E STIMATION OFC ARRIER -F REQUENCY O FFSET AND F REQUENCY-S ELECTIVE C HANNELS IN
MIMO OFDM S YSTEMS U SING A C OMMON T RAINING S IGNAL
Hlaing Minn, Member, IEEE and Naofal Al-Dhahir, Senior Member, IEEE
Department of Electrical Engineering, University of Texas at Dallas
Tel: +1 972 883 2889, Fax: +1 972 883 2710, Email: hlaing.minn, aldhahir @utdallas.edu
Abstract—This paper presents a common training signal design and training signal. We develop a common training signal and the cor-
corresponding estimation methods for carrier frequency offset and responding estimation methods which have low complexity, low
frequency-selective channels in MIMO OFDM systems. In designing
processing delay, low training overhead, and high performance.
the common training signal, a training signal structure which yields
low complexity estimation methods is developed while the optimality of Our proposed designs can be applied to systems with pilot-only
the training signal is maintained. Frequency offset estimation is based training signal as well as those with pilot-data multiplexed signal.
on the best linear unbiased estimation principle while channel estima- Extension of frequency offset estimation range by means of multi-
tion is based on the least squares (also maximum likelihood) approach. ple OFDM training symbols is also presented.
The proposed training signal and estimation methods can be applied to
systems with pilot-only training signals as well as those with pilot-data
multiplexed signals. The estimation range of the frequency offset can II. S IGNAL M ODEL
be flexibly adjusted. The performances of the proposed methods are Consider a MIMO OFDM system with à sub-carriers, ÆØ
transmit antennas and ÆÖ receive antennas. The training signals
very close to the Cramer-Rao bounds or theoretical minimum mean
square error.
from ÆØ transmit-antennas are transmitted over É OFDM symbols
where É ¾ ½ ¾ . The channel impulse response (CIR) for
each transmit-receive antenna pair (including filters’ effects) is as-
I. I NTRODUCTION
sumed to have Ä taps, and is quasi-static over É OFDM symbols.
The higher data rate requirement of future wireless communi-
Let Ò Õ =
Ò Õ ¼℄, . . . ,
Ò Õ Ã ½℄℄Ì be the pilot tones vector of
cations systems, the significant information theoretic capacity gain the Ò-th transmit-antenna at the Õ-th symbol interval and ×Ò Õ ℄
of MIMO systems, and the robustness and suitability of OFDM Æ
à ½ be the corresponding time-domain complex
for high data rate transmission highlight the significant potential baseband training samples, including Æ ´ Ä ½µ cyclic prefix
of MIMO OFDM systems. However, MIMO OFDM inherits a samples. Define Ë Ò Õ℄ as the training signal matrix of size Ã Ä ¢
high sensitivity to frequency offset error from OFDM. Hence, for the Ò-th transmit-antenna at the Õ-th symbol interval whose ele-
highly-accurate frequency synchronization is an important issue ments are given by Ë Ò Õ℄℄Ñ Ð ×Ò Õ Ð Ñ℄, Ñ ¼ ¾Ã ½ ,
in MIMO OFDM. The estimation of increased numbers of chan- о ¼
Ä ½ .
Let ×Ò Õ represent the ¼-th column of ËÒ Õ℄. Then the Ð-th col-
umn of Ë Ò Õ℄ is the Ð-sample cyclic-shifted version of ×Ò Õ de-
nels in MIMO systems presents another challenge in implementing
MIMO OFDM systems. ´´Ðµµ
noted by ×Ò Õ . Assume that à Åļ where Å =1, 2, . . . , and
Most previous approaches address frequency offset estimation ļ Ä. Let Ò Ñ denote the length-Ä CIR vector correspond-
and channel estimation separately using separate training signals ing to the Ò-th transmit antenna and Ñ-th receive antenna. After
(see [1]-[6] and references therein). There are only a few works the cyclic prefix removal at the receiver, denote the received vector
which address synchronization and channel estimation using a of length à from the Ñ-th receive antenna at the Õ-th symbol in-
common training signal (e.g., [10] for SISO OFDM systems). Due
terval by Ö Ñ Õ = ÖÑ Õ ´¼µ, ÖÑ Õ ´½µ, . . . , ÖÑ Õ ´Ã ½µ℄Ì . Then the
to the training overhead saving, the approaches using a common received vector over the É symbol-intervals at the Ñ-th receive
antenna is given by
training signal merit further investigation. For MIMO OFDM sys-
tems, [11] has recently presented a combined frequency offset and ÖÑ Ï ´Úµ Ë Ñ · ÒÑ (1)
channel estimation method based on a common training signal. where
[11] considers a pilot-data multiplexed scheme where the number Ì
of OFDM symbols required for transmission of pilot tones has to ÖÑ ÖÌ ¼ ÖÌ ½
Ñ Ñ ÖÌ É ½
Ñ (2)
be at least the same as the number of channel impulse response ¾ ˼ ¼℄ ˽ ¼℄ ËÆØ ½ ¼℄ ¿
taps. The authors use sub-space-based frequency offset estimation ˼ ½℄ ˽ ½℄ ËÆØ ½ ½℄
and linear minimum mean square error channel estimation. Hence, Ë .
.
.
. .. . (3)
. . . .
.
the method from [11] is more appropriate for systems which can ˼ É ½℄ ˽ É ½℄ ËÆØ ½ É ½℄
accommodate relatively high complexity, are insensitive to pro- Ì Ì Ì Ì
Ñ ¼ Ñ ½ Ñ ÆØ ½ Ñ ℄ (4)
cessing delay, and have knowledge of the channel covariance ma-
trix and the noise variance. Ï ´Ú µ Ï ´Úµ ¾ Ú´Æ ·Ãµ Ã Ï ´Úµ
¾ Ú ´É ½µ´Æ ·Ã µ Ã
In this paper, we consider a combined frequency offset and Ï ´Úµ℄ (5)
¾ Ú Ã ¾ ¾Ú Ã ¾ ´Ã ½µÚ Ã
channel estimation in MIMO OFDM systems based on a common Ï ´Úµ ½ ℄ (6)
The work of N. Al-Dhahir was supported in part by the Texas Advanced and ÒÑ is a length ÃÉ vector of zero-mean, circularly symmet-
Technology Program (ATP) project no. 009741-0023-2003 ric, uncorrelated complex Gaussian noise samples with equal vari-
¾
ance of Ò . The diagonal matrix Ï ´Úµ corresponds to the nor- The optimality of the sub-block signal for frequency offset esti-
malized frequency offset Ú, normalized by the sub-carrier spacing. mation is investigated in the following. In [14], we show for fre-
We consider a system where the RF branches of all antennas use quency offset estimation in SISO systems that the sub-block signal
a common local oscillator and hence, there is only one common is optimal in minimizing the average CRB of the frequency offset
normalized carrier frequency offset Ú between the transmitter and estimation in a frequency-selective fading channel if the sub-block
the receiver. signal possesses a zero autocorrelation for any non-zero correlation
lag (this type of signal is usually referred to as zero autocorrelation
III. D ESIGN OF A C OMMON OFDM T RAINING S YMBOL F OR (ZAC) signal). In other words, the ZAC signals result in minimum
E STIMATION OF F REQUENCY O FFSET AND C HANNELS fluctuation of the received training signal energy in a frequency-
selective fading channel which in turn translates into minimum
Training signals consisting of several consecutive identical sub- average CRB. In MIMO systems, the received training signal at
blocks are commonly used for frequency offset estimation in a receive antenna is the superposition of channel output training
SISO OFDM systems (e.g., IEEE 802.11a, HIPERLAN-2, [1] signals from all transmit antennas. For MIMO systems where the
[2]). On the other hand, optimal training signals for estimation of channels are independent, the minimum fluctuation of the total re-
frequency-selective channels in MIMO OFDM systems were pre- ceived training signal energy is achieved if each transmit antenna’s
sented in [6] and [9]. In [12], we have recently derived general channel output signal has minimum energy fluctuation. This is
classes of optimal training signals for estimation of frequency- readily obtained if each transmit antenna’s training sub-block sig-
selective channels in MIMO OFDM. The pilot tone allocation nal is a ZAC signal. Our training sub-block signal for Ò-th transmit
among transmit antennas are classified as frequency division mul- antenna, denoted by ×Ò = ×Ò ¼℄, ×Ò ½℄, . . . , ×Ò ´Ã µ ½℄℄Ì , can
tiplexing (FDM), time division multiplexing (TDM), code division be generated by à point IFFT of the corresponding à non-
multiplexing in time-domain (CDM-T), code division multiplexing zero pilot tones denoted by Ò =
Ò ¼℄,
Ò ℄, . . . ,
Ò Ã
℄℄Ì .
in frequency domain (CDM-F), and combinations thereof. Based The periodic autocorrelation of ×Ò with correlation lag Ð
´´Ðµµ ´´Ñµµ . By using ×´´Ðµµ ½ Ï ´Ðµ Ò
Ñ
on these optimal training signals for MIMO channel estimation, is given by ´×Ò µÀ ×Ò Ò Ã
a common training signal for estimation of both frequency offset
where à is the à point FFT matrix and Ï ´Ðµ=diag 1,
and MIMO frequency-selective channels will be derived. The goal ¾ Ð Ã , ¾ о à , . . . , ¾ дà ½µ à is a diagonal
is to obtain a training signal having two properties: (i) the train- ´´Ðµµ ´´Ñµµ = 0 for Ð Ñ.
matrix, it can be easily shown that ´×Ò µÀ ×Ò
ing signal for each transmit antenna consists of several consecu-
tive identical sub-blocks for efficient implementation of frequency This means that our training sub-block signal for each transmit
offset estimator and the sub-block signal is optimal for frequency antenna is a ZAC signal, hence an optimal sub-block signal for
offset estimation, (ii) the training signal is optimal for estimation frequency offset estimation.
of MIMO frequency-selective channels.
Let us consider the training signal design using one OFDM sym- IV. E STIMATION OF F REQUENCY O FFSET AND C HANNELS
bol, i.e., É=1, which contains pilot tones only. For simplicity, the U SING O NE OFDM T RAINING S YMBOL
symbol index Õ will be omitted.
(C.1) For the training signal to have consecutive identical At each receive antenna, after the CP removal, the received
training signal contains sub-blocks which are identical in the
sub-blocks within one OFDM symbol where à is an integer absence of frequency offset and noise. For this type of received
and ¾ ¾ ¿ , the non-zero pilot tones for each transmit training signal, the best linear unbiased estimation (BLUE) meth-
antenna must be located at the sub-carrier indices : =0, 1, ods (e.g., [1] [2]) show excellent performance (very close to CRB)
. . . , ´Ã µ ½ . and they have low implementation complexity. Hence, we adopt
the BLUE method from [2] in this paper. The frequency offset
(C.2) Among several classes of optimal training signals pre- estimate from Ñ-th receive antenna is given by
sented in [12], the above condition (C.1) is satisfied by the CDM-F
type pilot tone allocation if Ã Æ Ø Ä.
(C.3) The CDM-F pilot tone allocation requires that generally ÚÑ ÛÌ Ñ (10)
¾
all non-zero pilot tones must have the same amplitude and the op-
timal pilot tones for -th transmit antenna,
Ò℄ , are given by where
Ò℄
¼ Ò℄ ¾ ļ Ò Ã (7) Ñ Ñ ´½µ ½µ℄Ì
Ñ ´¾µ Ñ´ (11)
Ñ℄ Ò Ñ Ñ ¼ ½ ´Ã µ ½ ¡ Ö ÊѴе Ö ÊÑ´Ð ½µ ℄¾
¼ Ò℄ ¼ Ð× (8) Ñ ´Ðµ (12)
Ñ℄
½ Ð ½
¼ ¼ (9) ½ ½
Û Ñ
½
½Ì Ñ ½
(13)
where ļ Ä, à ļ is an integer equal to the number of (active)
transmit antennas within one OFDM symbol, =0, 1, . . . , à ļ ,
and Ñ℄ are constant modulus symbols. Here, ½ is an all ones column vector of length ½.
Ñ is
By combining the above conditions, we have the desired OFDM the covariance matrix of Ñ and its detailed expression is given in
training symbol given by (7)-(9) where à ÆØļ and ļ Ä. [2]. ÊÑ ´Ðµ is a correlation term defined as
This training signal contains consecutive identical sub-blocks
à Ðà ½
and satisfies the optimality condition for MIMO channel estima- ÊÑ ´Ðµ £
ÖÑ ´ µ ÖÑ ´ · ÐÃ µ ¼ Ð ½ (14)
tion which is inherited from the CDM-F pilot tone allocation. ¼
The final frequency offset estimate is simply given by the average Here, ½ is an all-ones column vector of length ½. ÑÕ is the
of estimates from all receive antennas as covariance matrix of ÑÕ . ÊÑÕ ´Ðµ is a correlation term defined as
Æ ½
½ Ö ½
Ú Ú Ã ÐÃ
ÆÖ Ñ ¼ Ñ
(15)
ÊÑÕ ´Ðµ £
ÖÑÕ ´ µ ÖÑÕ ´ · ÐÃ µ ¼ Ð ½
The frequency offset estimation range is ¦ ¾ sub-carrier spac- ¼
(24)
ing. Note that since à ÆØļ and ļ Ä, the estimation The final frequency offset estimate is simply given by the average
range depends on à ´ÆØļ µ. For a system with a large number of of estimates from all receive antennas over É symbols as
transmit antennas and a very large delay spread (very large Ä), the
É ½ ÆÖ ½
½
above estimation range may not be sufficient to account for trans- Ú Ú
ÆÖ É Õ ¼ Ñ ¼ ÑÕ
(25)
mit and receive local oscillators mismatch and the channel Doppler
shift. We will tackle this possible problem later in this paper.
The final frequency offset estimate is used in frequency offset If a smaller complexity is preferred, Ú can be calculated as the
compensation on the training signal and the data signal already re- average of ÚѼ only. For a given set of channel gains, the snap-
ceived (i.e., those in buffer). It is also used to correct the receiver shot CRB of Ú, after skipping details, is given by
local oscillator’s frequency for next incoming signal. This oscilla-
tor frequency correction may be performed immediately after the ¾
¿ Ò
frequency offset estimation or on packet by packet basis. The fre- Ê
¾ ¾ ´½ ½ ¾µ Ú ÈÆÖ ½ ´ À Ñ µ
Ñ ¼ Ñ
(26)
quency offset compensated received training signal from Ñ-th re-
ceive antenna is given by In the above equation, we have used the following property of the
ÖÑ Ï À ´Úµ ÖÑ (16) training signal [12]:
After the frequency offset compensation is performed, the least- ËÀ ËÒ
Ò ÚÁ Ò ¼ ½ ÆØ ½ (27)
square-type channel estimation at Ñ-th receive antenna is per- Ì ¼℄ Ë Ì ½℄ Ì É ½℄℄Ì
formed as Û Ö ËÒ ËÒ Ò ËÒ (28)
Ñ ´ËÀ Ë µ ½ Ë À ÖÑ ÆØ ½ É ½ Ã ½
℄¾
(17) ½
Ú ×
ÆØ Ò ¼ Õ ¼ ¼ Ò Õ
Since the training signal is designed to be optimal for MIMO (29)
OFDM channel estimation, it satisfies the following [12]:
´Ë À Ë µ ½ ´½ Ú µÁ (18) Define the training signal to noise ratio as
Hence, the channel estimation is simplified to ÆØ Ú
ËÆÊ ¾ (30)
Ñ
½
Ë À ÖÑ (19) Ã ÒÉ
Ú
Then the snap-shot CRB of (26) is simplified to
Ê
« (31)
V. E STIMATION OF F REQUENCY O FFSET AND C HANNELS
U SING É OFDM T RAINING S YMBOLS ¿ ËÆÊ ½
To extend the frequency offset estimation range, we can use Û Ö « ¾ ÃÉÆÖ ´½ ½ ¾ µ (32)
¾
É OFDM training symbols instead of only one OFDM train- ÈÆÖ ½ ÈÆØ ½ ÈÄ ½
ing symbol. We choose É such that both ÅØ ÆØ É and Ñ ¼ Ò ¼ Ð ¼ Ò Ñ Ð℄ ¾
à (33)
ÅØ Ä¼ are integers. Then, we partition ÆØ transmit anten- ÆÖ ÆØ
nas into É groups; each has ÅØ transmit antennas. In Õ-th OFDM
symbol, only one group of transmit antennas (with indices Ò The numerator of is the sum of central chi-square random vari-
¾ Ð ¼
ÕÅØ
´Õ · ½µÅØ ½℄) transmit training signals. In this case, ables Ò Ñ Ð℄ Ä ½Ò ¼ ÆØ ½ Ñ
¾
Ë Ò Õ℄ in (3) is a zero matrix for all Ò ÕÅØ ´Õ · ½µÅØ ½℄. ¼
ÆÖ ½ . can be well approximated by a Gamma random
Then, the single-symbol-based methods described in the previous variable (see [13], [14]). , Then, the average CRB of Ú is given by
section can be applied to estimate frequency offset and channels ½ «
for ÅØ transmit antennas in the current transmit antenna group. Ê Ê Ô´ µ Û ¾
℄ Þ
(34)
The training signal design discussed in the previous section is ap- ¼ ℄
plied to each symbol interval for the ÅØ active transmit antennas
and is now replaced with . The estimation range now is ¾¦ We assume that the channels are independent and have the same
¾
Ò Ñ Ð℄ ℄
¾
which is É times that of single-symbol-based method. Note that power delay profiles, i.e., Ð,Ð ¼, . . . , Ä ½,
É . The frequency offset estimation from Ñ-th receive
antenna at Õ-th OFDM symbol interval is
Ò Ñ. For the SNR defined in (30) to be the average received
SNR at a receive antenna, we must have Ä ½ Ð
Ð ¼
¾ ½. Then the È
CRB of Ú becomes
ÚÑÕ ÛÑÕ Ì ÑÕ (20) ¿ ËÆÊ ½
¾
where
Ê
¾ ¾ ÃÉ´½ ½ ¾µ´ÆÖ ÈÄ ½
Ð ¼ Ð ÆØ µ
(35)
ÑÕ ÑÕ ´½µ ÑÕ ´¾µ ÑÕ ´ ½µ℄Ì (21)
After the frequency offset compensation is performed, the
ÑÕ ´Ðµ
¡ Ö ÊÑÕ ´Ðµ Ö ÊÑÕ ´Ð ½µ ℄¾ least-square type channel estimation for a transmit antenna Ò ¾
½ Ð ½
(22)
ÕÅØ
´Õ · ½µÅØ ½℄ (which is active at Õ-th OFDM symbol)
and Ñ-th receive antenna is performed as
½ ½
ÑÕ
ÛÑÕ ½
½ Ì ½ ½ Ë À Õ℄ÖÑÕ Õ É ½ Ñ ÆÖ ½
(23)
ÒÑ Ò ¼ ¼ (36)
ÑÕ Ú
At perfect frequency recovery, the channel estimation MSE for conventional and modified schemes. 1 . In the simulation, the ratio
each channel tap is given by of total pilot energy to data energy is 5dB. Due to data signal inter-
¾ ference, MSE performance is degraded 2 but the modified scheme
ÅË Ò ØÖ ´ËÀ Ë µ ½ ÆØ (37) gives an appreciable improvement. The channel estimation results
ÄÆØ ÃÉËÆÊ for pilot-data multiplexed schemes are shown in Fig.5. For chan-
nel estimation, the effect of data signal interference are negligible
Note that we can also partition ÆØ transmit antennas into É groups
since residual frequency offset is small.
with unequal number of transmit antennas. For example, if ÆØ =6,
à , Ä Ä¼ ½ , and É ¾, then we can assign 2
transmit antennas in the first symbol and the remaining 4 transmit VII. C ONCLUSIONS
antennas in the second symbol. The frequency offset estimation
We have presented a common training signal design and estima-
can be based on the first symbol only and the estimation range is
¦ ½ sub-carrier spacing.
tion methods for carrier frequency offset and frequency-selective
channels in MIMO OFDM systems. The proposed training signals
For pilot-data multiplexed scheme, frequency offset estimation
are optimal for MIMO channel estimation. They contain several
would be affected by the data tones’ interference on the pilots since
identical sub-blocks to yield low complexity, high performance
the received pilots and data are no longer orthogonal in the pres-
frequency offset estimation. The sub-block signals are optimal
ence of a frequency offset. A modified scheme to alleviate the data
for frequency offset estimation in frequency-selective fading chan-
interference is described below. Data tones closer to a pilot tone
nels. In the proposed methods, the best linear unbiased estimation
cause larger interference on the pilot. For every pilot tone with sub-
carrier index Ô, the data tones at sub-carrier indices Ô ½℄Æ and
method is applied in frequency offset estimation while maximum
¡
Ô · ½℄Æ are set to be the same where ℄Æ denotes modulo-Æ op-
likelihod approach is adopted in channel estimation. The perfor-
mances of the proposed methods using the proposed training signal
eration. Since data tone interferences to the left and to the right in
are very close to the CRB or the minimum MSE of the estima-
the sub-carrier domain are almost anti-symmetric [15], the above
tion for pilot-only schemes. Due to data interference, the estima-
modified scheme almost cancels the largest interference term com-
tion performances in pilot-data multiplexed schemes suffer some
ing from the two data sub-carriers adjacent to the pilot.
degradation. This paper also presents a modified pilot-data multi-
plexed scheme which appreciably alleviates the data interference
VI. S IMULATION R ESULTS AND D ISCUSSIONS effect on the estimation performance.
We have evaluated the estimation methods presented in this pa-
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The channel estimation MSEs obtained from simulation and the
ideal MSE (the minimum MSE in the absence of frequency offset) ½ The CRB for pilot-data multiplexed scheme is calculated as CRB =
are shown in Fig.2. The 3 dB SNR advantage of the two-symbol- 1/Tr[ ÃÖ ½ ÚÖ ÃÖ ½ ÚÖ ] where the covariance matrices of channel
à Ã
based channel estimation is simply due to the use of twice the total and data are embedded in ÃÖ , the covariance matrix of the observation
vector Ö . Due to space limitation, it is omitted.
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The frequency offset estimation results for pilot-data multi- the estimation in addition to pilots but this approach is not considered in
plexed schemes are presented in Figs. 3 and 4, respectively, for this paper.
−3 −3
10 10
MSE (Q=1) MSE (Q=1) MSE (Q=1) MSE (Q=1)
CRB (Q=1) CRB (Q=1) CRB (Q=1) CRB (Q=1)
MSE (Q=2) MSE (Q=2) −3
MSE (Q=2) −3 MSE (Q=2)
CRB (Q=2) 10 CRB (Q=2) 10 CRB (Q=2)
CRB (Q=2)
Nr = 1 N =2
Nr = 1 Nr = 2 r
−4 −4
10 10
MSE & CRB
MSE & CRB
MSE & CRB
MSE & CRB −4 −4
−5 −5 10 10
10 10
0 5 10 15 20 0 5 10 15 20
−6 −6 SNR (dB) SNR (dB)
10 10
0 5 10 15 20 0 5 10 15 20
SNR (dB) SNR (dB)
Fig. 3. Frequency offset estimation performance for the (conventional)
pilot-data multiplexed scheme
Fig. 1. Frequency offset estimation performance for the pilot-only scheme
MSE (Q=1) MSE (Q=1) MSE (Q=1) MSE (Q=1)
ideal MSE (Q=1) ideal MSE (Q=1) MSE (Q=2) MSE (Q=2)
MSE (Q=2) MSE (Q=2) MSE (Q=1, mod) MSE (Q=1, mod)
−2 −2 CRB (Q=1, mod) CRB (Q=1, mod)
10 ideal MSE (Q=2) 10 ideal MSE (Q=2)
MSE (Q=2, mod) MSE (Q=2, mod)
N =1 Nr = 2 −3 CRB (Q=2, mod) −3 CRB (Q=2, mod)
r 10 10
Nr = 1 Nr = 2
MSE & CRB
MSE & CRB
MSE
MSE
−3 −3 −4 −4
10 10 10 10
−5 −5
10 10
−4 −4
10 10
0 5 10 15 20 0 5 10 15 20
SNR (dB) SNR (dB)
0 5 10 15 20 0 5 10 15 20
SNR (dB) SNR (dB)
Fig. 4. Frequency offset estimation performance for the modified pilot-
data multiplexed scheme (MSE performances of the conventional pilot-data
Fig. 2. Channel estimation performance for the pilot-only scheme multiplexed scheme are included as references.)
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ideal MSE (Q=2) ideal MSE (Q=2)
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−2
10
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r N =2
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MSE
MSE
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[12] H. Minn and N. Al-Dhahir, “Optimal Training Signals for MIMO −3
10
−3
10
OFDM Channel Estimation,” accepted in IEEE Globecom 2004.
[13] Q.T.Zhang and D.P.Liu, ”A Simple Capacity Formula for Correlated
Diversity Raician Fading Channels,” IEEE Commun. Let., Nov. 2002,
pp.481-483.
[14] H. Minn and S. Xing, “Optimal Periodic Training Signal for Fre-
−4 −4
quency Offset Estimation in Frequency Selective Fading Channels”, 10 10
IEEE ICC 2004 pp. 488-492.
0 5 10 15 20 0 5 10 15 20
[15] Y. Zhao and S-G. Haggman, “Intercarrier Interference Self- SNR (dB) SNR (dB)
Cancellation Scheme for OFDM Mobile Communication SYstems,”
IEEE Trans. Commun., July 2001, pp. 1185-1191.
Fig. 5. Channel estimation performance for the pilot-data multiplexed
schemes