A New Efficient Symbol Timing Synchronization Scheme for MB-OFDM UWB Systems

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A New Efficient Symbol Timing Synchronization Scheme for MB-OFDM UWB Systems Powered By Docstoc
					                                                              (IJCSIS) International Journal of Computer Science and Information Security,
                                                                                                             Vol. 9, No. 9, September 2011

     A New Efficient Symbol Timing Synchronization
         Scheme for MB-OFDM UWB Systems

                    Reza Shahbazian                                                          Bahman Abolhassani
           Department of Electrical Engineering                                      Department of Electrical Engineering
        Iran University of Science and Technology                                 Iran University of Science and Technology
                       Tehran, Iran                                                              Tehran, Iran
               Shahbazian@elec.iust.ac.ir                                                  Abolhassani@iust.ac.ir


Abstract— Conventional symbol timing synchronization                      non-ideal OFDM systems is degraded by imperfections caused
algorithms show improper performance in low SNR values. In                by timing offset, improper number of cyclic prefix (CP) and
this paper a new low complexity and efficient symbol timing               frequency offsets. Among all the imperfections, effect of
synchronization (ESTS) algorithm is proposed for MB-OFDM                  timing offset on the system performance and bit error rate is
UWB systems. The proposed algorithm locates the start of Fast             much more sever. Synchronization techniques for narrowband
Fourier Transform (FFT) window during packet/frame                        OFDM systems utilize maximum correlation between the
synchronization (PS/FS) sequences of the received signal. First, a        received signal and training timing symbols [2-3]. All such
cross correlation based function is defined to determine the time         techniques assume that the first received multipath component
instant of the useful and successfully detected OFDM symbol.              (MPC) is the strongest one. Therefore, in a channel with dense
The threshold value in detection of the OFDM symbol is
                                                                          multipath effects, a delayed stronger component, which is
predetermined by considering the trade-off between the
probability of false alarming and missed detection. The exact
                                                                          shown in “Fig 1”, may cause erroneous timing synchronization,
boundary of the FFT window for each OFDM symbol is                        which leads to Inter Symbol Interference (ISI), destroys the
estimated by a maximum likelihood metric and choosing the                 orthogonality of OFDM subcarriers, and degrades the overall
argument of the peak value. Verifying the estimated timing offset         performance [4].
is the last step to locate the start of the FFT window. The                   Several algorithms are proposed for timing synchronization
proposed algorithm shows great improvement in the MSE,                    in MB-OFDM systems [5-9]. In [5], the proposed algorithm
synchronization probability and bit error rate metrics compared
                                                                          (FTA) detects the significant path by comparing the difference
with those of earlier works.
                                                                          between two consecutive accumulated energy samples at the
   Keywords- MB-OFDM, Synchronization, Ultra Wide Band,                   receiver against a predetermined threshold. However, the
Fast Fourier Transform, Maximum Likelihood.                               threshold is only determined by the probability of false alarm,
                                                                          while other important error measures such as the missed
                                                                          detection probability is not exploited. Further, the
                I.   INTRODUCTION (HEADING 1)                             computational complexity is high due to the large amount of
    Ultra-Wideband (UWB) technology is the main candidate                 multiplications involved in the algorithm. In [6], a correlation
for short distance (<10 m) and high data rate (53-480 Mbps)               based symbol timing synchronization (CBTS) has also been
communications in Wireless Personal Area Networks                         reported. The idea is similar to that of [5] and estimates the first
(WPAN). Multi band orthogonal frequency division                          significant multipath of the received signal by comparing the
multiplexing (MB-OFDM) based communication scheme is the                  difference between two successive correlated MB-OFDM
most noteworthy, among the several proposals for efficient use            symbols against a predetermined threshold. Compared with
of the 7.5 GHz bandwidth allocated for UWB technology.                    that of [5], the computational complexity is reduced and
                                                                          performances in terms of both the mean square error (MSE) of
    MB-OFDM is the combination of OFDM modulation and
                                                                          timing offset and the perfect synchronization probability are
data transmission using frequency-hopping techniques. In this
                                                                          improved. These two algorithms [5-6] cannot operate properly
method, all the available bandwidth (3.1-10.6 GHz) is divided
                                                                          at low SNR values due to imperfections in autocorrelation
into 14 frequency bands each with 528 MHz of bandwidth.
                                                                          property of the base sequence and the dense multipath channel
These 14 frequency bands are categorized in five groups. Each
                                                                          environments. Combination of the autocorrelation function and
of the first four groups has three frequency bands and the fifth
                                                                          restricted and normalized differential cross-correlation (RNDC)
group contains only two frequency bands. Data is transmitted
                                                                          with a threshold-based detection is used in [7] to find the
over different frequency bands using a Time-Frequency code
                                                                          timing offset of the OFDM symbol. In [8], the proposed
(TFC), which causes frequency diversity and multiple access
                                                                          algorithm utilizes a maximum likelihood function to estimate
capability [1].
                                                                          the timing offset. Concentration of the algorithm in [8] is on
    OFDM systems have the advantage of being able to operate              frequency diversity. Moreover its computational complexity is
as a set of N (number of subcarriers in the system) parallel              rather high. In this paper, a modified and Efficient Symbol
links over flat fading channels. However, the performance of              Timing Synchronization (ESTS) algorithm for MB-OFDM



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                                                                                                       ISSN 1947-5500
                                                                                    (IJCSIS) International Journal of Computer Science and Information Security,
                                                                                                                                   Vol. 9, No. 9, September 2011
UWB systems is proposed, while utilizes time domain                                               the number of useful samples in one OFDM symbol and P is
sequences (TDS) to estimate the timing offset. The                                                the total number of transmitted symbols in PS , FS and
computational complexity of the proposed algorithm is reduced                                      CE sequences. MB-OFDM symbols prepared by suffixing 32
by simplification in correlation based and maximum likelihood
                                                                                                  null samples called zero padded (MZP) and 5 null guard
functions. The organization of this paper is as follows: in
                                                                                                  samples called (Mg) to FFT/IFFT output sequences of length M
Section II, we present the MB-OFDM system, signal model
                                                                                                  which is considered to be 128 samples according to the frame
and characteristics of an UWB channel. In Section III, we
                                                                                                  format [11]. The total length of M+Mzp+Mg samples of one
describe the proposed algorithm for MB-OFDM timing
                                                                                                  MB-OFDM symbol is denoted by MT, which is equal to 165
synchronization and Section IV shows simulation results of our
                                                                                                  samples.
proposed algorithm and compares them with those reported in
[5-9]. Important concluding remarks are made in Section V.




                                                                                                             Figure 2. Packet model for a MB-OFDM system [1]


                                                                                                           TABLE I.             TFC PATTERN I N MB-OFDM SYSTEMS [1]
           Figure 1. Impulse response of an UWB channel [9]                                             TFC           Preamble
                                                                                                                                                        TFC
                                                                                                       Number         Number
                                                                                                         1                1           1      2      3      1      2         3
                 II.    MB-OFDM SYSTEM MODEL
                                                                                                         2                2           1      3      2      1      3         2
                                                                                                         3                3           1      1      2      2      3         3
A. MB-OFDM Signal Model
                                                                                                         4                4           1      1      3      3      2         2
   Synchronization in MB-OFDM systems is data-aided [1].                                                 5                5           1      1      1      1      1         1
In standard preamble structure, the first 21 packet                                                      6                5           2      2      2      2      2         2
synchronization (PS) sequences are used for packet detection,                                            7                5           3      3      3      3      3         3
AGC     stabilization,  coarse timing and          frequency
synchronization. The next 3 frame synchronization (FS)
sequences are meant for a fine timing and frequency                                               B. UWB Channel Model
synchronization.                                                                                      IEEE802.15.3 channel modeling sub-committee has
    These sequences are followed by 6 channel estimation (CE)                                     specified 4 different channel models (CM1-CM4) depending
sequences as shown in “Fig 2”. Depending on the time-                                             on transmission distances based on a modified saleh-valenzuela
frequency code, a particular preamble pattern is selected which                                   (S-V) model [10]. UWB channel model is a cluster-based
is shown in “Table 1”. For a given TFC the PS and FS                                              model, where individual ray shows independent fading
sequences have the same magnitude but opposite polarity. The                                      characteristics. An UWB channel not only shows frequency
preamble structure for TFC 1 and 2 is shown in “Fig 2”. Delay                                     dependence of instantaneous channel transfer functions, but
period is defined as the minimum number of symbol timing                                          also the variations of averaged transfer function caused by
difference in the same frequency band. As an illustration, the                                    different attenuations of different frequency component of an
delay period=3 for TFC 1 or 2, delay period=6 for TFC 3 or                                        UWB signal [12].
TFC 4 patterns and delay period=1 for TFC 5.                                                         Impulse response model of an UWB channel can be
                              th                      th                                          represented as,
   Consider Ss , n (k ) as k sample of n                   transmitted OFDM
symbol, which is given by.                                                                                             L    K
                                                                                                             h(t )   ak ,l exp( jk ,l )  (t  Tl   k ,l ).               (2)
                                                                                                                      l  0 k 0

                        S s, n ( k )  Sc ( n)  Sb ( k ).            In “(2)”, {ak , l } and { k , l } are tap weighting coefficients
                                                                                                  and tap phases of the k th component in lth cluster respectively,
      In “(1)”, Sb ( k ) is the kth sample of the nth symbol [11].
                                                                                                  and h(t ) represents small scale fading amplitude. Delay of
 Sb ( k ) is a time domain base sequence that is chosen according
to the TFC employed and Sc ( n) is the spreading sequence for                                     k th MPC toward arrival time of lth cluster, {Tl } , is shown with
                                                                                                  { k ,l } . We denote h(t )   h(0), h (1),..., h( L  1) as the channel
the nth symbol and k  1, 2,..., M and n  1, 2,..., P , which M is
   Identify applicable sponsor/s here. (sponsors)



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                                                                                                                                     ISSN 1947-5500
                                                                   (IJCSIS) International Journal of Computer Science and Information Security,
                                                                                                                  Vol. 9, No. 9, September 2011
impulse response with L resolvable multipath components. We                                                 ( )  Re( Fp ( ))  Im( Fp ( )) .                        (8)
also define n(t ) as a zero mean additive white Gaussian noise
                            2
(AWGN) with variance  n . The received signal with timing                        The defined function performs well at all SNR values if it is
                                                                              assumed that the packet is successfully detected and the OFDM
offset equal to  could be described as the following,                        sequences are confirmed to be received. In practical scenarios
                  L 1                                                        there exists a noise sequence at the start of every frame [14]
          r ( k )   S s (k   ).h(i )  n( k ).                 (3)        which makes us to do a kind of packet detection at the start of
                  i0
                                                                              timing synchronization algorithm but Computational
                                                                              complexity is rather high and needs M multiplications just in
               III. PROPOSED ESTS ALGORITHM                                   one crosscorrelation function. So, we reduce the complexity by
    The main objective in the symbol timing synchronization is                simplifying “(4)” as described below,
to find the timing offset of the received symbol. Our proposed                                                          M 1

algorithm contains two steps, coarse and fine synchronization.                                             FP ( )   r ( k   ).sgn  Sb (k ) .                      (9)
The aim in coarse synchronization is to determine the time                                                              k 0

instant while a useful OFDM symbol has been successfully                         Define Vm 1    m,1,...,  m  M  1 as the time index that
detected. In fine synchronization, we use the gained boundary
in coarse synchronization to locate the exact starting point of               contains the sign of ( m  1)th , M sample base sequence. Also,
the FFT window. To do synchronization, we use modified                        define V0   0,1,..., M  1 as the time index that contains the sign
cross correlation based functions, which perform better than
                                                                              of M sample base sequence. We use M instead of MT because
auto correlation functions, in low SNR values. The cross
correlation function in general could be defined as,                          there is no useful information in MZP and Mg sequences, i.e.,
                                                                               S b (k )  0 M  k  M T . We assume that the channel and the noise
                      M 1
                                                                              are uncorrelated. The cross correlation function at time instant
          FP ( )   r ( k   ).S *b ( k ).
                                                                  (4)
                                                                                m  k is given by:
                      k 0

                                    *                                                                        M 1                              
    In “(4)”, the operator . represents complex conjugate                                               E   r   m  k  .sgn  Sb (k )                        (10)
                                                                                                             k 0                              
transpose of the signal and FP indicates the crosscorrelation
function between the received signal and the base sequence.                       This can be easily shown that by expanding “(10)” we can
The estimated and coarse boundary for timing offset could be                  drive the following formula,
found by the following Maximum Likelihood metric,                                   M 1  m
                                                                                                                                                                 L 1    
                                                                                              Sc ( n). S b (m  k ) .sgn  Sb ( m  k )  .sgn  Sb ( k )  .E  h( k )  .
                                                 FP 2 
                                                                                   k 0                                                                       k 0     
            arg max     arg max              2 
                                                           ,       (5)                                                                                                 (11)
                                            
                                                  FR 
                                                        
                                                                                  In “(11)”, when m  0 , a negative and positive peak of the
   Where we define                                                            crosscorrelation is generated if Sc ( n)  1 and Sc ( n)  1
                                          M 1                                respectively. It means that when the time index that contains
                      1  M 1         2            2
          FR ( )        r ( k   )   Sb ( k )  .           (6)        the first M sample of the received signal is considered, the peak
                      2  k 0            k 0                               value is generated. So, we use two sets of V0 and V1 for symbol
    Computational complexity in this method is high. As shown                 timing offset estimation.
in [13] we can use a simplified timing metric, which is a good                    As the timing offset decreases the value of  ( ) in “(8)”
approximation of “(5)”, described as,
                                                                              increases. We define S N as the index of a received M sample
                       F ( )  Re( Fp ( ))  Im( Fp ( )) .   (7)        sequence and  ( S N ) as the time instant of the first sample for
                                                                              that sequence.
    If the base sequence is characterized by a perfect
autocorrelation property, there is only one significant peak                                               S N   arg    S N      ,                       (12)
located at the first received sample. However, by imperfect                                                               
autocorrelation property of the base sequence, as indicated in
[1], there exist some undesired peaks at the other sample                        where    S N                                    
                                                                                                                Re Fp   S N    Im Fp    S N        and FP is
instants. By considering the AWGN and channel variations,                     defined in “(9)”. Parameter  in “(12)” is the threshold which
these undesired peaks may be amplified and their values are                   is predetermined by considering the trade-off between the
comparable with that of the first peak corresponding to the                   probability of false alarming and the probability of missed
desired symbol boundary. So the crosscorrelation function may                 detection. If the OFDM symbol is successfully detected the
trigger false alarm and the algorithms, which use these kinds of              value   SN  is used as a reference symbol boundary for fine
functions [5-9] show poor system performances. In order to
reduce false alarm probability especially at low SNR values,                  synchronization. Due to the modified S-V channel model, the
                                                                              first arriving path may not be the strongest one. As a result,
we modify the introduced metric in “(7)” as the following,
                                                                              using only the conventional cross-correlation function will




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                                                                                                                        ISSN 1947-5500
                                                                                   (IJCSIS) International Journal of Computer Science and Information Security,
                                                                                                                                  Vol. 9, No. 9, September 2011
locate a delayed multipath component with stronger amplitude
                                                                                                                                       S N  1,  ( S N )  1
as the reference one and hence will cause misdetection. To
correctly estimate the position of the first arriving path, we take
the moving average of  ( ( S N )) over a window of size L                                                                           M 1

                                                                                                           FP ( ( S N ))              r (k   ( S             )).sgn  S b (k ) 
where most of the channel energy is concentrated. In other                                                                              k 0
                                                                                                                                                              N


words,
                               L1
             '                                                                                               ( ( S N ))  Re( FP ( (S N )))  Im( FP ( (S N )))
            ( ( S N ))        ( ( SN ) w).
                               w0
                                                                                   (13)
                                                                                                                                                                      ( ( S N ))  ( ( S N ))  1
   To reduce the computational complexity the “(13)” could
be substituted by the following recursive equation as given                                                                                 
                                                                                                                                       arg     S N        
                                                                                                                                        
below,
     ' ( ( S N )  1)   ' ( ( S N ))   ( ( S N )  L )   ( ( S N )).   (14)
    In “(14)”, L is considered as the maximum delay spread of                                               '
                                                                                                            ( ( S N ))   ( ( S N ))   ( ( S N )  1)  ...   ( ( S N )  L   1)

the multipath channel. The exact symbol boundary ( o (SN ) )
could be found by the following equation
                                                                                                       o
                                                                                                                                  '                   '                   '
                                                                                                      ( S N )  arg max  ( ( S N )),  ( ( S N )  1), ...,  ( ( S N ))  M  1            
     (S N )  arg max  (( SN )),  ( (SN )  1),...,  ( (S N )  M  1) .
      o                        '              '                       '

                     
                                                                                   (15)
                                                                                                                           Symbol Boundary   o ( S N )
                                                  o
    If the calculated value of  (SN ) in “(15)”, stands in the
range of added zero prefix ( M ZP ), all the subcarriers would                                                                                     o
                                                                                                                                                  (SN )

experience the same phase shift that could be removed in the                                                                                      in ISI

receiver. And if the o (SN ) value stands out of this range, ISI                                                                               Free Zone ?

occurs and subcarriers try different phase shifts that degrade the
system performance. Since transmission channel varies in time,
timing offset of each symbol is different from the others.
                                                                                                           Figure 3. Flowchart of Proposed ESTS algorithm
Detailed flowchart of the proposed algorithm (ESTS) is shown
in “Fig 3”. When the estimated value stands in the ISI free zone
(sample index 1  M ZP ), synchronization is done. If the                                       The threshold value which is used in coarse
                                                                                                synchronization is defined so we have low MSE and high
estimated value stands in the sample index ( M ZP  1)  M T ,                                  Psync . By simulation results, threshold value is considered
wrong synchronization is performed and the false alarm                                          to be 24 dB and 23 dB for CM1 and CM2 respectively.
probability ( PF ) increases:
                                                                                                We also need to define the number of required cross
                                                                                                correlations to minimize the effect of delay spread in
                               IV.       EVALUATION                                             multipath fading channels. For a given threshold at a
                                                                                                certain SNR, the MSE decreases while the Psync increases
A. Simulation                                                                                   when L increases up to 15 and the performance measures
     In simulation of the proposed algorithm (ESTS), it is                                      stay constant afterwards. So we consider the L   15 as the
assumed that there are no other imperfections except timing                                     number of required cross correlations. Simulation results
offset. 100 realization of channel model CM1 (0-4 meter line of                                 for the MSE and Psync metrics are shown in “Fig 4” and
sight and 5 nanosecond delay spread) and CM2 (0-4 meter non                                     “Fig 5” respectively. As shown in “Fig 4” in the MSE
line of sight and 8 nanosecond delay spread) are considered in                                  metric, a great improvement is achieved in all SNR values
simulation. It is also assumed that the first pattern of time-                                  especially in low values both in CM1 and CM2 channel
frequency code (TFC1) is used in data transmission and                                          model compared with those of the CBTS and FTA. “Fig 5”
frequency synchronization is ideal. The performance of the
                                                                                                indicates that in Psync metric and high SNR values, the
system is evaluated by the probability of synchronization
                                                                                                performance is the same as that of the CBTS algorithm in
( Psync ), bit error rate (BER) and the MSE of timing offset as
                                                                                                CM1 channel. In low SNR values and both CM1 and CM2
defined below.                                                                                  channel models and high SNR values in CM1 channel
                                                                                                model, performance is improved compared with that of the
                                ˆ
                               ˆ
                                     
                   MSE      Psync ˆ                                       (16)         CBTS. In all SNR values and both channel models,
                                                                                                performance of the proposed algorithm is better than that
                ˆ     
   Where Psync  is the probability of synchronization at ˆ                                    of the FTA.
for the simulated channel realization and PF  Psync  1 .




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                                                                                                                                                ISSN 1947-5500
                                                                                                                           (IJCSIS) International Journal of Computer Science and Information Security,
                                                                                                                                                                          Vol. 9, No. 9, September 2011
    In “Fig 6” and “Fig 7” the bit error rate of the proposed                                                                                            -1
                                                                                                                                                        10
    algorithm is compared with those of, [6-7] in CM1 and
    CM2 channel model, respectively.                                                                                                                                                                         CBTS - CM2
                                                                                                                                                                                                             FTA - CM2
                                                                                                                                                                                                             ESTS - CM2
              30
                                                                                                        FTA-CM1
                                                                                                        FTA-CM2
                                                                                                        CBTS-CM1
              25                                                                                        CBTS-CM2
                                                                                                        ESTS-CM1
                                                                                                        ESTS-CM2




                                                                                                                                                  BER
                                                                                                                                                         -2
                                                                                                                                                        10
              20
       MSE




              15




              10




                5
                                                                                                                                                         -3
                                                                                                                                                        10
                                                                                                                                                              6   8   10        12             14       16     18         20
                                                                                                                                                                                     SNR(dB)
                0
                     0                5                10           15            20             25                   30
                                                                  SNR(dB)

                                                                                                                                    Figure 7. Comparison of BER for proposed algorithm (ESTS), FTA [6] and
Figure 4. Comparison of MSE for proposed algorithm (ESTS), FTA [6] and                                                                                CBTS [7] in CM2 channel model.
             CBTS [7] in CM1 and CM2 channel models.

                                                                                                                                    B. Computational Complexity
                         1


                     0.9
                                                                                                                                          To compare the computational complexity, we assume that
                     0.8
                                                                                                                                    there are no only pure noise packets as considered in [6] and
                                                                                                                                    [7]. So, we skip the coarse synchronization part (packet
                     0.7
                                                                                                                                    detection). We also assume that the recursive “(14)” is used
                     0.6
                                                                                                                                    instead of “(13)”. According to [6] and [7] the number of
             Psync




                     0.5                                                                              FTA-CM1
                                                                                                      FTA-CM2
                                                                                                                                    multiplications in FTA, CBTS and proposed algorithm are
                     0.4                                                                              CBTS-CM1
                                                                                                      CBTS-CM2
                                                                                                      ESTS-CM1
                                                                                                                                      5M      2 M  1 ,  5M      2M  1 and M   L  M  1
                                                                                                                                              T                             T
                     0.3
                                                                                                      ESTS-CM2
                                                                                                                                    respectively. The numbers of summations are also
                     0.2


                     0.1
                                                                                                                                      5M      2 M  2 
                                                                                                                                              T
                                                                                                                                                                          ,            5M      2M 
                                                                                                                                                                                                    T
                                                                                                                                                                                                              and
                         0
                             0                5         10          15           20         25                   30
                                                                                                                                       M  1   M  L   1  L   1 in the same order. As a numerical
                                                                  SNR(dB)
                                                                                                                                    result,          by         considering              M  128, M  32      and
                                                                                                                                                                                                                ZP


Figure 5. Comparison of Psync for proposed algorithm (ESTS), FTA [6] and                                                             M  5, M  165,   1 and L
                                                                                                                                          g              T
                                                                                                                                                                             15 , the number of multiplications
             CBTS [7] in CM1 and CM2 channel models.
                                                                                                                                    in the FTA, CBTS and proposed algorithm (ESTS) are 212282,
                                                                                                                                    210630 and 18176, respectively, which show that the proposed
                             -1
                         10
                                                                                                 FTA - CM1                          algorithm is less complex. In the same order, the numbers of
                                                                                                 ESTS - CM1
                                                                                                 CBTS - CM1                         summations are equal to 209804, 211456 and 18302.

                                                                                                                                                                      V.        CONCLUSION
                                                                                                                                       In this paper, a new efficient symbol timing
               BER




                         10
                             -2
                                                                                                                                    synchronization (ESTS) algorithm proposed for MB-OFDM
                                                                                                                                    UWB systems. In the proposed algorithm, was compared in
                                                                                                                                    MSE, synchronization probability and bit error rate metrics
                                                                                                                                    with those of [6] and [7]. Simulation results show a great
                                                                                                                                    improvement while the computational complexity is reduced.
                             -3
                         10
                                  6       8       10         12
                                                                  SNR(dB)
                                                                            14         16    18               20
                                                                                                                                                                           REFERENCES
                                                                                                                                    [1]       ECMA-368, “High Rate Ultra Wideband PHY and MAC standard, 3rd
Figure 6. Comparison of BER for proposed algorithm (ESTS), FTA [6] and                                                                        Edition”                         December                     2008,
                  CBTS [7] in CM1 channel model.                                                                                              http://ecmainternationa.org/publications/files/ECMA-ST/ECMA-368.pdf.
                                                                                                                                    [2]       J. Van De Beek, M. Sandell and P. O. Borjesson, “ML estimation of
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                                                                                                                                              synchronization scheme for OFDM systems,” IEEE Transactions on
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