MassiveMIMO_PPT

Note 11. Special Topics:
Massive MIMOSooyong Choi
School of Electrical and Electronic Engineering
Yonsei Universitycsyong@yonsei.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 / 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 problemVIII-2Introduction to Massive MIMOVIII-3???Introduction to Massive MIMO: Beyond 4G NetworkFuture mobile data 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, MTCVIII-4×20Further
capacity
enhancement
is neededMTC : Machine Type Communications
VoIP : Voice over Internet Protocol
M2M : Machine-to-machine???Introduction to Massive MIMO: Candidate of Beyond 4G NetworkUsing hundreds of antennas at BSSupport 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, Ljubljana, Slovenia, June 11–12, 2012.
[2] T. L. Marzettaet, “Beyond LTE: Hundreds of Base Station Antennas! “,
2010 IEEE Communication Theory WorkshopSolution for Capacity Demand[1],[2]Massive MIMOBenefit of Massive Antenna
?Capacity enhancement[1]?Mathematically Exact[2]?Required Tx energy/bitis arbitrarily small?Eliminatethe effects of
uncorrelated noise & fast fading
?Compensatethe poor-quality
CSIVIII-5CSI : Channel State Information???Introduction to Massive MIMO: Standardization for Massive MIMO3GPP[3]?TSG RAN Workshop
on Rel-12 and Onwards (2012.6)?42 company including
Samsung, LG, SK, Nokia, etc.
?Goals–Identify common requirements
for future 3GPP radio access tech.
–Investigate the potential tech
towards 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-12 and onwards, Ljubljana, Slovenia, June 11–12, 2012.
[4] “2010-2011 Annual Report”, Greentouch, 2011Greentouch Consortium[4]?Goals?Increasing network energy
efficiency by a factor of 1,000
by 2015?Launching the LSAS project
(2010)?Alcatel-Lucent Bell Labs,
Huawei, IMEC, etc.
?Project tasks for LSAS–Architecture and Deployment–Algorithms and Simulation
–Energy Modeling and Control.VIII-63GPP : 3rd Generation Partnership Project
LSAS : Large-Scale Antenna System???Motivation of Massive MIMO[5]?Consider a MIMO MAC ( M : # of BSs antennas, K: # of user)
?If the BS process its receive signal by matched filtering,
?By the strong law of large numbers,
?With an unlimited number of antennas?Uncorrelated inte

rference and noise vanish
?The matched filter is optimal
?The transmit power can be made arbitrarily smallM K
 y Hx n,H n: i.i.d. with zero mean
and unit variance1 1 1
H H HM M M
  y H y H Hx H n. .
, =const.1a s
H
M KM
H y x[5] T. L. Marzetta, “Noncooperativecellular wireless with unlimited numbers of base station antennas,” IEEE Trans. Wireless Commun., vol. 9, no. 11, pp. 3590–3600, Nov. 2010.Introduction to Massive MIMOMAC : Multiple Access Channel 1M M K 1K 1M2
1
1 2 1
2
2
2 1 2
2
1 21H H
K
H H
K
H
H H
K
K KM M M
M M M
M
M M M
 
 
 
 
 

 
 
 
 
 
 
h
h h h h
h
h h h h
H H
h
h h h h

  
as M . .0a s
M. .1a s
MBy strong law of large numbersVIII-7???Introduction to Massive MIMOSimulation result
?M= 1 ~ 500, hi= M X 1 Real Gaussian VectorVIII-80
50 100 150 200 250 300 350 400 450 500
-0.5
0
0.5
1
1.5
2
M2
iM
hH
i jM
h hConverges to 1 as M increases
Converges to 0 as M increases???On channel estimation and pilot contamination[5]?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& jusethe same pilot 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 small[6]?The performance is limited by pilot contamination
m  
H H H nm m
jpilot contamination
estimation noise. .
, =const.1H
a s
M KM 
H y x xm
m
j ~1/MIntroduction to Massive MIMO[6] H. Q. Ngo, E. G. Larsson and T. L. Marzetta, “Uplink power efciency of multiuser MIMO with very large antenna arrays,” in Proc. of Allerton Conference on Communication, Control, and Computing, Sept. 2011.By strong law of large numbersVIII-9  
y H x H x nm m
j jpilot 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
technique 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 problemVIII-10Introduction to Massive MIMOCSIT : Channel State Information at the Transmitter
CSIR : Channel State Information at the ReceiverFundamental O

verview: Massive MIMO???Fundamental Overview: Massive MIMO: Point-to-Point MIMO (1/4)Channel Model
?# of BS antennas M, # of UE antennas N
?IID complex-Gaussian channel H, x,n with zero mean and variance 1
?is downlink transmission power
?Receiver has perfect knowledge of H
Received SNR/ Capacity at ReceiverVIII-12
 
    
1 1
1
d
N M M N
Np
  
 
y H x n2log det( )H
d
N M Np
C
M 
I HH2
2
0SNRd
dpp
N
 
H
Hdp2log det( )H
d
M M Np
C
M 
I H HM>N
MN)
For large Mwith IID complex-Gaussian channel H,2log det( )H
d
Np
C
M
 I HH2
1 1 2 1
2
1
2 1 2
1
2
1 2 | |
1 1 1
|
|H H
N
H
H H H
N
N
H H
N N NM M M
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
h h h h h
h
h h h
HH h h
h
h h h h h

 
 
 1 2
1where i i i
i M
Mh h h 

 
h   
 2 2
2
2
1
1
0Var 1i i
M
ih h
h E h
M M
 
   
h


1H
NM
HH I
    * * *
1 2
1 1 2 2
Gaussian Gaussian
Gaussian1
0H
i j
i j i j i j
M
M M
i jg g g
h h h h h h E g E h
M M M 
  
 
       
 
 
hh


Conclusion
VIII-13???Fundamental Overview: Massive MIMO: Point-to-Point MIMO (3/4)Capacity at Receiver (N>M)
For large Nwith IID complex-Gaussian channel H,2log det( )H
d
Mp
C
M
 I H H2
1 1 2 1
2
1
2 1 2
1
2
1 2 | |
1 1 1
| |H H
M
H
H
H
M
H
M
H H
M M MN N
M M N M N
 
 
   
 
 
   
 
 
   
 
   
 
   
 
 
h h h h h
h
h h h
H H h h
h
h h h h h

 
 
 1 2
1where
T
i i i
i N
Nh h h 

 
h    2 2
2
2
1
1
0Var 1i i
N
ih h
h E h
N N
 
   
h


1H
MN N
M N M
H H I 


   * * *
1 2
1 1 2 2
Gaussian Gaussian
Gaussian1
0H
i j
i j i j i j
N
N N
i jg g g
h h h h h h E g E h
N N N 
  
       
 
 
 
hh

Conclusion
VIII-14???Fundamental Overview: Massive MIMO: Point-to-Point MIMO (4/4)Point-to-point MIMO?Large number of transmit antennas
?Large number of

receive antennas2 2
2 2log det( ) log det( )
1 0 0
log det 0 0 log (1 )
0 0 1H
d
M N N N d N
d
d
d
N Np
C p
M
p
N p
p
   
 

 
 
 
  
 
 
 
 

 
 
I HH I I
2 2
2 2log det log det( )
1 0 0
log det 0 0 log (1 )
0 0 1H
d d
N M M M M
d
d
d
M Mp Np
C
M M
Np
M
Np
M
M
Np
M
 
   
 
 
 
 

 
 
 
 
  
 
 
 
 
 

 
 
 
 
I H H I I
1H
NM
HH I1H
MN N
M N M
H H IIndependent with M
Linearly increase as N
Increase as N with log shape
VIII-15???Fundamental Overview: Massive MIMO: Multi-User MIMO (1/4)Multi-user MIMO Uplink
?Mantennas simultaneously serves Kusers
?Each user has single antenna, N= 1
?Channel modeling (large scale + small scale)?Propagation matrix GMassive MU-MIMO Uplink
?Only large scale fading coefficients remain 
  1/2
UL
M K K K
M K
 

G H DH: small scale fading
D: large scale fading (path loss, shadow fading)   1/2 1/2
H
H
K M M K
M KM M 
 
 
 
 
 
 
 
 
H H
G G
D D D
   1H
K
K M M KM 
H H IVIII-16???Fundamental Overview: Massive MIMO: Multi-User MIMO (2/4)Massive MU-MIMO Uplink
?UL Received vector for Kusers
?Total capacity of UL MU-MIMO
?Detection using MRC?SNR vector for Kusers[ 1]
[ ][ 1]
u
K
M K Kp  
y Gx n?Assume Perfect CSIT
?Symbol power: normalized to 1sum_UL 2log det( )
H
K uC p
 I G Gsum_UL >> 2log det( )M K K uC Mp I DH H H H
u t up M p
   G y G Gx G n Dx G n2 2 2 2
u u
u
HM p M p
Mp
M
  
D D
ρD
G G DAchievable by detection using MRC1/2 1/2
H H
M KM M   
 
   
   
G G H H
D D DVIII-17MRC: Maximal Ratio Combining???Fundamental Overview: Massive MIMO: Multi-User MIMO (3/4)Multi-user MIMO Downlink
?Mantennas simultaneously serves Kusers
?Each user has single antenna, N= 1
?Channel modeling (large scale + small scale)?Propagation matrix GMassive MU-MIMO Downlink
?Only large scale fading coefficients remainH: small scale fading
D: large scale fading (path loss, shadow fading)   1/2 1/2
H
H
K M M K
M KM M 
 
 
 
 
 
 
 
 
H H
GG
D D D
   1H
N
K M M KM 
H H I 
  1/2
DL
K K K M
K M
 

G D HVIII-18???Fundamental Overview: Massive MIMO: Multi-User MIMO (4/4)Massive MU-MIMO Downlink
?DL Received

vector for BS (equal power allocation assumption)
?Total capacity of DL MU-MIMO
?Maximal Ratio Transmission (MRT) precoding based received signal?SNR vector for Kusers:d
[ 1]
[ ][ 1]
K
K M Mp
  
y Gx nsum_DL 2 d 2 d
2 d 2 dlog det( ) log det( )
log det( ) log det( )H H
M M
H
K KC p p
p Mp
   
   
I G G I H DH
I DHH I D1/2 1/2 1/21 1H H
H
H H
d d
d dM
p p
Mp Mp
M M M 
        
x H x H x
HH
y GH x n D HH x n D x n D x n
 
   t dM p
ρDAchievable by
MRT1/2 1/2
H H
M KM M   
 
   
   
GG HH
D D DIKVIII-19???Effect of MRT for Massive MIMOFundamental Overview: Massive MIMO: Simulation of MRT based Massive MIMO[7] F. Rusek et al., “Scailing up MIMO: Opportunities and challenges with very large arrays,”Normalized field strength in a 10λx10λ area centered around the receiver
Simulation environmentSimulation Parameters?400 uniformly distributed scatters
? λ: signal wavelength?MRT precoder is used?Multipath component?Large-scale + small-scale considered
?Path-loss + Rayleigh fadingConclusion from simulation results?Field strength can be focused to a point
?More antennas improve the ability to focus energy to a certain point?MRT can eliminate interferenceM=10100, Improved ability to focus energy to a certain pointVIII-20Massive MIMO Downlink ChannelDeterministic Equivalent for 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 vectorkwkh[ ][ 1] [ 1]
[ ][ 1]
[ 1]
d d
K M M K
M K K
Kp p  
 
   
y H x n H W s n   1 1,..., , ,...,K KH h h W w w   2tr , ~ 0,1H
iE P n
 
 
 
x W WCNVIII-22???Massive MIMO Downlink Channel: Linear PrecodingConventional linear precoding
Received signal after using linear precoding
SINR of the kth user
MRT ZFBFH
W H 1
H H
W H HHnoise
1,
desired signal
interference
K
k d k k k d k i i
i i ky p s p s   h w h w n

2
2
1,SINR
1d k k
k
K
d k i
i i kp
p 
h w
h wVIII-23 2log 1 SINRk kR  sum
1
K
k
kR E RRate of user kErgodic sum rateMRT: Maximal Ratio Transmission
ZFBF: Zero-Forcing Beamforming???Massive MIMO Downlink Channel: Linear Precoding –Perfect CSIDeterministic form of the SINRk/Rsumas M, K→∞, M/K=α
?MRT
?ZFBF2
. .
2
1,SINR as ,
1
1H
d
k k
a s
mrt
d
k
K
H
d
d
k i
i i kp
p
M K
p
p

   

h h
h h
 where tr / : normalization fa

ctorHK W W 
 . .
1SINR 1 as ,
tra s
zf
d
k d
Hp
p M K   
H HVIII-24sum 2log 1
1mrt
d
dp
R K
p 
  
 

 
  sum 2log 1 1zf
dR K p   SINR: Signal-to-Interference-plus-Noise Ratio
CSI: Channel State Infromation
 

2 2 2 2
2
1,1
~ ,
K
H H H H
k i k i k i M
F
i i kE M KM
K
     h h h h h h H 
11/tr Diversity order of ZF-BFHM K
K
 H H???Massive MIMO Downlink Channel: Linear Precoding –Imperfect CSIEstimated CSI ( ) using MMSE channel estimation?
?Deterministic form of Rsumwith imperfect CSI 2?
1   
H H E?
H : Error matrix where ~ 0,1iE eCN: Reliability of the estimation  2
sum 2
21
log 1
1 1d
zf
dp
R K
p 
 

 
  
 
 
 2
sum 2log 1
1mf
d
dp
R K
p  
  
 

 MRT ZFBFVIII-25???Massive MIMO Downlink Channel: Linear Precoding –Simulation Results (2/2)Ergodic sum-rate vs. MSimulation parameters


Deterministic form of RsumPerfect CSI, Imperfect CSIThe approximations is very
close to the numerical resultIt is also accurate even for
small M, K.Performance comparisonAs α>>1, ZFBF > MRTAs α=1, MRT > ZFBF
0dBdp10
KVIII-260 50 100 150 200 250 300
0
5
10
15
20
25
30
35
40
45
50
MErgodic 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.)4 5 6 7 8{2 , 2 , 2 , 2 , 2 }
M20.5 M↑ Rsum↑
Cross pointChannelImperfectness???Massive MIMO Downlink Channel: Linear Precoding –Simulation Results (2/2)Ergodic sum-rate vs. KSimulation parameters


Performance comparisonAs α>>1, ZFBF > MRTAs α=1, MRT > ZFBFOptimal K* for ZFBF
ex)
0dBdp{10, 20, ..., 100}
KVIII-2710 20 30 40 50 60 70 80 90 100
25
30
35
40
45
50
55
60
65
70
75
MErgodic sum-rate

ZFBF(P-App.)
ZFBF(P-Num.)
MRT(P-App.)
MRT(P-Num.)128
M20.5 MRT:K↑ Rsum↑
ZFBF: Concave function of K
Cross point
Optimal K**
sum0zfR
K K
K
 

 
 

 *1
where 0dBdMK p
e

 Massive MIMO Uplink ChannelEnergy and Spectral Efficiency with Linear Receivers???Massive 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 tradeoffVIII-29???Massive MIMO Uplink Channel: System ModelParameters
?
?: small scale fading
?: path loss + shadowing
?SNR for the kth UE:
Received signalk k

k
g hkhku kp[ 1] [ 1]
[ ]
[ 1]
u
K M
M K
Mp 

 
y G x n  1/2
1 1
[ ], ,..., , diag ,...,K K
K K 
G H D H h h D  21, ~ 0,1k iE x n
 

 
CNVIII-30???Massive MIMO Uplink Channel: Linear DetectorConventional linear detectorReceived signal after using the linear detectorSINR of the kth user
1,
noise
desired signal
interference
K
H H H H H H H
u k u k k u k k k u k i i k
i i kp r p p x p x        r A Gx A n a Gx a n a g a g a n

2
k
2
2
1,SINRH
u k k
K
H
u k i k
i i kp
p 
a g
a g aVIII-31MRC
ZF MMSEA G 1
H
A G G G11H
K
up 
 
 
 
A G G G IMRC: Maximal Ratio Combining
ZF: Zero-Forcing
MMSE: Minimum Mean Square Error???Massive MIMO Uplink Channel: 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 Mtaccording to , where Euis fixed.
Then,?Massive MIMO effect?Small-scale fading/ Inter-user interference goes away in the limituE
u
Mp , 2log 1 , P k k uR E M   
 2
, 2 2
2
2
1,log SINR log 1H
u k k
P k k
K
H
u k i k
i i kp
R E E
p  
 
 
 
 
 
  
 
 
 

 
 
 
 a g
a g aVIII-32???Massive MIMO Uplink Channel: Uplink Power Efficiency –Perfect CSI (2/2)Uplink performance with MRC –Perfect CSI 4
mrc
, 2
2
2
1,
1
2
2
1,
2
4
mrc
2 ,
1,log 1
log 1
1
log 1
1u k
P k
K
H
u k i k
i i k
K
H
u k i k
i i k
u k
u t k
P k
K
u i
i i kp g
R E
p g g g
p g g g
E
p g
p M
R
p
 

 
  
 
 
 
 
 
 

 
 
 
 
 
 

 
 
 
 
 
 
 
 
 
 
 
 
 
 

 
 
 

 


Capacity lower bound
Limit case 
 mrc
, 2
1,
21
log 1
1
log 1 as u
uE
k
M
P k
K
E
i
M
i i k
k uM
R
E M

  
 

 
 
 

 
 
   Small-scale fading/ Inter-user
interference goes away in the
limit ! Tx power can be scaled as 1/ !!
MVIII-33pu=Eu/M???Massive MIMO Uplink Channel: Uplink Power Efficiency –Imperfect CSI (1/3)Estimated CSI ( ) using MMSE channel estimation?
??Rece

ived signal vector after using the linear detector ?
 G G E?
G
 1: Error matrix where ~ 0,i
p ii M
p
 E e I
CN: Uplink pilot powerp up p: # of pilots 1, 1
no
desired signal
interference from
inter-user interference
channel estimation error? ?
?
?
? ? ?
? ? ? ? ? ?H
u u
H H H
k u k u k k
K K
H H H H
u k k k u k i i u k i i k
i i k ip p
r p p
p x p x p x    
  
    r A Gx Ex n
a Gx a Ex a n
a g a g a e a n


iseVIII-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 Both 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 Euis fixed. Then,2
, 2
2
2 2
1, 1? ?
log 1
? ? ? ?
1H
u k k
IP k
K K
H
i
u k i u k k
i i k i
u ip
R E
p p
p
    
 
 
 
 
 
 
 
 
 
 
 
 

 
  a g
a g a au
E
u
Mp 2 2
, 2log 1 , as IP k k uR E M  VIII-35Pilot power (pp)???Massive MIMO Uplink Channel: Uplink Power Efficiency –Imperfect CSI (3/3)Uplink performance with MRC –Imperfect CSICapacity lower bound 
   2 2
mrc
, 2
1,1
log 1
1 1 1u k
IP k
K
u u k i u k
i i kp M
R
p p p 
      

 
 
 
   
 Limit case ( ) mrc
,
2 2
20 /
log 1 /u u
IP k u u
k u u up E
R p E M
E p E M

 


 


 


Tx power can be scaled asM1/ !!
MSquaring effect???Massive MIMO Uplink Channel: Uplink Power Efficiency –Simulation ResultsRequired Power vs. MSimulation parametersK=10Target rate: 1bit/s/HzPower scaling lowPerfect CSI Imperfect CSIAs Mincreases, the difference in performance between MRC and ZF (or
MMSE) decreases.Perfect CSI: less than 1dBImperfect CSI: less than 3dB1/M

1/MVIII-37
M↑ pu↓ as 1/MPerformance gap between
MRC and ZF (or MMSE)Multi-Cell Massive MIMOPilot Contamination & Inter-Cell Interference Problem???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 R1Multi-Cell Massive MIMO: Inter-Cell Interference Problem (1/3)1 1 1 1 1
1
2 2 2 2 2
21 1
1 1H H
H Hx x x
M
x x x
M
 
 

h h
h h
 
 For large
1HM
x x
M
 

 
 
h
1/2 1/2
1 1 1 1 1 2 2
H H
d d
I Ip p
y d x d x
M M
  hh h h n
 VIII-39???Multi-Cell Massive MIMO: Inter-Cell Interference Problem (2/3)1/2 1/2
1 1 1 1 1 2 2
H H
d d
I Ip p
y d x d x
M M
  hh h h n
 1/2 1/2
1 1 2
1 1 1 21 1H HI
d d Iy p d x p d x
M M
M M
  
hh h h
n
 
    2 2
2
2
1
1
0Var 1i i
M
ih h
h E h
M M
 
   
h


 
   * * *
1 2
1 1 2 2
Gaussian Gaussian
Gaussian1
0H
i j
i j i j i j
M
M M
i jg g g
h h h h h h E g E h
M M M 
  
 
       
 
 
hh


0VIII-40???Multi-Cell Massive MIMO: Inter-Cell Interference Problem (3/3)1/2 1/2
1 1 2
1 1 1 2
1/2
1 11 1H H
I
d d I
dy p d x p d x
M M
M M
p d x
  

h h h h
n
 
0
0
11/2
1 1 1dy p Md x

VIII-41???Multi-Cell Massive MIMO: Pilot Contamination Problem (1/5)Practical 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 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) 1 1 1 1 2 2 2 2
estimation noise estimation noise? ?
,d d I d d I     
g g g n g g g n   1 1 1 1 2 2 2
1 1 1 1 1 2 2 2 2 2? ?H H
d d
d d I d
H H H H H H
d d
d d I I d Ip p
y x x
M M
p p
x x
M M
  
      
g g g g n
g g g n g g g n n
 
 1/2
1 1 1
T T
I I Id
g h1/2
1 1 1
T T
d d dd
g h1/2
2 2 2
T T
I I I
dg h1/2
2 2 2
T T
d d dd
g hVIII-43???Multi-Cell Massive MIMO: Pilot Contamination Problem (3/5)SIR for 2-cell MU-MIMO with pilot contamination?Received signal at R1
?Desired signal
?Interference signal
?Received SIR
VIII-441/2
1 1 1
T T
I I Id
g h1/2
1 1 1
T T
d d dd
g h1/2
2 2 2
T T
I I Id
g h1/2
2 2 2
T T
d d dd
g h 1/2 1/2
1/2 1/2 1/2 1/2
1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1 1 1
H H H
H H H
d d d d d I I d
d d d d I I d d d dp d d
d d d x Mp d x Mp d x
M M
 
 
   


 
h h h h h n
h h h n
  
 1/2 1/2
1/2 1/2 1/2 1/2
2 2 2 2 2 2 2 1
2 2 2 2 2 2 2 2 2 2 2 2
H H H
H H H
d I d d I I I I
I I d d I I d I d Ip d d
d d d x Mp d x Mp d x
M M
 
 
   
 
 
h h h h h n
h h h n
  2 2
1 1
2 2
2 2
d d d
d I IMp d d
Mp d d

   1 1 1 1 1 1 2 2 2 2 2
H H H H H H
d d
d d I I d Ip p
y x x
M M
      g g g n g g g n n
 No small scale fading effects
Pilot contamination is independent from pilot power???SIR for multi-cell MU-MIMO with pilot contamination [7]
?MRT based SINR for l-th UE
?ZF-BF based SINR for l-th UE [7]?If pp0, MRT = ZF-BFMulti-Cell Massive MIMO: Pilot Contamination Problem (4/5):Large scale fading between BS and UE in cell
: Pilot Transmission Powerkjlpd j l kp2
MRT
2SIRjjl
l
jnl
n jd
d 
 2
2
ZF-BF
2
2/ 1/
SIR
/ 1/jjl ijl p
i
l
jnl inl p
n j id d p
d d p

 No small scale fading effects
Pilot contamination is independent from pilot power
No small scale fading effects
Pilot contamination is dependent from pilot power[7] F. Rusek et al., “Scailing up MIMO: Opportunities and challenges with very large arrays,”
 
  
 2
2
2
2
2
ZF-BF
2 2
2
2
2/ 1/
/ 1/
SIR
/ 1/
/ 1/jjl ijl p
jjl p
jjl
i
l
jnl
n j
jnl p
jnl inl p
n j
n j id d p
d p
d
d
d p
d d p


  



 VIII-45???Multi-Cell Massive MIMO: Pilot Contamination Problem (5/5)Simulation Results [7] SIR for MRT and ZF as function of M and K=10Simulation Parameters?MRT / ZF-BF is considered
?Number of users (K): 10
?Cell diameter: 1600m
?Large scale + small scale considered
?Performance is limited by pilot
contaminationConclusion from simulation results?Finite MMRT < ZF-BF
?Infinite MMRT > ZF-BFFinite M: ZF > MRT
Infinite M: ZF < MRTVIII-46[7] F. Rusek et al., “Scailing up MIMO: Opportunities and challenges with very large arrays,”

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