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Robust Design for Multiuser Block Design for Multiuser Block DiagonalizationRobust Design for Multiuser Block Diagonalization ... kkkkkkkk kk kk k ... IEICE Technical Report RCS2005-25

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  • 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

    1

  • ContentsContentsBackgroundgBlock diagonalizationCh l di tiChannel predictionMultiuser interferenceSimulation resultsC l iConclusion

    2

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know the channel stateBase station should know the channel state information (CSI): must feedback CSI.The CSI become outdated due to the time-varying e CS beco e outdated due to t e t e a y gnature of the channels.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

    3

  • 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.

    4

    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

    5

    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%

    6

    ( ) ( ) ( )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%

    7

    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( ) [ ] ( ) ( ) [ ] ( ) ( ) [ ],

    11

    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

    10

  • SISOSISO

    11

  • 2 X 2 MIMO2 X 2 MIMO

    12

  • 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

    14

    : 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.

    15

  • Throughput vs. Delay ( = 0)Throughput vs. Delay ( 0)

    16

  • Average SINRAverage SINR

    17

  • Throughput vs. Throughput vs.

    18

  • Throughput vs. (8 time slots delay)Throughput vs. (8 time slots delay)

    19

  • 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 .

    20