Waveform Design for the Massive MIMO Downlink - .Waveform Design for the Massive MIMO Downlink Erik

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  • MM

    YS

    Waveform Design for the Massive MIMO Downlink

    Erik G. Larsson

    May 27, 2014

    Div. of Communication SystemsDept. of Electrical Engineering (ISY)

    Linkoping UniversityLinkoping, Sweden

    www.commsys.isy.liu.se

  • Conventional Multiuser MIMO Precoding

    1/19

    Erik G. LarssonWaveform Design for the Massive MIMO Downlink

    Communication SystemsLinkoping University

  • A Unique Feature of the Massive MIMO Downlink

    I M K unused degrees of freedom

    I Channel nullspace:

    dim(null(HT )) =M K!

    I Exploit nullspace for hardware-friendly waveform shaping:

    y = HTx+w = HT (x+ z) +w if z null(HT )

    I Per-antenna constant envelope or low-PAR multiuser precoding

    2/19

    Erik G. LarssonWaveform Design for the Massive MIMO Downlink

    Communication SystemsLinkoping University

  • Discrete-Time Constant Envelope (DTCE) Precoding

    User 1

    User k

    User K

    Precoder

    {uk[n]}

    y1[n]

    yk[n]

    yK[n]

    psf

    psf

    psfChannel

    mf

    mf

    mf

    PA

    PA

    PA

    {u1[n]}

    {uK[n]}

    Not phase modulation! Not equal gain combining! Not constant modulus beamforming! Requires extra emitted power but allows for reduced PA backoff. Worth it?

    3/19

    Erik G. LarssonWaveform Design for the Massive MIMO Downlink

    Communication SystemsLinkoping University

  • Discrete-Time Constant-Envelope (DTCE) Precoding Algorithm

    I Channel model: yk[n] =

    P

    M

    Mm=1

    L1l=0

    hk,m[l]ejm[nl] + wk[n]

    =PEk uk[n] +

    P

    (Mm=1

    L1l=0 hk,m[l]e

    jm[nl]M

    Ekuk[n]

    )

    Jk[n] interference

    +wk[n]

    I Find {m[n]} via:

    min{m[n]}

    Nn=1

    Kk=1

    |Jk[n]|2.

    I Capacity lower bound, for uk[n] Gaussian with unit energy

    Rk = E

    log2 PEkP E[Jk JHk |H] + I1/N

    ' log2( PEkPJk + 1

    )

    I For fixed P , select {Ek} that maximizek Rk

    4/19

    Erik G. LarssonWaveform Design for the Massive MIMO Downlink

    Communication SystemsLinkoping University

  • Extra Power Cost of DTCE at R = 2 bpcu/terminal, M = 80, K = 10

    0 20 40 605

    4

    3

    2

    1

    0

    Window length

    Requir

    ed p

    ow

    er

    [dB

    ]L = 1, DTCE

    L = 4, DTCE

    L = 1, 4, Coop. lower bound

    5/19

    Erik G. LarssonWaveform Design for the Massive MIMO Downlink

    Communication SystemsLinkoping University

  • DTCE in Discrete vs. Continuous Time, RRC with = 0.3

    0.1 0.05 0 0.05 0.1 0.15

    0.1

    0.05

    0

    0.05

    0.1

    0.15Q

    uadra

    ture

    Am

    plit

    ude

    Inphase Amplitude

    (a) Discrete time

    0.1 0.05 0 0.05 0.1 0.15

    0.1

    0.05

    0

    0.05

    0.1

    0.15

    Inphase Amplitude

    Quadra

    ture

    Am

    plit

    ude

    PAR: 3.95 dB

    (b) Cont. time

    6/19

    Erik G. LarssonWaveform Design for the Massive MIMO Downlink

    Communication SystemsLinkoping University

  • Peak-to-Average Ratios, RRC with = 0.3

    SC TR-MRP 4-QAMOFDM MRP

    7/19

    Erik G. LarssonWaveform Design for the Massive MIMO Downlink

    Communication SystemsLinkoping University

  • Amplitude Transfer Characteristics

    8/19

    Erik G. LarssonWaveform Design for the Massive MIMO Downlink

    Communication SystemsLinkoping University

  • Amplifier DistortionI Transfer function (complex baseband)

    x(t) 7 y(t) = g(|x(t)|)ej arg x(t)+j(|x(t)|).I Example: Rapp Model (class B)

    g(|x|) = |x|/xmax

    (1 + (|x|/xmax)2p)1/(2p)

    (|x|) = 0I In-band distortion: with y=desired, y=actually received complex sample,

    NMSE =E[|y y|2]E[|y|2] , y = LMMSE est. of y

    Empirical observation: the error (y y) is independent of y in-band distortion effectively yields an extra noise term

    I Out-of-band distortion: Measured in terms of

    ACLR =maxf0,|f0|>B

    f0+B/2f0B/2

    Sx(f)df B/2B/2 Sx(f)df

    9/19

    Erik G. LarssonWaveform Design for the Massive MIMO Downlink

    Communication SystemsLinkoping University

  • In-Band Distortion, Example, M = 100

    2 1.5 1 0.5 0 0.5 1 1.5 22

    1.5

    1

    0.5

    0

    0.5

    1

    1.5

    2

    Inphase Amplitude

    Quadra

    ture

    Am

    plitu

    de

    10/19

    Erik G. LarssonWaveform Design for the Massive MIMO Downlink

    Communication SystemsLinkoping University

  • Out-of-Band Distortion, Example

    0 0.5 1 1.5 270

    60

    50

    40

    30

    20

    10

    0

    10P

    SD

    [dB

    ]

    Normalized Frequency, symbol rate = 1

    PA operation at 1dB compression

    10 dB back-off

    DTCE

    MRP

    11/19

    Erik G. LarssonWaveform Design for the Massive MIMO Downlink

    Communication SystemsLinkoping University

  • Amplifier Power Efficiency

    I For class B PA:

    =

    4 E[|x(t)|

    2]

    |ymax| E[|x(t)|] Pout

    Pin=

    1b,

    4 78%

    I Increased back-off (b) reduced

    I Max efficiency requires constant-envelope in continuous time (CPM)

    12/19

    Erik G. LarssonWaveform Design for the Massive MIMO Downlink

    Communication SystemsLinkoping University

  • Basic Tradeoff

    PAR (cont. time)

    Ra

    dia

    ted

    po

    we

    r to

    ach

    ieve

    ra

    te R

    10 dB4 dB

    P

    DTCE

    R-ZFZFMRP

    For MRP: Rk ' max log2(1 + M

    KP

    P+Dk+1

    ), P = Pcons.

    For ZF: Rk ' max log2(1 + MK

    KP

    Dk+1

    ), P = Pcons.

    For R-ZF: Rk ' max log2(1 +G P

    PJk+Dk+1

    ), P = Pcons.

    For DTCE: Rk ' maxEk, log2(

    PEkPJk+Dk+1

    ), P = Pcons.

    13/19

    Erik G. LarssonWaveform Design for the Massive MIMO Downlink

    Communication SystemsLinkoping University

  • In-Band Distortion versus Efficiency

    MRP and ZF

    14/19

    Erik G. LarssonWaveform Design for the Massive MIMO Downlink

    Communication SystemsLinkoping University

  • Out-Band Distortion versus Efficiency

    0 10 20 30 40 50 60 70 8090

    80

    70

    60

    50

    40

    30

    20

    10

    Efficiency [%]

    AC

    LR

    [dB

    ]

    20 dB

    DTCE

    MRP and ZF14 dB

    10 dB

    5.2 dB2.2 dB

    1.8 dB

    LTE

    15/19

    Erik G. LarssonWaveform Design for the Massive MIMO Downlink

    Communication SystemsLinkoping University

  • Amplifier Power Consumptionat the Optimal Operating Point

    0 10 20 30 40 50 60 70 80 90

    16/19

    Erik G. LarssonWaveform Design for the Massive MIMO Downlink

    Communication SystemsLinkoping University

  • Amplifier Power Consumptionat the Optimal Operating Point

    0 50 100 150 200

    17/19

    Erik G. LarssonWaveform Design for the Massive MIMO Downlink

    Communication SystemsLinkoping University

  • Conclusions and Future Work

    I Low-PAR precoding isI not likely to yield substantial net power savings, butI may greatly simplify the RF design

    I Massive MIMO vision:High-End Performance with Low-End Devices

    I Base stations built from handset technology!I Class-B, or similar, amplifiersoperating at (near) saturationI Using new low-PAR or CE waveformsI Per-antenna output power on the order of 20-50 mW

    I Ongoing work/unresolved issuesI Tightness of capacity boundsI Per-antenna continuous-time constant envelope (CPM-like) modulationI Imperfect CSI@TX

    18/19

    Erik G. LarssonWaveform Design for the Massive MIMO Downlink

    Communication SystemsLinkoping University

  • This talk was based on joint work with my colleagues

    Christopher Mollen (LiU, Sweden) Thomas Eriksson (Chalmers, Sweden) Saif K. Mohammed (IIT, Dehli)

    Thank You

    19/19

    Erik G. LarssonWaveform Design for the Massive MIMO Downlink

    Communication SystemsLinkoping University

  • Backup Slides

    20/19

    Erik G. LarssonWaveform Design for the Massive MIMO Downlink

    Communication SystemsLinkoping University

  • Complexity of ZF and DTCE

    For a block of N symbols

    I Zero-forcing requires O(NK2M) operations:I N pseudo inverses, each O(K2M),I N matrix-vector multiplications, each O(KM) andI (1 +K)M Fourier transforms (each transmit signal and each channel

    impulse response).

    I Discrete-time constant-envelope precoding requires O(NKML)operations.

    I summation of KL complex terms in each iterationI NM iterations needed, where 5

    21/19

    Erik G. LarssonWaveform Design for the Massive MIMO Downlink

    Communication SystemsLinkoping University