# A low-complexity frame synchronization and frequency offset compensation scheme for OFDM systems over fading channels

TL;DR: In this paper, a fast low-complexity synchronization scheme for orthogonal frequency division multiplexing (OFDM) systems over fading channels is presented. But the implementation can be simplified by only using the sign bits of the in-phase and the quadrature components of the received OFDM signal for frame synchronization and frequency offset compensation.

Abstract: This paper presents a fast low-complexity synchronization scheme for orthogonal frequency division multiplexing (OFDM) systems over fading channels. By utilizing the guard interval in OFDM signals, the frame synchronization and the frequency offset estimation are considered simultaneously. The implementation can be simplified by only using the sign bits of the in-phase and the quadrature components of the received OFDM signal for frame synchronization and frequency offset compensation. A frequency-offset independent frame synchronization algorithm is derived, and a low-complexity frequency offset estimator based on the synchronized correlator output is presented in this paper. Due to the subcarrier ambiguity in the guard-interval-based (GIB) frequency detector, the maximum correctable frequency range is limited to /spl plusmn/1/2 of the subcarrier spacing. In this paper, we also present a new frequency acquisition scheme that can solve the subcarrier ambiguity problem and extend the frequency acquisition range to nearly a half of the useful OFDM signal bandwidth.

## Summary (2 min read)

Jump to: [I. INTRODUCTION] – [II. FRAME SYNCHRONIZATION SCHEME] – [III. LOW-COMPLEXITY FREQUENCY OFFSET CORRECTION SCHEME] – [IV. CARRIER FREQUENCY ACQUISITION SCHEME] – [A. Residual Frequency Tracking Error] – [B. Preset Acquisition Range] and [V. CONCLUSION]

### I. INTRODUCTION

- T HE ORTHOGONAL frequency division multiplexing (OFDM) technique is an effective transmission scheme to cope with many channel impairments, such as cochannel interference, severe multipath fading, and impulsive parasitic noise [1] .
- A popular solution for the frame synchronization is to insert some synchronization symbols within the OFDM signals as the pilot symbols [2] .
- The frame synchronization scheme presented in [3] may not work properly under such condition.
- A data-aided frequency acquisition scheme has also been proposed in [8] , which uses a particular synchronization symbol to acquire the frequency offset.

### II. FRAME SYNCHRONIZATION SCHEME

- The authors consider the frame synchronization problem in the transmission system based on the OFDM technique.
- Therefore, each symbol at the FFT output is rotated and dispersed due to the intersymbol interference from other OFDM frame.
- Computer simulations are used to evaluate these four averaging schemes.
- The weighting factor for both EWMA scheme and EWA scheme is intentionally chosen such that , where is a positive integer.
- The authors also notice that the modified frame synchronization schemes tend to estimate the frame start position within the guard interval and hence produce less ISI.

### III. LOW-COMPLEXITY FREQUENCY OFFSET CORRECTION SCHEME

- In OFDM systems, a carrier frequency error often exists between the transmitter and the receiver due to the mismatch between the oscillators or the Doppler effect in mobile radio channels.
- The last category of algorithms utilizes the inherent data property of the OFDM signals and achieves synchronization accurately.
- As the frame error interferes the GIB frequency detector, the frequency offset also militates against the GIB frame synchronization scheme.
- The maximum likelihood estimate of the frequency offset is given by (13).
- The two-ray Rayleigh fading channel contains two Rayleigh fading paths with 10s time delay between them and equal power in these two paths.

### IV. CARRIER FREQUENCY ACQUISITION SCHEME

- In the GIB frequency offset correction schemes, the applicable range of the frequency offset is , that is, 1/2 of the intercarrier spacing.
- Fig. 11 shows that the amplitude of the channel difference is about 10-20 dB lower than the channel amplitude response when 1024 subcarriers are used.
- This enlightens us to use the data of subchannels with larger channel response to acquire the frequency offset.
- The maximal computational complexity of the acquisition scheme occurs when .
- Therefore, the missed lock probability of the acquisition scheme is acquisition scheme: the residual frequency tracking error and the preset acquisition range .

### A. Residual Frequency Tracking Error

- In the acquisition stage, the authors assume that the residual frequency error after the frequency tracking stage is an integral multiple of the subcarrier spacing.
- There exists a residual frequency tracking error that introduces ICI and degrades the performance of the acquisition scheme.
- Fig. 15 shows the plots of versus the normalized residual frequency tracking error.
- The authors can see that the missed lock probability of the acquisition scheme is still very low even the residual frequency tracking error is as large as 0.47 times of the subcarrier spacing.
- That is, the proposed acquisition scheme is insensitive to the tracking error.

### B. Preset Acquisition Range

- From (19), the authors realize that the preset acquisition range plays an important role in the acquisition scheme.
- As a result, the training sequence used to acquire the frequency offset becomes shorter and the autocorrelation property required by the acquisition scheme is more difficult to maintain.
- Fig. 16 shows the plots of versus the preset acquisition range for and .
- The acquisition operation of the proposed scheme can be accomplished within one training symbol interval, while the frequency correction scheme in [7] needs several hundreds of FFT block to acquire the frequency offset in ten times of the subcarrier spacing due to its small acquisition step.
- Furthermore, the maximal acquisition range of their acquisition scheme can be extended approximately up to a half of the useful signal bandwidth.

### V. CONCLUSION

- The authors have demonstrated how the cyclic extension of OFDM frames can be used to synchronize the frame position and the carrier frequency.
- The authors also find that the frame position estimator and the frequency offset estimator are mutually dependent, that is, the frame position and the frequency offset must be estimated at the same time.
- It is also found that if the authors average their estimate over several consecutive OFDM symbols, they obtain a similar performance as the estimate without quantization.
- For the cases whose frequency offset is larger than 1/2 of the subcarrier spacing, the authors propose a frequency acquisition scheme to estimate the additional frequency offset based on the assumption that the difference of the frequency response of the neighboring subchannels is very small.
- The training sequences used by their frequency acquisition scheme can be the same as the training sequences used by the equalizer, and, therefore, no additional modification is needed in the transmitter.

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1596 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 48, NO. 5, SEPTEMBER 1999

A Low-Complexity Frame Synchronization and

Frequency Offset Compensation Scheme

for OFDM Systems over Fading Channels

Meng-Han Hsieh, Student Member, IEEE, and Che-Ho Wei, Fellow, IEEE

Abstract—This paper presents a fast low-complexity synchro-

nization scheme for orthogonal frequency division multiplexing

(OFDM) systems over fading channels. By utilizing the guard

interval in OFDM signals, the frame synchronization and the

frequency offset estimation are considered simultaneously. The

implementation can be simpliﬁed by only using the sign bits

of the in-phase and the quadrature components of the received

OFDM signal for frame synchronization and frequency offset

compensation. A frequency-offset independent frame synchro-

nization algorithm is derived, and a low-complexity frequency

offset estimator based on the synchronized correlator output is

presented in this paper. Due to the subcarrier ambiguity in the

guard-interval-based (GIB) frequency detector, the maximum

correctable frequency range is limited to

666

1/2 of the subcarrier

spacing. In this paper, we also present a new frequency acqui-

sition scheme that can solve the subcarrier ambiguity problem

and extend the frequency acquisition range to nearly a half of

the useful OFDM signal bandwidth.

Index Terms— Frame synchronization, frequency offset com-

pensation, low-complexity algorithms, OFDM.

I. INTRODUCTION

T

HE ORTHOGONAL frequency division multiplexing

(OFDM) technique is an effective transmission scheme

to cope with many channel impairments, such as cochannel

interference, severe multipath fading, and impulsive parasitic

noise [1]. By inserting a guard interval between symbol blocks,

the intersymbol interference (ISI) in an OFDM system can

be mitigated.

For block transmission of the OFDM signals, a frame

synchronization is needed to detect the proper time instant to

start sampling a new frame. A popular solution for the frame

synchronization is to insert some synchronization symbols

within the OFDM signals as the pilot symbols [2]. These

symbols are then picked up by the receiver to generate

the frame clock. However, the insertion of the pilot sym-

bols decreases the system capacity. For nondata-aided frame

synchronization, a guard-interval-based (GIB) low-complexity

frame synchronization scheme has been presented in [3] to

estimate the start position of a new frame. The basic idea

of this scheme is to exploit the cyclic extension preceding

Manuscript received February 24, 1997; revised August 19, 1998. This

work was supported by the National Science Council of the Republic of

China under Grant NSC86-2221-E-009-059.

The authors are with the Department of Electronics Engineering,

National Chiao Tung University, Hsin Chu, Taiwan, R.O.C. (e-mail:

meng@clab.ee.nctu.edu.tw; chwei@cc.nctu.edu.tw).

Publisher Item Identiﬁer S 0018-9545(99)07395-8.

a symbol frame, known as guard interval. This scheme only

uses the in-phase and the quadrature sign bits of the OFDM

data to estimate the frame position. If the channel is time

dispersive, the intersymbol interference will introduce errors in

the frame synchronization scheme. In this paper, the inﬂuence

of the frame position error on the symbols at the fast Fourier

transform (FFT) output is investigated and some modiﬁcations

of the conventional frame synchronization schemes are also

made.

In the practical OFDM systems, a frequency offset due

to the Doppler effect or the oscillator mismatching usually

exists between the transmitter and the receiver. The frame syn-

chronization scheme presented in [3] may not work properly

under such condition. After some modiﬁcations of the original

scheme, we derive a frame synchronization scheme that is

independent of the frequency offset.

To compensate the carrier frequency offset, several data-

aided frequency offset correction techniques have been pro-

posed [4], [5], [7], [12]. Although those algorithms estimate

the frequency offset accurately, the data-aided structure limits

their applicable ﬁeld because some specialized synchroniza-

tion symbols must be generated in the transmitter side. For

the nondata-aided frequency offset compensation algorithms,

some GIB frequency detectors have been presented in [6] and

[10]. In [6], only the last few samples in the guard interval are

used to estimate the frequency offset, therefore, the estimate

is sensitive to the frame synchronization error. In [10], timing

recovery and carrier recovery are implemented by a maximum-

likelihood estimator based on the guard interval samples, but

the computational complexity is high. Similar to the estimator

in [10], we estimate the start position of the frame and the

carrier frequency offset at the same time. However, unlike the

maximum-likelihood estimator proposed in [10], only the sign

bits of the in-phase component and the quadrature component

of the received signal are used to estimate the frequency offset,

therefore the complexity is reduced drastically. By averaging

the estimate over a few frames or by using a closed tracking

loop, a more accurate frequency offset estimation scheme can

be obtained. Since only adders and buffers are required in our

synchronization scheme, we can estimate the frequency offset

and the frame position for each frame with low computational

complexity. Even in slow fading environment, the frequency

offset can be accurately tracked.

On the other hand, the subcarrier ambiguity problem will

limit the correctable frequency offset range within

1/2 sub-

0018–9545/99$10.00 1999 IEEE

HSIEH AND WEI: COMPENSATION SCHEME FOR OFDM SYSTEMS OVER FADING CHANNELS 1597

Fig. 1. OFDM system with synchronization scheme.

channel bandwidth [4], [6]. Several frequency offset acquisi-

tion schemes have been mentioned for some speciﬁc frequency

detectors [4], [5], [7]. A data-aided frequency acquisition

scheme has also been proposed in [8], which uses a particular

synchronization symbol to acquire the frequency offset. Here,

we present a frequency acquisition scheme adopted from [11]

to extend the acquisition range of the GIB frequency detector

from

1/2 of the subcarrier spacing to a large fraction of the

signaling rate. Since the training sequences of the frequency

domain equalization are used to acquire the carrier frequency

offset, no additional synchronization symbols are needed. The

inﬂuence of the frequency detection error on the frequency

acquisition scheme is also discussed in this paper.

This paper is organized as follows. Section II introduces

basic OFDM systems and the low-complexity frame synchro-

nization scheme based on the analysis of the guard intervals.

The analysis work and the simulation results for several

averaging schemes are also included in this section. Section III

presents a new GIB synchronization scheme that can estimate

the carrier frequency offset and the frame position simultane-

ously. Section IV introduces the frequency acquisition scheme

based on the frequency detector presented in the previous

section. Finally, Section V gives some conclusions.

II. F

RAME SYNCHRONIZATION SCHEME

We consider the frame synchronization problem in the

transmission system based on the OFDM technique. The block

diagram of a typical OFDM system is shown in Fig. 1. The

transmitted baseband signal

is composed of

complex sinusoids modulated with complex modulation

values

, i.e.,

(1)

We note that the

-point discrete Fourier transform (DFT) of

(1) is the

-point sequence

DFT

(2)

of modulation values, and the zeros in (2) are the virtual

carriers. Thus, if the orthogonality within each OFDM block

is preserved, the data

can be recovered in the receiver

by a DFT.

In time-dispersive channels, the intersymbol interference

caused by the multipath effect induces a loss in orthogonality

of OFDM signals. To maintain the orthogonality of OFDM

signals in multipath channels, a guard interval is inserted

in front of each OFDM block. The guard interval insertion

duplicates the last

samples of and appends them as

a preamble (cyclic preﬁx) to form an OFDM frame

.As

a result, the actual transmitted signal is not a white process.

In [3], van de Beek et al. presented a low-complexity frame

synchronization based on the inherent correlation property of

the OFDM signals with guard interval. The block diagram

of their frame synchronization scheme is shown in Fig. 2.

The in-phase and the quadrature components of the received

1598 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 48, NO. 5, SEPTEMBER 1999

Fig. 2. Block diagram of a low-complexity ML estimator for frame synchronization [3].

signal are quantized to . For the sake of reducing the

complexity, only sign bits of the in-phase and the quadrature

components are used. The OFDM signal in Fig. 2 can be pro-

cessed continuously. The output sequence of the moving sum

is a concatenation of loglikelihood functions for consecutive

OFDM frames.

Next, we investigate the inﬂuence of the frame errors on

the FFT output symbols while additive white Gaussian noise

(AWGN) channel is used. If the estimated start position of the

frame is located within the guard interval, each FFT output

symbol within the frame will be rotated by a different angle.

From subcarrier to subcarrier, the angle increases proportion-

ally to the frequency offset. If the estimated start position

of the frame locates within the data interval, the sampled

OFDM frame will contain some samples that belong to other

OFDM frame. Therefore, each symbol at the FFT output is

rotated and dispersed due to the intersymbol interference from

other OFDM frame. The phase rotation imposed by frame

synchronization error can thus be corrected by appropriately

rotating the received signal, but the dispersion of signal

constellation caused by ISI forms a bit error rate (BER) ﬂoor.

Another effect that we must take into account is the channel

impairment. The OFDM symbols are dispersed in time axis

due to the multipath effect. Consequently, the guard interval

used to estimate the frame location is interfered by the previous

symbol.

A solution to remedy this problem is to use different

smoothing algorithms in place of the moving sum scheme

shown in Fig. 2. Instead of using the moving sum shown in

Fig. 2 that weights

equally, an exponen-

tially decaying weighted function is applied to

. We consider four smoothing algorithms here. Let be

the number of samples in a guard interval, the loglikelihood

functions at time instant

for these algorithms are given as

follows.

Moving average (MA):

(3)

Shortened moving average (SMA):

where

(4)

Exponentially weighted moving average (EWMA):

(5)

Exponentially weighted average (EWA):

(6)

Note that the moving average (MA) scheme is identical to

the moving sum scheme presented in [3]. The MA, SMA, and

EWMA algorithms can be realized as FIR ﬁlters, and the EWA

algorithm can be realized as an IIR ﬁlter.

Computer simulations are used to evaluate these four av-

eraging schemes. The wireless urban channel adopted by [6]

is used and a complex white Gaussian noise is added to the

received OFDM signals. The signal-to-noise ratio (SNR) is

set to 10 dB. The delay spread of the multipath channel

used in our simulation is about 5

s. An OFDM system

consisting of 1024 subcarriers with a guard interval having

samples is employed. The sampling frequency

is 9 MHz and the symbol rate is 8

10 symbols/s. The

probability of the estimated frame position obtained from the

low-complexity frame synchronization scheme with various

averaging schemes are shown in Fig. 3. For each case, 20 000

frames are simulated. Three different window lengths, 32,

64, and 96 samples, are employed to the SMA scheme.

The weighting factor

for both EWMA scheme and EWA

scheme is intentionally chosen such that

,

where

is a positive integer. By appropriately choosing

the weighting factor, the multiplication operation within the

summing scheme can be replaced by an adder and a shifter.

Three different weighting factors employed in the simulations

are expressed by

, where and .

As shown in Fig. 3, the three modiﬁed frame synchroniza-

tion schemes have more concentrated probability distributions

than the MA scheme over the multipath fading channel by

appropriately choosing

and . We also notice that the

modiﬁed frame synchronization schemes tend to estimate

the frame start position within the guard interval and hence

produce less ISI. Fig. 3(a) shows that if the window length

HSIEH AND WEI: COMPENSATION SCHEME FOR OFDM SYSTEMS OVER FADING CHANNELS 1599

(a)

(b)

(c)

Fig. 3. Probability of estimated frame position: (a) moving average scheme and shortened moving average (SMA) scheme, (b) moving average scheme

and exponentially weighted moving average (EWMA) scheme with weighting factor

w

=1

0

2

0

M

;M

=4

;

6

;

8

, and (c) moving average scheme

and EWA scheme with weighting factor

w

=1

0

2

0

M

;M

=4

;

6

;

8

.

of SMA scheme is too small, the probability distribution of the

estimated frame position will disperse. Also, if the weighting

factor

is too large, the probability distribution of the EWA

scheme will disperse and the residual tails will introduce ISI, as

shown in Fig. 3(c). The EWMA scheme has no such problem

because the correlated values

output from the

buffer are discarded. For small

, the weight decays faster and

the effective SNR for estimating the frame position is smaller;

and thus, the probability distribution disperses. Comparing

Fig. 3(b) with (c), we can see that, if

is not too large,

the probability distribution of the EWMA scheme is almost

the same as the probability distribution of the EWA scheme.

Therefore, for smaller

( ), we can use

the EWA scheme instead of the EWMA scheme to reduce the

complexity. From our experimental results shown in Fig. 3,

a window length

for SMA scheme and a weighting

factor

for EWA and EWMA are

suitable choices for the urban channel. However, the EWA

1600 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 48, NO. 5, SEPTEMBER 1999

Fig. 4. Error variance of low-complexity frame synchronizer with various frequency offsets under AWGN channel, SNR

=25

dB.

scheme is more preferable because of its simpler hardware

structure for practical implementation.

III. L

OW-COMPLEXITY FREQUENCY

OFFSET CORRECTION SCHEME

In OFDM systems, a carrier frequency error often exists

between the transmitter and the receiver due to the mismatch

between the oscillators or the Doppler effect in mobile radio

channels. The carrier frequency offset introduces intercarrier

interference (ICI) in OFDM systems and reduces the or-

thogonality between the different subcarriers which assemble

the OFDM signal and, thus, degrades the overall system

performance. For the OFDM signals constructed by many

orthogonal subcarriers, the subchannel bandwidth is much

smaller than the total bandwidth. As described in [4], a small

frequency offset in the OFDM system will lead to a substantial

SNR degradation.

The frequency error in an OFDM system is often corrected

by a tracking loop with a frequency detector to estimate the

frequency offset. In the literature, several algorithms have been

proposed to estimate the frequency offset and can be classiﬁed

into three categories:

1) algorithms based on the analysis of special synchroniza-

tion blocks embedded in the OFDM temporal frame

(data-aided) [4], [7];

2) algorithms based on the analysis of the received data at

the output of the FFT (nondata-aided) [5], [12];

3) algorithms based on the analysis of the sampled received

signal before the FFT block and making use of the

redundancy introduced by the inserted guard interval in

the OFDM signal frame (GIB) [6], [10].

The algorithms belonging to the ﬁrst category require special

synchronization blocks to estimate the frequency offset, but

they provide better results. Since the insertion of synchro-

nization blocks will lower the information rate, the number

of synchronization blocks must be small comparing to the

number of data blocks. The ﬁrst category of algorithms es-

timates the frequency offset only when the synchronization

block is received, as a result, the acquisition time for these

algorithms is longer. Furthermore, the nonlinearity of the

channel increases the estimation complexity. The algorithms

in the second category do not need special synchronization

blocks, but the performance is poor, especially in the mobile

radio environments. The last category of algorithms utilizes

the inherent data property of the OFDM signals and achieves

synchronization accurately. The computational complexity of

the algorithms in the last category are comparatively lower

than those in the other two categories.

The GIB frequency detector in [6] uses the last few samples

of a guard interval to estimate the frequency offset, therefore,

a small frame synchronization error will induce deleterious

effect on the GIB frequency detector. As the frame error

interferes the GIB frequency detector, the frequency offset

also militates against the GIB frame synchronization scheme.

A simulation is conducted to illustrate the impact of the

frequency offset on the frame synchronization scheme. An

OFDM system consisting of 1024 subcarriers with a guard

space of 128 samples over AWGN channel is considered.

The SNR is set to 25 dB, and we estimate the error variance

as a function of the normalized frequency offset.

For each frequency offset value, 10 000 frames are simulated.

From Fig. 4, we can see that the frequency offset affects the

GIB frame estimation considerably.

To ensure the low-complexity frame synchronization

scheme to work properly in an OFDM system with carrier

frequency error, the frame position and the frequency

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06 Nov 1995TL;DR: In this paper, a data-based frame synchronization method for OFDM-systems is presented, based on only the sign bits of the in-phase and the quadrature components of the received OFDM signal, the maximum likelihood solution is derived.

Abstract: Orthogonal frequency-division multiplexing (OFDM) systems have gained an increased interest due to their use in wireless applications such as mobile communication systems. A novel data-based frame synchronization method for OFDM-systems is presented. OFDM frames are shown to contain sufficient information to synchronize a system without the use of pilots. The cyclic extension, preceding OFDM frames, is of decisive importance for this method. Based on only the sign bits of the in-phase and the quadrature components of the received OFDM signal, the maximum likelihood solution is derived. This solution basically consists of a correlator, a moving sum and a peak detector. The stability of the generated frame-clock is improved significantly by averaging over a few number of frames. Simulations show that this low-complex, averaging method can be used to synchronize an OFDM system on twisted pair copper wires and in slowly fading radio channels.

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