Waveform Design for the Massive MIMO Downlink - …ctw2014.ieee-ctw.org/slides/session3/Larsson-CTW-presentation.pdf · Waveform Design for the Massive MIMO Downlink Erik G. Larsson

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

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“Discrete-Time Constant Envelope” (DTCE) Precoding

User 1

User k

User K

Precoder

{uk[n]}

y1[n]

yk[n]

yK[n]

psf

psf

psfChannel ℋ

ℋ

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?

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Discrete-Time Constant-Envelope (DTCE) Precoding Algorithm

I Channel model: yk[n] =

√P

M

M∑m=1

L−1∑l=0

hk,m[l]ejθm[n−l] + wk[n]

=√P√Ek uk[n] +

√P

(∑Mm=1

∑L−1l=0 hk,m[l]ejθm[n−l]√M

−√Ekuk[n]

)︸︷︷︸

Jk[n] “interference”

+wk[n]

I Find {θm[n]} via:

min{θm[n]}

N∑n=1

K∑k=1

|Jk[n]|2.

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

Rk = E

log2

PEk∣∣∣P · E[Jk JHk |H] + I∣∣∣1/N

' log2

(PEk

PJk + 1

)

I For fixed P , select {Ek} that maximize∑k Rk

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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

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DTCE in Discrete vs. Continuous Time, RRC with β = 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

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

SC TR-MRP 4-QAMOFDM MRP

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Amplitude Transfer Characteristics

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Amplifier DistortionI Transfer function (complex baseband)

x(t) 7→ y(t) = g(|x(t)|)ej arg x(t)+jΦ(|x(t)|).

I Example: Rapp Model (class B)

g(|x|) = α ·|x|/xmax

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

Φ(|x|) = 0

I In-band distortion: with y=desired, y=actually received complex sample,

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

Empirical observation: the error (y − λy) 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/2

f0−B/2Sx(f)df∫ B/2

−B/2 Sx(f)df

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In-Band Distortion, Example, M = 100

−2 −1.5 −1 −0.5 0 0.5 1 1.5 2−2

−1.5

−1

−0.5

0

0.5

1

1.5

2

Inphase Amplitude

Quadra

ture

Am

plitu

de

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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

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Amplifier Power Efficiency

I For class B PA:

η =π

4· E[|x(t)|2]|ymax| · E[|x(t)|] ∼

Pout√Pin

=1√b, η ≤ π

4≈ 78%

I Increased back-off (b) ⇒ reduced η

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

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Basic Tradeoff

PAR (cont. time)

Ra

dia

ted

po

we

r to

ach

ieve

ra

te R

10 dB4 dB

ΔP

DTCE

R-ZFZFMRP

⇒ For MRP: Rk ' maxη log2

(1 + M

KP

P+Dk+1

), P = η · Pcons.

⇒ For ZF: Rk ' maxη log2

(1 + M−K

KP

Dk+1

), P = η · Pcons.

⇒ For R-ZF: Rk ' maxη log2

(1 +G · P

PJk+Dk+1

), P = η · Pcons.

⇒ For DTCE: Rk ' maxEk,η log2

(PEk

PJk+Dk+1

), P = η · Pcons.

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In-Band Distortion versus Efficiency

MRP and ZF

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Out-Band Distortion versus Efficiency

0 10 20 30 40 50 60 70 8090

80

70

60

50

40

30

20

10

Efficiency η [%]

AC

LR

[dB

]

20 dB

DTCE

MRP and ZF14 dB

10 dB

5.2 dB2.2 dB

1.8 dB

LTE

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Amplifier Power Consumption—at the Optimal Operating Point

0 10 20 30 40 50 60 70 80 90

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Amplifier Power Consumption—at the Optimal Operating Point

0 50 100 150 200

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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, amplifiers—operating 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

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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

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Backup Slides

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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 κNM iterations needed, where κ ≈ 5

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Documents

Waveform Design for the Massive MIMO Downlink - …ctw2014.ieee-ctw.org/slides/session3/Larsson-CTW-presentation.pdf · Waveform Design for the Massive MIMO Downlink Erik G. Larsson