A Low-Complexity Joint Time Synchronization and Channel Estimation Scheme for Orthogonal Frequency Division Multiplexing Systems Chin-Liang Wang Department of Electrical Engineering and Institute of Communications Engineering National Tsing Hua University Hsinchu, Taiwan 33, Republic of China E-mail: clwang@ee.nthu.edu.tw Hung-Chin Wang Institute of Communications Engineering National Tsing Hua University Hsinchu, Taiwan 33, Republic of China E-mail: d9963@oz.nthu.edu.tw Abstract In this paper, a novel training sequence structure along with a joint time synchronization and channel estimation scheme for orthogonal frequency division multiplexing (OFDM systems is proposed. The proposed training sequence structure is composed of an orthogonal sequence attached by cyclic prefix and cyclic postfix. Both the lengths of the cyclic extensions attached are chosen to be longer than the maximum delay spread of the wireless channel. Based on the unique structure of the training sequence, we present a low-complexity joint time synchronization and channel estimation scheme. Unlike conventional methods, which require either discrete Fourier transform (DFT operations or matrix inversions to acquire channel impulse response (CIR information, the proposed scheme requires only a correlator and a comparator. At the expense of the same training sequence overheads, computer simulation results show that the proposed joint scheme outperforms conventional time synchronization methods by orders. Furthermore, the overall bit error rate (BER performance of the proposed joint scheme is shown to be close to the ultimate bound characterized by perfect synchronization and channel estimation. The proposed joint scheme also provides significant BER performance gain as compared to a scheme that properly combines a conventional synchronization method with a DFT-based channel estimation method. Keywords-Orthogonal frequency division multiplexing (OFDM; synchronization; channel estimation; training sequence I. INTRODUCTION Orthogonal frequency division multiplexing (OFDM has been shown to be suitable to support high-rate wireless applications due to its high spectrum efficiency and robustness against frequency selective fading channels. In recent years, OFDM has received considerable attention and already been selected as standards for various wireless applications, such as the IEEE 82.a wireless local area networks (WLAN [], high performance local area networks (HIERLAN/2 [2], digital audio broadcasting (DAB [3], and digital video broadcasting (DVB [4]. OFDM is a multicarrier technique that divides the available bandwidth into several narrowband subchannels (subcarriers. Unlike conventional multicarrier techniques that adopt guard bands between adjacent subchannels to prevent interference among subchannels, the spectra of subchannels in OFDM systems are overlapped in an orthogonal manner to achieve higher spectrum efficiency. Accordingly, the orthogonality among subcarriers must be carefully maintained in order to prevent intercarrier interference (ICI in OFDM systems. The fundamental idea of OFDM technique is to partition a high-rate data stream into several lower-rate data streams, which can be then transmitted simultaneously over the parallel subchannels of the OFDM system. As a result, the corresponding symbol duration will be increased and the relative amount of intersymbol interference (ISI caused by multipath delay spread of the channel will thus be decreased. In order to eliminate the residual effect of ISI and preserve the orthogonality among subcarriers, a guard time called cyclic prefix (C is appended in front of each OFDM symbol. The C is exactly a replica of the last portion of the original OFDM symbol. OFDM systems are more sensitive to synchronization errors as compared to conventional single carrier systems and require synchronization in both time and frequency. Time synchronization decides where to place the discrete Fourier transform (DFT window in order to demodulate the received and down-converted OFDM signal. Frequency synchronization involves estimating and compensating the effect of carrier frequency offset (CFO, which is mainly caused by the mismatch of transmitter and receiver oscillators in indoor applications. Any amount of CFO destroys the orthogonality among subcarriers and thus introduces ICI that may considerably degrade the overall system performance. In order to acquire accurate synchronization and channel estimation results, which are necessary for coherent demodulation to OFDM signals, training sequences (preambles are often adopted especially in WLAN applications. Most training sequences are designed to be either periodic in the time-domain [], [2] or composed of elements with special properties [5]. However, joint designs of both the repetition structure and the elements of the training sequence are scarcely investigated. Most conventional synchronization techniques for OFDM systems are developed based on special repetition structures of time-domain training sequences [6]-[8]. These methods tend to locate the arrival time of the channel s strongest path. However, This work was supported by the National Science Council of the Republic of China under Grants NSC 93-223-E-7-97 and NSC 94-223-E-7-33.
the strongest path may not be the first path, and the arrival time of the first path is actually what we consider as the correct timing instant. Such a critical problem has limited the performance of the above-mentioned methods. In order to solve the above-mentioned problem, information about the channel impulse response (CIR is needed. However, such information cannot be obtained before synchronization stage. In [9], the authors have presented a CIR estimation method that is robust against synchronization errors. Through the CIR estimate, the accuracy of the time estimator can be further enhanced. In [], an algorithm that simultaneously adjusts symbol timing and the corresponding CIR estimate that based on it has been proposed. An initial timing instant that is prior to the correct timing instant should be obtained first. Start with this initial timing instant, each timing instant leads to a corresponding CIR estimate. By finding the timing instant along with the CIR estimate that minimizes the criterion based on maximum-likelihood (ML and the generalized Akaike information criterion (GAIC, the final estimates of symbol timing and CIR are determined simultaneously. However, for each timing instant within the observation range, the corresponding CIR estimate must be recomputed. In addition, both the received signal and the CIR estimate obtained by a particular timing instant must be transformed into frequency-domain by DFT to find out whether they minimize the criterion. In other words, the total DFT operations required will be proportional to the observation range. In this paper, we propose a low-complexity joint time synchronization and channel estimation scheme for OFDM systems based on a novel training sequence structure. The kernel of the proposed training sequence structure is an orthogonal sequence. By attaching sufficiently long cyclic prefix and cyclic postfix to the orthogonal sequence, the crosscorrelation function between the received training sequence and the original orthogonal sequence will contain a segment that approximates to the CIR. Unlike the methods described in [9] and [], both the symbol timing and the CIR estimate can be obtained jointly by a simple correlator and a comparator due to the unique training sequence structure. II. THE KERNEL OF THE ROOSED SCHEME A. Orthogonal Sequences A finite length sequence {g(, g(,, g( }, is said to be an orthogonal sequence if and only if its autocorrelation function satisfies gg ( i= δ ( (( d ( R d g i+ d g i = (( d, for = =, elsewhere where the notation (( represents the operation of modulo and g ( i denotes the complex conjugate of g( i. ( B. A Conventional Training Sequence Structure In [5], Mody and Stüber have utilized the modulatable orthogonal sequences, which are proposed by Suehiro and Hatori [], to form a training sequence structure suitable for synchronization in multiple-input multiple-output (MIMO OFDM systems. Different classes of modulatable orthogonal sequences are used as identifications to signals transmitted by different antennas. In addition, each modulatable orthogonal sequence is cyclically prefixed before transmission. The modulatable orthogonal sequences are polyphase orthogonal sequences which remain orthogonal when modulated by complex numbers of unity absolute value. The period (length of a modulatable orthogonal sequence must be the square of a natural number. In the following, we investigate properties of a particular arrangement of a -point orthogonal sequence attached by exactly points cyclic prefix where L denotes the number of effective paths of a sample-spaced multipath channel h L =[h(, h(,, h(]. Let g =[g(, g(,, g( ] denote the orthogonal sequence, and [g( L+, g( L+2,, g( ] be the cyclic prefix namely g(n=g(n+ for L+, L+2,,. After the entire sequence has been transmitted through the multipath channel, the received sequence, ignoring additive white Gaussian noise (AWGN, can be expressed as y( n = h( k g( n k. (2 k = The crosscorrelation function between the received sequence and the original orthogonal sequence (g is defined as ( + R d y n d g n = h k g n+ d k g n k= = h( k g( n+ d k g( n. k= The value of the crosscorrelation function at the correct timing instant can be shown to be R = h( k g( n k g ( n k= = h( k g( (( n k g( n k= = h k k = = h. δ (( k As we can see, R( matches h( due to the autocorrelation function property of an orthogonal sequence and a sufficiently long cyclic prefix (at least points. We also have (3 (4
R( = h( k g( n+ k g ( n. k= (5 By observing (5, we discover that besides the points cyclic prefix attached, if we also have g(=g(, (5 becomes R( = h( k g( n+ k g ( n k= = h( k g( (( n+ k g( n k= k = ( = h. δ (( k = h k In other words, by modifying the conventional training sequence structure (an orthogonal sequence attached by a sufficiently long cyclic prefix with an additional one-point cyclic postfix (g(=g(, R( will match h( as well as R( matches h(. Such an observation has enlightened us to present a new training sequence structure where an orthogonal sequence is attached by both cyclic prefix and cyclic postfix. C. A Novel Arrangement of an Orthogonal Sequence We consider the -point orthogonal sequence (g attached by both points cyclic prefix and postfix namely g(n=g(n+ for L+, L+2,, L 2. After the entire sequence has been transmitted through the multipath channel, the received sequence, ignoring AWGN, can be expressed as k = yn = h k g n k (6 h( k g (( n k, (7 = k = for,,, +L 2. Accordingly, the crosscorrelation function between the received sequence and the original orthogonal sequence can be shown to be ( + R d y n d g n = h( k g (( n+ d k g n k= = h( k g( (( n+ d k g( n k= k= δ (, = h k d k = h d (8 for d =,,,. As we can see, by attaching both points cyclic prefix and postfix to an orthogonal sequence, a segment of the crosscorrelation function between the received sequence and the original orthogonal sequence will coincide with the CIR. In other words, the correlator output will now contain both information for time synchronization and channel estimation. III. THE ROOSED SCHEME A. The roposed Training Sequence Structure for OFDM Systems The above-mentioned arrangement of an orthogonal sequence is sufficient to make a segment of the corresponding correlator output match the CIR as depicted in (8. However, longer cyclic extensions are required to identify which segment of the correlator output represents the CIR. When the cyclic prefix attached exceeds points, the corresponding correlator output will contain leading zeros in front of the desired segment that matches the CIR. Similarly, there will be tailing zeros in back of the desired segment when the cyclic postfix appended exceeds points. By extending both the lengths of the cyclic extensions beyond points, the corresponding correlator output will contain not only a segment that matches the CIR but also leading and tailing zeros around this desired region. In order to make the proposed training sequence structure more suitable to OFDM systems, both the lengths of the cyclic prefix and cyclic postfix are deliberately extended from to M and M, respectively, as depicted in Fig.. In other words, the proposed training sequence structure is also designed to contain two identical halves. The additional repetition structure contributes to CFO estimation, which is crucial in OFDM systems. Since we must have M > and M >, the selection of the length of the orthogonal sequence will be dependent on the maximum delay spread of the channel and must satisfy the inequality > 2( L. It should be noted that the total number of leading and tailing zeros around the desired segment of the correlator output is exactly 2(. Based on the proposed training sequence structure, part of the correlator output can be shown to be ( + R d y n d g n = h( k g (( n+ d k g n k= k= k= δ ( = h( k g( (( n+ d k g( n = h k d k h d, d =,, K, =,, elsewhere (9
for d = M +, M + L, K, M. The absolute value of a typical correlator output based on the proposed training sequence structure for =49, L=, and M=25 is depicted in Fig. 2 as an example. B. The roposed Joint Time Synchronization and Channel Estimation Scheme In section II, the received sequence is modeled as linear convolution between the transmitted sequence and the CIR. However, in OFDM systems, the effect of inevitable CFO should be taken into account. Since the proposed training sequence structure is additionally designed to contain two identical halves, a conventional synchronization technique [8] can be directly applied to obtain a coarse reference time and a CFO estimate. After compensating the effect of CFO, the received and compensated training sequence { ŷ( n } can be viewed as { y(n } garbled by residual CFO and AWGN. We can then define the crosscorrelation function between the received and compensated training sequence and the original orthogonal sequence as ˆ R( d yˆ ( n+ d g ( n. ( Since ŷ( n approximates to y(n, the corresponding correlator outputs ( ˆR( d and R(d share similar properties. In other words, ˆR( d will contain a segment that approximates to the CIR. In addition, this particular region will also be guarded by leading and tailing zeros garbled by noise. Therefore, the proposed joint time synchronization and channel estimation scheme can be accomplished by the following phases:. ( Calculate ˆ R( d yˆ ( n+ d g( n (2 Find the timing instant d that maximizes the absolute value of ˆR( d within a proper observation range Ψ. This particular timing instant accounts for the estimated arrival time of the channel s strongest path. Let h ˆ max = R ˆ ( d represent the estimated channel gain of the channel s strongest path and set a proper ratio α where < α <. (3 Determine the fine time synchronization instant (d opt and the estimated CIR ( h ˆ L jointly by { } d ˆ ˆ opt = d arg min d R d d hmax α d {,, K, D} hˆ ˆ, ˆ(,, ˆ L = R dopt R dopt + K R( dopt + where D represents the range for fine time adjustment. ( The entire process of the proposed joint scheme is also illustrated in Fig. 3. The parameter α represents the minimal ratio of the estimated channel s first effective gain to ĥ max. For each timing instant d ( d D d d such that the absolute ĥ α, the timing value of ˆR( d is greater than or equal to max instant d will be considered to be within the desired region where ˆR( d approximates h(d. It should be noted that the idea of setting a minimal ratio of the estimated channel gain to the largest one seems to be straightforward and has already been presented in [9]. The major contribution of this paper is to propose a novel training sequence structure that enables receivers to acquire accurate CIR information with low costs. Unlike the methods described in [9] and [], which acquire several matrix inversions or DFT operations to obtain CIR information, the proposed approach can be implemented by a simple correlator and a comparator. IV. SIMULATION RESULTS The performance of the proposed joint time synchronization and channel estimation scheme and the methods compared are tested under a multipath Rayleigh fading channel model described in [2], which is adopted by the IEEE 82. Working Group for software simulations. The channel is modeled by complex samples where the average power of these samples decays exponentially. Each of these samples has uniformly distributed phase and Rayleigh distributed amplitude. The kth-path fading gain is modeled as 2 2 = ( σk + ( σk h k N, 2 j N, 2, 2 2 k σ 2 = 2 where (, k 2 σ = e σ e kt T s s T T RMS RMS, (2 N σ denotes a zero mean Gaussian random 2 2 k variable with variance σ, T s is the sampling period, and T RMS is the root-mean-squared delay spread of the channel. In order to provide the tail of the simulated CIR with sufficient decay, the number of effective paths is chosen to be T RMS /T s. During our simulations, the channel is assumed to be quasi-stationary, i.e., the channel characteristics are assumed to be unchanged during the transmission of an entire OFDM packet. An OFDM packet is composed of a training sequence followed by several OFDM data symbols. The structure of OFDM data symbols within the transmitted packet followed the same specifications described in []. In frequency domain, each OFDM data symbol contains 64 subcarriers where 48 of them are used to transmit QSK-modulated data symbols and 4 of them are specified to transmit known pilot symbols. These pilot symbols can be extracted after OFDM demodulation to perform carrier phase tracking []. In the time domain, each OFDM data symbol is appended by 6 samples of cyclic prefix. Although the simulated channel is assumed to be quasi-stationary, it is generated independently from one packet to another. In our simulations, we set T s /T RMS = to generate -path Rayleigh fading channels. A CFO that uniformly distributed within ±.5 subcarrier spacing is also introduced independently from one packet to another.
During our simulations, we adopt the modulatable orthogonal sequence to form the proposed training sequence structure with parameters =49, and M=9. In order to simulate the performance of the methods compared, different types of training sequences are required. A training sequence (excluding cyclic prefix containing two identical halves in the time domain is dedicated to both the Minn s time synchronization method [7] and the DFT-based channel estimation method [3]. Sufficiently long cyclic prefix is also appended to make the entire training sequence be as long as the proposed one. Another training sequence, which is composed of a modulatable orthogonal sequence attached by cyclic prefix, is also used to perform Mody s method [5] in a single-input single-output (SISO case. Once again, the total length of the training sequence is chosen to be the same as that of the proposed one. The performance of the proposed joint time synchronization and channel estimation scheme is evaluated in several aspects. Simulation results of the proposed approach with different ratios (α and the methods compared [5], [7] are demonstrated in Figs. 4 and 5 in terms of the biases and variances of the corresponding time estimators versus signal-to-noise ratio (SNR. From these figures, we can see that the proposed estimator performs almost unbiased when SNR exceeds 2 db while both the estimators compared have significant biases that are positive numbers. The biases of the estimators compared cannot be reduced by increasing signal power due to the fact that these estimators tend to locate the channel s strongest path, which is frequently not the first arrival path but a delayed one. Unlike these methods, the proposed approach acquires time and CIR information jointly and therefore is able to identify the first arrival path of the channel even if it s not the strongest one. In terms of the variances of the estimators, the proposed approach outperforms conventional synchronization methods by orders due to the unique structure of the proposed training sequence. When a smaller α is used, the proposed estimator may achieve lower variance in high SNR region due to its ability to identify the first arrival paths that are relative small. On the contrary, a smaller α may degrade the estimator accuracy in low SNR region due to noise effect. The bit-error-rate (BER performance of the proposed scheme and a conventional scheme that properly combines the Minn s method [7] and the DFT-based channel estimation method [3] is demonstrated in Fig. 6. The ultimate BER bound provided that the receiver is able to acquire the exact knowledge of symbol timing, CFO, and CIR is also illustrated as a reference. Each BER estimate is obtained provided that the number of bit errors exceeds at least 5 to enhance the reliability of the estimate. It should be noted that both the proposed scheme and the conventional scheme for comparison require carrier phase tracking to compensate for the effect of inevitable residual CFO. Without proper phase compensation, a slight amount of residual CFO may significantly decrease the BER performance of the entire system since any residual CFO introduces linearly-increased phase error that accumulates with time. Although the proposed joint scheme requires only a correlator and a comparator, still it almost achieves the ultimate BER bound when E b /N exceeds 25 db. For a target BER of -3, the proposed joint scheme provides approximately a 5 db gain as compared to the conventional scheme that performs synchronization and channel estimation sequentially. V. CONCLUSIONS In this paper, we have proposed a novel training sequence structure along with a low-complexity joint time synchronization and channel estimation scheme for OFDM systems. With the unique structure of the proposed training sequence, the corresponding crosscorrelation function will contain a segment that approximates the CIR. In addition, this particular region will be guarded by several leading and tailing zeros garbled by slight noise, and therefore can be clearly identified. This key feature has enabled the proposed joint scheme. Unlike the methods described in [9] and [], which require several matrix inversions or DFT operations to obtain CIR information, the proposed scheme can be implemented by a simple correlator and a comparator. At the expense of the same training sequence overheads, the proposed joint scheme outperforms conventional time synchronization schemes [5], [7] by orders. Furthermore, the BER performance of the proposed joint scheme is close to the ultimate BER bound where the receiver is able to acquire the exact knowledge of symbol timing, CFO, and CIR. The proposed joint scheme also provides significant BER performance gain as compared to a scheme that properly combines a conventional time synchronization method [7] and a DFT-based channel estimation method [3]. In summary, the proposed joint scheme is not only effective but also suitable for implementation. REFERENCES [] IEEE, art : Wireless LAN Medium Access Control (MAC and hysical Layer (HY Specifications: High Speed hysical Layer in the 5-GHz Band, IEEE Std 82.a-999, Sept. 999. [2] Broadband Radio Access Networks (BRAN; High erformance Radio Local Area Networks (HIERLAN Type 2, System Overview, ETSI TR 683, v..2, 999. [3] ETSI, Radio broadcasting systems: Digital Audio Broadcasting to mobile, portable and fixed receivers, European Telecommunication Standard, ETSI EN 3 4 v.3.2, Sep. 2. [4] ETSI, Digital Video Broadcasting: framing structure, channel coding, and modulation for digital terrestrial television, European Telecommunication Standard, ETSI EN 3 744 v.3., Aug. 2. [5] A. 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[3] M. J. Fernández-Getino García, J. M. áez-borrallo, and S. Zazo, DFT-based channel estimation in 2D-pilot-symbol-sided OFDM wireless systems, in roc. 5st IEEE Veh. Technol. Conf. (VTC, Rhodes, Greece, May 2, vol. 2, pp. 8-84. M oints M oints Cyclic refix Original Orthogonal Sequence g Cyclic ostfix oints Figure. The proposed training sequence structure. Figure 4. Biases of the proposed time estimator and the estimators compared. Figure 2. The absolute value of a typical correlator output based on the proposed training sequence structure. Figure 5. Variances of the proposed time estimator and the estimators compared. ˆ ( + Rˆ d y n d g n d Ψ { Rˆ ( d } = R( d { ˆ ˆ } hˆ ˆ max d = d arg min d R d d h α opt { yˆ ( n } d = arg max Correlator max d {,, K, D} Comparator, (, K, ( h ˆ ˆ ˆ ˆ L = R dopt R dopt + R dopt + L d opt Figure 3. The process of the proposed joint time synchronization and channel estimation scheme. Figure 6. The BER performance of the proposed joint scheme and a combination of conventional methods in an ISI channel.