Large Mimo
Transcript of Large Mimo
-
7/29/2019 Large Mimo
1/30
MM
YS
Very Large MIMO Systems:Opportunities and Challenges
Erik G. Larsson
March 21, 2012
Div. of Communication Systems
Dept. of Electrical Engineering (ISY)Linkoping UniversityLinkoping, Sweden
www.commsys.isy.liu.se
-
7/29/2019 Large Mimo
2/30
With thanks to my team and collaborators:
Hien Q. Ngo (LiU, Sweden) Antonios Pitarokoilis (LiU) Saif Mohammed (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)
Christoph Studer (Rice Univ., USA)
1/29
Erik G. LarssonVery Large MIMO Systems
Communication Systems
Linkoping UniversityMM
YS
-
7/29/2019 Large Mimo
3/30
Why MIMO Array gain (beamforming)
Spatial division mult. access
Spatial multiplexing Rate min(nr, nt) log (1 + SNR)
Reliability pe SNRnrnt
2/29
Erik G. LarssonVery Large MIMO Systems
Communication Systems
Linkoping UniversityMM
YS
-
7/29/2019 Large Mimo
4/30
Very Large MIMO
M=
x100
antennas!K
terminals
k=1
k=K
We think of very large (multiuser) MIMO as a system with M K 1 coherent, but simple, processing
Potential to improving rate & reliability dramatically Potential to scaling down TX power drastically
3/29
Erik G. LarssonVery Large MIMO Systems
Communication Systems
Linkoping UniversityMM
YS
-
7/29/2019 Large Mimo
5/30
Large MIMO Arrays
Reduce bulky items (coax) Each antenna unit simple (low accuracy) Resilience against individual failures (hotswapping) Potential economy of scale in manufacturing Enable for mmWave radio (60-300 GHz)?
4/29
Erik G. LarssonVery Large MIMO Systems
Communication Systems
Linkoping UniversityMM
YS
-
7/29/2019 Large Mimo
6/30
Large MIMO: Some Known Facts(Notation: M antennas, K terminals, power per terminal P)
Linear processing (MRC/MRT, ZF, ... ) nearly optimal asM K 1
P and M large enough pilot contamination limitsperformance
Scaling down P with M noise will limit performance.
Perfect CSI & optimal processing P can be scaled as 1/M
Given linear processing and imperfect CSI, in a MU system,P can be scaled as 1/
M
5/29
Erik G. LarssonVery Large MIMO Systems
Communication Systems
Linkoping UniversityMM
YS
-
7/29/2019 Large Mimo
7/30
Large MIMO: Some Known Facts, cont.
System performance can be limited by
intracell interference
pilot contamination thermal noise + intercell interference
so there are several possible operating points depending on
number of antennas available TX power choice of receiver/precoder algorithm coherence time (dictates ultimately the number of users served)
6/29
Erik G. LarssonVery Large MIMO Systems
Communication Systems
Linkoping UniversityMM
YS
-
7/29/2019 Large Mimo
8/30
Large MIMO: Some Beliefs/Speculation
Not enough time for CSI feedback, so must operate in TDD mode. Not enough pilots
Not enough resources for fast CSI feedback System will operate in nearly-noise limited regime (1 bpcu/term)
Very aggressive spatial multiplexing; aggregate efficiency K bpcu Each user could get the full bandwidth simple MAC, little or no control signaling
Impairments, e.g., multiuser interference (almost) drown in noise linear or nearly-linear receivers
May even get away with equalization-free (matched filter only) SCtransmission
Vast excess (M K) of degrees of freedom: use for HW-friendly signal shaping and smart receiver algorithms Per-antenna constant envelope or low-PAR multiuser precoding Channel estimation exploiting subspaces
Channel will harden (random matrix theory) Larger array reveals new propagation phenomena
7/29
Erik G. LarssonVery Large MIMO Systems
Communication Systems
Linkoping UniversityMM
YS
-
7/29/2019 Large Mimo
9/30
Large MIMO: Some of the Most Important Questions
Processing will have to be simple (linear). How good is this?
Non-CSI@TX operation:broadcasting (control signaling) and acquisition
Hardware imperfections: phase noise, I/Q imbalance, A/D, PAs
Synchronization at low SNR
TDD will bring us pilot contamination in the downlink.How bad is this really in practice?
TDD will require reciprocity calibration.
How, when and at what cost?
8/29
Erik G. LarssonVery Large MIMO Systems
Communication Systems
Linkoping UniversityMM
YS
-
7/29/2019 Large Mimo
10/30
Favorable Propagation andIts Implications
9/29
Erik G. LarssonVery Large MIMO Systems
Communication SystemsLinkoping University
MM
YS
-
7/29/2019 Large Mimo
11/30
Favorable propagation and Rate Consider M K, MIMO link, channel H, M K. Rate:
R =
K
k=1
log21 +
SNR
K2
k , SNR =Ptot
N0
If |Hij | 1,K
k=1 2k = H2 M K, so
log2 (1 + MSNR)
rank-1 channel (LoS)21=MK, 2
2==2
K=0
R K log2
1 +M
KSNR
HHHI (full rank channel)
21==
2
K=M
Favorable propagation
H i.i.d. and M K favorable propagation. In MU-MIMO (H G), favorable propagation if
GHG
M
1 0 00 2
. . ....
.... . .
. . . 00 0 K
D, M K10/29
Erik G. LarssonVery Large MIMO Systems
Communication SystemsLinkoping University
MM
YS
-
7/29/2019 Large Mimo
12/30
Favorable propagation and ideal channels
40 30 20 10 0 10 20 300
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Prob(
a
bscissa)
ordered singular values [dB]
i.i.d 6x128
i.i.d. 6x6
11/29
Erik G. LarssonVery Large MIMO Systems
Communication SystemsLinkoping University
MM
YS
-
7/29/2019 Large Mimo
13/30
Do we have favorable propagation in practice?
Our partners at Lund Univ., Sweden have conducted uniquemeasurements [RPL2011+,GERT2011].
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.
12/29
Erik G. LarssonVery Large MIMO Systems
Communication SystemsLinkoping University
MM
YS
-
7/29/2019 Large Mimo
14/30
Lund measurements, example of results
40 30 20 10 0 10 20 300
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Prob(
a
bscissa)
ordered singular values [dB]
meas 6x128
meas 6x6
13/29
Erik G. LarssonVery Large MIMO Systems
Communication SystemsLinkoping University
MM
YS
-
7/29/2019 Large Mimo
15/30
Spectral/energy efficiency tradeoffs
14/29
Erik G. LarssonVery Large MIMO Systems
Communication SystemsLinkoping University
MM
YS
-
7/29/2019 Large Mimo
16/30
Uplink single-cell, model assumptions
gk =
khk. hk: small scale fading;
E[|hmk|2] = 1; zero mean. k: path loss+shadowing SNR for kth terminal: P k
RX signal:
y =
P
Kk=1
gk
M1
xk +n, E[|xk|2] = 1, ni CN(0, 1)
Write as
y =
P GMK
xK1
+n, G = HD1/2, H [h1, . . . ,hK], D
1. . .
K
15/29
Erik G. LarssonVery Large MIMO Systems
Communication SystemsLinkoping University
MM
YS
-
7/29/2019 Large Mimo
17/30
Spectral-energy efficiency tradeoff Sum-spectral efficiency:
R = 1 T
Klog2 1 + (M1)P
2
(K1)P2+(+K)P+1, for MRC
1 TKlog2 1 + (MK)P2(+K)P+1 , for ZF Energy efficiency: =
R
P Reference mode: K= 1,M= 1
arg max1T Single-user system: K= 1,M fixed
arg maxP,
, s.t. S= const., 1 T
Multi-user system: M fixed
arg maxP,K,
s.t. S= const.,K T(KM for ZF) 16/29
Erik G. LarssonVery Large MIMO Systems
Communication SystemsLinkoping University
MM
YS
C ( ) [ ]
-
7/29/2019 Large Mimo
18/30
Cellular UL, (BT)coh. = 14 14, M = 1 [NLM2011]
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
Re
lativeEnergy-Efficiency(bits/J)/(bits/J)
Spectral-Efficiency (bits/s/Hz)17/29
Erik G. LarssonVery Large MIMO Systems
Communication SystemsLinkoping University
MM
YS
C ll l UL (BT ) 14 14 M 100 [NLM2011]
-
7/29/2019 Large Mimo
19/30
Cellular UL, (BT)coh. = 14 14, M = 100 [NLM2011]
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
Re
lativeEnergy-Efficiency(bits/J)/(bits/J)
Spectral-Efficiency (bits/s/Hz)
K=1, M=100
18/29
Erik G. LarssonVery Large MIMO Systems
Communication SystemsLinkoping University
MM
YS
C ll l UL (BT ) 14 14 M 100 [NLM2011]
-
7/29/2019 Large Mimo
20/30
Cellular UL, (BT)coh. = 14 14, M = 100 [NLM2011]
0 10 20 30 40 50 60 70 80 9010
-1
100
101
102
103
104
K=1, M=1
MRC
20 dB
10 dB
0 dB
-10 dB
-20 dB
Re
lativeEnergy-Efficiency(bits/J)/(bits/J)
Spectral-Efficiency (bits/s/Hz)
K=1, M=100
M= 100
ZF
19/29
Erik G. LarssonVery Large MIMO Systems
Communication SystemsLinkoping University
MM
YS
C ll l UL (BT ) 14 14 M 50 [NLM2011]
-
7/29/2019 Large Mimo
21/30
Cellular UL, (BT)coh. = 14 14, M = 50 [NLM2011]
0 10 20 30 40 50 60 70 80 9010
-1
100
101
102
103
104
-20 dB
M=50
ZF
MRC
20 dB
10 dB
0 dB
-10 dB
RelativeEnergy-Efficiency(bits/J)/(bit
s/J)
Spectral-Efficiency (bits/s/Hz)
K=1, M=50
K=1, M=1
20/29
Erik G. LarssonVery Large MIMO SystemsCommunication Systems
Linkoping UniversityMM
YS
-
7/29/2019 Large Mimo
22/30
Large-Scale MU-MIMO
Downlink Precoding
21/29
Erik G. LarssonVery Large MIMO Systems Communication SystemsLinkoping University MM
YS
D li k di g g l ks
-
7/29/2019 Large Mimo
23/30
Downlink precoding - general remarks
In the downlink, the are M K unused degrees of freedom.These excess DoF could be used to Null out interference Shape the transmitted signals in a hardware-friendly way
An excess in the number of antennas also means that simpleprecoders (MRT, time-reversal) may be used to combat frequencyselectivity
22/29
Erik G. LarssonVery Large MIMO Systems Communication SystemsLinkoping University MM
YS
Constant Envelope MU MIMO Downlink Precoding
-
7/29/2019 Large Mimo
24/30
Constant Envelope MU-MIMO Downlink Precoding
Constant-envelope transmission [SM2011a,SM2011b]
x =
P
M
ej1
...ejM
Insensitive to PA non-linearity.
How well can we approximate a desired wavefield at K locations, byvarying only the phase of the transmitted signals?
Not to be confused with equal-gain transmission (something entirelydifferent)!
23/29
Erik G. LarssonVery Large MIMO Systems Communication SystemsLinkoping University MM
YS
Constant Envelope versus Beamforming
-
7/29/2019 Large Mimo
25/30
Constant Envelope versus Beamforming
u
P
h1
h
P
hm
h
P h
Mh
Amplitude range = [0
P|u|]
eju
1
eju
m
eju
M
Constant amplitude =
PM
PM
PM
PM
Antenna 1 Antenna 1
Antenna m Antenna m
Antenna M Antenna M
Beamforming Constant-envelope transmission
24/29
Erik G. LarssonVery Large MIMO Systems Communication SystemsLinkoping University MM
YS
Constant env MU MIMO precoding Gauss symbols
-
7/29/2019 Large Mimo
26/30
Constant-env. MU-MIMO precoding, Gauss. symbols
0 50 100 150 200 250 30012
9
6
3
0
3
6
9
12
1515
No. of Base Station Antennas (M)
Min.reqd.
PT
/2
(dB)toachiev
eaperuserrateof
2bpcu
K = 10, Proposed CE Precoder (CE)
K = 10, ZF Phaseonly Precoder (CE)
K = 10, GBC Sum Cap. Upp. Bou. (APC)
K = 40, Proposed CE Precoder (CE)
K = 40, ZF Phaseonly Precoder (CE)
K = 40, GBC Sum Cap. Upp. Bou. (APC)
1.7 dB
25/29
Erik G. LarssonVery Large MIMO Systems Communication SystemsLinkoping University MM
YS
PAR Aware MU MIMO OFDM Downlink [SL2012]
-
7/29/2019 Large Mimo
27/30
PAR-Aware MU-MIMO OFDM Downlink [SL2012]
Precoder design problem:
(PMP) minimizea1,...,aN
maxa1 , . . . , aNsubject to sw = Hwfw(a1, . . . , aN), w T0N1 = fw(a1, . . . , aN), w Tc.
Hw: time-frequency channel
fw(
) linear function; includes OFDM modulation and S/P
conversion T: used subcarriers; Tc: null subcarriers Convex optimization problem, fast algorithm; relaxation
26/29
Erik G. LarssonVery Large MIMO Systems Communication SystemsLinkoping University MM
YS
PAR-aware MU-MIMO OFDM DL (99% percentiles)
-
7/29/2019 Large Mimo
28/30
PAR-aware MU-MIMO OFDM DL (99% percentiles)
27/29
Erik G. LarssonVery Large MIMO Systems Communication SystemsLinkoping University MM
YS
Literature
-
7/29/2019 Large Mimo
29/30
LiteratureRPL+2011 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,arXiv:1201.3210, 2011.
NLM2011 H.Q. Ngo, E.G. Larsson and T. Marzetta, Energy andSpectral Efficiency of Very Large Multiuser MIMOSystems, arXiv:1112.3810, 2011.
LM2011a E.G. Larsson and S.K. Mohammed, Per-antenna ConstantEnvelope Precoding for Large Multi-User MIMO Systems,arXiv:1201.1634v1, 2011.
LM2011b E.G. Larsson and S.K. Mohammed, Single-UserBeamforming in Large-Scale MISO Systems...: TheDoughnut Channel, arXiv:1111.3752, 2011.
SL2012 C. Studer and E.G. Larsson, PAR-Aware Large-ScaleMulti-User MIMO-OFDM Downlink, arXiv:1202.4034,2012.
HBD2011 J. Hoydis, S. ten Brink, M. Debbah, Massive MIMO: HowMany Antennas do We Need?, arXiv:1107.1709, 2011.GERT2011 X. Gao, O. Edfors, F. Rusek, and F. Tufvesson, Linear
pre-coding p erformance in measured very-large MIMOchannels, IEEE VTC 2011
Mar2010 T. L. Marzetta, Noncooperative MU-MIMO with unlimitednumbers of base station antennas, IEEE Trans. Wireless.Comm. 2010.
JAMV2011 J. Jose, A. Ashikhmin, T. L. Marzetta, and S. Vishwanath,Pilot contamination and precoding in multi-cell TDDsystems, IEEE Trans. Wireless Commun., 2011.
GJ2011 B. Gopalakrishnan and N. Jindal, An Analysis of PilotContamination on Multi-User MIMO Cellular Systems withMany Antennas, IEEE SPAWC 2011.
NML2011 H. Q. Ngo, T. Marzetta and E. G. Larsson, Analysis of thepilot contamination effect in very large multicell multiuser
MIMO systems for physical channel models, IEEE ICASSP2011.
PML2012 A. Pitarokoilis, S. K. Mohammed and E. G. Larsson, Onthe optimality of single-carrier transmission in large scaleantenna systems, IEEE Wireless Communication Letters,submitted, 2012.
CMT2004 G. Caire, R. Muller and T. Tanaka, Iterative multiuserjoint decoding: optimal power allocation and low-complexityimplementation, IEEE Trans. IT, 2004.
ZLW2007 H. Zhao, H. Long and W. Wang, Tabu search detection forMIMO systems, IEEE PIMRC 2007.
VMCR2008 K. Vishnu Vardhan, S. Mohammed, A. Chockalingam, andB. Sundar Rajan, A low-complexity detector for largeMIMO systems and multicarrier CDMA systems, IEEEJSAC 2008.
Sun2009 Y. Sun, A family of likelihood ascent search multiuserdetectors: an upper bound of bit error rate and a lowerbound of asymptotic multiuser efficiency, IEEE JSAC 2009.
LH1999 A. Lampe and J. Huber, On improved multiuser detectionwith iterated soft decision interference cancellation, inProc. IEEE Communication Theory Mini-Conference, 1999.
28/29
Erik G. LarssonVery Large MIMO Systems Communication SystemsLinkoping University MM
YS
-
7/29/2019 Large Mimo
30/30
Thank You
29/29
Erik G. LarssonVery Large MIMO Systems Communication SystemsLinkoping University MM
YS