new paradigm of wireless communications – mimo1sloyka/papers/2001/presentation_mimo.pdf · new...

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: [email protected]

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


Key observation: transpose does not impact C !

THH ⇒ constn

=

⋅

ρ+ +HHIdet

12/19/2001 29

Transmit bound:

⋅

ρ+=≤ Tx

2 detlog RIn

CC Tx


∑=k

kjkiij hhr *Tx

receive index

Captures Txcorrelation only !

12/19/2001 30


Universal bound:

[ ]TxRx CCCC ,min=≤

captures both Tx & Rx correlation

12/19/2001 31


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


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


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!

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