Uplin Capacity Comparion o Non-Perect Frequency Synchronied Cellular OFDM Sytem Shameem Kabir Chaudhury, Harald Haa School o Engineering and Science International Univerity Bremen 8759 Bremen, Germany {.chaudhury & h.haa}@iu-bremen.de Abtract Orthogonal requency diviion multiplexing (OFDM i very enitive to requency oet which reult in coniderable intererence. Perormance o the ytem will be exacerbated in a cellular deployment with requency reue o one. A general mathematical model i developed to calculate the amount o intererence in cellular OFDM ytem conidering requency oet between tranmitter (Tx and receiver (Rx, depending on dierent multiple acce and duplexing technique. Adaptive modulation cheme i applied to compare the capacity o dierent cellular OFDM ytem. It i ound that the capacity o requency diviion multiple acce (FDMA ytem outperorm that o time diviion multiple acce (TDMA ytem due to multiuer diverity in FDMA. Moreover, time diviion duplexing (TDD ytem outperorm requency diviion duplexing (FDD ytem irrepective o multiple acce technique by exploiting time lot (TS oppoing algorithm. Keyword Cellular OFDM, SINR, oppoing algorithm, adaptive modulation. I. INTRODUCTION OFDM i regarded a a uitable modulation technique or high rate multimedia wirele ytem over requency elective ading channel but it i extremely enitive to carrier requency oet, which i mainly caued by the inherent intabilitie o the carrier requency ocillator in the Tx and the Rx. The eect o requency oet wa extenively tudied in dierent paper [1], []. Signal-to-noie (SNR degradation due to requency oet wa preented in [1], wherea [] dicued the bit-error-ratio (BER degradation due to the ame reaon. Both paper ocued on lin to lin communication and did not conider cellular intererence. Paper [3] [5] provided dierent cheme to ynchronize multiuer OFDM-FDMA ytem. In thee paper, only intercarrier intererence (ICI and multiple acce intererence (MAI in the ame cell wa conidered where co-channel intererence (CCI i a big ource o intererence in cellular deployment or high requency reue actor wa ignored. In thi paper, ignal-to-intererence-plu-noie ratio (SINR a well a capacity or dierent cellular OFDM ytem are analyzed or requency reue actor o one. Two dierent multiplexing technique viz. TDMA and FDMA are conidered in thi paper while calculating intererence. In a TDMA ytem, there i no ICI but multiuer diverity cannot be exploited. On the other hand, in an FDMA ytem, multiuer diverity can be exploited, but MAI occur in cae o lac o requency ynchronization between uer. With repect to duplexing, two technique viz. FDD and TDD are taen into conideration. No time ynchronization i required in FDD but there i no upport o channel reciprocity, multihop communication and channel aymmetry; wherea, TDD oer channel reciprocity which i a ey enabler or upport o channel aymmetry and multihop communication but time ynchronization i required in TDD. In [6], Rohling compare BER o dierent OFDM multiple acce technique or TDD ytem in the downlin conidering perectly ynchronized networ. Since requency ynchronization in the uplin o cellular OFDM ytem i diicult to attain [3] [5], a comparative tudy or dierent multiple acce and duplexing technique in the uplin o cellular OFDM ytem or a non-perect requency ynchronized networ i preented here. At any given time intant when only one mobile tation (MS and one bae tation (BS are involved in an intra-cell communication (uch a in a TDMA ytem, all ubcarrier o the MS are expoed to the ame requency oet caued by a dierence o the local ocillator requencie at the BS and the MS. The Rx (MS or BS can thereore etimate an exiting requency oet by which it i aected a part o it requency ynchronization unit and correct it by hiting the received ignal to the required requency [7]. Thereore, a TDMA ytem doe not experience any intererence rom it own cell ater requency correction. Wherea, the deired MS in an FDMA ytem can be made requency ynchronized with the deired BS, but other MS( tranmitting at the ame time in the ame cell which are not requency ynchronized with the BS, would produce coniderable amount o intererence. Depending on thee aumption, two dierent mathematical model are developed to calculate the SINR. Moreover, ideal time ynchronization i aumed in thi model. An FDD ytem primarily uer rom MS BS intererence, which i called other-entity intererence. In addition to that, in a TDD ytem MS MS and BS BS intererence exit ince uplin and downlin are on the ame carrier requency. Since ource and in o intererence are the ame, thi type o intererence i called ame-entity intererence. I the TDD networ i ynchronized, it i demontrated in [8] that the intererence cenario between neighboring cell can be manipulated by oppoing two TS( which i reerred a
oppoing algorithm. Hence, the co-channel intererence (CCI in the TDD mode can potentially be le than that in the FDD mode. Dierent order modulation allow u to end more bit per ymbol and thu achieve higher capacity or better pectral eiciencie [9]. However, it mut alo be noted that when uing a modulation technique uch a 64/56-QAM, better SINR are needed to overcome any intererence and maintain a certain bit error ratio (BER. The ue o adaptive modulation allow a wirele ytem to chooe the highet order modulation depending on the channel condition. Uing thi adaptive modulation cheme, it i ound in thi tudy that, the capacity o an FDMA-TDD ytem i the highet (3.3946 bp/hz/cell wherea, the TDMA-FDD ytem attain the lowet capacity (1.9156 bp/hz/cell. It ha to be noted that, capacity lo due to ignaling overhead o adaptive modulation, i not conidered in thi model. The aim o thi tudy i to get the upper bound o capacity auming ideal adaptive modulation. Moreover, in order to iolate the intererence eect rom requency oet, other ideal condition (e.g. time ynchronization are aumed. The outline o the paper i a ollow: ection II provide the detail about the model to calculate the SINR due to requency oet in cellular OFDM ytem; moreover, an outline i preented to ind the capacity uing adaptive modulation. Depending on thi model, the imulation reult are preented in ection III and concluding remar are given in ection IV. II. SYSTEM MODEL A coverage area o a cellular tructure i conidered in thi model. MS( are uniormly ditributed in the coverage area wherea, BS( are poitioned in the center o the cell. All Tx( (both the MS and BS tranmit with equal power, i.e. no power control i conidered. A low ading Rayleigh channel between Tx and Rx i aumed where the channel remain roughly contant over everal hundred ymbol. Moreover, the channel i aumed to be nown at the receiver. Thi ytem model i developed or uplin cenario. Dierent type o intererence occur in cellular OFDM ytem due to requency oet: 1 ICI rom it own ubcarrier, MAI rom other uer in the ame cell uing the ame OFDM ymbol, 3 CCI rom other cell uer. A. Calculation o intererence caued by requency oet or a ingle cell cenario For a ingle cell cenario, conidering requency oet, the received ymbol ater OFDM demodulation at the bae tation on ubcarrier o uer m can be written a [10], [11]: R (m = S (m H (m N + S (m =0 C(ǫ (m H(m C( + ǫ (m } {{ } ICI +N (1 where, C(θ = in(πθ N C in(πθ/n C e(jπθ(n/nc i the Dirichlet unction, ǫ (m i the requency oet relative to the ubcarrier pacing, (m are the time domain ample (S (m i the Fourier tranorm o correponding time ample. H(m i the modiied channel traner unction uch that H(m = H (m.e jφ(m where, H (m i the channel traner unction o uer m on ubcarrier and φ (m denote the accumulated phae rotation o uer m over conecutive OFDM ymbol due to it requency oet. N denote the AWGN contribution on ubcarrier. In thi equation any ditance dependent delay ha been included in the channel characterization ince it only caue an additional ubcarrier dependent phae rotation o the received modulation ymbol a long a the guard interval i not violated. B. Calculation o intererence caued by requency oet or a cellular cenario For a cellular ytem with requency reue actor o one, other uer rom adjacent cell uing the ame requency produce coniderable amount o intererence. Conequently, i a cellular ytem i deployed, (1 can be updated a: R (0 = [ S (0 + M ] H (0 C(ǫ(0 + ICI(0 N m =1 =0 S (m H(m C( + ǫ (m } {{ } CCI + N where the upercript (0 reer to the deired BS index, M i the number o interering mobile tation, ǫ (m i correponding requency oet relative to the ubcarrier pacing. Since it i nown that: S = ne b = Pr where E b i energy per bit, n i the number o bit in each ymbol, P r i the received power and R i the ymbol rate; ( can be rewritten a: [ ] R (0 pr = H (0 R C(ǫ(0 + ICI(0 M p (m N I + H (m C( + ǫ (m (3 R m =1 =0 + N where, p R i the received power rom the deired MS, p I i the intererence power rom an interering MS in the adjacent cell. In general, the received power P r can be calculated a: R ( P r = P t L P [db] (4
where, P t i the tranmitted power and L P i the pathlo which i ound by [1]: L P = 18.1 + 37.6 log 10 (r + X σ [db] (5 where, R i the Tx - Rx eparation in ilometer, i the carrier requency o GHz, and X σ i the lognormal hadowing component, wherein a zero mean and a tandard deviation o 10 db i aumed. relative channel gain 0.1 0.1 0.08 0.06 0.04 ubcarrier aignment or FDMA Frequency range given to one uer C. SINR calculation or cellular cenario Equation (3 i the general expreion or received ymbol ater OFDM demodulation at the receiver on ubcarrier. Thi expreion need to be modiied depending on the dierent multiple acce technique. 1 TDMA/FDD and TDMA/TDD: A TDMA ytem doe not experience any MAI ince all the ubcarrier in the ytem are aigned to only one Tx in a given TS. Moreover, requency oet (ǫ can be corrected between the Tx and the Rx, reulting in an ICI-ree ytem. In that cae, (3 would be: R (0 = pr + R H(0 M m =1 + N p (m N I H (m R C( + ǫ (m =0 From thi received ignal, the deired ignal power and intererence power can be calculated. Uing thee power, the SINR, γ (TDMA, or the TDMA ytem can be written a: γ (TDMA = pr R H(0 M p (m N I H (m R C( + ǫ (m + N m =1 =0 Fig. 1. Intererence cenario in the cellular ytem (6 (7 BS MS deired lin ame entity intererence other entity intererence 0.0 Frequency range given to other uer 0 0 50 100 150 00 50 ubcarrier index Fig.. ubcarrier aignment depending on channel gain For an FDD ytem, MS( are the only intererer (otherentity intererence; wherea, in a TDD ytem, MS and BS both contribute to the intererence (both ame-entity and otherentity intererence. The equation to calculate the SINR i ame or both cae but i depending on the poition o the intererer, i.e. the intererence power, p I, will be dierent. The intererence cenario or TDD ytem i hown in Fig. 1. FDMA/FDD and FDMA/TDD: Unlie the TDMA ytem, at a given time intant more than one Tx( are involved in an FDMA ytem. The deired MS can be made ynchronized with the BS a could be done in the TDMA ytem. But all the uer, tranmitting at the ame time, are not ynchronized with each other which reult in MAI. Moreover, a in TDMA, the FDMA ytem i ubject to CCI. In that cae, the SINR, γ (FDMA, or the FDMA ytem can be written a: γ (FDMA = MAI(0 + pr R H(0 M p (m N I H (m R C( + ǫ (m + N =0 (8 m =1 where MAI (0 correpond to multiple acce intererence ignal in the deired cell. Thi equation i valid or both the TDD and the FDD cae. Intererence or an FDMA ytem i higher than that o a TDMA ytem due to additional intererence rom the own cell. I it i poible to tranmit the OFDM ymbol at the requency range where the channel ha higher gain (bet channel condition, the SINR could be increaed. The propoed bloced ubcarrier aignment i given in Fig.. For implicity, a ubcarrier aignment or only two uer i hown in thi igure. Since the border ubcarrier experience the highet intererence rom other uer [11], the average intererence o all aigned ubcarrier o the deired uer i calculated to compare with the TDMA ytem. N i not taen into conideration in the imulation.
MS BS exchange TS' :1 le intererence which mean higher capacity. Thi above mentioned TS oppoing algorithm i applied or TDD ytem in thi paper. BS1 MS TS o interet High intererence 1: Fig. 3. Intererence cenario beore TS-oppoing the ize o the arrow indicate the potential everity o the intererence MS BS BS1 MS Fig. 4. exchanged TS' TS o interet Little intererence Intererence cenario ater TS-oppoing :1 1: Conequently, the ymbol rate R cancel out in (7 and (8. Thereore, the imulation provide ignal-to-intererence ratio (SIR. D. TS oppoing algorithm An important iue o a cellular TDD ytem i that it i ubject to additional intererence mechanim compared with an FDD ytem, in particular i uer demand dierent rate o aymmetry in neighboring cell. It i hown in [8] that the appearance o additional intererence cenario in TDD can be exploited contructively to minimize intererence between two neighboring cell by oppoing two TS(. The mechanim i demontrated in Fig. 3 and Fig. 4. Thee Figure how a impliied TS arrangement (only three TS( between entitie o two neighboring cell. In Fig. 3 it i aumed that MS i located at the cell boundary o it cell and cloe to the BS o the adjacent cell (BS1. Hence, the ignal power rom MS experienced at BS1 i much greater than the ignal power rom BS experienced at BS1 (indicated by the arrow. However, it can be een that the lower ignal power rom BS i without any eect a it terminate at a tranmit TS at BS1. In contrat, the greater ignal power rom MS terminate at the receive TS o BS1 and generate high intererence. It i obviou that exchanging both TS( in cell change the intererence ituation igniicantly. Thi i demontrated in Fig. 4. Now the greater ignal power rom MS terminate at the tranmit TS o BS1 and, hence, doe not caue intererence. Intead, only the maller ignal power rom BS reache the intererence enitive receive TS o BS1. A a conequence, although the total tranmitted power in both cenario i the ame, the cenario in Fig. 3 yield E. Capacity calculation The cumulative ditribution unction (cd o SINR or dierent multiple acce technique can be ound uing (7 or (8, depending on the multiple acce technique. Adaptive modulation technique i ued to increae the capacity o the ytem, i.e., when the SINR i lower, le number o bit are aigned to one ymbol (uch a BPSK, QPSK etc., when it i higher, higher number o bit are aigned to one ymbol (uch a 64 QAM, 56 QAM etc.. It mut be taen into account that, to apply adaptive modulation cheme at the tranmitter, the SINR hould be etimated beore tranmitting the ymbol. The capacity o the ytem i calculated or contant BER = 10 3. It i nown that a narrowband mobile lin may be modeled a a lat-ading channel which i the cae or an OFDM ytem. For large number o ubcarrier, the received SINR may be approximated by a contant or each ading region and the Rayleigh ading channel may be viewed at a given ubcarrier a an element in a et o AWGN channel with dierent but contant SINR [13]. Moreover, ince the intererence due to requency oet may be modeled a WGN [14], the uncoded BER curve or AWGN (Fig. 5 i ued to ind the correponding SINR or dierent modulation technique [15]. Six dierent modulation cheme (N = 6 are ued in thi model: BPSK, QPSK, 8-QAM, 16-QAM, 64-QAM and 56-QAM. At irt, the minimum SINR required to get BER = 10 3 or dierent modulation cheme are ound which are indicated in Fig. 5. Thee are the threhold value o γ i (i = 1,..., 6. When the intantaneou received SINR γ all in the region where γ i γ < γ i+1, the modulation correponding to γ i hould be ued. When γ < γ 1, no inormation i ent. The correponding cumulative probability (P i or thee modulation cheme are ound uing thee SINR(. Hence, BER 10 0 10 10 4 10 6 10 8 10 10 10 1 10 14 BPSK QPSK 8QAM 16QAM 64QAM 56QAM BER v. SIR or OFDM lat ading channel 0 5 10 15 0 5 30 SIR in db Fig. 5. BER veru SIR or OFDM lat ading channel
1 0.9 TDMA FDD TDMA TDD cd o SIR or TDMA ytem 1 0.9 FDMA FDD FDMA TDD cd o SIR or FDMA ytem cumulative probability o occurance 0.8 0.7 0.6 0.5 0.4 0.3 0. cumulative probability o occurance 0.8 0.7 0.6 0.5 0.4 0.3 0. 0.1 0.1 0 80 60 40 0 0 0 40 60 80 100 10 SIR in db 0 40 0 0 0 40 60 80 100 10 SIR in db Fig. 6. cd o SIR or TDMA ytem Fig. 7. cd o SIR or FDMA ytem TABLE I CAPACITY CALCULATION FOR TDMA SYSTEMS TABLE II CAPACITY CALCULATION FOR FDMA SYSTEMS cumulative cumulative i η i (modulation SIR probability probability (in db (FDD (TDD 1 1 (BPSK 6.8188 0.563 0.3457 (QPSK 9.880 0.5995 0.4 3 3 (8-QAM 14.4309 0.708 0.547 4 4 (16-QAM 16.5519 0.7454 0.5964 5 6 (64-QAM.5579 0.8447 0.7333 6 8 (56-QAM 8.464 0.9105 0.8351 C [bp/hz/cell] 1.9156.956 cumulative cumulative i η i (modulation SIR probability probability (in db (FDD (TDD 1 1 (BPSK 6.8188 0.314 0.506 (QPSK 9.880 0.3979 0.3303 3 3 (8-QAM 14.4309 0.530 0.4641 4 4 (16-QAM 16.5519 0.5930 0.584 5 6 (64-QAM.5579 0.7460 0.6954 6 8 (56-QAM 8.464 0.8530 0.8191 C [bp/hz/cell].9649 3.3946 the capacity (C o the ytem can be ound by: N C = (P i+1 P i η i [bp/hz/cell] (9 i=1 where, i correpond to the tep index o adaptive modulation (i = 1 or BPSK,..., i = 6 or 56-QAM, P i i the correponding cumulative probability (P 7 = 1.0, and η i i the number o bit in each ymbol or the pectral eiciency. Sytem level imulation are carried out to ind the SINR and capacity or dierent ytem and reult are dicued in the next ection. III. RESULTS AND DISCUSSION The analytical model i veriied with the ollowing imulation model wherein a even cell ytem with 1 m radiu or each cell and requency reue actor o one i conidered. The requency oet ǫ o each mobile tation i a random value uch that 0.5 ǫ 0.5. For all the imulation, Rayleigh ading channel i aumed where the delay pread i le than the guard period o the OFDM ymbol. The number o ubcarrier, N C = 56 and tranmit power or each Tx (both MS and BS i 30 dbm. A. TDMA All the 56 ubcarrier are aigned to one uer in one TS at a given cell. 1 TDMA-FDD: The cd o SIR i ound uing (7, which i hown in Fig. 6. A previouly explained in the ytem model, the capacity o the TDMA-FDD ytem can be ound rom Fig. 6 and (9. In thi cae, only the MS( contribute to the intererence rom neighboring cell. TDMA-TDD: Timelot aignment or uplin and downlin are randomly choen or dierent cell or the TDD ytem but ymmetric traic i aumed, i.e. the probability that TS( are oppoed i 0.5. The TS oppoing algorithm i applied to increae the capacity o TDD ytem. The cd o SIR or TDMA-TDD ytem i hown in Fig. 6 and the capacity calculation i given in Table I. It ha been ound rom Table I that, the capacity o the TDMA-TDD ytem outperorm that o TDMA-FDD ytem. It i nown that, TDD ytem experience potential intererence rom neighboring BS( which i not the cae in FDD ytem. However, the appearance o additional intererence in TDD can be exploited contructively by the TS oppoing algorithm. Uing thi algorithm the capacity o TDMA-TDD ytem i ound to be.956 bp/hz/cell which i approximately 1 bp/hz/cell higher than the capacity o TDMA-FDD ytem. B. FDMA The total number o ubcarrier N C = 56 are aigned in bloc to 16 dierent uer; i.e. each uer ha 16 ubcarrier
to tranmit ignal. The ubcarrier aignment cheme wa explained in the previou ection. 1 FDMA-FDD: It wa dicued in ection II-C. that FDMA ytem experience MAI when there i requency oet between uer. Moreover, a in TDMA, the ytem i ubject to CCI. In thi cae, requency oet between cell will aect the level o CCI. The cd o intererence i hown in Fig. 7 and the capacity calculation i given in Table II. FDMA-TDD: A in TDMA-TDD ytem, uplindownlin aignment o the cell are random with ymmetric traic and the TS oppoing algorithm i applied. The cd o SIR i hown in Fig. 7 and capacity i calculated in Table II. The capacity in TDD ytem i about 0.4 bp/hz/cell higher than that o FDD ytem. In general, the capacity o FDMA ytem i higher than that o TDMA ytem which i hown in Table I and Table II. Exploiting TS oppoing algorithm in TDD and uer cheduling in FDMA, capacity o FDMA-TDD ytem outperorm any other ytem. Moreover, the perormance o TDMA-TDD and FDMA-FDD ytem i almot imilar. IV. CONCLUSION Intererence due to requency oet and correponding capacity or dierent multiple acce and duplexing technique in OFDM ytem ha been analyzed in thi paper. The overall intererence in FDMA i lower than that o TDMA ytem depite the preence o MAI in the FDMA ytem when there i requency oet between uer. FDMA-TDD ytem attain the highet capacity (3.3946 bp/hz/cell conidering only the requency oet eect (capacity lo due to ignaling overhead and time ynchronization eect were not taen into account. Uer cheduling cannot be applied to TDMA ytem, a a reult TDMA ytem oer lower capacity. However, applying the TS oppoing algorithm, TDMA-TDD (.956 bp/hz/cell ytem attain imilar capacity o FDMA-FDD (.9649 bp/hz/cell ytem. The lowet capacity occur in TDMA-FDD ytem which i around 1.9156 bp/hz/cell. REFERENCES [1] P. H. Mooe, A technique or Orthogonal Frequency Diviion Multiplexing requency oet correction, IEEE Tran. Commun., vol. 4, pp. 908 914, Oct. 1994. [] T. Pollet, M. V. Bladel, and M. Moeneclaey, BER enitivity o OFDM ytem to carrier requency oet and wiener phae noie, IEEE Tran. Commun., vol. 43, pp. 191 193, Feb./Mar./Apr. 1995. [3] Z. Cao, U. Tureli, and Y.-D. Yao, Determinitic multiuer carrierrequency oet etimation or interleaved OFDMA uplin, IEEE Tran. Commun., vol. 5, pp. 1585 1594, Sep. 004. [4] M. Morelli, Timing and requency ynchronization or the uplin o an OFDMA ytem, IEEE Tran. Commun., vol. 5, pp. 96 306, Feb. 004. [5] J. jaap van de Bee, per Ola Börjeon, M.-L. Boucheret, D. L. J. M. Arena, P. Ödling, C. Ötberg, M. Wahlqvit, and S. K. Wilon, A time and requency ynchronization cheme multiuer OFDM, IEEE JSAC., vol. 17, pp. 1900 1914, Nov. 1999. [6] H. Rohling and R. Grünheid, Perormance comparion o dierent multiple acce cheme or the downlin o an OFDM communication ytem, in IEEE 47th Vehicular Technology Conerence, 1997, vol. 3, pp. 1365 1369, 4-7 May 1997. [7] T. M. Schmidl and D. C. Cox, Robut requency and timing ynchronization or OFDM, IEEE Tran. Commun., vol. 45, pp. 1613 161, Dec. 1997. [8] H. Haa, S. McLaughlin, and G. J. R. Povey, A novel intererence reolving algorithm or the TDD TD-CDMA mode in UMTS, in International Sympoium on Peronal, Indoor and Mobile Radio Communication PIMRC 000, (London, UK, pp. 131 135, Sep. 000. [9] A. J. Goldmith and S.-G. Chua, Variable-rate variable-power MQAM or ading channel, IEEE Tran. Commun., vol. 45, p. 118 130, Oct. 1997. [10] G. Auer, A. Dammann, S. Sand, and S. Kaier, On modelling cellular intererence or multi-carrier baed communication ytem including a ynchronization oet, in 6th International Sympoium on Wirele Peronal Multimedia Communication (WPMC 003, (Yooua, Japan, pp. 90 94, Oct. 003. [11] D. Galda, H. Rohling, and E. Cota, On the eect o uer mobility on the uplin o an OFDMA ytem, in IEEE Vehicular Technology Conerence, pp. 1433 1437, Apr. 003. [1] available at http://www.3gpp.org/pec/pec.htm. [13] K. J. Hole, H. Holm, and G. E. Oien, Adaptive multidimenional coded modulation over lat ading channel, IEEE Journal on Selected Area in Communication, vol. 18, p. 1153 1158, Jul. 000. [14] M. Speth, S. Fechtel, G. Foc, and H. Meyr, Optimum receiver deign or wirele broad-band ytem uing OFDM part I, IEEE Tran. Commun., vol. 47, pp. 1668 1677, Nov. 1999. [15] J. G. Proai, Digital communication. New Yor, NY: McGraw-Hill, ourth ed., 001.