# 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

May 27, 2014

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

www.commsys.isy.liu.se

• Conventional Multiuser MIMO Precoding

1/19

• 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

• 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

• 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

• 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

• 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

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

ture

Am

plit

ude

PAR: 3.95 dB

(b) Cont. time

6/19

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

SC TR-MRP 4-QAMOFDM MRP

7/19

• Amplitude Transfer Characteristics

8/19

• 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

• 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

ture

Am

plitu

de

10/19

• 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

• 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

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

• In-Band Distortion versus Efficiency

MRP and ZF

14/19

• 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

• Amplifier Power Consumptionat the Optimal Operating Point

0 10 20 30 40 50 60 70 80 90

16/19

• Amplifier Power Consumptionat the Optimal Operating Point

0 50 100 150 200

17/19

• 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

• 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

• Backup Slides

20/19

• 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

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