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TRANSMITTER
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#1
#1
Wireless
MIMO
channel
# nR
# nT
$% " , # # , " ! ! $% & $% $ ; , Q $ ? # $% .
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Chapter 1:
"Introduction"
Chapter 2:
"An Overview of Design
Strategies in Multi-Antenna
Systems"
Chapter 3:
"Joint Beamforming Design
in MIMO-OFDM SingleUser Communications"
Chapter 4:
"Joint Beamforming Design
in MIMO-OFDM MultiUser Communications"
Chapter 5:
"Sources of Imperfections
in the CSI and Robustness
Strategies"
Chapter 6:
"Robust Maximin Design of
MIMO Single-User
Communications"
Chapter 7:
"Conclusions and Future
Work"
Preceding block is required
Preceding block is recommended
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ROBUST
DESIGNS
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LINEAR PRE- AND
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no CSI
partial or
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perfect CSI
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BF
P samples (duration Ts)
D samples (duration TCP)
N samples (duration T)
cyclic prefix (CP)
n = -D,...,-1
xT(m,0)
xT(m,1)
xT(m,N-D-1)
xT(m,N-D)
xT(m,N-1)
D samples
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M @ ;
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;
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exp(j2 f0t)
s0(m)
s(n)
S/P
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exp(j2 fN-1t)
CP
addition
xT(n)
CP
addition
xT(n)
sN-1(m)
sampling frequency: fs
(a)
s0(m)
s(n)
IFFT
S/P
P/S
sN-1(m)
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n(n)
xT(n)
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Channel
h(n)
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P/S
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pre-beamforming
N
N
IFFT (OFDM
modulator)
N
s(n)
P/S
CP addition
#1
P/S
CP addition
# nT
CP removal
S/P
#1
CP removal
S/P
# nR
A;
b0
S/P
aN-1
s(m)
N
N
IFFT (OFDM
modulator)
(a)
post-beamforming
N
N
FFT (OFDM
demodulator)
N
a0
P/S
aN-1
N
N
FFT (OFDM
demodulator)
(b)
( ) %& " % & . G /
M
U
BF
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bp(0)
s0(m)
bp(1)
s1(m)
IFFT
modulation
+ P/S +
CP addition
s(m)
xT(p)(m,n)
bp(N-1)
sN-1(m)
(a)
a1*(k)
xR(1)(mP+n)
yk(1)(m)
CP removal
+ S/P +
FFT demodulation
a2*(k)
xR(2)(mP+n)
xR
(nR )
(mP+n)
yk(2)(m)
CP removal
+ S/P +
FFT demodulation
rk(m)
+
yk
CP removal
+ S/P +
FFT demodulation
( nR )(m)
dec{·}
QAM
demodulator
sk(n)
a n *(k)
R
(b)
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9 ' BA B: /
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M
9 + M
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M
9 + * 9 + * M
B;A
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AA
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AF
Cumulative Density Function of the Maximum Eigenvalues. As=30º (TX), 15º (RX). channel A.
1
0.9
0.8
Cumulative Density Function
0.7
0.6
0.5
0.4
0.3
0.2
1+1 antennas
2+2 antennas
3+4 antennas
5+5 antennas
0.1
0
0
5
10
15
Maximum eigenvalue
20
25
!0 12Ó 34Ó 5 ) 6 $5 K*%@@L ? ' " ! . K@;L ! N' %* *
" M
& ' M
BBA
9 + * ;
U
# ! ; 9 +
BB:
!
M ;
=.+ ! %* ! %* KD:L K8DA
( L = & " ) *##% % &+ %&, ##
AD
/
+
)
M
M
(
@
)
M
9 * 9 ;
; U
BBC
BB<
* 9 + + 9 * 9 +
M
BBF
B?A '
BB< M ;
) )
M @ 5* =.+ J G @ ! )
M
U
) BBD
. ! =.+ %* /
M ;
BA@
%* =.+
" $. " $. # ! %* $. !
+23+0 + +" ,
'
, %0+ 3 #
(
5 ( %0+ #
($ %
:@
%0+ #
#$ #
M
%0+ %0+ #
#
" B?A
# #
M
'
%0+ /
%0+
M %0+
M
"
+,"
M
M
+,"
BA;
. .>0 ! ( /
M
;
BA?
! %0+ %0+
M
! BAB
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;
BAA
5 %
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! + ! ! + !
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%
M
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23 ( 8
M
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9* ( 8
M
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M
M (
M
M ;
M ;
(
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3 ( 8
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:B
Maximum eigenvalues vs frequency
22
20
18
Maximum eigenvalues
16
14
12
10
8
6
4
2
0
0
10
20
30
Subcarrier index (k)
40
50
60
½ %& 8 19: $
' BF BD B;@ %0+
! 5*$. =.+%* .>0* / M ; J M ;@@ J $. %*
* ' BF BD B;@ ! . ( 5* " %0+ ( ' BF ' =.+ .>0 ! ! ' BD B;@ G $. %* *
.>0 !&
%0+ %0+ (&
M ;@@ J 5* ! G %* * ! $ $. 5* ! ' BF - # :A
Power allocation − GEOM − low P0
SNR − GEOM − low P0
1
0.04
0.8
SNR
power Pk
0.05
0.03
0.6
0.02
0.4
0.01
0.2
0
0
20
40
Subcarrier index (k)
0
60
0
Power allocation − CAP − low P0
0.04
0.8
SNR
power Pk
1
0.03
0.6
0.02
0.4
0.01
0.2
0
20
40
Subcarrier index (k)
60
SNR − CAP − low P0
0.05
0
20
40
Subcarrier index (k)
0
60
0
20
40
Subcarrier index (k)
60
Power allocation − GEOM − high P0
SNR − GEOM − high P0
30
2
25
power Pk
2.5
SNR
1.5
20
15
1
10
0.5
0
5
0
20
40
Subcarrier index (k)
0
60
0
Power allocation − CAP − high P
60
SNR − CAP − high P
0
0
2.5
30
2
25
power Pk
20
40
Subcarrier index (k)
SNR
1.5
20
15
1
10
0.5
0
5
0
20
40
Subcarrier index (k)
0
60
0
20
40
Subcarrier index (k)
60
* /. !$*
7
%& # %¼ ; 3 <& % & = %¼ ; 322 <&
) *##% % &+ %&, ##
Power allocation − HARM − low P0
SNR − HARM − low P0
1
0.04
0.8
SNR
power Pk
0.05
0.03
0.6
0.02
0.4
0.01
0.2
0
0
20
40
Subcarrier index (k)
0
60
0
Power allocation − MMSE − low P0
0.04
0.8
SNR
power Pk
1
0.03
0.4
0.01
0.2
20
40
Subcarrier index (k)
60
0.6
0.02
0
20
40
Subcarrier index (k)
SNR − MMSE − low P0
0.05
0
::
0
60
0
20
40
Subcarrier index (k)
60
Power allocation − HARM − high P0
SNR − HARM − high P0
30
2
25
power Pk
2.5
SNR
1.5
20
15
1
10
0.5
0
5
0
20
40
Subcarrier index (k)
0
60
0
Power allocation − MMSE − high P
60
SNR − MMSE − high P
0
0
2.5
30
2
25
power Pk
20
40
Subcarrier index (k)
SNR
1.5
20
15
1
10
0.5
0
5
0
20
40
Subcarrier index (k)
0
60
0
20
40
Subcarrier index (k)
60
* /. =$. 7
%& # %¼ ; 3 <& % & = %¼ ; 322 <&
- # :C
Power allocation − MAXMIN − low P0
SNR − MAXMIN − low P0
1
0.04
0.8
SNR
power Pk
0.05
0.03
0.6
0.02
0.4
0.01
0.2
0
0
20
40
Subcarrier index (k)
0
60
0
Power allocation − MEP − low P0
0.04
0.8
SNR
power Pk
1
0.03
0.6
0.02
0.4
0.01
0.2
0
20
40
Subcarrier index (k)
60
SNR − MEP − low P0
0.05
0
20
40
Subcarrier index (k)
0
60
0
20
40
Subcarrier index (k)
60
Power allocation − MAXMIN − high P0
SNR − MAXMIN − high P0
30
2
25
power Pk
2.5
SNR
1.5
20
15
1
10
0.5
0
5
0
20
40
Subcarrier index (k)
0
60
0
Power allocation − MEP − high P
60
SNR − MEP − high P
0
0
2.5
30
2
25
power Pk
20
40
Subcarrier index (k)
SNR
1.5
20
15
1
10
0.5
0
5
0
20
40
Subcarrier index (k)
0
60
0
20
40
Subcarrier index (k)
60
* /. $>/ *
7
%& # %¼ ; 3 <& % & = %¼ ; 322 <&
) *##% % &+ %&, ##
:<
3+4 antennas. BPSK. GEOM, CAP techniques. channel E. 2 interferences.
−1
uncoded effective BER
10
−2
10
CAP − SNR=5 dB − As=30º(TX), 15º(RX)
CAP − SNR=5 dB − As=40º(TX), 60º(RX)
GEOM − SNR=5 dB − As=30º(TX), 15º(RX)
GEOM − SNR=5 dB − As=40º(TX), 60º(RX)
CAP − SNR=10 dB − As=30º(TX), 15º(RX)
GEOM − SNR=10 dB − As=30º(TX), 15º(RX)
CAP − SNR=10 dB − As=40º(TX), 60º(RX)
GEOM − SNR=10 dB − As=40º(TX), 60º(RX)
−3
10
−15
−10
−5
0
SIR (dB)
5
10
15
! !$* 7
. . /. ? 4 32 5 1 : " ) 6 " ? 12Ó 34Ó 5 :2Ó @2Ó " A
7
( BB; ! =.+%* .>0*
BB? ' BD B;@ BBB " ! )*+ " %0+ %+ " / %0+ M
-
%+ M
-
.J50 '
' B;; 5* $. )*+ BUA " * ! ?:@ %+ ? ! %0+ / : ;@ ) G
B@
C@
;:
A@
' " 5* $. , 5* - # :F
2+2 antennas. BPSK. HARM, MMSE techniques. channel E.
−1
10
−2
uncoded effective BER
10
−3
10
MMSE − 1 interf. SIR=−5 dB − As=30º(TX), 15º(RX)
HARM − 1 interf. SIR=−5 dB − As=30º(TX), 15º(RX)
MMSE − 1 interf. SIR=−5 dB − As=40º(TX), 60º(RX)
HARM − 1 interf. SIR=−5 dB − As=40º(TX), 60º(RX)
MMSE − 0 interf. − As=30º(TX), 15º(RX)
HARM − 0 interf. − As=30º(TX), 15º(RX)
MMSE − 0 interf. − As=40º(TX), 60º(RX)
HARM − 0 interf. − As=40º(TX), 60º(RX)
−4
10
0
2
4
6
8
10
12
14
SNR (dB)
! =$. 7
. /. ? 3 ( . ; 4 5 A A " ) 6 " ? 12Ó 34Ó 5 :2Ó @2Ó . )*+ =.+ %* ! ' B;? ?U?
)*+ %0+ / %+ ! : ) " " " =.+ ! %0+ ) %* BB? =.+ %* =.+ '
%*
+ )*+
' B;B .>0 * )*+ . ( * & $G )*+ ) *##% % &+ %&, ##
:D
2+2 antennas. BPSK. MAXMIN, MEP techniques. channel E.
−1
10
−2
uncoded effective BER
10
−3
10
MAXMIN − 1 interf. SIR=−5 dB − As=30º(TX), 15º(RX)
MEP − 1 interf. SIR=−5 dB − As=30º(TX), 15º(RX)
MAXMIN − 1 interf. SIR=−5 dB − As=40º(TX), 60º(RX)
MEP − 1 interf. SIR=−5 dB − As=40º(TX), 60º(RX)
MAXMIN − 0 interf. − As=30º(TX), 15º(RX)
MEP − 0 interf. − As=30º(TX), 15º(RX)
MAXMIN − 0 interf. − As=40º(TX), 60º(RX)
MEP − 0 interf. − As=40º(TX), 60º(RX)
−4
10
0
2
4
6
8
10
12
14
SNR (dB)
! $>/ * 7
. /. ? 3 ( . ; 4 5 A A " ) 6 " ? 12Ó 34Ó 5 :2Ó @2Ó .>0 0 ( G
! ; ) %0+ .>0 * ' * ! ( .>0 . )*+ ' B;A B;: 5* %* =.+ .>0 ?U? ! B@
;:
/
%+ ! : ) ' B;A " . ! :@ ' B;: $ ! ;:@ '
"
! 5*
! .>0 =.+
! 0 %0+ - # C@
2+2 antennas. BPSK. As=30º (TX), 15º (RX). channel A.
−1
10
−2
uncoded effective BER
10
−3
10
GEOM − 1 interf. SIR=−5 dB
MAXMIN − 1 interf. SIR=−5 dB
MMSE − 1 interf. SIR=−5 dB
HARM − 1 interf. SIR=−5 dB
GEOM − 0 interf.
MMSE − 0 interf.
HARM − 0 interf.
MAXMIN − 0 interf.
−4
10
0
2
4
6
8
10
12
14
SNR (dB)
! 5 5 =$.5 $>/ 7
. /. ?
3 ( . ; 4 5 A A " ) 6 $ " 12Ó 34Ó .>0 =.+ 5 #"
$G .>0 &
)*+ BBB 0 5 .>0 =.+ %0+ %+ 0 %0+ .>0 )*+ 5* %* .>0 '
!
J ! ' B;A
B;: ' 5* !
.>0 =.+ $. %* *
) *##% % &+ %&, ##
C;
2+2 antennas. BPSK. As=30º (TX), 15º (RX). channel C.
−1
10
−2
uncoded effective BER
10
−3
10
GEOM − 1 interf. SIR=−5 dB
MMSE − 1 interf. SIR=−5 dB
MAXMIN − 1 interf. SIR=−5 dB
HARM − 1 interf. SIR=−5 dB
GEOM − 0 interf.
MMSE − 0 interf.
HARM − 0 interf.
MAXMIN − 0 interf.
−4
10
0
2
4
6
8
10
12
14
SNR (dB)
! 5 5 =$.5 $>/ 7
. /. ?
3 ( . ; 4 5 A A " ) 6 ! " 12Ó 34Ó &
# '
(
, ,
) #
" # (& %0+
. " G / 5* =.+ .>0 / $. %* *
.>0 =.+ ! G $ .>0 (& %0+ . ##" C?
%0+ ! G
( ! !
* & $G )*+ * ' ) *##% % &+ %&, ##
CB
#' "! '( )
*
%0+ %0+
M
M
B:@
( @ ! @ = ( " .
M
.
;
A
M
;
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M
$
M
#
;
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B:?
B:B
= ( "
M
K
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0
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M
;
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M
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( " .
/
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M
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K;
$%&
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B:A
!
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M
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M @ ;
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B:C
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1
Value of the temperature T. β=0.99
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0.8
0.7
0.6
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Main iteration
BEGIN
Initialization
2
b
0.95
2
b
Lar = 5
Initialization
Lar ?
T=1
= mean transmit
power with no MAI
(u)
bk = 0
2
b
T
0.9T
Lar < 5
Propose 100 solutions.
Na = number of nonaccepted solutions
Lar
Propose 100 solutions.
Na = number of nonaccepted solutions
Lar = 0
T
Lar+1
T
2T
0 < Na < 10
Na = 100
Na ?
Na < 95
95 < Na < 100
0.99T
Na ?
Na > 10
Na = 0
no
convergence ?
END
yes
END
(a)
(b)
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Initialization
Set all the transmit beamvectors equal to the
maximum eigenvectors of
(t(u),r(u)) H
Hk
(r(u))
O
In
-1
(k)Hk(t(u),r(u))
(without taking into account the MAI).
Calculate the power allocation: GEOM or MAXMIN.
Calculate the covariance
matrices:
(u)
{Rk }
Calculate the transmit beamvectors as the
maximum eigenvectors of
(t(u),r(u)) H
Hk
-1
(u)
(t(u),r(u))
Rk H k
Calculate the power allocation: GEOM or MAXMIN.
no
convergence ?
yes
END
( $ ( , ( !
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10
power
10
FD
1
10
5
10
0
10
8.5
9
9.5
user 1
user 2
user 3
10
x 10
0
10
0
1
2
3
4
5
flops
6
7
8
9
10
10
x 10
Simulated Annealing. Mean BER. Scenario 1.
0
10
mean BER
−100
−2
10
10
−200
10
−3
10
user 1
user 2
user 3
8.5
−300
10
0
1
2
3
4
5
flops
6
7
9
8
9.5
9
10
x 10
10
10
x 10
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Simulated Annealing. MTs power. Scenario 1.
10
1
10
power
10
5
10
0
10
8.5
user 1
user 2
user 3
9
9.5
10
x 10
0
10
0
1
2
3
4
5
flops
6
7
8
9
10
10
x 10
Simulated Annealing. Mean BER. Scenario 1.
0
10
−2
mean BER
−100
10
10
−200
10
−3
10
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user 2
user 3
−300
8.5
10
9
9.5
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0
1
2
3
4
5
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7
8
9
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10
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Simulated Annealing. MT’s power. Scenario 2.
10
D;
10
power
10
5
10
0
10
user 1
user 2
user 3
8.5
9
9.5
10
x 10
0
10
0
1
2
3
4
5
flops
6
7
8
9
10
10
x 10
Simulated Annealing. Mean BER. Scenario 2.
0
10
mean BER
−100
10
−2
10
−200
10
−3
10
user 1
user 2
user 3
−300
8.5
10
9
9.5
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0
1
2
3
4
5
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8
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2
10
power
user 3
user 1
1
10
user 2
user 1
user 2
user 3
0
10
0
1
2
3
4
5
flops
6
7
8
9
10
10
x 10
Gradient based method. Mean BER. Scenario 2.
−1
10
user 1
user 2
user 3
mean BER
user 3
−2
10
users 1,2
−3
10
0
1
2
3
4
5
flops
6
7
8
9
10
10
x 10
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4 TX ant. Quant. (4 bits). Non−robust
4 TX ant. Quant. (4 bits). Robust
4 TX ant. Gauss. noise power=0.01 − Non−robust
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Probability of service provision
1
0.9
Probability of service provision
0.8
0.7
0.6
0.5
0.4
0.3
nT=4, nR=4, SNRest=6 dB
nT=4, nR=4, SNRest=4 dB
nT=4, nR=4, SNRest=3 dB
nT=4, nR=4, SNRest=2 dB
nT=4, nR=4, SNRest=0 dB
nT=2, nR=2, SNRest=6 dB
0.2
0.1
0
−5
10
−4
−3
10
−2
−1
10
10
1−Pin (Probability of no QoS)
10
0
10
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Probability of service provision
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0.9
Probability of service provision
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0.7
0.6
0.5
0.4
0.3
nT=8, nR=8
nT=6, nR=6
nT=4, nR=4
nT=3, nR=3
nT=2, nR=2
n =1, n =1
0.2
0.1
T
0
−4
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0
2
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4
R
6
8
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System throughput with maximum BER constraints
8
Robust AM, nT=8, nR=8, g=0.4
Non−robust AM, nT=8, nR=8, g=0.4
Robust AM, nT=4, nR=4, g=0.6
Non−robust AM, nT=4, nR=4, g=0.6
Fixed modulation − Robust nT=4, nR=4, g=0.6
7
Throughput (bits/s/Hz)
6
5
4
16−QAM
3
2
QPSK
1
0
5
10
15
20
25
Maximum available power (dB)
30
35
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