Mult-eam multplexng usng multuser dversty and random eams n reless systems Sung-Soo ang Telecommuncaton R&D center Samsung electroncs co.ltd. Suon-cty Korea sungsoo.hang@samsung.com Yong-an Lee School of Electrcal Eng. and Computer Scence and INMC Seoul Natonal Unversty Seoul Korea ylee@snu.ac.r Astract In ths paper e propose a ne multple-access transmsson scheme that can smultaneously acheve oth dversty and multplexng gan n the mult-user doman y usng multple random eams. Multple eams are generated so that the users encounter multple channels at the same tme enalng the use of mult-user dversty through each channel. Snce the transmt poer s splt nto multple channels the sgnal-to-nose poer rato (SNR) of each channel s reduced n proporton to the numer of eams. oever multple eams are generated so that the multplexng gan s much larger than the decrease of SNR ncreasng the overall system capacty. The proposed scheme ors ell n oth Rcan and Raylegh fadng channels regardless of the channel correlaton provdng the maxmum capacty n multuser and mult-antenna systems n practce. The proposed scheme s applcale to oth MIMO and MISO systems enalng the use of recevers th flexle antenna structure. Keyords-multuser multple random eams multplexng MIMO I. INTRODUCTION The next generaton transmsson system should e ale to provde hgh data rate multmeda servces to users n mole nomadc and fxed envronment. The nature of multmeda servces may need the donln capacty much larger than the upln. In recent years the capacty of reless systems has een ncreased sgnfcantly th the development of to ey technologes; the use of multple antennas non as multnput mult-output (MIMO) [-3] and pacet schedulng non as opportunstc schedulng or mult-user dversty (MUD) [-7]. In ths paper e consder a mult-antenna transmsson scheme that can smultaneously provde mult-user dversty and multplexng (MUDAM) gan usng multple random eams. If e can provde multple channels smultaneously y generatng multple eams e can get oth the dversty and multplexng gan n the mult-user doman. Although the transmtted poer s splt nto multple channels total system capacty can e ncreased y ncreasng the multplexng gan much more than the decrease of the SNR. The multplexng scheme usng multple transmt antennas can e consdered as a comnaton of transmsson eamformng and drty paper pre-codng method [-9]. oever these prevous schemes requre perfect channel state nformaton (CSI) of all users. The use of multple orthogonal eams as refly dscussed n [] ut t may not provde a desred capacty gan hen the numer of users s small. In addton the capacty ncreases very sloly as the numer of users ncreases. We consder the generaton of multple eams n a random manner so that multple eams nterfere th each other at a controlled level thout regardng orthogonalty. Note that unle the opportunstc eamformng the proposed MUDAM scheme can provde a capacty mprovement even n fast Raylegh fadng channel snce t explots the multplexng n the mult-user doman. The proposed scheme can also mprove the capacty even n completely correlated channels snce t utlzes ndependent channels eteen dfferent users. The proposed scheme s applcale to oth the mult-nput sngleoutput (MISO) and MIMO systems. Ths paper s organzed as follos. In Secton II e ntroduce the system. A MUDAM scheme usng multple random eams s proposed n Secton III. The performance of the proposed MUDAM scheme s verfed y computer smulaton n Secton IV. Fnally Secton V concludes ths paper. II. SYSTEM MODEL Consder an ( M N ) MIMO system here the ase staton has M transmt antennas and each of K users has N receve antennas. The receved sgnal y () t of the -th user at tme t s can e represented as y () = t () t x() t + z () t = K () here x ( t) s an M-dmensonal (dm) transmtted symol vector z () t s an N-dm nose vector hose elements are zero mean complex crcular-symmetrc Gaussan process th the same varance σ z and () t s an ( N M )-dm channel matrx th element hnm () t representng the channel from the m-th transmt antenna to the n-th receve antenna of the -th user. ere the superscrpt and denote complex conjugate and conjugaton of the transpose respectvely. We assume that the channel h () t has flat fadng th a nm -73-939-5/5/$. (C) 5 IEEE
loc-fadng model (.e. the channel s unchanged durng each slot tme T and vares ndependently n the next tme slot) the channels of each user are ndependent and the transmt poer s fxed to P at all tmes.e. E{ x ( t) } = P here E{ x } denotes the expectaton of x. We also assume that nstantaneous channel qualty nformaton such as the SNR s avalale at the ase staton. The ase staton assgns the channel resource to a user th the est channel qualty at each tme explotng the user dversty. For ease of descrpton e frst consder an (Mx) MISO system. The receved sgnal of user can e represented as y () t = h () t () t s() t + z() t = K () here h ( t) = [ h ( t) h ( t)... hm ( t)] denotes the mpulse response of the MISO channel s( t ) s the user sgnal and ( t) = [ ( t) ( t)... ( )] T M t s the eght vector of the eamformer. III. MULTI-USER DIVERSITY AND MULTIPLEXING (MUDAM) A. asc concept of MUDAM We consder a multuser dversty system th a novel multplexng scheme n the mult-user doman usng multple random eams. For easy descrpton consder a (x) MISO system th to eams as llustrated n Fg.. here to sgnals d () t and d () t are multplexed y eght T T = [ ] and = [ ] yeldng a transmtted sgnal x() t = () t d() t + () t d() t. (3) The receved sgnal of user can e represented as () = y t h () t () t d() t + h () t () t d() t + z() t. () here the eght and can e generated n a successve manner. Frst the ase staton generates a random eam eght (as n the opportunstc eamformng) and each user reports the SNR to the ase staton. The SNR of user s gven y h /σ here σ s the nose poer of user. The ase staton selects a user havng the maxmum SNR γ = { σ } max h / (5) {... K} here γ s the maxmum SNR acheved through the frst eam. Assume that the ase staton selects user p n ths process. The selected user p reports ts channel response h p () t to the ase staton. Let g () t = h p () t here g () t denotes the channel response correspondng to the frst eam. The ase staton can generates the second eam so that t generates the nterference to the user of n a controlled manner.e. g () here ε should e chosen to e small enough for the SINR of the frst eam s nearly unaffected as γ = g σ p + ε. (7) Then the ase staton selects the est user through the second eam resultng an SINR represented as γ = max h σ + h. () p {... K} Note that the transmt poer of each eam s reduced nversely proportonal to the numer of multple eams snce the total transmt poer should e constant. Note that the nterference from the second eam to the frst eam user s controlled y (/ ) ε ut the nterference (/ ) h from the frst eam to the second eam user s not controllale. Thus t s requred for the ase staton to choose a user havng the maxmum SINR n an opportunstc manner. Consder a generalzed MUDAM structure. The ase staton transmts sgnals { d ( t) d ( t)... d ( t ) } to K users through eams th eght vector { () t ()... t () t } at the same tme. In ths case () can e rertten as y () t = h () t () t d () t + z () t = K (9) here d () t s the user sgnal such that d( t) { s( t) s( t)... sk( t) }.... () We assume that each sgnal has the same poer σ s. Let g ( t) denote the channel response of the est user through the -th eam ( t).e. { } g( t) h( t) h( t)... h K( t) =.... () Assume that the scheduler selects user p (.e. = p ) for the -th eam (.e. ). That s the ase staton transmts the user sgnal sp () t usng the -th eam () t (or d() t = sp() t and g() t = h p() t ). The receved sgnal r () t through the -th eam (.e. the receved sgnal of user p) can e represented as r() t = yp() t = hp () t () t sp() t + () t d() t + zp() t () p = g () t () t d () t + g () t () t d () t + z () t here the frst term s the desred sgnal the second term s the nterference due to mult-eam multplexng and the thrd term s addtve nose. As n the prevous example the ase staton performs the successve controllng the poer of nterference as -73-939-5/5/$. (C) 5 IEEE
ε < g = = (3) x > here x denotes the amount of uncontrollale nterference that vares dependng on the stuaton. The proposed MUDAM scheme generates the eght matrx W( = [... ]) satsfyng G W = F () here G s the channel matrx of the selected users defned y G = [ g g... g ] (5) and F s a constrant matrx defned y ε ε ε x ε ε F x x. () ε x x x Note that the tme ndex t s omtted for ease of descrpton ecause the eght vector () t and the channel g () t are assumed to unchanged durng each slot tme.. Generaton of multple random eams We consder the generaton of such multple eams n a random manner. We assume that the channel condton s unchanged durng the feedac process as n the opportunstc eamformng. The ase staton generates the frst eam = [... ] T M n a random manner as m m = αm e m =... M (7) here α m and θ m are tme-varant over a tme slot havng a random value eteen and and and π respectvely. Let g e the mpulse response of the channel of the frst user selected y the scheduler. Next the ase staton generates the next random eam such that g. ere for ease of mplementaton e assume ε and µ = µ for all. Note that the scheduler does not need the channel nformaton of all the users ut only that of the selected user. Snce the eght of the second eam s an M-dm vector th a sngle constrant (.e. an under-determned system) e can artrarly determne (M-) elements y (7). Thus e need to solve a sngle equaton satsfyng Then e have M m gm αm e + gm M () m = m αm e... M p (9) g e m M M m ε m αm = p g M here the constant / p s the normalzaton constant mang =. Smlarly the eght of the -th eam can e generated y determnng ( M + ) elements randomly and the rest (-) elements are determned y solvng equatons g =... () here rand = () sol hose elements are gven y m ( rand ) = ( p ) αm e... M + () m and g M + gm + 3 gm gm gm + gm + 3 gm gm ( ) sol = p gm + gm gm + gm + 3 gm gm M + m ε gm αm e M + m ε gm α me M + m ε α gm me (3) Fg. depcts the procedure of the proposed MUDAM scheme hen to eams are employed. Note that e can choose sngle eam mode (C) f the mult-eam mode (C M ) cannot acheve capacty gan (.e.c M <C). C. Extenson to MIMO systems The proposed scheme can e appled to the MIMO system n a straghtforard manner here the transmtted sgnals are multplexed as x() t = () t d() t. () The receved sgnal of user th an N-element receve antenna array can e represented as y () t = () t () t d () t + z () t = K (5) here z denotes the nose vector. Assume that the recever s explotng the receve antenna dversty such as the maxmum -73-939-5/5/$. (C) 5 IEEE
rato comnng (MRC) or MMSE comnng th comnng eght v ( ) [ ( ) ( )... ( )] T t = v t v t vn t. The output of the comner can e represented as = + r () t v () t () t () t d () t v () t z () t () Thus the proposed MUDAM scheme can e appled to the MIMO system th an equvalent channel h () t = v () t (). t (7) and an equvalent nose z ( t) = v ( t) z ( t). IV. PERFORMANCE EVALUATION The performance of the proposed MUDAM scheme s verfed y computer smulaton. The smulaton results are otaned y averagng over ndependent channel realzatons per user. We assume that channels of all the users are mutually ndependent flat fadng channel and have the same average SNR. Snce the multplexng s usually employed hen the SNR s hgh e consder the performance hen the SNR s d. Fg. 3 compares the performance of the opportunstc eamformng (denoted as sngle eam ) the multple orthogonal eam [] (denoted as orthogonal ) and the proposed MUDAM scheme hen a (x) MISO system s employed n Raylegh fadng channel th average SNR of d. The proposed MUDAM scheme s desgned usng ε =.. Multple orthogonal eams can smultaneously e generated such that W W = I here I s an dentty matrx. Note that the orthogonal eam scheme n [] does not consder the separaton of effectve channels g ut only the separaton of eams.... As a result unle the proposed MUDAM scheme the orthogonal multple eam scheme can provde a MUM gan only hen the users are separated y orthogonal eams. It can e seen that the proposed MUDAM scheme alays provdes a larger capacty than the sngle eam and orthogonal eam schemes. It can e also seen that the orthogonal eam scheme s poorer than the sngle eam scheme for a small numer of users. Ths s manly due to the fact that the orthogonal scheme cannot guarantee orthogonal separaton of multple users. Although t can acheve the MUM gan for a large numer of users t s stll poorer than that the proposed MUDAM scheme. It can e assumed that the channels { h h... h K } are ndependent. oever the channel h h... h M of user can e correlated unless the channel has rch scatterng. We assume a fully correlated channel th a lnear unform array. Then the channel of user s gven y hm = h exp{ j( m ) π( d / λ)sn β} () here M s unformly dstruted over[ π ] d s the antenna spacng and λ s the ave length of the carrer frequency. Fg. compares the capacty of (x) MISO MUDAM system th to eams and (x) MIMO system n [7] n ndependent and fully correlated Raylegh channel hen the SNR s d. The MIMO scheme n [7] (denoted as MIMO SVD ) can e nterpreted as a comnaton of the MUD and MIMO SVD. Although the proposed MUDAM scheme s a (x) MISO system the total system can e consdered as (x) MIMO system here the recever antennas are allocated to each user. It can e seen that the orthogonal eam scheme and MIMO SVD have smlar performance n ndependent channel. Note that the use of ater-fllng method has lttle effect n an ndependent channel hose egen-spread s not large. On the other hand t can e seen that the proposed MUDAM scheme ors ell regardless of the channel correlaton condton and thus outperforms the other schemes. It can also e seen that the orthogonal eam scheme s effectve hen the channel has correlaton outperformng the MIMO SVD scheme. The MIMO SVD can allevate the performance degradaton due to the channel correlaton y allocatng more poer to the antenna hose egen-value s large y usng ater-fllng. When the channel s fully correlated the channel elements h h... h M experence the same fadng null or pea. Thus the correlated channel may have peas hgher than the ndependent channel. As a result the eamformng method can provde a larger capacty gan n a correlated channel. V. CONCLUSIONS In ths paper e have proposed a ne multple antenna transmsson scheme that can smultaneously acheve the dversty and multplexng gan y generatng multple random eams. The multple random eams are generated so that each eam nterferes th other eams n a controlled manner. Unle the opportunstc eamformng scheme the proposed MUDAM scheme can provde the multplexng gan n Rcan and Raylegh fadng channel regardless of the channel correlaton. Smulaton results sho that the proposed MUDAM scheme can provde a large system capacty than the orthogonal mult-eam and MIMO schemes. In practce the proposed scheme can provde the maxmum capacty n multuser and mult-antenna systems. The proposed MUDAM scheme can e applcale to MIMO as ell as MISO systems enalng the use of recevers th flexle antenna structure. REFERENCES [] G. J. Foschn and M. J. Gans On lmts of reless communcatons n a fadng envronment hen usng multple antennas Wreless Personal Commun. Vol. No. 3 pp. 3 335 June 99. [] G. D. Golden G. J. Foschn V. A. Valenzuela and P. W. Wolnansy Detecton algorthm and ntal laoratory results usng V-LAST spacetme communcaton archtecture Electron. Lett. Vol. 35 pp. Jan. 999. [3] S. M. Alamout A smple transmt dversty technque for reless communcatons IEEE J. Select. Areas Commun. Vol. No. pp. 5 5 Oct. 99. [] W. Rhee W. Yu and J.M. Coff Utlzng multuser dversty for multple antenna systems IEEE Proc. Wreless Commun. Netor. Conf. -73-939-5/5/$. (C) 5 IEEE
(WCNC) Vol. pp. 5 Sept.. [5] R. Gozal R. M. uehrer and. D. Woerner The mpact of multuser dversty on space-tme loc codng IEEE Commun. Lett. Vol. 7 No. 5 pp. 3 5 May 3. [] P. Vsanath D. N. C. Tse and R. Laroa Opportunstc eamformng usng dum antennas IEEE Trans. Inform. Theory Vol. No. pp. 77 9 June. [7] J. Chung C. ang K. Km and Y. K. Km A random eamformng technque n MIMO systems explotng multuser dversty IEEE J. Select. Areas Commun. Vol. No. 5 pp. 55 June 3. [] G. Care and S. Shama On the achevale throughput of a multantenna Gaussan roadcast channel IEEE Trans. Inform. Theory Vol. 9 No. 7 pp. 9 7 July 3. [9] M. Shuert and. oche Jont 'drty paper' pre-codng and donln eamformng IEEE Int. Symp. Spread-Spectrum Technol. pp. 53 5 Sept.. User User Total capacty (ps/z) 5 5 5 3 35 MUDAM Orthogonal Sngle eam Fg. 3 The capacty n Raylegh fadng channel (SNR =d) d (t) d (t) g (t) g (t) g (t) g (t) User selected y User selected y User K User Fg. : The proposed MUDAM scheme appled to a (x) MISO system Yes Start Generate the frst random eam All user report ther SNR's Scheduler selects the user havng maxmum SNR The selected user reports ts channel g Generate the second random eam th constrant g All user except the frst user report ther SNR's C M > C? Use multple eams N o Use sngle eam S MS Total capacty (ps/z) Overall capacty (ps/z) (x) MUDAM (x) orthogonal eams (x) MIMO SVD / Water fllng (x) MIMO SVD /o Water fllng 5 5 5 3 35 (a) Independent channel (x) MUDAM (x) orthogonal eams (x) MIMO SVD / Water fllng (x) MIMO SVD /o Water fllng 5 5 5 3 35 () Correlated channel Fg. The capacty of (x) MISO and (x) MIMO SVD Fg.: The procedure of (x) MUDAM scheme -73-939-5/5/$. (C) 5 IEEE