Post on 22-Mar-2020
12/19/2001 1
New Paradigm of Wireless Communications – MIMO1
Architecture
1MIMO - Multiple-Input Multiple-Output, also known as BLAST - Bell Labs Layered Space-Time
School of Information Technology and Engineering (SITE)University of Ottawa, 161 Louis Pasteur
Ottawa, Ontario, Canada, K1N 6N5Email: sergey.loyka@ieee.org
by Dr. Sergey Loyka
12/19/2001 2
Why MIMO?
• High demand for spectrum → need for spectral efficiency
• Fading is a headache of system designers
• Time and frequency domain processing are at limits, space one - not!
12/19/2001 3
What is MIMO/BLAST?
• MIMO is an extraordinarily bandwidth-efficient approach to wireless communication
• It was originally developed in Bell Labs in 1995-1997
• It takes advantage of the spatial dimension • The central paradigm is exploitation rather
than mitigation of multipath effects
12/19/2001 4
Wireless system with single antennas
Tx Rx
Tx Data
Rx Data Wireless
Channel
• Classical Shannon’s limit for channel capacity :
( ) [ ]sHzbitSNRC //1log2 +=
• Increases as log of SNR → very slowly!
12/19/2001 5
• Channel capacity is low → few bits/Hz/s• Fading is huge → 20-40 dB• No space domain signal processing • Design is simple
Wireless system with single antennas (cont.)
12/19/2001 6
Wireless Channel Tx Rx
Tx Data
Rx Data
Wireless system with multiple antennas(phased array, diversity combining etc.)
( ) [ ]sHzbitnSNRC //1log 22 ⋅+=
• Increases as the log of n → very slowly!
12/19/2001 7
Wireless system with multiple antennas (cont.)
• Channel capacity is still low (few bits/Hz/s)• Fading is smaller but still large (10-20 dB)• Space-domain signal processing - partially• Complex antennas, beamforming etc.
12/19/2001 8
Tx
Data Splitter
Tx
Tx
Rx
Rx
Rx
Vector Signal
Processor
Tx Data
Rx Data
Wir
eles
s C
hann
el
b1
b2
b3
b3b2b1
MIMO: launch multiple bit streams!
12/19/2001 9
• Enormous channel capacity → 10 fold increase has been demonstrated
• Fading is small ( 1-5 dB)• Full space-domain signal processing• More complex design is fully compensated by
huge advantages
MIMO: launch multiple bit streams! (cont.)
[ ]sHzbitn
SNRnC //1log2
+⋅=
12/19/2001 10
Tx
Data Splitter
Tx
Tx
Rx
Rx
Rx
Vector Signal
Processor
Tx Data
Rx Data
Why and where it works ?
• Uncorrelated subchannels → parallel independent subchannels
12/19/2001 11
• Mathematically,
⋅
=
3
2
1
333231
322221
131211
3
2
1
xxx
hhhhhhhhh
yyy
⋅
=
3
2
1
33
22
11
3
2
1
000000
xxx
hh
h
yyy
Why and where it works ? (cont.)
12/19/2001 12
• Channel matrix diagonalization is a key operation for MIMO
• Signal processing at the receiver must do this job
• Correlated subchannels → complete diagonalization is not possible → increase in fading and decrease in channel capacity
Why and where it works ? (cont.)
12/19/2001 13
MIMO Key Advantages
• Extraordinary high spectral efficiency (from 30-40 bit/s/Hz)
• Large fade level reduction (10-30 dB)• Co-channel interference reduction (5-15 dB)• Multipath is not enemy, but ally !• Flexible architecture through DSP
12/19/2001 14
Spectral Efficiency
1 10 100 1 .10 310
100
1 .10 3
MIMOconvent.SISO
.
Cap
acity
, bit/
s/H
z
Number of antennas
12/19/2001 15
Fading Reduction
0 50 100 150 200 250 300 350 400 450 50030
20
10
0
10MIMO 2x2
.
0 50 100 150 200 250 300 350 400 450 50030
20
10
0
10SISO 1x1
.
Sign
al le
vel,
dB
time
12/19/2001 16
Fading Reduction
• Diversity order (DO) for MIMO ∝ n2 and for SIMO ∝ n
• MIMO efficiently exploits diversity at both Tx and Rx sites!
• Example: correlated fading at Rx → no SIMO diversity, but MIMO works!
• Consequence: 2-fold higher system availability for MIMO than for SIMO
12/19/2001 17
Number of MIMO publications
0
510
15
20
2530
35
40
1996 1997 1998 1999 2000
12/19/2001 18
Key Players
• Lucent• AT&T• Nokia• Nortel• Motorola• Ericsson
12/19/2001 19
Current R&D
• Matrix channel modeling, simulation, characterization & measurement
• Basic system architecture development
• Space-time coding/decoding & modulation/demodulation, and performance evaluation
• Elements of system-level simulation
• Prototyping
• Application areas (indoor, cellular, LMDS etc.)
12/19/2001 20
Future R&D
• Matrix channel will be still a problem
• Space-time codes into design!
• Adaptive MIMO architecture
• Nonlinear effects in Tx/Rx branches
• Full-scale system-level simulation
• First products on the market
12/19/2001 21
• http://www.bell-labs.com/project/blast/
Selected References (Non-Experts)
12/19/2001 22
Selected References (Experts)
• Foschini, G.J., Gans M.J.: ‘On Limits of Wireless Communications in a Fading Environment when Using Multiple Antennas’, Wireless Personal Communications, vol. 6, No. 3, pp. 311-335, March 1998.
• I.E. Telatar, "Capacity of Multi-Antenna Gaussian Channels," AT&T Bell Lab. Internal Tech. Memo., June 1995. (European Trans. Telecom., v.10, N.6, Dec.1999)
• Rayleigh, G.G., Cioffi, J.M.: "Spatio-Temporal Coding for Wireless Communications," IEEE Trans. Commun., v.46, N.3, pp. 357-366, 1998.
• http://www.bell-labs.com/project/blast/
12/19/2001 23
Matrix channel correlation is the main limitation to MIMO!
12/19/2001 24
MIMO Channel Capacity
⋅
ρ+= +HHI
nC detlog2
+⋅= HHR +⋅⋅= VDUH
Correlation matrix approach
Eigenvalue (SVD) approach
12/19/2001 25
MIMO Channel Capacity (cont.)
• Correlation matrix approach:
ρ
+= RIn
C detlog2
• Eigenvalue (SVD) approach:
( )∑ λρ+=i
iiC 22 1log
employed below
12/19/2001 26
Universal Upper Bound1
⋅
ρ+= RI
nC detlog2
Random channel → mean (ergodic) capacity:
( ) ( )xFxF ≤
Jensen Inequality, F - concave:
1S. Loyka, A. Kouki, New Compound Upper Bound on MIMO Channel Capacity, IEEE Comm. Letters, 2001, submitted
12/19/2001 27
Universal Upper Bound (cont.)
⋅
ρ+=≤ RI
nCC Rx detlog2
Receive bound (!!!):
∑=k
jkikij hhr *
transmit index
Captures Rx correlation only !
12/19/2001 28
Universal Upper Bound (cont.)
Key observation: transpose does not impact C !
THH ⇒ constn
=
⋅
ρ+ +HHIdet
12/19/2001 29
Transmit bound:
⋅
ρ+=≤ Tx
2 detlog RIn
CC Tx
Universal Upper Bound (cont.)
∑=k
kjkiij hhr *Tx
receive index
Captures Txcorrelation only !
12/19/2001 30
Universal Upper Bound (cont.)
Universal bound:
[ ]TxRx CCCC ,min=≤
captures both Tx & Rx correlation
12/19/2001 31
Universal Upper Bound (cont.)
0 0.2 0.4 0.6 0.8 1.00
10
30
50
70
mean capacity (eq.(3)) compound bound (eq.(10)) receive bound (eq.(5)) transmit bound (eq.(8))
Cap
acity
, bit/
s/H
z
correlation coefficient r
,,Txkm
Rxijkmij RRR ⋅= ,rRRx
ij = ,1 rRTxij −= ji ≠
12/19/2001 32
Simple Analytical Estimations
Uniform correlation matrix model2:
jirRij ≠= ,
Capacity
2S.L. Loyka, J.R. Mosig, Channel Capacity of N-Antenna BLAST Architecture, Electronics Letters, vol. 36, No.7, pp. 660-661, Mar. 2000.
( )
−
ρ+⋅≈ r
nnC 11log2
:)1,10( >>ρ<≤ nr r=0.5 → 3dB loss in SNR
12/19/2001 33
Simple Analytical Estimations (cont.)
Exponential correlation matrix model3:
1, ≤= − rrR jiij
Capacity :)1,1,1( >>>>ρ< nnr
−
ρ+⋅≈ 2
2 11log rn
nC
3S.L. Loyka, Channel Capacity of MIMO Architecture Using the Exponential Correlation Matrix, IEEE Comm. Letters, v.5, N. 9, pp. 369 –371, Sep 2001.
r=0.7 → 3dB loss in SNR
12/19/2001 34
Simple Analytical Estimations (cont.)
0.0 0.2 0.4 0.6 0.8 1.00
50
100
150
200
250
exponential model
n=10
n=50
full matrix computation approximate Uniform model
Cap
acity
, bit/
s/H
z
Correlation coefficient
ρ=30 dB
12/19/2001 35
=
−kn
k
I00R
R
MIMO Dimensionality Reduction
Block model of correlation matrix:
Capacity:
k correlated branches
n-k uncorrelated branches
( ) ( )
−
ρ+⋅+
ρ
+⋅−≈ rn
kn
knC 11log1log 22
4S. Loyka, A. Kouki, Correlation and MIMO Communication Architecture (Invited), 8th Int. Symp. on Microwave and Optical Technology, Montreal, June 19-23, 2001.
12/19/2001 36
MIMO Dimensionality Reduction (cont.)
1+−≈ knneEffective dimensionality:
High correlation ( )ρ−≥ 2/1 nr:)1( >>ρ n
9950.r ≥Example: n=10, ρ=30 dB
12/19/2001 37
MIMO Capacity in Realistic Environment5
… 1 2 n
incoming multipath
antenna array
Angle spread
Salz-Winters Model:
Incoming multipath signals arrive to the linear antenna array within some angle spread (±∆)
5S. Loyka, G. Tsoulos, Estimating MIMO System Performance Using the Correlation Matrix Approach, IEEE Comm. Letters, 2001, accepted
12/19/2001 38
MIMO Capacity in Realistic Environment (cont.)
0 5 10 15 20 25 300
30
50
70
upper bound piecewise-linear mean capacity
Cmax
dmin
∆=100 ∆=10
Cap
acity
, bit/
s/H
z
element spacing (d/λ)
12/19/2001 39
MIMO Capacity in Realistic Environment (cont.)
ρ
+⋅==n
nCC 1log2maxmindd >
Some observations: Capacity of n parallel channels
ϕ∆λ
=cos2mind the same as for space
diversity combining!
2∆ - angle spreadϕ - average angle of arrival
12/19/2001 40
Paradox of Zero Correlation
Keyhole: zero correlation but low capacity!
Tx
Rx
a1
a2
b1
b2
a1 , a2 , b1 , b2 - i.i.d. complex gaussian
( )21 ϕ−ϕ= jeR 0=R
( ) ( )2211 arg,arg bb =ϕ=ϕ
12/19/2001 41
Paradox of Zero Correlation (cont.)
Solution to the paradox: distinguish between average (conventional) and instantaneous capacity6 !
6S. Loyka, A. Kouki, On MIMO Channel Capacity, Correlations and Keyholes, IEEE Trans. Comm., 2001, submitted
( ) 01 222112211
2 =
−+λ+−λ Rrrrr
( )21 ϕ−ϕ= jeR 1=R One non-zero eigenvalue
r11 , r22 - received powers, λ - eigenvalue
12/19/2001 42
Paradox of Zero Correlation (cont.)
Some observations:
• average (conventional) correlation is not a reliable tool for estimating MIMO capacity
• ⟨R⟩=0 is necessary but not sufficient• R=0 is sufficient• mean magnitude correlation gives an accurate
estimation
12/19/2001 43
Paradox of Zero Correlation (cont.)
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
7
8
9
10
11
12
mean capacity capacity using RMS correlation capacity using mean magnitude correlation capacity using mean correlationC
apac
ity, b
it/s/
Hz
RMS correlation
( ) 11,exp ≤≤−
α⋅= R
RcRfExample: 0=R
12/19/2001 44
Measurement Issues
• Wireless channel is the most critical MIMO component
• Lack of measured data (validate theory, estimate performance in realistic scenarios etc.)
• Consequence: MIMO channel measurement is a key to future success
12/19/2001 45
• Channel matrix statistics• Key channel parameters: angular & delay
spread, number of multipath components, correlation
• Polarization diversity
What to Measure?
12/19/2001 46
How to Measure?• Full-scale MIMO measurements:
complexity ~ n2
• Reduced-complexity SIMO measurements ~ n
• After-measurement DSP: adaptive array algorithms
• Indoor versus outdoor
12/19/2001 47
Conclusion
• MIMO architecture is the first breakthrough in communication theory for last 50 years
• Order-of-magnitude improvement in performance
• Numerous potential applications (WLAN, LMDS, cellular etc.)
• Three-fold potential of MIMO:1. Research (scientific)2. Applications (industrial)3. Education
12/19/2001 48
The Future of Wireless is MIMO!