Robust Design for Multiuser Block DiagonalizationRobust Design for Multiuser Block DiagonalizationMIMO Downlink System with CSI Feedback Delay
CHANG YuyuanCHANG Yuyuan
Araki Sakaguchi LaboratoryAraki Sakaguchi LaboratoryMobile Communication Research Group
T k I tit t f T h lTokyo Institute of Technology
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ContentsContentsBackgroundgBlock diagonalizationCh l di tiChannel predictionMultiuser interferenceSimulation resultsC l iConclusion
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BackgroundBackgroundMultiuser MIMO System for Higher Spatial Di it G iDiversity Gain.
Block Diagonalization (BD): cancel the multiuser interference with designed precoding matrixinterference with designed precoding matrix.
The problem of BDBase station should know the channel stateBase station should know the channel state information (CSI): must feedback CSI.The CSI become outdated due to the time-varying e CS beco e outdated due to t e t e a y gnature of the channels.
Channel prediction was proposed for single guser MIMO, but unpredictable CSI error still remains.
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Multiuser MIMOMultiuser MIMOH1
N1
K
t r kN N N =s1
1
Nt
N
UE 1s1
1k=
BS: base station.UE: user equipments2
H2
BSUE 2
N2
s2 UE: user equipment.Hk: channel matrix for user kSk: data stream for user k
s2BS
NK
s2
sk
HKUE K
K
sk
The purpose:Analysis of multiuser interference.
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yRobust scheme for adaptive modulation.
System ModelSystem Model= +r HMs n
H: total channel matrixM: total pre-coding matrixs: data vector for users Received signal: s: data vector for usersn: received noise vector
g
1 1 1 1 r H s n
2 2 2 21 2 K
= +
r H s nM M ML
M M M M
K K K K
r H s n
If H M 0 fo ij
1 1 1 1 2 1 1 1K r H M H M H M s n
H M H M H ML1 1 1 1 1
r H M 0 s n
H M
If HiMj=0 for ij.
2 2 1 2 2 2 2 2K = +
r H M H M H M s nLM M M O M M M
2 2 2 2 2 = +
r H M s nM O M M
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1 2K K K K K K K r H M H M H M s nLK K K K K r 0 H M s n
Block Diagonalization (BD)
Block Diagonalization I
Aggregate channel matrix beside that of user k:
Block Diagonalization I
gg g
1 1 1TT T T T
k k k K + = H H H H H% L L
Null space:( ) ( )1 0 H H U 0 V V
%% % % % For null space of H%( ) ( )k k k k k = H U 0 V V
( ) ( )( ) ( )( ) ( )( ) ( )( )0 0 0 0 01 1 1TT T T T
k k k k k k k K k+ = =
H V H V H V H V H V 0% % % % % %L L
For null space of kH
Decoded signals:
( ) ( ) ( ) ( )1 1 1k k k k k k k K k + H V H V H V H V H V 0
Decoded signals:
Effective Channel
( ) ( ) ( )0 1 0 H H H V U 0 V V% ( ) ( )0 1M V V%
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( ) ( ) ( )0 1 0k k k k k k k = = H H V U 0 V V
( ) ( )0 1k k k=M V V
SVD: singular value decompositions.
Block Diagonalization IIBlock Diagonalization II
T itt d i lTransmitted signals:( ) ( )0 1
k k k k k k= =x M s V V s%{ }{ }
Hj jj
H
tr E
t E P
=
x x
Received signals:K
+r H x n
{ }Hj j tj tr E P = s s
( ) ( ) ( ) ( )
1
0 1 0 1
k k j kj
K
=
= +
r H x n
H V V H V V% %
Decoded signals:
( ) ( ) ( ) ( )0 1 0 1
1, k k k k k j j j k
j j k=
= + +H V V s H V V s nkH jM
Decoded signals:
( ) ( )0 1H H Hk k k k k k k k k k k k k = = + = +y U r U H V V s U n s n%
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k k k k k k k k k k k k kykH
Channel Prediction IChannel Prediction I( ) [ ]kh ( ) [ ]1kh ( ) [ ]2kh ( ) [ ]1kh L +
Wiener filter
DelayEstimatedCSI
Delay Delay
( ) [ ]kijh n ( ) [ ]1kijh n ( ) [ ]2kijh n ( ) [ ]1kijh n L +
( ),1kijw
( ),2kijw
( ),3kijw
( ),k Lijw
L( ) [ ] ( ) ( ) [ ] ( ) ( ) [ ],
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Lk k l k k H k
ij ij ij ij ijl
h n q w h n l n=
+ = + = w h
( ) [ ] ( ) [ ] ( ) [ ] ( ) [ ]( ) ( ) ( ) ( ), 1 , 2 ,
1 1Tk k k k
ij ij ij ij
k H k k k Lij ij ij ij
n h n h n h n L
w w w
= + =
h
w
L
L
8Reference: K. Kobayashi, etc., MIMO Systems in the Presence of Feedback Delay,IEICE Technical Report RCS2005-25 (2005-5).
ij ij ij ij
Channel Prediction IIChannel Prediction II
MMSE: MSE:
( )
( )
( )
, 1
, 21
kij
kijk
w
w
R
MMSE:
( ) [ ]22 11k Hk ij k k kE n
= = u R u
MSE:
( )
( )
1
,
ijkij k k
k Lw
= =
w R uM
[ ]k ij k k k ( ) [ ] ( ) [ ] ( ) [ ]k k kij ij ijn h n q h n q = + +
ijw
( ) [ ] ( ) [ ] ( ) [ ] ( ) [ ] ( ) [ ] ( ) [ ]( ) [ ] ( ) [ ] ( ) [ ] ( ) [ ] ( ) [ ] ( ) [ ]
1 1
1 2
k k k k k kij ij ij ij ij ij
k k k k k kij ij ij ij ij ij
E h n h n E h n h n E h n h n l
E h n h n E h n h n E h n h n l
+ + =R
L
L
( ) [ ] ( ) [ ]( ) [ ] ( ) [ ]1
k kij ij
k kij ij
E h n h n q
E h n h n q
=u
( ) [ ] ( ) [ ] ( ) [ ] ( ) [ ] ( ) [ ] ( ) [ ]1 2
k
k k k k k kij ij ij ij ij ijE h n h n l E h n h n l E h n h n
=
+ +
RM M O M
L ( ) [ ] ( ) [ ]1k kij ijE h n h n q l
=
+
uM
9Reference: K. Kobayashi, etc., MIMO Systems in the Presence of Feedback Delay,IEICE Technical Report RCS2005-25 (2005-5).
Mean Squared ErrorMean Squared Error
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SISOSISO
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2 X 2 MIMO2 X 2 MIMO
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Multiuser Interference IMultiuser Interference IChannel error matrix:
kH
kH
: real channel matrix.
: predicted channel matrixk : predicted channel matrix.
( )K
Received signals: ( )1,
k k k k k k j j kj j k
K
=
= + + +r H M s H M s n
( ) 11,
k k k k j kj j k
=
= + +H M s x nH =n U n
j j j=x M s
Decoded signals: ( ) 1
1 1
k k k k
KH
=
+ +
y H M r
s U x n
k k k=n U n
131,
k k k k j k kj j k
=
+ +s U x n
Multiuser Interference IIMultiuser Interference IIDecoded signal for user kg
Ergodic average of SINRg g
: average SNR.
: channel MSE.ith i l f
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: ith eigenvalue for effective channel matrix of user k.
Robust SchemeRobust SchemeThe estimated SINR for adaptive pmodulation:
If is set large the system will beIf is set large, the system will be more robust in multiuser interference, b l dbut lower transmit data rate.
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Throughput vs. Delay ( = 0)Throughput vs. Delay ( 0)
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Average SINRAverage SINR
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Throughput vs. Throughput vs.
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Throughput vs. (8 time slots delay)Throughput vs. (8 time slots delay)
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ConclusionConclusionIn BD MIMO downlink system with ychannel prediction,
we analyzed the multiuser interferencewe analyzed the multiuser interference caused by feedback delay , andwe proposed a robust scheme for adaptivewe proposed a robust scheme for adaptive modulation.
Future workUser scheduling for multiuser MIMO DL gsystem when Nr > Nt .
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