Mattias Wennström Signals & Systems Group Mattias Wennström Uppsala University Sweden Promises of Wireless MIMO Systems

Mattias WennströmSignals & Systems Group

Mattias WennströmUppsala University

Sweden

Promises of Wireless Promises of Wireless MIMO SystemsMIMO Systems


Outline• Introduction...why MIMO??• Shannon capacity of MIMO systems • The ”pipe” interpretation• To exploit the MIMO channel

– BLAST– Space Time Coding– Beamforming

• Comparisons & hardware issues• Space time coding in 3G & EDGE

Telatar, AT&T 1995

Foschini, Bell Labs 1996

Tarokh, Seshadri & Calderbank 1998

Release ’99


Why multiple antennas ????Why multiple antennas ????

• Frequency and time processing are at limits• Space processing is interesting because it does not increase bandwidth

Adaptive Antennasinterference cancellation

Phased array range extension,

interference reduction MIMO Systems

(diversity)

”Specular”channels

”Scattering”channels

outdoor indoor


Initial AssumptionsInitial Assumptions

• Flat fading channel (Bcoh>> 1/ Tsymb)• Slowly fading channel (Tcoh>> Tsymb)• nr receive and nt transmit antennas• Noise limited system (no CCI)• Receiver estimates the channel

perfectly• We consider space diversity only


H11

H21

””Classical” receive diversityClassical” receive diversity

= log2[1+(PT2)·|H|2] [bit/(Hz·s)]

H = [ H11 H21] Capacity increases logarithmically with number of receive antennas...

*

22 detlog HHIt

T

nσ

PC


Transmit diversity / beamformingTransmit diversity / beamforming

H11

H12

Cdiversity = log2(1+(PT2)·|H|2) [bit/(Hz·s)]

Cbeamforming = log2(1 +(PT2 )·|H|2) [bit/(Hz·s)]

• 3 dB SNR increase if transmitter knows H• Capacity increases logarithmically with nt


H11

H22

Multiple Input Multiple Output systemsMultiple Input Multiple Output systems

H12

H21

2221

1211

HH

HHH

Cdiversity = log2det[I +(PT2 )·HH†]=

222122 2

1log2

1log

TT PP

Where the i are the eigenvalues to HH†

m=min(nr, nt) parallel channels, equal power allocated to each ”pipe”

Interpretation:

ReceiverTransmitter


MIMO capacity in generalMIMO capacity in general

m

ii

t

T

t

T

n

P

HHn

PIC

122

*22

1log

detlog

H unknown at TX H known at TX

m

i

iipC1

22 1log

Where the power distribution over”pipes” are given by a water filling solution

m

i

m

i iiT pP

1 1

1

p1

p2

p3

p4

),min( tr nnm


The Channel EigenvaluesThe Channel Eigenvalues

Orthogonal channels HH† =I, 1= 2= …= m= 1

)/1(log),min(1log 22

122 tTrt

m

ii

t

T nPnnn

PC

diversity

• Capacity increases linearly with min( nr , nt )• An equal amount of power PT/nt is allocated to each ”pipe”

Transmitter Receiver


Random channel models andRandom channel models andDelay limited capacityDelay limited capacity

• In stochastic channels,the channel capacity becomes a random variable

Define : Outage probability Pout = Pr{ C < R }

Define : Outage capacity R0 given a outageprobability Pout = Pr{ C < R0 }, this is the delaylimited capacity.

Outage probability approximates the Word error probability for coding blocks of approx length100


Example : Rayleigh fading channelExample : Rayleigh fading channelHij CN (0,1)

nr=1 nr= nt

Ordered eigenvaluedistribution for nr= nt = 4 case.


To Exploit the MIMO ChannelTo Exploit the MIMO Channel

Time

s0

s0

s0

s0

s0

s0

s1

s1

s1

s1

s1

s2

s2

s2

s2

V-BLAST

D-BLAST

Ante

nna

s1 s1 s1 s1 s1 s1

s2 s2 s2 s2 s2 s2

s3 s3 s3 s3 s3 s3

• nr nt required• Symbol by symbol detection. Using nulling and symbol cancellation• V-BLAST implemented -98 by Bell Labs (40 bps/Hz)• If one ”pipe” is bad in BLAST we get errors ...

Bell Labs Layered Space Time Architecture

{G.J.Foschini, Bell Labs Technical Journal 1996 }


Space Time CodingSpace Time Coding

• Use parallel channel to obtain diversitydiversity not spectral efficiency as in BLAST• Space-Time trellistrellis codes : coding and and diversity gain (require Viterbi detector)• Space-Time blockblock codes : diversity gain

(use outer code to get coding gain)• nr= 1 is possible• Properly designed codes acheive diversity of nr nt

*{V.Tarokh, N.Seshadri, A.R.CalderbankSpace-time codes for high data rate wireless communication: Performance Criterion and Code Construction, IEEE Trans. On Information Theory March 1998 }


Orthogonal Space-time Block Orthogonal Space-time Block CodesCodes

STBC

Block of K symbols

• K input symbols, T output symbols T K• R=K/T is the code rate code rate • If R=1 the STBC has full rate full rate • If T= If T= nt the code has minimum delayminimum delay• Detector is Detector is linearlinear !!! !!!

Block of T symbols

nt transmit antennas

Constellation mapper

Data in

*{V.Tarokh, H.Jafarkhani, A.R.CalderbankSpace-time block codes from orthogonal designs, IEEE Trans. On Information Theory June 1999 }


STBC for 2 Transmit STBC for 2 Transmit AntennasAntennas

[ c0 c1 ]

*01

*10

cc

cc

Time

Antenna

Full rateFull rate andminimum delayminimum delay

1*02

*111

012010

nchchrnchchr

Assume 1 RX antenna:

Received signal at time 0

Received signal at time 1


ncHr

1

0*1

0*1

*2

21*

1

0 ,,,c

c

n

n

hh

hh

r

rcnHr

ncHnHcHHrHr ~~ 2*** F

Diagonal matrix due to orthogonality

The MIMO/ MISO system is in fact transformed to an equivalent SISO system with SNR

SNReq = || H ||F2 SNR/nt

|| H ||F2 =


The existence of Orthogonal STBCThe existence of Orthogonal STBC

• Real symbols : Real symbols : For nt =2,4,8 exists delay optimalfull rate codes.For nt =3,5,6,7,>8 exists full ratecodes with delay (T>K)

• Complex symbols : Complex symbols : For nt =2 exists delay optimalfull rate codes.For nt =3,4 exists rate 3/4 codesFor nt > 4 exists (so far) rate 1/2 codes

Example: nt =4, K=3, T=4 R=3/4

*12

*3

*13

*2

*2

*31

321

321

0

0

0

0

sss

sss

sss

sss

sss


Outage capacity of STBCOutage capacity of STBC

2

2 1logF

t

Hn

SNRCSTBC

HHn

SNRIC

t

detlog2diversity

Optimal capacity

STBC is optimal wrt capacity if HH† = || H ||F

2 which is the case for• MISO systems• Low rank channels


Performance of the STBC… Performance of the STBC… (Rayleigh faded channel)

|| H ||F2 = m

nt=4 transmit antennas andnr is varied.

The PDF of Assume BPSK modulation BER is then given by

tr

trnn

b nn

nn

SNRP

tr 12

4

1

Diversity gainnrnt which is same as fororthogonal channels


MIMO With BeamformingMIMO With Beamforming

Requires that channel H is known at the transmitterIs the capacity-optimal transmission strategy if

Cbeamforming = log2(1+SNR·1) [bit/(Hz·s)]

SNR12

11

Which is often true for line of sight (LOS) channels

Only one ”pipe” is used


Comparisons...Comparisons...2 * 2 system. With specular component (Ricean fading)

One dominatingeigenvalue. BF putsall energy into that ”pipe”


Correlated channels / Mutual Correlated channels / Mutual coupling ...coupling ...

When angle spread () is small, we have a dominating eigenvalue.The mutual coupling actuallyimprovesimproves the performance of the STBC by making the eigenvalues ”more equal”in magnitude.


WCDMA Transmit diversity conceptWCDMA Transmit diversity concept(3GPP Release ’99 with 2 TX antennas)

•2 modes• Open loop (STTD)• Closed loop (1 bit / slot feedback)

• Submode 1 (1 phase bit)• Submode 2 (3 phase bits / 1 gain bit)

Open loop mode is exactly the 2 antenna STBC

*01

*10

ss

ss

The feedback bits (1500 Hz) determines the beamformer weightsSubmode 1 Equal power and bit chooses phase between {0,180} / {90/270}

Submode 2 Bit one chooses power division {0.8 , 0.2} / {0.2 , 0.8} and 3 bits chooses phase in an 8-PSK constellation


GSM/EDGE Space time coding proposalGSM/EDGE Space time coding proposal

• Frequency selective channel …• Require new software in terminals ..• Invented by Erik Lindskog

Time Reversal Space Time Coding Time Reversal Space Time Coding (works for 2 antennas)(works for 2 antennas)

Time reversal Complex conjugate

Time reversal Complex conjugate -1

S(t)

S1(t)

S2(t)

Block


””Take- home message”Take- home message”• Channel capacity increases linearlylinearly

with min(nr, nt)

• STBC is in the 3GPP WCDMA proposal

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Mattias Wennström Signals & Systems Group Mattias Wennström Uppsala University Sweden Promises of Wireless MIMO Systems