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know the channel stateBase station should know the channel state information (CSI): must feedback CSI.The CSI become outdated due to the time-varying e CS beco e outdated due to t e t e a y gnature of the channels.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( ) [ ] ( ) ( ) [ ] ( ) ( ) [ ],

11ˆ

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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