Int. J. Communications, Network and System Sciences, 2009, 2, 775-785
doi:10.4236/ijcns.2009.28090 blished Online November 2009 (http://www.SciRP.org/journal/ijcns/).
Copyright © 2009 SciRes. IJCNS
Pu
Subcarrier Availability in Downlink OFDM Systems with
Imperfect Carrier Synchronization in Deep Fading Noisy
Doppler Channels
Litifa NOOR1, Alagan ANPALAGAN1, Sithamparanathan KANDEEPAN2
1WINCORE Research Lab, Ryerson University, Toronto, Canada
2Wireless Signal Processing Group, National ICT, Australia
Email: alagan@ee.ryerson.ca, lnoor@ee.ryerson.ca
Received July 11, 2009; revised August 30, 2009; accepted September 19, 2009
Abstract
Multicarrier systems such as orthogonal frequency division (OFDM) are considered as a promising candidate
for wireless networks that support high data rate communication. In this article, we investigate the perform-
ance of a multiuser OFDM system under imperfect synchronization. Analytical results indicate that the SNR
degrades as the average power of the channel impairments such as AWGN, carrier frequency offset due to
Doppler frequency and fading gain is increased. The SNR degradation leads to imperfect synchronization
and hence decreases the total number of subcarriers available for allocation. Monte Carlo analysis shows up
to 22% loss in the number of allocatable subcarriers can be expected under a specific imperfect synchroniza-
tion condition as compared to perfect synchronization. We utilize empirical modelling to characterize the
available number of subcarriers as a Poisson random variable. In addition, we determine the percentage de-
crease in the total number of allocatable subcarriers under varying channel parameters. The results indicate
19% decrease in the number of available subcarriers as average AWGN power is increased by 10dB; 44%
decrease as the Doppler frequency is varied from 10Hz to 100Hz; and 56% decrease as the fading gain is
varied from 0dB to -30dB.
Keywords: OFDM, Subcarrier Availability, Synchronization
1. Introduction
The growing demand for high-speed wireless communi-
cations has led to the investigation of spectrally effcient
systems for downlink transmission in multicarrier sys-
tems [1]. Multicarrier systems such as Orthogonal Fre-
quency Division Multiplexing (OFDM) enable the net-
work to provide high data rate communication by using
adaptive subcarrier allocation. Although high data rate
communication is subject to inter-symbol interference
(ISI) due to dispersive nature of wireless channels,
OFDM enables the radio network to support high data
rates while reducing the effect of ISI [2,3].
However, OFDM based systems are sensitive to car-
rier frequency offset (CFO), which leads to the loss of
orthogonality between the subcarriers and thus introduc-
tion of inter-channel interference (ICI) [4]. CFO is
caused by differences in transmitter and receiver oscilla-
tor frequencies, Doppler frequency due to relative mobil-
ity between transceivers and phase noise introduced by
non-linear channels. Since accurate frequency synchro-
nization is very important for reliable signal reception [5],
OFDM systems utilize different synchronization schemes
to facilitate acquisition and tracking of carrier frequency.
However, the distortion inherent in wireless channels
requires special design techniques and rather sophisti-
cated adaptive coding and modulation algorithms to
achieve accurate synchronization. Different methods
have been suggested to reduce the effect of CFO [6–8],
but obtaining perfect synchronization in wireless chan-
nels remains a challenging task. Hence, in this article we
investigate the performance of multiuser OFDM under
imperfect synchronization.
In the literature, various subcarrier allocation algo-
rithms have been presented for multiuser OFDM systems.
Many of these algorithms support high aggregate data
*This work was supported in part by a grant from National Science and
Engineering Research Council of Canada..
L. NOOR ET AL.
776
rate and maximize system capacity [9–14]. However, the
performance improvement is achieved when the system
is based on perfect synchronization and the utilization of
instantaneous channel information to adaptively allocate
subcarriers. Assuming that the channel variation in a
frequency selective fading environment is independent of
each other, adaptive subcarrier allocation based on in-
stantaneous channel information is an effective method
to resource allocation in multiuser OFDM systems.
However, obtaining the instantaneous channel condition
under hostile wireless channels is not attainable in prac-
tical systems. Hence identifying the subcarriers with rela-
tively low SNR and avoiding allocation of such subcarri-
ers is a more practical approach to subcarrier allocation.
In this article, we determine the percentage loss in the
available number of subcarriers under imperfect syn-
chronization in comparison to perfect synchronization.
The frequency synchronization scheme used is the
open-loop maximum likelihood (ML) estimator. The
performance of synchronization depends on noise, Dop-
pler frequency and deep-fades in the channel that reduce
the effective SNR associated with the subcarrier, which
in turn degrades the allocatability of the subcarrier. The
purpose of evaluating the system performance under im-
perfect synchronization is to restrict allocation of the
subcarriers that are not suitable for transmission. Al-
though the number of allocatable subcarriers as com-
pared to perfect synchronization decreases which trans-
lates to a decrease in the aggregate data rate for a given
number of users, the BER performance of the system
could be improved by avoiding allocation on subcarrriers
that are not suitable for transmission. Hence, any subcar-
rier allocation algorithm can be utilized while consider-
ing the variations in the total number of subcarriers. To
the best of our knowledge, this is the first paper to char-
acterize the subcarrier availability in deep fading noisy
Doppler channels.
The organization of this article is as follows. In Sec-
tion 2, the OFDM system model is discussed. In Section
3, we discuss the frequency synchronization utilized for
the OFDM system. Following, a detailed analysis of
SNR is provided in Section 4. In Section 5, we discuss
the number of available subcarriers under imperfect syn-
chronization and model the statistical characteristics of
allocatable subcarriers. Following, in Section 6 we
evaluate the number of available subcarriers under vari-
able SNR. In Section 7, the paper is concluded.
2. System Model
Figure 1 shows the baseband equivalent model of the
OFDM system that is being considered in this paper.
This analysis is independent of mapping of the transmit-
ted data as complex values a0,i . . . aN 1,i , and is there-
fore applicable to all forms of modulation which is util-
ized in OFDM systems. As indicated in Figure 1, the
IFFT is performed on the complex data symbols ak,i for k
= 0, 1, . . . , N 1, to produce the time-domain samples
bn,i for n = 0, 1, . . . , N 1 as follows:
12( )
,,
0
1n
N
j
k
N
ni ki
k
bae
N
(1)
where N is the number of data samples. The OFDM
symbol bn,i is transmitted through the frequency selective
Doppler channel. The frequency response of the channel
is indicated by:
2()
=
k
jfT
N
K
K
He
k
(2)
where αk is the (Rayleigh) fading gain for the kth subcar-
rier, ej2πfT is the CFO due to Doppler frequency with f
indicating the Doppler frequency and T indicating the
symbol period, and ηk is the Additive White Gaussian
Noise (AWGN) component on the kth subcarrier.
The system is based on the characteristics of multiuser
frequency-selective fading channels where different sub-
carriers are subject to different fading levels and the cha-
nnel variations in a multiuser environment are indepen-
dent of each other. To ensure frequency selectivity, the
coherence bandwidth of the channel, which is the recip-
rocal of the multi-path spread, is assumed to be smaller
in comparison to the bandwidth of the transmitted signal.
Figure 1. Baseband Equivalent OFDM System Model.
Copyright © 2009 SciRes. IJCNS
L. NOOR ET AL. 777
Under the assumption of AWGN channel, the received
signal with the frequency offset and the fading gain is
given as:
12( )2()
0
12( )
0
nfT
Njkj k
NN
kkk
n
nfT
Njk
NN
kk k
n
yaee
ae

C
opyright © 2009 SciRes. IJCNS
k



(3)
The received signal on the kth subcarrier and in the ith
symbol period can be written as:
yk,i = ak,iαk,iej2πN(fT)+ηk , (4)
where ak,i is the transmitted data on the kth subcarrier in
the ith symbol period, and f T is the normalized fre-
quency offset.
The received signal after FFT is expressed as:
12
,,
11
2( )
,,
0
1
km
NjN
mi kim
ko
k
NN
jlmfT
N
li lim
lo k
zye
ae
N






(5)
Using the properties of geometric series, zm,i can be
expressed as:
1
1()
,,,
0
1sin()
sin ()
N
NjlmfT
N
mili lim
l
lm fT
za e
Nlm fT
N



(6)
The analysis of ICI can be simplified by defining N
complex weighting coefficients, c0, ...., cN 1, which give
the contribution of each of the N point values a0,I , ....aN 1,i
to the output value. Based on this, zm,i is written as:
1
,,, ,,
0,
N
miomimil mlilim
llm
zcac a


(7)
where the first term is the desired signal and second term
is the ICI. co is the attenuation factor, am,i is the transmit-
ted data on the mth subcarrier in the ith symbol period,
and αm,i is the (Rayleigh) fading gain on the mth subcar-
rier during ith symbol period.
Using geometric series expansion, zm,i can be written
as:
1 1
()()()()
,,, ,,
0,
1sin ()1sin ()
sin ()sin ()
N N
NI
jfT jlmfT
N N
mimi mili lim
llm
fTl mfT
zea ae
NN
fTl mfT
NN
 



 





(8)
For noiseless case, when f T = 0, zm,i = am,i + ηm
which indicates the transmitted data plus noise. In the
case where f 0, the transmitted data is subject to
attenuation and ICI.
In addition, the relationship between the attenuation
component c0 and f T indicates that attenuation in the
desired signal component increases as the f T is in-
creased. Given that an increase in CFO is caused by an
increase in the Doppler frequency, it can be seen that as
the Doppler frequency is increased the attenuation in the
desired signal increases leading to a decrease in the SNR.
The αm,i is the (Rayleigh) fading gain for the mth sub-
carrier in the ith symbol period which attenuates the de-
sired signal, which in turn reduces the SNR. Each sub-
carrier experiences a different level of fading and the
maximum number of subcarriers that are in deep fade are
dependent on the channel condition and vary every
transmission time. The deep-fading in the channel de-
grades the corresponding subcarriers by reducing the
effective SNR associated with the subcarrier.
3. Frequency Synchronization
To emulate imperfect synchronization, the system is
considered under channel impairments such as Doppler
frequency and frequency selective fading. The Doppler
frequency leads to substantial CFO and the frequency
selective fading subjects the subcarriers to independent
fading gains. The CFO and the deep-fades in the channel
degrade the corresponding subcarriers which reduces the
effective SNR associated with the subcarrier. This makes
the synchronization system at the receiver to perform
poorly, and eventually lose lock with the corresponding
subcarriers. Hence, the system experiences imperfect
synchronization.
The frequency synchronization scheme utilized for the
OFDM system is the well-known open-loop maximum
likelihood (ML) estimator [15–17]. The frequency esti-
mator gives rise to some jitter in the estimated frequency,
increasing with decreasing SNR, due to the input noise.
Correspondingly, the symbol error probability perform-
ance also degrades due to imperfect carrier recovery at
low SNR. To avoid this, we set a threshold limit on the
synchronizer, making sure that the frequency jitter does
not exceed a certain limit. The frequency jitter has to be
less or equal to the threshold frequency for the subcarrier
to be declared as available for allocation. In this work,
the threshold frequency is set as 10Hz. If the synchro-
nizer is unable to lock to the carrier with this threshold
limit, due to noise, Doppler frequency or deep fades,
then we declare the subcarrier to be un-lockable during
the given transmission time. Hence, the subcarrier is de-
clared as not suitable for allocation.
Under the assumption of constant received signal
power, as the noise power increases the number of sub-
L. NOOR ET AL.
778
carriers available for transmission decreases. The de-
crease in the total number of subcarriers available for
reliable transmission imposes limitation on the total
achievable data rate by the system. Hence, determining
the decrease in the number of available subcarriers under
imperfect synchronization which is the case in practical
systems is important in assessing the accurate system
performance.
4. SNR Analysis
In this section, we derive the expression for the SNR on
the mth subcarrier as:
m
mm
D
m
IN
p
SNR PP
(9)
where PDm is the average power of the desired signal, PIm
is the average interference power and PNm is the average
noise power on the mth subcarrier. The average power of
the desired, interference and noise on the mth subcarrier
is defined as
22
,
Mm
DmIm
PED PEN
 

 
, and 2
m
Nm
PEN
respectively. Hence, the average SNR on the mth subcar-
rier is formulated as:
2
2
m
m
mm
ED
SNR
EI EN




2
(10)
where the average power of the desired signal is calcu-
lated as:
2
2
,,momi mi
EDEc a


(11)
Assuming that the transmitted data and the fading gain
are independent, the average power of the desired signal
can be written as:
22 2
,
() ()
mo mimi
EDc EE

 2
,
 
 
 (12)
The ICI power is expressed as:
 
2
1
2
,,
0,
2
122
,,
0,
N
mlmlili
llm
N
l mlili
llm
EIEc a
cE Ea









(13)
The above equation can be simplified as [4]:
 
2
22
,,
1
molim
EIcEE a


 
 
2
i
(14)
The power of the noise is expressed as :
2
m
EN No

 (15)
Hence, the SNR on the mth subcarrier is written as:
222
,,
222
,,
() ()
(1) ()()
omi mi
m
oli mi
cE Ea
SNR
cEEa N





o
(16)
The above equation indicates the dependence of the
SNR on the noise, frequency offset due to Doppler fre-
quency and fading gain. Hence, as the average noise
power increase the SNR decreases. In addition, to show
the dependence of SNR on the CFO due to Doppler fre-
quency, we express co as a function of f T. Hence, the
SNR is written as:
22
,,
22
,,
()()()
(1()) ()()
mi mi
m
limi o
fT EEa
SNR
f
TEE aN

 

 

(17)
Figure 2. SNR versus Fading gain with different Doppler Frequency and constant average noise power of -10dB.
Copyright © 2009 SciRes. IJCNS
L. NOOR ET AL. 779
Figure 3. SNR versus Fading gain with different AWGN power and constant Doppler Frequency of 10Hz.
This expression clearly indicates that the desired signal
and interfering power decrease due to CFO which in turn
causes the SNR to decrease.
Analysis is performed to study the changes in the SNR
as the average power of channel parameters such as av-
erage noise power, Doppler frequency and fading gain
are varied.
Figure 2 indicates the changes in the SNR as the av-
erage fading gain is varied between -30dB to 0dB when
average noise power is kept constant at -10dB. The SNR
performance is evaluated under Doppler frequency of
10Hz, 30Hz, and 50Hz. As evident from (17), the aver-
age power of the fading gain degrades the signal power
as well as the interference power. Hence, the increase in
the average power of the fading gain degrades the SNR
as indicated in Figure 2. Also, the increase in the Dop-
pler frequency causes the interference power to increase.
It is evident from this figure that as the Doppler fre-
quency increases, the SNR decreases. The increase in the
Doppler frequency from 10Hz to 50Hz results in 12dB
decrease in the SNR for an average fading gain of 0dB.
Figure 3 indicates the changes in the SNR as the av-
erage fading gain is varied between -30dB to 0dB and
the Doppler frequency is kept at 10Hz. The SNR per-
formance is evaluated under average noise power of
-10dB, -3dB and -0.5dB. As evident from (17), the in-
crease in the average noise power increases the noise
power and hence degrades the SNR. As illustrated in Fig.
3, when the average noise power is increased by 9.5dB,
the SNR decreases by 9dB for an average fading gain of
0dB.
To maintain the adaptivity of the system further sim-
plifying of (17) is avoided. Instead, Monte Carlo analysis
is performed with values generated from Rayleigh dis-
tributions. Due to random nature of time variant multi-
path channels, it is reasonable to characterize such chan-
nels statistically. The random variable αm is usually
modelled using Rayleigh distribution and the subcarriers
that are in deep-fade are not utilized during any trans-
mission time interval in our case. To analyze the random
effect, Monte Carlo analysis is performed to obtain the
characteristics of the channel. Although the fading gains
follow Rayleigh distribution, only the subcarriers that are
identified as allocatable by the ML threshold limit are
declared as allocatable.
5. Available Subcarriers with Imperfect
Synchronization
In this section, an analysis is performed to quantify the
variations in the number of available subcarriers under
imperfect synchronization which results from noise, Do-
ppler shift and frequency selective fades in the channel.
To emulate the effect of imperfect synchronization in
a multiuser OFDM system, the average noise power,
Doppler frequency and average fading level are selected
as 3dB, 25Hz and 4dB respectively. The threshold
frequency is set as 10Hz. The carrier frequency of the
system is selected to be 4GHz and the forward link
channel bandwidth is 20MHz. The total number of sub-
carriers, N, is 64 and the subcarrier bandwidth is
312.5kHz. The objective of the simulation is to obtain
the average number of subcarriers for each user under
imperfect synchronization and the variations in the total
available subcarriers as the number of users is varied.
5.1. Number of Available Subcarriers under
Constant SNR
The simulation results indicate that the number of sub-
carriers available for users varies in each transmission
C
opyright © 2009 SciRes. IJCNS
L. NOOR ET AL.
780
time slot and under imperfect synchronization the total
number of subcarriers available for reliable transmission
is smaller compared to perfect synchronization. The
availability of subcarriers for a certain user can be de-
fined as follows:
kK
aT
NNN
k
a
(18)
where is the number of available subcarriers,
k
a
N
K
T
N
is the total number of subcarriers and k
a
N is the number
of subcarriers that are not suitable for allocation for the
kth user. The k
a
N varies for different users supporting
the fact that the channel conditions in a multipath envi-
ronment is random and changes for each user.
Under the specified channel conditions, in a multiuser
environment the average number of subcarriers available
for User-1 is 49 and for User-2 is 48. This translates to
77% and 75% available subcarriers for User-1 and User-
2 respectively in comparison to perfect synchronization.
To ensure reliable data trans mission, subcarrier alloca-
tion algorithms should consider the variations in the total
available subcarriers for each user and avoid allocating
subcarriers from k
a
N .
In addition, we determine the maximum and minimum
number of available subcarriers under a given SNR in a
multiuser environment. As indicated in Figure 4, as the
number of users increase, the minimum number of
available subcarriers for transmission decreases while the
maximum number of subcarriers available for transmis-
sion increases. This indicates that over a large number of
trials the average number of allocatable subcarrier is 46.
Figure 4. Number of available subcarriers versus number of users.
(a) User-1 (b) User-2
Figure 5. Probability mass function of the available subcarriers.
Copyright © 2009 SciRes. IJCNS
L. NOOR ET AL. 781
(a) User-1 (b) User-2
n addition, the maximum and minimum available sub-
.2. Statistical Model of the Subcarrier
this section, empirical analysis is used to determine
number of available subcar-
rie
-1 and
U
The DRV is identified as a PRV because it has the
xplained bellow:
od of Nt
th
s are statistically independent because
th
for trans- mission can
be
ean, λ =
0.
transmission, perfect synchronization
is
Figure 6. Cumulative distribution function of the available subcarriers.
I
carriers indicate the upper and lower bound of the
achievable data rate for the users since the data rate is
directly proportional to available subcarriers. It can be
stated that while the average available subcarriers does
not vary significantly with the increase in the number of
users, the minimum and maximum available subcarriers
indicate noticeable variations. As the number of users
increases, the difference between the maximum and
minimum available subcarrier increases, which provides
flexibility in the total number of allocatable subcarriers.
This system characteristic supports multiplexing gain
which in turn increases the aggregate data rate.
5
Availability
In
the statistical characteristics of the number of available
subcarriers. Given that the number of available subcarri-
ers for transmission is a random variable that takes
countable values, it is modelled as a discrete random
variable (DRV) [18]. The obtained results are used to
develop the probability mass function (PMF) of the
available subcarriers for User-1 and User-2, which is
indicated in Figure 5. The PMFs are used to obtain the
cumulative distribution function (CDF) for both users
which is given in Figure 6.
Based on the PMF of the
rs, it is identified as a Poisson random variable (PRV)
with the parameter λ that defines the average number of
available subcarriers in a given time interval.
In our simulation, it is observed that λ for User
ser-2 are 51 and 49 respectively. In general, for all us-
ers λ is the same on average and hence the number of
allocatable subcarriers is a PRV.
characteristics of a PRV which are e
1) The number of available subcarriers is determined
in transmission time slot with a fixed length, ts.
2) The number of available subcarriers for each user
varies in the time interval ts but over a time peris
e number of available subcarriers for each user has a
constant average.
3) The number of subcarriers that are available in dis-
joint time interval
e fading gains are uncorrelated.
Although the number of available subcarriers is a PRV,
the availability of each subcarrier
modelled as a Bernoulli random variable (BRV)
where the availability of the each is indicated by a 0 in-
dicating not available for allocation and 1 available for
allocation. Each subcarrier availability can be viewed as
a Bernoulli trial because the number of available subcar-
rier in each trial is independent, and at most a certain
number of subcarriers is determined in each trial. This
further supports modelling of the total number of avail-
able subcarrier as a PRV since a sequence of Bernoulli
trials occurring in time is modelled as a PRV.
Based on the above observations, the number of avail-
able subcarriers is identified as a PRV with m
78N, where N is the total number of subcarriers. Hence,
the average percentage loss of the subcarriers under im-
perfect synchronization is 22% under the specified
channel condition.
To avoid performance degradation in terms of subcar-
rier availability for
required. Since practical systems are subject to imper-
fect synchronization, the analysis indicates that deter-
mining the availability of subcarriers for transmission is
essential in the optimization process of radio resource
allocation for multiuser systems.
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opyright © 2009 SciRes. IJCNS
L. NOOR ET AL.
782
Figure 7. Number of available subcarriers versus AWGN power.
Figure 8. Number of available subcarriers versus Doppler Frequenc.
6. Number of Availa
In estigate the variations in the total
umber of subcarriers as the factors such as, average
the changes in the number of available
bcarriers, the AWGN power is varied while the Dop-
carriers under different
AWGN power. Based on the results, as the AWGN
ber of available
requency is changed while
ading gain are kept constant
values of 3dB and 4dB respectively. As illustrated
y
ble Subcarriers under the number of available sub
Variable SNR
this section, we inv
n
noise power, which is modelled as AWGN, Doppler fre-
quency, and fading gain are changed.
6.1. AWGN
To determine
su
pler frequency and the fading gain are kept constant at
values of 25Hz and 4dB respectively. Figure 7 shows
power is varied between 10dB to 0dB, the number of
available subcarriers decreases by 19%.
6.2. Doppler Frequency
To investigate the variations in the num
subcarriers as the Doppler f
the AWGN power and the f
at
in Figure 8, as the Doppler frequency is varied between
10Hz to 100Hz the number of available subcarriers de-
creases by 44%.
Copyright © 2009 SciRes. IJCNS
L. NOOR ET AL.
783
Figure 9. Number of available subcarriers versus fading level.
Figure 10. Number of available subcarriers versus AWGN power for different Doppler Frequency.
6.3. Freque
ber of available
aried, the AWGN
ower and the Doppler frequency are kept constant at
available subcarriers is
de
ng gain
ailable sub-
carriers with the variations in AWGN power and Dop-
able s
ncy Selective Fading and the Doppler frequency under a constant fadi
of 4dB. Figure 10 shows the number of av
To determine the changes in the num
subcarriers as the fading level is v
p
3dB and 25Hz respectively. Figure 9 depicts the corre-
sponding number of subcarriers as the fading level is
varied between 30 to 0dB. Hence, as the fading level is
varied between 0dB to 30dB the number of available
subcarries decreases by 56%.
To further analyze the effect of the hostile channel
conditions such as AWGN power, deep-fading and Dop-
pler frequency, the number of
termined with the variation in both the AWGN power
pler frequency. Based on the results, it can be stated that
40Hz increase in the Doppler frequency leads to 20%
decrease in the number of available subcarriers for an
AWGN power of 0dB.
In addition, the number of available subcarriers is de-
termined with the variation in both the AWGN power
and the fading level under a constant Doppler frequency
of 25Hz. Figure 11 shows the number of available sub-
carriers with the variations in AWGN power and fading
levels. As evident from this figure, 20dB increase in fad-
ing gain results in 12% decrease in the number of avail-
ubcarriers for an AWGN power of 0dB.
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opyright © 2009 SciRes. IJCNS
L. NOOR ET AL.
784
Figure 11. Number of available subcarriers versus AWGN power for different fading gain.
Hence, channel constraints such as AWGN, Doppler
effect and frequ
implication on sy
vailable subcarriers changes with the variation in the
A
adation in terms of subcarrier
smission, perfect synchronization is
tical systems are subject to imperfect
nchronization, the analysis indicates that determining
10Hz to 100Hz in Dopplefrequency causes 44% de-
ubcarriers, and
o 30dB result
in 56% decrease in the number of allocatable subcarriers.
ncy division multiplex-
ansaction on Communications, pp. 665–675,
] J. A. C. Bingham, “Multicarrier modulation for data
er sensitivity of
d R. Reggiannini, “Carrier frequency acquisi-
tion and tracking for OFDM systems,” IEEE Transaction
ency selective fading impose noticeable
stem performance. The total number of
crease in the number of allocatable s
changes in the fading level between 0dB t
a
WGN power, Doppler shift and fading level. Thus,
under imperfect synchronization, which is the case in
most communication systems, not all the subcarriers are
available for transmission.
7. Conclusions
o avoid performance degrT
availability for tran
required. Since prac
sy
the availability of subcarriers for transmission is essential
in the optimization process of radio resource allocation.
In this paper, we perform an analysis to determine the
SNR degrades as the average power of the channel im-
pairments such as AWGN, CFO due to Doppler fre-
quency and fading gain are increased. The decrease in
SNR causes imperfect synchronization and hence re-
duces the total number of available subcarriers for allo-
cation. We use empirical modelling to characterize the
number of available subcarriers as Poisson random vari-
able and it is determined that under imperfect synchro-
nization up to 22% of the subcarriers are not suitable for
transmission as compared to perfect synchronization
under certain channel conditions. We have determined
the variations in the number of available subcarriers with
the changes in the parameters such as AWGN, Doppler
frequency and deep fades that introduce imperfect syn-
chronization. It has been illustrated that a 10dB increase
in the average AWGN power leads to 19% decrease in
the total number of allocatable subcarriers; a variation of
Thus, under imperfect synchronization all the subcarriers
are not available for transmission. Given that the data
rate is directly proportional to the total number of avail-
able subcarriers for transmission, to provide a realistic
measure of the system capacity subcarrier allocation al-
gorithms should be based on the number of avail- able
subcarriers under imperfect synchronization. Although
subcarrier allocation under the constraint of imperfect
synchronization does not support more users or higher
data rates, it improves system reliability by eliminating
allocation on unavailable subcarriers and hence improv-
ing the system BER performance.
8. References
[1] D. H. J. Sun and J. SauVola, “Features in future: 4g vi-
sions from a technical perspective,” IEEE GLOCOM,
Vol. 6, pp. 3533–3537, November 2001.
[2] L. J. Cimini, “Analysis and simulation of a digital mobile
channel using orthogonal freque
r
ing,” IEEE Tr
July 1995.
[3
transmission: An idea whose time has come,” IEEE Com-
munication Magazine, pp. 5–14, 1990.
[4] M. v. B. T. Pollet and M. Moeneclaey, “B
ofdm systems to carrier frequency offset and wiener
phase noise,” IEEE Transaction on Communications, Vol.
43, pp. 191–193, 1995.
[5] M. Luise an
Copyright © 2009 SciRes. IJCNS
L. NOOR ET AL. 785
correction,” IEEE
offset in ofdm systems,” I
um ml estimation of
. M. C. Y. Wong, and R. S. Cheng, “Multiuser
K. B. Lee, “Transmit power adaptation
FDM systems,” IEEE Global Tele-
ol. 2, 2000.
ectrum Tech-
t trans-
Transaction
on Communications, Vol. 44, 1996.
[6] P. H. Moose, “A technique for orthogonal frequency
division multiplexing frequency offset
Transaction on Communications, Vol. 42, pp. 2908–2913,
1994.
[7] P. B. J. van de Beek and M. Sandell, “Ml estimation of
timing and frequency EEE n
Transaction on Signal Procesings, Vol. 45, pp. 1800–
1805, 1997.
[8] S. K. N. Lashkarian, “Globally optim miss
timing and frequency offset in ofdm systems,” IEEE In-
ternational Conference on Communications, Vol. 2, pp.
1044–1048, 2000.
[9] K. L. R on In
OFDM with adaptive subcarrier, bit, and power alloca-
tion,” IEEE Journal, Selected Areas in Communications,
Vol. 17, 1999.
[10] J. Jang and for [17] S. Kandeepan and S. Reisenfeld, “Performance analysis
of a correlator based maximum likelihood frequency es-
timator,” SPCOM, pp. 169–173, 2004.
multiuser OFDM systems,” IEEE Journal, Selected Areas
in Communications, Vol. 21, 2003.
[11] B. E. Z. Shen and J. G. Andrews, “Optimal power alloca-
tion in multiuser O
communications Conference, Vol. 1, 2003.
[12] J. C. W. Rhee, “Increased in capacity of multiuser ofdm
system using dynamic subchannel allocation,” IEEE 51st,
Vehicular Technology Conference, V
[13] S. Y. C. Suh and Y. Cho, “Dynamic subchannel and bit
allocation in multiuser OFDM with a priority user,” IEEE
Eighth International Symposium, Spread Sp
iques and Applications, pp. 919–923, 2004.
[14] P. Song and L. Cai, “Multi-user subcarrier allocation with
minimum rate request for downlink OFDM packe
ion,” IEEE 59th Vehicular Technology Conference,
Vol. 4, 2004.
[15] D. Rife and R. Boostyn, “Single-tone parameter estima-
tion from discrete-time observations,” IEEE
formation Theory, Vol. 5, 1974.
[16] S. Kandeepan, “Synchronisation techniques for digital
modems,” PhD thesis, University of Technology, Sydney,
July 2003.
[18] S. Ross, “Introduction to probability models,” Academic
Press, 2003.
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