A Hybrid Synchronization Technique for the Frequency Offset Correction in OFDM

A Hybrid Synchronization Technique for the Frequency Offset Correction in OFDM Sameer S. M Department of Electronics and Electrical Communication Engineering Indian Institute of Technology Kharagpur West Bengal 721 302, India. sameer@ece.iitgp.ernet.in Abstract Accurate estimation of carrier frequency offset is an important requirement in OFDM based wireless communication systems. The paper proposes a new technique to accomplish this tas. It employs a hybrid approach combining the cyclic prefix (CP) associated with the OFDM symbols and a few null subcarriers. Compared to earlier approaches that use only null subcarriers, the bandwidth overhead of the proposed method is quite low. The method is capable of correcting frequency offset in the range of multiples of subcarrier spacing. In the proposed approach, the fractional part of the frequency offset is estimated with the help of CP and integer part using the null subcarriers. A brief analytical formulation of the method is presented. Extensive simulation studies are carried out in the presence of both AWG and multipath fading channel. For moderate SR values, the new algorithm is shown to greatly outperform a recently published method that use only null subcarriers. 1. Introduction Orthogonal Frequency Division Multiplexing (OFDM), the first and foremost multicarrier communication system, has been adopted as the major technique for the current and future broadband communication systems lie Wireless LA, Wireless MA, Digital Audio and Video Broadcasting systems (DAB and DVB). OFDM systems are much more sensitive to frequency synchronization errors than single carrier systems. The presence of carrier frequency offset (CFO) will introduce severe intercarrier interference (ICI), which, if not properly compensated, would significantly degrade the system performance. Various techniques have been proposed in the literature in order to estimate the frequency offset in OFDM systems. They can be broadly classified into three categories. The class of training sequence based methods either employs one or more OFDM symbols as preamble before the actual data transmission or a set of nown pilot signals. The synchronization parameters are R. V. Raja Kumar Department of Electronics and Electrical Communication Engineering Indian Institute of Technology Kharagpur West Bengal 721 302, India. rumar@ece.iitgp.ernet.in usually estimated by correlation techniques. A timing and frequency acquisition algorithm is presented in [1], widely nown as Schmidl-Cox method. It employs two training OFDM symbols. The training overhead associated with the method is high and the estimation range is low. A modified form of Schmidl-Cox algorithm is proposed in [2], where one training symbol with L identical subparts in time domain is used, and the estimation range is shown to be +/-L/2 subcarrier spacing. A maximum lielihood OFDM carrier frequency estimator based on distinctively spaced pilot tones are presented in [3]. The second category, blind synchronization methods, does not rely on training symbols or pilot subcarriers for estimating the synchronization parameters. Hence they are highly bandwidth efficient. But they have limitations lie high computational complexity, convergence time, and estimation variance. Most of them use the CP associated with the OFDM symbol. [4] proposed an idea for the joint estimation of timing and frequency offsets using the phase of the autocorrelation between the CP samples and its counterpart. This technique gained acceptance but due to the inherent property of the CP autocorrelation function, the frequency offset estimation range is limited to half subcarrier spacing. There is another class of frequency synchronizers which use either the intrinsic virtual carriers included in some OFDM based wireless communication standards or deliberately introduced null subcarriers in between the data carriers. A subspace based approaches that rely on the utilization of virtual subcarriers is derived in [5]. Since the method is based on consecutive virtual carriers, the cost function is highly channel dependent and hence the ambiguity associated with offset estimation is high. In an attempt to minimize the ambiguity problem, [6] proposed the use of distributed null subcarriers. However the cost function proposed in [6] do not converge at times and the search involved is too high. Recently a null subcarrier based method is proposed which use one complete OFDM symbol with all odd subcarriers as null subcarriers and many of the even subcarriers also as null subcarriers whose selection is done with the

help of an extended maximal length sequence [7]. The method yields high estimation range but the training overhead in terms of number of null subcarriers is quite high. In this paper, we propose a hybrid frequency offset estimation technique for OFDM utilizing both cyclic prefix and null subcarriers. The proposed estimator is capable of correcting frequency offsets that are fractions and multiples of subcarrier spacing. The proposed technique yields high estimation range with minimum computational complexity compared to many of the existing schemes which use only null subcarriers. The rest of the paper is organized lie this. Section II describes the system model considered and an outline of the proposed technique. A brief mathematical formulation of the method is given in section III. Section IV discusses the simulation studies and results followed by the concluding remars in section V. 2. System model An OFDM system with subcarriers, equi-spaced at a separation of Δ F = B, where B is the total system bandwidth is considered. All subcarriers are mutually orthogonal over a time interval of lengtht = 1. Each OFDM bloc is preceded by a Δ F cyclic prefix whose duration is longer than the delay spread of the propagation channel, so that inter-bloc interference can be eliminated at the receiver, without affecting the orthogonality of the sub-carriers. Out of the total carriers, d carriers are used as data carriers and remaining are made as null subcarriers. ull subcarriers need to be inserted only in the first OFDM symbol in a frame. The positions of the null subcarriers are selected according the frequency offset estimation range required. The transmitted OFDM symbol will in general be affected with a frequency offset of the order of a few subcarrier spacing due to oscillator mismatches and Doppler frequency shifts and a time shift. The received signal will also have the usual impairments due to complex AWG and multipath channels. The fractional frequency offset is estimated from the phase of the correlation of cyclic prefix samples and their counterpart. Then it is corrected. The integer frequency offset is estimated in the frequency domain through a search method by minimizing the energy spread in to the null subcarrier locations. One of the novelties of the proposed method is that, this search need to be carried out only with integer values over the range of interest as fractional part is already estimated and corrected. Hence the computational complexity is quite less compared to pure search based techniques. [D&K, Tureli]. Once the integer frequency offset is estimated, it is corrected and the remaining receiver processing is done. 3. Analytical formulation The transmitted OFDM signal is given by n j 1 ( ) = de (1) Γd xn where n = L,..,0,.. 1, d is the data symbol at the -th subcarrier, Γ d is the set of indices of the data subcarriers and L is the length of the cyclic prefix. Assuming that the timing is perfect, the received time domain OFDM symbol is given by j( + 2 πφ ) n 1 ( ) = ( ) ( ) (2) + Γd yn Hde zn where, H ( ) is the channel frequency response at the -th subcarrier,φ is the normalized (to the subcarrier spacing) frequency offset and zn ( ) is complex AWG 2.1. Fractional frequency offset estimator The fractional frequency offset is estimated by correlating the samples in the CP and their counterpart in the actual OFDM symbol. The autocorrelation of these samples is given by [14] γ m+ L 1 * ( m) = y( n) y ( n+ ) (3) n= m where m represents the timing uncertainty and is assumed to be zero. From the analysis of the log-lielihood function (LLF) associated with the maximum lielihood estimation of fractional frequency offset, the optimum frequency offset estimate would be ˆ 1 φf = γ( m) + n (4) where n is an integer. Since the integer frequency offset is separately estimated, n can be set to zero. Because of the periodicity of the cosine function, the unambiguous frequency estimation range is limited to half subcarrier spacing. Once the fractional frequency offset is estimated, it is corrected before taing the FFT. 2.2. Integer frequency offset estimation The integer frequency offset estimation is done in the frequency domain with the help of a few null subcarriers by minimizing the energy spread in the null

subcarrier locations. In the proposed scheme, the number of null subcarriers and their locations are decided according to the estimation range required. After removing the CP, eqn(2) can be written in vector notation as y ( n ) = P W d + Z (5 ) 2 2 ( 1) j i j i P diag e π φ e π φ where = (1,,..., ), W is an x d FFT matrix, d Hd and φi is the integer frequency offset. Using the LLF for d andφ i, a cost function that is to be minimized can be expressed as d ˆ H ˆH H ˆ i φi = r r r = 1 J ( ) v P y( n) y ( n) Pv (6) that of the other two methods when the SR is greater than 8 db and 6dB when 4 and 8 null subcarriers respectively are used. But the synchronization overhead of the proposed method is only 6.25% (12.5% for 8 nulls) of the total number of subcarriers, where as the D&K and M&M methods have 75% and 93.75% overheads respectively. Hence the proposed technique saves considerable amount of bandwidth and is an attractive candidate for bandwidth constrained applications. The bandwidth efficiency of the proposed method is summarized in Table 1, where the efficiency is calculated based on the OFDM symbol in which training sequence or null subcarriers are used. where vr is the r-th column of the FFT matrix and - d represents the number of null subcarriers. The integer frequency offset is estimated by a search technique. If Pˆ is the actual frequency offset estimate, the cost function will reach a minimum. The computational complexity of this technique is very low compared to a similar method proposed in [22], where search is performed over fractional values also. 4. Simulation studies The proposed method is simulated by using an OFDM system with 64 subcarriers (). The cyclic prefix length is varied from 4 to 16. Out of the 64 subcarriers, a few are set as nulls and remaining as data carriers. The numbers of nulls are varied from 4 to 16. Spacing between the nulls is adjusted so as to yield the desired estimation range which is to the tune of half of OFDM signal bandwidth. Simulations are conducted for both AWG channel and multipath fading channel with SUI-3 channel model [8] (3-tap channel) and another 8- tap complex channel. The performance metric chosen is ormalized Mean Square Error (MSE) defined as 1 t ˆ 2 MSE = ( φ φ) (7) t t = 1 Figure-1 shows the MSE performance of the proposed method in the presence of SUI-3 channel for a normalized frequency offset of 6.25 subcarrier spacing. Simulation is done for 4 and 8 null subcarriers. The performance of the proposed method is compared with two important methods proposed in the literature namely Morelli and Mengali (M&M) method in frequency domain [2] and David and Khaled (D&K) method [7]. It is observed that the MSE performance of the proposed method is equivalent to Figure 1 : MSE v/s SR of the proposed, M&M and D&K methods.. Table 1: Comparison of bandwidth efficiency Method Bandwidth Requirement (% of OFDM Bandwidth) Proposed - 8 ulls 12.5 % Proposed - 12 ulls 18.75 % Morelli & Mengali (M&M) method David & Khaled (D&K) method 93.75 % 75 % The impact of number of null subcarriers on the performance of the proposed estimator is shown in Fig- 2. Eight path complex multipath channel, with no equalization is used. The frequency offset is set as -4.7 subcarrier spacing. The numbers of null subcarriers

used are 4, 8 and 12 and the cyclic prefix is 16 samples. It has been observed that there is a remarable improvement of around 4dB at a normalized mean square error of 10-3 when the numbers of null subcarriers are increased from 4 to 8 where as the increase from 8 to 12 shows only a minor improvement. In all the cases, the performance is alie when the SR is beyond 10dB. The performance with 12 null subcarriers, in the presence of complex additive white Gaussian noise is also given for the sae of comparison. It has been seen that in those applications where moderate SR can be ensured, then just 8 null subcarriers are sufficient to estimate frequency offsets as high as multiples of subcarrier spacing. If bandwidth efficiency is the primary concern, it is possible to achieve the same estimation range with further reduction in the number of null subcarriers. Figure 3 : MSE v/s SR of proposed method (by varying the CP samples) Figure 2 : MSE v/s SR of proposed method ((by varying number of nulls) As the fractional frequency offset is solely estimated with the help of CP, the number of samples in the CP is important in deciding the performance of the estimator. Simulation is conducted with various CP lengths lie 4, 8 and 16 in the presence of SUI-3 channel. The frequency offset created is 4.4 subcarrier spacing. It can be seen from Fig. 3 that, for an MSE of 10-3, an improvement of 8 db can be achieved when the CP length is increased from 4 to 8 samples. Increasing from 8 to 16 yields an improvement of 2.5 db. 8 or 16 CP samples are enough to deal with most of the multipath channel scenarios. The variation of estimated frequency with respect to SR is shown in Fig-4. An offset of 3.4 subcarrier spacing has been introduced in to the transmitted OFDM symbol and estimation is carried out by varying the null subcarriers as 4, 8, 12 and 16. When 4 null subcarriers are used, the proposed algorithm could estimate the correct frequency at an SR of 7dB. The same estimation is possible at 5dB when the number of Figure 4 : Estimated frequency v/s SR of proposed method (by varying number of nulls) null subcarriers is increased to 8. An improvement of 5dB is obtained when the numbers of null subcarriers are increased from 4 to 16. With 8 null subcarriers, the estimated frequency offset coincides with the actual frequency offset at SR as low as 4 db. 5. Conclusions We presented the mathematical model and simulation results of a novel technique for correcting the carrier frequency offset in OFDM systems. The method uses a combination of cyclic prefix associated with the OFDM symbol and a few null subcarriers placed at distinct locations in the OFDM symbol. Hence it can be treated as a semi-blind approach. Futuristic receivers will be required to correct large frequency offsets with minimum computational complexity. The proposed frequency synchronization technique is best suited to the above requirements. With minimum

complexity and bandwidth requirements, the technique yields a performance comparable to some of the existing complex methods, at moderate SR values. 6. References 1) T. M. Schmidl and D. C. Cox, Robust frequency and timing synchronization for OFDM, IEEE Trans. Commun., vol. 45, no.12, pp. 1613-1621, Dec. 1997. 2) M. Morelli and U. Mengali, An improved frequency offset estimator for OFDM applications, IEEE Commun. Lett., vol. 3, no. 3, pp. 75-77, Mar.1999. 3) Jing Lei and Tung-Sang g, A consistent OFDM carrier frequency offset estimator based on distinctively spaced pilot tones, IEEE Trans. Wireless Commun., vol. 3, no. 2, pp. 588-599, Mar. 2004. 4) J. J. van de Bee, M. Sandell, and P. O. Borjesson, ML Estimation of time and frequency offset in OFDM systems, IEEE Trans. Signal Proc., vol. 45, no.7, pp. 1800-1805, July 1997. 5) H. Liu and U. Tureli, A high efficiency carrier estimator for OFDM communications, IEEE Commun. Lett., vol. 2, pp. 104-106, Apr. 1998. 6) X. Ma, C. Tepedelenlioglu, G. B. Giannais, and S. Barbarossa, on-data-aided carrier offset estimators for OFDM with null subcarriers: Identifiability, Algorithms, and Performance, IEEE J. Select. Areas Commun., vol. 19, no. 12, pp. 2504-2511, Dec. 2004. 7) Defeng (David) Huang and K. B. Letaief, Carrier frequency offset estimation for OFDM systems using null subcarriers, IEEE Trans. Commun., vol. 54, no.5, pp. 813-822, May 2006. 8) IEEE 802.16 Broadband Wireless Access Woring Group, Channel Models for Fixed Wireless Applications, Available online at www.ieee802.org/16/tg3/contrib/802163c- 01_29r4.pdf