Hadi Alasti. Department of Electrical Engineering, University of North Carolina at Charlotte

Transcription

1 Hadi Alasti Departet of Electrical Egieerig, Uiversity of North Carolia at Charlotte ABSTRACT A iterferece tolerat OFDMA schee is proposed for ultiuser wireless couicatios with specific applicatio i feto cells. A iterleaved set of subcarriers is dedicated to each user to provide with a high order of frequecy diversity. A reduced coplexity digital ipleetatio of the techique is proposed ad discussed for the iterleaved sub-carrier arrageet. Both iter-sybol iterferece ad other-user iterferece are itigated usig a proper cyclic extesio, provided that the relative propagatio delays of the users are a iteger ultiple of a sybol period. The effect of other-user iterferece due to o-iteger propagatio delays is ivestigated usig coputer siulatios. The bit error rate perforace ad sigal to iterferece ratio are preseted for a few exaple systes over both a Additive White Gaussia Noise (AWGN) ad a frequecy selective Rayleigh fadig chael. The aout of other-user iterferece is show to be reduced as the uber of sub-carriers per user is icreased. The effect of desig paraeters o the iterferece level is discussed. KEYWORDS Multiuser OFDMA, Iterferece, extesio 1. INTRODUCTION Two ajor probles associated with data couicatios over terrestrial wireless chaels are iter sybol iterferece ad fadig caused by ultipath propagatio. I ulti user applicatios such as persoal obile couicatios, other-user iterferece could also liit the syste perforace ad capacity. Various ultiple access techiques have bee devised for ulti user wireless applicatios. Code Divisio Multiple Access (CDMA) schees use a wide frequecy bad ad therefore, a high order of frequecy diversity could be achieved whe the sigal badwidth is sufficietly larger tha the chael coherece badwidth [1,2,9]. The capacity of the CDMA techiques usig biary codes such as Walsh-Hadaard codes are liited by the users sigal iterferece. This is resulted fro o-zero cross correlatio betwee biary codewords with differet tie shifts. The trasit codewords arrive at each user receiver with differet tie shifts because of various propagatio delays associated with the users scattered over a cell ad also because of ultipath propagatio. Cobied tie ad frequecy divisio ultiple access schees usually use sigals with a arrower badwidth. Slow frequecy hoppig is soeties used to cobat fadig of statioary ad slow ovig users i such schees. I this paper, a iterferece tolerat widebad ultiple access schee is discussed based o the orthogoal frequecy divisio ultiplexig (OFDM). The schee is desiged as such, the aout of other-user iterferece ad iter sybol iterferece are reduced. This is achieved usig both a cyclic prefix ad a cyclic suffix i the trasit data fraes ad otig that the Fourrier codewords used i OFDM have a zero cross correlatio o all cyclic shifts. A set of o-adjacet subcarriers is proposed for each user. This provides with a high order of frequecy diversity, which ca be realized usig proper error correctig codes [3]. As is the case 152

2 with orthogoal frequecy divisio ultiplexig, o chael estiatio ad equalizatio is required if differetially coheret QPSK odulatio are used [4,5]. The proposed schee ca be used i a sigle cell as well as a cellular syste ad could be cobied with other ultiple access techiques to satisfy the requireets of a specific applicatio. The drawbacks of the proposed schee iclude high sesitivity to oliearities due to large peak to average power ratio ad the carrier frequecy offset which are the coo probles with OFDMA [5,6]. Accurate sychroizatio of the wireless users ad syste i uplik ad dowlik is usually assued for efficiet chael allocatio ad spectru aageet i OFDMA based techologies such as WiMAX ad LTE [9]. Due to rado distributio of the users i the cells ad ultipath propagatio, accurate sychroizatio of all of the active users i acro-cells ad feto-cells is alost ipossible, which causes other-user iterferece. I this paper, a iterferece tolerat ulti-user OFDMA schee is proposed for applicatio i feto-cells. The schee is based o isertio of a cyclic prefix ad suffix with proper legth at the begiig ad at the ed of OFDM frae. The legth of the cyclic suffix, which is related to the axiu tiig offset betwee the users frae at receiver correlator s widow, is sall i feto-cells. Accordigly, a sall percetage of the badwidth is wasted for additioal cyclic suffix i feto cells ad co-existig acro cells (Figure 1). Moreover, because of the sall regio, feto-cells are expected to have less PAPR proble. The orgaizatio of the paper is as follows: I the followig sectio, the backgroud ad related work is reviewed. I sectio 3, the ai idea ad a reduced coplexity digital ipleetatio of the proposed techique is discussed. Sectio 4 is devoted to the iterferece reductio echais usig a proper cyclic extesio i various situatios. I sectio 5, the effect of other-user iterferece due to o-iteger propagatio delays is discussed usig coputer siulatio results. Coclusios ad proposed future work o this topic are preseted i sectio RELATED WORK To suppress the other user iterferece i quasi-sychroous ultiple access CDMA systes, special code desig were proposed [10,11,12,13,14]. As the out-of-phase autocorrelatio of the discussed codes was ot zero, the iter-sybol iterferece could ot be avoided i ultipath 153

3 fadig chaels. The idea of usig poly-phase codes was itroduced i [14] to have zero out-ofphase autocorrelatio ad sall cross correlatio i frequecy selective radio chaels. To add the diversity gai to OFDMA, dedicatio of o-adjacet sub-chaels over a widebad frequecy rage was proposed i [15, 16]. Dedicatio of o-adjacet equally spaced subchaels i frequecy selective wavefor chael was discussed i [17]. To extract the full diversity gai, a geeralized structure was proposed for ulti-carrier CDMA (MC-CDMA) i [18]. OFDM has bee proposed for IEEE , WiMAX systes, which eed accurate sychroizatio for extractio of the user s data. The effect of iter-sybol iterferece ad other user iterferece due to ultipath propagatio ad iaccurate tiig is reducible by additio of cyclic prefix ad suffix to the OFDM frae as is discussed i this paper. Siultaeous isertio of log cyclic suffix ad prefix reduces the badwidth efficiecy. I uplik trasissio, whe tiig offset betwee the users is sall (like feto cells), the badwidth efficiecy reductio due to isertio of cyclic suffix ight be egligible. Sychroizatio techiques for OFDMA i uplik ad dowlik trasissios were extesively discussed i [19]. 3. SYSTEM DESCRIPTION AND IMPLEMENTATION The iterferece tolerat OFDMA schee ad its discrete ipleetatio are discussed i this sectio. It is assued that the couicatio chael is a frequecy selective fadig chael ad a badwidth sufficietly larger tha the chael coherece badwidth is available. Sufficietly large badwidth is oe which provides with the required order of frequecy diversity i the syste. The available frequecy bad is divided ito a uber of flat fadig orthogoal sub-chaels. A set of o-adjacet sub-chaels are dedicated to each user. For istace, as is show i Figure 2 every oe of 3 sub-chaels is give to each of 3 users sharig the sae frequecy bad. Such a frequecy assiget guaratees a high order of frequecy diversity as o-adjacet sub-chaels are expected to fade idepedetly or with a saller correlatio. Figure 2: A exaple frequecy assiget for users sharig the sae badwidth A straightforward digital ipleetatio of the proposed schee uses the foral -based OFDM ipleetatio [3-6,8] with iforatio set oly over a subset of sub-chaels for each user. The trasceiver fuctioal block diagra for such a ipleetatio is show i Figure 3. I Figure 3, the equivalet discrete chael is a equivalet block for the trasit ad receive filters, Quadrature odulator ad deodulator, the physical wireless chael ad also the periodic sapler. It is assued that root Nyquist filters are used both i the trasitter ad the receiver. The cyclic extesio blocks help to iiize both itersybol ad other-user iterferece as is discussed i sectio 4. The Discrete Fourrier Trasfor () ad its iverse () are used to partitio the chael alog the frequecy axis [3,4,6]. A total of MN frequecy sub-chaels are geerated, N of the for each of M users sharig the available frequecy bad. The coded ad digitally odulated coplex-valued sequece of N copoets N 1 { V } is up-sapled = 0 accordig to (1). V / M = 0,,,...,( ) U = M 2 M N 1 M (1) 0 otherwise f 154

4 ad cyclically shifted right ties where = 0,1,2,...,M-1, is the user idex. At the receiver the output sequece is deciated. ~ ~ V = U M, = 0,1,2,..., N 1 (2) after beig cyclically shifted left ties. The coplexity of the OFDM ultiplexer ad deultiplexer as arked i Figure 3 ca be reduced otig the equivalet operatios show i Figure 4 [7]. I Figure3 the phase adjustet ad the phase correctio blocks are respectively defied accordig to (3) ad (4). k yk = uk W MN, k = 0,1,2,..., MN -1 (3) u~ ~ k = y W MN, k = 0,1,2,..., MN -1 (4) k k Biary Iforatio { } Codig & Modulatio N 1 V = 0 Decodig & Deodulatio Estiated Biary Iforatio { } U = 0 M { ~ N 1 V } = { ~ } 0 Up-Sapler Shift Right (User Idex) Multi Carrier Multiplexer Multi Carrier Deultiplexer M U = 0 Deciator Shift Left { Y } =0 { ~ Y } =0 (User Idex) { y k } k =0 Extesio Equivalet Discrete Chael Extesio Reoval { ~ y k Figure 3: The straightforward digital ipleetatio of iterferece tolerat OFDM { U } =0 { Y } =0 { y k } k=0 { } U =0 { u k { y k { ~ y k N-1 { V } =0 { ~ u k Shift Right User Idex M { ~ Y } =0 { U } =0 { ~ U } =0 { ~ U } =0 Shift Left User Idex b) M { u k { ~ N -1 V } =0 c) d) a) { ~ y k N-1 { V } =0 { ~ u k } k =0 Phase Correctio User Idex (N) Phase Adjustet User Idex { ~ u k N-1 { v k } k =0 Sequece Accuulator (M) { ~ N-1 v k } k =0 Sequece Repeater (M) (N) Figure 4: Equivalet discrete operatios { ~ U } =0 { u k { ~ N -1 V } =0 155

5 where 2π WMN = exp(-j ) MN where = 0,1,2,...,M-1 is the user idex. The sequece repeater ad the sequece accuulator blocks are respectively defied accordig to (5) ad (6). uk = v ( k ) od N, k = 0,1,2,..., MN -1 (5) M 1 v~ ~ k = u ( N + k ), k = 0,1,2,..., N -1 = 0 Usig equivalet operatios show i Figure4a ad Figure 4c, the OFDMA ultiplexer is reduced to what is show i Figure 5a. Usig Figure 4b ad Figure 4d, the OFDMA deultiplexer is reduced to Figure5b. Reductio i coplexity is ade aily because of reductio i the ad the frae legths fro MN poits to N poits. (6) N -1 N-1 { V } =0 { v k } k =0 { } { ~ N-1 V } =0 (N) (N) Sequece Repeater (M) u k k =0 Phase Adjustet User Idex a) Multi Carrier Multiplexer { ~ N-1 v k } k =0 Sequece Accuulator (M) { ~ u k Phase Correctio User Idex b) Multi Carrier Deultiplexer { y k } k =0 { ~ y k Figure 5: Reduced coplexity ulti carrier ultiplexer (a) ad deultiplexer (b). 4. CYCLIC EXTENSION AND INTERFERENCE Appedig a proper cyclic extesio to the output frae y i Figure 3, the = { y k } k = 0 aout of other-user iterferece ay be reduced. Whe the trasit sigal badwidth, B is occupied oly by oe user, the cyclic extesio is usually a prefix of legth L BT, where T is the total ultipath spread [3,4]. The output vector y ca be obtaied fro its iput vector = { y k } k= 0 Y = { Y } = 0 ultiplyig it by the Fourrier atrix. If each row of the Fourrier atrix is cosidered as a coplex-valued Fourrier codeword W, the process ay be viewed as a for of code divisio ultiplexig p where y = Y W (7) = 0 W (8) 0 1 (MN 1) W MN W MN... W = MN I fact each Fourrier codeword represets oe of the subbads geerated by the process. A good property of these codewords is that they have zero cross correlatio o all cyclic shifts. This property holds eve if the codewords are ultiplied by a real or a coplex-valued costat. Each trasit data Y set over the codeword W is resolved correlatig the received frae y%by the coplex cojugate of W. Because of the orthogoality of the Fourier 156

6 * codewords, oly Y passes through its correlator W. Whe the chael is a ultipath chael, shifted versios of the trasit frae also appear at the receiver. If the trasit frae icludes * a cyclic prefix, the each correlator W sees oly cyclic shifts of other Fourrier codewords ultiplied by a data sybol ad scaled by a chael coefficiet. Sice the Fourrier codewords { W } = 0 are orthogoal o all cyclic shifts, o iterferece fro other data sybols appears at the correlator output. I ulti user applicatios, depedig o the situatio, we ay have to odify the sigle user cyclic extesio to cotrol iterferece fro other users. First, cosider a case where the users are scattered i oe cell trasittig data to a base statio. The users data fraes are arrived at the base statio with differet tie shifts because of differet propagatio delays associated with each user. Figure 6 shows exaple equivalet discrete chael ipulse resposes correspodig to 3 users i a cell. For ow assue that the propagatio delays{ τi} relative to the user # 0, are iteger ultiples of the trasit sybol period T, for istaceτ 1 2T, τ 2 2T. The effect of o-iteger propagatio delays is discussed i sectio 5 usig coputer siulatio results. The users fraes arrival at the base statio receiver is depicted i Figure 7. Usig a cyclic suffix of Ls ax( τ i ) i, i = 0, 1, 2,...,M-1 (9) T h 00 h 01 h 02 h 03 T 0 User # 0 τ h 20 h 21 h 10h1 1 h 12 h 1 3 T 1 User # 1 τ h 22 h 2 3 τ 2 τ 1 T 2 τ User # 2 Figure 6: Relative propagatio delays of the users sharig the sae badwidth User # 0 User # 1 User # 2 { { { h 00 y 0 h 01 y 0 h 10 y 1 h 11 y 1 h 20 y 2 y h 21 2 Receiver Correlatio Widow τ 2 τ 1 Figure 7: The users frae arrival at the base statio receiver 157

7 ad a cyclic prefix of ax( τi + T i) i Lp T, i = 0, 1, 2,...,M -1 (10) the data fraes arrived at the base statio appear as cyclic shifts of scaled Fourrier codewords withi the correlator widow. Therefore, o iterferece fro other data sybols ad other users passes the correlator. The cyclically exteded trasit frae is therefore give by ymn L... ymn y0 y... ymn y y... y p Ls 1 I dowlik, where data is set by the base statio to the obile users, the trasit data fraes of all the users are sychroized ad therefore τ i = 0, i = 0, 1, 2,...,M -1. Hece, o cyclic suffix is required ad the cyclic prefix is reduced to T i Lp ax( ), i = 0,1,2,..., M -1 (11) i T 5. PERFORMANCE EVALUATION 5.1. BER i AWGN ad Rayleigh fadig chael As discussed i the previous sectio, usig a proper cyclic extesio, o iterferece fro other users is expected if the user propagatio delays would be a iteger ultiple of the sybol period. This ay ot be achieved i practice whe obile users trasit data to a base statio. The effect of other-user iterferece resulted fro o-iteger propagatio delays are ivestigated usig coputer siulatios. The results are obtaied for a exaple syste where 3 obile users i oe cell share the sae frequecy bad. Root raised cosie filter with a roll-off factor of 0.25 are used both i the trasitter ad receiver. The syste is assued to have a power cotrol echais as such the users have the sae power at the base statio. The subcarrier odulatio is the coheret DQPSK ad o chael codig has bee perfored. Figure 8 shows the bit error rate perforace over a AWGN chael for various relative propagatio delays τ i associated with the two iterferig users. The results are achieved assuig L = L = 1 ad usig N = 4 subcarriers per user. As is see i Figure 8 the best p s perforace is achieved, whe τ 1 adτ 2 is either zero or equal to a sybol period T. The worst perforace is obtaied whe τ 1 = τ 2 = 0.5T. Figure 8: Perforace copariso for various propagatio delays over AWGN chael. Figure 9: Worst case perforace copariso for various uber of sub-carriers per user over the AWGN chael. 158

8 Figure 9 shows the worst case perforace usig 8 sub-carriers per user. As is see, the bit error rate (BER) perforace is substatially ehaced by icreasig the uber of subcarriers. Siilar results are obtaied over Rayleigh fadig chaels as is see i Figure 10. The results of Figure 10 are obtaied usig a 3-tap chael odel with a expoetial itesity profile for all the 3 users ad idepedet fadig for each oe. The prefix legth, L p is accordigly set to 3. The chael Doppler spread is assued to be of the trasit sybol rate. Figure 10: Worst case perforace copariso for various ubers of sub-carriers per user over a Rayleigh fadig chael Iterferece aout The other user iterferece varies with the syste desig paraeters such as size, the pulse shape, ad the size of cyclic extesio (prefix ad suffix) Effect of the pulse shape Isertio of cyclic prefix ad suffix at the begiig ad at the ed of the OFDM frae guaratees that the iterferece fro the other user s with tiig offset of T S is copletely reoved (regardless of the power of the iterferer user), where is a iteger uber. Whe the tiig offset betwee users is ot a iteger ultiples of the sybol rate, the residual iterferece aout at the output of the uit i receiver depeds o the aout of offset ad the pulse shape. Figure 11 illustrates the iterferece to sigal ratio for differet tie oralized offsets whe the roll-off factor of the root-raised cosie filter varies betwee zero ad 1. As this figure shows by icreasig the roll-off factor of the root-raised cosie filter, the iterferece to sigal is reduced. This iproveet is due to the decrease of the sidelobes aplitude which is show i Figure 12. For =1, the iterferer sigal is reoved at iteger ultiples of 0.5T S. Techically, =1 does ot have good badwidth efficiecy ad is ot used. This result is achieved with coputer siulatios i AWGN chael whe the average power of iterferer sigals ad the ai sigal are equal. Each user has N=4 sub-chaels, Lp = Ls = 3 ad three users are assued i siulatio. 159

9 Iterferece to Sigal ratio Tiig offset (oralized to T S ) Figure 11: Iterferece to sigal ratio versus tie offset for soe (N=4, K=3). Aplitude of the sidelobes Tie Figure 12: Sidelobes of the root-raised cosie pulse versus tie for soe Effect of the size Figure 13-a ad 13-b preset the variatio of the iterferece to sigal level for two values of (K) ad differet uber of sub-chaels. As these figures show, for specific K, as the uber of the sub-chaels per users icreases, the iterferece level is reduced. Icrease of the uber of users (K) fro 3 to 7, iproves the iterferece tolerace of the syste. I these siulatio the legth of cyclic prefix L p = 5 ad the legth of cyclic suffix L s = 3, the radio chael AWGN, ad oly oe iterferer user with ozero tiig offset are assued Iterferece to Sigal ratio Tiig offset (oralized to T S ) Tiig offset (oralized to T S ) (a) (b) Figure 13: Iterferece to sigal ratio versus tie offset for soe size (KN) whe oly oe users has ozero tie offset, =

10 6. CONCLUSION A widebad iterferece tolerat ultiuser OFDMA schee is discussed for wireless couicatios i feto cells. To provide with a high order of frequecy diversity, a iterleaved set of subcarriers is dedicated to each user. A reduced coplexity digital ipleetatio of the proposed techique is preseted. It is show that with a proper selectio of the cyclic extesio ad the uber of subcarriers per user, the other-user iterferece as well as iter sybol iterferece ay be reduced to a acceptable level. The residual iterferece due to ozero tiig offset is ivestigated. Usig proper chael codes to exploit the provided high order of diversity, wireless systes with a good perforace ad a high capacity could be desiged usig the proposed schee i cojuctio with the other ultiple access techiques. ACKNOWLEDGEMENTS The author would like to specially thak Dr. A. Chii for his directios throughout the work. REFERENCES [1] K. Pahlava, A. Levesque, Wireless Iforatio Networks, New York,Wiley [2] J.G. Proakis, Digital Couicatios, McGraw-Hill, [3] A. Chii, M.S. El-Taay ad S.A. Mahoud, O the perforace of a coded MCM over ultipath Rayleigh fadig chaels, IEEE - ICC 95,pp: [4] A. Chii, Multi Carrier Modulatios i Frequecy Selective Fadig Chaels, Ph.D. dissertatio, Carleto Uiversity, Caada, [5] A. Chii, M.S. El-Taay ad S.A. Mahoud, Trasissio of high rate ATM packets over idoor radio chaels, IEEE JSAC,Vol. 14,No. 3,pp: ,April [6] J.A.C. Bigha, Multicarrier odulatio for data trasissio: A idea whose tie has coe, IEEE Cou. Magazie, pp: 5-14, May [7] J.G. Proakis ad D.G. Maolakis, Itroductio To Digital Sigal Processig,Maxwell Macilla,1989. [8] S.B. Weistei ad P.M. Ebert, Data trasissio by frequecy divisio ultiplexig usig the discrete fourrier trasfor, IEEE Tras. Couicatios. Vol. COM-19, No.5, pp: , October [9] T. S. Rappaport, Wireless Couicatio Systes, Pretice Hall, [10] N. Suehiro, A sigal desig without co-chael iterferece for approxiately sychroized CDMA systes, IEEE J. Selected Areas i Couicatios, vol. JSAC-12, pp , Jue [11] P.Z. Fa, N. Suehiro, N. Kuroyaagi ad X.M. Deg, Class of biary sequeces with zero correlatio zoe, IEE Electroic Letters, vol. 36, pp , May 1999 [12] R.D. Gaudezi, C. Elia ad R. Viola, Badliited quasi-sychroous CDMA: a ovel satellite access techique for obile ad persoal couicatio systes, IEEE Joural o Selected Areas i Couicatios, Vol. 10, Issue 2, pp , [13] X.D. Li ad K.H. Chag, Optial PN sequece desig for quasi-sychroous CDMA couicatio systes, IEEE Tras. Couicatios, vol. 45, pp , 1997 [14] S.R. Park, I. Sog, S. Yoo ad J. Lee, A ew poly-phase sequece with perfect eve ad good odd cross correlatio fuctio for DS/CDMA systes, IEEE Tras. Vehi. Tech., vol. 51, No.5,

11 [15] Hadi Alasti, A. Chii, M.S. El-Taay ad S.A. Mahoud, A Discrete Multi-Carrier Multiple Access (MCMA) Techique for Wireless Couicatios, i the proceedigs of IEEE VTC98, Ottawa, Caada, May 18-21, 1998 [16] T. Seki, M. Itai, H. Ohta ad K. Itoh, A study of OFDM syste applyig frequecy diversity, i the proceedigs of the 11th IEEE Iteratioal Syposiu o Persoal, Idoor ad Mobile Radio Couicatios,. PIMRC 2000, Vol. 2, pp , [17] Hadi Alasti, A Multi-Carrier Multiple Access Techique for Wireless Couicatios, Master Thesis, Isfaha Uiversity of Techology, Isfaha, IR, [18] S. Zhou, G.B. Giaakis, Frequecy-hopped geeralized MC-CDMA for ultipath ad iterferece suppressio, i Proc. of MILCOM coferece, pp , [19] M. Morelli, C.-C.J. Kuo ad M.-O. Pu, Sychroizatio Techiques for Orthogoal Frequecy Divisio Multiple Access (OFDMA): A Tutorial Review, IEEE Proceedigs, vol. 95, Issue 7, pp , Author Hadi Alasti received BEE, MEE ad PhD all i Electrical Egieerig with focus i couicatios ad sigal processig fro the Uiversity of Tehra, Isfaha Uiversity of Techology, ad the Uiversity of North Carolia at Charlotte, respectively. His research iterests are wireless sesor etwork applicatios, wireless couicatios, ad sigal processig applicatios. Dr. Alasti has worked a few years i power syste couicatio syste area as cosultat egieer. 162