Frequency offset estimation with fast acquisition in OFDM system assignment help | www.sampleassignment.com
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This document presents a new carrier frequency offset estimation scheme for orthogonal frequency-division multiplexing (OFDM) systems, featuring both acquisition and tracking capabilities with a large acquisition range of up to half the overall signal bandwidth. The proposed maximum-likelihood tracking estimator performs well in both AWGN and multipath channels, achieving better performance compared to existing methods, particularly under high signal-to-noise ratio conditions. Additionally, accurate timing synchronization can be conducted simultaneously with the acquisition process.
![IEEE COMMUNICATIONS LETTERS, VOL. 8, NO. 3, MARCH 2004 171
Frequency Offset Estimation With
Fast Acquisition in OFDM System
Zhongshan Zhang, Ming Zhao, Haiyan Zhou, Yuanan Liu, Member, IEEE, and Jinchun Gao
Abstract—A new carrier frequency offset estimation scheme
in orthogonal frequency-division multiplexing (OFDM) system is
proposed. The carrier frequency offset estimation includes acqui-
sition and tracking, and the acquisition range is as large as one
half of overall signal bandwidth. The proposed tracking estimator
is a maximum-likelihood estimator, and in AWGN channel, the
Cramer-Rao lower bound is met at high signal-to-noise ratio
(SNR); in multipath channel, the tracking algorithm works well
at moderate SNR. Timing synchronization can be also performed
during the course of acquisition.
Index Terms—Frequency offset estimation, multipath channel,
orthogonal frequency-division multiplexing (OFDM).
I. INTRODUCTION
ORTHOGONAL frequency-division multiplexing
(OFDM) systems are very sensitive to carrier fre-
quency offset, and frequency offset with even a small
fraction of subcarrier spacing will degrade the performance
of OFDM receiver greatly [1]. Many methods have been
presented for frequency offset estimation [1]–[4]. All these
algorithms transmit identical patterns at the transmitter; based
on the phase rotations between these patterns at the receiver,
carrier frequency offset can be estimated. In this letter, a new
pattern is proposed for carrier frequency offset estimation.
Based on the special structure of a training-symbol-block, the
acquisition range for the proposed scheme is as large as one
half of overall signal bandwidth, and high performance tracking
is also obtained. The same training-symbol-block can be also
used for accurate timing synchronization. Section II describes
the frequency offset acquisition algorithm and Section III
presents the tracking algorithm. Simulation results are given in
Section IV, and conclusions are drawn in Section V.
II. CARRIER FREQUENCY OFFSET ACQUISITION
A new carrier frequency offset estimation scheme is proposed
in this letter. A special training-symbol-block is used for both
carrier frequency offset estimation and timing synchronization.
At the transmitter, the training-symbol-block contains two
equal-length training symbols in time domain, and the second
training symbol is the inverse repeat of the first one. The
training-symbol-block has the following form:
(1)
Manuscript received June 2, 2003. The associate editor coordinating the
review of this letter and approving it for publication was Prof. P. Loubaton.
This work was supported in part by 863 project “the Research of Wireless
Transportation Techniques in the Next Generation Mobile Communication
under 2001AA121031”, by the Key Project of Ministry of Education of China
and Doctorial Foundation, and by the Panasonic Joint Project.
The authors are with the Center for Wireless Communication, Beijing
University of Posts and Telecommunications (BUPT), Beijing 100876, China
(e-mail: adhoc@bupt.edu.cn; manyzhao@163.com; mumuzhou@263.net;
yuliu@bupt.edu.cn; gjc@bupt.edu.cn).
Digital Object Identifier 10.1109/LCOMM.2004.823423
Fig. 1. Expectations of M(d) for correct synchronization (d = 0) and
incorrect synchronization (d <> 0).
where denotes the DFT length of training symbols.
At the receiver, without considering of the channel atten-
uation and additive white Guassian noise (AWGN), the rela-
tionship between corresponding samples in a received training-
symbol-block is:
(2)
where denotes the th sample of and denotes the carrier
frequency offset normalized to a subcarrier spacing of training
symbols.
A timing metric is defined:
(3)
where is a time index corresponding to the first sample in a
window of samples.
Fig. 1 shows the expectations of when dB
and . Without loss of generality, the start position index
of a training-symbol-block is assumed to be zero. It is shown
in Fig. 1 that the expectation of is a function of with
period of , and within each period, a main lobe appears;
the expectation of is a constant independent of .
Within one period (without loss of generality,
is assumed), is satisfied only in a small
vicinity which stands in the center of the main lobe; in the main
lobe, increases as approaches to the main lobe center.
This property is the basis for the proposed carrier frequency
offset acquisition algorithm.
The detailed illustration of acquisition is shown in Fig. 2.
Since the expectation of is a function of with period of
1089-7798/04$20.00 © 2004 IEEE](https://image.slidesharecdn.com/frequencyoffsetestimationwithfastacquisitioninofdmsystem-141229101124-conversion-gate02/85/Frequency-offset-estimation-with-fast-acquisition-in-OFDM-system-assignment-help-www-sampleassignment-com-1-320.jpg)
![172 IEEE COMMUNICATIONS LETTERS, VOL. 8, NO. 3, MARCH 2004
Fig. 2. Frequency offset acquisition.
, the acquisition range of the proposed algorithm is limited
within subcarrier spacings, which equals to one half of
overall signal bandwidth. At the transmitter, 2 identical training-
symbol-blocks are transmitted. At the receiver, samples of
the training sequence are buffered. The length of guarantees
one integral training-symbol-block being buffered.
Because the carrier frequency offset is fully
unknown at the start of acquisition, a method
of lookup is used: presupposed values
where and )
are used to compensate for the carrier frequency offset
of the buffered samples (multiplying the buffered
samples by where and
). denotes the lookup interval (in the
following section we will know that the tracking range for the
proposed scheme is subcarrier spacing,
and guarantees the remaining
carrier frequency offset being not beyond the tracking range).
For th compensated training sequence, the
maximum ( ) is represented as which
implies the appearance of an integral training-symbol-block; if
for each , then denotes the
carrier frequency offset estimated by acquisition algorithm. The
estimated start of that integral training-symbol-block is also
the output of acquisition.
After acquisition, if the remaining carrier frequency offset ex-
ceeds the tracking range, tracking algorithm will not work cor-
rectly, and this is called Missing Lock. For usable SNR, if
is large enough, the probability of Missing Lock ( ) is neg-
ligible. For example, when , dB and the
carrier frequency is assumed to be 2.5 subcarrier spacings, if
is set to 0.2, is far less than .
III. CARRIER FREQUENCY OFFSET FINE ADJUSTMENT
After acquisition, the remaining frequency offset needs to be
further corrected. For a received training-symbol-block under
certain SNR condition, the log-likelihood function for the car-
rier frequency offset , is the logarithm of the probability
density function . Using the correlation properties of
samples in , the log-likelihood function can be written as
(4)
Like in [2], the 2-D complex-valued Guassian distribution
is
(5)
where
(6)
(7)
The carrier frequency offset can be estimated by maxi-
mizing the log-likelihood function. By taking the partial deriva-
tive of with respect to and setting the result to zero, the
maximum-likelihood estimate of is given by (8) at the bottom
of the following page.](https://image.slidesharecdn.com/frequencyoffsetestimationwithfastacquisitioninofdmsystem-141229101124-conversion-gate02/85/Frequency-offset-estimation-with-fast-acquisition-in-OFDM-system-assignment-help-www-sampleassignment-com-2-320.jpg)
![ZHANG et al.: FREQUENCY OFFSET ESTIMATION WITH FAST ACQUISITION IN OFDM SYSTEM 173
In order to make the proposed tracking algorithm work
correctly, for each
should be satisfied, i.e., the tracking range is
subcarrier spacing. By using the method
in [5], its Cramer–Rao lower bound is
(9)
IV. SIMULATION RESULTS
In this letter, it is assumed that the channel character does
not change during one training-symbol-block period. A wireless
system operating at 5 GHz and with bandwidth of 10 MHz is
assumed. An outdoor dispersive, fading environment is chosen:
the channel is modeled to consist of 4 independent Rayleigh-
fading taps with path delay of 0, 5, 9, and 12 samples and
path gains are:
(10)
Since the proposed acquisition algorithm reliably guarantees
the remaining carrier frequency offset being not beyond the
tracking range, only tracking performance is evaluated in this
section. The performance of the proposed tracking algorithm
with (not including cyclic-prefix) is compared to
that of Schmidl’s algorithm (fractional part carrier frequency
offset estimator) [3] with training symbol length of 256 and
a cyclic-prefix length of 16. In simulation, QPSK modulation
is assumed. Estimation variance error is used for evaluating
the algorithms’ performances. Variance error is defined as
where denotes the true carrier frequency
offset. Carrier frequency offset is assumed to be 7.813 kHz,
which is not beyond the tracking ranges of both algorithms.
Simulation results are shown in Fig. 3. In the AWGN channel,
for high SNR, the performance of proposed algorithm is about
7.27 dB better than that of Schmidl’s algorithm. In multipath
channel, the performance of Schmidl’s algorithm will not
degrade too much comparing to that in AWGN channel, pro-
vided that the cyclic-prefix is longer than the channel impulse
response; while for the proposed algorithm, is estimated
based on the maximum power tap signal, and other taps become
interference noise, which reduces the effective SINR. For large
, the Cramer-Rao lower bound of the proposed tracking algo-
rithm in multipath channel nearly equals to .
That for Schmidl’s algorithm is ( denotes one
half of the training symbol length, and in this letter, ).
For the proposed tracking algorithm, if
is satisfied, its tracking error will be smaller than that of
Schmidl’s algorithm.
Fig. 3. Performance of Schmidl’s tracking algorithm (fractional part carrier
frequency offset estimator) and that of the proposed tracking algorithm.
V. CONCLUSIONS
In this letter, a new carrier frequency offset estimation scheme
is proposed. The acquisition range for the proposed scheme is
as large as one half of the total signal bandwidth. The proposed
tracking estimator is an ML estimator, and in AWGN channel,
its performance is about 7.27 dB better than that of Schmidl’s
estimator at high SNR. In multipath channel, at moderate SNR,
comparison of the proposed estimator with Schmidl’s estimator
also illustrates the superior performance of the proposed scheme
with regard to estimation accuracy; at high SNR, as SNR in-
creases, a performance floor appears in the proposed estimator.
Accurate timing synchronization can be also performed during
the course of acquisition.
REFERENCES
[1] P. H. Moose, “A technique for orthogonal frequency division multi-
plexing frequency offset correction,” IEEE Trans. Commun., vol. 42, pp.
2908–2914, Oct. 1994.
[2] J.-J. van de Beek and M. Sandell, “ML estimation of time and frequency
offset in OFDM systems,” IEEE Trans. Signal Processing, vol. 45, pp.
1800–1805, July 1997.
[3] T. M. Schmidl and D. C. Cox, “Robust frequency and timing synchro-
nization for OFDM,” IEEE Trans. Commun., vol. 45, pp. 1613–1621,
Dec. 1997.
[4] M. Louise and R. Reggiannini, “Carrier frequency acquisition and
tracking for OFDM systems,” IEEE Trans. Commun., vol. 44, pp.
1590–1598, Nov. 1996.
[5] D. Rife and R. Boorstyn, “Single-tone parameter estimation from dis-
crete-time observations,” IEEE Trans. Inform. Theory, vol. IT-20, pp.
591–598, Sept. 1974.
(8)](https://image.slidesharecdn.com/frequencyoffsetestimationwithfastacquisitioninofdmsystem-141229101124-conversion-gate02/85/Frequency-offset-estimation-with-fast-acquisition-in-OFDM-system-assignment-help-www-sampleassignment-com-3-320.jpg)
Frequency offset estimation with fast acquisition in OFDM system assignment help | www.sampleassignment.com
- 1. IEEE COMMUNICATIONS LETTERS, VOL. 8, NO. 3, MARCH 2004 171 Frequency Offset Estimation With Fast Acquisition in OFDM System Zhongshan Zhang, Ming Zhao, Haiyan Zhou, Yuanan Liu, Member, IEEE, and Jinchun Gao Abstract—A new carrier frequency offset estimation scheme in orthogonal frequency-division multiplexing (OFDM) system is proposed. The carrier frequency offset estimation includes acqui- sition and tracking, and the acquisition range is as large as one half of overall signal bandwidth. The proposed tracking estimator is a maximum-likelihood estimator, and in AWGN channel, the Cramer-Rao lower bound is met at high signal-to-noise ratio (SNR); in multipath channel, the tracking algorithm works well at moderate SNR. Timing synchronization can be also performed during the course of acquisition. Index Terms—Frequency offset estimation, multipath channel, orthogonal frequency-division multiplexing (OFDM). I. INTRODUCTION ORTHOGONAL frequency-division multiplexing (OFDM) systems are very sensitive to carrier fre- quency offset, and frequency offset with even a small fraction of subcarrier spacing will degrade the performance of OFDM receiver greatly [1]. Many methods have been presented for frequency offset estimation [1]–[4]. All these algorithms transmit identical patterns at the transmitter; based on the phase rotations between these patterns at the receiver, carrier frequency offset can be estimated. In this letter, a new pattern is proposed for carrier frequency offset estimation. Based on the special structure of a training-symbol-block, the acquisition range for the proposed scheme is as large as one half of overall signal bandwidth, and high performance tracking is also obtained. The same training-symbol-block can be also used for accurate timing synchronization. Section II describes the frequency offset acquisition algorithm and Section III presents the tracking algorithm. Simulation results are given in Section IV, and conclusions are drawn in Section V. II. CARRIER FREQUENCY OFFSET ACQUISITION A new carrier frequency offset estimation scheme is proposed in this letter. A special training-symbol-block is used for both carrier frequency offset estimation and timing synchronization. At the transmitter, the training-symbol-block contains two equal-length training symbols in time domain, and the second training symbol is the inverse repeat of the first one. The training-symbol-block has the following form: (1) Manuscript received June 2, 2003. The associate editor coordinating the review of this letter and approving it for publication was Prof. P. Loubaton. This work was supported in part by 863 project “the Research of Wireless Transportation Techniques in the Next Generation Mobile Communication under 2001AA121031”, by the Key Project of Ministry of Education of China and Doctorial Foundation, and by the Panasonic Joint Project. The authors are with the Center for Wireless Communication, Beijing University of Posts and Telecommunications (BUPT), Beijing 100876, China (e-mail: adhoc@bupt.edu.cn; manyzhao@163.com; mumuzhou@263.net; yuliu@bupt.edu.cn; gjc@bupt.edu.cn). Digital Object Identifier 10.1109/LCOMM.2004.823423 Fig. 1. Expectations of M(d) for correct synchronization (d = 0) and incorrect synchronization (d <> 0). where denotes the DFT length of training symbols. At the receiver, without considering of the channel atten- uation and additive white Guassian noise (AWGN), the rela- tionship between corresponding samples in a received training- symbol-block is: (2) where denotes the th sample of and denotes the carrier frequency offset normalized to a subcarrier spacing of training symbols. A timing metric is defined: (3) where is a time index corresponding to the first sample in a window of samples. Fig. 1 shows the expectations of when dB and . Without loss of generality, the start position index of a training-symbol-block is assumed to be zero. It is shown in Fig. 1 that the expectation of is a function of with period of , and within each period, a main lobe appears; the expectation of is a constant independent of . Within one period (without loss of generality, is assumed), is satisfied only in a small vicinity which stands in the center of the main lobe; in the main lobe, increases as approaches to the main lobe center. This property is the basis for the proposed carrier frequency offset acquisition algorithm. The detailed illustration of acquisition is shown in Fig. 2. Since the expectation of is a function of with period of 1089-7798/04$20.00 © 2004 IEEE
- 2. 172 IEEE COMMUNICATIONS LETTERS, VOL. 8, NO. 3, MARCH 2004 Fig. 2. Frequency offset acquisition. , the acquisition range of the proposed algorithm is limited within subcarrier spacings, which equals to one half of overall signal bandwidth. At the transmitter, 2 identical training- symbol-blocks are transmitted. At the receiver, samples of the training sequence are buffered. The length of guarantees one integral training-symbol-block being buffered. Because the carrier frequency offset is fully unknown at the start of acquisition, a method of lookup is used: presupposed values where and ) are used to compensate for the carrier frequency offset of the buffered samples (multiplying the buffered samples by where and ). denotes the lookup interval (in the following section we will know that the tracking range for the proposed scheme is subcarrier spacing, and guarantees the remaining carrier frequency offset being not beyond the tracking range). For th compensated training sequence, the maximum ( ) is represented as which implies the appearance of an integral training-symbol-block; if for each , then denotes the carrier frequency offset estimated by acquisition algorithm. The estimated start of that integral training-symbol-block is also the output of acquisition. After acquisition, if the remaining carrier frequency offset ex- ceeds the tracking range, tracking algorithm will not work cor- rectly, and this is called Missing Lock. For usable SNR, if is large enough, the probability of Missing Lock ( ) is neg- ligible. For example, when , dB and the carrier frequency is assumed to be 2.5 subcarrier spacings, if is set to 0.2, is far less than . III. CARRIER FREQUENCY OFFSET FINE ADJUSTMENT After acquisition, the remaining frequency offset needs to be further corrected. For a received training-symbol-block under certain SNR condition, the log-likelihood function for the car- rier frequency offset , is the logarithm of the probability density function . Using the correlation properties of samples in , the log-likelihood function can be written as (4) Like in [2], the 2-D complex-valued Guassian distribution is (5) where (6) (7) The carrier frequency offset can be estimated by maxi- mizing the log-likelihood function. By taking the partial deriva- tive of with respect to and setting the result to zero, the maximum-likelihood estimate of is given by (8) at the bottom of the following page.
- 3. ZHANG et al.: FREQUENCY OFFSET ESTIMATION WITH FAST ACQUISITION IN OFDM SYSTEM 173 In order to make the proposed tracking algorithm work correctly, for each should be satisfied, i.e., the tracking range is subcarrier spacing. By using the method in [5], its Cramer–Rao lower bound is (9) IV. SIMULATION RESULTS In this letter, it is assumed that the channel character does not change during one training-symbol-block period. A wireless system operating at 5 GHz and with bandwidth of 10 MHz is assumed. An outdoor dispersive, fading environment is chosen: the channel is modeled to consist of 4 independent Rayleigh- fading taps with path delay of 0, 5, 9, and 12 samples and path gains are: (10) Since the proposed acquisition algorithm reliably guarantees the remaining carrier frequency offset being not beyond the tracking range, only tracking performance is evaluated in this section. The performance of the proposed tracking algorithm with (not including cyclic-prefix) is compared to that of Schmidl’s algorithm (fractional part carrier frequency offset estimator) [3] with training symbol length of 256 and a cyclic-prefix length of 16. In simulation, QPSK modulation is assumed. Estimation variance error is used for evaluating the algorithms’ performances. Variance error is defined as where denotes the true carrier frequency offset. Carrier frequency offset is assumed to be 7.813 kHz, which is not beyond the tracking ranges of both algorithms. Simulation results are shown in Fig. 3. In the AWGN channel, for high SNR, the performance of proposed algorithm is about 7.27 dB better than that of Schmidl’s algorithm. In multipath channel, the performance of Schmidl’s algorithm will not degrade too much comparing to that in AWGN channel, pro- vided that the cyclic-prefix is longer than the channel impulse response; while for the proposed algorithm, is estimated based on the maximum power tap signal, and other taps become interference noise, which reduces the effective SINR. For large , the Cramer-Rao lower bound of the proposed tracking algo- rithm in multipath channel nearly equals to . That for Schmidl’s algorithm is ( denotes one half of the training symbol length, and in this letter, ). For the proposed tracking algorithm, if is satisfied, its tracking error will be smaller than that of Schmidl’s algorithm. Fig. 3. Performance of Schmidl’s tracking algorithm (fractional part carrier frequency offset estimator) and that of the proposed tracking algorithm. V. CONCLUSIONS In this letter, a new carrier frequency offset estimation scheme is proposed. The acquisition range for the proposed scheme is as large as one half of the total signal bandwidth. The proposed tracking estimator is an ML estimator, and in AWGN channel, its performance is about 7.27 dB better than that of Schmidl’s estimator at high SNR. In multipath channel, at moderate SNR, comparison of the proposed estimator with Schmidl’s estimator also illustrates the superior performance of the proposed scheme with regard to estimation accuracy; at high SNR, as SNR in- creases, a performance floor appears in the proposed estimator. Accurate timing synchronization can be also performed during the course of acquisition. REFERENCES [1] P. H. Moose, “A technique for orthogonal frequency division multi- plexing frequency offset correction,” IEEE Trans. Commun., vol. 42, pp. 2908–2914, Oct. 1994. [2] J.-J. van de Beek and M. Sandell, “ML estimation of time and frequency offset in OFDM systems,” IEEE Trans. Signal Processing, vol. 45, pp. 1800–1805, July 1997. [3] T. M. Schmidl and D. C. Cox, “Robust frequency and timing synchro- nization for OFDM,” IEEE Trans. Commun., vol. 45, pp. 1613–1621, Dec. 1997. [4] M. Louise and R. Reggiannini, “Carrier frequency acquisition and tracking for OFDM systems,” IEEE Trans. Commun., vol. 44, pp. 1590–1598, Nov. 1996. [5] D. Rife and R. Boorstyn, “Single-tone parameter estimation from dis- crete-time observations,” IEEE Trans. Inform. Theory, vol. IT-20, pp. 591–598, Sept. 1974. (8)