Iterative Multiuser Receiver Utilizing Soft Decoding Information

Transcription

1 teratve Multuser Recever Utlzng Soft Decodng nformaton Kmmo Kettunen and Tmo Laaso Helsn Unversty of Technology Laboratory of Telecommuncatons Technology emal: Abstract n ths paper we propose a novel recever structure that utlzes the soft nformaton provded by the channel decoder n the multuser detecton. Ths recever structure s based on a sngle-user verson of the uncoded maxmum a pror crteron. We derve the optmal multuser lelhood calculaton algorthm for ths structure. n addton, suboptmal algorthms are proposed that are based on nterference cancellaton. Numercal smulatons are reported whch ndcate that these suboptmal algorthms have a close-tooptmal coded BER performance even n the presence of hghpower nterferers.. NTRODUCTON The past research on code dvson multple access (CDMA multuser detecton has manly concentrated on the uncoded case, that s, the channel codng s assumed to be totally ndependent from the multuser detecton and s thus gnored n the analyss and algorthm desgn [1]. Recently, there has been a growng nterest for an ntegrated approach, where the channel codng s taen nto account n the desgn and analyss of the multuser recevers. An optmal detector/decoder for a convolutonally coded CDMA system was derved n [] by Gallorenz and Wlson, who also proposed several suboptmum multuser recever structures n [3]. Dfferent suboptmum approaches have been studed n [4-6,10,1,13]. On the other hand, n the area of codng theory teratve decodng has become a popular research topc, manly because of the Turbo codes [7]. A number of approaches combnng teratve decodng and multuser detecton have also been studed. n [9], an teratve structure consstng of a combnng algorthm followed by parallel MAP-decoders (one for each user was nvestgated. n [8], an teratve multuser recever wth channel decodng was derved by usng the uncoded maxmum a posteror (MAP crteron jontly for all users. n these recevers, the channel decoder output can be used to further mprove the recever performance. Ths s done n an teratve fashon smlar to the teratve decodng algorthms used for concatenated codes [11]. n ths paper we propose a novel recever structure that utlzes the soft nformaton provded by the channel decoder n multuser detecton. n ths structure, the uncoded MAP crteron s used separately for each user for multuser lelhood calculatons nstead of the jont uncoded MAP crteron that was used n [8]. We derve the optmal multuser lelhood calculaton (MULC algorthm for ths structure. Ths algorthm has a rather hgh complexty and thus several suboptmal algorthms are proposed that are based on nterference cancellaton. Numercal smulatons show that even these suboptmal algorthms have a close-tooptmal coded BER performance, especally when the varance estmaton of the data s performed ndvdually for each teraton round.. SYSTEM MODEL The CDMA system modeled n ths paper s the upln chp and symbol-synchronous drect sequence DS-CDMA communcaton system wth K users. We assume BPSK modulaton. The model uses convolutonal channel codng to mprove the BER performance of the system. The channel s modeled as a tme-nvarant sngle-path channel where Gaussan nose wth zero mean and varance s added. The bloc dagram of the system s shown n Fgure 1. n a synchronous CDMA system, the matched flter output at tme can be expressed as y RAx + n (1 where x (x (1,,x ( T s the coded data vector contanng the transmtted data symbols of every user and n s the Gaussan nose. Furthermore, R s the correlaton matrx and A s the channel matrx, that s 1 ρ1 ρ1 K ( R ρ1 1 ρ K ρk1 ρk 1 A dag ( a 1,, a K, (3 where ρ j s the cross-correlaton between users and j. The channel matrx s dagonal snce we assume sngle-path propagaton. Ths wor s part of a research project of the nsttute of Rado Communcaton (RC funded by Technology Development Center (TEKES, NOKA Research Center, Telecom Fnland and the Helsn Telephone Company.

2 ( 1 x ( K x Encoder 1 Encoder K Spreadng Spreadng Σ a 1 a K n MF 1 MF K y (1 y (K Fgure 1: Bloc dagram of the communcaton system. TERATVE C-TYPE RECEVER STRUCTURE Jont detecton and decodng The decoder structure used n the teratve decodng algorthms of (serally concatenated codes provdes the prncpal model for our recever structure. Naturally, there s no need for the nner consttuent decoder n a system usng non-concatenated channel codng. However, substtutng the nner decoder wth a multuser lelhood calculaton (MULC unt allows the utlzaton of the feedbac from the channel decoder n the lelhood calculatons. Ths approach s smlar to the recever structure consdered n [8]. n [8], the multuser lelhood calculatons are based on the jont uncoded MAP crteron ~ x arg max p( x y (4 x Thus the soft nformaton nput provded for each channel decoder contans the nformaton about the whole matched flter sample vector y. n tradtonal nterference cancellaton algorthms for uncoded data, the symbol decson s based only on the code matched flter output for user and the tentatve symbol decsons for the nterferng users. Snce our recever structure s desgned for MULC algorthms that are based on these nterference cancellaton algorthms, we adopt the correspondng approach n multuser lelhood calculaton. t means that a sngle-user verson of the uncoded MAP crtera ~ ( ( x arg max p( x y (5 ( x s used for each user separately. For each user, the soluton of ths optmzaton problem requres, n addton to the nowledge of the nose varance, only the nowledge of ( the user matched flter output y and the estmates of the symbol probablty dstrbutons for every nterferng user. These estmates of the symbol probablty dstrbutons are presented as log-lelhood ratos (LLR, where the LLR for symbol s s defned as P s Ls ( log ( + 1 (6 P( s 1 where P(s±1 s the probablty for the symbol s to be ±1. Where necessary, we extend ths notaton also to the case wth condtonal probabltes. The proposed recever has an teratve structure wth the mth stage of the recever for user s shown n Fgure. We use the term teratve C-type recever to emphasze the fact that the recever has a dsjont user-by-user structure and the channel symbol nformaton s shared between the sngleuser recevers and used for nterference cancellaton. Durng the mth teraton, the MULC unt calculates the ( symbol lelhoods based on the matched flter output y of the respectve user and the estmates ((m-1 of the LLRs for the channel symbols transmtted by the nterferng users. These estmates are calculated durng the prevous teraton round by addng the output of the outer unt wth the earler lelhood estmate produced by the MULC unt. The outer unt s a soft-nput-soft-output (SSO decoder, a unt that s commonly used as a consttuent decoder when decodng concatenated codes, and t produces ts output by adjustng the symbol lelhoods based on ts nowledge of the channel code trells. The SSO unt also produces the fnal data symbol decsons after the last teraton round. y ( j ( m 1 MULC ( j LO ( x ; m 1 ( ( m L ( x SSO LO ( x Decoded data symbol Fgure : The mth stage of the teratve C-type recever structure utlzng channel decodng There are several possbltes for the actual algorthm to be used n the SSO. We have selected the well-nown MAP algorthm [11] that uses two-way recursons to calculate both the nformaton symbol and channel symbol probablty dstrbutons based on a pror channel and nformaton symbol probablty dstrbutons and the nowledge of the code trells. The calculaton s based on mnmzng the nformaton symbol error probablty. We use a varant where all the nput and output dstrbutons are expressed n the form of log-lelhood ratos. n our case the nformaton symbols are a pror equprobable and can thus be gnored n the SSO unt. Furthermore, we use the extrnsc channel bt probabltes nstead of the channel symbol probabltes as the output of the SSO unt. These are calculated by usng ( the formula derved n [11]. Thus f P (x (resp. P O (x ( s the a pror (resp. extrnsc a posteror probablty dstrbuton for channel bts then we can form the correspondng log-lelhood ratos as: P ( x + 1 L ( x log P ( x 1 (7

3 PO ( x + 1 (8 LO ( x log PO ( x 1 As was mentoned above, the MULC unt uses for each user the code matched flter output y and the channel bt LLRs of the nterferng users for lelhood calculaton. n the next secton we present alternatve algorthms for the MULC unt. V. MULTUSER LKELHOOD CALCULATONS n ths secton we derve alternatve lelhood calculaton algorthms for the recever structure gven n the prevous secton. Although our prmary focus s on algorthms that use some form of nterference cancellaton procedure for these calculatons, we also derve an algorthm that s optmal soluton wth respect to the uncoded separated MAP crtera. Ths provdes a useful reference pont for evaluatng suboptmal algorthms and gves an upper lmt for the performance of ths nd of a recever structure. A. Optmal Lelhood Calculaton The optmal lelhood calculaton algorthm s derved from the separated uncoded MAP crtera (5. Thus the algorthm requres the nowledge of the nose varance, the matched ( flter output sample y and the probablty dstrbutons of (j the channel symbols x for j. By usng the well-nown Bayes formula, the (a posteror LLR can be presented as Lx ( y Ly ( x + Lx ( (9 Py ( x + 1 Px ( + 1 (10 log + log Py ( x 1 Px ( 1 where the second term contans the a pror nformaton about the transmtted nformaton symbol and the frst term ( ( s the LLR for the recepton of y on the condton that x was transmtted. n an AWGN channel the frst term s just a ( multplcaton of the matched flter output sample y wth the channel relablty coeffcent a /. A smple calculaton shows that the presence of multple access nterference (MA adds an extra term to the AWGN case: where L MA, a y L( y x + L log e e P( e e P( e e MA, ( y a e e ( y+ a e e 1/( ( µ ( µ ( 1/( ( µ ( µ ( (11 (1 The summatons are over all such e that e 0 and e j ±1 for j and P (e s the probablty of the transmsson of symbol e j by user j for all users j at tme. The functon µ ( e s defned as ( e P RAe (13 µ where the P s the projecton operator that returns the th element of a vector. Thus µ ( e s the total nterference sgnal n the case the symbol transmtted by user was e. ( For any teraton round m, the L MA, term can be obtaned by usng the estmates ((m-1. Denotng the estmate by ( (m, the followng lelhood calculaton step at stage m L MA, can be derved: a y (14 L( x + L MA, ( m + LO ( x ; m 1 B. Suboptmal Approaches n ths secton we consder the lelhood calculaton algorthms that use an nterference cancellaton step durng the calculaton. The smplest such algorthm (the hard decson cancellaton can n fact be obtaned as an approxmaton of the optmal calculaton. Consder the optmal algorthm whch ncludes the calculaton of the logarthm of an exponental sum (1. Snce the sum s taen over all possble bt combnatons sent by all the users, the number of terms n the sum s K, where K s the number of users. Ths nd of log-exponental sums are often encountered n MAP algorthms and they can be approxmated by the maxmum of the exponents [11]. f one assumes that the bt estmates are hghly relable for all users then for each there exsts e such that P( e 1 and P( e 0 for all other e and we can approxmate the L MA, term as Ths gves L MA, a ( µ e (15 a y a a µ ( e ( ( L( y x ( y µ ( e (16 Ths approxmaton can thus be obtaned by a hard decson nterference cancellaton followed by multplcaton wth the channel coeffcent. Durng the teraton round m, the vector e can be estmated by sgn(, defned as a vector wth the jth element sgn( (j(m-1 for j and 0 for the th element. Wth ths notaton and when usng the approxmaton (16, the lelhood calculaton step becomes: a( y µ ( sgn( (17 L( x + LO( x ; m 1 The smulatons show (see Secton V that the performance of ths hard decson cancellaton algorthm s rather poor when the base staton receved dfferent users wth dfferent powers. One possble reason for ths can be the fact that the algorthm actually conssts of two steps: the nterference cancellaton step and the multplcaton wth the channel

4 relablty coeffcent. We can vew the nterference cancellaton step as a method to transform a channel wth MA nto a pure AWGN channel, after whch the lelhood calculaton for the transformed channel s done n the second step. The transformed channel s naturally no longer an AWGN channel and there wll be a certan approxmaton error ntroduced n the lelhood calculatons. However, an even more serous performance degradng s ntroduced because the varance of the transformed channel s not the same as that of the orgnal added nose. Usng the orgnal varance n the channel relablty coeffcent ntroduces an error to (17 that has a severe degradng effect on the performance of the algorthm especally when the amount of nterference to be canceled s large, for nstance when a hgh power nterferer s present. Ths wll be llustrated n Secton V. We can remove ths source of error wth a smple modfcaton to the algorthm. All that needs to be done s to estmate the varance separately after each cancellaton procedure and use ths estmate n the channel relablty coeffcent. As a result, we get the followng twostep varant of the lelhood calculaton at stage m. Frst, we perform the nterference calculaton step to obtan the corrected matched flter output samples y ( y µ sgn( (18 ( and calculate a new varance estmate based on the modfed sample set y. Then calculate the lelhoods usng formula a( y ( (19 L( x + LO( x ; m 1 As wll be seen n Secton V, ths mproves the performance dramatcally. The hard decson nterference calculaton step can be substtuted wth some other nterference calculaton method. n ths paper we only consder one varant of the basc nterference cancellaton procedure, called here the soft nterference cancellaton. Ths varant s obtaned by usng the mean E( µ ( e nstead of µ ( e that was used above. Ths results n an algorthm where the nterference calculaton step (18 s replaced by: y ( y µ tanh( / (0 ( V. NUMERCAL RESULTS n ths secton we wll report some numercal results obtaned through smulatons. The channel codng used here s a rate 1/ convolutonal code wth the generator (7,5. The SNR s db and the number of smultaneous users s K4. The correlaton coeffcent ρ0.3 s used for each user par. 10 Hard decson C Hard decson C wth varance estmaton Soft C wth varance estmaton Optmal LC Sngle user bound teraton 10 Fgure 3: Recever performance wth equal receved powers Hard decson C Hard decson C wth varance estmaton Soft C wth varance estmaton Optmal LC Sngle user bound teraton Fgure 4: BER performance for a user wth a decreased (-3dB power level Fgure 3 shows the case, where the receved power levels of all users are the same. All tested MULC algorthms, except the one usng (17, gve approxmately the same BER performance. The performance decrease of the hard decson C algorthm s at least partally due to heavy nterference cancellaton caused by relatvely large correlaton coeffcents. Fgure 4 gves the coded BER for user 1 after each teraton step n a stuaton, where user 1 s receved wth a power level 3 db lower than that of the other users that are receved wth equal powers. One can see that the optmal lelhood calculaton obtans a near sngle user performance after few teraton rounds. The performance s n fact better than n the equal power case, manly because the ncreased power levels

5 of the nterferng users also ncrease ther respectve SNRs and thus provde more relable symbol estmates to be used n the multuser lelhood calculatons. t s also worth notng that whle the hard decson C wthout varance reestmaton after each teraton round performs rather badly, the performance mproves dramatcally when varance s estmated from the sample data after each teraton round. The performance mprovement acheved by usng the soft C nstead of hard decson C s almost none snce both soft and hard varants of the algorthm have near-optmal performance. nterference cancellaton technques can be appled to produce algorthms that have a close to optmal coded BER performance, even wth unequal receved powers, when the varance estmaton of the data s performed ndvdually for each teraton round. ACKNOWLEDGMENT The authors want to than Dr. J. Llleberg and Mr. A. Hottnen for valuable dscussons. REFERENCES [1] A. Duel-Hallen, J. Holtzman, and Z. Zvonar, Multuser detecton for CDMA systems, EEE Pers. Comm., vol., pp , Aprl Hard decson C Hard decson C wth varance estmaton Soft C wth varance estmaton Optmal LC Sngle user bound [] T. R. Gallorenz, and S. G. Wlson, Multuser ML sequence estmator for convolutonally coded asynchronous DS-CDMA systems, EEE Trans. Comm., vol. 44, pp , August [3] T. R. Gallorenz, and S. G. Wlson, Suboptmum multuser recevers for convolutonally coded asynchronous DS-CDMA systems, EEE Trans. Comm., vol. 44, pp , September [4] A. Hafeez, and W. E. Star, Soft-output multuser estmaton for asynchronous CDMA channels, Proc. EEE Vehcular Technology Conference, pp , May, [5] M.-R. Koohrangpour, and A. Svensson, Jont nterference cancellaton and Vterb decodng n DS-CDMA, Proc. of PMRC 97, pp , September teratons Fgure 5: BER performance wth three nterferng users (wth power levels 0dB, 3dB and 6dB Fgure 5 shows the performance of the smulated algorthms n a stuaton, where there are three nterferng users: one receved wth equal power level, one recever wth a power level 3dB hgher and one wth a power level 6dB hgher. Ths stuaton s more demandng for the effcent nterference cancellaton than the prevous case, snce now even the tentatve symbol decsons of two other users are dstorted by one hgh power level user. Ths s reflected as decreased performance of the C algorthms. The soft C algorthm has somewhat better performance than the one usng hard tentatve decsons, whch s natural n the presence of a hgh-power nterferng user. V. CONCLUSONS We have studed an teratve recever structure that utlzes the soft nformaton provded by the channel decoder n the multuser detecton. The smulatons presented n ths paper support the concluson made n [8] that such an teratve recever structure combned wth channel decodng gves a great ncrease of performance. The results show that the performance gan s substantal even wth a smple convolutonal channel codng. Furthermore, tradtonal [6] R. Herzog, nterference cancellaton for a hgh data rate user n coded CDMA systems, Proc. of CC 98, June [7] R. Lucas, M. Bossert, and M. Bretbach, On teratve soft-decson decodng of lnear bnary bloc codes and product codes, EEE JSAC, vol.16, pp , February [8] M. C. Reed, P. D. Alexander, J. A. Asenstorfer, and C. B. Schlegel, Near sngle user performance usng teratve mult-user detecton for CDMA wth turbo-code decoders, Proc. of PMRC 97, pp , September1997. [9] M. L. Moher, Turbo-based multuser detecton, Proc. of ST 1997, p. 195, June [10] M. Brandt-Pearce, and M.-H. Yang, Soft-decson multuser detector for coded CDMA systems, Proc. of CC 98, June [11] S. Benedetto, G. Montors, D. Dvsalar, and F. Pollara, A soft-nput soft-output maxmum a posteror (MAP module to decode parallel and seral concatenated codes, The Telecommuncatons and Data Acquston Progress Report 4-17, July-September 1996, Jet Propulson Laboratory, Pasadena, Calforna, pp.1-0, November 15, [1] W. Hafeng, J. Llleberg and K. Rnen, Jont multuser detector wth decodng and feedbac n asynchronous CDMA systems, Proc. of SSSTA 98, September [13] J. Llleberg, and W. Hafeng, Novel teratve mult-user recever for asynchronous CDMA systems n Raylegh fadng channels, Proc. of PMRC 98, September 1998.