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					2784                                                                 IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, VOL. 5, NO. 10, OCTOBER 2006




  Enhanced Carrier Frequency Offset Estimation for
      OFDM using Channel Side Information
                       Defeng (David) Huang, Member, IEEE, and Khaled B. Letaief, Fellow, IEEE



   Abstract— Carrier frequency offset (CFO) in OFDM systems,                     by the oscillator discrepancy between the transmitter and the
which induces the loss of orthogonality among OFDM sub-                          receiver and/or the Doppler phenomena due to the movement
carriers, can result in significant performance degradation. As a                 of the mobile terminals, can destroy the orthogonality among
result, it needs to be estimated and compensated for. In this paper,
we present a general CFO estimator based on the maximum                          OFDM sub-carriers and induce ICI (intercarrier interference).
likelihood (ML) estimation criterion, with which CFO can be                      This results in significant performance degradation and as a
obtained using training OFDM symbols, pilot tones, null sub-                     result, it is very important that the CFO should be estimated
carriers, or a combination of them. Using the proposed CFO                       and compensated for. A significant amount of works [1]–[8]
estimator, the performance of CFO estimation can be significantly                 have been devoted to the CFO estimation issue. In [1]–[3],
improved by taking advantage of the channel side information.
In particular, using the channel statistics information, such                    CFO estimators were developed using a training sequence with
performance improvement can be achieved for low SNR values                       two or multiple identical components. In [5], null sub-carriers
and all SNR values over Rayleigh fading channels and Ricean                      in OFDM symbols were employed for CFO estimation, and
fading channels, respectively. When the complete channel impulse                 a good way to allocate the null sub-carriers was proposed in
response (CIR) information is available, simulation results will                 [6]. In [7], [8], the cyclic property of OFDM signals was used
show that the performance improvement can be more than 6dB.
To further demonstrate the capability of the proposed CFO                        for CFO estimation.
estimator, we will consider an OFDM system using the signal                         All of the above works assumed that the channel side
structure of the IEEE WLAN standard 802.11a. Compared with                       information1 is unavailable to the CFO estimator. However, it
previous work using null sub-carriers alone, we will show that                   is known that the availability of the channel statistics informa-
by taking advantage of the pilot tones, null sub-carriers, and
                                                                                 tion is beneficial to many channel estimation and space-time
channel statistics, the performance of CFO estimation can be
improved by about 2dB.                                                           coding schemes (See [9]–[11] and references therein). As a
                                                                                 result, we can expect that the channel statistics information
  Index Terms— OFDM, carrier frequency offset, IEEE 802.11a,
null sub-carrier.
                                                                                 can also be useful for CFO estimation in OFDM. On the
                                                                                 other hand, the channel impulse information (CIR) can be
                                                                                 available to CFO estimation. As pointed out in [12], channel
                          I. I NTRODUCTION                                       estimation and synchronization can be achieved in an iterative
                                                                                 way. In particular, we can expect that the performance of
O     FDM (Orthogonal Frequency Division Multiplexing) is
      an enabling technology for future broadband wireless
communications due to its high spectral efficiency and ca-
                                                                                 CFO estimation can be improved using the CIR information
                                                                                 estimated in previous iterations.
pability in combating multi-path propagations. Many broad-                          For flat fading channels, some schemes have been proposed
band wireless communication standards and proposals such as                      for CFO estimation with the aid of channel statistics [13]–[15].
802.11a, DVB-T (Terrestrial Digital Video Broadcasting), and                     However, only a few works employed channel side informa-
802.15.3a (a proposal that uses the Ultrawideband Communi-                       tion for CFO estimation over frequency selective channels.
cations Spectrum), have adopted OFDM as the key technology.                      In [16], the second order channel statistics were assumed to
  To achieve good performance in OFDM systems, the or-                           be known and the marginal likelihood function of the CFO
thogonality among OFDM sub-carriers must be maintained                           was used for CFO estimation. But, as pointed out in [17], the
[1]. However, carrier frequency offset (CFO), which is induced                   performance of the scheme proposed in [16] is poor due to
                                                                                 the bias in the estimation. The use of a training sequence to
   Manuscript received July 26, 2004; revised February 23, 2006; accepted
May 6, 2006. The editor coordinating the review of this paper and approving it   jointly estimate the CIR and the CFO based on the maximum
for publication is H. Li. This work was supported in part by the Hong Kong       likelihood (ML) estimation criterion has also been proposed
Telecom Institute of Information Technology. This paper was presented in         in [17]. In this paper, we will demonstrate, however, that this
part at the 2005 Asia-Pacific Conference on Communications, Perth, Western
Australia, October 3-5, 2005.                                                    can be only achieved under the assumption that the number of
   D. Huang was with the Center for Wireless Information Technology,             distinct paths in the channel is known. The mismatch between
Electrical and Electronic Engineering Department, The Hong Kong University       the presumed and the actual number of distinct paths in the
of Science and Technology, Clear Water Bay, Kowloon, Hong Kong. He is
now with the School of Electrical, Electronic and Computer Engineering,          channel can significantly impact system performance.
The University of Western Australia, Crawley, WA 6009, Australia (e-mail:           By approximating the received signal as a Gaussian random
huangdf@ee.uwa.edu.au).                                                          variable, we propose in this paper a general CFO estimator
   K. B. Letaief is with the Center for Wireless Information Technology,
Electronic and Computer Engineering Department, The Hong Kong University
of Science and Technology, Clear Water Bay, Kowloon, Hong Kong (e-mail:             1 Throughout this paper, the channel side information includes two specific
eekhaled@ee.ust.hk).                                                             cases: the channel statistics and the complete CIR (channel impulse response)
   Digital Object Identifier 10.1109/TWC.2006.04507.                              information.
                                                             1536-1276/06$20.00 c 2006 IEEE
HUANG and LETAIEF: ENHANCED CARRIER FREQUENCY OFFSET ESTIMATION FOR OFDM USING CHANNEL SIDE INFORMATION                                   2785



                   D                      Add      s(n)              it will be demonstrated that the complexity of the global
      Source             IDFT            Guard
                                        Interval
                                                                     search can be significantly reduced by using FFT (Fast
                                                                     Fourier Transform) to simultaneously calculate the measures
                                                          ~     f1   for all attempted CFO values in the search space. Therefore,
                                                                     complexity is not a critical issue for the proposed scheme
                                                                     especially considering the dramatic development of the VLSI
                        Remove      x                                technology.
                         Guard             DFT                Sink
                        Interval
                                                                        This paper is organized as follows. In Section II, the
                                                                     system model is described, along with the optimal ML CFO
               ~   f2                                                estimation using the Gaussian approximation. The extension
                                                                     of this CFO estimator to other scenarios is presented in Section
Fig. 1.   Block diagram of the OFDM system.                          III. Finally, simulation results and concluding remarks are
                                                                     given in Sections IV and V, respectively.

based upon the ML criterion, with which the CFO can be                    II. S YSTEM M ODEL AND ML CFO E STIMATION
estimated using training OFDM symbols, pilot tones, and/or             We consider an OFDM system with N sub-carriers as
null sub-carriers. Using the proposed CFO estimator, the             shown in Fig. 1. The transmitted signal is given by
performance of CFO estimation can be significantly improved
                                                                                     N −1
by taking advantage of the channel side information.                           1
   When the training OFDM symbol is available, simulation              s(n) = √             dk ej2πnk/N , n = −Ng , · · · , N − 1         (1)
                                                                                N     k=0
results will show that the performance of CFO estimation
using the proposed scheme can be much better than that               where dk is the data symbol at the kth sub-carrier, and Ng is
proposed in [17] owing to the exploitation of the channel            the length of the guard interval, which is assumed to be longer
side information. For Rayleigh fading channels, simulation           than that of the CIR.
results will show that the performance of CFO estimation               At the receiver, we assume that time synchronization is
can be improved significantly especially at low SNR values            perfectly achieved. After sampling and guard interval removal,
by taking advantage of the second order channel statistics.          the received signal is given by
We note here that the low SNR values are especially of                                         N −1
                                                                                 1
practical interest when MC-CDMA [18] is used. When low                   x(n) = √ ej2πnφ              H(k)dk ej2πnk/N + zn ,
order modulation, low coding rate, or high performance codes                     N              k=0
such as LDPC codes and turbo codes [12] are used, the                                                        n = 0, · · · , N − 1         (2)
SNR values of practical interest are also relatively low. For
Ricean fading channels, we will show that the performance            where φ is the CFO normalized by the sampling interval, H(k)
of CFO estimation can be improved for all SNR values with            is the channel frequency response at the kth sub-carrier, and
the aid of the second order channel statistics. For a channel        zn is the additive white Gaussian noise with zero mean and
with log-normal distribution, simulation results will show that      variance σ 2 . We note here that the CFO can be induced by
the performance of CFO estimation can also be improved by            the oscillators discrepancy between the transmitter and the
using the second order channel statistics. Finally, when the         receiver (i.e., f1 and f2 in Fig. 1 are not exactly the same). It
complete CIR information is available, further performance           can also be induced by the Doppler shift due to the movement
improvement can be achieved.                                         of the mobile terminals.
   Null sub-carriers and pilot tones in OFDM systems were               We assume that there are L distinct paths in the CIR. h(l)
originally employed to mitigate the adjacent channel inter-          is used to denote the CIR at the lth path, and its delay is
ference and achieve channel estimation, respectively [5]. By         nl samples. The relationship between the channel frequency
using null sub-carriers and pilot tones for CFO estimation,          response and the CIR is then as follows:
transmission efficiency can be improved because no extra                                                                         T
                                                                                 H = H(0), H(1), · · · , H(N − 1)
training OFDM symbols are required. In this paper, we will
show that null sub-carriers and pilot tones can also be used                       = FN ×L h                                              (3)
for CFO estimation due to the flexibility of the proposed CFO         where [.]T in the superscript denotes transpose,
estimator. Specifically, we take the signal structure of the IEEE     h = [h(0), h(1), · · · , h(L − 1)]T , and FN ×L is an N × L
802.11a as an example. We then demonstrate that by using             matrix with [FN ×L ]n,l = √1 e−j2πnnl /N .
pilot tones, null sub-carriers, and the second order channel                                       N
                                                                        For convenience, we rewrite (2) into a vector form as
statistics, the performance of CFO estimation can be improved
                                                                     follows:
by about 2dB compared with the case where only null sub-
                                                                                                                                T
carriers are used.                                                                x = X(0), X(1), · · · , X(N − 1)
   In the proposed scheme, a global search is needed to                             = P(φ)WDH + z                                         (4)
estimate the CFO. As a result, the complexity of our scheme
                                                                                                                                 1
                                                                                                                                √ ej2πnk/N ,
is higher than the one proposed in [16]. However, the per-           where W is the IFFT matrix with W               n,k
                                                                                                                            =    N
formance of our proposed method is much better especially
when a large CFO estimation range is required. Furthermore,                             z = [z0 , z1 , · · · , zN −1 ]T ,
2786                                                                  IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, VOL. 5, NO. 10, OCTOBER 2006



             P(φ) = diag 1, ej2πφ , · · · , ej2π(N −1)φ ,                         Using (11) to find φ in general induces great complexity due
                                                                                  to the requirement of a global search. To reduce the search
                    D = diag d0 , d1 , · · · , dN −1 ,                            complexity, (11) can be written into the following form:3
and diag(.)is a diagonal matrix with the elements in the main                                                             N −1
diagonal given by (.).                                                                         S(φ) = −ρ(0) + 2Re                  ρ(m)e−j2πmφ            (12)
  By substituting (3) into (4), we have                                                                                   m=0

                     x = P(φ)WDFN ×L h + z.                                (5)    where
                                                                                                N −1
   As pointed out in [19], in a frequency selective fading                         ρ(m) =              A   k−m,k
                                                                                                                   x(k)x∗ (k − m) − b∗ (m)x(m), (13)
channel, the delay axis is typically divided into bins whose                                    k=m
size is comparable to the inverse of the signal bandwidth. For                             ∗
                                                                                  and (.) in the superscript denotes the conjugate of (.). We
relatively narrowband signals, the number of scatters that fall
                                                                                  then define the following variables:
in a bin is large. Therefore, we can assume that the entries in
h are with a multivariate complex Gaussian distribution.2 As                                                  ρ(m), 0 ≤ m ≤ N − 1
                                                                                                ρ (m) =                                                   (14)
a result, given P(φ) and D, x is a complex Gaussian random                                                    0,    N ≤ m ≤ JN − 1
vector, and its average is given by                                               where J is a parameter that characterizes the precision of the
                     E(x) = P(φ)WDFN ×L μh                                 (6)    global search. The outputs of the FFT of ρ (m) are then put
                                                                                  into (12) for the search of φ with a precision of 1/JN . Since
where E(.) is the expectation of (.) and μh is the expectation                    there are a lot of zeros at the input of the FFT, the complexity
of h. After some manipulations, the covariance matrix of x                        can be significantly reduced by using the pruning technique
can be shown to be given by                                                       [20].
                                                            H
               Cx = E        x − E(x) x − E(x)
                                                                                           III. CFO E STIMATION IN OTHER S CENARIOS
                    = P(φ)A P(φ)H                                          (7)      In the previous section, given the training OFDM symbol
where (.)  H
               in the superscript denotes the conjugate transpose                 and the second-order channel statistics at the receiver, we
of (.),                                                                           obtained a CFO estimator with φ obtained by minimizing (11).
                                                                                  In this section, by simply presenting A and b in (11) into a
A = WDFN ×L E((h−μh )(h−μh )H )FH ×L DH WH +σ 2 I,
                                N                                                 proper form, the CFO estimator can be found in many other
                                                                                  scenarios. As a result, our proposed CFO estimator is quite
and I denotes the identity matrix. From (7), we have
                                                                                  general and can be considered as a generalization of various
           −1
          Cx = P(φ)(A )−1 P(φ)H = P(φ)AP(φ)H                               (8)    schemes that have already been proposed in the literature.

where A = (A )−1 and (.)−1 denotes the inverse of (.).
                                                                                  A. CFO estimation using null sub-carriers
  Given φ and D, the likelihood function of x is then given
by                                                                                   To improve the transmission efficiency of an OFDM system,
                                                                                  blind methods or methods using the inherent structure of
                        1                               H    −1
p(x; φ, D) =                     exp − x−E(x)               Cx x−E(x)             OFDM signals can be employed for CFO estimation. As
                 π N det(Cx )                                                     mentioned in the introduction, null sub-carriers can be used
                                                         (9)
                                                                                  for CFO estimation using the sub-space based method [5]. The
where det(.) denotes the determinant of (.). Note that
                                                                                  CFO estimation scheme proposed in [2], [3], where the CFO
det(Cx ) = det(A ) and is independent of φ.
                                                                                  is estimated using an OFDM symbol with several identical
  Based upon the ML estimation criterion, φ is found by max-
                                                                                  components, can also be regarded as a CFO estimation scheme
imizing (9), which is equivalent to minimizing the following
                                                                                  using null sub-carriers with specific null sub-carrier allocations
measure:
                           H                                                      [6]. In [4], it was shown that the sub-space based CFO
                              −1
               x − E(x) Cx x − E(x) .                   (10)                      estimation is equivalent to the ML CFO estimation.
  By substituting (6) and (8) into (10), the normalized CFO                          Assume that the number of null sub-carriers used in an
can be obtained as                                                                OFDM system is M . The set that contains all the null sub-
                                                                                  carrier indices is denoted by a1 , a2 , · · · , aM . Using the null
                            ˆ min
                            φ = φ Λ (x; φ)                                        subcarriers and based on the ML criterion, it can be shown
                                                                                  that the CFO estimation can be achieved by minimizing (11)
where                                                                             with A and b given by
  Λ (x; φ) = xH P(φ)AP(φ)H x − 2Re bH P(φ)H x , (11)                                                               A = VVH                                (15)
                                                                                                                                                 1
                                                                                                                                                √ ej2πnai /N ,
Re(.) denotes the real part of (.), and                                           where V is an N × M matrix with V                   n,i
                                                                                                                                            =    N
                                            T                                     and
   b = b(0), b(1), · · · , b(N − 1)             = AH WDFN ×L μh .                                       b=0                                               (16)
   2 When the signal bandwidth is very large, this assumption is in general not   where 0 is the all-zero vector.
accurate. For example, for ultrawideband communications, the log-normal or
the Nakagami distribution is more appropriate.                                      3A   similar approach has been used in [17].
HUANG and LETAIEF: ENHANCED CARRIER FREQUENCY OFFSET ESTIMATION FOR OFDM USING CHANNEL SIDE INFORMATION                                     2787



B. CFO estimation using training OFDM symbols                        and
   In a frequency selective channel, the CFO estimation can                               b = AH WD1 FN ×L μh .                            (23)
also be achieved using a known training sequence with cyclic           In an 802.11a system, there are both null sub-carriers and
property [17]. Using such a sequence, the CFO and the CIR           pilot tones. By taking null sub-carriers as special pilot tones
can be jointly estimated. By comparing the sequence used in         with zeros transmitted, we can then define D1 accordingly,
[17] with an OFDM symbol, it can be seen that an OFDM               and the CFO estimation can also be achieved by minimizing
symbol has the same structure as the sequence used in [17]. In      (11) with A and b defined by (21)-(23).
particular, the guard interval in an OFDM symbol can function
as the precursors of the sequence used in [17]. As a result, we     D. CFO estimation using training OFDM symbol and com-
can use the scheme proposed in [17] for CFO estimation in           plete CIR information
OFDM with the aid of a training OFDM symbol. Comparing
the results in [17] with (11) and after some manipulations,           When the training OFDM symbol and the CIR are both
it can be seen that the CFO estimation can be achieved by           perfectly available at the receiver, the CFO can be obtained
minimizing (11) with A and b given by                               by minimizing (11) with A and b given by (See Appendix II)
                                           −1                                                         A=0                                  (24)
  A = WDFN ×L FH ×L DH DFN ×L
               N                                FH ×L DH WH
                                                 N
                                                          (17)      and
and                                                                                           b = WDFN ×L h.                               (25)
                            b = 0.                          (18)    When the CIR is obtained with an estimation error,4 we can
                                                                    use the following to represent the estimated CIR
  Note that for this CFO estimator, FN ×L is required to be
known, which implies that the number of distinct paths in                                          ˆ
                                                                                                   h= h+e                                  (26)
the channel should be available. As will be shown by the
simulation results in Section IV, the mismatch between the          where e is a vector used to denote the CIR estimation error.
presumed number and actual number of distinct paths in the          We assume that the mean of e is zero and its covariance matrix
channel can significantly impact system performance.                 is Λ. By substituting (26) into (5), we have
                                                                                          ˆ
                                                                          x = P(φ)WDFN ×L h − P(φ)WDFN ×L e + z.                           (27)
C. CFO estimation using pilot tones and channel statistics          Using (27), we can then get the likelihood function of φ as
   Pilot tones are often used in OFDM systems for channel           shown in Appendix II. Through maximizing the likelihood
estimation. In this subsection, we will show that pilot tones       function, the CFO can then be obtained by minimizing (11)
can also be used for CFO estimation. Assume that there              with A and b given by
are K pilot tones in an OFDM system, which are denoted                                                          −1
                                                                                                 A= A                ,                     (28)
by pk , k = 0, 1, · · · , K − 1. Other sub-carriers are data sub-
carriers with independent zero mean Gaussian distribution, and                  A = WDFN ×L ΛFH ×L DH WH + σ 2 I,
                                                                                              N                                            (29)
the transmitted signal power of each data sub-carrier is Es .       and
For convenience, we use an N × N diagonal matrix D1 to                                                     ˆ
                                                                                            b = AH WDFN ×L h.                              (30)
represent the pilot tones as follows:
                pk , if the nth sub-carrier is the kth pilot tone                   IV. S IMULATION R ESULTS
 D1         =
      n,n       0, otherwise                                          In this section, extensive simulations are conducted to
                                                             (19)   demonstrate the performance of CFO estimation with the aid
and an N × N diagonal matrix I2 to represent the data sub-          of channel side information. In the simulations, we use the
carriers allocation as follows:                                     normalized mean square error (NMSE) as the performance
              1, if the nth sub-carrier is a data sub-carrier       measure, which is defined by
 I2         =
      n,n     0, otherwise.                                                                                Nt
                                                                                                                            2
                                                                                                      N          ˆ
                                                          (20)                         N M SE =                  φt − φ                    (31)
By approximating the received signal x as a Gaussian random                                           Nt   t=1
vector, we can obtain the likelihood function. Through max-         where Nt is the number of Monte Carlo trials, φ is the actual
imizing the likelihood function and as shown in Appendix I,                               ˆ
                                                                    normalized CFO, and φt is the estimated normalized CFO at
we can then obtain the CFO by minimizing (11) with A and            the tth trial.
b given by                                                            When the CIR is perfectly available and as shown in
                                  −1
                        A= A                              (21)      Appendix III, the Cramer Rao bound (CRB) is given by
where                                                                                              1
                                                                        CRB = 2 H H                                          (32)
                                           H
                                                                                   8π h FN ×L DH WH M2 WDFN ×L h
 A =WD1 FN ×L E         h − μh h − μh           FH ×L DH WH
                                                 N     1
                                                                       4 When an iterative algorithm is used for both CFO estimation and channel

        + Es WI2 diag FN ×L E hhH FH ×L WH + σ 2 I
                                   N
                                                                    estimation, the channel estimation in the first several iterations should bear
                                                                    the impact of the residual CFO. This is modeled as the channel estimation
                                                            (22)    error as shown in (26).
2788                                                                IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, VOL. 5, NO. 10, OCTOBER 2006



where M = diag(0, 1, · · · , N − 1). Since we are interested in
                                                                                                1
                                                                                       10
                                                                                                                                                                                         J = 64
the average performance of the CFO estimation for all channel                                                                                                                            J=4
                                                                                                0
realizations, in the following, we average (32) over all channel                       10                                                         HTE

realizations and the result is taken as the baseline.
                                                                                                −1
   When null sub-carriers are used for CFO estimation, some                            10
                                                                                                                                     With Channel Statistics
sub-channels may not be excited by the transmitted signal.
Therefore, if we fix the transmitted signal power, a low                                10
                                                                                                −2




                                                                                NMSE
                                                                                                                                                     Without Channel Statistics
instantaneous received signal power may not mean a poor in-                                          Channel Known

stantaneous channel realization. To make the SNR independent                           10
                                                                                                −3



of the null sub-carrier allocations, we fix the transmitted signal
power as                                                                               10
                                                                                                −4


                             N −1
                       N=           E |dk |2 .                        (33)             10
                                                                                                −5


                             k=0
                                                                                                                             Cramer Rao Bound
The SNR is then defined by                                                              10
                                                                                                −6

                                                                                         −10             −8      −6     −4         −2         0        2           4          6      8            10
                                                 2                                                                                 Instantaneous SNR (dB)
                                 N −1
                                 k=0    H(k)
                    SN R =                           .                (34)    Fig. 2. NMSE performance of the CFO estimation over Rayleigh fading
                                     N σ2                                     channels when the actual normalized CFO is uniformly distributed between
                                                                              −0.25 and 0.25.
A. CFO estimation using training OFDM symbols
                                                                                            1
                                                                                       10
  We first present the CFO estimator proposed in [16] for                                                                                                                                 J = 64
                                                                                                                                                                                         J=4
comparison. This estimator is called the HTE estimator in [17].                             0
                                                                                       10
For convenience, we rewrite the CIR into the following form
                                                         T                                                                           With Channel Statistics
          h = h (0), h (1), · · · , h (N − 1)                = Λh     (35)             10
                                                                                            −1




where Λ is an N × L matrix with ’1’ in its                                                  −2                                                  Without Channel Statistics
(nl , l)th (l = 0, 1, · · · , L − 1) entries and ’0’ in other                          10
                                                                               NMSE




entries. In the HTE estimator, the CFO is obtained as
                                                                                       10
                                                                                            −3          Channel Known
                                         η
                ˆ      1
                φ=          arg               ϕ(m)                    (36)
                   (η + 1)π             m=1                                            10
                                                                                            −4


                                                                                                                                                                             HTE

where η is a design parameter and ϕ(m) is given by (37). In                                 −5
                       ∗                                                               10
(37), μ(l1 , l2 ) = E h (l1 )h (l2 ) and ak is the mod(k,N )th
element of √1 WD1, where 1 is the N × 1 all-one vector,
                 N                                                                     10
                                                                                            −6
                                                                                                                         Cramer Rao Bound

                                                                                         −10            −8       −6     −4         −2         0        2           4          6      8            10
and mod(k,N ) is the remainder after k is divided by N . As                                                                        Instantaneous SNR (dB)

shown in [16], [17], along with the increase of η, the estima-
tion accuracy is improved. At the same time, the estimation                   Fig. 3. NMSE performance of the CFO estimation over Rayleigh fading
                                                                              channels when the actual normalized CFO is uniformly distributed between
range is decreased, which is given by |φ| ≤ 1/(η + 1). From                   −0.0025 and 0.0025.
(36), it can be seen that the HTE estimator is simple because
                                                                                         1
                                                                                       10
no global search is required.                                                                                                                    J = 64
   In the following, we consider an OFDM system with 64                                                                                          J=4
                                                                                                                                                 Using complete covariance matrix
                                                                                         0
sub-carriers. The length of the guard interval is 12 samples. In                       10                                                        Using diagonal elements of covariance matrix

the simulations, one training OFDM symbol is used for CFO
estimation. The sub-carriers in the training OFDM symbol are                           10
                                                                                         −1




BPSK modulated, and their values are arranged based upon
an extended m-sequence as proposed in [6] with length 64 as                            10
                                                                                         −2
                                                                               NMSE




follows (in hexadecimal):5
                                                                                         −3
                                                                                       10
                     A4E2F28C20FD59BA.                                (38)
                                                                                         −4
                                                                                       10

  Each bit in the extended m-sequence is used to denote the
value of the corresponding sub-carrier in the training OFDM                            10
                                                                                         −5


symbol. Specifically, ’1’ is used to denote a sub-carrier with
value 1, and ’0’ is used to denote a sub-carrier with value −1.                        10
                                                                                         −6

                                                                                         −10            −8       −6     −4         −2         0        2          4           6      8            10
  In Figs. 2 and 3, we present the simulation results of the                                                                       Instantaneous SNR (dB)

CFO estimation using the GSM channel model. This model
                                                                              Fig. 4. NMSE performance of the CFO estimation using channel statistics
  5 The  good performance of using a white noise like sequence for CFO        over Rayleigh fading channels when the actual normalized CFO is uniformly
estimation is also justified by [21] using an asymptotic analysis.             distributed between −0.25 and 0.25.
HUANG and LETAIEF: ENHANCED CARRIER FREQUENCY OFFSET ESTIMATION FOR OFDM USING CHANNEL SIDE INFORMATION                                                                    2789


                                                                        N −1                           N −1 N −1
                                                            1
                                      ϕ(m) =                                       x(k)x∗ (k − m)                     μ(l1 , l2 )a∗ 1 ak−m−l2
                                                                                                                                  k−l                                      (37)
                                                          N −m
                                                                        k=m                             l1 =0 l2 =0




           1
         10
                                                                                    ξ2 = −40dB
                                                                                                      set the non-diagonal elements to be zero. Using the same
                                                                                    ξ2 = −30dB        channel parameters as those in Figs. 2 and 3, we show in
           0                                                                         2
         10                                    J=64                                 ξ = −20dB
                                                                                     2
                                                                                    ξ = −10dB
                                                                                                      Fig. 4 the performance of the CFO estimator with the diagonal
                                With Channel Statistics
                                                                                     2
                                                                                    ξ = 0dB           elements of the covariance matrix set to zero. It can be seen
           −1
         10
                                                                                                      that its performance is basically the same as that using perfect
                                                                                                      covariance matrix information.
           −2
         10
                                                                                                         In Fig. 5, we demonstrate the NMSE performance of the
  NMSE




                                                      Without Channel Statistics
                                                                                                      CFO estimation with imperfect channel estimation. The chan-
           −3
         10                                                                                           nel model and the distribution of the actual normalized CFO
                                                                                                      values are the same as those used in Fig. 2. In the simulations,
         10
           −4
                                                                                                      we assume that the estimation of the ith path of the CIR is as
                                                                                                      follows:
           −5
         10
                                                                                                                 ˆ
                                                                                                                 h(i) = h(i) 1 + f (i)       i = 0, 1, · · · , L − 1       (39)
                            Cramer Rao Bound
           −6

                                                                                                      where f (i) is a zero mean Gaussian random variable with
         10
           −10   −8   −6   −4     −2         0        2             4         6          8       10
                                  Instantaneous SNR (dB)
                                                                                                      variance σ 2 . We further assume that f (i) is independent for
Fig. 5. NMSE performance of the CFO estimation with imperfect channel                                 different values of i. As a result, the covariance matrix of the
estimation.                                                                                           estimation error e is given by

                                                                                                                                Λ = ξ 2 diag hhH .                         (40)
is a Rayleigh fading channel model, which is also used in
[6], [17]. In Fig. 2, the actual normalized CFO is uniformly                                             From Fig. 5, it can be seen that the performance of the
distributed between −0.25 and 0.25. In this case, η is set                                            CFO estimation deteriorates along with the increase of ξ 2 .
to 3 for the HTE scheme. In Fig. 3, the actual normalized                                             However, even when ξ 2 is as large as 0dB, the performance
CFO is uniformly distributed between −0.0025 and 0.0025.                                              of the CFO estimation is still as good as that of the CFO
In this case, η is set to 63 for the HTE scheme. By comparing                                         estimation scheme with the aid of channel statistics. When
Fig. 2 with Fig. 3, it can be seen that the performance of                                            the channel estimation is very good (e.g., ξ 2 is -40dB), it can
the HTE estimator is much poorer when the actual CFO                                                  be seen from Fig. 5 that the performance of CFO estimation
variation range is large. This is because there is a bias for                                         can be improved significantly compared with the case using
the HTE estimator and the bias is proportional to the actual                                          channel statistics.
normalized CFO value as can be seen from the simulation                                                  We show in Fig. 6 the impact of the presumed number
results in [17]. For other schemes, the CFO variation range                                           of distinct paths in the channel on the performance of the
basically does not impact system performance. Compared with                                           CFO estimation scheme proposed in [17]. For convenience,
the conventional CFO estimation scheme that does not use                                              we use L to denote the presumed number of distinct paths
the channel statistics (i.e., the scheme proposed in [17]), a                                         in the channel. In this case, the scheme in [17] is equivalent
close observation of Figs. 2 and 3 shows that the performance                                         to minimizing (11) with A and b given by (17) and (18)
of CFO estimation can be significantly improved using the                                              with the matrix FN ×L in (17) replaced by FN ×L . In the
channel side information. For example, when perfect CIR                                               simulations, the channel used is an exponentially decaying
information is available and the search precision is in a high                                        Rayleigh fading channel model with the root mean square
level (J=64), the performance can be improved by more                                                 (rms) delay spread set to 0.5.6 The actual number of distinct
than 6 dB for large SNR values. By using the second order                                             paths in the channel is L = 12 and the actual normalized
channel statistics, it can be seen from Figs. 2 and 3 that the                                        CFO is set to be uniformly distributed between −0.25 and
performance can be improved for low SNR values. When                                                  0.25. From Fig. 6, it can be seen that for high SNR values
the search precision is at a low level (J=4), an error floor                                           (SNR=6dB, 10dB), as long as the presumed number of distinct
appears for the proposed scheme. However, when the actual                                             paths is more than 4, a good performance can be achieved.
CFO variation range and the instantaneous SNR values are                                              However, when SNR=−2dB, the best performance is achieved
both relatively large, it can still be seen from Fig. 2 that the                                      only when L = 2 or L = 6. When SNR=−6dB, the best
performance of the proposed scheme is much better than that                                           performance is achieved only when L = 2. Therefore, to use
of the HTE estimator.                                                                                 the CFO estimation scheme proposed in [17], we should select
   In general, the covariance matrix of the CIR is non-diagonal                                       a proper L to achieve a good performance. As a result, it is
(e.g., for the GSM channel model used for Figs. 2 and 3).
                                                                                                         6 Here we assume that different paths in the CIR are uncorrelated. When
As a result, a large number of parameters are needed to be
                                                                                                      they are correlated, the performance of the channel estimation can be
estimated. To reduce the complexity induced by this, we only                                          improved by using the singular value decomposition method [11]. Similarly,
estimate the diagonal elements of the covariance matrix and                                           the performance of the CFO estimation might be improved further.
2790                                                                                              IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, VOL. 5, NO. 10, OCTOBER 2006


          1                                                                                                           −3
        10                                                                                                          10
                                                                                                                                                                                               J=64
                                                                                                                                  Without Channel Statistics                                   J=4
          0
        10
                                                                                                                                           With Channel Statistics


          −1
        10
                                                                                                                      −4
                                                                                                                    10

          −2
        10
 NMSE




                                                                                                             NMSE
                                                                                   SNR= −6dB

        10
          −3
                                        L=12                                       SNR=−2dB
                                                                                   SNR=6dB
                                             5
                                        rms=0.                                                                        −5
                                                                                   SNR=10dB                         10
          −4
        10                              J=64



          −5
        10



          −6                                                                                                          −6
        10                                                                                                          10
               2   4    6     8        10        12        14        16       18     20        22     24              −10    −8       −6        −4        −2         0        2    4   6   8          10
                                                      L’                                                                                                  Instantaneous SNR (dB)


Fig. 6. NMSE performance of the CFO estimation versus the presumed                                          Fig. 8. NMSE performance of the CFO estimation over log-normal fading
number of distinct paths in the channel.                                                                    channels.

          1
        10
                                                                                             K=0dB
                                                                                             K=20dB         by (32) over the Ricean fading channels is basically the same
          0                                                                                  K=40dB
        10                                                                                                  for different values of K.
                                                                                                               In the following, we use the UWB channel model (the
          −1
        10
                                                                                                            CM1 model in [22]) to show the performance of the CFO
          −2
                                                                                                            estimation when the CIRs are non-Gaussian distributed. In
        10                                                      J=64
                                                                                                            the UWB channel model, each distinct path of the CIR is
                                                                                                            log-normal distributed. We consider 128 sub-carriers in one
 NMSE




          −3
        10
                                                                                                            OFDM symbol and the length of the guard interval is 32
        10
          −4                                                                                                samples, which are the same as those in the multi-band OFDM
                                                                                                            proposal for 802.15.3a [23]. In the simulations, the actual CFO
        10
          −5
                                                                                                            value is set to be uniformly distributed between −1/8 and 1/8
                                   Cramer Rao Bound
                                                                                                            of the sub-carrier spacing.7 Furthermore, we use one training
          −6
        10                                                                                                  OFDM symbol for the CFO estimation. In the training OFDM
          −7
                                                                                                            symbol, the values of the sub-carriers of the training OFDM
        10
          −10      −8   −6        −4        −2         0        2         4         6         8       10    symbol are set based on the extended m-sequence [6]. In this
                                            Instantaneous SNR (dB)
                                                                                                            case, similar to (38), we use an extended m-sequence with
Fig. 7.   NMSE performance of the CFO estimation over Ricean fading                                         length 128 to denote the training OFDM symbol, which is
channels. The solid lines denote the scheme in [17]. The dotted lines denote                                given by
the CFO estimation scheme with the aid of channel statistics.
                                                                                                                           CEA7D0E24DADEC697732AFE041851E44.                                      (42)

fair to say that the scheme proposed in [17] also partially takes                                           From Fig. 8, it can be seen that the performance of CFO
advantage of the channel side information.                                                                  estimation can still be improved by using the channel statistics
                                                                                                            over a log-normal fading channel especially for low SNR
   For Ricean fading channels, we define K as follows:
                                                                                                            values.
                                                                 α2
                             K(dB) = 10log10                                                        (41)    B. CFO estimation using null sub-carriers
                                                                 β2
                                                                                                               In this subsection, we use the inherent structure (i.e., null
 where α2 is the signal power of the specular component and                                                 sub-carriers and pilot tones) of OFDM signals to achieve the
β 2 is the total power of the non-line of sight components.                                                 CFO estimation. In the simulations, we use the same signal
For the non-line of sight components, we use a two-ray equal                                                structure as that in 802.11a [24], where there are 64 sub-
gain Rayleigh fading channel model. The actual normalized                                                   carriers in one OFDM symbol. Among the 64 sub-carriers,
CFO is assumed to be uniformly distributed between −0.25                                                    48 are data sub-carriers, 4 are pilot sub-carriers, and 12 are
and 0.25. The simulation results of the CFO estimation over                                                 null sub-carriers. In our simulations, the positions of the 12
Ricean fading channels are shown in Fig. 7. It can be seen                                                  null sub-carriers and the 4 pilot tones are also the same as
that by using the channel statistics, the performance of the                                                those in 802.11a. The channel used is an 8-ray exponentially
CFO estimation can be significantly improved along with the
                                                                                                               7 In the multi-band OFDM proposal [23], the sub-carrier spacing is about
increase of K. On the other hand, when the scheme in [17] is
                                                                                                            4 MHz. If we use an oscillator with a precision of 50 ppm and a center
employed, the value of K does not have much impact on the                                                   frequency of 10 GHz, the actual CFO is then at most about 500 kHz.
performance. We note here that the Cramer Rao bound given                                                   Therefore, it is between -1/8 and 1/8 of the sub-carrier spacing.
HUANG and LETAIEF: ENHANCED CARRIER FREQUENCY OFFSET ESTIMATION FOR OFDM USING CHANNEL SIDE INFORMATION                                                         2791

         1
        10
                                                      With channel statistics and pilot tones        The covariance matrix of x can then be shown as (44). Let us
         0
                                                      With channel statistics
                                                      Without channel statistics                     now separate D into the data part and the pilot tones part as
        10
                                                                                                     follows:
                                                                                                                           D = D1 + D2                       (45)
         −1
        10
                                                                                                     where D1 is used to denote the pilot tones as defined by (19)
         −2
        10
                                                                                                     and D2 is used to denote the data sub-carriers. We assume
                                                                                                     that E(D2 ) = 0, and that the data at different sub-carriers
 NMSE




         −3
        10
                                                                                                     are independent. By substituting (45) into (44), the covariance
                                                                                                     matrix of x can be shown as (46). Assume that x is a complex
                       J=64
         −4
                                                                                                     Gaussian random vector, then the likelihood function can
        10
                                                                                                     be easily obtained. It can then be seen that maximizing the
         −5
                                                                                                     likelihood function is equivalent to minimizing (11) with A
        10
                                                                                                     and b given by (21)-(23).
         −6
        10
              0   2    4      6     8       10       12        14        16        18           20
                                                                                                                             A PPENDIX II
                                  Instantaneous SNR (dB)
                                                                                                           CFO E STIMATION WHEN THE CIR IS AVAILABLE
Fig. 9. NMSE performance of the CFO estimation using the same signal                                    Given D and h, then from (5) the likelihood function is
structure as 802.11a.                                                                                given by (47). We can then obtain φ by maximizing the above
                                                                                                     likelihood function, which is equivalent to minimizing
decaying quasi-static Rayleigh fading channel with an rms                                                 Λ (x; φ) = −2Re hH FH ×L DH WH P(φ)H x .
                                                                                                                              N                                (48)
delay spread of 0.95. We use 10 OFDM symbols for the
CFO estimation and the actual normalized CFO is uniformly                                            The above metric is equivalent to (11) with A and b given
distributed between −0.25 and 0.25. Fig. 9 shows the CFO                                             by (24) and (25), respectively.
estimation performance of such an OFDM system. It can be                                                When there are channel estimation errors, the average of x
seen that by using null sub-carriers alone, the performance of                                       is given by (See (27))
the CFO estimation is exactly the same with or without the                                                            E(x) = P(φ)WDFN ×L h.    ˆ              (49)
use of the channel statistics. This is not surprising because
null sub-carriers do not excite the channel. On the other hand,                                      By assuming that the channel estimation error and the additive
by using pilot tones and null sub-carriers, it can be seen from                                      white Gaussian noise are independent, the covariance matrix
Fig. 9 that the performance of the CFO estimation can be                                             of x is then given by
improved by taking advantage of the channel statistics for                                            Cx = P(φ)WDFN ×L ΛFH ×L DH WH P(φ)H + σ 2 I. (50)
                                                                                                                         N
about the entire SNR region. For instance, the performance
                                                                                                     Given φ and D, the likelihood function of x is then given
can be improved by about 2 dB at an instantaneous SNR value
                                                                                                     by (51). To find φ, we can maximize the likelihood function
of about 13 dB.
                                                                                                     given by (51), which is equivalent to minimizing (11) with A
                        V. C ONCLUSION                                                               and b given by (28)-(30).
   In this paper, we proposed a general CFO estimator for                                                                  A PPENDIX III
OFDM systems, with which the performance of CFO estima-                                               C RAMER R AO B OUND WHEN P ERFECT CIR IS AVAILABLE
tion can be improved by using more channel side information.
                                                                                                        When the CIR is known, the derivative of (48) with respect
Using the second order channel statistics and for Rayleigh
                                                                                                     to φ is as follows:
fading channels, it was shown that better CFO estimation
performance can be achieved for low SNR values. For Ricean                                                dΛ (x; φ)                       dP(φ)H
                                                                                                                    = −2Re hH FH ×L DH WH
                                                                                                                               N                 x
fading channels, the performance of the CFO estimation can be                                                dφ                             dφ
improved for all SNR values. When the complete CIR infor-
mation is available, the performance of CFO estimation can be                                                       = 4πjRe hH FH ×L DH WH MP(φ)H x
                                                                                                                                N
further improved. Using the proposed CFO estimator, we can                                                                                                     (52)
take advantage of not only the channel side information, but
also the inherent structure of OFDM signals. For example, in                                         where M = diag(0, 1, · · · , N − 1). The second order deriva-
an IEEE 802.11a system, the CFO estimation can be achieved                                           tive of (48) with respect to φ is then as follows:
by using not only the null sub-carriers, but also the pilot tones                                     d2 Λ (x; φ)
                                                                                                                   = −8π 2 Re hH FH ×L DH WH M2 P(φ)H x .
                                                                                                                                     N
and channel statistics.                                                                                   dφ2
                                                                                                                                                       (53)
                        A PPENDIX I                                                                  By substituting (5) into (53), we have
        CFO E STIMATION U SING P ILOT T ONES AND
                                                                                                           d2 Λ (x; φ)
                   C HANNEL S TATISTICS                                                              −E                = 8π 2 hH FH ×L DH WH M2 WDFN ×L h.
                                                                                                                                  N
                                                                                                               dφ2
  Assume that the transmitted data and the CIR are indepen-
                                                                                                                                                            (54)
dent. From (5), the average of x is given by
                                                                                                     According to [25], the Cramer Rao bound is then as given by
                      E(x) = P(φ)WE(D)FN ×L μh .                                           (43)      (32).
2792                                                               IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, VOL. 5, NO. 10, OCTOBER 2006



                                                H
       Cx = E       x − E(x)      x − E(x)

                                                                                                                                         H
         =E      P(φ)WDFN ×L h − P(φ)WE(D)FN ×L μh P(φ)WDFN ×L h − P(φ)WE(D)FN ×L μh                                                          + σ2 I         (44)


                                                                                                                                                         H
   Cx = E       P(φ)W(D1 + D2 )FN ×L h − P(φ)WD1 FN ×L μh P(φ)W(D1 + D2 )FN ×L h − P(φ)WD1 FN ×L μh
           +σ 2 I
                                                             H
         = P(φ)WD1 FN ×L E             h − μh h − μh             FH ×L DH WH P(φ)H
                                                                  N     1

           +E P(φ)WD2 FN ×L hhH FH ×L DH WH P(φ)H + σ 2 I
                                 N     2
                                                             H
         = P(φ)WD1 FN ×L E             h − μh h − μh             FH ×L DH WH P(φ)H
                                                                  N     1

           +Es P(φ)WI2 diag FN ×L E hhH FH ×L WH P(φ)H + σ 2 I
                                         N                                                                                                                   (46)
                           1                                              H
  p x; φ, D, h =                exp − x − P(φ)WDFN ×L h                        x − P(φ)WDFN ×L h                                                             (47)
                       π N σ 2N
                          1                          ˆ                         H                   ˆ
  p x; φ, D =                  exp − x − P(φ)WDFN ×L h                             x − P(φ)WDFN ×L h                                                         (51)
                    π N det Cx



                             R EFERENCES                                           [16] M. G. Hebley and D. P. Taylor, “The effect of diversity on a burst-
                                                                                        mode carrier-frequency estimator in the frequency-selective multipath
 [1] P. H. Moose, “A technique for orthogonal frequency division multiplex-             channel,” IEEE Trans. Commun., vol. 46, no. 4, pp. 553–560, Apr. 1998.
     ing frequency offset correction,” IEEE Trans. Commun., vol. 42, no. 10,       [17] M. Morelli and U. Mengali, “Carrier-frequency estimation for transmis-
     pp. 2908–2914, Oct. 1994.                                                          sions over selective channels,” IEEE Trans. Commun., vol. 48, no. 9,
 [2] T. M. Schmidl and D. C. Cox, “Robust frequency and timing synchro-                 pp. 1580–1589, Sept. 2000.
     nization for OFDM,” IEEE Trans. Commun., vol. 45, no. 12, pp. 1613–           [18] R. Prasad and S. Hara, “Overview of multi-carrier CDMA,” IEEE
     1621, Dec. 1997.                                                                   Commun. Mag., vol. 35, no. 12, pp. 126–133, Dec. 1997.
 [3] M. Morelli and U. Mengali, “An improved frequency offset estimator            [19] A. F. Molisch, J. R. Foerster, and M. Pendergrass, “Channel models
     for OFDM applications,” IEEE Commun. Lett., vol. 3, no. 3, pp. 75–77,              for ultrawideband personal area networks,” IEEE Wireless Commun.,
     Mar. 1999.                                                                         vol. 10, no. 6, pp. 14–21, Dec. 2003.
 [4] B. Chen, “Maximum likelihood estimation of OFDM carrier frequency             [20] J. D. Markel, “FFT pruning,” IEEE Trans. Audio and Electroacoustics,
     offset,” IEEE Signal Processing Lett., vol. 9, no. 4, pp. 123–126, Apr.            vol. AU-19, no. 4, pp. 305–311, Dec. 1971.
     2002.                                                                         [21] O. Besson and P. Stoica, “Training sequence selection for frequency off-
                                                                                        set estimation in frequency selective channels,” Digital Signal Process-
 [5] H. Liu and U. Tureli, “A high-efficiency carrier estimator for OFDM
                                                                                        ing, vol. 13, no. 1, pp. 106–127, Jan. 2003.
     communications,” IEEE Commun. Lett., vol. 2, no. 4, pp. 104–106, Apr.
                                                                                   [22] J. Foerster et al., “Channel modeling sub-committee report final,” IEEE
     1998.
                                                                                        P802.15 Wireless Personal Area Networks P802.15-02/490r1-SG3a, July
 [6] D. Huang and K. B. Letaief, “Carrier frequency offset estimation for
                                                                                        2003.
     OFDM systems using null subcarriers,” IEEE Trans. Commun., vol. 54,
                                                                                   [23] A. Batra et al., “Multi-band OFDM physical layer proposal for IEEE
     no. 5, pp. 813– 823, May 2006.
                                                                                        802.15 task group 3a,” IEEE P802.15-03/268r1, Sept. 2003.
 [7] J. V. de Beek, M. Sandel, and P. O. Borjesson, “ML estimation of time         [24] Part 11: Wireless LAN Medium Access Control (MAC) and Physical
     and frequency offset in OFDM systems,” IEEE Trans. Signal Processing,              Layer (PHY) specifications: high-speed physical layer in the 5 GHz
     vol. 45, no. 7, pp. 1800–1805, July 1997.                                          band, IEEE Std. P802.11a/D7.0, Feb. 1999.
 [8] N. Lashkarian and S. Kiaei, “Class of cyclic-based estimators for             [25] H. L. V. Trees, Detection, Estimation, and Modulation Theory. Part I:
     frequency offset estimation of OFDM systems,” IEEE Trans. Commun.,                 Detection, Estimation, and Linear Modulation Theory. John Wiley and
     vol. 48, no. 12, pp. 1590–1598, Dec. 2000.                                         Sons, 1968.
 [9] Y. Li, L. J. Cimini, and N. R. Sollenberger, “Robust channel estimation
     for OFDM systems with rapid dispersive fading channels,” IEEE Trans.
     Commun., vol. 46, no. 7, pp. 902–915, July 1998.                                                       Defeng (David) Huang (M’01-S’02-M’05) received
[10] A. F. Naguib, N. Seshadri, and A. R. Calderbank, “Increasing data rate                                 the B. E. E. E. and M. E. E. E. degree in elec-
     over wireless channels: Space-time coding and signal processing for                                    tronic engineering from Tsinghua University, Bei-
     high data rate wireless communications,” IEEE Signal Processing Mag.,                                  jing, China, in 1996 and 1999, respectively, and the
     vol. 17, no. 3, pp. 76–92, May 2000.                                                                   Ph.D. degree in electrical and electronic engineering
[11] O. Edfors, M. Sandell, J.-J. van de Beek, S. K. Wilson, and P. O. Bor-                                 from the Hong Kong University of Science and
     jesson, “OFDM channel estimation by singular value decomposition,”                                     Technology (HKUST), Kowloon, Hong Kong, in
     IEEE Trans. Commun., vol. 46, no. 7, pp. 931–939, July 1998.                                           2004.
[12] H. Loeliger, “An introduction to factor graphs,” IEEE Signal Processing                                   From 1998, he was an assistant teacher and later
     Mag., vol. 21, no. 1, pp. 28–41, Jan. 2004.                                                            a lecturer with Tsinghua University. Currently, he is
[13] W. C. Kuo and M. P. Fitz, “Frequency offset compensation of pilot                                      a lecturer with School of Electrical, Electronic and
     symbol assisted modulation in frequency flat fading,” IEEE Trans.              Computer Engineering at the University of Western Australia. His research
     Commun., vol. 45, no. 11, pp. 1412–1416, Nov. 1997.                           interests include broadband wireless communications, OFDM, OFDMA,
[14] M. Morelli, U. Mengali, and G. M. Vitetta, “Further results in carrier        cross-layer design, multiple access protocol, and digital implementation of
     frequency estimation for transmissions over flat fading channels,” IEEE        communication systems.
     Commun. Lett., vol. 2, no. 12, pp. 327–330, Dec. 1998.                           Dr. Huang serves as an Editor for the IEEE Transactions on Wireless Com-
                                                                                   munications. He received the Hong Kong Telecom Institute of Information
[15] O. Besson and P. Stoica, “On frequency offset estimation for flat-fading
                                                                                   Technology Postgraduate Excellence Scholarships in 2004.
     channels,” IEEE Commun. Lett., vol. 5, no. 10, pp. 402–404, Oct. 2001.
HUANG and LETAIEF: ENHANCED CARRIER FREQUENCY OFFSET ESTIMATION FOR OFDM USING CHANNEL SIDE INFORMATION                                                          2793



                           Khaled B. Letaief (S’85-M’86-SM’97-F’03) re-              Series (as Editor-in-Chief) and the IEEE Transactions on Communications. He
                           ceived the BS degree with distinction in Electri-         has been involved in organizing a number of major international conferences
                           cal Engineering from Purdue University at West            and events. These include serving as the Technical Program Chair of the
                           Lafayette, Indiana, USA, in December 1984. He             1998 IEEE Globecom Mini-Conference on Communications Theory, held in
                           received the MS and Ph.D. Degrees in Electri-             Sydney, Australia as well as the Co-Chair of the 2001 IEEE ICC Communi-
                           cal Engineering from Purdue University, in August         cations Theory Symposium, held in Helsinki, Finland. In 2004, he served as
                           1986, and May 1990, respectively. From January            the Co-Chair of the IEEE Wireless Communications, Networks and Systems
                           1985 and as a Graduate Instructor in the School of        Symposium, held in Dallas, USA as well as the Co-Technical Program Chair
                           Electrical Engineering at Purdue University, he has       of the 2004 IEEE International Conference on Communications, Circuits
                           taught courses in communications and electronics.         and Systems, held in Chengdu, China. He is the Co-Chair of the 2006
                           From 1990 to 1993, he was a faculty member at             IEEE Wireless Ad Hoc and Sensor Networks Symposium, held in Istanbul,
the University of Melbourne, Australia. Since 1993, he has been with the             Turkey. In addition to his active research and professional activities, Professor
Hong Kong University of Science and Technology where he is currently                 Letaief has been a dedicated teacher committed to excellence in teaching
Chair Professor and Head of the Electronic and Computer Engineering                  and scholarship. He received the Mangoon Teaching Award from Purdue
Department. He is also the Director of the Hong Kong Telecom Institute               University in 1990; the Teaching Excellence Appreciation Award by the
of Information Technology as well as the Director of the Center for Wireless         School of Engineering at HKUST (four times); and the Michael G. Gale
Information Technology. His current research interests include wireless and          Medal for Distinguished Teaching Highest university-wide teaching award
mobile networks, Broadband wireless access, OFDM, CDMA, and Beyond                   and only one recipient/year is honored for his/her contributions).
3G systems. In these areas, he has published over 280 journal and conference            He is a Fellow of IEEE, an elected member of the IEEE Communications
papers and given invited talks as well as courses all over the world.                Society Board of Governors, and an IEEE Distinguished lecturer of the
   Dr. Letaief served as a consultant for different organizations and is currently   IEEE Communications Society. He also served as the Chair of the IEEE
the founding Editor-in-Chief of the IEEE Transactions on Wireless Commu-             Communications Society Technical Committee on Personal Communications
nications. He has served on the editorial board of other prestigious journals,       as well as a member of the IEEE ComSoc Technical Activity Council.
including the IEEE Journal on Selected Areas in Communications — Wireless

				
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