Carrier Offset Estimation for MIMO-OFDM Based on CAZAC Sequences

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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
*
d_samaha@hotmail.com

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-

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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
maximum:
Tx Rx OFDM
L −1 2
OFDM Nt Nr
∑
DemodNr
ModNt
x0 = sn (3)
n=0
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

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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)
2πgN
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
N
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
L
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
IV. FREQUENCY SYNCHRONIZATION ALGORITHM
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.

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-3
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
-4
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)
-5
i =1 10

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

MSE
-6
10
©
the i-th Matlab trial, and N matlab is the total number of
©
Matlab trials. 10
-7

In the first simulation experiment, comparison results of
using PN and zadoff sequences in AWGN channel are shown -8
10
in Fig.(3). Single-g estimator (g=1) (acquisition) and multiple-
g estimators (m=2, g=2, 3) (tracking) are considered for both
-9
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.
-2
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
MSE

-5
-5 10
10

-6
MSE

-6 10
10

-7
-7 10
10

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

-9
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

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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
-2
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
-3
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.
-4
[6] F.Tufvesson, M. Faulkner and O. Edfors, “Time and frequency
10
synchronization for OFDM using PN-sequence preambles,” Proceedings
of IEEE Vehicular Technology Conference, Amsterdam, September 19-
22, pp. 2203-2207, 1999.
MSE

-5
10
[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,
-6
10
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,
-7
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
-8
10 Conference Fall 2003 (VTC Fall 2003), Orlando (FL), 6-9 October
-5 0 5 10 15 20 25 30 2003.
SNR
[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.

REFERENCES
[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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