Beam Management for Millimeter Wave Beamspace MU-MIMO Systems

Transcription

1 Beam Managemen for Millimeer Wave Beamspace MU-MIMO Sysems Qing Xue and Xuming Fang Key Lab of Informaion Coding & Transmission Souhwes Jiaoong Universiy, Chengdu 6003, China Ming Xiao Communicaion Theory Deparmen Royal Insiue of Technology, Sockholm 00 44, Sweden Absrac Millimeer wave (mmwave) communicaion has araced increasing aenion as a promising echnology for 5G neworks. One of he key archiecural feaures of mmwave is he use of massive anenna arrays a boh he ransmier and he receiver sides. Therefore, by employing direcional beamforming (BF), boh mmwave base saions (MBSs) and mmwave users (MUEs) are capable of supporing muli-beam simulaneous ransmissions. However, mos researches have only considered a single beam, which means ha hey do no make full poenial of mmwave. In his conex, in order o improve he performance of shor-range indoor mmwave neworks wih muliple reflecions, we invesigae he challenges and poenial soluions of downlink muli-user muli-beam ransmission, which can be described as a high-dimensional (i.e., beamspace) muli-user muliple-inpu muliple-oupu (MU-MIMO) echnique, including muli-user BF raining, simulaneous users grouping, and muli-user mulibeam power allocaion. Furhermore, we presen he heoreical and numerical resuls o demonsrae ha beamspace MU-MIMO compared wih single beam ransmission can largely improve he rae performance of mmwave sysems. Index Terms Millimeer wave (mmwave), beamspace MIMO, muli-user beamforming (BF) raining, iner-beam inerference coordinaion. I. INTRODUCTION According o Cisco forecas, global mobile daa raffic will increase sevenfold beween 06 and 0 []. Recen researches showed ha mmwave communicaions, operaing in GHz bands, are promising echnologies for meeing he explosive growh of mobile daa demand. Compared wih exising microwave sysems, mmwave sysems are faced wih wo major challenges: severe propagaion loss and sensiiviy o blockage. To compensae for high propagaion loss, direcional BF has been widely used as an essenial echnique o form a highly direcional beam paern wih large anenna gain. Thanks o he shor wavelenghs of mmwave radios ranging from 0 mm o mm, massive anenna arrays can be packed ino he limied dimensions of mmwave ransceivers. Therefore, wih direcional BF, i is possible o form muliple beams a boh mmwave ransmier and receiver sides in mobile neworks. Tha is, mmwave sysems are in fac able o provide high-dimensional MIMO operaions [] [4] and can realize spaial specrum reuse a close disance [5]. However, mos curren work does no make full poenial of mmwave. For insance, he work in [6] [9] was focused on single beam ransmission scenarios, and he work in [5], [0] [] considered he scenarios where only he ransmier side was operaing wih muliple beams. Moreover, since mmwave radios have limied abiliy o diffrac around obsacles (e.g., human body), he connecion beween each pair of ransmier and receiver is vulnerable o blockage evens. In his conex, aiming a increasing he achievable rae and mainaining conneciviy of mmwave mobile neworks, we invesigaed he challenges and poenial soluions (including muli-beam selecion, cooperaive beam racking, muli-beam power allocaion, and synchronizaion) associaed wih singleuser muli-beam simulaneous ransmissions (i.e., beamspace SU-MIMO) in [3]. I is worh menioning ha he proposed scheme is only applicable o he shor-range scenarios wih muliple NLOS pahs (e.g., firs or second order reflecions from floor and/or ceiling in indoor scenarios). In order o furher enhance he performance of mmwave sysems, we exend our previous work o muli-user scenarios, namely beamspace MU-MIMO, on he basis of exising research resuls. To he bes of our knowledge, here has been no work on his issue. Since he communicaion environmen wih muli-user is more complex han ha wih single user, no only need we o furher expand he sraegies proposed in [3], bu also will we face some new challenges for implemening beamspace MU-MIMO. For insance, due o he ransmi beams seleced by differen MUEs may be (parially) overlapped, he ineruser inerference should be seriously considered in beamspace MU-MIMO. This sudy mainly focuses on he issues of muliuser BF raining, simulaneous users grouping, and muli-user muli-beam power allocaion in beamspace MU-MIMO. The res of he paper is organized as follows. In Secion II, he nework model and he basic idea of beamspace MU- MIMO are inroduced. Secion III firs describes mui-user BF raining and hen proposes a muli-user grouping mechanism. In Secion IV, he poenial soluions of power allocaion for beamspace MU-MIMO are presened and analyzed. Secion V shows some numerical resuls o evaluae he proposed scheme. Finally, Secion VI concludes he paper. II. SYSTEM OVERVIEW In his sudy, we consider a shor-range indoor mmwave nework wih one reference MBS and U oal sparsely disribued MUEs. Le R denoe he se of hese MUEs. Meanwhile, boh he MBS and MUEs are equipped wih massive anenna arrays.

2 Thus, wih direcional BF and space division echnique, hey are capable of supporing muliple orhogonal beams simulaneously and can realize specrum reuse, as illusraed in Fig.. Le b MBS max and b u max denoe he maximum number of beams ha he MBS and MUE u (u R) can form, respecively, we generally have b MBS max b u max. Le Q (Q R) be he se of MUEs served simulaneously by he MBS and U be he number of MUEs in Q, we have U b MBS max. Furhermore, supposing ha b and b u are he number of operaing beams of he MBS and MUE u in acual ransmissions, respecively, and considering ha he ransmi and receive beams are used in pairs in mmwave neworks, we have b = b u b MBS max, where b u b u max. The muli-user muli-beam simulaneous ransmission scheme invesigaed in his sudy can be described as beamspace MU-MIMO defined as Definiion. Fig. shows an example of beamspace MU-MIMO in wo-dimensional (D) perspecive. Noe ha he analysis is also applicable o hree-dimensional (3D) mode. For ease of analysis, similar o [0], [3], [4], we replace he MBS wih U virual MBSs (vmbss) locaed a he same posiion. Each vmbs serves differen MUEs wih differen ransmi beam ses. Moreover, when < b u b u max, he ransmission mode beween MUE u and is corresponding vmbs is beamspace SU-MIMO (e.g., for MUE and MUE3 in Fig. ) and i is beamspace SU-SISO when b u = (e.g., for MUE). In his conex, beamspace MU-MIMO can be defined as a se of beamspace SU-MIMO and/or SU-SISO echnologies wih space division echnique. Definiion (Beamspace MU-MIMO): The beamspace MU- MIMO is defined as an mmwave communicaion mode ha an MBS wih muliple orhogonal beams can ransmi simulaneously o a se of MUEs, where each MUE is wih one or more operaing beams. Tha is, denoing Q as he se of MUEs, b and b u as he number of ransmiing and receiving beams of he MBS and MUE u (u Q), respecively, he muli-user mulibeam simulaneous ransmissions can be ermed as N N U beamspace MU-MIMO, where U is he number of MUEs in Q, N is he oal number of ransmiing and receiving (T-R) beam pairs beween he MBS { and he simulaneous ransmiing MUEs, N min b, b u }. In order o implemen beamspace MU-MIMO and, meanwhile, o achieve opimal sysem performance, we face many challenges as below. ) Muli-user BF raining: Since only one ransmi/receive direcion s link qualiy can be deeced a a ime in radiional BF raining (e.g., in 80.ad/ay), he efficiency of he opimal beam selecion is generally very low. I means ha he exising beam selecion soluions are no enirely applicable o beamspace MU-MIMO. This sudy uilizes he capabiliy of supporing muliple beams boh a he MBS and MUEs o deec he qualiy of muliple links simulaneously, and hus o increase he efficiency of muli-beam selecion for beamspace MU-MIMO. ) Iner-user inerference coordinaion: The bes ransmi beam MUE3 MBS (vmbss) LOS link NLOS link MUE MUE Fig.. An example of D view of beamspace MU-MIMO (U = 3). Noe ha, in order o make he figure clear, we do no show he side lobes here. ses seleced by differen MUEs may be (parially) overlapped, e.g., in Fig., one NLOS link for MUE is in conflic wih he LOS link for MUE over he ransmi beam. And he iner-user inerference will be severe in his case. To address his issue, we can swich some MUEs iniial seleced T-R beam pairs wih conflicing beams o a suiable candidae (if available), or assign he MUEs wih he same conflicing ransmi beam o differen groups. MUEs in differen groups will be served in ime division manner. 3) Power allocaion: Considering ha he ransmission performance of differen links for differen MUEs may vary widely, he appropriae power allocaion sraegies should be seriously considered o maximize he achievable rae of beamspace MU-MIMO. III. BEAM/USER MANAGEMENT FOR BEAMSPACE MU-MIMO In his secion, we firs give an efficien muli-user BF raining mechanism for beamspace MU-MIMO. I is worh menioning ha he BF raining (or beam seering) operaions are designed o deermine he bes T-R beam pair se N u pair (u R) ha bes maches he LOS pah and/or NLOS pahs beween a vmbs and is corresponding MUE, hereafer called vmbs-mue. In his sudy, afer he successful compleion of BF raining, direcional BF is esablished. Moreover, o guaranee he nework performance, we furher adjus he iniial seleced T-R beam pair ses by analyzing iner-user inerference. Table I summarizes he main noaions used hroughou he paper. A. Muli-user BF Training The muli-user BF raining mechanism in his sudy aims a improving he downlink performance of beamspace MU- MIMO. The corresponding sraegies for uplink ransmission are lef as our fuure work. For ease of illusraion, we divide he region of he MBS/MUEs ino a number of ransmi/receive secors (i.e., orhogonal beam direcions). Meanwhile, we assume ha MUEs can disinguish signals received from differen beams. The proposed mechanism mainly consiss of hree phases and, moreover, he concepual flow of he firs wo phases is illusraed in Fig.. The deails are as follows. (i) Transmi Training: In his phase, all MUEs are in he quasi-omni mode and he MBS scans ransmi secors

3 TABLE I SUMMARY OF MAIN NOTATIONS. MBS: direcional beam scan MUE: quasi-omni mode Symbol Definiion R The se of MUEs wihin he coverage of he MBS Q The se of MUEs served simulaneously (Q R) U Number of MUEs in Q b MBS max Maximum number of simulaneous ransmi beams a MBS b u max Maximum number of simulaneous receive beams a MUE u b Number of he operaing beams a he MBS b u Number of he operaing beams a MUE u (u Q) N u TX Bes ransmi beam se of MUE u (u R) N u RX Bes receive beam se of MUE u (u R) N u pair Bes T-R beam pair se of vmbs-mue u (u R) N u cd Candidae T-R beam pair se of vmbs-mue u (u R) N u Operaing T-R beam pair se of vmbs-mue u (u Q) C m The se of MUEs wih conflicing beam m (C m R) η Threshold of SNR (or SINR) ξ Transmiing beamwidh ξ r Receiving beamwidh Ri u Transmission disance of link i for MUE u (i N u ) qualiy simulaneously wih direcional beams. Here, differen secors are scanned by differen beams which are muually orhogonal. Assuming ha he oal number of ransmi secors is S MBS, we have min { b MBS } max, S MBS. () Hence, we only need o es SMBS imes o deermine he bes ransmi beam se N u TX for MUE u ( u R), while he radiional ransmi raining operaing wih only one beam a a ime is required o es S MBS imes. (ii) Receive Training: In his phase, i reverses he scanning roles from he ransmi raining. Tha is, MUEs deec muliple receive secors simulaneously wih muliple direcional beams and he MBS remains in he quasi-omni mode a his ime. Similar o ransmi raining, MUE u ( u R) can obain is bes receive beam se N u RX afer scaning Su n imes, where u rx S u is he oal number of MUE u s receive secors, n u rx is he number of simulaneous scanning beams, and n u rx min {b u max, S u }. () Since he number of simulaneous receive beams suppored by each MUE may be differen, he number of ess required for compleing heir respecive receive raining will also be differen. Supposing ha S u = S MUE for u R, he number of ess required o complee muli-user receive raining is S MUE min u R nu rx. (iii) Beam Combining: We firs es he ransmi and receive beams in N u TX and Nu RX in pairwise combinaions o ge muliple T-R beam pair candidaes which mee cerain communicaion requiremens, e.g., SNR η, where η is a given hreshold. Then, by adoping he muli-beam combinaion selecion algorihm proposed in [3], we can deermine N u pair ( u R) in which here are b u T-R beam pair candidaes, b u b u max. Furhermore, he link qualiy of each candidae should mee SINR u,i η ( i N u pair ) when muliple links are ransmied simulaneously. Noe ha MUEs make he Transmi Training Receive Training MUE u MBS: quasi-omni mode MUE u u MBS Receive secor u MBS Transmi secor v v MUE v MUE: direcional beam scan MUE v Fig.. Illusraion of ransmi and receive raining for downlink beamspace MU-MIMO, given ha U oal =. The beams drawn wih solid lines are operaed concurrenly and i is he same o ha drawn wih doed lines. decision independenly in his phase and hey may obain several alernaive (or sub-opimal) T-R beam pair ses. B. Simulaneous MUEs Grouping Considering he diversiy and finieness of he number of simulaneous operaing beams ha can be suppored by he MBS and MUEs, he MBS is generally unable o serve all MUEs in is coverage simulaneously. Moreover, he sysem performance of beamspace MU-MIMO is various for differen combinaions of simulaneous MUEs. To ensure he performance, his subsecion is devoed o grouping simulaneous MUEs hrough he analysis of iner-user inerference. Since he decision of muli-beam selecion for each MUE is relaively independen, he ransmi beams seleced by hem may be (parially) overlapped. We assume ha one beam can serve only one MUE a he same ime. To avoid beam conflics, we need o adjus or re-selec N u pair ( u R), e.g., by beam swiching. Afer ha, we can proceed wih he selecion of simulaneous MUEs as described in Algorihm, he main idea of which can be oulined as follows: Denoing C m as he se of MUEs wih conflicing ransmi beam m, he MBS gives prioriy o MUE s (s C m ) which saisfies SINR s,m = max SINR u,m. u C m The MUEs (e.g., MUE u, u C m \s), which saisfy SINR u,m max i N u pair SINR u,i, can swich heir iniial seleced T-R beam pair ses o he bes suiable candidaes N u cd (if available). Here, suiable candidae refers o he alernaive

4 Algorihm Muli-user grouping Inpu: he maximum number of ransmi beams b MBS max ; he bes T-R beam pair ses N u pair ( u R); : Iniialize Q = ; : Compare N u pair and Nv pair ( u, v R, u v); 3: Record he MUEs wihou beam conflics ino Q ; 4: if Q = R or b = b u > b MBS max hen 5: Rank MUEs in Q in decreasing order according o he average link qualiy SINR, e.g., SINR u = i N u SINR u,i pair b u ; 6: Record he firs U MUEs ino Q which saisfies b = b u b MBS max ; 7: else 8: Selec an MUE (e.g., MUE s) in each se of MUEs wih conflicing beam (e.g., C m ), which saisfies SINR s,m = max u C m SINR u,m, and record hem ino Q ; 9: Record he MUEs who can swich o a suiable candidae T-R beam pair se in (R Q ) ino Q ; 0: Rank MUEs in Q and Record he firs U MUEs ino Q as in sep 5 and sep 6, respecively; : end if Oupu: he se of simulaneous MUEs Q T-R beam pair se which saisfies: () N u cd Nv pair =, v Q\u; () SINR u,i η, i N u cd. If hese MUEs have no suiable candidaes, hey will be served in ime division manner. The oher MUEs (e.g., MUE k, k C m \s, u) should be assigned o differen simulaneous MUE groups and will be served in ime division manner. Denoing N u as he operaing T-R beam pair se of MUE u, we have N u = N u pair or Nu = N u cd. In his sudy, he MBS carries ou he decision of muli-user grouping and informs MUEs of he decision resul. Before each ransmission cycle, Algorihm can realize he selecion of simulaneous MUEs for beamspace MU-MIMO. Meanwhile, he nonseleced MUEs have relaive high prioriies in he nex cycle o ensure fairness. IV. POWER ALLOCATION FOR BEAMSPACE MU-MIMO Since he qualiy of differen links may vary widely among simulaneous MUEs, we should make reasonable power allocaion for beamspace MU-MIMO in order o maximize is achievable rae. The NLOS links in his sudy are assumed o be firs order reflecions, because mmwave signals are generally negligible afer high-order reflecions and he acual ransmission pahs of hem are unpredicable. For racabiliy of he analysis, we approximae he acual anenna paern by an ideal secored anenna model [7], [5]. The direciviy gain can be expressed as [8], [4] { π (π ξ)z G (ξ) = ξ, in he main lobe, z, in side lobes, where ξ is he operaing beamwidh and z is he average gain of side lobes, 0 z <. Furhermore, he pah loss of mmwave can be modeled as [6] (3) L (R) [db] = A + 0 log 0 (f c ) + 0n log 0 (R), (4) where f c is he carrier frequency in GHz, R is ransmission disance in km, A is he aenuaion value, and n is he pah loss exponen. Since he T-R beam pairs for beamspace MU- MIMO are muually orhogonal (i.e., he main lobes are nonoverlapping), we assume ha he iner-beam inerference is mainly caused by side lobes. Therefore, he SINR of link i for MUE u (u Q) is ( ) P i g ξ u,i g ( ) ξr u,i SINR u,i [db] = 0 log 0 P N + ( P j z g j M ( where P i is he ransmied power; g ) π (π ξ = u,i r )z ξ u,i ξ u,i r L(R u i ) ) L(R u i ) ) (5) = π (π ξu,i ξ u,i, )z and g ( ξr u,i are he average main lobe ξr u,i gains of ransmi and receive beams, ( respecively; P N is he hermal noise power; M = (N u \i) N ). v Moreover, v Q\u he achievable rae of link i can be esimaed as Rae u,i = B log ( + SINR u,i ) according o Shannon capaciy formula, where B is he operaing bandwidh. To maximize he achievable rae of beamspace MU-MIMO,, and P i ( u Q, i N u ) in vecors ξ, ξ r and p, respecively, and hen formulae he problem under consideraion as an opimizaion problem (P) given by we firs collec he variables ξ u,i maximize ξ,ξ r,p,q subjec o, ξ u,i r Rae = B log ( + SINR u,i ) i N u (6a) ξ,min ξ u,i < π, (6b) ξ r,min ξr u,i < π, (6c) U b MBS (6d) max, 0 P i, (6e) 0 < P i P max, (6f) i N u where ξ,min and ξ r,min are he minimum beamwidh of ransmi and receive beams, respecively; and P max are he maximum ransmission power of each ransmi beam and he MBS, respecively. Noe ha funcion argumens have been discarded for noaional simpliciy. Considering he simples scenario wih pencil beams, i.e., z, we can neglec he iner-beam inerference and opimize he operaing beamwidh for each link individually. Tha( is, he ) opimal beamwidh of ransmi and receive beams are ξ u,i = ξ,min and ( ) ξr u,i = ξr,min, respecively. Hereafer, he opimized

5 parameers are idenified by he on he upper righ corner. Meanwhile, he SINR expression formulaed in Eq. (5) reduces o SNR according o ( ) P i π π SNR ξ,min ξ r,min L(Ri u,i = u ). (7) P N As P is difficul o obain is opimal soluion, we invesigae wo low complexiy and easy o implemen soluions for muli-user muli-beam power allocaion o subopimally address P ha wih pencil beams. Average Power Allocaion (APA): Each link s ransmission power is he same wihou considering he difference of link qualiy, i.e., ( ) P i APA = P max, where Q and b u can be b u obained by Algorihm. Prioriy Power Allocaion (PPA): Considering he qualiy of differen links may vary widely, we give prioriy o opimize he ransmission power of he links ha wih high link qualiy o address P. Furhermore, his soluion includes he following wo cases. ) Considering fairness: When he fairness of power allocaion among simulaneous MUEs is aken ino accoun, we will give prioriy o opimize ( he bes ) link for each MUE (e.g., link l for MUE u), i.e., P u,l =. Then, we FP employ ( APA ) o allocae power for oher links (e.g., link i), i.e., p max, i (N u ) \l, where U is P u,i FP = Pmax U (b u ) he number of MUEs in Q. ) Wihou considering fairness: We rank all he links in N in decreasing order according o he link qualiy, where N = N u. Denoing N OFP as he se of he firs P max links in N, we have ( ) P i = p OFP max for i N OFP. Furher, P if he res of he power p = P max max can mee he communicaion requiremens of a link in (N N OFP ), we have U P = max ; Oherwise, U P = max. Subsiuing he opimized parameers ino Eq. (6) and (7), we can easily obain he maximum achievable rae wih APA and wih PPA, respecively. Since he lengh of he paper is limied, we do no give hese resuls here. TABLE II SIMULATION PARAMETERS. Parameers Values Carrier frequency, f c 60GHz Bandwidh, B.5GHz Maximum ransmi power of MBS, P max 0dBm Maximum power of ransmi beams, 3dBm Maximum number of ransmi beams, b MBS max 0 Maximum number of receive beams, b MUE max 3 Aenuaion value, A A LOS = 3.5; A NLOS = 45.5 Pah loss exponen, n n LOS =.0; n NLOS =.4 Transmission disance, R R LOS = 7m; R NLOS = 0m Noise figure, NF 6dB Algorihm b u ( u Q) Opimizaion for APA Inpu: he se of simulaneous MUEs Q; he operaing T-R beam pair ses N u for u Q; : P = P max b u ; : if P > hen 3: Le P = ; 4: end if 5: SNR u,i = P π π ξ,min ξ r,min L(R i u) P N for u Q, i N u ; 6: if min SNR,i N u u,i < η hen 7: Remove link j from N s (s Q), he link saisfies SNR s,j = min,i N u SNR u,i; 8: b s = b s ; 9: if b s = 0 hen 0: Remove MUE s from Q; : end if : Go o sep ; 3: else 4: Q = Q; 5: (N u ) = N u and b u = b u for u Q ; 6: end if Oupu: b u ( u Q ) V. PERFORMANCE EVALUATION This secion presens some numerical resuls on he performance of beamspace MU-MIMO. The objecive of his work is wo-fold: (i) o verify he effeciveness of he proposed muliuser BF raining mechanism; (ii) o compare and analyze he performance of APA and PPA. To simplify simulaions, we assume ha ξ u,i = ξ, ξr u,i = ξ r, and b u max = b MUE max, for i N u, u Q. Moreover, we consider a shor-range indoor mmwave nework wih Ri u = R LOS for LOS links and Ri u = R NLOS for NLOS links. Table II summarizes he deailed simulaion parameers. In addiion, a a sandard emperaure of 7 C, we le P N [db] = 74 [dbm/hz] + 0 log 0 (B) + NF, where NF is noise figure in db. Fig. 3 shows ha he proposed muli-beam ransmi raining can effecively improve he efficiency of beam selecion. For example, when ξ = 0, we have S MBS = 36 and 0 which can be known from Eq. (). Hence, if = 5, o obain he bes ransmi beam ses (i.e., N u TX, S u Q), he MBS only needs o scan MBS = 8 imes by adoping he proposed soluion. However, using he radiional ransmi raining operaing wih single beam, he number of scans required is S MBS = 36. Similarly, we can verify he effeciveness of he proposed muli-beam receive raining for selecing he bes receive beam ses (i.e., N u RX, u Q). Furhermore, he larger he values of and, he more superior he muli-user BF raining. In Fig. 4, we invesigae he rae performance of beamspace MU-MIMO wih APA and wih PPA, respecively. Here we consider he nework is wih hree MUEs, i.e., U = 3 and,

6 Scan Times for Transmi Training Muli beam: ξ =5 Single beam: ξ =5 Muli beam: ξ =0 Single beam: ξ =0 Muli beam: ξ =5 Single beam: ξ =5 Achievable Rae (Gbps) MU-SISO MU-MIMO wih APA MU-MIMO wih PPA Achievable Rae (Gbps) MU-SISO MU-MIMO wih APA MU-MIMO wih PPA Number of simulaneous ransmi beams, SINR Threshold, η (db) (a) SINR Threshold, η (db) (b) Fig. 3. Performance comparison beween he proposed muli-beam ransmi raining and he radiional soluion. Fig. 4. Achievable rae performance versus SINR hreshold η for beamspace MU-SISO and MU-MIMO wih PPA and wih APA, respecively, given ha ξ = 0, ξ r = 5, and (a) z = 0.0, (b) z = 0.. meanwhile, each of hem is operaing wih a LOS link and wo NLOS links, i.e., b = b u = 9. Moreover, we assume ha he qualiy of each LOS link is beer han ha of NLOS links. In his conex, he rae performance of beamspace MU-MIMO wih PPA is he same regardless of wheher he fairness of power allocaion among simulaneous MUEs is aken ino accoun. Clearly, he performance of PPA is generally beer han ha of APA for beamspace MU-MIMO. Furher, he resuls indicae ha beamspace MU-MIMO compared wih beamspace MU-SISO can largely improve he rae performance of mmwave neworks. Noe ha U > and b u = ( u Q) in beamspace MU-SISO sysems. For example, when η = 0dB shown in Fig. 4(a), we have Rae APA MU MIMO = 0Gbps and Rae PPA MU MIMO = 0Gbps while Rae MU SISO = 49Gbps. To make he resuls more general, he iner-beam inerference caused by side lobes is no ignored in our simulaions, i.e., z 0. By comparing Fig. 4(a) wih Fig. 4(b), we can see ha he greaer he value of z, he greaer he inerference, and he more obvious he impac on he sysem performance. VI. CONCLUSIONS In his sudy, in order o furher enhance he performance of mmwave neworks wih muliple reflecions, we exended our previous work o muli-user scenario, namely beamspace MU- MIMO, and invesigaed is challenges and poenial soluions for downlink ransmission. Firs, we improved he efficiency of muli-beam selecion for beamspace MU-MIMO by uilizing he capabiliy of supporing muliple beams boh a he MBS and MUEs. Second, o avoid beam conflics, we grouped simulaneous served MUEs. Third, we analyzed wo low complexiy muli-user muli-beam power allocaion soluions, i.e., APA and PPA. The numerical resuls demonsraed ha hey are very effecive o improve he achievable rae of beamspace MU-MIMO. Furhermore, he corresponding sraegies for uplink beamspace MU-MIMO will be also our fuure work. REFERENCES [] Cisco, Cisco visual neworking index: Global mobile daa raffic forecas updae, 06-0, Whie Paper, Feb. 07. [] A. M. Sayeed, Deconsrucing mulianenna fading channels, IEEE Trans. Signal Process., vol. 50, no. 0, pp , Oc. 00. [3] J. Brady, N. Behdad, and A. M. Sayeed, Beamspace MIMO for millimeer-wave communicaions: Sysem archiecure, modeling, analysis, and measuremens, IEEE Trans. Anennas Propag., vol. 6, no. 7, pp , Jul. 03. [4] A. Sayeed and J. 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