waveform design for the massive mimo downlink -...
TRANSCRIPT
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
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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 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?
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
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
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 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
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
Amplitude Transfer Characteristics
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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)+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
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 2−2
−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:
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)
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
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
In-Band Distortion versus Efficiency
MRP and ZF
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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 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
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
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
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
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 κNM iterations needed, where κ ≈ 5
21/19
Erik G. LarssonWaveform Design for the Massive MIMO Downlink
Communication SystemsLinkoping University