Carrier Offset Estimation for MIMO-OFDM Based on CAZAC Sequences by ijcsis


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									                                                              (IJCSIS) International Journal of Computer Science and Information Security,
                                                                                                                 Vol. 9, No. 1, 2011

     Carrier Offset Estimation for MIMO-OFDM Based on
                       CAZAC Sequences
                                             Dina Samaha*, Sherif Kishk, Fayez Zaki
                                    Department of electronics and communications engineering
                                                   Mansoura University, Egypt

Abstract— The combination of Multi-Input Multi-Output                     MIMO-OFDM systems are much more sensitive to frequency
(MIMO) with Orthogonal Frequency Division Multiplexing                    synchronization errors. Therefore, these errors must be
(OFDM) is regarded as a winning technology for future                     accurately estimated and compensated in order to avoid severe
broadband communication. However, its sensitivity to Carrier
                                                                          error rates. The synchronization techniques for single-input
Frequency Offset (CFO) is a major contributor to the Inter-
Carrier Interference (ICI), this effect becomes more severe by the        single-output (SISO) OFDM either exploit the inherent
presence of multipath fading in wireless channels. This paper is          structure of the OFDM symbol using the cyclic prefix part
concerned with CFO estimation for MIMO-OFDM system. The                   without bandwidth overhead [2]. This approach relies only in
presented algorithm uses a two-step strategy. In the proposed             the redundancy introduced by the cyclic prefix. Other
method a preamble structure is used which made up of repeated             techniques use specifically designed training symbols
orthogonal polyphase sequences such as Zadoff and Chu
                                                                          consisting of repeated parts [2-4]. Moose [3] proposed a
sequences. Both of them belong to the class of Constant
Amplitude Zero Auto-Correlation (CAZAC) sequences. The                    Maximum Likelihood (ML) estimator which can correct the
repeated preambles that are constructed using a CAZAC code                CFO after Fast Fourier Transform (FFT) of two identical
are simultaneously transmitted from all transmit antennas to              training symbols. He also described how to increase the
accomplish frequency offset estimation. Simulation results show           estimation range by using shorter training symbols, on the
the robustness, accuracy and time-efficiency of the proposed              expense of reducing estimation accuracy. Schmidl and Cox
algorithm compared to existing similar algorithms that use PN
                                                                          [4] concluded that a first symbol is sent with two identical
codes especially in multi-path channel.
                                                                          halves which lead to easier detection based on correlation
   Keywords-— CFO, MIMO, OFDM, Zadoff-Chu sequences.                      properties. That is when the CFO is partially corrected in the
                                                                          first training phase, a second training symbol is sent to correct
                      I.    INTRODUCTION                                  the remaining frequency offset. Tufvesson et al. [5] proposed
                                                                          an approach for frequency offset estimation using Pseudo-
Nowadays, the limitations of modulation schemes in existing
                                                                          Noise (PN) sequence that can correct frequency offset with
communication systems have become an obstruction in further
                                                                          large estimation range. Recent works tackled the CFO
increasing the data rate. Orthogonal Frequency Division
                                                                          proplem in MIMO-OFDM systems [6-9]. Mody and Stuber [6]
Multiplexing (OFDM) is a promising modulation technique
                                                                          applied a scheme using orthogonal polyphase sequences as
used in a wide range of communications systems. A key
                                                                          training sequence, to estimate fine frequency offsets in time
aspect of OFDM is the overlapping of individual orthogonal
                                                                          domain and coarse frequency offsets in frequency domain.
sub-carriers which leads to efficient spectral efficiency. One
                                                                          Schenk and Van Zelst [7] extended Moose's method using
advantage of OFDM is that it reduces the effect of multipath
                                                                          repeated sequence with constant envelope as orthogonal
environments. Multi-Input Multi-Output (MIMO) wireless
                                                                          training sequence to realize coarse and fine frequency
system is a system that is equipped with multiple antennas at
                                                                          synchronization in one step in time domain. Yao and Tung-
transmitter and receiver, takes spectral efficiency to a new
                                                                          Sang [8] proposed frequency offset estimation in MIMO
level. MIMO systems are an efficient method to enhance data
                                                                          systems assuming that the frequency offset between the
transmission rate requiring no extra bandwidth in rich
                                                                          transmit and receive antennas is different, whereas time delay
scattering environments. The combination of OFDM and
                                                                          is the same. Recently Liming [9] proposed frequency
MIMO technologies referred to as MIMO-OFDM is a winning
                                                                          synchronization scheme using repeated (PN) as training
combination for wireless technology [1]. MIMO-OFDM has
                                                                          sequences to correct CFO.
gained more and more interests in recent years. Carrier
                                                                             In this study an algorithm is proposed based on the idea of
Frequency Offset (CFO) is caused by the Doppler effect of the
                                                                          [9] which aims to apply its frequency synchronization
channel or the mismatch between the transmitter and receiver.
                                                                          algorithm for MIMO-OFDM system, using a modified
In OFDM systems, CFO destroys the orthogonality between
                                                                          preamble consists of training symbol of constant envelope
the subcarriers, hence results in Inter Carrier Interference (ICI)
                                                                          orthogonal codes with good periodic correlation properties,
and performance degradation. As the core technique is OFDM,
                                                                          such as Frank-Zadoff [10] and Chu [11] sequences. Zadoff-


                                                                                                     ISSN 1947-5500
                                                                        (IJCSIS) International Journal of Computer Science and Information Security,
                                                                                                                           Vol. 9, No. 1, 2011

Chu sequences possess good correlation properties which are                                               III.      SEQUENCE ANALYSIS
essential in a variety of engineering applications such as                           The main contribution of the proposed frequency
establishing synchronization, performing channel estimation                       synchronization algorithm is implementation of Zadoff and
and reducing peak-to-average power ratio. The use of these                        Chu sequences as synchronization sequences. Both of these
sequences leads to better frequency offset estimation at each                     sequences are considered as Constant Amplitude Zero
transmitting antenna under the assumption of perfect timing                       Autocorrelation (CAZAC) sequences. The proposed frequency
synchronization.                                                                  synchronization algorithm uses the good correlation property
   In the proposed method CFO is compensated in two stages,                       of CAZAC sequences. It is worthwhile to mention that
at first CFO correction is performed in an acquisition stage,                     complexity of polyphase and PN sequences could be
but there will still be existing residual CFO that has to be                      compared using two different perspectives .First, a polyphase
compensated. To remove these CFO residuals a tracking stage                       sequence in frequency domain is also a polyphase sequence in
is implanted.                                                                     time domain, in other word Zadoff-Chu sequence is also
   The paper is organized as follows .Section ΙΙ describes the                    Zadoff-Chu sequence after FFT which can help even in the
system model. In section ΙΙΙ frequency synchronization                            implementation. Second, the frequency domain correlation of
preamble structure is explained in conjunction with properties                    a PN sequence cannot give reliable sequence detection. Thus,
of Zadoff and Chu sequences. The proposed frequency offset                        keeping in mind the above mentioned comparison it has been
estimation algorithm is explained in section IV. System                           decided to choose polyphase sequences as the basic sequence
performance is evaluated through computer simulation in                           in the proposed study.
section V. Conclusion remarks are presented in section VI.
                                                                                  A. Frank-Zadoff code sequence
                             II.    SYSTEM MODEL                                     It is defined as cyclic shifted orthogonal code with good
  A general MIMO-OFDM system comprising Nt transmitter                            periodic correlation properties for preamble sequences. Frank-
antennas and Nr receiver antennas is depicted in Fig. 1.                          Zadoff code was described as a more general form of another
                                                                                  code introduced by Heimiller [12]. For a code sequence of
                                                                                  length L, {s0, s1, s2... sL-1}, the complex cyclic correlation
                              Tx1         Rx1                                     function is defined as:
                     OFDM                        OFDM
Source               Mod 1                       Demod 1           Sink                     L −1
                                                                                     xi =          s n +i s n                   (2)
                              Tx2          Rx2    OFDM                                      n =0
MIMO                 OFDM                                          MIMO
coding               Mod 1
                                                 Demod 2
                                                                   Decoder        note that s* denotes the complex conjugate of s, sm = sm + L
                                                                                  because it is a cyclic code. For i = 0, the value of xi reaches its
                              Tx          Rx     OFDM
                                                                                              L −1              2
                    OFDM      Nt          Nr
                                                                                    x0 =                sn                       (3)
                    Fig.1. MIMO-OFDM system block diagram.                        On the other hand, for 0 < i ≤ L − 1 the values of xi should be
                                                                                  zero. That means each code is orthogonal to its own phase
  The received signal on the lth receive antenna is described in                  shifted version.
equation (1), supposing that time has been synchronized
correctly                                                                         B. Chu sequence
            Nt                                                                       The autocorrelation function of Chu sequences is known to
                                      j 2πnε                                      be zero except at the lag of an integer multiple of the sequence
 rl (n) =          hq,l sq (n) exp{      L
                                             } + wl (n)      (1)                  length. The length of Zadoff codes is restricted to perfect
            q =1                                                                  squares. But, Chu sequences have the same correlation
Where sq(n) is the synchronization training sequence                              properties and can be constructed for any code length. A set of
transmitted on qth transmit antenna, w(n) is the AWGN on the                      Chu sequence with length L is considered as Sn, 0 < n < L-1,
qth receive antenna, ε is the frequency offset factor, L is the                   where the kth element of Sn, Sn(k), is defined as:
length of the training sequence, and hq,l is the channel gain                                          nk 2
                                                                                                exp( jπ       )      ; L even
between the qth transmit antenna and the lth receive antenna .In                     Sn (k) =           L                                (4)
the present study the same frequency offset for each transmit                                  
                                                                                               exp( jπ nk ( k +1)
                                                                                                                   ) ; L odd
and receive antenna pair has been assumed .                                                                L

                                                                                                                      ISSN 1947-5500
                                                                     (IJCSIS) International Journal of Computer Science and Information Security,
                                                                                                                        Vol. 9, No. 1, 2011

C. Preamble design                                                                          j 2πgεL
                                                                              rl ( n) exp(          )                                                 (5)
   The data packet is preceded by a section of pre-defined data,                                N
                                                                              l (1, Nr ),n (0, L −gN −1)
preamble, which is constructed using a repeated CAZAC code.
Each transmitter transmits the same code, but with different                  Where g is the correlation period (the number of Chu or
cyclic shifts. The preamble is followed by a data transmission                Zadoff sequences) denoting the distance between two
on all transmitters. The advantage of this MIMO preamble is                   correlated samples .The CFO can be estimated as:
that it takes only as much time as a SISO preamble and it is                         L                                     ¡
independent of the number of transmitting antennas. For the                   ε =        × angle(φ g ) ,  g (1, M − 1)         (6)
proposed frequency synchronization algorithm a repetition of
the CAZAC training sequence is considered. The training                       Where φ g is defined as:
sequences from different transmit antennas have to be
                                                                                         Nt L _ gN _ 1
orthogonal to each other for at least the maximum channel
delay length to preserve orthogonality.                                       φg = ∑               ∑ rl (n + gN )rl
                                                                                                                          ( n)                           (7)
             N                                                                          l =1       n=0
                                                                              In (6), ε is estimated with single “g”. This kind of estimators
                                         data                 TX1             is named as single-g estimators. They are adopted for CFO
   0                                                                          acquisition, the estimation range is ε <
                                                                                                                                     2 gN
                                         data                TX2
                                                                                B.     CFO Tracking
   0                                                 Time (sample)
                                                                                 For different “g”, multiple different single-g estimators can
       Fig.2. MIMO-OFDM system preamble schematic diagram using 2
                        transmitting antennas
                                                                              be used together in estimating CFO to improve estimation
                                                                              accuracy. This is called as multiple-g estimator. The number
  Fig. 2 shows an example of preamble including a CAZAC                       of used “g” will be pointed to by parameter “m”. One
sequence repetition with N periods for 2 transmitters MIMO                    multiple-g estimator is given by:
system. It is transmitted twice by 2 transmitters
                                                                                    m      L × angle(φ g j ) × ( 2πg j N ) −1
simultaneously with a different cyclic shift.
                                                                              ε=∑                                                               (8)
                                                                                    j =1                      m
The proposed CFO estimation specifies a unique training                                        ¢
                                                                              Where: m (1, M −1) , g 1 , g 2 , g 3 ,....g m            £    (1, M − 1)
sequence at each transmit antenna to designate the antennas
and estimate the CFO. Chu and Zadoff sequences are adopted                    The          estimation         range          of     multiple-g        estimator
as training sequences in different transmit antenna with their                                            L
                                                                              is   ε <                                         . The estimation error of one
shift and orthogonal properties. Assume the length of training                             2 N max( g 1 , g 2 ,...., g m )
sequence is L, and the period length of Chu or Zadoff                         multiple-g estimator may be much smaller than each single-g
sequence is N, then M=L/N. M is positive integer pointed to                   estimator used by it, especially when all these single-g
number of Chu or Zadoff sequences contained in the training                   estimators have the same or close accuracy.
sequence. Generally CFO estimation will be switched
between two operation modes, the first called acquisition                                                V.   SIMULATION RESULTS
mode and the other is tracking mode. In the acquisition mode,                    In order to examine the synchronization performance,
a wide range of CFO can be estimated and the remaining                        number of simulation experiments will be performed for the
CFO should be much less than half of the space between                        proposed synchronization scheme and that described in [9].
subcarriers. During the tracking mode only small frequency                    Results reported here are carried out using Matlab©. There are
fluctuations will be dealt with                                               a number of parameters that describe the system. In the
  A.      CFO Acquisition                                                     simulations, the following parameters are held constant:
                                                                              (1) Length of the training sequences: L = 1024.
   CFO acquisition is performed only once when the
                                                                              (2) Normalized CFO factor=0.5, that uniformly distributed
transmissions begin. Therefore, the time of acquisition is not
                                                                              within ±0.5 subcarrier spacing.
critical. When there is no channel fading and noise, the
                                                                              (3) The multipath channel consists of six paths that have
relationship between corresponding samples from different
                                                                              uniformly distributed delays over the interval [0, 2π].
Chu or Zadoff sequences in a received training sequence on
                                                                              (4) Results are calculated for a 6x6 MIMO-OFDM system
the same antenna is given by:
                                                                              under the assumption of ideal modulation.

                                                                                                                   ISSN 1947-5500
                                                                                       (IJCSIS) International Journal of Computer Science and Information Security,
                                                                                                                                          Vol. 9, No. 1, 2011

The performance of the estimator is evaluated by the Mean-                                                   10
                                                                                                                                                         PN sequence,single-g,g=2
Square Error (MSE) of the frequency offset estimates. The
                                                                                                                                                         chu code,g=2
MSE for the p-th transmit antenna is defined as                                                              10
                                                                                                                                                         PN sequence,m=4,g=3,4,5,6
                               N matlab
                       1                                      2                                                                                          chu code,m=4,g=3,4,5,6
MSE p =
                    N matlab
                                 ∑          ε est , p − ε p           (9)
                                 i =1                                                                        10

Where ε est , p (i ) the frequency is offset estimate obtained in

the i-th Matlab                trial, and N matlab is the total number of
Matlab trials.                                                                                               10

   In the first simulation experiment, comparison results of
using PN and zadoff sequences in AWGN channel are shown                                                           -8
in Fig.(3). Single-g estimator (g=1) (acquisition) and multiple-
g estimators (m=2, g=2, 3) (tracking) are considered for both
used sequences. The using preamble consists of four repeated                                                 10
                                                                                                                     -5       0   5      10         15          20       25           30
sequences and, N=256 (the period length of training                                                                                           SNR
sequence). It can be shown that in acquisition stage                                                       Fig.4. MSE versus SNR for PN and Chu sequence in acquisition and
performance of zadoff sequence better than PN sequence. In                                                                     tracking in AWGN ch.
the tracking mode it is obvious that using zadoff sequence                                                 10
                                                                                                                                                           Pn sequence,single-g,g=1
improves the estimation of CFO.                                                                                                                            Frank code,single-g,g=1
           -3                                                                                                -3
          10                                                                                               10                                              Pn sequence,m=2,g=2,3
                                                                   Pn sequence,single-g,g=1                                                                Frank code,m=2,g=2,3
                                                                   Frank code,single-g,g=1
           -4                                                                                                -4
          10                                                       Pn sequence,m=2,g=2,3                   10
                                                                   Frank code,m=2,g=2,3

           -5                                                                                              10


           -6                                                                                              10

           -7                                                                                              10

           -8                                                                                              10
          10                                                                                                    -5        0       5      10         15         20        25           30

                                                                                                             Fig. 5 MSE versus SNR for PN and zadoff sequence in acquisition
          10                                                                                                                  and tracking in multipath ch.
               -5          0            5         10          15       20        25           30
                                                       SNR                                             The other side in our simulation experiment is examining
          Fig.3. MSE versus SNR for PN and zadoff sequence in acquisition
                          And tracking in AWGN ch.
                                                                                                    the sequences influence in the estimation with the effect of the
                                                                                                    multipath channel described before.In Fig.(5) and Fig.(6) the
   To obtain the results of Fig.(4), simulation experiment                                          same parameters mentioned before are assumed for
results run using Chu sequences compared with PN sequences                                          simulating, but with the effect of multipath channel. The better
in AWGN channel. The using preamble structured of 8                                                 performance comparison of zadoff code and Chu code with
repeated sequences (N=128.). Single-g estimator (g=2)                                               PN sequence is demonstrated.
(acquisition) and multiple-g estimators (m=4, g=3, 4, 5, 6)                                            From all previous simulation experiments, it can be seen
(tracking) are considered for both PN and Chu sequences. The                                        that the performance of zadoff and Chu sequences is identical;
comparison obviously illustrates that Chu sequence performs                                         they are nearly with the same trend, with same variations in all
much better in acquisition stage and it is more accurate for low                                    the simulation experiments depicted previously.
and high different value of ‘‘g’’ in tracking stage.                                                   In general both sequences impact on the offset estimation
   From Figs.3 and 4, it can be seen that the performance of                                        performance nearly the same, which gives wide choices to
zadoff and Chu sequences in multiple-g estimator is better                                          enhance the system performance, the proposed preamble using
than that of single-g estimator. Both sequences impact on the                                       either zadoff sequence or chu sequence as training sequence is
offset estimation performance nearly the same, which gives                                          more robust and accurate from two sides. The first one is its
wide choices to enhance the system performance.                                                     superior performance and the other is saving required time

                                                                                                                                      ISSN 1947-5500
                                                                                   (IJCSIS) International Journal of Computer Science and Information Security,
                                                                                                                                      Vol. 9, No. 1, 2011

which makes the system more accurate especially with                                         [3]   Time and Frequency Offset in OFDM Systems,” IEEE Trans. Signal
                                                                                                   Processing, vol. 45, pp. 1800-1805, July 1997.
existing of the multipath effects
                                                                                             [4] P. H. Moose, “A Technique for Orthogonal Frequency Division
            10                                                                                     Multiplexing Frequency Offset Correction,” IEEE Trans. Commun., vol.
                                                       PN sequence,single-g,g=2                    42, pp. 2908-2914, October 1994.
                                                       chu code,g=2                          [5] T. M. Schmidl and D. C. Cox, “Robust Frequency and Timing
            10                                         PN sequence,m=4,g=3,4,5,6                   Synchronization for OFDM,” IEEE Trans. Commun., vol. 45, pp. 1613-
                                                       chu code,m=4,g=3,4,5,6                      1621, December 1997.
                                                                                             [6] F.Tufvesson, M. Faulkner and O. Edfors, “Time and frequency
                                                                                                   synchronization for OFDM using PN-sequence preambles,” Proceedings
                                                                                                   of IEEE Vehicular Technology Conference, Amsterdam, September 19-
                                                                                                   22, pp. 2203-2207, 1999.

                                                                                             [7] A. N. Mody and G. L. Stuber, “Receiver Implementation for a MIMO
                                                                                                   OFDM System,” Proc. of IEEE GLOBECOM 2002, vol. 1, pp. 716-720,
                                                                                                   November 2002.
                                                                                             [8] T. C. W. Schenk and A. Van Zelst, ‘’Frequency Synchronization for
                                                                                                   MIMO OFDM Wireless LAN Systems,” Proc. of IEEE VTC 2003-Fall,
            10                                                                                     vol. 2, pp. 781-785, October 2003.
                                                                                              [9] Y. Yao, and Tung-Sang Ng, “Correlated-Based Frequency offset
                                                                                                   Estimation in MIMO System”, Proc. IEEE Vehicular Technology
            10                                                                                     Conference Fall 2003 (VTC Fall 2003), Orlando (FL), 6-9 October
                 -5    0        5      10         15          20       25          30              2003.
                                                                                              [10] LimingHe,       “Frequency Synchronization in MIMO OFDM Systems,”
             Fig.6 MSE versus SNR for PN and Chu sequence in acquisition                           Wireless Communications Networking and Mobile Computing
                           and tracking in multipath ch                                            Conference (WICOM), China, 2010.

                              VI.    CONCLUSION                                              [11] R. Frank, and S Zadoff, ‘’Phase Shift Pulse Codes With Good Periodic
                                                                                                  Correlation Properties,‘’IRE Trans. on Inform. Theory, IT-8, 381–382,
    A new CFO synchronization method for MIMO-OFDM                                                1962.
systems with modified preamble method using repeating                                        [12] D. C. Chu, “Polyphase Codes With Good Periodic Correlation
                                                                                                  Properties,” IEEE Trans. Info. Theory 18,531-532 (July 1972).
CAZAC sequences is carried out. The performance of a two
stage synchronization structure has been studied. Simulation                                 [13] R. C. Heimiller, “Phase Shift Pulse Codes With Good Periodic
results show that fast and robust synchronization can be                                          Correlation Properties,” IRE Trans. Info. Theory IT-6, 254- 257
                                                                                                  (October 1961).
established. The proposed method enhances the
synchronization performance even under low SNR. The new
method surpasses the traditional one using regular PN
sequences in both the AWGN channel and multipath channel.
It achieves better performance without consuming much
computation time. This is considered a very important feature
in wireless communication systems in general.

[1]    WILLINK T.J.: ‘MIMO OFDM for broadband fixed wireless access’,
       IEEE Proc. Commun., 2005, 152, (1), pp. 75–81
[2]    J. Van de Beek, M. Sandell, and P. O. Brjesson, “ML Estimation of

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