waveform design for the massive mimo downlink -...
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![Page 1: 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](https://reader031.vdocuments.us/reader031/viewer/2022022021/5b9ff16e09d3f2385c8c9445/html5/thumbnails/1.jpg)
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
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Conventional Multiuser MIMO Precoding
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Erik G. LarssonWaveform Design for the Massive MIMO Downlink
Communication SystemsLinkoping University
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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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Erik G. LarssonWaveform Design for the Massive MIMO Downlink
Communication SystemsLinkoping University
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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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Erik G. LarssonWaveform Design for the Massive MIMO Downlink
Communication SystemsLinkoping University
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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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Erik G. LarssonWaveform Design for the Massive MIMO Downlink
Communication SystemsLinkoping University
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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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Erik G. LarssonWaveform Design for the Massive MIMO Downlink
Communication SystemsLinkoping University
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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
6/19
Erik G. LarssonWaveform Design for the Massive MIMO Downlink
Communication SystemsLinkoping University
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Peak-to-Average Ratios, RRC with β = 0.3
SC TR-MRP 4-QAMOFDM MRP
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Erik G. LarssonWaveform Design for the Massive MIMO Downlink
Communication SystemsLinkoping University
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Amplitude Transfer Characteristics
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Erik G. LarssonWaveform Design for the Massive MIMO Downlink
Communication SystemsLinkoping University
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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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Erik G. LarssonWaveform Design for the Massive MIMO Downlink
Communication SystemsLinkoping University
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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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Erik G. LarssonWaveform Design for the Massive MIMO Downlink
Communication SystemsLinkoping University
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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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Erik G. LarssonWaveform Design for the Massive MIMO Downlink
Communication SystemsLinkoping University
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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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Erik G. LarssonWaveform Design for the Massive MIMO Downlink
Communication SystemsLinkoping University
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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.
13/19
Erik G. LarssonWaveform Design for the Massive MIMO Downlink
Communication SystemsLinkoping University
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In-Band Distortion versus Efficiency
MRP and ZF
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Erik G. LarssonWaveform Design for the Massive MIMO Downlink
Communication SystemsLinkoping University
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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
15/19
Erik G. LarssonWaveform Design for the Massive MIMO Downlink
Communication SystemsLinkoping University
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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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Erik G. LarssonWaveform Design for the Massive MIMO Downlink
Communication SystemsLinkoping University
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Amplifier Power Consumption—at the Optimal Operating Point
0 50 100 150 200
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Erik G. LarssonWaveform Design for the Massive MIMO Downlink
Communication SystemsLinkoping University
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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
18/19
Erik G. LarssonWaveform Design for the Massive MIMO Downlink
Communication SystemsLinkoping University
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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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Erik G. LarssonWaveform Design for the Massive MIMO Downlink
Communication SystemsLinkoping University
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Backup Slides
20/19
Erik G. LarssonWaveform Design for the Massive MIMO Downlink
Communication SystemsLinkoping University
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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
21/19
Erik G. LarssonWaveform Design for the Massive MIMO Downlink
Communication SystemsLinkoping University