On the Performance Analysis of SC-FDMA Uplink Communication Systems using Multiple-CFO Synchronization with Null-Subcarriers

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1 On the Performance Analysis of SC-FDMA Uplink Communication Systems using Multiple-CFO Synchronization with ull-subcarriers Mustafa Anıl Reşat and Özgür Ertuğ Gazi University Telecommunications and Signal Processing Laboratory Electrical and Electronics Engineering Department Ankara, TURKEY Abstract Due to its low peak-to-average power ratio (PAPR) advantage, single-carrier frequency-division multiple-access (SC- FDMA) has been selected for the Long Term Evolution (LTE) uplink access scheme. However, like orthogonal frequency-division multiplexing (OFDM) based systems, carrier frequency-offset (CFO) is one of the major problems that should be solved in SC- FDMA and thus LTE uplink. There are two kinds of effects that occur due to CFO; inter-carrier interference (ICI), which occurs between a user s own subcarriers and multiple-access interference (MAI), which occurs between different users subcarriers. Since different users experience different CFOs, CFO suppression in uplink is harder than suppression in downlink communications. In this paper, we proposed a suppression method to overcome the multiple CFOs estimation and suppression in LTE uplink problem. In this algorithm, null subcarriers which are present in LTE uplink standard are used. For CFO estimation, the energy of the signal in null subcarriers is measured and when the CFO value which provides minimum energy is found, this value is used during CFO suppression. In addition, the effects of FFT size, number of users and subcarrier mapping scheme on this system are analyzed. I. ITRODUCTIO 3GPP has selected SC-FDMA as the LTE uplink technique for high data-rate communications in future cellular systems 1]. The main advantages include efficient spectrum usage, resistance to frequency-selective fading and lower complexity compared to contemporary systems. As being a OFDM based system, SC-FDMA has also the advantages of orthogonal frequency-division multiple-access systems. However, the most promising feature of SC-FDMA is its low peakto-average power ratio (PAPR) which makes it the optimal technique for uplink communications. Besides these advantages, like other OFDM based systems, CFO, which is mainly caused by oscillator mismatch between transmitter and receiver and Doppler shift, decreases the system performance severely by destroying the orthogonality among subcarriers 2]. In uplink communications, multiple signals sent from multiple users are affected by different CFO values. After passing from these channels, these signals are combined at the receiver. This combination results in MAI. In order to obtain a reliable system performance, efficient CFO estimation and suppression is very important. Due to these different CFOs and multiplexed signals, synchronization of CFO is harder in uplink than in downlink communications. There are CFO correction methods in the literature used for downlink communications like the one in 3]; however these kind of methods are designed for single-user systems and gives inferior performance in uplink communications. Besides downlink communication methods, there are also techniques designed for OFDMA uplink communications like the ones in 4,5,6]. These methods are also feasible for SC-FDMA systems, since they are designed for uplink communications and OFDMA is OFDM based like SC- FDMA. The proposed system in this paper also uses a previous technique used for OFDM and OFDMA systems 7,8] and extends it to SC-FDMA systems. Before defining the proposed technique, classification of synchronization methods used for uplink communication will be held. The first class of methods is called feedback methods. These methods exploit a downlink feedback channel, which transmits the CFO estimation information, calculated by the base station. Then, each user corrects his offset according to these messages. The drawbacks of these techniques are increased transmission overhead and possible outdated estimations. The other class of methods is called signal processing methods. These methods do not require a feedback channel and achieve synchronization by signal processing at the receiver 9,10,11,12,13]. These methods include Successive Interference Cancellation and Parallel Interference Cancellation 10,11] which categorizes the received signals as reliable, that are detected directly and cancelled, and unreliable, that are detected after the cancellation of effects caused by the reliable signals. There are methods which use inverse interference matrix such as 12,13]. Another contribution uses inverse interference matrix along with pilot symbols in SC-FDMA uplink system; however in this contribution, it is assumed that different users start to communicate with the base station at different symbol periods, which is not a common situation for multi-user systems 14]. In this paper, the proposed method does not require transmission of known training sequences, as in 15], and has a channel-independent performance. In this method, not all of

2 the subcarriers are used for transmission but some of them are used as null or virtual subcarriers. These null subcarriers are used for carrier frequency offset synchronization which is based on measuring the energy within these subcarriers. Virtual subcarriers were also used by the single-user OFDM subspace-based methods in 16,17]. Unlike these methods our technique does not suffer from an ambiguity problem and provides unambiguous CFO estimation regardless of the channel zeros location. In addition to this, the method is applicable to multiuser systems such as LTE uplink communications. Another advantage of this technique is that null subcarriers does not waste any power, so this is feasible with the principle of SC-FDMA. The remainder of this paper is organized as follows: In Section II., the system model concerning LTE uplink SC- FDMA and the syncronization method is given. In Section III., the effect of multiple CFOs on the received signal is shown. In Section IV, we define our method for estimating the multiple carrier frequency offsets. In Section V, we present simulation results to analyze the performance of our method with regard to varying FFT size, number of users and subcarrier mapping scheme. II. SYSTEM MODEL Fig.1 shows the block diagram of the proposed system model, which is based on SC-FDMA uplink system. Fig. 1. SC-FDMA uplink system block diagram adjusted for CFO estimation method In SC-FDMA uplink communications, subcarriers are divided into several sub-channels for multi-user communications. A user sends its data symbols from one of these subchannels instead of using all of the subcarriers. For example, let be the total number of subcarriers, K be the number of sub-channels and K be the number of active users. Then, we can assign one of the K sub-channels to one of the K active users. The sub-channel assigned to the kth user is denoted as S k, the subcarrier number of S k is M k and the transmitted data of ] the kth user is denoted by d k = d k T. 0,d k 1,d k 2,..., d k M k 1 Firstly d k would be processed by M k point FFT in order to obtain the frequency domain symbols D k = D0,D k 1,D k 2, k..., DM k T k 1] of the kth user, where a frequency domain symbol is defined with: D k i = 1 M k 1 m=0 d k m e j2πmi/m k. (1) After FFT, outcoming signal is subcarrier mapped and the symbol vector of ] the kth user is showed as X k = X k T. 0,X1 k,x2 k,..., X k This vector is constructed by assigning some of the subcarriers to the elements of the vector D k (Xi k = Dj k ) and leaving the remaining ones equal to zero (Xi k =0). For subcarrier mapping scheme there are two main approaches. First one is the Localized Frequency Division Multiple Access (LFDMA), where a users data symbols occupy a set of consecutive subcarriers. The main advantage of LFDMA is multi-user diversity. When used with sub-band mapping, a subband enters between different users subcarrier sets. Second mapping scheme is the Interleaved Frequency Division Multiple Access (IFDMA), where a user s data symbols occupy a set of subcarriers distributed over the entire frequency range. The main advantage of this scheme is frequency-diversity. When used with sub-band mapping, a sub-band enters between different users symbols, but this time much shorter than LFDMA. Later comes the IFFT block which provides the time domain signal of the kth user which is defined with: s k (n) = l=0 X k l e j2πnl/ = l=0 X k l p n,l. (2) The last step before transmission on the channel is the addition of a cyclic prefix (CP) in front of the signal. CP is a duplicate of the signal s last part and prevents inter-symbol interference (ISI). The channel is a frequency-selective fading channel with a time domain impulse response h k (n) and each user experiences a different channel impulse response. Then, the signals coming from different users combine at the base station which can be written as: r(n) = K s k (n) h k (n)+v k (n) ]. (3) k=1 where denotes convolution and v k (n) is the AWG on the kth user. At the receiver the incoming signal is firstly passed from a bank of bandpass filters, which seperates each user s signal. Assuming the symbol time offset effect is neglected,, after removing the CP and passing from the FFT block, the output

3 on the ith subcarrier can be written as (assuming perfect filtering): Y k i = 1 s k (n) h k (n)+v k (n) ] e j2πni/. (4) After CFO estimation and compensation, there comes subcarrier demapping and IFFT blocks which recover the transmitted data of the user. III. EFFECT OF MULTIPLE CARRIER FREQUECY-OFFSETS I SC-FDMA UPLIK In this section the effect of multiple CFOs in SC-FDMA uplink communications and the interferences ICI and MAI, as a consequence of them, in the absence of filtering and CFO synchronization will be analyzed 14]. Assuming that the CFO of the kth user is Δf k, after passing from the channel and cyclic prefix removal, the received signal at the base station can be written as: r(n) = K { s k (n) h k (n) ] e j2πδfkn + v k (n) } (5) k=1 After the FFT block for frequency domain conversion, the signal on the ith subcarrier can be written as: Y i = 1 = 1 K k=1 = 1 K k=1 + 1 K k=1 l=0,l i r(n) e j2πni/ { s k (n) h k (n) ] e j2πδf kn } e j2πni/ + V i X k i Hk i ej2πδf kn Xl khk l e j2πn(l i)/ e j2πδfkn + V i (6) Hl k is the frequency domain channel response and V i is the frequency domain additive white Gaussian noise on the ith subcarrier. For all of the subcarrier mapping methods, a subcarrier can only be assigned to one user. As a result of this, only one Xi k which uses the ith subcarrier is the transmitted data of the user, and other K-1 Xi ks are zero. If this Xk i belongs to the k th user Y i can be rewritten as: Y i = X k i + K Hk i Ik k=1,k k l=0,l i 0 + l=0,l i ɛ k is the normalized CFO value and: I k L = 1 is the interference coefficient. X k l H k l I k l i X k l Hk l Ik l i + V i e j2πn(l+ε k)/ (7) (8) From (7) it can be seen that the received signal at the base station has four components. First one corresponds to the original data transmitted on the ith subcarrier of the kth user. Second one corresponds to ICI caused by other data of the kth user. Third one corresponds to MAI caused by other users data. Finally fourth one corresponds to additive white Gaussian noise. From this analysis, it can be seen that both ICI and MAI affect the received signal to a significant extent and make it harder for the detector to correctly identify the original signal. For our method we will use bandpass filtering to cope with MAI and the following algorithm to eliminate ICI. IV. ULL-SUBCARRIERS BASED CFO ESTIMATIO The CFO estimation and suppression blocks are mainly based on the algorithms in 7,8], which are designed for OFDMA. By proper adjustments, this method becomes also feasible for SC-FDMA systems, since it is designed for uplink communications and OFDMA is OFDM-based like SC- FDMA. Firstly, assume that there are two users (m = 0 and m = 1) and estimate the CFO estimation of the mth user by ṽ m. Fig. 2 shows the CFO estimation algorithm. Fig. 2. Block diagram of the CFO estimation block Estimator block (mth is used for generation of the estimation ṽ m. First of all each incoming block is multiplied with e j2πv (n)(q(+l)+i) which is generated by numerically controlled oscillator (CO) in order to compensate the effect of CFO. Here v (n) is the guess of CFO in the nth search for user m. After this process, the FFT block which is found in SC-FDMA technique works in order to convert resulting sequence into frequency domain Y (q,k). After repeating this process for b blocks, J m which is the average energy falling in the virtual subcarriers of the mth user s sub-band. For v (n) sweeping the range -1/2,1/2] in steps (usually equal to the FFT size), the v (i) which minimizes J m is found. v (i) becomes the accurate CFO estimate and the blocks are reprocessed in the receiver with this new ṽ m and passed to the subcarrier demapping block and onwards. In the nth search: J m (n) = 1 b 1 b q=0 mj a+i q k=(m 1)J a+j+1+i q Y (q; k) 2 (9) is the average energy falling in the null subcarriers for b consecutive blocks. The reason for trying to find the estimate

4 giving the minimum energy value is that if there was no noise, perfect synchronization would lead to a null energy in the null subcarriers. Therefore, this forms the backbone of the CFO estimation method. Another important point is the bandpass filters found in the receiver before the CFO estimation algorithm starts to work. This is crucial for eliminating the effect of MAI in multiuser systems. Because, as each user has a different CFO, even if user mth CFO is compensated completely (by multiplying y(q;i) by e j2πvm(q(+l)+i) ) so that no energy of user m falls into its neighboring null subcarriers, we still can not observe a null energy because interference from other users still falls into this band. Therefore, separation of users with bandpass filters and applying independent estimations to them is required to get an accurate ṽ m. V. SIMULATIO RESULTS In this work, we consider a SC-FDMA system with parameters suitable for LTE uplink. For modulation scheme 16-QAM is used. Cyclic prefix length is 32 symbols. The normalized frequency offset of each user is a random value uniformly distributed between -0,1 and 0,1. For the channel model Extended Pedestrian-A (EPA) channel model, which 3GPP has approved for LTE modelling, is used. It s a multipath fading channel which can be modelled as a tapped-delay line with 7 non-uniform delay taps. The channel gain of taps are 0,-1,-2,-3,-8,-17.2,-20.8] db. Delays are neglected in our simulation in order to study only the effect of CFO. In the first simulation, number of subcarriers per symbol is 512 and number of subcarriers per user is 128. There are two users in the system and the subcarrier spacing is 15 khz. For subcarrier mapping method, localized method is used. It can be seen from Fig. 4 that the proposed CFO synchronization method highly decreases the error rate compared to the no CFO synchronization scenario. It also gives a close performance to the no CFO scenario. system performance due to increased null subcarrier number. This helps in both ways, firstly increasing the null subcarrier number decreases the effect of MAI by increasing the null gap between users, and secondly more null subcarrier means more information for estimating the CFOs accurately. Fig. 4. BER performance with regard to FFT size In the third simulation, the effect of user number is analyzed. Parameters are the same with the first one, except the FFT size is 2048 and the number of users is changing. As it can be seen from Fig. 6, increasing the number of users clearly decreases the system performance due to decreased null subcarrier number. In contrast with the previous simulation, the decreased null subcarriers worsen the effect of MAI by decreasing the gaps between users. In addition, as there is less information for estimating the CFOs now, estimation errors increase and overall system performance decreases. Fig. 5. BER performance with regard to user number Fig. 3. BER performance of proposed method In the second simulation the effect of FFT size (number of subcarriers per symbol) is analyzed. Parameters are the same with the previous one except the FFT size. As it can be seen from Fig. 5, increasing the FFT size clearly increases the In the fourth simulation, the effect of subcarrier mapping scheme on the performance is analyzed. Parameters are the same with the first one, except for subcarrier mapping IFDMA scheme is also used. To make our method applicable, both of the subcarrier mapping schemes are realized with sub-bands coming after transmitted symbols. As it can be seen from Fig. 7, LFDMA with sub-bands gives better performance than IFDMA with sub-bands, especially at higher SR values. This shows us that our method is more vulnerable to MAI than ICI, as IFDMA with sub-bands has the main aim of decreasing the effect of ICI in contrast with LFDMA with sub-bands,

5 which has the main aim of decreasing the effect of MAI. As a result of this, LFDMA gives the better performance; LFDMA cancels the excess MAI caused by imperfect filtering, whereas the algorithm of the method estimates ICI very accurately. Fig. 6. BER performance with regard to subcarrier mapping scheme VI. COCLUSIO In this paper, we have analyzed the system architecture of LTE uplink SC-FDMA systems, the effect of multiple CFOs, the null subcarrier method which is used to avoid this problem and obtained simulation results which show the effect of CFO synchronization method, FFT size, number of users and subcarrier mapping scheme on the BER performance of overall system. It can be seen that the proposed method highly increases the performance with respect to the nonsynchronized scenario and brings it closer to the no CFO scenario. Increasing the FFT size, decreasing the number of users and using LFDMA with sub-bands are other factors that increase the performance of the system. 9] X. Dai. Carrier frequency offset estimation and correction for OFDMA uplink. IET Communications, Vol. 1, Issue 2, pp , April ] R. Fantacci, D. Marabissi and S. Papini. Multiuser interference cancellation receivers for OFDMA uplink communications with carrier frequency offset. IEEE Global Communications Conference 04, Vol. 5, pp , ov ] S. Manohar, D. Sreedhar, V. Tikiya and A. Chockalingam, Cancellation of Multiuser Interference Due to Carrier Frequency Offsets in Uplink OFDMA. IEEE Transactions on Wireless Communications, Vol. 6, Issue 7, pp , July ] Zhongren Cao, U. Tureli, Yu-Dong Yao and P. Honan. Frequency synchronization for generalized OFDMA uplink. IEEE Global Communications Conference 04, Vol. 2, pp , ov ] Pengfei Sun and Li Zhang. A ovel Pilot Aided Joint Carrier Frequency Offset Estimation and Compensation for OFDMA Uplink Systems. IEEE Vehicular Technology Conference Spring 2008, pp , May ] X.P. Zhang, H.G. Ryu. Suppression of ICI and MAI in SC-FDMA communication system with carrier frequency offsets. IEEE Transactions on Consumer Electronics, Vol. 56, Issue 2, pp , ] J. 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, pp , July ] H. Liu and U. Tureli. A high-efficiency carrier estimator for OFDM communication. IEEE Commun. Lett., Vol. 2, pp , Apr ] U. Tureli, H. Liu, and M. Zoltowski. OFDM blind carrier offset estimation: ESPRIT. IEEE Trans. Commun., Vol. 48, pp , Sept REFERECES 1] H. G. Myung, Junsung Lim and D. J. Goodman. Single carrier FDMA for uplink wireless transmission. IEEE Vehicular Technology Magazine, Vol. 1, Issue 3, pp , Sept ] M. Morelli. Timing and frequency synchronization for the uplink of an OFDMA system. IEEE Transactions on Communications, Vol. 52, Issue 2, pp , Feb ] J. J. van de Beek, P. O. Borjesson, M. L. Boucheret, D. Landstrom, J. M. Arenas, P. Odling, C. Ostberg, M. Wahlqvist and S. K. Wilson. Time and frequency synchronization scheme for multiuser OFDM, IEEE Journal on Selected Areas in Communications, Vol. 17, Issue 11, pp , ov ] a Yanxin and Minn Hlaing, Line Search Based Iterative Joint Estimation of Channels and Frequency Offsets for Uplink OFDMA Systems. IEEE Global Communications Conference 06, pp. 1-5, ov ] M. Movahedian, Yi Ma, and R. Tafazolli. MUI resilient approach for blind CFO estimation in OFDMA uplink. IEEE 19th International Symposium on Personal, Indoor and Mobile Radio Communications 2008, pp. 1-5, Sept ] Cao Zhongren, U. Tureli, and Yao Yu-Dong. Deterministic multiuser carrier-frequency offset estimation for interleaved OFDMA uplink. IEEE Transactions on Communications, Vol. 52, Issue 9, pp , Sept ] S. Barbarossa, M. Pompili, G.B. Giannakis. Channel-independent synchronization of orthogonal frequency division multiple access systems. IEEE Journal on Selected Areas in Communications, Vol. 20, Issue 2, pp , Feb ] D. iu, X. Dai. Iterative Carrier Frequency Offset Estimation for OFDMA Uplink based on ull Subcarriers th Annual Conference on Information Sciences and Systems, pp , 2006.