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Journal ArticleDOI

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

01 Sep 1999-IEEE Transactions on Vehicular Technology (IEEE)-Vol. 48, Iss: 5, pp 1596-1609
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)

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
AbstractThis 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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TL;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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This paper presents a fast low-complexity synchronization scheme for orthogonal frequency division multiplexing ( OFDM ) systems over fading channels. 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. In this paper, the authors 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.