1900 IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS, VOL. 17, NO. 11, NOVEMBER 1999
A Time and Frequency Synchronization
Scheme for Multiuser OFDM
Jan-Jaap van de Beek, Per Ola B¨orjesson, Member, IEEE, Marie-Laure Boucheret, Member, IEEE,
Daniel Landstr
¨
om, Julia Martinez Arenas, Per
¨
Odling,
Associate Member, IEEE,
Christer
¨
Ostberg, Mattias Wahlqvist, and Sarah Kate Wilson
Abstract— We present a multiuser synchronization scheme
for tracking the mobile’s uplink time and frequency offsets. It
uses the redundancy introduced by the cyclic prefix and does
not need additional pilots. We show performance results of
an orthogonal frequency division multiplexing (OFDM)-based
radio interface based on universal mobile telecommunication
system (UMTS) parameters. For a UMTS-typical mobile channel
environment, the performance of a coherent system employing
the scheme is virtually indistinguishable from the performance
of a perfectly synchronized system. In a differentially modulated
system, synchronization errors decrease the system performance
by about 0.7 dB compared to a perfectly synchronized system.
Index Terms— Communication system, delay estimation, fre-
quency estimation, multicarrier, multiuser system, orthogonal
frequency division multiplexing (OFDM), synchronization, uni-
versal mobile telecommunication system (UMTS).
I. INTRODUCTION
O
RTHOGONAL frequency division multiplexing
(OFDM) has been proposed for multiuser systems
such as the universal mobile telecommunication system
(UMTS) [1] and wireless local area networks (WLAN’s)
[2]. In multiuser OFDM, the orthogonality of the subcarriers
facilitates a subcarrier division of different users, where
one OFDM symbol contains many users. In the uplink of
such systems, users must be aligned in time and frequency
to maintain the orthogonality of the subcarriers. How to
synchronize different users in the uplink of such a multiuser
OFDM-based system has been unclear so far and is a
frequently raised question.
Multiuser OFDM uplink synchronization is more difficult
than synchronization in a broadcast or downlink scenario
for a couple of reasons. First, because one OFDM symbol
carries data for many users, the correction of one user’s
Manuscript received September 1, 1998; revised July 25, 1999. This paper
was presented in part at the 48th IEEE Vehicular Technology Conference
VTC’98, May 1998, Ottawa, Ontario, Canada.
J.-J. van de Beek is with Nokia Svenska AB, Stockholm SE-164 25
Sweden.
P. O. B
¨
orjesson, D. Landstr
¨
om, and P.
¨
Odling are with the Department of
Applied Electronics, Lund University, Lund SE-221 00 Sweden.
M.-L. Boucheret is with the
´
Ecole Nationale Sup
´
erieure des
T´el´ecommunications, Toulouse 4004 CEDEX France.
J. Martinez Arenas and M. Wahlqvist are with Ericsson Radio Systems
AB, Stockholm SE-164 80 Sweden.
C.
¨
Ostberg is with Ericsson Mobile Communications AB, Lund SE-221 83
Sweden.
S. K. Wilson is with the Division of Signal Processing, Lule
˚
a University
of Technology, Lule
˚
a SE-971 87 Sweden.
Publisher Item Identifier S 0733-8716(99)08957-X.
time and frequency offsets cannot be accomplished at the
base station receiver, as the correction to one user would
misalign other initially aligned users. In our scheme, we have
the base station estimate time and frequency offsets, then
transmit the information to the mobile. The mobile can then
adjust its transmitted signal so that it is in alignment with the
other users’ signals. This method of having the base station
feedback timing information is also used in time division
multiple access (TDMA) systems, such as the global system
for mobile communication (GSM) [3]. Second, estimation of
time and frequency offsets is more difficult in such a multiuser
system. The performance of the estimator in [4], for example,
decreases as the number of subcarriers assigned to each user
decreases. The receiver signal-to-noise ratios (SNR’s) also
vary for different users. Proper synchronization is, however,
necessary to keep the orthogonality of the users, which is
essential for reliable transmission. This paper describes a
novel synchronization scheme for tracking in the uplink of
multiuser OFDM systems. Acquisition of the symbol clock and
carrier frequency is discussed in [5]. Our scheme is generally
applicable to OFDM-based systems where users are separated
in bands of adjacent subcarriers. The work presented in this
paper was motivated by the UMTS proposal [1]. We evaluate
the scheme for a target system similar to this proposal.
Symbol time and carrier frequency offset estimation
methods for OFDM transmission systems have been
presented in a number of contributions, see, e.g., [4],
[6], and [7]. Most of these offset estimators are explicitly
evaluated for a broadcast or downlink scenario. Multiuser
synchronization provides some extra challenges not addressed
in these papers. Our synchronization scheme contains an
implementable time and frequency offset estimator structure
based on results in [4]. This estimator uses the redundancy
in the received signal due to the cyclic prefix. We adapt this
estimator to properties of the multiuser system and the fading
channel. The estimates of the users’ offsets are returned
on a downlink control channel to the mobile transmitters,
which adapt their clocks and oscillators to the free-running
reference clocks and oscillators at the base station.
Whereas frequency requirements on the estimator perfor-
mance are tight (see, e.g., [8]), the time offset requirements
are relaxed by an additional extension of the cyclic prefix.
If a time offset error is within the range of this extension, a
channel estimation algorithm, required for coherent detection,
acts as a fine-tuning time synchronizer. In differential systems,
0733–8716/99$10.00
1999 IEEE
VAN DE BEEK et al.: TIME AND FREQUENCY SYNCHRONIZATION SCHEME 1901
which do not employ channel estimation and equalization, this
extra extension provides some robustness too. The absence
of a channel equalizer with its fine-tuning synchronizing
capabilities in these systems, however, causes a small perfor-
mance degradation compared to coherent systems. We show
by simulation that the time and frequency offset estimator
satisfies both the tight frequency requirements and the coarse
time requirements.
This paper is organized as follows. We first describe the
multiuser OFDM scenario in Section II. In particular, we focus
on the multiple access schemes OFDM offers. In Section III,
we focus on synchronization of a multiple access scheme
where users are divided across the subcarriers and potentially
also in time. We discuss the system sensitivity to time and fre-
quency offsets and present the novel synchronization scheme
including the offset estimator at the base station. In Section IV,
we then present simulation results illustrating the performance
of the offset estimation algorithm and the system performance
in terms of symbol error rate, and we conclude this paper with
Section V, which summarizes the main results.
II. M
ULTIUSER OFDM
A. OFDM Transmission and Multiple Access
In an OFDM transmission system, the available spectrum
is accessed by a large number of subcarriers. Data symbols
are efficiently modulated on these carriers by means of a
fast Fourier transform (FFT) [9], both in the uplink and the
downlink. We assume a frequency division duplex scheme
and concentrate on the uplink frequency band. In a multiuser
mobile environment, an OFDM scheme has two main advan-
tages. First, the receiver does not require an adaptive time-
domain equalizer if a cyclic prefix is properly used and if the
channel does not change much during one OFDM symbol [10].
Secondly, dynamic channel assignment across the spectrum is
straightforward as each user can conveniently access all of the
subcarriers by the FFT-implemented modulation.
Fig. 1 illustrates the OFDM transmission technique. The
complex data symbols
are coherently modulated on
subcarriers by an inverse discrete Fourier transform (IDFT),
and the last
samples are copied and put as a preamble
(cyclic prefix) to form the OFDM symbol. This data vector
is serially transmitted over a discrete-time channel, whose
impulse response is shorter than
samples. At the receiver,
the cyclic prefix is removed, and the signal
is demodulated
with a discrete Fourier transform (DFT). In OFDM systems
employing this cyclic prefix, the frequency-selective channel
distortion appears as a multiplicative distortion of the trans-
mitted data symbols [9], and the received data symbol during
the
th OFDM symbol at the th subcarrier becomes
(1)
where
is the channel attenuation at the th subcarrier
during the
th OFDM symbol and is additive white
Gaussian noise (AWGN).
Fig. 1. An OFDM system.
Data symbols can modulate the subcarriers coherently or
differentially. Proposal [1] suggests a differential scheme
across the subcarriers in an OFDM symbol (a coherent
extension is suggested for future system extensions). In
Section IV, we evaluate our synchronization scheme for both
a differential and a coherent modulation scheme. For coherent
modulation, the base station receiver must estimate and
compensate for the channel attenuations. For this purpose, pilot
symbols are transmitted. Our simulations confirm that channel
equalization can act as a fine-tuning synchronizer [11], [12],
making coherent systems less sensitive to synchronization
errors than differential systems.
Because OFDM separates symbols in both time and fre-
quency, it allows for a number of multiple access schemes.
First, in a TDMA structure, users are assigned entire OFDM
symbols, and they share the channel by a time-slot struc-
ture. Secondly, the large number of subcarriers allows for
a frequency division multiple access (FDMA)-like multiple
access scheme, where different users are assigned different
subcarriers. Since OFDM subcarriers spectrally overlap, this
scheme is not true FDMA. However, for convenience, we
will use the acronym FDMA for OFDM-subcarrier divided
access schemes. Finally, OFDM can be combined with a code
division multiple access scheme [13]. A TDMA scheme is
proposed for the European WLAN standard and an FDMA
scheme combined with a time-slot structure and a frequency-
hopping scheme was proposed for the UMTS radio interface
[1]. In Section IV, we evaluate our synchronization scheme
for such a hybrid TDMA/FDMA multiple access scheme.
Fig. 2 illustrates this access scheme. The available spectrum
is subdivided in bands of adjacent subcarriers (FDMA). Within
each of these bands, a TDMA scheme is applied. Users are
thus separated both in frequency (each user is allocated to
a particular subband) and in time (each user is to allocated
a particular time slot). In our target system, the minimum
access entity is 22 adjacent subcarriers during three consec-
utive OFDM symbols (see Fig. 2), as will be explained in
Section IV.
B. Synchronization Requirements
Accurate demodulation and detection of an OFDM signal
requires subcarrier orthogonality. Variations of the carrier
oscillator, the sample clock, or the symbol clock affect the
orthogonality of the system (see [8], [14], and [15]). Whereas
sample clock variations below 50 ppm have little effect on
1902 IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS, VOL. 17, NO. 11, NOVEMBER 1999
Fig. 2. Time-frequency grid for the UMTS scenario. The users are assigned
transmission blocks consisting of 22 adjacent subcarriers and three adjacent
OFDM symbols. Each transmission block contains pilot symbols supporting
the channel estimation.
the system performance [14], symbol time and frequency off-
sets may cause intersymbol interference (ISI) and intercarrier
interference (ICI) [8], [15] and must usually be counteracted.
Therefore, we assume that the sample clocks of the users and
the base station are identical (no offset effects), and we focus
on a frequency offset and a symbol time offset. We separately
consider their effects on the system performance.
The effect of a symbol time offset is the following (assume
first perfect carrier frequency synchronization). The demodu-
lator FFT at the base station processes blocks of
samples
in the FFT. If different users’ transmitted signals are not
time-aligned, ISI and ICI (or in a multiuser system: interuser
interference) appear at the FFT outputs. Fig. 3 illustrates
this interference caused by one user being misaligned with
the others. Note first that since we assume perfect sample
clocks, such an offset is modeled by an integer-valued number
of samples. Note also that the receiver at the base station
may identify (and as we will see estimate) each user’s time
offset, but has no simple means to counteract this offset
without becoming misaligned with other users. This is the
particular synchronization problem distinguishing broadcast
and multiuser synchronization. We focus on the unknown
integer-valued time offset
of a user’s symbol clock: that
is, how much this user is misaligned with the block of
samples the receiver processes in the FFT.
Consider a system in which the cyclic prefix is longer
than the length of the channel impulse response. Such extra
overhead provides robustness against symbol time offsets: as
long as a symbol time offset is shorter than the difference
between the length of the cyclic prefix and the length of
the channel impulse response, the cyclic appearance of the
OFDM symbol is preserved, and the offset appears as a linear
phase across the subcarrier FFT outputs [16]. In a coherent
system, this effect is identified by the channel estimator,
Fig. 3. How one user being misaligned in time with the other users affects
the receiver demodulation.
which does not distinguish between phase shifts introduced
by the radio channel and those introduced by symbol timing
delays [15]. Therefore, the channel equalizer provides the fine
synchronization, see also [11]. The requirements on the coarse
synchronizer in a coherent system are thus determined by the
number of samples the cyclic prefix exceeds the length of the
channel impulse response. This provides a system designer
with a trade-off tool: by sacrificing data rate, a longer cyclic
prefix relaxes the requirements of the symbol synchronizer.
A carrier frequency offset (assuming perfect symbol syn-
chronization) causes a loss of orthogonality between the sub-
carriers resulting in ICI [8], [17]. We assume that within a
user’s group of subcarriers, the frequency offset is constant
across all tones. This also assumes that in the acquisition
mode, some coarse frequency adjustment has been made and
we are left with fine-frequency adjustment, i.e. the frequency
offset is a fraction of the subcarrier spacing. In [17], it is
shown that the effect of a frequency offset is threefold. First,
the amplitudes of the FFT outputs are reduced. Secondly, as
with symbol time offsets, one user’s frequency misalignment
with the base station causes the subcarriers to loose their
orthogonality resulting in ICI. These first two effects cause
a loss of the effective SNR and are hard to counteract.
A third effect of a frequency offset is a common rotation
of the subcarriers [12]. This effect will be recognized by a
channel estimator, which does not distinguish between phase
offsets caused by the channel and those caused by a frequency
offset. Thus, a channel equalizer appears also to have fine
frequency synchronization capabilities (see also [12]). The
analysis of multiuser OFDM systems in [8] shows that a
frequency accuracy of 1%–2% of the intercarrier spacing
is necessary to obtain a signal-to-interference ratio (SIR)
of 30 dB or higher. A frequency offset may be estimated
at the receiver. However, as for symbol time offsets, an
adjustment of the receiver base station oscillator would cause
the misalignment in frequency with other users.
III. A M
ULTIUSER SYNCHRONIZATION SCHEME
Synchronization in broadcast OFDM systems has been
investigated in [4] and [6] for instance, and it is in most cases
identified with the actual estimation of the offsets. Although
synchronization in the downlink yields some difficulties, the
uplink in a multiuser system is a more challenging task. In this
VAN DE BEEK et al.: TIME AND FREQUENCY SYNCHRONIZATION SCHEME 1903
Fig. 4. The structure of the receiver at the base station. One path serves
the detection of the data, while other paths estimate the time and frequency
offsets for each user.
section, we propose a tracking scheme based on a multiuser
time and frequency offset estimator and a downlink control
channel on which estimates are fed back to the mobiles.
A. Base Station Receiver Structure and Control Channel
In Fig. 4, the receiver structure of the base station is shown.
It consists of two parts. In one part, the cyclic prefix is
removed, and the data are demodulated by means of an FFT.
In our target system, the demodulated symbols are equalized
by a one-tap channel equalizer and fed into the detector. The
channel equalizer also compensates for small time offsets and
some of the effects of a frequency offset as discussed earlier.
In systems employing convolutional coding, the channel esti-
mates may also be used by the decoder for metric calculation.
The second part of the base station receiver serves to track
the users’ time and frequency offsets. We need to separate
one user from another to estimate a given user’s time and
frequency offset. Grouping the subcarriers together makes
separation by filters possible and ensures that within a user’s
group of subcarriers, there will be little ICI. Subcarriers within
the user group may experience ICI from another user group’s
subcarriers whose time and frequency offset is different. This
ICI will be strongest at the outermost tones and will be
mitigated by the use of guard intervals. The received sampled
baseband signal is fed into a bank of filters, each selecting
the frequencies of one band of adjacent subcarriers. This filter
bank may be efficiently implemented by means of polyphase
filters [18]. Depending on the filter characteristics, a guard
carrier may be used between adjacent frequency bands. Each
filter output roughly represents one user’s signal from which
time and frequency offsets can be estimated.
The important difference between the broadcast and mul-
tiuser synchronization is how symbol and frequency synchro-
nization is accomplished. In a broadcast or downlink scenario,
offsets are estimated by the mobile receiver. These offset
estimates then control the adjustments of the local symbol
clock and demodulation oscillator. Synchronization thus takes
place at the receiver. In the uplink, on the other hand, time
and frequency offset estimation is performed in the base
station but the clock and oscillator adjustments are made in
the user’s transmitter. Since all users must arrive at the base
station aligned in time and frequency in order to maintain the
orthogonality between the subcarriers, all users adapt to the
base station’s receiver clock and oscillator by adjusting their
oscillators and scheduling their transmission according to the
base station information.
Therefore, in our scheme, for every connected user a con-
trol channel is embedded in the downlink on which control
information based on the offset estimates is transmitted back
to the user. With the aid of these control parameters, the user
aligns its transmitted signal to the receiver reference symbol
clock and to the receiver oscillator. The control channel is
embedded in the downlink frequency band, which may have
a similar multiuser structure as the uplink band and is set up
during the initial phase of the connection. Apart from offset
estimates, other control parameters for one user include, for
instance, which time slots and subbands must be used for the
uplink transmission and which transmission power must be
applied. Successful tracking synchronization of the user thus
relies on the control channel.
B. Time and Frequency Offset Estimation
1) ML Time and Frequency Estimator for Multiuser OFDM:
The estimation of time and frequency offsets is addressed in
a number of contributions, e.g., [4], [6], [7], and [17]. As
a key part of our synchronization scheme, we propose an
estimator based on the concept in [4] which works without
the aid of pilot symbols and is independent of the modulation
of the carriers. In this concept, statistical redundancy in the
received signal, introduced by the cyclic prefix, provides the
information about the offsets. Our estimator modifies this
concept to suit the multiuser and fading channel environment.
Consider one OFDM symbol received by the base station.
Assume that the
subcarriers constituting this symbol are
subdivided in
bands of subcarriers, the indexes of which
we collect in the set
. One transmitted OFDM symbol in
the
th band of subcarriers is
(2)
where
is the duration of the OFDM symbol without the
cyclic prefix, and
is the length of the cyclic prefix. We
associate with the
th transmitted signal a time offset
relative to the receiver symbol clock and a frequency offset
relative to the receiver demodulation frequency. We consider
at the base station the sampled received OFDM signal and
model the received signal as
(3)
1904 IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS, VOL. 17, NO. 11, NOVEMBER 1999
(a)
(b)
Fig. 5. The effect of the number of subcarriers in one subband on the mean-squared error of (a) the time offset estimator and (b) the frequency offset estimator.
The target system consists of 1024 subcarriers, and the subbands consist of 22 subcarriers (solid), 44 subcarriers (dashed), and 88 subcarriers (dash-dotted).
where the is the transmitted signal. The previous model
focuses on the frequency or subband division property of the
multiple access scheme as this property significantly affects
the offset estimation. The receiver offset estimator addresses
the time-division property of our target system by applying
one estimator to every time slot.
The bank of bandpass filters in the receiver, discussed
in Section III-A, separates the users’ signals. Note that the
signals
spectrally overlap and that even the use of
ideal brickwall filters in the filterbank does not perfectly
separate these bands. Perfect separation of the users typically
is accomplished by the removal of the cyclic prefix and the
demodulation by the FFT. Such separation, however, removes
the redundancy that is needed by the offset estimation in our
synchronization scheme. Therefore, we use bandpass filters to
separate the subcarriers groupings. We will see that the filters
separate different users’ signals sufficiently for our estimation
purpose.
We apply the following estimator (analyzed below) to the
outputs of the
th filter [4]
(4)
where
(5)
(6)
where
SNR SNR and SNR
Estimator (4) exploits the correlation introduced by the cyclic
prefix to estimate the offsets (see [4]). Its strength is that it
is independent of the modulation and that it does not need
pilot symbols. It is a one-shot estimator in the sense that the
estimates are based on the observation of a single OFDM
symbol.
2) ML Estimator Analysis: This estimator is shown to be
the joint maximum likelihood (ML) estimate of
and [4] if
the output of each filter can be written as
(7)
where the samples
are Gaussian distributed and uncorre-
lated except for the pairs of identical samples contained in the
cyclic prefix. In our multiuser scenario, the
th transmitted
signal is a narrowband signal and has correlation in time
in addition to the correlation between pairs of points in the
cyclic prefix. This correlation in time was not modeled in the
derivation of the time and frequency offset algorithm [4] and
is the main source of degradation in our estimator.
The performance of estimator (4) is shown in Fig. 5. There
is only one user present in the system in this simulation so the
degradation shown is due solely to the increased correlation
in time due to the narrowband signal.
Note that the estimator’s performance is very sensitive to
the number of subcarriers in one subband. This is because the
time and frequency offset estimator was designed to operate in
an AWGN channel on signals that are uncorrelated outside the
cyclic prefix. Using only a small subset of tones violates the
assumption of uncorrelated signals. How correlated the data
is depends on the number of tones. To see how correlated the