LETTER An MMSE-Nulling Partial-PIC Receiver for Multiuser Downlink MIMO MC-CDMA Systems

Transcription

1 IEICE TRANS. COMMUN., VOL.E88 B, NO.4 APRIL LETTER An MMSE-Nullng Partal-PIC Recever for Multuser Downlnk MIMO MC-CDMA Systems Jeong-Hoe KU a, Kyeongyeon KIM, Sejoon SHIM,MnGooKIM, and Chungyong LEE, Nonmembers SUMMARY A mnmum mean square error (MMSE nullng partal parallel nterference cancellaton (PPIC recever for downlnk multplenput multple-output (MIMO multcarrer (MC-CDMA systems s proposed. Our analyss shows that, for multuser MIMO MC-CDMAsystems, nterference due to frequency selectvty n multpath fadng channel causes detrmental effects on cancellng, thus V-BLAST recever shows severe performance degradaton. The proposed recever wth multstage processng does not produce an error floor n frequency selectve fadng channel envronments and acheves substantal performance gans. The system performance of the proposed recever was evaluated through computer smulatons. The smulaton results show that, wth two stage PPIC processng, the proposed recever acheves performance gans of db at target BER of 10 3 over the lnear MMSE recever. key words: MIMO, MC-CDMA, V-BLAST, PIC 1. Introducton The development of wreless communcaton systems for hgh data rate transmsson and hgh system flexblty s one of the man targets n next generaton wreless communcatons research. MIMO MC-CDMA systems have attracted sgnfcant research nterest due to ts hgh spectral effcency, large system capacty and hgh flexblty for data rate, and t has been proposed as one of the promssng canddates for 4th generaton wreless communcaton systems [1]. MIMO MC-CDMA systems are combnatons of MIMO transmsson, orthogonal frequency dvson multplexng (OFDM sgnalng and CDMA schemes. MC modulaton, realzed va OFDM, s well suted to hgh data rate applcatons such as multmeda packet transmsson and moble nternet n frequency selectve fadng channels. MIMO systems can acheve very hgh spectral effcency wthout addtonal power or bandwdth n a rch multpath envronment by explotng the extra space dmenson. Vertcal Bell Labs layered Space Tme (V-BLAST s a popular sngle-carrer sngle-user MIMO detecton algorthm, whch s based on the ordered successve nterference cancellaton (OSIC [2]. The prncple behnd OSIC s that at the begnnng of each stage, the substream wth the hgh- Manuscrpt receved September 27, Manuscrpt revsed November 9, The authors are wth the Dept. of Electrcal and Electronc Eng., Yonse Unversty, Seoul, Korea. The author s wth Telecommuncaton R&D Center, Samsung Elec. Co. Ltd., Suwon, Korea. Ths work was supported by Samsung Electroncs as a part of the project, 4G wreless communcaton systems. a E-mal: mrku69@yonse.ac.kr DOI: /etcom/e88 b est post-detecton sgnal to nose rato (SNR s selected for cancellaton. Ths mproves the qualty of the decson and has been known to be optmal for pont-to-pont MIMO recever. However, the performance of V-BLAST detector can deterorate, snce the OSIC structure s very vulnerable to nterference due to unknown users for multuser downlnk MIMO MC-CDMA systems [3]. The multstage parallel nterference cancellaton (PIC was shown to possess several desrable propertes ncludng the potental for near optmum performance, very low computatonal complexty and low decson latency. Recently, the basc PIC recever has been extended to MC-CDMA systems [5]. In ths paper, drawbacks, such as the degradaton of performance of conventonal V-BLAST, are analyzed and a new recever based on partal PIC (PPIC for nter-antenna nterference (IAI cancellaton s proposed. Also, analytcal results exposng several aspects on the performance are presented. 2. System Model The block dagram of a MIMO MC-CDMA system s shown n Fg. 1, where k and ẋ j k denote the jth chp sgnal spread by kth code before and after chp nterleavng, respectvely. At the chp nterleaver, successve chps are nterleaved n the frequency doman usng the pattern descrbed n Fg. 1, where the nterleavng sze s N c. The system contans M transmt antennas and N receve antennas (M N. At the transmtter, a sngle data stream s de-multplexed nto M substreams. Each block fed to one of the M transmt antennas has P modulaton symbols that are frst seral-toparallel converted and then spread wth a pre-assgned code at spreadng factor of SF.AllP SFchps per antenna are mapped onto N c subcarrers wth optonal chp nterleavng and transformed nto the tme doman by N c pont nverse fast Fourer transform (IFFT. The parallel tme-doman sgnals are frst converted to seral and then added wth a guard nterval (GI before transmsson to the MIMO channel. We assume a slow frequency selectve Raylegh fadng MIMO channel. At the recever, the GI of a receved sgnal at each of the N receve antennas are removed and an N c pont fast Fourer transform (FFT s performed. A frequency doman sgnal model for the outputs correspondng to jth ( j = 1,, N c subcarrer at all N receve antennas can be wrtten as (1. Copyrght c 2005 The Insttute of Electroncs, Informaton and Communcaton Engneers

2 1726 IEICE TRANS. COMMUN., VOL.E88 B, NO.4 APRIL 2005 nose (AWGN vector on the jth subcarrer. It s assumed that the multuser downlnk MIMO MC-CDMA system supports only two users smultaneously for smplcty of explanaton snce t captures the key aspects of the proposed recever, thus K codes among total K codes ( K K are assgned to the desred user n (1. Snce, as shown n (1, the receved sgnal per subcarrer of MIMO MC-CDMA systems after FFT has a smlar representaton to that of sngle carrer systems, when there s no room for confuson, we wll omt the subcarrer ndex j for smplcty hereafter. 3. Analyss of V-BLAST Recever for MIMO MC- CDMA Systems Fg. 1 Block dagram of the MIMO MC-CDMA system. y j = H j + n j, 1 j N c = = h j h j h j M M + n j,k +,k, where H j s a channel matrx, where hm j = [h j 1,m h j 2,m h j N,m ]T ndcates a channel vector whose element hn,m j s the frequency doman channel response between transmt antenna m (m = 1,, M and receve antenna n (n = 1,, N, and = [ 1 2 M ]T and y j = [y j 1 y j 2 y j N ]T denote transmtted sgnal and receved sgnal mapped on jth subcarrer, respectvely. In (1,,k s a chp sgnal after spreadng wth code k transmtted from th antenna on jth subcarrer, and n j = [n j 1 n j 2 n j N ]T mples the addtve whte Gaussan (1 V-BLAST s composed of sequental nullng and cancellng for each transmt antenna based on the averaged postdetecton SNR crteron. In ths paper, we adopt a nullng vector based on mnmum mean square error (MMSE nullng crteron n [2] and [8]. Usng (1 and nullng vector w = [ w,1 w,m ] T for th transmt antenna, the nullng and cancellng for a multuser MIMO MC-CDMA system can be wrtten as follows: z j = (w j T y j x,k = MF k (z 1,, zsf y j = y j h j,k, where z j, x,k, MF k (x andy j denote jth chp sgnal of th transmt antenna after nullng, detected symbol of th transmt antenna after despreadng wth code k, matched flter recever for code k, and receved sgnal after cancellng of the regenerated sgnal for the th transmt antenna, respectvely. In V-BLAST recever for MIMO MC-CDMA systems, chp level nullng s performed per subcarrer. On the other hand, orderng for SIC s determned after despreadng n symbol level based on the averaged post-detecton SNR crteron. (2 z 1 = w T 1 y = wt 1 (h 1 x 1 + h 2 x h M x M + n = α 11 x 1 + α 12 x α 1M x M + n 1 = α α 12 x 2,k + α 13 x 3,k + + α 1M x + n 1 (3 y = y h 1 ( z 2 = w T 2 y = w 2 = h 1 T h 1 ( = α 22 x 2,k + x 2,k + α 21 D+I 1 K + h 2 x 2 + h 3 x h M x M + n (4 + h 2 x 2 + h 3 x h M x M + n E s + α 23 x 3,k + + α 2M x +n 2 (5 } {{ } I 2

3 LETTER 1727 Thus, cancellng s performed per subcarrer after spreadng accordng to the symbol level orderng. In the case of a multuser downlnk scenaro, the desred user knows only K codes among all K codes, thus only K detected symbols are removed n cancellng. We assume that nullng s ordered wth ncreasng antenna ndex for smplcty. Then, nullng for antenna 1 s gven by (3, where α 1 j and n 1 denote the nner product of w 1 and h j, and w 1 and n, respectvely. After nullng for antenna 1, the K code sgnals are detected by MF k (x. The detected K code sgnals for antenna 1 are spread and subtracted out from the receved sgnal by cancellng asshownn(4,where s an estmate of and ε 1,k denotes the detecton error for. Then, subsequent nullng for antenna 2 s performed by a new nullng vector w 2 obtaned after h 1 s removed from H [2]. Nullng for antenna 2 after cancellng sshownn(5,whered, I 1, I 2, E s and α 2 denote the desred sgnal from antenna 2, nterference due to unknown codes from antenna 2, nterference arsng from other antennas, nterference from prevous cancellng, and the nner product of w 2 and h, respectvely. In (5, as can be seen n E s, the propagated detecton error ε 1,k and nterference from unknown codes are accumulated. The accumulated nterference E s ncreases wth subsequent nullng and cancellng of V-BLAST and t causes severe performance degradaton. 4. MN-PPIC Recever In ths secton, we frst show the reasons for performance degradaton of V-BLAST from a vewpont of the effects of nterference due to frequency selectvty and the accumulated nterference descrbed by E s n (5 for downlnk MIMO MC-CDMA systems. Then, we propose a new detecton algorthm and present some analytcal results that show several aspects on the performance gan of the proposed algorthm. For MC-CDMA systems, as the number of multpath ncreases, the receved chp sgnal undergoes more severe frequency selectvty and we can obtan hgher frequency dversty. However, orthogonalty between codes s destroyed and the nter-code nterference ncreases n proporton to the frequency selectvty. Thus, we can obtan more frequency dversty by chp nterleavng wth larger degree of nterference, and there s some tradeoff between the frequency dversty and the nterference [6]. From these features, the man reasons for the drawbacks of V-BLAST are as follow. Frst, V-BLAST based on OSIC s not effectve n hgh frequency selectve channels, snce there are not sgnfcant dfferences among receved sgnal powers due to the ncreased frequency dversty. Second, snce w 2 n (5 s obtaned regardless of h 1, t can not suppress h 1 fully and α 21 may be large to some degree. Thrd, as can be seen n (5, nterference from antenna 1, composed of ε 1,k and, s multpled by α 21 and accumulated n E s, thus E s s susceptble to amplfcaton, and nterference effects due to E s ncrease wth subsequent nullng and cancellng of antenna 3 and so on. Consequently, the three nterference effects mentoned above become domnant factors for the performance degradaton of V-BLAST recever. Although t was shown that the lnear MMSE recever s superor to V-BLAST for multuser MIMO MC-CDMA systems [3], t s not optmal wthout cancellaton for MIMO detecton [4]. Thus, based on the dea that t s most mportant to control the effect of E s n (5, we propose combnatons of MMSE nullng (MN and partal PIC (PPIC recever, whch mtgate the excessve amplfcaton of E s effectvely and cancel nterference from other transmt antenna suffcently. The proposed algorthm substtutes V-BLAST block n Fg. 1 and the detals are as follow. We present the dervaton for antenna 1 only, however extensons to the remanng antennas are straghtforward. Frst, MMSE nullng s smultaneously performed for all transmt antennas and we obtan x,k (1 M, 1 k K n the same manner as (2. It s used n lth stage PPIC as an estmates of the x,k of prevous stage. Each MMSE nullng s followed by a PPIC to suppress nterference from other transmt antennas, as shown denote output sgnal of lth stage PPIC for transmt antenna 1 and an estmate of x (l,k obtaned from the prevous PPIC stage, respectvely. Second, snce sgnals from other antennas act as nterference for detectng antenna 1 substream, we perform PPIC n order to cancel the nterference assocated wth other antennas by usng the matched fltered outputs of prevous n (6, where z (l+1 1 and,k stage,,k (2 M, 1 k K n (6, where β s an nterference rejecton weght that controls the degree of nterference cancellaton [7]. In (6, we defned detecton error usng β as ε (l,k = x,k β,k (2 M. After lth stage PPIC for all transmt antennas, we obtan z (l+1 (1 M, the output of the lth stage PPIC. In the subsequent stage, after matched flterng n the same manner as (2, z (l+1 substtutes for,k n (6 wth ncreased relablty, snce nterference from other antennas are suppressed. The man reasons for the performance enhancement of the MN-PPIC recever are as follow. Frst, at the hgh frequency selectve envronments, there are not sgnfcant dfferences among nterference sgnal powers due to the ncreased frequency dversty, thus the detectons of the current stage usng PIC wth the nterference estmatons of the prevous stage become more accurate than OSIC, snce the orderng becomes less effectve. Thus, MN-PPIC recever s more advantageous than V-BLAST. Fgure 2 shows chp level post-detecton SNR and symbol level averaged postdetecton SNR correspondng to each transmt antenna for two typcal cases of frequency selectve channel envronments. We assume L = 2 and 24-paths Raylegh fadng channel wth an exponental decay of the average receved power levels wth a samplng nterval of 0.01 µsec [9], whose maxmum delay spread s shown n Table 1. As shown n Fg. 2, the dfference between post-detecton SNR of transmt antennas decreases as the frequency selectvty ncreases.

4 1728 IEICE TRANS. COMMUN., VOL.E88 B, NO.4 APRIL 2005 z (l+1 1 = w T 1 y β h 2 2,k + + h M = α α 12 D+I 1 ε (l = z 1 β α 12 ε (l 2,k + + α 1M } {{ } E p + α 12 2,k + + α 1M x 2,k + + α 1M x } {{ } I 2 +n 1 (6 Table 1 Smulaton parameters. Parameters Value Number of Tx., Rx. antenna (M, N 4 Spreadng sequence Walsh code Spreadng factor (SF 32 Modulaton scheme QPSK Channel model Quas-statc Raylegh Channel estmaton Ideal Rado Frequency ( f c 2.4 GHz Number of subcarrers (N c 1024 Guard nterval (GI 64 (0.64 µsec Max. delay spread of 2-path channel 0.01 µsec Max. delay spread of 24-path channel 0.23 µsec Interference rejecton weght (β 0.4 Fg. 2 Post-detecton SNR for each transmt antenna. (a Low frequency selectve case wth delay spread of 0.01 µsec, where the largest dfference s almost 4.3 db as shown n (b. (c Hgh frequency selectve case wth delay spread of 0.23 µsec, where the largest dfference s almost 1.5 db as shown n (d. Second, as shown n (6, there s no nterference due to unknown codes n E p, and detecton errors n E p become lower wth well chosen β and multstage processng. Thrd, nullng vectors for all correspondng transmt antennas functon reasonably well and nterference due to unknown codes n I 2 are well controlled. From these observatons, the effects of E p n (6 s more effectvely controlled as the stage of the MN-PPIC recever ncreases. In a computatonal complexty pont of vew, the proposed MN-PPIC recever has advantages over V-BLAST. The proposed method requres nullng vector calculaton only once, whle V-BLAST calculates nullng vector per transmt antenna. Snce pseudo nverse s the domnant factor n computatonal complexty and requres O(M 3 computatonal order, V-BLAST requres O(M 4 computatonal order and MN-PPIC requres almost O(M 3 order wth two stage PPIC [10]. Thus, MN-PPIC recever requres less computatonal power than V-BLAST. 5. Smulaton Results The performance of V-BLAST and MN-PPIC recever for multuser downlnk MIMO MC-CDMA system was evalu- ated through computer smulatons. The smulaton parameters used are shown n Table 1, where the optmal value of β was emprcally determned to be 0.4. As can be seen n Table 1, there are no multpath waves wth delay tme exceedng the guard nterval n the smulaton. For the multuser case, two users were consdered, and the frst user was assumed to be the desred user. In ths case, 14 codes are evenly assgned to each user ( K = 14, K = 28. The degree of frequency selectvty s mportant to the recever performance, thus we performed smulatons for two dfferent cases of delay spread as shown n Table 1 wth chp nterleavng. Smulaton results showed that sgnfcant performance mprovement s achevable wth the proposed method over V-BLAST. Fgure 3 and Fg. 4 show smulaton results of BER vs. E b /N o for 2 and 24-paths channel, respectvely. As can be seen n Fg. 3 and Fg. 4, for multuser downlnk MIMO MC-CDMA systems, the V-BLAST recever yelds an error floor n the hgher E b /N o regon under hgh frequency selectve envronments, but the proposed method does not gve an error floor. Wth the two stage PPIC processng, we are able to obtan a sgnfcant gan of 4 db and 2.5 db over the lnear MMSE recever at target BER of 10 3 for the two cases of delay spread shown n Table 1, respectvely. Wth the smulaton results, two stages of MN-PPIC s suffcent for overall system performance consderng system complexty.

5 LETTER 1729 recever for multuser downlnk MIMO MC-CDMA systems and proposed MN-PPIC recever to enhance system performance based on the dea that PIC can obtan more attractve trade-off benefts betweendverstyandnterference due to frequency selectvty. Smulaton results llustrate that, whle V-BLAST detecton shows an error floor for multuser MIMO MC- CDMA systems under hgh frequency selectve envronments, the proposed MN-PPIC recever s not nterference lmted and gves performance gans of db at target BER of 10 3 wth two stage PPIC processng over lnear MMSE recever. Fg. 3 BER comparson for MIMO MC-CDMA systems wth chp nterleavng (2-paths wth delay spread of 0.01 µsec. For PPIC, expermentally chosen optmal nterference rejecton weght β of 0.4 was used. Fg. 4 BER comparson for MIMO MC-CDMA systems wth chp nterleavng (24-paths wth delay spread of 0.23 µsec. For PPIC, expermentally chosen optmal nterference rejecton weght β of 0.4 was used. 6. Conclusons We analyzed some drawbacks of the conventonal V-BLAST References [1] R. van Nee, G. Awater, M. Morkura, H. Takanash, M. Webster, and K.W. Halford, New hgh-rate wreless LAN standards, IEEE Commun. Mag., vol.37, no.12, pp.82 88, Dec [2] P.W. Wolnansky, G.J. Foschn, G.D. Golden, and R.A. Valenzuela, VBLAST: An archtecture for realzng very hgh data rates over the rch scatterng wreless channel, ISSSE 98, pp , [3] Z. Le, X. Peng, and F.P.S. Chn, V-BLAST recevers for downlnk MC-CDMA systems, IEEE 58th VTC 2003-Fall, pp , Oct [4] A. Paulraj, R. Nabar, and D. Gore, Introducton to Space-Tme Wreless Communcatons, Cambrdge Unversty Press, [5] H. Claussen, H.R. Karm, and B. Mulgrew, Hgh-performance MIMO recevers based on mult-stage partal parallel nterference cancellaton, IEEE 58th VTC 2003-Fall, vol.1, pp , Oct [6] S. Kaser, OFDM code-dvson multplexng n fadng channels, IEEE Trans. Commun., vol.50, no.8, pp , Aug [7] D. Dvsalar, M.K. Smon, and D. Raphael, Improved parallel nterference cancellaton for CDMA, IEEE Trans. Commun., vol.46, no.8, pp , Feb [8] K. Km, J. Ham, and C. Lee, Performance analyss of a downlnk MIMO MC-CDMA system wth turbo codng and channel nterleavng, IEEE 59th VTC 2004-Fall, to be publshed. [9] N. Maeda, H. Atarash, and M. Sawahash, Performance comparson of channel nterleavng methods n frequency doman for VSF- OFCDM broadband wreless access n forward lnk, IEICE Trans. Commun., vol.e86-b, no.1, pp , Jan [10] W. Zha and S.D. Blosten, Modfed decorrelatng decsonfeedback detecton of BLAST space-tme system, IEEE ICC 2002, vol.1, pp , Aprl/May 2002.