On the Comparative Performance Analysis of

GFDMA and SC-FDMA Systems Under Multiple

CFO Synchronization Using Null Sub-carriers

Mustafa Anıl Resat

Telecommunications and Signal Processing Laboratory

Gazi University

Ankara, Turkey

Email: anilresat@yahoo.com

Ozgur Ertug

Electrical and Electronics Engineering Department

Gazi University

Ankara, Turkey

Telephone: +90 (312) 5823340

Fax: +90 (312) 2308434

Email: ertug@gazi.edu.tr

Abstract—In this article the performances of grouped fre-quency division multiple access (GFDMA) and single-carrierfrequency division multiple access (SC-FDMA) techniques usingnull-subcarriers based carrier frequency offset (CFO) synchro-nization are compared with respect to various parameters.GFDMA, is a new emerging technique, which uses multiuserinterference cancellation to separate the users sharing the samesub-carrier sets. It also uses the iterative scheme in order toupdate the estimates and reduce errors iteration by iteration.However, just like SC-FDMA, GFDMA also suffers from carrierfrequency offset (CFO), which is formed by multiple accessinterference (MAI) and inter-carrier interference (ICI). Also, dueto the multiple signals, having different CFO values, combiningat the receiver, CFO synchronization is much more difficultthan that in single-user systems. This paper proposes a nullsubcarrier-based CFO synchronization method for the uplinkof GFDMA and SC-FDMA systems, adopting sub-band basedsubcarrier assignment scheme. Performances of both techniquesare compared under various parameters by simulations.

I. INTRODUCTION

Single-carrier frequency division multiple access (SC-FDMA) has been selected to be the multiple access techniquefor the uplink of 3GPP LTE (Third-Generation PartnershipProject Long Term Evolution) [1]. SC-FDMA, which has asimilar structure and performance as orthogonal frequencydivision multiple access (OFDMA), is a combination of FDMAand single-carrier modulation with frequency-domain equal-ization (SC-FDE). SC-FDMA has the advantage of low peak-to-average power ratio (PAPR) owing to using single-carriertransmission rather than multi-carrier transmission such asOFDMA.

Despite of their distinctive advantages, orthogonal mul-tiple access schemes such as SC-FDMA can not approachthe optimal capacity of multiple access channel. GFDMA(Grouped FDMA) is a new emerging non-orthogonal tech-nique, which adds iterative multiuser detection with frequencydomain equalization (IMD-FDE) to SC-FDMA, studied in[2,3]. IMD-FDE, separates the added signals of multiple userswith the help of distinct interleavers, channel coding andfrequency domain detection. It is also compatible with SC-FDMA, due to its single-carrier property. GFDMA has a lotof promising features like [2]:

- GFDMA can achieve higher throughput values thanorthogonal schemes such as FDMA, TDMA, OFDMA and SC-FDMA.

- GFDMA provides multiuser diversity and frequencydiversity for fading environments, whereas SC-FDMA systemallows only one of these diversity gains.

- GFDMA has a low PAPR, which is important for uplinkcommunications and uses a simple single-tap equalizer, whichhelps to decrease the complexity.

- GFDMA can be utilized to supress intercell interference(ICI) in the cell edge, where the same resource is reused inneighboring cells for increasing total throughput. GFDMA canalso avoid the loss of spectral efficiency in relay networks withhalf-duplex constraint.

Like other OFDM based systems, SC-FDMA is vulnerableto CFO, which is mainly caused by Doppler shift and oscil-lator mismatch between the transmitter and the receiver. CFOdestroys the orthogonality among subcarriers, which causessevere ICI that decreases the system performance [4]. In uplinkcommunications, multiple signals sent from multiple users areaffected by different CFO values. After passing from thesechannels, these signals are combined at the receiver. Thiscombination results in MAI. GFDMA also suffers from CFO;however due to its non-orthogonal nature, CFO is comprisedmainly from MAI arising from assigned users in a chunk. Asa result, in order to obtain a reliable system performance,efficient CFO synchronization is very important for bothGFDMA and SC-FDMA.

As different users have different CFOs, synchronization ofCFO is harder in uplink than in downlink scenarios. There havebeen CFO correction methods for downlink communicationslike the one in [5]; however these methods are applicable foronly single-user systems and gives inferior performance inuplink communications. In contrast, there are also techniquesdesigned for OFDMA uplink communications like the ones in[6,7,8]. These kind of methods are also feasible for GFDMAand SC-FDMA systems, since they are designed for uplinkcommunications and an OFDM based technique (OFDMA).The proposed system in this paper also uses a previous tech-nique designed for OFDM and OFDMA systems [9,10] and

extends it for GFDMA and SC-FDMA usage. Before definingthe proposed technique, uplink sycnhronization methods willbe classified.

The first class of methods is called feedback methods.These methods exploit a downlink feedback channel, whichtransmits the CFO estimation information sent by the basestation. Each user corrects his offset according to these mes-sages. These techniques have the disadvantages of increasedtransmission overhead and possible outdated estimations. Theother class is called signal processing methods. These methodsdo not acquire a feedback channel and achieve synchronizationby signal processing at the receiver [11,12,13,14,15]. Thesemethods include Successive Interference Cancellation andParallel Interference Cancellation which classes the receivedsignals as reliable, which are detected directly and cancelled,and unreliable, which are detected after the cancellation ofeffects caused by the reliable signals [12,13]. Also there aremethods which use inverse interference matrix such as [14,15].

In this paper, we propose a method which does not requirethe transmission of known training sequences, as in [16], andhas a channel-independent performance. In this method not allof the subcarriers are used for transmission but used as null orvirtual subcarriers. These null subcarriers are used for carrierfrequency offset synchronization which is based on measuringthe energy within these subcarriers. Virtual subcarriers werealso used by the single-user OFDM subspace-based methodsin [17,18]. Unlike these methods our technique does not sufferfrom an ambiguity problem and provides unambiguous CFOestimation regardless of the channel zeros location. In additionto this, this method is applicable to multiuser systems suchas LTE Uplink communications. Another advantage of thistechnique is that null subcarriers does not waste any power sothis is feasible with the principles of GFDMA and SC-FDMA.

The remainder of this paper is organized as follows: InSection II, the principles of SC-FDMA communications isgiven, in Section III, the principles of GFDMA is shown,in Section IV, the sub-carrier mapping methods for GFDMAand SC-FDMA are described, in Section V, we analyze themultiple access channel, in Section VI, we propose our methodfor uplink null sub-carrier based CFO synchronization, finally,in Section VII, we report simulation results to analyze theperformance of our method and finally Section VIII, closesthe paper with the conclusion part.

II. SC-FDMA PRINCIPLES

Fig. 1 shows the basic structure of a SC-FDMA systemwhere transmission of one block of data is carried out. As itcan be seen from the figure, SC-FDMA is OFDM based andrealized by adding a FFT block to the OFDMA transmitterand an IFFT block to the OFDMA receiver.

Fig. 2 shows the block diagram of the proposed systemmodel in this paper, which adapts the basic SC-FDMA uplinksystem to be compatible with the proposed CFO synchroniza-tion algorithm.

In SC-FDMA uplink communications, subcarriers are di-vided into several sub-channels for multi-user communica-tions. A user sends his data symbols from one of these sub-channels instead of using all of the subcarriers. One of the

Fig. 1. Basic structure of SC-FDMA

Fig. 2. Adapted SC-FDMA structure

sub-channels is assigned to one of the active users. Firstly theinput data of users would be processed by the FFT block inorder to obtain the frequency domain symbols.

After FFT, outcoming signal is subcarrier mapped. Thisprocess is realized by assigning some of the subcarriers tothe elements of the mapped vector and leaving the remainingones equal to zero. Then comes IFFT block which providesthe time domain signal of the users. The last step beforetransmission to the channel is the addition of cyclic prefix(CP) in front of the signal. CP is a duplicate of the signalslast part and prevents inter-symbol interference (ISI). Thechannel is a frequency selective fading channel and eachuser experiences a different channel impulse response. Thenthe signals coming from different users combine at the basestation. After CFO estimation and compensation there comessubcarrier demapping and IFFT blocks which recover thetransmitted data of the user.

III. GFDMA PRINCIPLES

GFDMA is a partly changed version of SC-FDMA, whichuses IMD-FDE in order to seperate multiple users that sharethe same set of subcarriers (chunk). This allows GFDMAto have more users than SC-FDMA in the same frequencybandwidth. GFDMA uses different interleaving patterns foreach user at the transmitter side unlike SC-FDMA. As a resultof utilizing discrete interleavers, the channel decoder treatsunwanted users uncorrelated (white) interferences as noise andcan make detection of the desired users data easier.

Fig. 3. GFDMA structure: a) Transmitter b) Basic Receiver c) AdaptedReceiver

In Figure 3 the general block diagram of GFDMA is given.Figure 3(a) shows the transmitter side, where users’ data arefirstly encoded and interleaved by user-specific interleavers.After the modulation process, P symbols are grouped and con-verted to the frequency domain by a P-point DFT block. Then,each of the P frequency domain symbols are assigned to oneof the N sub-carriers with the help of the sub-carrier mappingblock. Each sub-carrier group can be shared by multiple users.After the conversion to time domain and addition of the CP,the signal is transmitted to the channel. If U is defined as thenumber of users sharing the same chunk, the received signalcan be represented as:

R =U∑

u=1

ΛuFPxu +W (1)

Figure 3(b) shows the basic receiver block diagram ofa GFDMA system. In order to separate multiple users of achunk successfully, iterative decoding is used in GFDMA. Thisdecoding is a procedure that can be described as:

1. Computing mean vector and variance: MMSE equal-ization step requires the mean vector and variance (xu andvu) of the transmitted symbols. These values are functions ofa priori log likelihood ratios (LLR), obtained from the decoderoutputs. For the first iteration, these values are accepted as zeroand one, respectively.

2. Multi-user interference cancellation: Multi-user inter-ference cancellation (MUIC) for the uth user is performed andother components of the received signal are eliminated as:

Zu = R−U∑

u=1,u′ 6=1

Λu′FPxu′ (2)

3. Equalization: Equalization can be performed by usingMMSE technique as:

Xu = GHu Zu − (GH

u Λu −trace(GH

u Λu)

P)FPxu (3)

Gu,k =Λu,k

U∑u′=1

vu′ |Λu′,k|2+ σ2

w

, ∀k (4)

4. Computing extrinsic LLRs: After equalization, P-pointIDFT is used for time-domain conversion. Following this, theextrinsic LLRs are obtained, deinterleaved and given to thedecoder. The decoder computes the extrinsic information forthe coded bits which are used as the a priori information ofMUIC and MMSE equalizer.

Fig. 3(c) shows the block diagram of the proposed receivermodel in this paper, which adapts the basic GFDMA uplinkreceiver to be compatible with the proposed CFO synchro-nization algorithm. As it can be seen from the figure, oneof the differences is the band-pass filter bank found at thebeginning of the receiver that filters the incoming receivedsignal according to the desired frequency bands. Anotherdifference is the CFO synchronization block that exists rightafter the MUIC block. This block performs the proposedsynchronization algorithm, after the MUIC block seperates theusers sharing the same sub-carrier sets (frequency bands).

IV. SUB-CARRIER MAPPING

Figure 4 shows the sub-carrier mapping methods for SC-FDMA and GFDMA. For sub-carrier mapping, there are twomain methods (localized and distributed) for both methods anda mixed method (hybrid) for GFDMA.

In the first method, Localized Frequency Division Mul-tiple Access (LFDMA), a set of consecutive subcarriers areoccupied by a users data symbols. When utilized with sub-band mapping, a sub-band drops in the middle of differentusers subcarrier sets or chunks. In particular, the subcarriersare assigned so that each user has a set of continuous fre-quencies and the distance between each users subcarrier set ismaximized. Fig. 4(a) shows an exemplary LFDMA subcarriermapping for SC-FDMA, whereas Fig. 4(b) shows the samemethod with sub-bands. Fig. 4(c) shows an exemplary LFDMAsubcarrier mapping for GFDMA, whereas Fig. 4(d) shows thesame method with sub-bands.

In the second method, Interleaved Frequency Division Mul-tiple Access (IFDMA), a users information symbols occupy aset of subcarriers distributed over the whole frequency range.Any time utilized with sub-band mapping, a sub-band drops in

Fig. 4. Sub-carrier mapping methods a) SC-FDMA, LFDMA b) SC-FDMA,LFDMA with null sub-bands c) GFDMA, LFDMA d) GFDMA, LFDMAwith null sub-bands e) SC-FDMA, IFDMA f) SC-FDMA, IFDMA with nullsub-bands g) GFDMA, IFDMA h) GFDMA, IFDMA with null sub-bands i)Hybrid j) Hybrid with null sub-bands

the middle of different users symbols, yet this time shorter thanLFDMA. In particular, the subcarriers are assigned so that eachuser has a set of equally spaced frequencies and the distancebetween a users sub-carriers is maximized. Fig. 4(e) showsan exemplary IFDMA sub-carrier mapping for SC-FDMA,whereas Fig. 4(f) shows the same method with sub-bands.Fig. 4(g) shows an exemplary IFDMA sub-carrier mappingfor GFDMA, whereas Fig. 4(h) shows the same method withsub-bands.

The hybrid method gives the advantage of using bothLFDMA and DFDMA methods simultaneously, which is im-portant for scenarios where both low and high mobility usersexist at the same time. For low mobility users hybrid methodprovides multiuser diversity gain in frequency-selective fading,whereas for high mobility users it provides frequency diversitygain. Fig. 4(i) shows an exemplary hybrid sub-carrier mappingfor GFDMA, whereas Fig. 4(j) shows the same method withsub-bands.

V. NULL-SUB-CARRIERS BASED CFO ESTIMATION

As denoted before synchronization in uplink scenario ismuch harder than downlink because of the multiple CFOs.If the users are stable and frequency offset is caused onlyby oscillator mismatches, synchronization at only MUs canbe enough. Nevertheless, if the users are moving and causingDoppler shift, a synchronization algorithm is required also atthe BS.

The CFO estimation and suppression blocks are primarilybased upon the algorithms in [11,12], which are configured forOFDMA. By proper adjustments, this strategy ends up beingalso feasible for GFDMA and SC-FDMA systems, since it isconfigured for uplink communications and OFDMA is OFDM-based like GFDMA and SC-FDMA.

Firstly, assume that there are two users (k = 0 and k = 1)and the CFO estimation of the kth user is shown by vk. Fig.5 shows the CFO estimation algortihm.

Fig. 5. Null sub-carrier based CFO synchronization algorithm

The estimation algorithm works as follows:

1. Estimator block k is used for producing the esti-mation vk. Each incoming block y(q;n) is multiplied withej2πv0(z)(q(N+L)+n) which is produced by numerically con-trolled oscillator (NCO) with a specific end goal to compensatethe impact of CFO. Here q is the block index, L is the CPlength and v(z) is the guess of CFO in the zth look for user k.

2. The FFT block which is present in SC-FDMA andGFDMA techniques works with a goal to change over theresulting sequence into frequency domain Y(q,i).

3. After repeating the first two steps for Nb blocks, Jk(z)which is the average energy falling in the virtual sub-carriersof the kth users sub-band is calculated.

4. The first three steps are repeated for v(z) sweeping therange [-1/2N,1/2N] in z steps (generally equivalent to the FFTsize), until the vk which provides the minimum Jk(z) is found.

5. vk becomes the accurate CFO estimate and the blocksare reprocessed in the receiver with this new v(z) and passedto the subcarrier demapping block and onwards. For LFDMAwith sub-bands, in the zth search:

Jk(z) =1

Nb

Nb−1∑

q=0

(k+1)Ja∑

i=kJa+J+1

|Y ′(q; i)|2

(5)

is the average energy falling in the null subcarriers for Nb

consecutive blocks. Also for IFDMA with sub-bands, in thezth search:

Jk(z) =1

Nb

Nb−1∑

q=0

N−1∑

i 6=kJ0+nMk

|Y ′(q; i)|2

(6)

is the average energy falling in the null subcarriers for Nb

consecutive blocks. The purpose behind attempting to find theestimate giving the minimum energy value is that if there wasno noise, perfect synchronization would bring up null energyin the null subcarriers. Therefore, this forms the backbone ofthe CFO estimation strategy.

An additional important point is the bandpass filters andthe multiuser interference cancellation step found in the re-ceivers of SC-FDMA and GFDMA respectively, before theCFO estimation process begins to work. These are vital fordispensing the impact of MAI in multiuser systems. Because,as each user has a distinctive CFO, even if the CFO ofthe user k is compensated totally (by multiplying y(q;n) byej2πDfk(q(N+L)+i) so that no energy of user k falls into itsneighboring null subcarriers, we still can not observe a nullenergy in light of the fact that interference from different usersstill falls into this band. Consequently, detachment of userswith bandpass filters and applying independent estimations tothem is required to get a precise vk.

VI. SIMULATION RESULTS

In this work, we compare SC-FDMA and GFDMA com-munications with parameters suitable for LTE Uplink . Formodulation scheme QPSK is used. Cyclic prefix length is 32symbols. The normalized frequency offset of each user is arandom value uniformly distributed between -0,1 and 0,1. Forthe channel model 12-tap typical urban (TU) channel channelmodel is used. Also, perfect channel estimation is considered.

In the first simulation, for both GFDMA and SC-FDMAsystems, number of subcarriers per symbol is 512 and num-ber of subcarriers per user is 128. There are two users atGFDMA and a single user at SC-FDMA. Subcarrier spacingis chosen as 15 kHz. For subcarrier mapping method localizedmethod is used. It can be seen from Fig. 6 that the proposedCFO synchronization method highly decreases the error ratiocompared to the no CFO synchronization scenarios. It alsogives a close performance to the no CFO scenarios for bothof systems. It is also shown that GFDMA with multipleusers can approach the single user performance of SC-FDMA.GFDMA can effectively cancel interferences with user-specificinterleavers and iterative multiuser detection. This result alsomeans that GFDMA can increase the spectral efficiency ofSC-FDMA by a factor of two.

In the second simulation the effect of FFT size (numberof subcarriers per symbol) is analyzed. Parameters are thesame with the previous one except the FFT size. As it can beseen from Fig. 7, increasing the FFT size clearly increases thesystem performance due to increased null subcarrier number.This helps in both ways, firstly increasing the null subcarriernumber decreases the effect of MAI by increasing the null gap

Fig. 6. SC-FDMA and GFDMA with and without CFO and the proposedCFO synchronization algorithm

Fig. 7. SC-FDMA and GFDMA with FFT sizes: 512, 1024 and 2048

between users, and secondly more null subcarrier means moreinformation for estimating the CFOs accurately.

In the third simulation the effect of user number is ana-lyzed. Parameters are the same with the first one, except theFFT size is 2048 and the user number is changing. As it can beseen form Fig. 8, increasing the user number clearly decreasesthe system performance due to decreased null subcarrier num-ber. In contrast with the previous simulation, the decreased nullsubcarriers worsen the effect of MAI by decreasing the gapsbetween users. Also as there is less information for estimatingthe CFOs now, estimation errors increase and overall systemperformance goes down.

Fig. 8. SC-FDMA and GFDMA with user numbers 2, 4, 8 and 1, 2, 4respectively

In the fourth simulation, the effect of subcarrier mapping

scheme on the performance is analyzed. Parameters are thesame with the first one, except for subcarrier mapping IFDMAscheme is also used. To make our method applicable, both ofthe subcarrier mapping schemes are realized with sub-bandscoming after transmitted symbols. As it can be seen fromFig. 9, LFDMA with sub-bands gives better performance thanIFDMA with sub-bands, especially at higher SNR values. Thisshows us that our method is more vulnerable to MAI than ICI,as IFDMA with sub-bands has the main aim of decreasingthe effect of ICI in contrast with LFDMA with sub-bands,which has the main aim of decreasing the effect of MAI. As aresult of this, LFDMA gives the better performance; LFDMAcancels the excess MAI caused by imperfect filtering, whereasthe algorithm of the method estimates ICI very accurately.

Fig. 9. SC-FDMA and GFDMA using LFDMA and IFDMA with sub-bandssub-carrier mappings

VII. CONCLUSION

In this paper, we have analyzed the system architecture ofuplink GFDMA and SC-FDMA systems, sub-carrier mappingmethods suitable, the null sub-carrier method which is usedto avoid CFO problem and obtained simulation results whichshow the effect of CFO synchronization method, FFT size,number of users and subcarrier mapping scheme on the BERperformance of overall system. The first simulation shows thatthe proposed method highly increases the performance withrespect to the non-synchronized scenario and brings it closerto the no CFO scenario. Meanwhile, the following simulationsdemonstrate that other factors that increase the performance ofthe system are increasing the FFT size, decreasing the numberof users and using LFDMA with sub-bands. It is also shownfor all the simulations that, GFDMA is affected less fromCFO than SC-FDMA, as it encounters much less ICI than SC-FDMA, owing to its non-orthogonal nature. As a result multi-user GFDMA systems achieve the performance of single-userSC-FDMA systems.

REFERENCES

[1] MYUNG, H. G., LIM, J., GOODMAN, D. J. Single carrier FDMAfor uplink wireless transmission. IEEE Vehicular Technology Magazine,2006, vol. 1, no. 3, p. 30-38.

[2] YUNE, T., CHOI, C., IM, G., SC-FDMA with Iterative MultiuserDetection: Improvements on Power/Spectral Efficiency. CommunicationsMagazine, IEEE, 2010, vol. 48, no. 3, p. 164-171. 365.

[3] LIM, H., KIM, T., IM, G., A Proportional Fair Scheduling Algorithm forSC-FDMA with Iterative Multiuser Detection. Information and Commu-nication Technology Convergence (ICTC), 2010 International Conferenceon, 2010, p. 243-244.

[4] MORELLI, M. Timing and frequency synchronization for the uplink ofan OFDMA system. IEEE Transactions on Communications, 2004, vol.52, no. 2, p. 296-306.

[5] VAN DE BEEK, J. J., BORJESSON, P. O., BOUCHERET, M. L.,LANDSTROM, D., ARENAS, J. M., ODLING, P., OSTBERG, C.,WAHLQVIST, M., WILSON, S. K. Time and frequency synchroniza-tion scheme for multiuser OFDM. IEEE Journal on Selected Areas inCommunications, 1999, vol. 17, no. 11, p. 1900-1914.

[6] YANXIN, N., HLAING, M. Line Search Based Iterative Joint Estimationof Channels and Frequency Offsets for Uplink OFDMA Systems. IEEEGlobal Communications Conference 06, 2006, p. 1-5.

[7] MOVAHEDIAN, M., MA, Y., TAFAZOLLI, R., MUI resilient approachfor blind CFO estimation in OFDMA uplink. IEEE 19th InternationalSymposium on Personal, Indoor and Mobile Radio Communications2008, 2008, p. 1-5.

[8] ZHONGREN, C., TURELI, U., YU-DONG, Y. Deterministic multiusercarrier-frequency offset estimation for interleaved OFDMA uplink. IEEETransactions on Communications, 2004, vol. 52, no. 9, p. 1585-1594.

[9] BARBAROSSA, S., POMPILI, M., GIANNAKIS, G. B. Channelinde-pendent synchronization of orthogonal frequency division multiple accesssystems. IEEE Journal on Selected Areas in Communications, 2002, vol.20, no. 2, p. 474-486.

[10] NIU, D., DAI, X., Iterative Carrier Frequency Offset Estimation forOFDMA Uplink based on Null Subcarriers. 2006 40th Annual Confer-ence on Information Sciences and Systems, 2006, p. 295-299.

[11] MANOHAR, S., SREEDHAR, D., TIKIYA, V., CHOCKALINGAM, A.Cancellation of Multiuser Interference Due to Carrier Frequency Offsetsin Uplink OFDMA. IEEE Transactions on Wireless Communications,2007, vol. 6, no. 7, p. 2560-2571.

[12] CAO, Z., TURELI, U., YAO, Y., HONAN, P. Frequency synchronizationfor generalized OFDMA uplink. IEEE Global Communications Confer-ence 04, 2004, vol. 2, p. 1071-1075.

[13] SUN, P., ZHANG, L., A Novel Pilot Aided Joint Carrier FrequencyOffset Estimation and Compensation for OFDMA Uplink Systems. IEEEVehicular Technology Conference Spring 2008, 2008, p. 963- 967.

[14] FANTACCI, R., MARABISSI, D., PAPINI, S., Multiuser interferencecancellation receivers for OFDMA uplink communications with carrierfrequency offset. IEEE Global Communications Conference 04, 2004,vol. 5, p. 2808-2812.

[15] DAI, X., Carrier frequency offset estimation and correction for OFDMAuplink. IET Communications, 2007, vol. 1, no. 2, p. 273- 281.

[16] VAN DE BEEK, J. J., SANDELL, M., BORJESSON, P. O. MLestimation of time and frequency offset in OFDM systems. IEEE Trans.Signal Processing, 1997, vol. 45, p. 1800-1805.

[17] TURELI, U., LIU, H., ZOLTOWSKI, M., OFDM blind carrier offsetestimation: ESPRIT. IEEE Trans. Commun., 2000, vol. 48, p. 1459-1461.

[18] LIU, H., TURELI, U., A high-efficiency carrier estimator for OFDMcommunication. IEEE Commun. Lett., 1998, vol. 2, p. 104-106.