7
Integer Frequency Offset Algorithm for Digital Radio Mondiale System Cheng Yan and Ming Yan Communication University of China, Beijing, China Email: [email protected]; [email protected]; AbstractThis paper proposes one integer frequency offset estimation algorithm for orthogonal frequency division multiplexing (OFDM) based digital radio mondiale (DRM) system. The algorithm exploits the correlation of frequency pilots to construct a novel angle vector. As the power factor of the pilots in the correlated calculation is inevitably disturbed by the multipath and noise, the angle vector only utilizes the phase factor of the pilots. The integer frequency offset can be obtained by detecting the shift of the vector norm of the pilots, because the vector norm is maximum at the position of the pilots. The performance of the proposed algorithm is compared with that of conventional algorithms. The simulation results show that the proposed algorithm can effectively combat multipath and noise with wider range and higher accuracy of the frequency offset estimation. Index TermsDigital radio mondiale, orthogonal frequency division multiplexing, integer frequency offset I. INTRODUCTION The DRM system utilizes OFDM modulation [1]. OFDM as an orthogonal multi-carrier modulation system is much more sensitive to carrier frequency offset than the single-carrier system. As the carrier frequency offset can destroy the orthogonality of sub-carriers and bring the inter-carrier interference (ICI), the frequency synchronization is particularly important to OFDM system. The carrier frequency offset (CFO) estimation is usually divided into two parts: integer frequency offset (IFO) [2]-[4] and fractional frequency offset (FFO) [5]- [9]. Lots of research has been done for OFDM frequency synchronization algorithms. Basically, they are summarized into two categories: the training sequence assisted and non-data assisted. The non-data assisted algorithm, for example, ML (maximum likelihood) based on CP (cyclic prefix). With the help of the correlation between the CP and the back portion of the OFDM symbol, the algorithm can complete the symbol synchronization estimation [10]. As the frequency offset estimation range | | 0.5 which is normalized to the sample interval, the algorithm cant do integer frequency offset estimation [11]. The method based on the training sequence is the joint estimation of time and frequency. To get accurate integer Corresponding author email: [email protected]. frequency offset, the estimation of time-delay and the fractional frequency offset are necessary. S&C [12] is proposed by T. M. Schmidl and D. C. Cox, in which the presence of peak platforms leads to the vague timing synchronization. Minn [13] re-designs the first two OFDM symbols, and the algorithm eliminates the flat effect of the timing metric function. However, the method has a large root mean square error in multipath channel, and in a quarter of the cyclic prefix to the number of subcarriers, the performance is not satisfactory. Park [14] proposes one synchronization algorithm which can produce a sharp peak. However it would be accompanied by side peaks. Conventional synchronization algorithm based on the correlated property of the time-domain pseudo-noise (PN) sequence may not work well in multipath channels. An algorithm is proposed in [15] where the PN sequence in the frame head is considered as a CP of the OFDM training symbol. The frequency synchronization algorithm based on the training sequence develops the synchronization performance by increasing the system overhead with the low spectrum utilization and limited estimated range. This paper will focus on the integer frequency offset estimation algorithm for DRM receiver [16]. Basically, they are summarized into two categories: the time pilot reference and frequency pilot reference. The problem of frequency offset estimation has been widely explored, but there is still room for a better estimator which has a wider range and higher accuracy. The section II mainly introduces the DRM system model. The section III describes the conventional frequency synchronization algorithm for DRM system. The section IV will introduce the proposed algorithm. Finally, the proposed algorithm is verified by simulation. II. THE DRM SYSTEM MODEL The DRM system utilizes the OFDM modulation. At the transmitter, an OFDM symbol ( ), [ , 1] g xn n N N , is generated by performing an N-point inverse fast fourier transform (IFFT) on the information symbol X(k) for max min [ , ] k k k and adding N g cyclic prefix samples. The reference parameters of min k and max k are shown in the Table I. The numerical values of the OFDM parameters are shown in the table II [1]. Journal of Communications Vol. 8, No. 9, September 2013 572 ©2013 Engineering and Technology Publishing doi:10.12720/jcm.8.9.572-578 Manuscript received July 12, 2013; revised September 21, 2013.

Integer Frequency Offset Algorithm for Digital Radio ...The carrier frequency offset is usually divided into integer part and fractional part, and it can be calculated respectively

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Integer Frequency Offset Algorithm for Digital Radio

Mondiale System

Cheng Yan and Ming Yan Communication University of China, Beijing, China

Email: [email protected]; [email protected];

Abstract—This paper proposes one integer frequency offset

estimation algorithm for orthogonal frequency division

multiplexing (OFDM) based digital radio mondiale (DRM)

system. The algorithm exploits the correlation of frequency

pilots to construct a novel angle vector. As the power factor of

the pilots in the correlated calculation is inevitably disturbed by

the multipath and noise, the angle vector only utilizes the phase

factor of the pilots. The integer frequency offset can be obtained

by detecting the shift of the vector norm of the pilots, because

the vector norm is maximum at the position of the pilots. The

performance of the proposed algorithm is compared with that of

conventional algorithms. The simulation results show that the

proposed algorithm can effectively combat multipath and noise

with wider range and higher accuracy of the frequency offset

estimation. Index Terms—Digital radio mondiale, orthogonal frequency

division multiplexing, integer frequency offset

I. INTRODUCTION

The DRM system utilizes OFDM modulation [1].

OFDM as an orthogonal multi-carrier modulation system

is much more sensitive to carrier frequency offset than

the single-carrier system. As the carrier frequency offset

can destroy the orthogonality of sub-carriers and bring

the inter-carrier interference (ICI), the frequency

synchronization is particularly important to OFDM

system.

The carrier frequency offset (CFO) estimation is

usually divided into two parts: integer frequency offset

(IFO) [2]-[4] and fractional frequency offset (FFO) [5]-

[9]. Lots of research has been done for OFDM frequency

synchronization algorithms. Basically, they are

summarized into two categories: the training sequence

assisted and non-data assisted.

The non-data assisted algorithm, for example, ML

(maximum likelihood) based on CP (cyclic prefix). With

the help of the correlation between the CP and the back

portion of the OFDM symbol, the algorithm can complete

the symbol synchronization estimation [10]. As the

frequency offset estimation range | | 0.5 which is

normalized to the sample interval, the algorithm can’t do

integer frequency offset estimation [11].

The method based on the training sequence is the joint

estimation of time and frequency. To get accurate integer

Corresponding author email: [email protected].

frequency offset, the estimation of time-delay and the

fractional frequency offset are necessary. S&C [12] is

proposed by T. M. Schmidl and D. C. Cox, in which the

presence of peak platforms leads to the vague timing

synchronization. Minn [13] re-designs the first two

OFDM symbols, and the algorithm eliminates the flat

effect of the timing metric function. However, the method

has a large root mean square error in multipath channel,

and in a quarter of the cyclic prefix to the number of

subcarriers, the performance is not satisfactory. Park [14]

proposes one synchronization algorithm which can

produce a sharp peak. However it would be accompanied

by side peaks. Conventional synchronization algorithm

based on the correlated property of the time-domain

pseudo-noise (PN) sequence may not work well in

multipath channels. An algorithm is proposed in [15]

where the PN sequence in the frame head is considered as

a CP of the OFDM training symbol. The frequency

synchronization algorithm based on the training sequence

develops the synchronization performance by increasing

the system overhead with the low spectrum utilization

and limited estimated range.

This paper will focus on the integer frequency offset

estimation algorithm for DRM receiver [16]. Basically,

they are summarized into two categories: the time pilot

reference and frequency pilot reference. The problem of

frequency offset estimation has been widely explored, but

there is still room for a better estimator which has a wider

range and higher accuracy.

The section II mainly introduces the DRM system

model. The section III describes the conventional

frequency synchronization algorithm for DRM system.

The section IV will introduce the proposed algorithm.

Finally, the proposed algorithm is verified by simulation.

II. THE DRM SYSTEM MODEL

The DRM system utilizes the OFDM modulation. At

the transmitter, an OFDM symbol ( ), [ , 1]gx n n N N ,

is generated by performing an N-point inverse fast fourier

transform (IFFT) on the information symbol X(k) for

maxmin[ , ]k k k and adding Ng cyclic prefix samples. The

reference parameters of min

k and maxk are shown in the

Table I. The numerical values of the OFDM parameters

are shown in the table II [1].

Journal of Communications Vol. 8, No. 9, September 2013

572©2013 Engineering and Technology Publishing

doi:10.12720/jcm.8.9.572-578

Manuscript received July 12, 2013; revised September 21, 2013.

max

min

2 /1( ) ( )

kj kn N

k kx n X k e

N

. (1)

TABLE I: CARRIER NUMBERS FOR EACH MODE

Robust

Mode

Carrier Spectrum occupancy patterns

0 1 2 3 4

A Kmin 2 2 -102 -114 -98

Kmax 102 114 102 114 314

B Kmin 1 1 -91 -103 -87 Kmax 91 103 91 103 279

C Kmin - - - -69 -

Kmax - - - 69 - D Kmin - - - -44 -

Kmax - - - 44 -

TABLE II: NUMERICAL VALUES OF THE OFDM PARAMETERS

Robust

Mode

Tu (ms) Tg(ms) Ts(ms)

A 24 2.6 26.66 B 21.33 5.33 26.66

C 14.66 5.33 20

D 9.33 7.33 16.66

where Ts is the OFDM symbol period, Tg is the cyclic

prefix, Tu is the useful part of OFDM symbol.

After passing over DRM channel with Nt paths, the

receiver symbol:

,

12 /

( ) ( ( ) ( )) ( )

0L t L

L L

Nt j n Nz n h n x n e w n

t

. (2)

where L is the symbol index, is the frequency offset

normalized to carrier spacing which can be divided into

two parts: IFOinteger

and FFOfraction

f ,,

( )L t

h n is the

channel impulse response of the tth path, ( )L

w n is the

contribution of the AWGN.

The receiver symbol in the frequency domain can be

expressed:

( ) ( ) ( ) ( )L L L L

Z k H k X k W k . (3)

.

12 /

( ) ( )

0L t

L

Nt j k NtH k H k e

t

. (4)

where ,

( )L t

H k : the channel frequency response of the tth

path, t :the time-delay normalized to sample interval of

the tth path , ( )LW k : the AWGN.

III. THE CONVENTIONAL FREQUENCY

SYNCHRONIZATION FOR DRM

The carrier frequency offset is usually divided into

integer part and fractional part, and it can be calculated

respectively. With the influence of the fractional

frequency offset, the accuracy of integer frequency offset

estimation will greatly decrease.

The fractional frequency offset estimation can use the

most commonly used algorithm: ML (maximum

likelihood).

Figure 1. The transmitted symbols

argm

ax

2.

22

.2

( )z n NZ

*.

(.)

(.)

.

1

2

fractionf

ML

Summation

Summation

Figure 2. The fractional frequency offset acquisition algorithm

Define two sets:

{ ,......, 1}gI N (5)

' { ,......, 1}gI N N N (6)

where I is cyclic prefix of the symbol L. According to

the features of cyclic prefix, it contains the same elements

in 'I .

2 2

s

* 2

s

- j2

+ = 0

{ (n) (n+ m)} = ,

0

w

fractionf

d d m

E z z d e m N n I

others

(7)

where 2

sd and 2

wd denote the energy of the useful symbol

and Gaussian white noise. The algorithm is shown in Fig.

2.

arg max(| ( ) | - | ( ) |)ML

(8)

-1

*( ) ( ) ( )n Ng

n

z n z n N

(9)

-11 2 2( ) ( ( ) ( ))2

n N g

n

z n z n N

(10)

symbol

L

Symbol

L-1

symbol

L+1

I

'I

Journal of Communications Vol. 8, No. 9, September 2013

573©2013 Engineering and Technology Publishing

where SNR

=SNR+1

, SNR is Signal to Noise Ratio, ML is

the estimation of time-delay. So, the fractional frequency

offset is:

1

( )2

fraction MLf

(11)

2

(n) (n) fractionj f n N

L Ly z e

(12)

where (n)L

y is the receiver symbol which eliminates

fractional frequency offset. Making FFT (Fast Fourier

Transform) operation on (n)L

y and removing the cyclic

prefix, we can get (n)L

Y .

A. The Integer Frequency Offset Estimation based on

Time Pilots

Define a TRC (time reference cell) as:

2 ( ) /1024( ) 2 j kP k e k (13)

where 2 is a pilot boost factor and 2 ( ) /1024k

denotes a predefined phase rotation of the pilot cell.

denotes the set of TRC indices. The exact position and

phase rotation of the TRCs are depicted in [1].

The traditional integer frequency synchronization

algorithm based on the time pilot exploits the correlation

of the time pilots and receiver symbol [17].

*int

| |

{| ( ) ( ) |}arg maxL Neger

kd F

Y k d P k

(14)

where ( )N is modular arithmetic, is the modulus

operation, F is the maximum allowable ofinteger

, d is

the trial value of integer

, *(.) denotes the complex

conjugation.

*

2 /2

*

( ) ( )

{ ( ) | ( ) |

( ) ( )}

L N

L

L

k

j k N

k

Y k d P k

H k P k e

W k P k

(15)

The algorithm is susceptible to multipath and noise.

The algorithm in [18] is based on the partial correlation

and splits the correlation into the B blocks ( 2 aB T , aT :

the allowed symbol time-delay error).

*int

1| |

{ | ( ) ( ) |}arg maxN

B

egerm k Bd F m

Y k d P k

.(16)

The algorithms in [17] [18] are suitable for DAB

(Digital Audio Broadcasting) system that utilizes the

block-type pilot, while they are not suitable for DRM

system because the time pilots are not uniformly

distributed. The frequency estimation algorithm in [19],

implemented by TRC partitioning for DRM systems, is

proposed. The TRC partitioning scheme is used for

weakening the effect of frequency-selective fading:

/ 2

int1 1| | ,

*{ | ( ) ( ) |}arg max

NN mc

eger Nm n k Pd F m n

Y k d P k

. (17)

where cN and / 2mN

are the numbers of pilot clusters

and sub-groups in the mth cluster, respectively, ,m nP is the

set of TRC indices, rounds the element to the nearest

integer. Note that the total number of sub-groups is

1 /2cNm mtN N [20].

B. The Integer Frequency Synchronization Algorithm

based on the Frequency Pilots

Define a FRC (frequency reference cell) as:

2 ( ) /1024( ) 2 1j kQ k e k (18)

where 2 is a pilot boost factor and 2 ( ) /1024k

denotes a predefined phase rotation of the pilot cell. 1

denotes the set of FRC indices. The exact position and

phase rotation of the FRCs are depicted in [1].

One frequency synchronization algorithm for DRM

system based on the frequency pilots is proposed by

Communications Technology Institute of Darmstadt

University. The following will introduce the algorithm

[21]:

Firstly, the algorithm should make FFT operation on

receiver symbols to estimate the power spectrum:

224 1

4

0 0

1( ( ) )( )

aver

sL

j nkNN s Ns

i naver

R k z n L i N eN

.(19)

where s gN NN , averN is the number of spectra used

for averaging. In the presence of frequency offset, the

peak of the pilot will shift .The frequency offset can be

obtained by detecting the shift of the pilots.

( ) 4 ( 1) 1g

fac

NP k k k

N (20)

int

^

( ( ))arg max4

L

k

egerd

s

s

f R d P kfacf

N (21)

where sf is the sampling rate, int

^

egerf is the estimation of

integer frequency offset.

IV. THE PROPOSED ALGORITHM

A. The Proposed Algorithm

Based on the characteristics of DRM frequency pilots,

this paper proposes one integer frequency offset

estimation algorithm for DRM. The proposed algorithm

utilizes M+1 consecutive received symbols. After the

conjugate multiplication of two adjacent symbols, the

power spectrum of corresponding carriers ( )L iPow k :

Journal of Communications Vol. 8, No. 9, September 2013

574©2013 Engineering and Technology Publishing

*

1

( ) ( ) ( )

[0, 1] [0, 1]

L i L i L i

k

Pow k Y k Y k

N i M

. (22)

where L is the index of symbols. According to (23), the

phase ( )L iPh kof ( )L iPow k

:

( ) tan( ( )) [0, 1] [0, 1]L i L iPh k ac Pow k k N i M . (23)

where tan()ac is the function of phase acquired. Define

the angle vector _Angl temp :

1

01

0

_ ( ) cos( ( ))

sin( ( ))

M

iM

i

L i

L ij

Angl temp k ph k

ph k

. (24)

where 1j . Therefore, integer frequency offset can

be obtained by (25):

int

| _ ( 1) | | _ ( 2) |arg max

| _ ( 3) |N N

N

egerd

Angl temp d k Angl temp d k

Angl temp d k

[0, 1]d N . (25)

where d is the trial value of integer

, 1, 2, 3k k k are the

position of the frequency pilots without frequency offset.

Finally, combined with the fractional part, the actual

frequency offset is

int

ˆfraction egerf . (26)

B. The algorithm analysis

Before the estimation of integer frequency offset, the

time-delay and fractional frequency offset have been

already compensated. The proposed algorithm exploits

the known correlation of frequency pilots.

*

1

int int

1int

*

1int

( 1 )

( 1 ) ( 1 )

( ( 1 ) ( 1 )

( 1 ) )( ( 1 )

( 1 ) ( 1 ) )

L iN

L iN L i N

L ieger N eger N

L i L iN eger N

L ieger N N

Pow k d

Y k d Y k d

H k d Q k d

W k d H k d

Q k d W k d

(27)

*

1

int int

1int

*

1int

( 2 )

( 2 ) ( 2 )

( ( 2 ) ( 2 )

( 2 ) )( ( 2 )

( 2 ) ( 2 ) )

L iN

L iN L i N

L ieger N eger N

L i L iN eger N

L ieger N N

Pow k d

Y k d Y k d

H k d Q k d

W k d H k d

Q k d W k d

(28)

*

1

int int

1int

*

1int

( 3 )

( 3 ) ( 3 )

( ( 3 ) ( 3 )

( 3 ) )( ( 3 )

( 3 ) ( 3 ) )

L iN

L iN L i N

L ieger N eger N

L i L iN eger N

L ieger N N

Pow k d

Y k d Y k d

H k d Q k d

W k d H k d

Q k d W k d

(29)

If int eger

d , according to (18):

*

int nt

2 ( 1 ) /1024int

2 ( 1 ) /1024int

( 1 ) ( 1 )i

2

2

2

eger N eger N

j k d Neger

j k d Neger

Q k d Q k d

e

e

. (30)

The ( 1 )L iN

Pow k d can be expressed as :

int

*

1 int

( 1 ) 2 ( 1 )

( 1 )

( 1 )

L i L iN eger N

L i eger N

N

Pow k d H k d

H k d

WN k d

. (31)

int

*

1int

*

1

*

1 int

*

int

( 1 ) ( 1 )

( 1 ) ( 1 )

( 1 ) ( 1 )

( 1 )

( 1 ) ( 1 )

L iN eger N

L ieger N N

L i L iN N

L i eger N

L ieger N N

WN k d H k d

Q k d W k d

W k d W k d

H k d

Q k d W k d

. (32)

According to the DRM channel parameters:

maxsT . (33)

where max is the maximum time-delay. So the DRM

channel is flat-fading in the frequency domain [22].

When the SNR is high, the ( 1 )L iN

Pow k d can be

expressed as :

2

int( 1 ) 2 | ( 1 ) |L i L i

N eger NPow k d H k d . (34)

So the ( )L iPh k at the position of the pilots can be

expressed as :

( ) 0 [ 1, 2, 3]L i N

ph k d k k k k

. (35)

1

1

2

2

1

2

1

2 2(

2 2( (1 1

| _ ( ) |

(cos( ( )) ... cos( ( )))

(sin( ( )) ... sin( ( )))

cos ( )) sin ( ( )) ...

cos ( )) sin ( ))

2cos( ( )) cos( ( ))

2sin( ( ))sin( ( )

L L

L L

L L

L L M

L L M

L M L M

Angl temp k

Ph k Ph k

Ph k Ph k

Ph k Ph k

Ph k Ph k

Ph k Ph k

Ph k Ph k

3 1

2 1

1

1

3 1

2 1

) ...

2sin( ( ))sin( ( ))

2sin( ( ))sin( ( ))

2cos( ( )) cos( ( ))

2sin( ( ))sin( ( )) ...

2sin( ( ))sin( ( ))

2sin( ( ))sin( ( ))

L M L M

L M L M

L L

L L

L M L M

L M L M

Ph k Ph k

Ph k Ph k

M Ph k Ph k

Ph k Ph k

Ph k Ph k

Ph k Ph k

. (36)

Journal of Communications Vol. 8, No. 9, September 2013

575©2013 Engineering and Technology Publishing

Finally, 2| _ ( ) |Angl temp k can be expressed as:

1

2

2

3 1

2 1

2

| _ ( ) |

2cos( ( ) ( ))

2cos( ( ) ( )) ....

2cos( ( ) ( ))

2cos( ( ) ( ))

[0, 1]

L L

L L

L M L M

L M L M

Angl temp k

M Ph k Ph k

Ph k Ph k

Ph k Ph k

Ph k Ph k

M k N

. (37)

The equation (36) (37) is monotone decreasing in the

range [0, ]2

. When

1 2 1( ) - ( ) ... ( ) - ( ) 0

L L L M L MPh k Ph k Ph k Ph k

,

the value of 2| _ ( ) |Angl temp n is equal to 2M . Due to the

correlation, 1 2 1| ( ) - ( ) | ... | ( ) - ( ) |L L L M L MPh k Ph k Ph k Ph k

of frequency pilots tend to 0 to its fullest extent, while

1 2 1| ( ) - ( ) | ... | ( ) - ( ) |L L L M L MPh k Ph k Ph k Ph k of other

carriers are much more than 0 .

The conventional algorithms mainly exploit the power

factor of the pilots in the correlated calculation. As the

power factor of the pilots is inevitably disturbed by the

noise and multipath, the correlated peak may be

weakened. The proposed algorithm gets rid of the power

factor of the pilots in correlated calculation and only

retains the phase factor of the pilots. Because the DRM

channel is flat-fading in the frequency domain, the phase-

difference 1 2 1| ( ) - ( ) | ... | ( ) - ( ) |L L L M L MPh k Ph k Ph k Ph k

can efficiently weaken the impact of the noise and

multipath. In addition, superposition of pilots and a set of

consecutive received symbols can be used to combat the

noise. Consider the complexity and accuracy of the

proposed algorithm, 10 consecutive symbols are selected.

V. SIMULATION

The channel bandwidth is 10Hz and the Robust mode

B is selected in this paper. The DRM channel parameters

are shown in the Table III. Ts is 26.66 ms, Tg is 5.33 ms,

the carrier spacing is 7 /846 Hz.

TABLE III: THE CHANNEL PARAMETERS

Channel 1 Path 1 Path 2 Path 3 Path 4

gain 1

delay 0 ms

Df 0 Hz Dp 0 Hz

Channel 2 Path 1 Path 2 Path 3 Path 4

gain 1 0.5 delay 0 ms 1 ms

Df 0 Hz 0 Hz

Dp 0 Hz 0.1 Hz Channel 3 Path 1 Path 2 Path 3 Path 4

gain 1 0.7 0.5 0.25

delay 0 ms 0.7 ms 1.5 ms 2.2 ms Df 0.1 Hz 0.2 Hz 0.5 Hz 1 Hz

Dp 0.1 Hz 0.5 Hz 1 Hz 2 Hz

Channel 4 Path 1 Path 2 Path 3 Path 4 gain 1 1

delay 0 ms 2 ms

Df 0 Hz 0 Hz

Dp 1 Hz 1 Hz

Channel 5 Path 1 Path 2 Path 3 Path 4

gain 1 1 delay 0 ms 4 ms

Df 0 Hz 0 Hz

Dp 2 Hz 2 Hz Channel 6 Path 1 Path 2 Path 3 Path 4

gain 0.5 1 0.25 0.00625

delay 0 ms 2 ms 4 ms 6 ms Df 0 Hz 1.2 Hz 2.4 Hz 3.6 Hz

Dp 0.1 Hz 2.4 Hz 4.8 Hz 7.2 Hz

* Df is doppler shift; Dp is doppler spread.

Fig. 3 shows the integer frequency offset estimation of

the proposed algorithm in the channel 6. Set the

frequency offset to 1200.64 Hz. The peak is at position of

the 26th sampling point, and the estimated frequency

offset is 1200.58 Hz according to (24), (25), (26).

Simulation test shows that the proposed algorithm meets

the requirements of the DRM system.

0 50 100 150 200 250 3000

5

10

15

20

25

30

the sampling points

Energ

y

the integer frequency offset estimate

SNR=10dB

Figure 3. Integer frequency offset estimation.

-1500 -1000 -500 0 500 1000 1500-10

-8

-6

-4

-2

0

2

4

6

8

10

Frequency offset

the m

ean e

rror

of

frequency o

ffset

estim

ation

Figure 4. Frequency offset estimation range.

Define mean error of Frequency Synchronization:

=ˆ ˆ( ) [ ]M E . (38)

where is the actual frequency offset, ̂ is the

estimation of frequency offset. Fig.4 shows the mean

error of frequency offset estimation. Set the range of the

Journal of Communications Vol. 8, No. 9, September 2013

576©2013 Engineering and Technology Publishing

frequency offset from -1600 to 1600. The SNR is 10 dB.

Simulation test shows that approximately within the

range [-1500, 1500], the accuracy of the proposed

algorithm can fulfill the requirements of the DRM system.

Define MSE (Mean Squared Error) of Frequency

Synchronization:

2ˆ ˆ( )J E

. (39)

5 10 15 20 2510

-6

10-5

10-4

10-3

10-2

SNR/dB

MS

E

Channel 2

the proposed algorithm

Reference 19

Reference 21

Reference 18

Reference 17

Figure 5. MSE of the traditional algorithms and the proposed

algorithm versus SNR in channel 2

5 10 15 20 2510

-6

10-5

10-4

10-3

10-2

10-1

100

101

Channel 6

SNR/dB

MS

E

the proposed algorithm

Reference 19

Reference 21

Reference 18

Reference 17

Figure 6. MSE of the traditional algorithms and the proposed

algorithm versus SNR in channel 6.

The mean square error (MSE) of normalized frequency

offset is used to measure the performance of the

algorithm. Fig. 5 shows that the MSE of the proposed

algorithm and traditional algorithms versus SNR in the

channel 2. Set the frequency offset to 150.24 Hz. From

MSE curves, it is clear that the proposed algorithm has a

small variance than traditional algorithms. Moreover,

under the same MSE conditions, the performance of the

proposed algorithm is about 2-4 dB higher than the

traditional algorithms.

Fig. 6 shows that the MSE of the proposed algorithm

and traditional algorithms versus SNR in the channel 6.

Set the frequency offset to 220.24 Hz. There are only

minor changes for the MSE cure of the proposed

algorithm with respect to Fig.5, while the algorithms in

[17], [18], [21] can no longer meet the requirements of

frequency offset estimation with large MSE. Compared

with Fig.5, the performance of the algorithm in [19] is

about 6 dB smaller. As the fading caused by multipath

channel makes the symbol power spectrum ups and

downs, the accuracy of the algorithm in [21] can’t be

guaranteed. The algorithms in [17], [18] must satisfy the

condition that time pilots are uniformly distributed, are

not suitable to the DRM system.

Fig. 7 shows the MSE of the proposed algorithm

versus SNR in DRM channels. Channel 1 is the AWGN

channel, while channel 6 is multi-path channel.

Compared with channel 6, the MSE of channel 1 is about

1dB smaller

5 10 15 20 2510

-6

10-5

10-4

10-3

SNR/dB

MS

E

channel 1

channel 2

channel 3

channel 4

channel 5

channel 6

Figure 7. MSE of the proposed algorithm versus SNR.

VI. CONCLUSION

Based on the characteristic of the frequency pilots, one

integer frequency offset estimation method is proposed

for DRM system. The proposed algorithm gets rid of the

power factor of the pilots in correlated calculation and

only retains the phase factor of the pilots. The structure of

the angle vector is beneficial to weaken the impact of the

noise and multipath. Simulation results show that the

proposed algorithm improves the range and accuracy of

the frequency offset estimation.

REFERENCES

[1] Digital Radio Mondiale (DRM)-System Specification ETSI ES

201 980 V3.1.1, draft, Aug 2009.

[2] M. Morelli, A. N. D'Andrea, and U. Mengali, “Frequency

ambiguity resolution in OFDM systems,” IEEE Commun. Lett, vol.

4, pp. 134-136, Apr 2000.

[3] C. Chen and J. Li, “Maximum likelihood method for integer

frequency offset estimation of OFDM systems,” Electronics

Letters, IEEE, vol. 40, pp. 813-814, Jun 2004.

[4] D. Toumpakaris, J. Lee, and H.-L. Lou, “Estimation of integer

carrier frequency offset in OFDM systems based on the maximum

likelihood principle,” IEEE Trans. Broadcasting, vol. 55, pp. 95–

108, Mar 2009.

Journal of Communications Vol. 8, No. 9, September 2013

577©2013 Engineering and Technology Publishing

[5] K. Shi and E. Serpedin, “Coarse frame and carrier synchronization

of OFDM systems: a new metric and comparison,” IEEE Trans.

Wireless Commun, vol. 3, pp. 1271-1284, July 2004.

[6] M. Henkel and W. Schroer, “Pilot based synchronization strategy

for a coherent OFDM receiver,” in Proc. WCNC, March 2007, pp.

1982-1986.

[7] J. Li, G. Liu, and G. B. Giannakis, “Carrier frequency offset

estimation for OFDM-based WLANs,” IEEE Signal Process. Lett.,

vol. 8, pp. 80–82, Mar 2001.

[8] S. Attallah, “Blind estimation of residual carrier offset in OFDM

systems,” IEEE Signal Process. Lett., vol. 11, pp. 216–219, Feb

2004.

[9] V. Fischer and A. Kurpiers, “Frequency synchronization strategy

for a PC-based DRM receiver,” in Proc. APCCS, Dec 2004, pp.

989–992.

[10] J.-J. van de Beek, M. Sandell, and P. O. Borjesson, “ML

estimation of time and fequency offset in OFDM systems,” IEEE

Transactions on Signal Processing, vol. 45, pp. 1800-1805, Jul

1997.

[11] B. G. Yang, K. B. Letaief, R. S. Cheng, et al., “Timing recovery

for OFDM transmission,” IEEE Journal on Selected Areas in

Communications, vol. 18, pp. 2278-2291, Nov 2000.

[12] T. M. Schmidl and D. C. Cox, “Robust frequency and timing

synchronization for OFDM,” IEEE Transactions on

Communications, vol. 45, pp. 1613-1621, Aug 1997.

[13] H. Minn, V. K. Bhargava, and K. B. Letaief, “A robust timing and

frequency synchronization for OFDM systems,” IEEE

Transactions on Wireless Communications, vol. 2, pp. 822-839,

July 2003.

[14] B. Park, C. Hyunsoo, C. Kang, and D. Hong, “A novel timing

offset estimation method for OFDM systems,” IEEE

Communications Letters, vol. 7, pp. 239-241, May 2003.

[15] L. F. He, F. Yang, C. Zhang, and Z. C. Wang, “Synchronization

for TDS-OFDM over multipath fading channels,” Consumer

Electronics, IEEE Transactions on, vol. 56, pp. 2141-2147, 2010.

[16] X. Y. Jiang and Z. W. Dong, “Carrier frequency offset estimation

of DRM receiver,” in Proc. 4th International Conference on

Proceedings Microwave and Millimeter Wave Technology, Aug

2004, pp. 822-825.

[17] H. Nogami and T. Nagashima, “A frequency and timing period

acquisition technique for OFDM systems,” in Proc. PIRMC, vol. 2,

Sep 1995, pp. 1010-1015.

[18] K. Bang, N. Cho, J. Cho, H. Jun, K. Kim, H. Park, and D. Hong,

“A coarse frequency offset estimation in an OFDM system using

the concept of the coherence phase bandwidth,” IEEE Trans.

Commun, vol. 49, pp. 1320-1324, August 2001.

[19] Eu-Suk Shim, J. B. Kim, and Y-H. You, “Low-cost integer

frequency offset estimation for OFDM-based DRM receiver,”

IEEE Trans. Consumer Electronics, vol. 56, pp. 2155-2160, Nov

2010.

[20] Y-H. You and K-W. Kwon, “Multiplication-Free estimation of

integer frequency offset for OFDM-Based DRM systems,” Signal

Processing Letters, IEEE , vol. 17, pp. 851 - 854, Oct 2010.

[21] A. F. Kurpiers and V. Fischer, “Open-source implementation of a

Digital Radio Mondiale (DRM) receiver,” in Proc. Ninth

International Conference on HF Radio Systems and Techniques,

June 2003, pp. 86-90.

[22] K. Li and M. Yan, “Simulation of digital radio mondiale channel

model ,” in Proc. IEEE 3rd International Conference on

Communication Software and Networks, May 2011, pp. 325-327.

Cheng Yan received his B.S. degree from the

School of Electronic Information and Control Engineering at Shandong Polytechnic University

Jinan, China, in 2011. He is currently pursuing a

M.S. degree at Communication University of China. His research interests include signal

processing, mobile multimedia and wireless

communication.

Yan Ming received his B.S. in communication engineering from the Nanjing University of Posts

and Telecommunications (NJUPT) in 2002 and

his M.S. in signal and information processing from the Communication University of China

(CUC) in 2006. He received his Ph.D. in

communication and information system from

CUC in 2012. In January 2012, Dr. Yan Ming joined the GxSOC Research Institute at CUC as a

Research Assistant.

Dr. Yan Ming leads the China Mobil Multimedia Broadcasting (CMMB) Research Group at Communication University of China,

whose mission is to conduct tracking research of mobile multimedia

broadcast technology and the related support services in China. He also participates with the Team for Research in broadband multimedia

communication at the Institute of Microelectronics of the Chinese

Academy of Sciences (IMECAS). In addition to his research activities,

Dr. Yan Ming serves as the Administrator of Postgraduate Studies in

GxSOC Research Institute. Dr. Yan Ming is an Expert Member of both the Next Generation

Broadcasting (NGB) workgroup and the Audio Video Standard (AVS)

workgroup.

Journal of Communications Vol. 8, No. 9, September 2013

578©2013 Engineering and Technology Publishing