MM YS Conventional Multiuser MIMO Precoding 1/19 Erik G. Larsson - - PowerPoint PPT Presentation

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MM YS Conventional Multiuser MIMO Precoding 1/19 Erik G. Larsson - - PowerPoint PPT Presentation

Feb 21, 2023 32 likes •253 views

Waveform Design for the Massive MIMO Downlink Erik G. Larsson May 27, 2014 Div. of Communication Systems Dept. of Electrical Engineering (ISY) Link oping University Link oping, Sweden www.commsys.isy.liu.se MM YS Conventional

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SLIDE 1

MM YS

Waveform Design for the Massive MIMO Downlink

Erik G. Larsson May 27, 2014

  • Div. of Communication Systems
  • Dept. of Electrical Engineering (ISY)

Link¨

  • ping University

Link¨

  • ping, Sweden

www.commsys.isy.liu.se

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SLIDE 2

Conventional Multiuser MIMO Precoding

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SLIDE 3

A Unique Feature of the Massive MIMO Downlink

◮ M − K unused degrees of freedom ◮ Channel nullspace:

dim(null(HT )) = M − K!

◮ Exploit nullspace for hardware-friendly waveform shaping:

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

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

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SLIDE 4

“Discrete-Time Constant Envelope” (DTCE) Precoding

User 1 User k User K

Precoder

{uk[n]} y1[n] yk[n] yK[n]

psf psf psf

Channel ℋ ℋ

mf mf mf

P A P A P A

{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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SLIDE 5

Discrete-Time Constant-Envelope (DTCE) Precoding Algorithm

◮ 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 M

m=1

L−1

l=0 hk,m[l]ejθm[n−l]

√ M − √ Ekuk[n]

  • Jk[n]

“interference”

+ wk[n]

◮ Find {θm[n]} via:

min

{θm[n]} N

  • n=1

K

  • k=1

|Jk[n]|2.

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

Rk = E   log2    PEk

  • P · E[Jk JH

k | H] + I

  • 1/N

      log2

  • PEk

PJk + 1

  • ◮ For fixed P, select {Ek} that maximize

k Rk

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SLIDE 6

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

20 40 60 5 4 3 2 1

Window length Required power [dB] L = 1, DTCE L = 4, DTCE L = 1, 4, Coop. lower bound

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SLIDE 7

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

−0.1 −0.05 0.05 0.1 0.15 −0.1 −0.05 0.05 0.1 0.15

Quadrature Amplitude Inphase Amplitude (a) Discrete time

−0.1 −0.05 0.05 0.1 0.15 −0.1 −0.05 0.05 0.1 0.15

Inphase Amplitude Quadrature Amplitude

PAR: 3.95 dB

(b) Cont. time

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SLIDE 8

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

SC TR-MRP 4-QAM OFDM MRP

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SLIDE 9

Amplitude Transfer Characteristics

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Amplifier Distortion

◮ Transfer function (complex baseband)

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

◮ Example: Rapp Model (class B)

g(|x|) = α · |x|/xmax (1 + (|x|/xmax)2p)1/(2p) Φ(|x|) = 0

◮ In-band distortion: with y=desired, ˜

y=actually received complex sample, NMSE = E[|y − λ˜ y|2] E[|y|2] , λ˜ y = LMMSE est. of y Empirical observation: the error (y − λ˜ y) is independent of y ⇒ in-band distortion effectively yields an extra noise term

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

ACLR = maxf0,|f0|>B f0+B/2

f0−B/2 Sx(f)d

f B/2

−B/2 Sx(f)d

f

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SLIDE 11

In-Band Distortion, Example, M = 100

−2 −1.5 −1 −0.5 0.5 1 1.5 2 −2 −1.5 −1 −0.5 0.5 1 1.5 2

Inphase Amplitude Quadrature Amplitude

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SLIDE 12

Out-of-Band Distortion, Example

0.5 1 1.5 2 70 60 50 40 30 20 10 10

PSD [dB]

Normalized Frequency, symbol rate = 1 PA operation at 1dB compression 10 dB back-off DTCE MRP

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SLIDE 13

Amplifier Power Efficiency

◮ For class B PA:

η = π 4 · E[|x(t)|2] |ymax| · E[|x(t)|] ∼ Pout √Pin = 1 √ b , η ≤ π 4 ≈ 78%

◮ Increased back-off (b)

⇒ reduced η

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

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SLIDE 14

Basic Tradeoff

PAR (cont. time) Radiated power to achieve rate R 10 dB 4 dB ΔP DTCE R-ZF ZF MRP

⇒ For MRP: Rk maxη log2

  • 1 + M

K P P +Dk+1

  • ,

P = η · Pcons. ⇒ For ZF: Rk maxη log2

  • 1 + M−K

K P Dk+1

  • ,

P = η · Pcons. ⇒ For R-ZF: Rk maxη log2

  • 1 + G ·

P P Jk+Dk+1

  • ,

P = η · Pcons. ⇒ For DTCE: Rk maxEk,η log2

  • P Ek

P Jk+Dk+1

  • ,

P = η · Pcons.

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SLIDE 15

In-Band Distortion versus Efficiency

MRP and ZF

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SLIDE 16

Out-Band Distortion versus Efficiency

10 20 30 40 50 60 70 80 90 80 70 60 50 40 30 20 10

Efficiency η [%] ACLR [dB]

20 dB

DTCE MRP and ZF

14 dB 10 dB 5.2 dB 2.2 dB 1.8 dB

LTE

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SLIDE 17

Amplifier Power Consumption—at the Optimal Operating Point

10 20 30 40 50 60 70 80 90

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SLIDE 18

Amplifier Power Consumption—at the Optimal Operating Point

50 100 150 200

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Conclusions and Future Work

◮ Low-PAR precoding is

◮ not likely to yield substantial net power savings, but ◮ may greatly simplify the RF design

◮ Massive MIMO vision:

High-End Performance with Low-End Devices

◮ Base stations built from handset technology! ◮ Class-B, or similar, amplifiers—operating at (near) saturation ◮ Using new low-PAR or CE waveforms ◮ Per-antenna output power on the order of 20-50 mW

◮ Ongoing work/unresolved issues

◮ Tightness of capacity bounds ◮ Per-antenna continuous-time constant envelope (CPM-like) modulation ◮ Imperfect CSI@TX 18/19 Erik G. Larsson Waveform Design for the Massive MIMO Downlink Communication Systems Link¨

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SLIDE 20

This talk was based on joint work with my colleagues

  • Christopher Moll´

en (LiU, Sweden)

  • Thomas Eriksson (Chalmers, Sweden)
  • Saif K. Mohammed (IIT, Dehli)

Thank You

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SLIDE 21

Backup Slides

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SLIDE 22

Complexity of ZF and DTCE

For a block of N symbols

◮ Zero-forcing requires ∼ O(NK2M) operations:

◮ N pseudo inverses, each ∼ O(K2M), ◮ N matrix-vector multiplications, each ∼ O(KM) and ◮ (1 + K)M Fourier transforms (each transmit signal and each channel

impulse response).

◮ Discrete-time constant-envelope precoding requires ∼ O(NKML)

  • perations.

◮ summation of KL complex terms in each iteration ◮ κNM iterations needed, where κ ≈ 5 21/19 Erik G. Larsson Waveform Design for the Massive MIMO Downlink Communication Systems Link¨

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