Frequency Synchronization in OFDM System

doi:10.4236/jsip.2013.43B024

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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.

Email: [email protected], [email protected]

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)

()(). 01

Njnk

xnX knN







 

 (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)







))(sin

(5947.01/

)/(sin.

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).

ˆˆ

(())/fangle P





 (3)

The acquisition range for the carrier frequency offset

is only ˆ

≤ 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

≤ 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

≤ 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

≤ 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)/

()

un nNzc





 (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

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/

Njπkn N

xce





 (10)

where ck is the complex modulated symbol on the k

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





 (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)

kkN

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)







 (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

 is calculated as in (15)

'()0,1, 2,...,1rk kN





(15)

8) The received signal compensated for offset within

the range of ±1 using Schmidl’s method, is mul-

tiplied with the conjugate





to obtain





r as

given in (16)





 (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



12/

() 2

qk N

Iq e







 (17)

10) The argument q which maximizes I(q) is estimated

as in (18)

ˆargmax(),......,0,1,.....,

qIqq

 (18)

11) The total frequency offset is calculated according

to the ZC method as given by (19)

ˆˆˆ1





 (19)

If the CFO to be estimated ˆ



is 24.5 subcarrier spac-

ing, first the frequency offset 1



=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

ˆ1



and which are

calculated separately, the total CFO can be estimated as

ˆˆˆ1





.

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.

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.

Tap delay

in nS

Power in

Tap delay

in nS

Power in

Tap delay in

Power in dB

Tap delayin

Power in

Tap delay

in nS

Power in

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.

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Frequency Synchronization in OFDM System

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