Massive MIMO_PPT

1、Note 11. Special Topics: Massive MIMO Sooyong Choi School of Electrical and Electronic Engineering Yonsei University csyongyonsei.ac.kr Contents Introduction to Massive MIMO Fundamental overview: Massive MIMO Single-cell Massive MIMO Massive MIMO DL Linear precoding schemes (ZF-BF/MRT) Perfect CSIT

2、/ imperfect CSIT Massive MIMO UL Linear receiver techniques (ZF-R/MRC/MMSE) Perfect CSIR / imperfect CSIR Multi-cell Massive MIMO Inter-cell interference problem Pilot contamination problem VIII-2 Introduction to Massive MIMO VIII-3 Introduction to Massive MIMO : Beyond 4G Network Future mobile data

3、 traffic Global exponential mobile data traffic increase By a factor of 20 from 2011 until 2016, and more expected in 2020. More devices, higher bit rates, always active Larger variety of traffic types e.g. Video, MTC VIII-4 20 20 Further capacity enhancement is needed MTC : Machine Type Communicati

4、ons VoIP : Voice over Internet Protocol M2M : Machine-to-machine Introduction to Massive MIMO : Candidate of Beyond 4G Network Using hundreds of antennas at BS Support the dozens of UEs (Multi-user MIMO) 1 RWS-120002, “Technologies for Rel-12 and Onwards,” Samsung, 3GPP RAN WS on Rel-12 and onwards,

5、 Ljubljana, Slovenia, June 1112, 2012. 2 T. L. Marzetta et, “Beyond LTE: Hundreds of Base Station Antennas! “, 201 0 IEEE Communication Theory Workshop Solution for Capacity Demand1,2 Massive MIMO Benefit of Massive Antenna Capacity enhancement1 Mathematically Exact2 Required Tx energy/bit is arbitr

6、a rily small Eliminate the effects of uncorrel ated noise & fast fading Compensate the poor-quality C SI VIII-5 CSI : Channel State Information Introduction to Massive MIMO : Standardization for Massive MIMO 3GPP3 TSG RAN Workshop on Rel-12 and Onwards (2012.6) 42 company including Samsung, LG, SK,

7、Nokia, etc. Goals Identify common requirements fo r future 3GPP radio access tech. Investigate the potential tech tow ards Release 12 and onwards Massive MIMO Key technology for B4G (Rel. 12 and Onwards) Various title Massive MIMO Full Dimension MIMO Large Scale MIMO 3 RWS papers, 3GPP RAN WS on Rel

8、-12 and onwards, Ljubljana, Slovenia, June 1112, 2012. 4 “2010-2011 Annual Report”, Greentouch, 2011 Greentouch Consortium4 Goals Increasing network energy efficie ncy by a factor of 1,000 by 2015 Launching the LSAS project (201 0) Alcatel-Lucent Bell Labs, Huawei , IMEC, etc. Project tasks for LSAS

9、 Architecture and Deployment Algorithms and Simulation Energy Modeling and Control. VIII-6 3GPP : 3rd Generation Partnership Project LSAS : Large-Scale Antenna System Motivation of Massive MIMO5 Consider a MIMO MAC ( M : # of BSs antennas, K : # of user) If the BS process its receive signal by match

10、ed filtering, By the strong law of large numbers, With an unlimited number of antennas Uncorrelated interference and noise vanish The matched filter is optimal The transmit power can be made arbitrarily small MK yHxn ,H n: i.i.d. with zero mean and unit variance 111 HHH MMM yH yH HxH n . . ,=const.

11、1 a sH MK M H yx 5 T. L. Marzetta, “Noncooperative cellular wireless with unlimited numbers of base station antennas,” IEEE Trans. Wireless Commun., vol. 9, no. 11, pp. 35903600, Nov. 2010. Introduction to Massive MIMO MAC : Multiple Access Channel 1M MK 1K 1M 2 1 121 2 2 212 2 12 1 HH K HH K H HH K

12、 KK MMM MMM M MMM hh hh h hh hh h H H hh hh h as M . . 0 a s M . . 1 a s M By strong law of large numbers VIII-7 Introduction to Massive MIMO Simulation result M = 1 500, hi = M X 1 Real Gaussian Vector VIII-8 050100150200250300350400450500 -0.5 0 0.5 1 1.5 2 M 2 i M h H ij M h h Converges to 1 as M

13、 increases Converges to 0 as M increases On channel estimation and pilot contamination5 The receiver estimates the channels based on pilot sequences. The # of orthogonal sequences is limited by the coherence time Thus, the pilot sequences must be reused Assume that transmitter m & j use the same pil

14、ot sequence Thus, the BS process its receive signal by matched filtering With an unlimited number of antennas Uncorrelated interference, noise and estimation errors vanish The matched filter is optimal The transmit power can be made arbitrarily small6 The performance is limited by pilot contaminatio

15、n m HHHn mmj pilot contaminationestimation noise . . ,=const. 1 H a s MK M H yxx mmj 1/M Introduction to Massive MIMO 6 H. Q. Ngo, E. G. Larsson and T. L. Marzetta, “Uplink power effi ciency of multiuser MIMO with very large antenna arr ays,” in Proc. of Allerton Conference on Communication, Control

16、, and Computing, Sept. 2011. By strong law of large numbers VIII-9 yH xH xn mmjj pilot contamination Analysis of Massive MIMO with sufficient large # of BS antennas Single-cell massive MIMO scenario Massive MIMO Downlink scenario Analysis the performance of various linear precoding/beamforming tech

17、nique for Massive MIMO based on channel information Perfect CSIT/ imperfect CSIT cases Massive MIMO Uplink scenario Linear receiver technique for Massive MIMO Uplink Perfect CSIR/ imperfect CSIR cases Multi-cell massive MIMO scenario Inter-cell interference problem Pilot contamination problem VIII-1

18、0 Introduction to Massive MIMO CSIT : Channel State Information at the Transmitter CSIR : Channel State Information at the Receiver Fundamental Overview: Massive MIMO Fundamental Overview: Massive MIMO : Point-to-Point MIMO (1/4) Channel Model # of BS antennas M, # of UE antennas N IID complex-Gauss

19、ian channel H, x, n with zero mean and variance 1 is downlink transmission power Receiver has perfect knowledge of H Received SNR/ Capacity at Receiver VIII-12 11 1 d N MMN N p yHxn 2 log det() H d NMN p C M IHH 2 2 0 SNR d d p p N H H d p 2 log det() H d MMN p C M IH H MN MN) For large M with IID c

20、omplex-Gaussian channel H, 2 log det() H d N p C M IHH 2 1121 21 212 1 2 12 | | 111 | | HH N H HHH N N HH NNN MMM hh hh h h h hh HHhh h h hh hh 12 1 where iii iM M hhh h 22 2 2 1 1 0 Var1 ii M i hh hE h MM h 1 H N M HHI * 12 1 122 GaussianGaussian Gaussian 1 0 H ijijijij M MM ij ggg h hh hh hE gE h

21、MMM h h Conclusio n VIII-13 Fundamental Overview: Massive MIMO : Point-to-Point MIMO (3/4) Capacity at Receiver (NM) For large N with IID complex-Gaussian channel H, 2 log det() H d M p C M IH H 2 1121 21 212 1 2 12 | | 111 | | HH M H H H M H M HH MMM NN MM NM N hh hh h h h hh H Hhh h h hh hh 12 1 w

22、here T iii iN N hhh h 22 2 2 1 1 0 Var1 ii N i hh hE h NN h 1 H M NN M NM H HI * 12 1122 GaussianGaussianGaussian 1 0 H ijijijij N NN ij ggg h hh hh hE gE h NNN h h Conclusio n VIII-14 Fundamental Overview: Massive MIMO : Point-to-Point MIMO (4/4) Point-to-point MIMO Large number of transmit antenna

23、s Large number of receive antennas 22 22 log det()log det() 100 log det00log (1) 001 H d MNNNdN d d d N N p Cp M p Np p IHHII 22 22 log detlog det() 100 log det00log (1) 001 H dd NMMMM d d d M M pNp C MM Np M Np M M Np M IH HII 1 H N M HHI 1 H M NN M NM H HI Independent with M Linearly increase as N

24、 Increase as N with log shape VIII-15 Fundamental Overview: Massive MIMO : Multi-User MIMO (1/4) Multi-user MIMO Uplink M antennas simultaneously serves K users Each user has single antenna, N = 1 Channel modeling (large scale + small scale) Propagation matrix G Massive MU-MIMO Uplink Only large sca

25、le fading coefficients remain 1/2 UL M KK K M K GH D H: small scale fading D: large scale fading (path loss, shadow fading) 1/21/2 H H K MM K MK MM HH G G DDD 1 H K K MM K M H HI VIII-16 Fundamental Overview: Massive MIMO : Multi-User MIMO (2/4) Massive MU-MIMO Uplink UL Received vector for K users

26、Total capacity of UL MU-MIMO Detection using MRC SNR vector for K users 11 u KM KK p yGxn Assume Perfect CSIT Symbol power: normalized to 1 sum_UL2 log det() H Ku CpIG G sum_UL 2 log det() MKKu CMpID HHHH utu pMpG yG GxG nDxG n 2222 uu u H M pM p Mp M DD D G GD Achievable by detection using MRC 1/21

27、/2 HH MK MM G GH H DDD VIII-17 MRC: Maximal Ratio Combining Fundamental Overview: Massive MIMO : Multi-User MIMO (3/4) Multi-user MIMO Downlink M antennas simultaneously serves K users Each user has single antenna, N = 1 Channel modeling (large scale + small scale) Propagation matrix G Massive MU-MI

28、MO Downlink Only large scale fading coefficients remain H: small scale fading D: large scale fading (path loss, shadow fading) 1/21/2 H H K MM K MK MM H H GG DDD 1 H N K MM K M H HI 1/2 DL K KK M K M GDH VIII-18 Fundamental Overview: Massive MIMO : Multi-User MIMO (4/4) Massive MU-MIMO Downlink DL R

29、eceived vector for BS (equal power allocation assumption) Total capacity of DL MU-MIMO Maximal Ratio Transmission (MRT) precoding based received signal SNR vector for K users: d 11KK MM p yGxn sum_DL2d2d 2d2d log det()log det() log det()log det() HH MM H KK Cpp pMp IG GIH DH IDHHID 1/21/21/2 11 HH H

30、 HH dd dd M pp MpMp MMM xH xH x HH yGH xnD HH xnDxnD xn td M pD Achievable by M RT 1/21/2 HH MK MM GGHH DDD IK VIII-19 Effect of MRT for Massive MIMO Fundamental Overview: Massive MIMO : Simulation of MRT based Massive MIMO 7 F. Rusek et al., “Scailing up MIMO: Opportunities and challenges with very

31、 large arrays,” Normalized field strength in a 10 x10 area centered around the receiver Simulation environment Simulation Parameters 400 uniformly distributed scatters : signal wavelength MRT precoder is used Multipath component Large-scale + small-scale considered Path-loss + Rayleigh fading Conclu

32、sion from simulation results Field strength can be focused to a point More antennas improve the ability to fo cus energy to a certain point MRT can eliminate interference M=10 100, Improved ability to focus energy to a certain point VIII-20 Massive MIMO Downlink Channel Deterministic Equivalent for

33、the Achievable Sum Rate Massive MIMO Downlink Channel : System Model Parameters : small scale fading : beamforming vector M : # of BS antenna K: # of users Single antenna at user Received vector k w k h 111 1 dd K MMKM KK K pp yHxnH Wsn 11 ,., ,., KK HhhWww 2 tr, 0,1 H i EP n xW WCN VIII-22 Massive

34、MIMO Downlink Channel : Linear Precoding Conventional linear precoding Received signal after using linear precoding SINR of the kth user MRTZFBF H WH 1 HH WHHH noise1, desired signal interference K kdkkkdki i ii k ypsps h wh wn 2 2 1, SINR 1 dkk kK dki ii k p p h w h w VIII-23 2 log1 SINR kk R sum 1

35、 K k k RE R Rate of user k Ergodic sum rate MRT: Maximal Ratio Transmission ZFBF: Zero-Forcing Beamforming Massive MIMO Downlink Channel : Linear Precoding Perfect CSI Deterministic form of the SINRk/Rsum as M, K , M/K= MRT ZFBF 2 . . 2 1, SINR as , 1 1 H d kk a s mrt d kK H d d ki ii k p p M K pp h

36、 h h h where tr/: normalization factor H KW W . . 1 SINR 1 as , tr a s zf d kd H p pM K H H VIII-24 sum2 log1 1 mrt d d p RK p sum2 log11 zf d RKp SINR: Signal-to-Interference-plus-Noise Ratio CSI: Channel State Infromation 2222 2 1, 1 , K HHHH kikikiM F ii k EMKM K h hh hh hH 1 1/trDiversity order

37、of ZF-BF H MK K H H Massive MIMO Downlink Channel : Linear Precoding Imperfect CSI Estimated CSI ( ) using MMSE channel estimation Deterministic form of Rsum with imperfect CSI 2 1HHE H : Error matrix where 0,1 i EeCN : Reliability of the estimation 2 sum2 2 1 log1 11 dzf d p RK p 2 sum2 log1 1 mf d

38、 d p RK p MRTZFBF VIII-25 Massive MIMO Downlink Channel : Linear Precoding Simulation Results (2/2) Ergodic sum-rate vs. M Simulation parameters n n n n Deterministic form of Rsum nPerfect CSI, Imperfect CSI nThe approximations is very cl ose to the numerical result nIt is also accurate even for s m

39、all M, K. Performance comparison nAs 1, ZFBF MRT nAs =1, MRT ZFBF 0dB d p 10K VIII-26 050100150200250300 0 5 10 15 20 25 30 35 40 45 50 M Ergodic sum-rate ZFBF(P-App.) ZFBF(P-Num.) MRT(P-App) MRT(P-Num.) ZFBF(IP-App.) ZFBF(IP-Num.) MRT(IP-App) MRT(IP-Num.) 45678 2 , 2 , 2 , 2 , 2 M 2 0.5 M Rsum Cros

40、s point Channel Imperfectness Massive MIMO Downlink Channel : Linear Precoding Simulation Results (2/2) Ergodic sum-rate vs. K Simulation parameters n n n n Performance comparison nAs 1, ZFBF MRT nAs =1, MRT ZFBF Optimal K* for ZFBF n nex) 0dB d p 10, 20, ., 100K VIII-27 102030405060708090100 25 30

41、35 40 45 50 55 60 65 70 75 M Ergodic sum-rate ZFBF(P-App.) ZFBF(P-Num.) MRT(P-App.) MRT(P-Num.) 128M 2 0.5 MRT: K Rsum ZFBF: Concave function of K Cross point Optimal K* * sum 0 zf R KK K * 1 where 0dB d M Kp e Massive MIMO Uplink Channel Energy and Spectral Efficiency with Linear Receivers Massive

42、MIMO Uplink Channel : Contents Massive MIMO Uplink Channel System model Uplink power efficiency Perfect CSI case Uplink power efficiency Imperfect CSI case Energy efficiency and spectral efficiency tradeoff VIII-29 Massive MIMO Uplink Channel : System Model Parameters : small scale fading : path los

43、s + shadowing SNR for the kth UE: Received signal kkk gh k h k uk p 11 1 u KMM K M p yGxn 1/2 11 , ,., diag,., KK K K GH DHhhD 2 1, 0,1 ki Exn CN VIII-30 Massive MIMO Uplink Channel : Linear Detector Conventional linear detector Received signal after using the linear detector SINR of the kth user 1,

44、 noise desired signal interference K HHHHHHH ukukkukkkukiik ii k prppxpx rA GxA na Gxa na ga ga n 2 k 2 2 1, SINR H ukk K H ukik ii k p p a g a ga VIII-31 MRCZFMMSE AG 1 H AG G G 1 1 H K u p AG G GI MRC: Maximal Ratio Combining ZF: Zero-Forcing MMSE: Minimum Mean Square Error Massive MIMO Uplink Cha

45、nnel : Uplink Power Efficiency Perfect CSI (1/2) Ergodic achievable uplink rate of the kth user Proposition 1: Assume that the BS has perfect CSI and the transmit power of each user is scaled with Mt according to , where Eu is fixed. The n, Massive MIMO effect Small-scale fading/ Inter-user interfer

46、ence goes away in the limit u E uM p ,2 log1, P kku REM 2 ,22 2 2 1, logSINRlog1 H ukk P kkK H ukik ii k p REE p a g a ga VIII-32 Massive MIMO Uplink Channel : Uplink Power Efficiency Perfect CSI (2/2) Uplink performance with MRC Perfect CSI 4 mrc ,22 2 1, 1 2 2 1, 24 mrc 2, 1, log1 log1 1 log1 1 uk

47、 P k K H ukik ii k K H ukik ii k uk utk P kK ui ii k pg RE pg gg pg gg E pg pM R p Capacity lower boundLimit case mrc ,2 1, 2 1 log1 1 log1 as u u E kM P kK E iM ii k ku M R EM Small-scale fading/ Inter-user i nterference goes away in the li mit ! Tx power can be scaled as 1/ !M VIII-33 pu=Eu/M Mass

48、ive MIMO Uplink Channel : Uplink Power Efficiency Imperfect CSI (1/3) Estimated CSI ( ) using MMSE channel estimation Received signal vector after using the linear detector GGE G 1 : Error matrix where 0, i pi iMp EeICN : Uplink pilot power pu pp : # of pilots 1,1 no desired signal interference from

49、 inter-user interference channel estimation error H uu HHH kukukk KK HHHH ukkkukiiukiik ii ki pp rpp pxpxpx rAGxExn a Gxa Exa n a ga ga ea n ise VIII-34 Massive MIMO Uplink Channel : Uplink Power Efficiency Imperfect CSI (2/3) Ergodic achievable uplink rate of the kth user If we cut the Tx power Bot

50、h data and pilot signal suffer from the reduction in power. We cannot reduce power proportionally to 1/M. Proposition 2: Assume that the BS has imperfect CSI, obtained by MMSE estimation from uplink pilots, and that the transmit power of each user is , where Eu is fixed. Then, 2 ,2 2 22 1,1 log1 1 H

51、 ukk IP kKK H i ukiukk ii ki ui p RE pp p a g a gaa u E u M p 22 ,2 log1, as IP kku REM VIII-35 Pilot power (pp) Massive MIMO Uplink Channel : Uplink Power Efficiency Imperfect CSI (3/3) Uplink performance with MRC Imperfect CSI Capacity lower bound 22 mrc ,2 1, 1 log1 111 uk IP kK uukiuk ii k pM R

52、ppp Limit case ( ) mrc , 22 2 0/ log1/ uu IP kuu kuuu pE RpEM EpEM Tx power can be scaled as M 1/!M Squaring effect Massive MIMO Uplink Channel : Uplink Power Efficiency Simulation Results Required Power vs. M Simulation parameters nK=10 nTarget rate: 1bit/s/Hz Power scaling low nPerfect CSI nImperf

53、ect CSI As M increases, the differenc e in performance between M RC and ZF (or MMSE) decrea ses. nPerfect CSI: less than 1dB nImperfect CSI: less than 3dB 1/ M 1/M VIII-37 M pu as 1/M Performance gap between MRC and ZF (or MMSE) Multi-Cell Massive MIMO Pilot Contamination & Inter-Cell Interference P

54、roblem Non-cooperative multi-cell environment Assumption: MRT precoder / 2 cell assumption MRT based transmit signal Transmit signal at BS 1: Transmit signal at BS 2: Received signal for R1 Multi-Cell Massive MIMO : Inter-Cell Interference Problem (1/3) 11111 1 22222 2 11 11 HH HH xxx M xxx M hh hh

55、For large 1 H M xx M h 1/21/2 1111122 HH dd II pp ydxdx MM h hh hn VIII-39 Multi-Cell Massive MIMO : Inter-Cell Interference Problem (2/3) 1/21/2 1111122 HH dd II pp ydxdx MM h hh hn 1/21/2 112 1112 11 HH I ddI yp dxp dx MMMM h hh h n 22 2 2 1 1 0 Var1 ii M i hh hE h MM h * 12 1 122 GaussianGaussian

56、 Gaussian 1 0 H ijijijij M MM ij ggg h hh hh hE gE h MMM h h 0 VIII-40 Multi-Cell Massive MIMO : Inter-Cell Interference Problem (3/3) 1/21/2 112 1112 1/2 11 11 HH I ddI d yp dxp dx MMMM p dx h hh h n 0 0 1 1/2 111d yp Mdx VIII-41 Multi-Cell Massive MIMO : Pilot Contamination Problem (1/5) Practical

57、 problems for non-cooperative multi-cell Assumption 7 Non-cooperative multi-cell with TDD mode MIMO-OFDM system with MU-MIMO To perfectly mitigate interference at large M, exact MRT scheme is needed Perfect CSIT is necessary to design exact MRT precoder UL pilots are allocated in same time-frequency

58、 elements to obtain perfect CSIT UL pilots can be separated by orthogonal sequences Can obtain perfect CSIT Problem: Exact same time-frequency elements with same pilot sequence Perfect CSIT is impossible pilot contamination problem 7 F. Rusek et al., “Scailing up MIMO: Opportunities and challenges with very large arrays,” VIII-42 Multi-Cell Massive MIMO : Pilot Contamination Problem (2/5) 11112222 estimation noiseestimation noise , ddIddI gggngggn 111 1222 1111122222 HH dd ddId HHHHHH dd ddIIdI pp yxx MM pp xx MM g gg g