massive mimo
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MM
YS
Massive MIMO:
Fundamentals, Opportunities and Challenges
Erik G. Larsson
June 9, 2013
Div. of Communication SystemsDept. of Electrical Engineering (ISY)
Linkoping UniversityLinkoping, Sweden
www.commsys.isy.liu.se
-
With thanks to my team and collaborators:
Hien Q. Ngo (LiU, Sweden) Antonios Pitarokoilis (LiU) Hei Victor Cheng (LiU) Daniel Persson (LiU)
Fredrik Rusek (Lund, Sweden) Ove Edfors (Lund) Buon Kiong Lau (Lund) Fredrik Tufvesson (Lund)
Thomas L. Marzetta (Bell Labs/Alcatel-Lucent, USA)
Saif Mohammed (IIT/Delhi, India)
Christoph Studer (Rice Univ., USA)
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Erik G. LarssonMassive MIMO: Fundamentals, Opportunities and Challenges
Communication Systems
Linkoping University
-
Massive MIMO
M=
x100
antennas!K
terminals
k=1
k=K
Massive multiuser MIMO (MISO): M K 1 (think 100 10 or 500 50) coherent, but simple, processing
Potential to dramatically improve rate & reliability
Potential to drastically scale down TX power
Not only theory, at least one known testbed (64 10)
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Erik G. LarssonMassive MIMO: Fundamentals, Opportunities and Challenges
Communication Systems
Linkoping University
-
Large MIMO Deployment Scenarios
Reduce bulky items (coax) Each antenna unit simple (low accuracy) Resilience against individual failures (hotswapping) Potential economy of scale in manufacturing Grid-free powering
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Erik G. LarssonMassive MIMO: Fundamentals, Opportunities and Challenges
Communication Systems
Linkoping University
-
Massive MIMO Operation
Not enough resources for pilots & CSI feedback, so operate in TDD.
On the uplink, acquire CSI from uplink pilots and/or blindly from data detect symbols M K linear processing (MRC, ZF, MMSE) nearly optimal
On the downlink, use CSI obtained on the uplink make necessary adjustments based on reciprocity calibration apply multiuser MIMO precoding simple precoders desirable (and very good!): MRT, ZF, MMSE, ...
MRC/MRT operation intracell interference will appear as noise 1 bps/Hz/terminal; K bps/Hz/terminal total distributed implementation
ZF/MMSE operation can cancel out intra cell interference computationally more demanding
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Erik G. LarssonMassive MIMO: Fundamentals, Opportunities and Challenges
Communication Systems
Linkoping University
-
MRT versus ZF precoding
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Erik G. LarssonMassive MIMO: Fundamentals, Opportunities and Challenges
Communication Systems
Linkoping University
-
Massive MIMO Opportunities
Multiplexing gain K, Array power gain M (ideally)
Rely on the law of large numbers average out fast fading and thermal noise
Channel hardens h2/M constant no FD scheduling, full BW to all terminals, simple MAC almost no air-interface latency
In the 1 bps/Hz/t regime, many impairments drown in thermal noise
M K unused degrees of freedom (e.g. 500 50 = 450)
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Erik G. LarssonMassive MIMO: Fundamentals, Opportunities and Challenges
Communication Systems
Linkoping University
-
Massive MIMO Challenges and Questions
Multiplexing gain can only materialize if channel responses are(nearly) orthogonal
Array gain relies on coherency getting CSI is the main thing
HW power consumption (RF) must scale fast enough with PHW power consumption (BB) must scale slow enough with M
Scaling down P thermal noise eventually limits performance.
P large enough, interference limits performance intracell interference intercell interference
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Erik G. LarssonMassive MIMO: Fundamentals, Opportunities and Challenges
Communication Systems
Linkoping University
-
Limits Imposed by Propagation
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Erik G. LarssonMassive MIMO: Fundamentals, Opportunities and Challenges
Communication Systems
Linkoping University
-
Favorable propagation in Point-to-Point MIMO
M K MIMO link H , M K
Favorable propagation (f.p.) if
HHH I 21 = . . . = 2K For H2 = constant, log
I + 1N0HHH max if f.p.
(maxmin
)2= extra power needed to use all eigenmodes
Hmk zero mean & i.i.d., and M K f.p.
9/44
Erik G. LarssonMassive MIMO: Fundamentals, Opportunities and Challenges
Communication Systems
Linkoping University
-
Favorable propagation in MU-SIMO
Favorable propagation if
1
MgHi gj 0 for i 6= j
gi2 depends on path loss and shadow fading10/44
Erik G. LarssonMassive MIMO: Fundamentals, Opportunities and Challenges
Communication Systems
Linkoping University
-
I.i.d. channels give favorable propagation
tail no tail
~20 dB ~3 dB
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Erik G. LarssonMassive MIMO: Fundamentals, Opportunities and Challenges
Communication Systems
Linkoping University
-
Do we have favorable propagation in practice?
Our partners at Lund Univ., Sweden have conducted uniquemeasurements [RPL2013,GERT2011,GTER2012].
Indoor 128-ant. (4x16 dual-pol.) array. 3 users indoor, 3 outdoor.
2.6 GHz CF, 50 MHz BW, 100 snapshots (10m).
Normalized to retain only small-scale fading.
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Erik G. LarssonMassive MIMO: Fundamentals, Opportunities and Challenges
Communication Systems
Linkoping University
-
Lund measurements, example of results
tail no tail
~26 dB ~7dB
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Erik G. LarssonMassive MIMO: Fundamentals, Opportunities and Challenges
Communication Systems
Linkoping University
-
Summary
Assumptions on f.p. have substantial support in measurements
I.i.d. model for small-scaled fading appears reasonable
More details and models in F. Tufvessons tutorial next
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Erik G. LarssonMassive MIMO: Fundamentals, Opportunities and Challenges
Communication Systems
Linkoping University
-
Limits Imposed by Noise and Intracell Interferencewith Linear Processing
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Erik G. LarssonMassive MIMO: Fundamentals, Opportunities and Challenges
Communication Systems
Linkoping University
-
Single-Cell (Noise-Limited) Uplink
M antennas K terminals Power (SNR) per terminal: P i.i.d. Rayleigh fading
Coherence interval: T symbols (e.g. 2 100kHz 1ms = 200) K mutually orthogonal pilots of length (K T )
pilots data
t T-t MMSE channel estimation
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Erik G. LarssonMassive MIMO: Fundamentals, Opportunities and Challenges
Communication Systems
Linkoping University
-
Spectral-energy efficiency tradeoff
Sum-spectral efficiency bounds [NLM2013]:
R =
(1
T
)K log2
(1 + (M1)P
2
(K1)P 2+(+K)P+1), for MRC(
1 T
)K log2
(1 + (MK)P
2
(+K)P+1
), for ZF
Energy efficiency: ,R
P SISO system: K = 1,M = 1
maxP,
, s.t. R = const.
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Erik G. LarssonMassive MIMO: Fundamentals, Opportunities and Challenges
Communication Systems
Linkoping University
-
UL, T = 200, SISO reference, M = K = 1
0 10 20 30 40 50 60 70 80 9010
-1
100
101
102
103
104
K = 1, M = 1
20 dB
10 dB
0 dB
-10 dB
Rel
ativ
e En
ergy
-Ef
ficie
ncy
(b
its/J)
/(bits
/J)
Spectral-Efficiency (bits/s/Hz)18/44
Erik G. LarssonMassive MIMO: Fundamentals, Opportunities and Challenges
Communication Systems
Linkoping University
-
Spectral-energy efficiency tradeoff, cont.
Sum-spectral efficiency bounds [NLM2013]:
R =
(1
T
)K log2
(1 + (M1)P
2
(K1)P 2+(+K)P+1), for MRC(
1 T
)K log2
(1 + (MK)P
2
(+K)P+1
), for ZF
Energy efficiency: =R
P SISO system: K = 1,M = 1
maxP,
, s.t. R = const.
Single-user SIMO system: K = 1,M = 100
maxP,
, s.t. R = const.
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Erik G. LarssonMassive MIMO: Fundamentals, Opportunities and Challenges
Communication Systems
Linkoping University
-
UL, T = 200, SISO and SU-SIMO
0 10 20 30 40 50 60 70 80 9010
-1
100
101
102
103
104
K=1, M=1 (SISO)
20 dB
10 dB
0 dB
-10 dB
Rel
ativ
e En
ergy
-Ef
ficie
ncy
(b
its/J)
/(bits
/J)
Spectral-Efficiency (bits/s/Hz)
K=1, M=100 (SU-SIMO)
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Erik G. LarssonMassive MIMO: Fundamentals, Opportunities and Challenges
Communication Systems
Linkoping University
-
Spectral-energy efficiency tradeoff, cont. Sum-spectral efficiency bounds [NLM2013]:
R =
(1
T
)K log2
(1 + (M1)P
2
(K1)P 2+(+K)P+1), for MRC(
1 T
)K log2
(1 + (MK)P
2
(+K)P+1
), for ZF
Energy efficiency: =R
P SISO system: K = 1,M = 1
maxP,
, s.t. R = const.
Single-user SIMO system: K = 1,M = 100
maxP,
, s.t. R = const.
Multi-user SIMO system: M = 100, K 1 adapted
maxP,,K
, s.t. R = const.
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Erik G. LarssonMassive MIMO: Fundamentals, Opportunities and Challenges
Communication Systems
Linkoping University
-
UL, T = 200, SISO, SU-SIMO & MU-SIMO
0 10 20 30 40 50 60 70 80 9010
-1
100
101
102
103
104
(MU-SIMO)M = 100K adaptive
ZF processing
K=1, M=1 (SISO)
20 dB
10 dB
0 dB
-10 dB
-20 dB
Rel
ativ
e En
ergy
-Ef
ficie
ncy
(b
its/J)
/(bits
/J)
Spectral-Efficiency (bits/s/Hz)
K=1, M=100 (SU-SIMO)
MRC processing
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Erik G. LarssonMassive MIMO: Fundamentals, Opportunities and Challenges
Communication Systems
Linkoping University
-
Analysis Methodology - MRC & Perfect CSI
y =PGGGxxx+ nnn
noise, i.i.d. CN (0,1)
zmrc ,GGGHyyy =GGGH
(PGGGxxx+ nnn
)=PGHGx+GHn
zk,mrc =Pgggk2xk desired signal
+Pi6=k
gggHk gggixi interference
+gggHk nnnnoise
Achievable ergodic rate
Rk,mrc = E
{log2
(1 +
Pgggk2PK
i6=k |gi|2 + 1
)} log2
1 +
(E
{PK
i6=k |gi|2 + 1Pgggk2
})1= log2
(1 +
P (M 1)P (K 1) + 1
)
Observe that: gi ,gggHk gggigggk
CN (0, 1), indep. of gk Use E[log(1 + 1/x)] log(1 + 1/E[x])
Here: E{
1
gk2
}= 1
M1, since E
{tr
(WWW1
)}= m
nm, if
WWW Wm (n,IIIn).
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Erik G. LarssonMassive MIMO: Fundamentals, Opportunities and Challenges
Communication Systems
Linkoping University
-
Analysis Methodology - MRC & Estimated CSI CSI from pilots: GGG =GGG + EEE , where i CN
(0, 1
Pp+1IIIM
), gggi CN
(0,
Pp
Pp+1IIIM
),
Pp = P , =#pilots MRC
zmrc = GGGHyyy = GH (
PGx+ n) = GGG
H(
PGGGxxxPEEExxx +nnn
) zk,mrc =
Pgggk2xk +
P
Ki6=k
gggHk gggixi
P
Ki=1
gggHk ixi + ggg
Hk nnn
Achievable ergodic rate per terminal
Rk,mrc =
(1
T
)E
{log2
(1 +
Pgggk2P
Ki6=k |gi|2 + P
Ki=1
1P+1
+ 1
)}
(1
T
)log2
1 +(E{PKi6=k |gi|2 + PKi=1 1P+1 + 1Pgggk2
})1=
(1
T
)log2
(1 +
P 2 (M 1)P (P + 1) (K 1) + ( + 1)P + 1
)
gk and gi ,gggHk gggi
gggk, i 6= k are independent
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Erik G. LarssonMassive MIMO: Fundamentals, Opportunities and Challenges
Communication Systems
Linkoping University
-
Summary
10 spectral efficiency and 1000 radiated energy efficiencypossible with M = 100 antennas and MRC
Results for DL are similar (no D.o.F penalty for pilot transmission)
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Erik G. LarssonMassive MIMO: Fundamentals, Opportunities and Challenges
Communication Systems
Linkoping University
-
Limits Imposed by Intercell Interference
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Erik G. LarssonMassive MIMO: Fundamentals, Opportunities and Challenges
Communication Systems
Linkoping University
-
Pilot Contamination Problem
(Probably) must rely on UL pilots to get CSI
On UL, may rely partly on blind/joint channel estimation and datadecoding techniques to avoid pilot based estimation
But on DL, need explicit CSI to precode
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Erik G. LarssonMassive MIMO: Fundamentals, Opportunities and Challenges
Communication Systems
Linkoping University
-
Pilot Contamination Problem, cont.
Consider UL training; one interferer
YpM
= GMK
K
+N + fffM1
T1
LS estimation, with orthogonal pilots(H = PpI, say Pp = 1)
G = YpH = G
MK+NH
i.i.d.
+ fffM1
TH 1K
rank1
1
2
M
g1
gk
gK
1
K
k
f
Say g1 used for MRC data detection: y = Gx+ fffz + n
1M
gH1 y =1
M
(gH1 Gx+ g
H1 fffz + g
H1 n
)=
1
MgH1 G eeeT
1
x
x1
+1
M
(fffH
)1fffz
1M()
1fffHfffz
()1z
+ O(
1M
)
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Erik G. LarssonMassive MIMO: Fundamentals, Opportunities and Challenges
Communication Systems
Linkoping University
-
Pilot Contamination Problem, cont.
In principle, could project away fffT :
YpT = G
T +N
T
and estimate G from YpT . But rank
(T
)= 1, so we
sacrifice signal space
The effect on the downlink is similar
Can show: p.c. fundamentally limits performance of massive MIMOif P is fixed and M [Mar2010]
Can show: other cells transmitting data is as bad as other cellssending pilots [NLM2013]
But currently not clear, how bad the p.c. effect is if other types ofCSI estimation is used
29/44
Erik G. LarssonMassive MIMO: Fundamentals, Opportunities and Challenges
Communication Systems
Linkoping University
-
Summary
Interference from other cells can significantly impair CSI estimationand the ensuing UL detection & DL precoding: pilotcontamination
Possible (partial) countermeasures (on UL) Blind (partial pilot-free) CSI estimation (NL2011) identify subspace associated with different cells exploiting power
control & channel hardening [MVC2013] clever allocation of pilots in different cells [YGFL2013,FAM2013] pilot cont. precoding [AM2012]
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Erik G. LarssonMassive MIMO: Fundamentals, Opportunities and Challenges
Communication Systems
Linkoping University
-
Excess Degrees of Freedom in Massive MIMO:
A Unique Opportunity for Hardware-Friendly SignalShaping
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Erik G. LarssonMassive MIMO: Fundamentals, Opportunities and Challenges
Communication Systems
Linkoping University
-
Excess Degrees of Freedom
There are M K unused degrees of freedom.
In the downlink, these excess DoF may be used to shape thetransmitted signals in a hardware-friendly way
Per-antenna constant envelope or low-PAR multiuser precoding Robust to PA non-linearity/less PA backoff Exploit nullspace of HT :
nullspace dimension = M K!
y = HTx+w = HT (x+ z) +w
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Erik G. LarssonMassive MIMO: Fundamentals, Opportunities and Challenges
Communication Systems
Linkoping University
-
Beamforming versus Low-PAR Signal Shaping
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Erik G. LarssonMassive MIMO: Fundamentals, Opportunities and Challenges
Communication Systems
Linkoping University
-
Constant-env. MU-MIMO, Flat channel [ML2013]
0 50 100 150 200 250 30010
8
6
4
2
0
2
4
6
8
Number of Base Station Antennas (M)
Min
. req
d. P
T/2
to a
chie
ve a
per
use
r rat
e of
2 b
pcu
K = 10, Proposed CE Precoder (CE)
K = 10, GBC Sum Cap. Upp. Bou. (APC)
1.7 dB
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Erik G. LarssonMassive MIMO: Fundamentals, Opportunities and Challenges
Communication Systems
Linkoping University
-
Constant-env. MU-MIMO, Freq. sel. channel [ML2013a]
0 10 20 30 40 50 604
3
2
1
0
1
2
3
Min
. req
d. P
T/
2 (dB
) to ac
hieve
2 bp
cu/us
er
L=1,2,4,8. ZF upper bound (TAPC)L = 1,2,4,8. Coop. lower bound (TAPC)L = 1, CEL = 2, CE (T >> )L = 4, CE (T >> )L = 8, CE (T >> )
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Erik G. LarssonMassive MIMO: Fundamentals, Opportunities and Challenges
Communication Systems
Linkoping University
-
CE-MU-MIMO PrecodingAnalysis Methodology Ek: energy per information symbol uk (per user) P : total transmit power Received signals:
yk =
P
M
Mi=1
hk,ieji+nk =
PEkuk+
P
(Mi=1 hk,ie
ji
M
Ekuk
)
,k
+nk
With Gaussian symbols per user:
I(yk;uk) = h(uk) h(uk | yk) = h(uk) h(uk yk
PEk
yk) h(uk) h(uk ykPEk
) h(uk) h
( kEk
+nkPEk
)= log2(pie) h
( kEk
+nkPEk
)
log2(pie) log2(pie var
[ kEk
+nkPEk
])
log2(pie) log2(pieE
[ kEk
+nkPEk
2 ])
= log2(pie) log2(pie[E[|k|2]Ek
+1
PEk
])
Downlink signal design:
mini[pi,pi)
Kk=1
|k|2 mini[pi,pi)
Kk=1
M
i=1 hk,ieji
M
Ekuk
2
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Erik G. LarssonMassive MIMO: Fundamentals, Opportunities and Challenges
Communication Systems
Linkoping University
-
PAR-Aware MU-MIMO OFDM Downlink [SL2013]
Precoder design problem:
(PMP)
minimize max{a1 , . . . , aN}
subject to yw = Hwsw + noise, w Tyw = only noise, w T c.
Hw: time-frequency channel
T : used subcarriers; T c: null subcarriers Convex optimization problem, fast algorithm; relaxation
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Erik G. LarssonMassive MIMO: Fundamentals, Opportunities and Challenges
Communication Systems
Linkoping University
-
PAR-aware MU-MIMO OFDM DL (99% percentiles)
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Erik G. LarssonMassive MIMO: Fundamentals, Opportunities and Challenges
Communication Systems
Linkoping University
-
PAR-aware MU-MIMO OFDM DL (99% percentiles)
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Erik G. LarssonMassive MIMO: Fundamentals, Opportunities and Challenges
Communication Systems
Linkoping University
-
Summary
Low PAR may be desirable to enable high overall energy efficiency &low cost
Large number of antennas offers entirely new and uniqueopportunities for low PAR signal design
40/44
Erik G. LarssonMassive MIMO: Fundamentals, Opportunities and Challenges
Communication Systems
Linkoping University
-
Massive MIMOa Goldmine of Research Problems Base station receiver processing
Partially distributed processing (MRC/ZF/MMSE hybrids) Advanced channel estimation (exploit excess DoF) Synchronization at low SNR
Base station transmitter processing Partially distributed processing Low-complexity low-PAPR precoders OFDM or single-carrier?
Effects of hardware imperfections: Will the law of large numbersdeliver? phase noise and clock distribution, I/Q imbalance, A/D resolution, PA linearity
Pilot contamination (both UL & DL) may be mitigated by Blind channel estimation algorithms [NL2012] Coordination and planning of pilot reuse [YGFL2013]
TDD operation using UL channels for DL precoding requiresreciprocity calibration Cost? (BW & power), algorithms?, dedicated hardware?
Other system issues Time and frequency synchronization at low SNR Idle-terminal paging (DL) under non-CSI@TX
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Erik G. LarssonMassive MIMO: Fundamentals, Opportunities and Challenges
Communication Systems
Linkoping University
-
Eq.-Free SC vs. OFDM @ 1 bps/Hz/t [PML2012]
50 100 150 200 250 300 350 40018
16
14
12
10
8
6
4
2
0
No of Base Station Antennas (M)
Pow
er (n
ormali
zed)
[dB]
Time reversal MRT precodingCoop. SumCapacity BoundOFDM Bound T
cp=Tu/4
K=10
42/44
Erik G. LarssonMassive MIMO: Fundamentals, Opportunities and Challenges
Communication Systems
Linkoping University
-
Literature
RPL+2013 F. Rusek, D. Persson, B. K. Lau, E. G. Larsson, T. L.Marzetta, O. Edfors, and F. Tufvesson, Scaling up MIMO:Opportunities and Challenges with Large Arrays, IEEE SPMagazine, Jan. 2013
NLM2013 H.Q. Ngo, E.G. Larsson and T. Marzetta, Energy andSpectral Efficiency of Very Large Multiuser MIMOSystems, IEEE Trans. Comm. 2013, arXiv:1112.3810.
ML2013 S.K. Mohammed and E.G. Larsson, Per-antenna ConstantEnvelope Precoding for Large Multi-User MIMO Systems,IEEE Trans. Comm. 2013, arXiv:1201.1634v1.
ML2013a S.K. Mohammed and E.G. Larsson, Constant-EnvelopeMulti-User Precoding for Frequency-Selective MassiveMIMO Systems, arXiv:1305.1525.
SL2013 C. Studer and E.G. Larsson, PAR-Aware Large-ScaleMulti-User MIMO-OFDM Downlink, IEEE JSAC, Feb.2013.
HBD2013 J. Hoydis, S. ten Brink, M. Debbah, Massive MIMO in theUL/DL of cellular networks: How many antennas do weneed, IEEE JSAC, Feb. 2013.
GERT2011 X. Gao, O. Edfors, F. Rusek, and F. Tufvesson, Linearpre-coding performance in measured very-large MIMOchannels, IEEE VTC 2011
GTER2012 X. Gao, F. Tufvesson, O. Edfors, and F. Rusek, Measuredpropagation characteristics for very-large MIMO at 2.6GHz, in Proc. Asilomar, 2012 VTC 2011
YGFL2013 H. Yin, D. Gesbert, M. Filippou, and Y. Liu, ACoordinated Approach to Channel Estimation in Large-scaleMultiple-antenna Systems, IEEE JSAC, Feb. 2013.
AM2012 A. Ashikhmin and T. Marzetta, Pilot ContaminationPrecoding in Multi-Cell Large Scale Antenna Systems, inProc. ISIT 2012.
NL2012 H. Q. Ngo and E. G. Larsson, EVD-Based ChannelEstimations for Multicell Multiuser MIMO with Very LargeAntenna Arrays, ICASSP 2012.
GJ2011 B. Gopalakrishnan and N. Jindal, An Analysis of PilotContamination on Multi-User MIMO Cellular Systems withMany Antennas, IEEE SPAWC 2011.
NML2013 H. Q. Ngo, T. Marzetta and E. G. Larsson, The multicellmultiuser MIMO uplink with very large antenna arrays anda finite-dimensional channel, IEEE TCOM, 2013.
PML2012 A. Pitarokoilis, S. K. Mohammed and E. G. Larsson, Onthe optimality of single-carrier transmission in large scaleantenna systems, IEEE Wireless Communication Letters,2012.
PML2012b A. Pitarokoilis, S. K. Mohammed and E. G. Larsson, Effectof Oscillator Phase Noise on Uplink Performance of LargeMU-MIMO Systems, in Proc. Allerton, 2012.
Mar2010 T. L. Marzetta, Noncooperative MU-MIMO with unlimitednumbers of base station antennas, IEEE Trans. WC 2010.
JAMV2011 J. Jose, A. Ashikhmin, T. L. Marzetta, and S. Vishwanath,Pilot contamination and precoding in multi-cell TDDsystems, IEEE Trans. WC 2011.
ZYP2013 J. Zhang, X. Yuan, and L. Ping, Hermitian Precoding forDistributed MIMO Systems with Individual Channel StateInformation, IEEE JSAC 2013.
SY...2012 C. Shepard et al., Argos: practical many-antenna basestations, in Proc. MobiCom 2012.
MVC2013 R. R. Muller, M. Vehkapera, and L. Cottatellucci, BlindPilot Decontamination, in Proc. WSA 2013.
FAM2013 F. Fernandes, A. Ashikhmin, and T. L. Marzetta, Inter-CellInterference in Noncooperative TDD Large Scale AntennaSystems, IEEE JSAC, Feb. 2013.
LTEM2013 E. G. Larsson, F. Tufvesson, O. Edfors and T. L. Marzetta,Massive MIMO for Next Generation Wireless Systems,arXiv:1304.6690.
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Erik G. LarssonMassive MIMO: Fundamentals, Opportunities and Challenges
Communication Systems
Linkoping University
-
Thank You
Visit the massive MIMO website
www.commsys.isy.liu.se/ egl/vlm/vlm.html
44/44
Erik G. LarssonMassive MIMO: Fundamentals, Opportunities and Challenges
Communication Systems
Linkoping University
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