Timing Synchronization in OFDM-TDMA based Power Line Communication Systems

Eun-Woo Ahn and Yong-Hwan Lee

School of Electrical Engineering and Computer Science and INMC

Seoul National University Kwanak P.O. Box 34, Seoul, 151-744 Korea

E-mail: ylee@snu.ac.kr

Abstract

Time division multiple access (TDMA) scheme can be

used as an efficient multiple access scheme for power line

communications (PLC) due to its simplicity and reliability.

Orthogonal frequency division multiplexing (OFDM)

scheme is known more efficient than single carrier schemes

under frequency selective power line channel condition.

When the Cox’s method is applied to synchronization of

TDMA-OFDM signals for PLC, it can cause ambiguity of

finding the start of a frame. We alleviate this ambiguity

problem by modifying the Cox’s pilot signal without an

additional implementation complexity. The proposed

synchronization method is verified by computer

simulation.

I. INTRODUCTION

Great attention has recently been given to the use of

power line for home networking due to no need of

additional wiring. However, the power line channel has

unpredictable and frequency selective channel

characteristics due to random change of the load [1]. The

use of a time division multiple access (TDMA) scheme can

be practical as the multiple access scheme for power line

communications (PLC) due to its simplicity and reliability

[2][3]. In a TDMA scheme, it is necessary to accurately

maintain the frame and timing synchronization in the

receiver. As a modulation scheme, OFDM scheme is

known more efficient than single carrier schemes under

frequency selective power line channel condition [3][4].

There have been a number of propositions for

synchronization with the use of a cyclic prefix in

OFDM-based TDMA schemes [5]. The symbol timing can

be obtained using the cyclic prefix but the frame

synchronization may not easily be achieved [6]. To

alleviate this problem, the use of pilot signals was

considered for frame and symbol synchronization [6]. The

use of pilot signals has also been applied to

synchronization in PLC [3][7].

Most of the previous studies consider the use of a pilot

symbol in each frame rather than each slot. Since all the

terminals use the same pilot symbol in the downlink

control slot (TS0) for synchronization, their performance

can be degraded due to the timing offset [3][8]. This

problem can be alleviated using a pilot symbol in each slot.

However, it can result in ambiguity of finding the start of a

frame. This problem can be removed using a special

sequence, but it may require an additional complexity

because it needs channel information to recover the

sequence in the receiver. In this paper, we improve the

synchronization problem by using a modified pilot signal.

This paper is organized as follows. In Section II, we

describe an OFDM transmission model and a conventional

synchronization method. The proposed synchronization

method is presented in section III. In section IV, the

performance is verified by computer simulation. Finally,

conclusions are summarized in Section V.

II. Cox’s synchronization method in OFDM systems

Fig. 1 depicts an OFDM system model where kx is

quadrature amplitude modulated input signal, )(kh is the

channel impulse response and )(kn is additive white

Gaussian noise (AWGN). The data symbol kx is

modulated by means of the inverse discrete Fourier

transform (IDFT) on 2L parallel sub-carriers. The last M

samples of the symbol are appended as a preamble to avoid

the inter-symbol interference (ISI). The data ky is

obtained by demodulating the 2L remaining samples by

means of the DFT after discarding the first M samples from

the received signal )(kr .

Cox proposed a method that uses a unique pilot symbol

for synchronization [6]. The pilot signal can be generated

by transmitting a pseudo-noise (PN) sequence in the even

frequency, while zeroes in the odd frequency. The Cox’s

training symbol can be represented as

Lkk ss += , 0,..., 1k L= − . (1)

in the time domain. Let us define a timing metric by [6] 2

2

( )( )

( )P k

M kR k

= (2)

where 1

*

0

( )L

k m k m Lm

P k r r−

+ + +=

=∑ , (3)

∑−

=++=

1

0

2)(L

mLmkrkR . (4)

When the pilot symbol is received, the signals in )(kP

have the same phase and thus )(kM can have a

maximum value. Otherwise, the signal terms in )(kP

have random phases, making )(kM have a magnitude

close to zero. Due to the use of a cyclic prefix, when the

pilot symbol is received, )(kM reaches a maximum

value for an amount of duration equal to the length of the

cyclic prefix minus the length of )(kh . Since )(kM

linearly decreases and has a symmetry around the

maximum value, the symbol timing can be determined by

finding the mid-point of the two points corresponding to

90% of the maximum value in the rightmost and leftmost,

respectively [6]. When )(kM is larger than a given

threshold, the start of the frame is declared.

Fig. 2 depicts a TDD-TDMA frame structure that

consists of eight time slots each of which has 1.06ms time

duration. When the Cox’s pilot symbol is used in each slot,

it can cause ambiguity of finding the start of the frame. To

avoid this problem we consider modification of the Cox’s

method.

III. The proposed synchronization method in

OFDM systems

The Cox’s pilot symbol is inserted only in time slot TS0

and a modified pilot symbol is inserted in other slots. The

modified pilot is designed so that the timing metric for

frame acquisition has a peak value only in time slot TS0.

The modified pilot signal can be generated taking the

conjugate of the second half of the Cox’s pilot symbol, i.e., *

Lkk ss += , 0,..., 1k L= − . (5)

IDFT

P/S S/P

DFT+)(kh

)(kn

)(kr)(ks

1Lx− +

kx

Lx

1s

2Ls

2L Ms +

1r

Mr

2L Mr +

1Ly− +

ky

Ly

Fig. 1. OFDM system

TS0 TS1 TS2 TS3 TS4 TS5 TS6 TS7 TS0 TS1 TS2 TS3 TS4 TS5 TS6 TS7

Downlink Uplink

1.06ms

8.48ms 8.48ms Fig. 2. Frame structure

This modified signal is inserted in time slots other than slot

TS0. Then, the received modified pilot signal can be

represented as

0

j

k i k i ki

r h s n−=

= +∑

kjkjkk nshshsh ++++= −− ...110 , 1,..., −+−= LjMk (6)

and

0 1 1 ...k L k L k L j k L j k Lr h s h s h s n+ + + − + − += + + + +

Lkjkjkk nshshsh +−− ++++= **11

*0 ... , 1,..., −+−= LjMk .(7)

Since 1

*

0( )

L

k m k m Lm

P k r r−

+ + +=

=∑

*{ }k k LL E r r +≈ ⋅

}{)...( 2*221

20 kj sEhhhL +++⋅=

22 2 2 20 1( ... ) {Re( ) Im( ) 2Re( ) Im( )}j k k k kL h h h E s s j s s= ⋅ + + + − − ⋅

0= , (8)

the timing metric )(kM has a magnitude close to zero

with the use of the modified pilot signal. Thus, )(kM can

be larger than the threshold only in slot TS0 during the

frame acquisition. This means that the ambiguity of finding

the start of a frame can occur only at two slots, the

downlink slot TS0 and uplink slot TS0.

For ease of description, let )(' kP be the timing metric

when the modified pilot signal is used, i.e., 1

'

0( )

L

k m k m Lm

P k r r−

+ + +=

=∑ . (9)

In additive white Gaussian noise (AWGN) channel with

0 ,10 == ihh , for ji ,...,2,1= , )(kP and )(' kP can

be represented as

)()( ***21

0

1

0

*LmkmkmkmkLmkmk

L

mmk

L

mLmkmk nnsnnssrrkP ++++++++

−

=+

−

=+++ +++== ∑∑

, (10) 21 1

' *

0 0( ) ( )

L L

k m k m L k m k m k m L k m k m k m k m Lm m

P k r r s s n n s n n− −

+ + + + + + + + + + + += =

= = + + +∑ ∑ .

(11)

Using the central limit theorem, )(kP and )(' kP

can be approximated as Gaussian random variables with

mean 2{ }kL E s⋅ . In frequency selective channels, )(kP

and )(' kP can be expressed as

∑−

=+++=

1

0

*)(L

mLmkmk rrkP

)...()...( 0*

0

1

0Lmkjmkjmkmkjmkjmk

L

m

nshshnshsh ++−+++−++

−

=

++++++=∑

}{)...( 2221

20 kj sEhhhL ++⋅≈ , (12)

1

0

'( ) L

k m k m Lm

P k r r−

+ + +=

=∑

)...)(...( **00

1

0Lmkjmkjmkmkjmkjmk

L

m

nshshnshsh ++−+++−++

−

=

++++++=∑}{)...( 222

120 kj sEhhhL +++⋅≈ . (13)

It can be seen that the terms in )(' kP are not added in the

same phase in frequency selective channels. As a result, the

timing metrics in other user slots slightly less than that in

slot TS0 with the use of the modified pilot symbol. The

timing metric '( )M k is used to find the symbol timing in

other user slots after frame acquisition with the use of the

Cox’s pilot symbol in slot TS0. Since the timing metric is

scaled down by a constant value, the two points whose

magnitude is equal to 90% of the maximum value remains

the same and thus the symbol timing corresponding to the

midpoint of these two is not affected. The use of the

proposed pilot signal results in symbol synchronization

performance similar to the use of the Cox’s one.

When the received signal is a random signal, the terms

in )(' kP are added with random phases as those in

)(kP . Thus, ' ( )M k can be approximated as 22

12L

χ [6],

where 22χ is a Chi-square random variable with mean 2

and variance 4.

Since the start of the frame or random access of the

terminal in the uplink is detected by using the Cox’s

method [6] and the distribution of the timing metric for the

modified pilot signal can be given with the channel

information as in (13), the probability of miss detection

and false detection is not considered here.

IV. Performance evaluation

To evaluate the synchronization performance of the

proposed method, we consider the use of a TDMA-OFDM

based PLC transceiver with modulation parameters

summarized in Table 1. The frequency response of the

tested power line channels is depicted in Fig. 3.

We first examine the improvement in finding the frame

timing with the use of the proposed pilot signal. Fig. 4

depicts the timing metric )(kM with the use of the

proposed signal when the SNR is 20dB in the loop-1a

channel. It can be seen that the use of the proposed pilot

signal removes the ambiguity for frame synchronization.

When the modified pilot symbol is used in slots other

than slot TS0 to find the symbol timing, Fig.5 depicts the

distribution of the timing estimate when the SNR is 20dB

in the loop-1a and loop-2a channels. Note that a cyclic

prefix of an OFDM symbol corresponds to the range from

0 to 0.1T. The FFT timing has to start from the sample of

the cyclic prefix except the first samples whose length is

equal to the channel impulse response to avoid the ISI. It

can be seen that the proposed scheme can provide the

symbol synchronization performance comparable to the

Cox scheme.

Table 1. OFDM system parameters

Guard interval 2 sµ

Symbol duration 20 sµ

Sub-carrier spacing 50 kHz

Number of sub-carriers 128

Modulation QPSK

5 6 7 8 9 10 11-35

-30

-25

-20

-15

-10

-5

Frequency(MHz)

chan

nel a

tten

uatio

n(dB

)

(a) Loop-1a

5 6 7 8 9 10 11-30

-28

-26

-24

-22

-20

-18

-16

-14

-12

-10

-8

Frequency(MHz)

chan

nel a

tten

uatio

n(dB

)

(b) Loop-2a

Fig. 3. Magnitude response of the power line channels

0 0.5 1 1.5 2 2.5 3 3.50

0.2

0.4

0.6

0.8

1

time (Time slot)

timin

g m

etric

(a) Cox’s method

0 0.5 1 1.5 2 2.5 3 3.50

0.2

0.4

0.6

0.8

1

time (Time slot)

timin

g m

etric

(b) The proposed method

Fig. 4. Frame acquisition

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.10

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

time (Symbol)

Pro

babi

lity

o:the Cox method

+:the proposed method

(a) Loop-1a

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.10

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

time (Symbol)

Pro

babi

lity

o: the Cox method

+:the proposed method

(b) Loop-2a

Fig. 5. Distribution of the timing estimate

21 22 23 24 25 26

1E-5

1E-4

1E-3

BER

channel SNR(dB)

Cox's method the proposed method

(a) Loop-1a

20 21 22 23 24

1E-5

1E-4

1E-3

BER

channel SNR(dB)

Cox's method the proposed method

(b) Loop-2a

Fig. 6. BER performance with symbol synchronization

Fig. 6 shows the BER performance of a TDMA-OFDM

based PLC transceiver employing the Cox’s method and

the proposed method.

V. Conclusion

We have designed a pilot signal for timing

synchronization in OFDM-TDMA based PLC transceiver.

To alleviate the ambiguity of finding the start of the frame,

the pilot signal is designed by modifying the Cox’s signal.

The proposed scheme can provide symbol synchronization

performance similar to the Cox’s method, while reducing

the implementation complexity compared to the use of the

Cox’s signal.

References

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[4] J. A. C. Bingham, “Multicarrier Modulation for Data

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