Robust Brute Force and Reduced Complexity Approaches for Timing Synchronization in IEEE a/g WLANs

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1 Robust Brute Force and Reduced Complexity Approaches for Timing Synchronization in IEEE a/g WLANs Leïla Nasraoui 1, Leïla Najjar Atallah 1, Mohamed Siala 2 1 COSIM Laboratory, 2 MEDIATRON Laboratory Higher School of Communications, University of Carthage, Tunisia s: nasraouileila@supcom.rnu.tn, leila.najjar@supcom.rnu.tn, mohamed.siala@supcom.rnu.tn Abstract This paper applies a recently proposed efficient technique that has been conducted regarding timing synchronization in OFDM systems, to the IEEE a/g standards. The time synchronization is fulfilled using the structure specificity of the short training sequence of IEEE a/g preamble. Two versions of the applied technique are considered: a singlestage brute force approach, which carries differential correlation exclusively, and a two-stage reduced complexity approach comprising coarse and fine stages. The coarse synchronization is achieved using sliding correlation, characterized by its low computational load, whereas the fine synchronization is realized by differential correlation, characterized by its high computational load and carried around the coarse time estimate. In the two stage approach, the combined use of sliding correlation and differential correlation, carried for short interval, results in an overall reduced complexity approach. Simulation results show that, applied in the IEEE a/g norm, both of the considered approaches provide accurate time synchronization in the AWGN and multipath channels. Moreover, the two-stage version has a low computational load, which makes it suitable for fast symbol timing synchronization in bursty IEEE a/g OFDM systems. Index Terms IEEE a/g, OFDM, time synchronization, sliding correlation, differential correlation I. INTRODUCTION Thanks to its strong ability in combating multipath fading implied by high data rate transmission over frequency-selective channels, OFDM has been used in most of the modern communication systems [1]. Among them, we here study the standards IEEE a/g adopted in Wireless Local Area Networks (WLAN). They support a data rate up to 54 Mb/s and operate in the 5 GHz and 2.4 GHz bands respectively, employing a bursty transmission mode [2] [3]. In packetized data transmission, even if the insertion of a Cyclic Prefix (CP) avoids Inter Symbol Interference (ISI), incorrect positioning of the Fast Fourier Transform (FFT) window within an OFDM symbol reduces the tolerance to large delay spread channels. Time synchronization is therefore an important tasks that must be performed at IEEE a/g receivers. The synchronization process in IEEE a/g standards exploits a preamble with a specific structure, known at the receiver, which has been carefully designed to provide enough information for a good /13/$31.00 c 2013 IEEE synchronization performance. Indeed, the preamble contains two parts with respectively 10 repeated short and 2 repeated long symbols as shown in Fig. 1. Many synchronization techniques, originally proposed for general OFDM systems [4]-[6] can be applied to IEEE a/g WLANs. However, these techniques may lead to unsatisfactory performance especially in the presence of multipath effects. Other techniques that are specifically designed for IEEE a/g WLANs have been reported in [7]-[11]. In the IEEE a/g standards, the timing synchronization process is split into an initial coarse synchronization stage (packet detection) and a later fine one (frame start detection). A coarse metric, based on auto-correlating the received signal, is used for packet detection. For the frame start detection, a fine metric based on cross-correlating the received signal with the short symbol part is used. The same principles of exploiting the preamble repetitive structure and splitting into two stages were adopted in the technique proposed in [12] and [13] respectively for the Additive White Gaussian Noise (AWGN) and multipath channels. Two versions of this technique are possible. The first one, referenced by Brute Force (BF) single-stage approach, calculates a metric based on differential correlation leading to a high complexity. The second one, referenced by Reduced Complexity (RC) two-stage approach, calculates a coarse metric based on simple sliding correlation to determine an uncertainty interval over which the fine metric, based on differential correlation, is carried. The performance of this technique (in terms of detection accuracy and computational load) was appreciated in the general OFDM case. This work focuses on the suitability of the technique proposed in [12] and [13] to time synchronization for the standards IEEE a/g. Indeed, the repetitive structure of the short and long preamble symbols allows a flexible synchronization processing, respecting the considered scheme that is based on a two identical part preamble. Even if the two IEEE a/g preamble parts (short and long symbols) can be used by our scheme, in this work we consider the part composed of 10 short symbols. This paper is organized as follows. Section II describes the IEEE a/g signal and synchronization process. In section III, the considered timing synchronization approaches

2 are described. Simulation results and comparison are provided in section IV. Finally, the conclusion of the paper is drawn in section V. II. IEEE A/G STANDARDS DESCRIPTION A. IEEE a/g signal The IEEE a/g standards consider an OFDM system that employs N IFFT points for the transmission of complex mapped data X(k) in parallel data streams modulating N u sub-carriers. The n th time domain sample of the OFDM symbol is then expressed as x(n) = 1/ N N u 1 X(k)e j2πkn/n n = 0, 1,..., N 1. (1) The CP prepended OFDM symbol is of length N = N u + N g samples. In the standards IEEE a/g, N = 64, N u = 52 (including 4 pilot sub-carriers) and N g = 16. The time domain symbols are then D/A converted, RF modulated and transmitted. At the receiver, the reciprocal operations are performed to reconstruct the baseband signals. The received signal after multipath channel propagation is expressed as N h 1 r(n) = e j2πνn/n i=0 h(i)x(n i τ) + ω(n), (2) where h(i) is the sampled complex channel impulse response, N h is the channel memory length, τ is the time offset normalized with respect to the sampling period, ν is the normalized carrier frequency offset with respect to the subcarriers spacing and ω(n) is complex white Gaussian noise. Since IEEE a/g transmits packets in a bursty manner, synchronization is a crucial issue. To help the receiver to accomplish synchronized reception, the preamble presented in Fig. 1 is sent at the beginning of each transmitted packet. The IEEE a/g preamble is carefully designed to be B. IEEE a/g synchronization The timing estimation is usually divided into packet detection known as coarse synchronization and symbol detection known as fine synchronization. According to the standards IEEE a/g, the received signal is auto-correlated with a delayed version of it to accomplish initial coarse timing synchronization as expressed in the metric C (n) = r(n + k)r (n + k + D), (3) where D = 16 samples is the length of the short symbols. Once the packet detector has estimated the start of the packet, the symbol timing algorithm refines the estimate to samplelevel precision. In the standard, short symbol t 1 is used instead of a delayed version of the received signal to perform crosscorrelation as F (n) = r(n + k)t 1(k). (4) Both coarse metric C(n) and fine metric F (n) are normalized by the received signal energy given by R(n) = r(n + k + D) 2. (5) As shown in Fig. 2, the auto-correlation of the received signal creates a plateau whose length equals the length of 9 short symbols, whereas the correlation with the known symbol t 1 creates peaks at the start of each short symbol. If the correlation peaks are within the plateau, the last peak is used as the beacon position from where the start of the next symbol is determined. Fig. 1. IEEE a/g preamble [2]. used for synchronization. It consists of two parts: the first with 10 short repeated symbols and the second with two long repeated symbols, as illustrated in Fig. 1. The short training symbols are denoted by t 1 to t 10, each of length D = 16 samples (0.8µs), whereas T 1 and T 2 denote the long training symbols, of length 64 samples each (3.2µs), preceded by a 32-sample CP (1.6µs). The total preamble length is 320 samples (16µs). These symbols are used for multiple processing in the receiver, including frame synchronization, Automatic Gain Control (AGC) level setting, carrier frequency offset estimation, symbol timing synchronization and channel estimation [2]. The training preamble is followed by the signal field and data. Fig. 2. Coarse and fine timing metric using short symbols in ideal channel. III. SURVEY IN TIME SYNCHRONIZATION In this section, we briefly describe the considered synchronization technique that was proposed in [12] and [13] and its

3 adjustment to the IEEE a/g. As this approach requires a preamble with two repetitive parts, both short and long preamble symbols can be used for time synchronization. In this paper, we consider the short symbols part, which offers a flexible choice of the twice repeated part. The use of the first short symbols is also justified by its earlier transmission to allow other reception tasks (frequency synchronization, channel estimation,...) that exploit the long preamble symbols. Exploiting the IEEE a/g preamble structure, many synchronization approaches which use similar metrics, specifically designed for the standard, were proposed [8]-[10]. We consider the approach proposed in [12] and [13], which uses a preamble of two identical parts and achieves the synchronization in either a single-stage brute force approach or a twostage reduced-complexity approach. The ten repetitive short symbols of the IEEE a/g preamble are considered as two repetitive parts of five short symbols each. A. Brute Force approach In the single-stage BF approach, differential correlation is exclusively used during the synchronization process to calculate the metric M (n) = L u 1 α (k)y (k + n), (6) where L u stands for the chosen preamble repetitive part length and Y is a differentially modulated version of the received signal defined as Y (n) = r (n)r(n + q), (7) where q is the correlation shift that must be different from 0 and L u multiples and α is the encoding sequence generated from the preamble as α(n) = t(n) t(n + q), n [0, L u 1], (8) where t = [t 1,..., t 5 ] is the repetitive part of the preamble. The metric in (6) is also normalized by the energy calculated similarly to (5), over the corresponding correlation window of width (D = L u ). The time estimate ˆτ is selected as the argument that maximizes the normalized version of M. The metric leads to a pronounced sharp peak thus increasing the estimation accuracy. However, it is costly in terms of computational load due to the differential correlation carried during the synchronization process. B. Reduced Complexity approach To reduce the complexity of the differential correlation operations keeping the accuracy provided by them, the idea was to split in two stages. In the first stage, a Cox and Schmidllike metric (CS) [4], based on sliding correlation characterized by its low complexity, is calculated to provide the coarse estimate ˆτ c. This metric exhibits a plateau of length equal to the CP length minus the channel impulse response length, which leads to an ambiguity in the frame start detection. In the second stage, a differential correlation based metric is calculated as in (6), over a short interval τ around the coarse time estimate ˆτ c. The differentially modulated version of the received signal Y in (7) is here calculated over the interval [ ˆτ c τ/2 + 1, ˆτ c + τ/2 + L u ]. The combined use of a coarse synchronization metric of low computational load and a fine synchronization metric of high computational load that is calculated for short interval, results in an overall reduced complexity approach. It is worth to note that depending on the repetitive part length L u, the coarse and the fine metric shapes change. As shown in Fig. 3 (a), using a length L u = 5D, without considering any CP, the coarse metric has wide shape and exhibits a single peak corresponding to the start of the preamble, which we consider as a coarse estimate ˆτ c. Around this peak, the fine metric is carried over a limited interval, leading to a high sharp peak at the same time index. In Fig. 3 (b), we consider the first 2 short symbols (t 1 and t 2 ) as the CP of the first preamble part. The useful part is then composed of two identical parts, each of length L u = 4D. The coarse time estimate ˆτ c is taken N g /2 sample following the middle of the plateau, exhibited in the metric, whose length is 2D. The peak offered by the fine metric here indicates the start of the 3 rd short symbol corresponding to the useful part of the preamble. Fig. 3. Coarse and fine timing metric of the RC approach using the short symbols with different correlation delays: (a) L u = 5D, (b) L u = 4D. We notice that, going on calculating the coarse metric, the long symbol also allows a synchronization respecting the RC approach (using the second metric plateau in Fig. 3 (b)) [12]. For the considered IEEE a/g systems, we use the first preamble part to achieve an early time synchronization

4 thus allowing the processing of the other processes (carrier frequency offset estimation, channel estimation) that use the second preamble part and must be carried after time synchronization. C. Optimized algorithm In [8], symbol timing synchronization algorithms for OFDM system based on IEEE a were put forward. Some of them are based on energy detection and other based on crosscorrelation that exploits the repetitive structure of the preamble. Among them, we choose as benchmark an optimized algorithm that uses one period of short training symbol in the IEEE a preamble. As the real part and the imaginary part of the former 8 data and the latter 8 data in each short symbol (t n, n [1, 10]) can be exchanged, the optimized algorithm decreases the period of short training symbol to 8 sampling points. The metric proposed by this algorithm is given by R(n) = 7 r n k (imag(r n k 8 ) + (j real(r n k 8 )). (9) This algorithm can make sure that frame synchronization detection has been finished when the first short training sequence symbol is coming. A. Parameters IV. SIMULATION RESULTS AND DISCUSSION The performances of the considered methods are evaluated by computer simulation respecting the Monte Carlo method. A selection of the parameters of the OFDM system according to IEEE a/g standards is listed in Table 1 The OFDM TABLE I PARAMETERS FOR THE OFDM IEEE A/G SYSTEM Parameter value Number of IFFT points, N 64 Number of used sub-carrier, N u 52 Number of data sub-carriers 48 Cyclic prefix duration, N g 16 Modulation QPSK following sequence L [2] L 26,26 = [0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0]. We consider the cases of AWGN and exponential power delay profile multipath channels. Two multipath channels are used, having respectively 4 and 6 uniformly spaced paths with regular normalized path delays of 4 and 2 samples, resulting in a channel memory length of 16 samples for both channels. The ratio of the first tap to the last tap is set to 15 db with a constant adjacent path gains ratio. The uncertainty interval τ is set to the CP length (32 samples). B. Performance evaluation The performance is here evaluated in terms of Correct Detection Rate (CDR), defined as the percentage of realizations where ˆτ f coincides with the correct frame start (no error tolerance). This latter corresponds to the start of the second short training symbol as presented in the Fig. 3 (a). In addition to the Brute-Force (BF) and Reduced-Complexity (RC) approaches, we consider as benchmark the IEEE a/g standards synchronization approach, Cox and Schmidl algorithm [4] (also corresponding to the coarse synchronization) and the optimized algorithm proposed in [8]. Fig. 4 presents the CDR in the monopath AWGN channel. As in the general case of OFDM systems, the considered BF and RC approaches provide satisfactory detection accuracy and outperform the processing employed in the standards IEEE a/g WLAN. Indeed, even at low SNR (< 0 db) the detection is good and it becomes perfect (CDR=100% ) above an SNR of 1 db. For an SNR lower than 8 db, the considered technique outperforms the standard and it realizes a gain of about 7 db for a target CDR of about 90 %. Compared to signal specified in the standard [2], comprises 52 sub-carriers numbered from 26 to 26 with no DC component. For the short OFDM training symbol, transmission is confined to the sub-carriers whose numbers are multiples of four, so that only 12 sub-carriers are used, which are modulated by the elements of the sequence S, given by [2] S 26,26 = ( 13/6) [0, 0, 1 + j, 0, 0, 0, 1 j, 0, 0, 0, 1 + j, 0, 0, 0, 1 j, 0, 0, 0, 1 j, 0, 0, 0, 1 + j, 0, 0, 0, 0, 0, 0, 0, 1 j, 0, 0, 0, 1 j, 0, 0, 0, 1 + j, 0, 0, 0, 1 + j, 0, 0, 0, 1 + j, 0, 0, 0, 1 + j, 0, 0]. The multiplication by a factor of 13/6 is to normalize the average power of the resulting OFDM symbol, which uses only 12 out of 52 sub-carriers. All sub-carriers are used to generate the long preamble symbol, which consists of 53 sub-carriers that are modulated by the elements of the Fig. 4. Correct Detection Rate of the symbol start in the monopath AWGN channel. the BF and RC approaches, the optimized algorithm provides lower detection rate for all SNR ranges, but for a very low

5 SNR (< 2 db), it outperforms the standard. The CS approach provides the worst detection rate and its curve stagnates at a target CDR of about 90 %, reached from an SNR of 15 db. We note that the BF approach provides a CDR slightly better than the RC approach at the expense of much higher computational load. Fig. 5 and Fig. 6 show the CDR of the previously cited approaches achieved in the multipath channels CI (4-tap channel) and CII (6-tap channel). Due to the multipath effect, the detection of all the considered approaches are degraded. Under the same conditions the RC and BF approaches achieve more or less the same detection performance and outperform the other techniques. It is worth to note that in the simulation we tolerate an error of 2 samples for only the CS approach, which has the worst detection rate. Generally, when applied to the OFDM IEEE a/g system and in both AWGN and multipath channels, the studied technique (in its two versions: BF and RC), provides satisfactory detection accuracy even at very low SNR. The capability of the optimized algorithm is not as satisfactory as the standardized algorithm because of the half sampled points used but it has lower complexity. Fig. 5. Correct Detection Rate of the frame start in 4-tap multipath power delay profile channel. V. CONCLUSION In this paper, we evaluated an OFDM symbol timing synchronization technique, according to the short preamble symbols defined by the standards IEEE a/g. The studied technique exploits the repetitive structure of the preamble and can be applied in its two versions. Namely, the single-stage brute-force and two-stage reduced-complexity approaches. The first one uses differential correlation exclusively that yields to high computational load, whereas the latter one uses sliding correlation in the coarse stage and differential correlation in the fine stage. The combined use of sliding and differential correlations and the designed metric provide a satisfactory performance in terms of detection accuracy and complexity. Fig. 6. Correct Detection Rate of the frame start in 6-tap multipath power delay profile channel. Simulation results proved the robustness of the studied technique in both AWGN and multipath channels and showed that it outperforms the synchronization processing specified by the IEEE a/g standards and other algorithms considered as benchmark. REFERENCES [1] R. Prasad, OFDM for wireless communications systems, Artech House, [2] IEEE standard a: Wireless LAN medium access control (MAC) and physical layer (PHY) specifications: high-speed physical layer in the 5 GHz band, December [3] IEEE standard g: Wireless LAN medium access control (MAC) and physical layer (PHY) specifications: Further Higher Data Rate Extension in the 2.4 GHz Band, June [4] T.M. Schmidl and D. Cox, Robust frequency and timing synchronization in OFDM, IEEE Trans. on Comm., vol. 45, pp , Dec [5] J.-J. Kim, Y.-J. Ryu, H.-S. Oh and D.-S. Han, Frame selection algorithm with adaptive FFT input for OFDM systems, in Proc. ICC, vol. 1, pp , April [6] H. Minn, V. K. Bhargava and K. B. Letaief, A novel timing estimation method for OFDM systems, IEEE Trans. Comm., vol. 2, no. 4, pp , July [7] G. Liu, J. Liy and G. B. Giannakis, Joint Symbol Timing and Channel Estimation for OFDM Based WLANs, IEEE Letter vol. 5, pp , Aug [8] H. Yuan, X. Hu and Y. Ling New symbol synchronization algorithms for OFDM systems based on IEEE a, in Proc. IEEE ICII, pp , July [9] S. Wensheng and Z. Yuanyuan, A Frame Synchronization and Symbol Timing Synchronization Algorithm in Burst OFDM Communication Based on IEEE a, IFITA, vol. 1, pp , May [10] K. Chen, J. Lu, W. Xia, J. Zhang, S. Huang and Y. Ma Synchronization Algorithm of an OFDM-based IEEE a Transmission System, Global Mobile Congress, pp. 1-5, Oct [11] C. L. Nguyen, A. Mokraoui, P. Duhamel and N. Linh-Trung Time synchronization algorithm in ieee a communication system, in Proc. EUSIPCO, pp , Aug [12] L. Nasraoui, L. Najjar Atallah, and M. Siala, An Efficient Reduced- Complexity Two-Stage Differential Sliding Correlation Approach for OFDM Synchronization in the AWGN Channel, in Proc. IEEE VTC- Fall, pp. 1-5, Sept [13] L. Nasraoui, L. Najjar Atallah, and M. Siala, An Efficient Reduced- Complexity Two-Stage Differential Sliding Correlation Approach for OFDM Synchronization in the Multipath Channel, in Proc. IEEE WCNC, pp , April 2012.

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