Massive MIMO

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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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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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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MRT versus ZF precoding

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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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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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Limits Imposed by Propagation

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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.

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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




I.i.d. channels give favorable propagation

tail no tail

~20 dB ~3 dB

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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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Lund measurements, example of results

tail no tail

~26 dB ~7dB

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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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Limits Imposed by Noise and Intracell Interferencewith Linear Processing

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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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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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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




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


maxP,

, s.t. R = const.

Single-user SIMO system: K = 1,M = 100

maxP,

, s.t. R = const.

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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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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


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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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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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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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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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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Limits Imposed by Intercell Interference

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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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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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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

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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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Excess Degrees of Freedom in Massive MIMO:

A Unique Opportunity for Hardware-Friendly SignalShaping

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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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Beamforming versus Low-PAR Signal Shaping

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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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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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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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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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PAR-aware MU-MIMO OFDM DL (99% percentiles)

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PAR-aware MU-MIMO OFDM DL (99% percentiles)

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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

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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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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

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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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Thank You

Visit the massive MIMO website

www.commsys.isy.liu.se/ egl/vlm/vlm.html

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