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(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
23 http://sites.google.com/site/ijcsis/
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( jk ,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
i0
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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(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,
L1
' ( ( S N )) Re( FP ( (S N ))) Im( FP ( (S N )))
( ( S N )) ( ( SN ) w).
w0
(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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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
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Vol. 9, No. 9, September 2011
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