Robust Design for Multiuser Block … Design for Multiuser Block DiagonalizationRobust Design for...
Transcript of Robust Design for Multiuser Block … Design for Multiuser Block DiagonalizationRobust Design for...
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know the channel stateBase station should know the channel state information (CSI): must feedback CSI.The CSI become outdated due to the time-varying e CS beco e outdated due to t e t e a y gnature of the channels.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
HK
UE 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 i≠j
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 i≠j.
2 2 1 2 2 2 2 2K⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥= +⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥
r H M H M H M s nL
M M M O M M M2 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 1
TT 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 1′M V V%
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( ) ( ) ( )0 1 0k k k k k k k⎡ ⎤′ ′ ′ ′ ′= = ∑⎡ ⎤⎣ ⎦ ⎣ ⎦H H V U 0 V V ( ) ( )0 1
k 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 nk′H jM
Decoded signals:
( ) ( )0 1H H Hk k k k k k k k k k k k k′ ′ ′ ′ ′ ′= = + = Σ +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 kyk′H
Channel Prediction IChannel Prediction I( ) [ ]kh ( ) [ ]1kh ( ) [ ]2kh ( ) [ ]1kh L +
Wiener filter
DelayEstimatedCSI
Delay Delay
( ) [ ]kijh n ( ) [ ]1k
ijh n − ( ) [ ]2kijh n − ( ) [ ]1k
ijh n L− +
( ),1kijw ( ),2k
ijw ( ),3kijw ( ),k L
ijw
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 H
k ij k k kE nσ ε −⎡ ⎤= = −⎢ ⎥⎣ ⎦u R u
MSE:
( )
( )
1
,
ijkij k k
k Lw
⎢ ⎥= =⎢ ⎥⎢ ⎥⎢ ⎥⎣ ⎦
w R uM
[ ]k ij k k k⎢ ⎥⎣ ⎦( ) [ ] ( ) [ ] ( ) [ ]ˆk k kij ij ijn h n q h n qε = + − +
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:
kHˆ
kH
: real channel matrix.
: predicted channel matrixk : predicted channel matrix.
( )ˆK
∑Received signals: ( )1,
k k k k k k j j kj j k
K
ρ= ≠
= + + +∑r H M s H M s n
( ) 1
1, k k k k j k
j j kρ
= ≠
= + +∑H M s x n
H′ ′=n U nj j j=x M s
Decoded signals: ( ) 1
1 1
k k k k
KHρ
−
− −
=
′ ′ ′ ′≈ + ∑ +∑∑
y H M r
s U x n
k k k=n U n
131,
k k k k j k kj j k
ρ= ≠
≈ + ∑ +∑∑s U x n
Multiuser Interference IIMultiuser Interference IIDecoded signal for user kg
Ergodic average of SINRg g
: average SNR.
: channel MSE.i’th i l f
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: i’th eigenvalue for effective channel matrix of user k.
Robust SchemeRobust SchemeThe estimated SINR for adaptive pmodulation:
If α is set large the system will beIf α 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 (α = 0)Throughput vs. Delay (α 0)
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Average SINRAverage SINR
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Throughput vs. αThroughput vs. α
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Throughput vs. α (8 time slots delay)Throughput vs. α (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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