Frequency-domain Pre-equalization Transmit Diversity for MC-CDMA

Transcription

1 Frequeny-domain Pre-equalization ranmit Diverity for MC-CDMA iromihi omeba, Shinuke akaoka, and Fumiyuki Adahi Dept. of Eletrial and Communiation Engineering, Graduate Shool of Engineering, ohoku Univerity 5 Aza-Aoba, Aramaki, Aoba-ku, Sendai, Japan Phone: tomeba@mobile.eei.tohoku.a.p Abtrat Reently, multi-arrier ode diviion multiple ae (MC-CDMA) ha been attrating muh attention for the broadband wirele ae in the next generation mobile ommuniation ytem. In the ae of uplink tranmiion, the orthogonality property among uer ignal i lot ine eah uer ignal goe through different fading hannel and hene, multi-ae interferene (MAI) i produed, thereby ignifiantly degrading the tranmiion performane ompared to the downlink ae. he ue of frequeny-domain equalization (FDE) at the reeiver annot uffiiently uppre the MAI. In thi paper, we propoe frequeny-domain pre-equalization tranmit diverity (FPD), whih employ pre-equalization uing multiple tranmit antenna with tranmit power ontraint, in order to tranform a frequeny-eletive hannel een at a reeiver to the frequeny-noneletive hannel. he BER performane with propoed frequeny-domain pre-equalization tranmit diverity i evaluated by omputer imulation. Keyword Pre-equalization, tranmit diverity, MC-CDMA, frequeny-domain equalization, frequeny-eletive hannel I. INRODUCION igh peed and high quality tranmiion are required for the next generation mobile ommuniation ytem. owever, mobile hannel i ompoed of many propagation path with different time delay, produing evere frequeny-eletive fading hannel, and therefore, the tranmiion performane degrade due to evere inter-ymbol inferene (ISI) []. Reently, multi-arrier ode diviion multiple ae (MC-CDMA), whih ue a number of lower rate ubarrier to redue the ISI reulting from frequeny-eletive hannel, ha been attrating muh attention [,3]. Multiple ae apability i attained by frequeny-domain preading uing uer-peifi orthogonal preading ode. In the ae of downlink, a good bit error rate (BER) performane an be ahieved by uing frequeny-domain equalization (FDE) at the reeiver [4]. owever, in the ae of uplink, eah uer ignal goe through different fading hannel, and the orthogonality property among uer i lot, reulting in multi-ae interferene (MAI), and hene, the BER performane degrade [3]. he BER performane annot be uffiiently improved by uing only FDE at the reeiver. Reently, frequeny-domain pre-equalization at a tranmitter ha been under tudy to improve the MC-CDMA uplink tranmiion performane [5-7]. In [5-7], a ingle antenna i ued and FDE imilar to the frequeny-domain equalization ued at the reeiver i applied at the tranmitter. Unlike the previou work [5-7], in thi paper, we apply tranmit antenna diverity [8-] to eah ubarrier of MC-CDMA ignal and propoe a frequeny-domain pre-equalization tranmit diverity (FPD) to effetively uppre the MAI for MC-CDMA uplink tranmiion. In the propoed FPD, ubarrier-by-ubarrier pre-equalization ahieved by antenna diverity tranmiion i employed and orthogonal preading ode are ued by different uer unlike the onventional MC-CDMA uplink tranmiion. For performing FPD, the knowledge of the uplink fading hannel i required. he uplink hannel an be etimated uing the downlink hannel for the ae of time diviion duplex (DD) []. In thi paper, FPD i preented for MC-CDMA/DD and then, the BER performane of MC-CDMA/DD uplink with FPD i evaluated by omputer imulation. II. PROPOSED FPD FOR MC-CDMA UPLINK RANSMISSION Figure illutrate the tranmitter and reeiver truture employing the propoed FPD for the th uer. At the tranmitter, a equene of modulated ymbol to be tranmitted i pread in time-domain by an orthogonal preading ode with the preading fator to obtain the hip equene (we aume that orthogonal preading ode are ued unlike the onventional uplink tranmiion of MC-CDMA, where peudo-random preading ode are ued by different uer). After erialto-parallel () onverion, the hip equene i onverted into N (N i the number of ubarrier) parallel tream, eah of whih i multiplied by pre-equalization weight, where repreent the number of tranmit antenna. hen, N -point invere fat Fourier tranform (IFF) i applied to tranform the timedomain pread ignal into the frequeny-domain pread ignal, whih i the pre-equalized MC-CDMA ignal to be tranmitted from tranmit antenna after inertion of the guard interval (GI). pre-equalized MC-CDMA ignal tranmitted over a frequenyeletive hannel are uperimpoed and reeived at a bae tation reeiver. At the bae tation reeiver, after removal of GI from the reeived MC-CDMA ignal, N -point FF i applied to deompoe it into the N ubarrier omponent. After parallel-to-erial () onverion, depreading i arried out, followed by demodulation. Note that no FDE i required at the bae tation reeiver, while it i needed at the mobile terminal reeiver for the downlink ignal reeption. In what follow, without lo of generality, we aume a tranmiion of N / ymbol {d (m); mn /-} over one MC-CDMA ignaling interval. A. Pre-equalization Uing the pre-equalization weight vetor w ( [w (,, w (,,..., w ( -,], the tranmit ignal vetor of the th uer at the kth ubarrier an be expreed a with ( [ (,, S w ( k ) ( (,,..., ( N ( k mod ) d w, () t, ] ( m) ()

2 Reeived demod. Reeiver Depreading Σ ode FDE FF Channel etimation -GI # - # downlink +GI N Point IFF From other uer From other uer ode ranmit mod. ranmitter ranmit mod. ranmitter ode w (,) Pre-equalization w (,N -) +GI IFF uplink -GI N Point FF ode Σ Depreading demod. Reeiver Reeived th uer mobile terminal Fig. ranmitter and reeiver truture of MC-CDMA uing FPD Bae tation where S, (, and d (m) denote the tranmit ignal power, the kth hip of the orthogonal preading ode with preading fator, and the mth -modulated ymbol, repetively, and repreent the vetor norm operation. We ue ubarrier-byubarrier pre-equalization heme baed on the well-known diverity ombining heme [], i.e., maximal ratio ombining (), equal gain ombining (), and eletion ombining (). he nth element of w ( i given by ( n,, Nt ( n, n ( n, w ( n,, ( n, ( n,,if ( n, arg max{ ( n, } ( n, n,, otherwie, (3) where (n, repreent the nth element of the hannel gain vetor of ( [ (,, (,,..., ( -,] of the th uer. It an be undertood from Eq. (3) that ine the omplex onugation of the hannel gain i ued in the pre-equalization weight, all uer ignal are reeived in phae and hene the MAI an be redued. pre-equalization maximize the intantaneou reeived ignal-to-noie power ratio (SNR) at the mobile reeiver, while pre-equalization equalize the phae only. In, one of the tranmit antenna providing the tronget hannel gain i eleted to tranmit eah ubarrier after phae equalization. he differene of our pre-equalization from the tranmit antenna diverity heme preented in Ref. [] i that in our propoed heme, phae equalization i ued in order to make all ubarrier omponent arrive at the reeiver in phae. Applying N -point IFF to (, the pre-equalized MC- CDMA ignal vetor i obtained a After inertion of the GI, the pre-equalized MC-CDMA ignal vetor i tranmitted uing tranmit antenna. B. Fading hannel he fading hannel ompoed of L independent propagation path i aumed. he time delay of the lth path i aumed to be l with repreenting the FF/IFF ampling period. Uing path gain vetor ξ,l [ξ,l,, ξ,l,,..., ξ,l,nt- ] of the lth path for the th uer, the hannel gain vetor ( an be expreed a ( ) exp π k ( L ) N [ ξ,..., ξ,..., ξ ] exp( π k l N ) (,, l, L. (5) C. Reeived ignal and depreading ranmit timing ontrol i aumed uh that the time delay of all path of all uer are within the GI. he reeived ignal i the uperpoition of MC-CDMA ignal tranmitted from U different uer and an be expreed a r( t) L l ξ ( t l) n( ), (6), l + t where n(t) repreent the omplex-valued additive white Gauian noie (AWGN) having zero mean and variane σ. After removal of GI from the reeived MC-CDMA ignal, N -point FF i applied to deompoe it into the N ubarrier omponent. he kth ubarrier omponent R( i repreented a R( S ( ( + N( ( ( k mod ) d ( m) + N(, (7) N ( t) k ( exp ( π t k N ) [ (, t), (, t),..., ( N t, t)], for t N. (4) where ( ( w ( (8) i the equivalent hannel gain aoiated with the th uer at the kth ubarrier and N( i the noie omponent at the kth ubarrier

3 owing to the AWGN. he oft deiion value dˆ ( m), mn /-, for the mth -modulated ymbol of the th uer i obtained by depreading a ) R( k m d ˆ ( m) ( k mod ). (9) Subtituting Eq. (7) into Eq. (9), we have m S ( d m + ) k d m + µ MAI + µ ˆ ( ) ( ) ( ) k m AWGN, () where the firt term repreent the deired ignal omponent and the eond and third term denote the MAI omponent and the noie omponent due to the AWGN, repetively, and are given by µ µ MAI AWGN S ) k m ) k m N( u u u ( u ( k mod ) ( k mod ) d u ( m). () ( k mod ) III. COMPUER SIMULAION D. Simulation ondition he average BER performane of MC-CDMA uplink with FPD i evaluated by omputer imulation. able ummarize the imulation ondition. Quadrature phae hift keying (QPSK) modulation, N 56, N g 3, and a ample-paed L-path frequeny-eletive Rayleigh fading hannel having an exponential power delay profile with deay fator α db are aumed. Ideal hannel etimation i aumed. E. BER performane with frequeny-domain equalization reeption (no pre-equalization) Firt of all, the BER performane with no tranmit diverity but -, MMSE-, and -FDE at a reeiver are evaluated by omputer imulation. Figure how the average BER performane with FDE reeption a a funtion of the reeived E b /N (.5(E /N )(+N g /N )) with the number U of uer a a parameter, where E (SN ) i the tranmit ymbol energy. he FDE weight i given by [3], [3] (, ( w (, MMSE, () E N ( + ( (, where ( i the kth ubarrier hannel gain between the th uer and the bae tation. When U>, the BER floor i produed due to the MAI. It i only een that the uplink BER performane annot be improved with FDE reeption only. In the following ubetion, we preent the average BER performane when the propoed FPD i ued. ab.. Simulation ondition. modulation QPSK MC-CDMA No. of ubarrier N 56 Guard interval N g 3 Pre-equalization weight,, FPD No. of tranmit antenna,, 4 fator No. of path L6 Channel model Power delay profile Exponential with deay fator α, 8 (db) Normalized maximum f D. Doppler frequeny ((N +N g ) ) Channel etimation Ideal L 6, αdb U U8 U U 6 U3 MMSE 5 5 Average reeived E b /N (db) Fig.. Simulated average BER performane with FDE reeption only. F. Equivalent hannel gain with FPD In thi etion we diu how FPD tranform the preequalized hannel to be loe a frequeny non-eletive hannel a poible. Figure 3 how a one-hot obervation of the equivalent hannel gain ( k ) oberved at the bae tation reeiver with FPD. Without pre-equalization, large variation in ( k ) are een. owever, a the number of tranmit antenna inreae, variation in ( k ) are uppreed and the reultant hannel approahe the frequeny non-eletive hannel. ene, the detrution in orthogonality i redued, reulting in le MAI. G. Comparion of FPD uing,, and preequalization weight Figure 4 ompare the average BER performane ahievable with FPD uing,, and pre-equalization weight when 4 and α db. he pre-equalization provide the bet BER performane among the three pre-equalization weight ine the maximize the intantaneou SNR while

4 .E+ ( L 6, αdb Original hannel Subarrier index k.e+ (a) ( L 6, αdb 4 Original hannel Subarrier index k (b) 4 Fig. 3. Equivalent hannel gain with FPD. U L 6 α db 4 U 6 U 6 U L 6 α db FPD uing Reeive MMSE-FDE 4 U ranmit E b /N (db) 5 5 ranmit E b /N (db) Fig. 4.Performane omparion of,, and pre-equalization. Fig. 5. Effet of no. of tranmit antenna.

5 .E-6 L 6 4 αdb α8db U ranmit E b /N (db) Fig. 6. Effet of deay fator. uppreing the variation in ( k ). ene, only i onidered in the following imulation.. Effet of number of tranmit antenna and deay fator Figure 5 plot the average BER performane with FPD uing a a funtion of the tranmit E b /N with a a parameter. he BER performane an be ignifiantly improved by inreaing the number of tranmit antenna, although the BER performane degrade with inreaing U. Alo een i that the BER performane of FPD uing i uperior to that of FDE reeption. It i intereting to note that even with, FPD an provide better BER performane than with FDE reeption only. hi i beaue, with the FPD, all the ubarrier are in phae for all uer and hene, the ode orthogonality among different uer i retored to ome extent, thu uppreing the MAI. owever, without FPD, different uer ubarrier are out of phae, and hene, the ode orthogonality annot be retored by the ue of FDE reeption only. Figure 6 how the average BER performane with FPD uing a a funtion of the tranmit E b /N for α and 8 db. When U i mall (U, 6), α db give a better BER performane than for α8 db due to larger frequeny diverity effet. owever, when U i large (U), the performane for α db i wore than for α8 db. hi i beaue, a the frequenyeletive beome everer, larger MAI i produed and offet the frequeny diverity effet IV. CONCLUSION In thi paper, frequeny-domain pre-equalization tranmit diverity (FPD) for improving the uplink BER performane of MC-CDMA wa propoed. Unlike the onventional MC-CDMA uplink tranmiion, orthogonal preading ode are ued by different uer. With FPD, all the ubarrier are in phae for all uer and hene, the orthogonality among different uer i retored, thereby ahieving a better BER performane than uing FDE reeption at the reeiver. We onidered variou preequalization weight of,, and, and evaluated by the omputer imulation the average BER performane ahievable with them to how that provide the bet performane. Referene [] W.C., Jake Jr, Ed, Mirowave mobile ommuniation, Wiley, New York, 974. [] S. ara and R. Praad, Overview of Multiarrier CDMA, IEEE Commun. Mag., Vol. 35, No., pp. 6-33, De. 997 [3] S. ara and R. Praad, Deign and performane of multiarrier CDMA ytem in frequeny-eletive Rayleigh fading hannel, IEEE ran. Vehi. ehnol., Vol. 48, No. 5, pp , Sept [4]. Sao and F. Adahi, Comparative tudy of variou frequeny equalization tehnique for downlink of a wirele OFDM-CDMA ytem, IEICE ran. Commun., Vol. E86-B, No., pp. 35-3, Jun. 3. [5] D. Mottier and D. Catelain, SINR-baed hannel pre-equalization for uplink multi-arrier CDMA ytem, Pro. IEEE Int. Symp. On Peronal, Indoor and Mobile Radio Commun. (PI), Vol. 4, pp , Sept.. [6] S. Kaier, Spae frequeny blok oding in the uplink of broadband MC-CDMA mobile radio ytem with pre-equalization, Pro. IEEE VC 3 fall, Vol. 3, pp , Ot. 3. [7] I. Coovi, M. Shnell and A. Springer, On the performane of different hannel pre-ompenation tehnique for uplink time diviion duplex MC-CDMA, Pro. IEEE VC 3 fall, Vol., pp , Ot. 3. [8]. Lo, Maximum ratio tranmiion, IEEE ran. Commun., Vol. 47, No., pp , Ot [9] K. Caver, Single-uer and multiuer adaptive maximal ratio tranmiion for Rayleigh hannel, IEEE ran. Vehi. ehnol., Vol. 49, No. 6, pp. 43-5, Nov.. [] R.. Derryberry, S. D. Gray, D. M. Ioneu, G. Mandyam and B. Raghothaman, ranmit diverity in 3G CDMA ytem, IEEE Commun. Mag., Vol. 4, No. 4, pp , Apr.. []. Shi, M. Katayama,. Yamazato,. Okada and A. Ogawa, An adaptive antenna eletion heme for tranmit diverity in OFDM ytem, Pro. IEEE VC fall, Vol. 4, pp. 68-7, Ot.. [] R. zadeh, M. Nakagawa and A. Jone, DD-CDMA for the 4th generation of wirele ommuniation, IEEE Wirele Communiation, Vol., No. 4, pp. 8-5, Aug. 3. [3] D. Garg and F. Adahi, SD deoding ombined with MMSE equalization and diverity reeption for MC-CDMA in the preene of multiple uer, Pro. WPMC3, Vol., pp. 8-84, Ot. 3.