
nodes, transmission probability, SER and Doppler spread are
depicted in Figs. 5–9, respectively. It can be observed from
Figs. 5 and 6that the throughput increases with the increase of
Lor Nwhen they are relatively small, and it will be close to
zero when they approach to infinity. This is because that we
have limL1(1 −Ps)L=0whenPs,1, and there will be
less collisions with other nodes when Nis relatively small;
whereas more collisions exist when Nis relatively large. We can
see from Fig. 7 that the throughput performance depends
Figure 2 BER against SNR with L
PLCP
¼35 OFDM symbols
Figure 3 BER against SNR with L
PLCP
¼60 OFDM symbols
Figure 4 BER against SNR with L
PLCP
¼225 OFDM symbols
822 IET Commun., 2010, Vol. 4, Iss. 7, pp. 817– 825
&The Institution of Engineering and Technology 2010 doi: 10.1049/iet-com.2009.0071
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positively on the transmission probability of each node.
Additionally, it is shown obviously from Fig. 7 that the optimal
transmission probability is different for a different frame size:
the transmission probability moves to the right-hand side along
the X-axis (increasing) with the decrease of the frame size. This
is because that with the increase of the frame size, the more
collisions may happen. Figs. 8 and 9illustrate that the
throughput performance decreases smoothly with the increase
of Psor fdTwhen they are small; while it reduces sharply to
zero when they are large, for example, about 0.01. Furthermore,
if compared to Ps,fdTis more sensitive to the throughput
performance because of the high velocity of vehicles. Hence, a
novel MAC that is capable to work with a resilience to the
Doppler effect will paly an important role for sure.
5 Conclusions
In this paper, we have studied the issues on the ICI power, SER
performance and saturation throughput performance of WAVE
systems in the presence of the Doppler spread. Both theoretical
analysis and simulation results have been used to validate the
Figure 6 Saturation throughput against number of nodes
(P
s
¼10
26
)
Figure 8 Saturation throughput against SER (N ¼30)
Figure 9 Saturation throughput against Doppler spread
f
d
T(N¼30)
Figure 5 Saturation throughput against frame size (N ¼30)
Figure 7 Saturation throughput against transmission
probability (N ¼30 and P
s
¼10
26
)
IET Commun., 2010, Vol. 4, Iss. 7, pp. 817– 825 823
doi: 10.1049/iet-com.2009.0071 &The Institution of Engineering and Technology 2010
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effectiveness of the proposed scheme. It is shown from the
results that Doppler spectrum has a negative influence on
SER and throughput performance. Consequently, in order to
improve the performance of a WAVE system, the priority is
to use the optimal frame size and transmission probability,
and to support a suitable number of nodes in the network.
Another important approach is to work out a MAC protocol
with an excellent resilience against Doppler spread to improve
the SER performance in physical layer. However, the design
ofanovelMACprotocolsuitableforWAVEsystemsisour
future research work.
6 Acknowledgments
The work presented in this paper was supported in part by
research grants no. NSFC-60971082, NSFC-60872049 and
NSFC-60972073, National Key Basic Research Program of
China (973Program) 2009CB320407, and National Great
Science Specific Project(2009ZX03003-001, 2009ZX03003-
011), P.R. China. The authors would like to thank the editor
and anonymous reviewers for their constructive suggestions and
comments which helped us to improve the quality of the paper.
7 References
[1] IEEE P802.11p/D5.0:‘Part11:wirelessLANmedium
access control (MAC) and physical layer (PHY)
specifications’. Amendment 7: Wireless Access in
Vehicular Environments (WAVE), November 2008
[2] IEEE Std 802.11
TM
-2007 (Revision of IEEE Std 802.11-
1999): ‘Part 11: wireless LAN medium access control
(MAC) and physical layer (PHY) specifications’, June 2007
[3] BILSTRUP K.,UHLEMANN E.,STROM E.G.,ET AL.: ‘Evaluation of
the IEEE 802.11p MAC method for vehicle-to-vehicle
communication’. IEEE Vehicular Technology Conf., 2008,
VTC 2008, Fall, pp. 1– 5
[4] CHENG L.,HENTY B.E.,COOPER R.,STANCIL D.D.,BAI F.:‘A
measurement study of time-scaled 802.11a waveforms
over the mobile-to-mobile vehicular channel at 5.9 GHz’,
IEEE Commun. Mag., 2008, 46, (5), pp. 84 – 91
[5] SCHOCH E.,KARGL F.,WEBER M.: ‘Communication patterns in
VANETs’, IEEE Commun. Mag., 2008, 46, (11), pp. 119 – 125
[6] RABADI N.M.,MAHMUD S.M.: ‘On finding the optimal settings of
the IEEE 802.11 DCF for the vehicle intersection collision
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Vehicular Environments (WAVE), Detroit, USA, December 2008
[7] BIANCHI G.: ‘Performance analysis of the IEEE 802.11
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Commun., 2000, 18, pp. 535 – 547
[8] WU H.,PENG Y.,LONG K.,CHENG S.,MA J.: ‘Performance of
reliable transport protocol over IEEE 802.11 wireless LAN:
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2002, pp. 599– 607
[9] HADZI-VELKOV Z.,SPASENOVSKI B.: ‘Saturation throughput:
delay analysis of IEEE 802.11 DCF in fading channel’. Proc.
IEEE ICC 2003, May 2003, pp. 121– 126
[10] HE J.,TAN G Z . ,YANG Z . ,CHENG W.,CHOU C.T.: ‘Performance
evaluation of distributed access scheme in error-prone
channel’. Proc. IEEE TENCON 2002, October 2002,
pp. 1142– 1145
[11] VISHNEVSKY V.,LYAKHO V A.: ‘802.11 LANs: saturation
throughput in the presence of noise’. Proc. NETWORKING
2002, 2002, pp. 1008– 1019
[12] JAMES DONG X.,VARAIYA P.: ‘Saturation throughput analysis
of IEEE 802.11 wireless LANs for a lossy channel’, IEEE
Commun. Lett., 2005, 9, (2), pp. 100 – 102
[13] WANG T.(R.),PROAKIS J.G.,MASRY E.,ZEIDLER J.R.: ‘Performance
degradation of OFDM systems due to Doppler spreading’,
IEEE Trans. Wirel. Commun., 2006, 5, (6), pp. 1422 –1432
[14] STANTCHEV B.,FETTWEIS G.: ‘Time-variant distortions in
OFDM’, IEEE Commun. Lett., 2000, 4, (9), pp. 312 – 314
[15] CHOI Y.-S.,VOLTZ P.J. ,CASSARA F.A.: ‘On channel estimation
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(8), pp. 1375– 1387
[16] HEISKALA J.,TERRY J.: ‘OFDM wireless LANs: a theoretical
and practical guide’ (Sams Publishing, Indianapolis, IN, 2001)
[17] SIMON M.K.,ALOUINI M.-S.: ‘Digital communication over
fading channels’ (Wiley, 2005, 2nd edn.)
8 Appendix
To facilitate the calculation of the ICI power in (5), we can
deduce the autocorrelation of Hk(n) first. Using (3), we have
E[|Hk(n)|2]=E{Hk(n1)H∗
k(n2)} =ej[(2
p
(n1−n2)1/N)+
f
(n1)−
f
(n2)]
×
L0−1
l1=0
L0−1
l2=0
E{h(n1,l1)h∗(n2,l2)}e(−j2
p
(l1−l2)k/N)
=cJ0
2
p
fdT(n1−n2)
N
×ej[(2
p
(n1−n2)1/N)+
f
(n1)−
f
(n2)]
L0−1
l=0
e−l/L0
=c2J0
2
p
fdT(n1−n2)
N
×ej[(2
p
(n1−n2)1/N)+
f
(n1)−
f
(n2)]
(18)
824 IET Commun., 2010, Vol. 4, Iss. 7, pp. 817– 825
&The Institution of Engineering and Technology 2010 doi: 10.1049/iet-com.2009.0071
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where c2=[(1 −e−1)/(1 −e−1/L)]c. Then, the numerator of
(5) becomes
E
N−1
n=0
Hk(n)
2
=E
N−1
n1=0
Hk(n1)
N−1
n2=0
H∗
k(n2)
=
N−1
n1=0
N−1
n2=0
E{Hk(n1)H∗
k(n2)}
=c2
N−1
n1=0
N−1
n2=0
J0
2
p
fdT(n1−n2)
N
×ej[(2
p
(n1−n2)1/N)+
f
(n1)−
f
(n2)] (19)
Similarly, we obtain
E[|I(k)|2]=E[I(k)I∗(k)] =
N−1
m=0,m=k
E{|d(m)|2}
×E
N−1
n1=0
Hk(n1)
N−1
n2=0
H∗
k(n2)
ej2
p
(n1−n2)(m−k)/N
=c2
N−1
m=0,m=k
N−1
n1=0
N−1
n2=0
J0
2
p
fdT(n1−n2)
N
×ej[(2
p
(n1−n2)1/N)+
f
(n1)−
f
(n2)]ej2
p
(n1−n2)(m−k)/N
=c2
N−1
m=0,m=k
N−1
n1=0
N−1
n2=0
J0
2
p
fdT(n1−n2)
N
×ej[(2
p
(n1−n2)(m−k+1)/N)+
f
(n1)−
f
(n2)] (20)
Obviously, it can be concluded from (18) – (20) that both
E[|Hk(n)|2] and E[|N−1
n=0Hk(n)|2] do not change with the
subcarrier index k, while E[|I(k)|2] is a function of k.
Therefore substituting (19) and (20) into (5), we obtain
(see (21))
PICI(k)=E[|I(k)|2]
E[|N−1
n=0Hk(n)|2]
=N−1
m=0,m=kN−1
n1=0N−1
n2=0J0{2
p
fdT(n1−n2)/N}ej[(2
p
(n1−n2)(m−k+1)/N)+
f
(n1)−
f
(n2)]
N−1
n1=0N−1
n2=0J0{2
p
fdT(n1−n2)/N}ej[(2
p
(n1−n2)1/N)+
f
(n1)−
f
(n2)] (21)
IET Commun., 2010, Vol. 4, Iss. 7, pp. 817– 825 825
doi: 10.1049/iet-com.2009.0071 &The Institution of Engineering and Technology 2010
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