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Mattias
Wennstrm
Signals &Systems Group
Mattias Wennstrm
Uppsala University
Sweden
Promises of Wireless
MIMO Systems
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Mattias
Wennstrm
Signals &Systems Group
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
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Mattias
Wennstrm
Signals &Systems Group
Why multiple antennas ????
Frequency and time processing are at limits
Space processing is interesting because it
does not increase bandwidth
Adaptive Antennasinterference cancellation
Phased arrayrange extension,
interference reduction MIMO
Systems
(diversity)
Specular
channels
Scattering
channels
outdoor indoor
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8/10/2019 STBC2
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Mattias
Wennstrm
Signals &Systems Group
Initial 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
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8/10/2019 STBC2
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Mattias
Wennstrm
Signals &Systems Group
H11
H21
Classical receive diversity
= log2[1+(PT/s2)|H|2] [bit/(Hzs)]
H = [ H11 H21]Capacity increases logarithmically
with number of receive antennas...
*
22detlog HHI
t
T
n
PC
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Mattias
Wennstrm
Signals &
Systems Group
Transmit diversity / beamforming
H11
H12
Cdiversity= log2(1+(PT/2s2)|H|2) [bit/(Hzs)]
Cbeamforming= log2(1 +(PT/s2)|H|2)
[bit/(Hzs)]3 dB SNR increase if transmitter knows H
Capacity increases logarithmically with nt
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8/10/2019 STBC2
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Mattias
Wennstrm
Signals &
Systems Group
MIMO capacity in general
m
i
i
t
T
t
T
n
P
HHn
PIC
122
*
22
1log
detlog
s
s
H unknown at TX H known at TX
m
i
iipC1
22 1log
s
Where the power distribution over
pipes are given by a water filling
solution
m
i
m
i i
iT pP1 1
1
1
2
3
4
p1
p2
p3
p4
),min( tr nnm
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8/10/2019 STBC2
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Mattias
Wennstrm
Signals &
Systems Group
The Channel Eigenvalues
Orthogonal channels HH =I, 1=2== m=1
)/1(log),min(1log 221
22 tTrt
m
i
i
t
T nPnnn
PC s
s
diversity
Capacity increases linearly with min( nr , nt )
An equal amount of power PT/ntis allocated
to each pipe
Transmitter Receiver
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8/10/2019 STBC2
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Mattias
Wennstrm
Signals &
Systems Group
Random channel models and
Delay limited capacity
In stochastic channels,
the channel capacity becomes a random
variable
Define : Outage probability Pout= Pr{ C < R }
Define : Outage capacity R0given a outage
probability Pout= Pr{ C < R0}, this is the delay
limited capacity.
Outage probability approximates the
Word error probability for coding blocks of approx length100
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8/10/2019 STBC2
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Mattias
Wennstrm
Signals &
Systems Group
Example : Rayleigh fading channel
HijCN (0,1)
nr=1 nr= nt
Ordered eigenvalue
distribution for
nr= nt = 4 case.
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8/10/2019 STBC2
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Mattias
Wennstrm
Signals &
Systems Group
To Exploit the MIMO Channel
Time
s0
s0
s0
s0
s0
s0
s1
s1
s1
s1
s1
s2
s2
s2
s2
V-BLAST
D-BLAST
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 LayeredSpace Time Architecture
{G.J.Foschini, Bell Labs Technical Journal 1996 }
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8/10/2019 STBC2
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Mattias
Wennstrm
Signals &
Systems Group
Space Time Coding
Use parallel channel to obtain diversitynot
spectral efficiency as in BLAST
Space-Time trelliscodes : coding and diversity
gain (require Viterbi detector)Space-Time blockcodes : 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.Calderbank
Space-time codes for high data rate wireless communication:
Performance Criterion and Code Construction
, IEEE Trans. On Information Theory March 1998 }
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8/10/2019 STBC2
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Mattias
Wennstrm
Signals &
Systems Group
Orthogonal Space-time Block Codes
STBC
Block of K
symbols
K input symbols, T output symbols TK
R=K/T is the code rateIf R=1 the STBC has full rate
If T= nt the code has minimum delayDetector is linear!!!
Block of T
symbols
nt transmit
antennas
Constellation
mapper
Data in
*{V.Tarokh, H.Jafarkhani, A.R.Calderbank
Space-time block codes from orthogonal designs,
IEEE Trans. On Information Theory June 1999 }
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Mattias
Wennstrm
Signals &
Systems Group
STBC for 2 Transmit Antennas
[ c0 c1 ]
*
01
*
10
cc
cc
Time
Antenna
Full rateand
minimum delay
1
*
02
*
111
012010
nchchr
nchchr
Assume 1 RX antenna:
Received signal at time 0
Received signal at time 1
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8/10/2019 STBC2
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Mattias
Wennstrm
Signals &
Systems Group
ncHr
1
0
*
1
0
*
1
*
2
21
*
1
0,,,
c
c
n
n
hh
hh
r
rcnHr
ncHnHcHHrHr ~~ 2***
FDiagonal matrix due to orthogonality
The MIMO/ MISO system is in fact
transformed to an equivalent SISO system
with SNR
SNReq= ||H ||F2SNR/nt
||H ||F2 =
1
2
1
2
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8/10/2019 STBC2
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Mattias
Wennstrm
Signals &
Systems Group
The existence of Orthogonal STBC
Real symbols : For nt=2,4,8 exists delay optimal
full rate codes.For nt=3,5,6,7,>8 exists full rate
codes with delay (T>K)
Complex symbols : For nt=2 exists delay optimal
full rate codes.For nt=3,4 exists rate 3/4 codes
For 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
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Mattias
Wennstrm
Signals &
Systems Group
Outage capacity of STBC
2
2 1log Ft
Hn
SNRCSTBC
HHn
SNR
ICt
detlog 2diversity
Optimal capacity
STBC is optimalwrt capacity if
HH= ||H||F2
which is the case for
MISO systemsLow rank channels
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Mattias
Wennstrm
Signals &
Systems Group
Performance of the STBC(Rayleigh faded channel)
||H ||F2 =
1
2
.. m
nt=4 transmit antennas and
nr is varied.
The PDF ofAssume BPSK modulation
BER is then given by
tr
tr
nn
b nn
nn
SNRP
tr 12
4
1
Diversity gain
nrnt which is
same as for
orthogonalchannels
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8/10/2019 STBC2
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Mattias
Wennstrm
Signals &
Systems Group
MIMO With Beamforming
Requires that channel His known at the transmitter
Is the capacity-optimal transmission strategy if
Cbeamforming= log2(1+SNR1) [bit/(Hzs)]
SNR12
11
Which is often true for line of sight (LOS) channels
Only one pipe is used
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8/10/2019 STBC2
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Mattias
Wennstrm
Signals &
Systems Group
Comparisons...
2 * 2 system. With specular component (Ricean fading)
One dominating
eigenvalue. BF putsall energy into
that pipe
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8/10/2019 STBC2
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Mattias
Wennstrm
Signals &
Systems Group
Correlated channels / Mutual coupling ...
When angle spread (D)
is small, we have a
dominating eigenvalue.
The mutual coupling
actually
improvesthe performanceof the STBC by making the
eigenvalues more equal
in magnitude.
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8/10/2019 STBC2
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Mattias
Wennstrm
Signals &
Systems Group
WCDMA Transmit diversity concept
(3GPP Release 99 with 2 TX antennas)
2 modesOpen 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 1Equal power and bit chooses phase between
{0,180} / {90/270}
Submode 2Bit one chooses power division {0.8 , 0.2} / {0.2 , 0.8}
and 3 bits chooses phase in an 8-PSK constellation
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8/10/2019 STBC2
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Mattias
Wennstrm
Signals &
Systems Group
GSM/EDGE Space time coding proposal
Frequency selective channel Require new software in terminals ..
Invented by Erik Lindskog
Time Reversal Space Time Coding (works for 2 antennas)
Time reversal Complex conjugate
Time reversal Complex conjugate -1
S(t)
S1(t)
S2(t)
Block
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Mattias
Wennstrm
Signals &
Systems Group
Take- home message
Channel capacity increases linearly
with min(nr, nt)
STBC is in the 3GPP WCDMA proposal