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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) 24 http://sites.google.com/site/ijcsis/ 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 25 http://sites.google.com/site/ijcsis/ 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, 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 . 26 http://sites.google.com/site/ijcsis/ 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 time and frequency offset in OFDM systems,” IEEE Trans. Signal Processing, vol.45, no. 7, pp.1800-1805, July 1997. [3] Guo Yi, Liu Gang and Ge Jianhua, “A novel time and frequency synchronization scheme for OFDM systems,” IEEE Transactions on Consumer Electronics. vol.54, no.2, pp.321-325, 2008. 27 http://sites.google.com/site/ijcsis/ ISSN 1947-5500 (IJCSIS) International Journal of Computer Science and Information Security, Vol. 9, No. 9, September 2011 [4] Juan I. Montojo and Laurence B. Milstein, “Effect of Imperfections on [9] Sen, S. Chakrabarti, and R.V. 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India.pp. 5-10, 2008. 2005, vol.54, no.5, pp.1528-1545. [7] Xiaoyan Wang, Zaichen Zhang and Chuanyou Chen,” A Robust Time [13] S. Johansson, M. Nilsson, and P. Nilsson, “An OFDM timing Synchronization Scheme for MB-OFDM UWB System,” IEEE synchronization ASIC,” in Proceedings of IEEE ICECS, December International Conference on Signal Processing Systems. Dalian, pp.529- 2000, pp. I.324-I.327. 532, 2010. [14] Dardari and M. Z. Win, “Threshold-based time-of-arrival estimators in [8] M.N. Suresh, D.C. Mouli, M.G Prasath, V. Abhaikumar and S.J. UWB dense multipath channels,” in Proceedings of IEEE ICC, June Thiruvengadam, “Symbol timing estimation in multiband OFDM based 2006, pp. 4723-4728. ultra wideband system,” IEEE International Conference on Signal Processing and Communications, India, pp. 1–4, 2010. 28 http://sites.google.com/site/ijcsis/ ISSN 1947-5500

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