Parallel Interference Cancellation in Multicarrier DS-CDMA Systems

Transcription

1 N Parallel Interferene Canellation in ultiarrier D-CD ystems K. R. hankar kumar and. Chokalingam Department of ECE Indian Institute of iene Bangalore INDI bstrat In this paper we present and analyze the performane of a parallel interferene anellation (PIC sheme for multiarrier (C diret-sequene ode-division multiple-aess (D-CD systems. t eah anellation stage in the proposed PIC sheme on eah subarrier a weighted sum of the soft outputs of the other users in the urrent stage is anelled from the soft output of the desired user (rather than making hard bit deisions of the other users and regenerating and aneling the interfering signals to form the input to the next stage. t the last stage the interferene anelled outputs from all the subarriers are maximal ratio ombined (RC to form the deision statisti. The sheme has the advantage of not requiring the amplitude estimates of the other users. We derive analytial expressions for the bit error rate (BER at different stages in the proposed PIC sheme on Rayleigh fading hannels. nalytial results are found to agree well with the simulation results. The results show that the proposed PIC sheme offers better interferene suppression apability than the onventional mathed filter reeiver. We also obtain bounds on the oded BER of the proposed PIC sheme for a onvolutionally oded multiarrier D-CD system the PIC-RC output feeds a soft deision iterbi deoder. Keywords Parallel interferene anellation multiarrier D-CD fading hannels. I. INTRODUCTION ultiarrier (C approah offers several advantages inluding robustness in fading and interferene operation at lower hip rates and non-ontiguous bandwidth operation. everal studies have analyzed the performane of multiarrier D-CD systems [1]-[2]. In this paper we onsider parallel interferene anellation (PIC for multiarrier D- CD. PIC shemes for multiarrier D-CD have been studied in [4]-[5]. These studies onsider hard deision PIC reeivers hard bit deisions are made on the output of the mathed filters (F whih are then is used to regenerate and anel the multiple aess interferene (I in parallel. Our ontribution in this paper is that we propose and analyze a PIC sheme whih diretly uses the soft output of the Fs (rather than the hard bit deisions for anellation and does not require the estimation of the amplitudes of the users. In the proposed PIC sheme at eah anellation stage on eah subarrier a weighted sum of the soft outputs of the other users in the urrent stage is subtrated from the soft output of the desired user (rather than making hard bit deisions of the other users and regenerating and aneling the I to form the input to the next stage. t the last stage the interferene anelled outputs from all the subarriers are maximal ratio ombined (RC to form the deision statisti. We derive analytial expressions for the bit error rate (BER for the first and seond stages in the proposed PIC sheme on Rayleigh fading hannels. nalytial results are found to agree well with the simulation results. The proposed PIC sheme is shown to offer better performane than the onventional F reeiver. We also obtain bounds on the oded BER of the proposed PIC sheme for a onvolutionally oded multiarrier D-CD system the PIC-RC output feeds a soft deision iterbi deoder. II. YTE ODEL We onsider a -user synhronous D-CD system. Eah user employs a multiarrier modulator the transmit data sequene multiplied by a spreading sequene modulates subarriers as shown in Fig. 1. The transmitted signal for the th user is given by #"%$'&( + - os / is the transmitted energy-per-hip for the th user (assumed to be same for all users is the transmitted bit of the th user T is one bit duration is the number of subarriers. + is the 8 th subarrier frequeny is the phase of the 8 th subarrier of the th user whih is uniformly distributed over : ; <=> and? is the signature waveform of user given KJ DI #"%L D 1E@F & 7 (2 D is the spreading sequene of the F th user is the proessing gain J is the impulse response of the hip Owave P shaping filter assumed to satisfy the onstraint 'Q1 O RT QU and &W X & & is one hip duration in a single arrier ( (1 system. The hannel in eah subband is assumed to be slow-varying flat Rayleigh hannel with transfer funtion Y 54 + [ 54 + exp \I] 54 + ^ 4 +` are i.i.d Rayleigh random variables with unit seond moment and ^ ] 4 +` are i.i.d uniform random variables over : ; < => for both user and subarrier 8. The reeived signal is given by

2 O = n o p 2 noise with psd of 1 E32 54 " $# os &% '( $# '+- / ] 54 + and L0 is white aussian. PIC Reeiver truture The proposed -stage PIC reeiver for multiarrier D- CD is shown in Figs Fig. 2 shows the multiuser multistage PIC demodulator on the 8 th subarrier (there are suh demodulators one on eah subarrier and Fig. 3 shows the maximal ratio ombining (of outputs from all subarriers of the th user and bit deision for the th user. III. PERFORNCE NLYI In this setion we derive analytial expressions for the BER at the output of the 2nd- and 3rd-stages of the PIC reeiver. The lowpass filter output of the 8 th subarrier for the th user 54 LPF^ ;: os. + C is given by <3=>?@CBEDFI = FKJ LN = P F5Q O R P= T >? = (3 >? Q5U =>? D&W PX 1 ^ D "%L D CE@F ` & (5 L E 4 + LPF^ L : os /. + > ( ba 1 O P 'Q1 O R and and L are respetively 7 and L 0 after passing through the 8 th bandpass filter. The power spetral density of L E54 + is 1 E 2. Without any loss of generality in the following we analyze the system deision for the $ th bit of the th user. Let 54 denote the soft output of the $ th bit of the th user ( 9<?$e$e8e7 on the 8 th subarrier (8 9< 8e$e8e7 of the \ th stage ( \ 9<?$e$e8e of the PIC reeiver. The soft output of the $ thd bit of the th user on the 8 th subarrier of the 1st stage 54 is given by 54 DI 54 & 03L D 1E@F & f4 (7 54 onsists of the desired signal omponent The output I and noise omponents and an be written as 54 g 54 >0ih 54 7 (8 d (4 g (9 l h 54 l 54 -m kj 03L>54 (10 54 g 4 + $ os "%2 4 + ( m D D LU"XL D 1E@F D CE F 9 & (12 L 54 D L E54 &0 L D 1E@F & 7 (13 and the variane of L 54 + $ is 1 E2.. 2nd tage Output tatistis of the 8 -th ubarrier The soft outputs from the 1st stage 54 are fed as input to the 2nd stage anellation is performed. The objetive of the interferene anellation is to estimate the I of the th user in parallel and anel the estimate from the th user s total signal. It is noted that from (10 we an ompute the I as long as we have the knowledge of l 54 and m. iven the knowledge of the spreading sequenes of all the users m an be determined. Thus the problem to estimate the I of the th user is to find an aurate enough estimate of l 54 + $. n estimate of l 54 though imperfet may be obtained by multiplying 4 + $ by a fator n 4 + i.e. l 54 + $ 4 n 4 + (14 n 4 + is given by 4 + os "%2 4 + \m 4 (15 Using the approximate estimate of l 54 in R (14 the 54 an interferene anelled output of the 2nd stage be obtained as 54 R 54 " - 4 j l o 54 + $f4 (1 Note that in the anellation proess the th user signal omponent remains unaltered as the interferene omponent is altered. The statistis of the interferene and noise terms at the 2nd stage output is of interest. Eqn. (1 an be written as 54 R + $ rq sut&v/w $# yxzt{}~ $# xz { ƒ /# T 4 R + $ (17 osx # ˆ f# {3 $Š $# xzt{; (18

3 1 0 p s D D For large r.v. with zero mean and variane h 54 an be approximated as a aussian l 7 ^ h 54 j R m R 0 1 E 4 (19 Therefore the variane of the interferene and noise at the 2nd stage output for the th user 1 54 R + 1 E # 4 j R m R 54 R + an be obtained as l 7 ^ h 54 + $ 4 (20 B. 3rd tage Output tatistis of the 8 -th ubarrier In the 3rd stage we essentially try to anel the interferene aused by the imperfet anellation in the 2nd stage. s we did in the 2nd stage anellation here also we obtain an imperfet estimate of the interferene term and use it in the anellation. Further in the 3rd stage anellation this estimate must be added (not subtrated to the previous stage output in order to the anel the negative imperfet anellation term introdued in the 2nd stage anellation. ordingly the interferene anelled output of the th user at the 3rd stage 54 an be written as `t w $# xzt{ t&v/w $# xz { $# t&v/w # xzt{ f# t w xzt{ tv/w # xz { (21 The variane of the interferene and noise at the 3rd stage output for the th user 1 l 7 q 54 W q the aussian approximation. 54 R 54 + is given by 1 C. aximal Ratio Combining and BER The last stage (stage- outputs of the 54 + and an be obtained using subarrier demodulators of the th user are maximal ratio ombined and a hard bit deision is made on the ombined output a shown in Fig. 3. If we assume perfet knowledge of the hannel fading gain of the th user the output of the PIC followed by the RC is given by ^ (22 in order to maximize the signal-to-noise ratio [3] we set ^ 54 + to be ^ 4 + \ 54 O l 7 4 O + # 4 + The average bit-error probability is then given by 4 (23 E : Q = (24 a losed-form solution of whih an be obtained as [3] x. 0/ D. Coded PIC heme &%(' " {$# x - {$# (25 21 and 3 is the average NR per subarrier. + Now we extend the proposed PIC sheme to a onvolutionally oded multiarrier D-CD system and study its performane. We onsider a onvolutionally oded multiarrier D-CD system the user data bits are input to a rate- 254 onvolutional enoder whih generates 4 oded symbols for eah data bit. The output ode symbols are interleaved and serial-to-parallel onverted suh that the 4 parallel ode symbols may be transmitted simultaneously. Then eah of the 4 ode symbols multiplied by the userspeifi spreading sequene modulates subarriers whih subarriers. results in 4 The PIC reeiver for the above oded multiarrier system PIC demodulators Note that in the subarriers are remapped employs a bank of 4 symbol demapper a total of 4 into 4 subarrier groups and eah group onsists of subarriers whih arries the same ode symbol. In the demapper the outputs from subarriers whih arry the same ode symbol are ombined. The output of the demapper is parallel-to-serial onverted and deinterleaved. The output of the deinterleaver is then fed to the soft deision iterbi deoder. The anellation proess in the -stage PIC demodulator is the same as that for the unoded system shown in Figs. 2(a(b exept that ode symbols are onsidered here instead of unoded data bits. lso the RC and hard bit deision as shown in Fig. 2( are not performed here. Instead the 4 soft outputs orresponding to the 4 subarriers at the last anellation stage is fed to the demapper the outputs from subarriers whih arry the same ode symbol are ombined as follows: D $ ( [;: $ LW 9$e$e8e7 4 is the demapper output orresponding to the L th onvolutionally oded symbol ^=< D?> ^ L L 0 4 $444L 0 " 5 4 represents the set of subarriers whih arry the L th oded symbol. Let the data blok length be bits. The soft outputs from the demapper/deinterleaver $ L3K9$e8e$e7 4 9$e8e$e7 $ are fed as input to the soft deision iterbi deoder.

4 .. uppose the deoder hooses that path whih has the maximum path metri the branh metris. and path metris of the 7 th path respetively are defined as D - D $ D 4 and # (27 D 4 represents the L th oded symbol of the 7 th trellis path at time index $ then with suffiient interleaving of the oded symbols an upper bound on the oded BER performane an be obtained using the transfer funtion of the onvolutional ode used as [2] & [? J (28 Y D 3 > 2 1 and & R $444 transfer funtion of the onvolutional ode used. I. PERFORNCE REULT is the In this setion we present the numerial results of the bit error rate performane of the proposed PIC reeiver for multiarrier D-CD both for the unoded as well as oded shemes. We have assumed perfet hannel estimation at the reeiver. We ompare the BER performane at various stages of the PIC (i.e. I. Fig. 4 shows the BER performane of the PIC reeiver as a funtion of the number of users ( at various stages of the PIC ( I<? for the unoded system. The figure shows the plots orresponding to both the analytial results evaluated through Eqn. (25 as well as the results obtained through bit error simulations. In the simulations random binary sequenes are used for spreading. From Fig. 4 we observe that the proposed PIC B gives signifiant improvement reeiver with 2 stages ( in the BER performane ompared to the onventional F- RC reeiver (i.e.. This improvement is further enhaned when one more additional stage of anellation ( is used. Fig. 5 ompares the BER performane of the unoded system for different values of the number of subarriers ( and proessing gains ( at the 2nd ( and 3rd ( stages of the PIC. s expeted for a given number of PIC stages the performane improves as the number of subarriers is inreased beause of the frequeny diversity benefit offered by the multiarrier approah. The BER performane of the PIC for the onvolutionally oded system is shown in Figs. and 7. In Fig. upper bounds on the oded BER evaluated from Eqn. (28 are plotted for rate 2? 2 and 2 onvolutional odes (i.e. 4 and different number of subarriers (?. Three different systems all having same system bandwidth with a total number of 8 subarriers (i.e 4 but with different ombinations of 4 and namely (4? (4 and (4 are onsidered. For all these three systems the BER performane at various stages of the PIC ( 9< are also shown. It is observed that for all the three oded systems the proposed PIC reeiver provides signifiantly improved BER performane ompared to the onventional F-RC ( reeiver. lso for a given number of PIC stages the performane of the (4? (4 systems are similar with the lowest rate and (4 ode (4 K system performing slightly better. larger implies a smaller 4 to keep the system bandwidth onstant the frequeny diversity benefit is more (due to large but the time diversity benefit due to a high rate ode (i.e. small 4 is less. On the other hand a low rate ode (large 4 implies more time diversity benefit and less frequeny gain (due to small. Thus to ahieve a desired performane in a given system bandwidth Fig. points to a possible omplexity tradeoff between systems having different values of 4 and. In Fig. 7 the theoretial upper bounds on oded BER are ompared with simulation BER results for various stages of anellation for 4 and " 2 1 E $# db. The analytial results are found to reasonably agree with the simulation results. Thus the proposed PIC reeiver effetively anels the I and improves the BER performane both in unoded and oded systems.. CONCLUION We presented and analyzed the performane of a parallel interferene anellation (PIC sheme for multiarrier D- CD systems. The sheme has the advantage of not requiring the amplitude estimates of the other users. We derived analytial expressions for the bit error rate (BER at different stages in the proposed PIC sheme on Rayleigh fading hannels both for unoded as well as onvolutionally oded systems. nalytial results were shown to agree well with the simulation results. The proposed PIC reeiver was shown to effetively anel the I and signifiantly improve the BER performane ompared to onventional F-RC reeiver both for unoded as well as oded systems. REFERENCE [1]. Kondo and L. B. ilstein Performane of multiarrier D-CD systems IEEE Trans. Commun. vol. 44 no. 2 pp Feb [2] D. N. Rowith and L. B. ilstein Convolutionally oded multiarrier D CD systems in a multipath fading hannel - Part I: Performane analysis IEEE Trans. Commun. vol. 47 pp Ot [3] J. Proakis Digital Communiations New York: raw-ill [4]. K. Park E. Kim Y. Lee and K.. Thah ultiarrier CD system with Parallel Interferene Canellation for ultipath Fading Channels Pro. IEEE PIRC 98 vol. 2 pp ept [5]. Nahler R. Irmer and. P. Fettweis Parallel interferene anellation with redued omplexity for multiarrier spread spetrum FCD Pro. IEEE th IT pp ept

5 2 Cos( ω 1 t + θ κ1 i b k C k (n. I.. I..: Impulse odulator Energy/Chip = Ek Chip wave shaping filter h(t 2 Cos( ω Μ t + θ κμ k (t = 1 N = 4 2nd stage = 2 N = 32 2nd stage = 4 N = 1 2nd stage = 1 N = 4 3rd stage = 2 N = 32 3rd stage = 4 N = 1 3rd stage 10 5 Fig. 1. ultiarrier D-CD Transmitter of th user E b N-1 L (t (i+1t+nt (1 1m 1m LPF n=0 1 ( n 2 Cos( ω t + m θ 1m N C 1 F on mth subarrier for user 1 (1 F for user 2 on r(t (f - f + m r 2m m (t mth subarrier (f + f m Interferene Canellation (2 1m (2 2m (L-1 1m (L-1 2m Interferene Canellation (L 1m (L 2m 10 Fig. 5. versus number of users at different stages of the PIC for the unoded system with different values of (.... nalysis plots only. % db. Fig. 2. F for user K on mth subarrier tage 1 (1 Km (2 Km -stage PIC demodulator on the th subarrier (L-1 Km tage 2 tage L (L Km R = 2 = 4 1st stage (L=1 R = 4 = 2 1st stage (L=1 R = 8 = 1 1st stage (L=1 R = 2 = 4 2nd stage (L=2 R = 4 = 2 2nd stage (L=2 R = 8 = 1 2nd stage (L=2 R = 2 = 4 3rd stage (L=3 R = 4 = 2 3rd stage (L=3 R = 8 = 1 3rd stage (L=3 (L k1 2 Fig. 3. (L k2 (L k aximal Ratio Combiner k RC and bit deision for the th user b k 4 N = 32 E b Fig.. Upper bound on the oded BER versus number of users at different PIC stages of the onvolutionally oded system with different ombinations of ode rate ( and number of subarriers (. % db. 1st stage (L=1 imulation 1st stage (L=1 nalysis 2nd stage (L=2 imulation 2nd stage (L=2 nalysis 3rd stage (L=3 imulation 3rd stage (L=3 nalysis 1st stage (L=1 imulation 1st stage (L=1 nalysis 2nd stage (L=2 imulation 2nd stage (L=2 nalysis 3rd stage (L=3 imulation 3rd stage (L=3 nalysis E b = 2 N = 32 N = 32 E b R = 2 = 1 Fig. 4. versus number of users at different stages of the PIC reeiver for the unoded system. nalysis and simulation plots. % db Fig. 7. Comparison of the analytial bounds on the oded BER versus the simulated BER at different PIC stages of the onvolutionally oded system. % db.