Journal of Signal and Information Processing, 2013, 4, 138-143
doi:10.4236/jsip.2013.43B024 Published Online August 2013 (http://www.scirp.org/journal/jsip)
Frequency Synchronization in OFDM System
C. Geetha Priya1, A. M. Vasumathi2
1Department of Electronics and Communication Engineering, K.L.N. College of Information Technology, Pottapalayam-630611,
Sivagangai District, Tamil Nadu, India; 2Dean Academic & Research Committee Chairman, K.L.N. College of Information Tech-
nology, Pottapalayam-630611, Sivagangai District, Tamil Nadu, India.
Received April, 2013.
ABSTRACT
An accurate frequency synchronization method using the zadoff-chu (ZC) constant envelop preamble is analyzed, and a
new preamble weighted by pseudo-noise sequence is used for orthogonal frequency division multiplexing (OFDM)
systems. Using this method, frequency offset estimator range is greatly enlarged with no loss in accuracy. The range of
the frequency estimation is ±30 of subcarrier spacing using ZC sequence as preamble. Simulations in the MATLAB for
an AWGN channel show that the proposed method achieves superior performance to existing techniques in terms of
frequency accuracy and range.
Keywords: Orthogonal Frequency Division Multiplexing (OFDM); Additive White Gaussian Noise (AWGN); Carrier
Frequency Offset (CFO); Constant Amplitude Zero Auto Correlation (CAZAC); Zadoff-Chu (ZC)
1. Introduction
Orthogonal frequency division multiplexing (OFDM) is a
digital multi-carrier modulation technique that has be-
come an increasingly popular scheme in modern digital
communications. It is the attractive technique for high
speed wireless communications. It is robust against fre-
quency-selective fading in a multipath channel eliminat-
ing the need for complex time-domain equalization. Sev-
eral wireless communication systems adopt OFDM as
their modulation technique such as wireless local area
networks (WLAN), wireless fidelity WiFi, mobile
worldwide interoperability for microwave access (Mobile
WiMAX), 3rd generation partnership project long term
evolution (3GPP LTE), digital audio broadcasting (DAB),
digital video broadcasting (DVB), digital video broad-
casting-terrestrial transmission systems (DVB-T), digital
video broadcasting-handhelds (DVB-H), digital video
broadcasting- satellite services to handhelds(DVB-SH)
wireless standards. Especially, mobile digital broadcast-
ing system has attracted considerable attention which
provides not only TV and radio services but also data and
multimedia services to mobile phone and portable de-
vices. The disadvantages of OFDM system are peak to
average power ratio (PAPR), carrier frequency offset
(CFO) and timing offset (TO).
OFDM is very sensitive to carrier frequency offsets in
the received signal due to doppler shifts or instabilities in
the local oscillator (LO) and results in a loss of subcarrier
orthogonality leading to inter carrier interference (ICI).
Hence, it is required to reduce the frequency errors to a
small fraction of the subcarrier spacing. These offsets are
considered constant for simulation purposes as the oscil-
lators drift with temperature, supply voltage, load and the
other slowly changing environmental parameters. The
variations in the CFO due to doppler effects are also con-
sidered to be slow in comparison to simulation time. In
practical system scenarios, the frequency offset can be
many multiples of the subcarrier spacing due to the use
of consumer-grade oscillators in the receiver. Therefore,
a wide frequency estimation range enables greater flexi-
bility in terms of reducing the cost of OFDM receivers to
mass-market consumers. Various techniques have been
proposed in the literature for the frequency synchroniza-
tion in OFDM.
2. Literature Review
Moose [1] derived the maximum likelihood estimation
(MLE) for carrier frequency offset (CFO) in the fre-
quency domain. The limit of the acquisition for the CFO
is ±1/2 the subcarrier spacing. Van de Beek et al. [2]
have shown the joint Maximum Likelihood (ML) esti-
mator of time and frequency offset. This algorithm ex-
ploits the cyclic prefix preceding the OFDM symbols
reducing the need for pilots. Schmidl and Cox [3] pro-
posed frequency and timing synchronization algorithm
by using repeated data symbol. The range of CFO esti-
mation is ±1. Michele et al. proposed a training symbol
of more than two identical parts to achieve better accu-

Frequency Synchronization in OFDM System 139
racy. The estimation range can be made as large as de-
sired without the need of the second training symbol [4].
Fredrik Tufvesson et al. compared and analyzed the
preambles for OFDM systems based on repeated OFDM
data symbols or repeated short pseudo noise sequences.
Synchronization based on PN-sequence preambles of-
fered greater power reductions in stand-by model [5].
Minn et al. [6] compared the performance of timing off-
set estimation methods with modification in the training
structure and found a smaller estimator variance in his
scheme. Ren et al. [7] proposed the modified preamble in
WLANs with a typical structure weighted by the pseudo-
noise sequence which enlarged range of frequency offset
estimation to ±4. Hlaing Minn et al. [8] presented a fre-
quency offset estimation approach using a maximum-
likelihood principle with a sliding observation vector
(SOV-ML). Chin-Liang Wang et al. [9] proposed a
method to make a modulatable orthogonal sequence par-
tially geometric for large CFO estimation. Wei Zhong
[10] proposed a novel integral frequency offset (IFO)
estimation method which examined the phase changes of
synchronization signals in frequency domain. This
method provided excellent IFO estimation performance
with very low computational complexity. Sung-Ju Lee et
al. [11] proposed the carrier frequency offset mitigation
scheme in wireless digital cooperative broadcasting sys-
tem using multi-symbol encapsulated orthogonal fre-
quency division multiplexing (MSE-OFDM), which uses
one cyclic prefix (CP) for multiple OFDM symbols.
Adegbenga B. Awoseyila et al. [12] proposed a novel
technique for 3GPP LTE specifications using only one
training symbol with a simple structure of two identical
parts to achieve robust, low-complexity and full-range
time-frequency synchronization in OFDM systems. E. C.
Kim et al. [13] enhanced the performance frequency off-
set compensation by adding a ternary sequence to OFDM
signals in the time domain which finds application in
design of synchronization block of OFDM scheme for
wireless multimedia communication services. The power
level of the ternary sequence to be added needs to be low
enough in order not to affect the normal operation of the
OFDM system. Ilgyu Kim et al. [14] proposed an effi-
cient synchronization signal structure for OFDM-based
Cellular Systems The sequence used for the Primary
Synchronization signal is generated from a frequency-
domain ZC sequence for high rate and multimedia data
service systems such as LTE in the 3GPP. Ji-Woong
Choi et al. [15] described the joint ML estimation using
correlation of any pair of repetition patterns, providing
optimized performance.
In Moose method, the limit of the estimation for the
CFO is ±1/2 the subcarrier spacing. In Schmidl and Cox
method, the limit of the estimation for the CFO is ±1 the
subcarrier spacing. In Minn method, the limit of the es-
timation for the CFO is ±2 the subcarrier spacing. In Ren
method, the limit of the estimation for the CFO is ±4 the
subcarrier spacing. The method using ZC sequence as
preamble, the limit of the estimation for the CFO is ±30
the subcarrier spacing. Hence the Carrier Frequency
Offset estimation range is large when compared to the
previous methods.
This paper is based on preamble-aided methods that
can be applied to both burst-mode and continuous
OFDM applications. The organization of the paper is as
follows. In Section I, the OFDM system model and
importance of frequency offset estimation is described.
In Section II, the frequency offset estimation of previous
methods is explained. The algorithm for frequency offset
estimation using ZC sequence is given in Section III.
Simulation results and discussions are presented in
Section IV. Finally, in Section V, conclusions are drawn.
3. The OFDM System Model
The incoming input binary streams are first mapped into
constellation points according to any of the digital
modulation schemes such as QPSK/QAM. In QPSK
(Quadrature Phase Shift Keying) modulation, the incom-
ing binary bits are combined in the form of two bits and
are mapped into constellation point. After mapping into
constellation points, the incoming serial bits are con-
verted into parallel bits transmitting N OFDM samples at
a time. The OFDM signal is generated using N subcarri-
ers. The total bandwidth is divided into 64 sub channels.
The N constellation points are modulated using N sub-
carriers whose carrier frequencies are orthogonal in na-
ture. The modulation is similar to taking inverse dis-
crete/fast fourier transform (IDFT/IFFT) operation. The
output of N point (IFFT) block is the OFDM signal. Now
the N OFDM signal samples are combined and then
transmitted i.e., the parallel samples are now converted
into serial sequence and then it is transmitted. The
OFDM baseband signal at the transmitter is expressed as
in (1)
12
0
1
()(). 01
Njnk
N
k
xnX knN
e
N




 
 (1)
where
n -time domain sample index
X (k) -modulated QPSK data symbol on the kth
subcarrier
N -total number of subcarriers and
x (n) -OFDM signal.
In order to maintain a signal to noise ratio (SNR) of 20
decibels or greater for the OFDM carriers, offset is limited
to 4% or less than the inter carrier spacing which is
simulated in Figure 1. The lower bound for the SNR at
the output of the DFT for the OFDM carriers in a channel
with AWGN and frequency offset is derived as in [1] and

Frequency Synchronization in OFDM System
140
is given by (2)



2
))(sin
0
(5947.01/
2
)/(sin.
0
v
N
Ec
vv
N
Ec
SNR  






 (2)
Ec is the energy of subcarrier
All the preamble based frequency offset estimation
methods given in literature aims at accuracy and
increasing the range of frequency offset estimation [2-8].
The importance of frequency offset estimation in various
high speed broadband wireless applications can be
understood from the literature in [11-15].
Figure 1. SNR versus relative frequency offset for OFDM.
This paper deals with frequency offset estimation us-
ing ZC sequence as preamble. A ZC sequence is a com-
plex-valued mathematical sequence of constant ampli-
tude. The cyclically shifted versions of the sequence do
not cross-correlate with each other when the signal is
recovered at the receiver. The cyclic-shifted versions of
sequence remain orthogonal to one another, provided that
each cyclic shift within the time domain of the signal is
greater than the combined propagation delay and multi-
path delay-spread of that signal between the transmitter
and receiver. ZC sequences are used in the 3GPP LTE air
interface in the definition of primary synchronization
signal, random access preamble (PRACH) and HARQ
ACK/NACK responses (PUCCH). The ZC sequences are
used in LTE because they provide an advantage of hav-
ing a lower PAPR ratio.
4. Frequency Offset Estimation
The basic principle behind frequency estimation is cor-
relation function (CF) within the preamble denoted as
P(d) to obtain maximum value. This is the notification of
the arrival of preamble. The signal power representing
normalization function (NF) denoted as R(d) is then
found out. Timing metric denoted as M(d) is got by di-
viding CF by NF i.e., normalizing the correlated values.
Maximum point of timing metric ˆ

indicates the start-
ing point of preamble. The estimation of frequency offset
f using one training symbol in Schmidl method [3] is
given by (3).
ˆ
ˆˆ
(())/fangle P

  (3)
The acquisition range for the carrier frequency offset
is only ˆ
f
≤ 1 due to periodicity of angle(.). Minn [6]
used negative valued samples at the second half of the
training symbols and calculated the offset using (4).
ˆˆ
(())2/fangleP

  (4)
The acquisition range for the carrier frequency offset
is ˆ
f
≤ 2
Ren [7] used a preamble of identical symbol with N
complex samples. The repetitive nature of the preamble
gives robustness against frequency offset which is calcu-
lated as in (5).
ˆˆ
4(())fangle P/

   (5)
The acquisition range for the carrier frequency offset
is ˆ
f
≤ 4
Kasami sequence is generated with period k and the
same sequence is repeated in the next half of the duration.
The preamble structure is defined with Kasami sequence
of period eight and offset is estimated using (6).
ˆˆ
(())/4fangle P



 (6)
The acquisition range for the carrier frequency offset
estimated using (6) is found to be very poor ˆ
f
≤ 0.25
5. Algorithm for CFO Estimation Using ZC
Sequence
The algorithm for estimating the frequency offset by ZC
sequence is explained below
1) ZC sequence generated and that has not been shifted
is known as a root sequence. The complex value at each
position (n) of root ZC sequence (u) is generated using (7)
with u=1 and NZC =32.
(1)/
()
j
un nNzc
un
xe
 
 (7)
where 0 ≤ n ≤ NZC -1.
NZC is the length of the ZC sequence
2) The constant envelop preamble generated from DFT
of a CAZAC sequence is given as in (8) with N=64.
...
01 1
xx x Xpreamble N




 (8)
xi’s are the samples of the preamble in the time domain
which satisfies the condition in (9)
/2,0,...,/2 1
xx
iiN iN



(9)

Frequency Synchronization in OFDM System 141
3) The samples of a complex-valued baseband OFDM
symbol is described as in (10)
12/
0
Njπkn N
n
k
xce
k


 (10)
where ck is the complex modulated symbol on the k
th
sub-carrier generated by the DFT of xu(n) and mapped to
constellation points. N is the size of IFFT and k is the
index of samples. These preamble samples are transmit-
ted as RF signal after a parallel to serial conversion along
with the data symbols.
4) In the receiver side, the timing offset is modelled as
a delay and the frequency offset as a phase distortion of
the received data in the time domain, so, the nth received
sample is represented as given in (11)
(2/ )
() ()()
jvnN
rn ynwn
e

  (11)
where r(n) is the received signal
ε is the integer-valued unknown arrival time of a
symbol,
v is the frequency offset normalized by the sub-carrier
spacing,
w(n) is the sample of zero-mean complex Gaussian
noise process
5) If the absolute frequency offset is within ±1, using
Schmidl Cox method, the offset is estimated as ˆ1

based on the correlation values P(d) given in eqn.(12).
The range of the frequency estimate given by (13) is due
to the period of phase function.
/2 1*
/2
0
()( )(/2)
N
kkN
k
pdssrd krd kN




 (12)
1(( ))
ˆ1opt
angle P




(13)
6) r1(k) represents the received preamble compensated
using Schmidl’s algorithm if offset is within the range of
±1 and is given as in (14)

ˆ
2/
1
1
j
kN
e rr
kk
 
 (14)
7) If the absolute frequency offset is greater than 1, the
second estimation is done using the offset compensated
received signal r1(k). The kth sample of the original pre-
amble has the PN sequence sk weighted factor which has
the value of ±1. The vector s = [-1 -1 -1 -1 1 -1 1 -1 1 1 1
-1 1 1 -1 -1 -1 1 1 1 1 1 -1 -1 1 1 -1 1 -1 -1 1 -1] is used
as PN sequence. The
x
k
 is calculated as in (15)
'()0,1, 2,...,1rk kN
xs
kk


(15)
8) The received signal compensated for offset within
the range of ±1 using Schmidl’s method, is mul-
tiplied with the conjugate

1
rk
x
k

to obtain


k2
r as
given in (16)

21
x
rr
k kk

 (16)
9) Then I(q) is calculated as in (17) is the periodogram
of the signal r2(k). The integer part is estimated from the
index, q of the periodogram of the received training
symbol represented as given by

2
12/
0
() 2
N
j
qk N
k
Iq e
rk



 (17)
10) The argument q which maximizes I(q) is estimated
as in (18)
ˆargmax(),......,0,1,.....,
22
NN
qIqq
q
 (18)
11) The total frequency offset is calculated according
to the ZC method as given by (19)
ˆˆˆ1 q



 (19)
If the CFO to be estimated ˆ

is 24.5 subcarrier spac-
ing, first the frequency offset 1
ˆ

=0.5 (which is less than
1) subcarrier spacing can be estimated by Schmidl Cox
method and = 24 subcarrier spacing frequency offset
can be estimated by the proposed ZC method. By these
two estimation procedures for
ˆ q
ˆ1

and which are
calculated separately, the total CFO can be estimated as
ˆ q
ˆˆˆ1
q



.
If the CFO is less than or equal to one subcarrier
spacing, the first procedure alone is needed. But if the
CFO is greater than one, the two procedures are carried
out separately to estimate the total carrier frequency off-
set.
6. Simulations and Discussion
Figure 2. Comparison of the mean of CFO offset estimation
methods.
Figure 2 gives a comparison of the estimation ranges
of the different methods using preamble structure defined
by Schmidl, Minn, Ren and also by using Kasami and
ZC sequence as preambles. From the simulation results,

Frequency Synchronization in OFDM System
142
it is found that preamble based on ZC sequence gives
accuracy and the estimation range is much larger than
that of the others.
Figure 3. Comparison of the mean of CFO offset estimation
methods with normalised frequency offset ±30 subcarrier
spacing.
Method Schmidl Minn Ren Kasami Zadoff-Chu
Frequency
Offset
Estimation
Range
│f│≤ 1 │f│≤ 2 │f│≤ 4 │f│≤ 0.2 │f│≤ 30
The performance of proposed CFO estimator is evalu-
ated in AWGN and different channel environment ac-
cording to the HIPERLAN specifications using the Table.
2.
Here, Model A, corresponds to a typical office envi-
ronment for NLOS conditions and 50ns average rms de-
lay spread. Model B, corresponds to typical large open
space and office environments for NLOS conditions and
100ns average rms delay spread. Model C, corresponds
to a typical large open space environment for NLOS
conditions and 150 ns average rms delay spread. Model
D is the same as model C but for LOS conditions. A 10
dB spike at zero delay has been added resulting in a rms
delay spread of about 140ns. Model E, corresponds to a
typical large open space environment for NLOS condi-
tions and 250 ns average rms delay spread.
The Zadoff-Chu based CFO estimator performance is
good under all the channel conditions which is simulated
in the Figure 4. The performance is stable for all envi-
ronments like typical office environment, typical large
open space with different rms delay spreads.
Channel AChannel BChannel C Channel D Channel E
Sl.
No
Tap delay
in nS
Power in
Db
Tap delay
in nS
Power in
dB
Tap delay in
nS
Power in dB
Tap delayin
nS
Power in
dB
Tap delay
in nS
Power in
dB
1 00 0 -2.6 0 -3.3 0 0 0 -4.9
2 10-0.9 10-310 -3.6 10 -10 10-5.1
3 20-1.7 20 -3.5 20 -3.9 20 -10.3 20-5.2
4 30-2.6 30 -3.9 30 -4.2 30 -10.6 40-0.8
540-3.5500 50 0 50 -6.4 70-1.3
6 50-4.3 80 -1.3 80 -0.9 80 -7.2 100-1.9
760 -5.2 110 -2.6 110 -1.7 110 -8.1 140-0.3
870 -6.1 140 -3.9 140 -2.6 140 -9 190-1.2
980 -6.9 180 -3.4 180 -1.5 180 -7.9 240-2.1
1090-7.8230-5.6230 -3 230 -9.4 3200
11110-4.7 280 -7.7 280 -4.4 280 -10.8 430-1.9
12140-7.3 330 -9.9 330 -5.9 330 -12.3 560-2.8
13170-9.9 380-12.1400 -5.3 400 -11.7 710-5.4
14200-12.5430-14.3490 -7.9 490 -14.3 880-7.3
15240-13.7490-15.4600 -9.4 600 -15.8 1070-10.6
16290-18560 -18.4730 -13.2 730 -19.6 1280-13.4
17340-22.4 640-20.7880 -16.3 880 -22.7 1510-17.4
18390 -26.7730-24.6 1050 -21.2 1050 -27.6 1760-20.9
Figure 4. Performance of the proposed Zadoff Chu based
CFO estimator with offset = 3.3 subcarrier spacing in dif-
ferent channel environments.
7. Conclusions
The method using ZC sequence as preamble for Fre-
quency Offset Estimator enlarges the range of estimation
to ±30 of subcarrier spacing for OFDM based WLAN
system. The accuracy of estimation has improved when
compared to other methods. Compared to other data
aided techniques simulated in this paper like Schmidl,
Minn, Ren for CFO estimation, this method gives better
accuracy in the estimation of frequency offset.
REFERENCES
[1] P. H. Moose, “A Technique for Orthogonal Frequency
Division Multiplexing Frequency Offset Correction,”

Frequency Synchronization in OFDM System
143
IEEE Transactions on Communications, Vol. 42, 1994,
pp. 2908-2914.doi:10.1109/26.328961
[2] J.-J. Van de Beek, M. Sandell and P. O. Börjesson, “ML
Estimation of Time and Frequency Offset in OFDM Sys-
tems,” IEEE Trans. Signal Processing, Vol. 45, 1997, pp.
1800-1805. doi:10.1109/78.599949
[3] T. M. Schmidl and D. C. Cox, “Robust Frequency and
Timing Synchronization for OFDM,” IEEE Trans. Com-
mun., Vol. 45, 1997, pp. 1613-1621.
doi:10.1109/26.650240
[4] M. Morelli and U. Mengali, “An Improved Frequency
Offset Estimator for OFDM Applications,” IEEE Com-
munications Letters, Vol. 3,1999, pp. 75-77.
doi:10.1109/4234.752907
[5] F. Tufvesson, O. Edfors and M. Faulkner, “Time and
Frequency Synchronization for OFDM using
PN-sequence Preamble,” in Proc. Veh. Technol. Conf.,
Vol. 4, 1999, pp. 2203-2207.
[6] H. Minn, M. Zeng and V. K. Bhargava, “On Timing Off-
set Estimation for OFDM Systems,” IEEE Commun. Let-
ters, Vol. 4, 2000, pp. 242-244.
[7] G. L. Ren, Y. L. Chang, H. Zhang and H. N. Zhang, “A
Novel Burst Synchronization Method for OFDM Based
WLAN Systems,” IEEE Trans. Consumer Electron, Vol.
50, 2004, pp. 829-834.doi:10.1109/TCE.2004.1341687
[8] H. Minn, V. K. Bhargava and K. B. Letaief, “A Com-
bined Timing and Frequency Synchronization and Chan-
nel Estimation for OFDM Systems,” IEEE Transactions
on Communications, Vol. 54, 2006, pp. 416-422.
doi:10.1109/TCOMM.2006.869860
[9] W. Zhong, “A Simple and Robust Estimation of Integral
Frequency Offset for OFDM Systems,” IEEE Transac-
tions on Consumer Electronics Vol. 54, 2008, pp.
411-413.doi:10.1109/TCE.2008.4560107
[10] C. L. Wang and H. C. Wang, “Large CFO Acquisition
using Partial Geometric Modulatable Orthogonal Se-
quences,” IEEE VTC Spring , 2009, pp. 1-5.
[11] S. J. Lee, J. S. Yoon and H. K. Song, “Frequency Offset
Mitigation of Cooperative OFDM System in Wireless
Digital Broadcasting,” IEEE Transactions on Consumer
Electronics, Vol. 55, 2009, pp. 385-390.
[12] A. B. Awoseyila, C. Kasparis and B. G. Evans, “Robust
Time-domain Timing and Frequency Synchronization for
OFDM Systems,” IEEE Transactions on Consumer Elec-
tronics, Vol. 55, 2009, pp. 391-399.
[13] E. C. Kim, J. Yang and J. Y. Kim, “Novel of DM Frame
Synchronization and Frequency Offset Compensation
Scheme for Wireless Multimedia Communication Sys-
tems,” IEEE Transactions on Consumer Electronics, Vol.
55, 2009, pp. 1141-1148. doi:10.1109/TCE.2009.5277968
[14] I. Kim, Y. Han and H. K. Chung, “An Efficient Synchro-
nization Signal Structure for OFDM-Based Cellular Sys-
tems,” IEEE Transactions on Wireless Communications,
Vol. 9, 2010, pp. 99-105.
doi:10.1109/TWC.2010.01.090516
[15] J. W. Choi, ,J. W. Lee, Q. Zhao and H. L. Lou, “Joint ML
Estimation of Frame Timing and Carrier Frequency Off-
set for OFDM Systems employing Time-Domain Re-
peated Preamble,” IEEE Transactions on Wireless Com-
munications, Vol. 9, 2010, pp. 311- 317.
doi:10.1109/TWC.2010.01.090674