Pushing IA to the (SNR) Limit: M. Guillaud Experimental Results - - PowerPoint PPT Presentation

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Pushing IA to the (SNR) Limit: M. Guillaud Experimental Results - - PowerPoint PPT Presentation

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telecommunications institute of Pushing IA to the (SNR) limit Pushing IA to the (SNR) Limit: M. Guillaud Experimental Results from the Vienna MIMO Testbed Objectives IA in theory... ... and in practice Maxime Guillaud Vienna MIMO Testbed

slide-1
SLIDE 1

Pushing IA to the (SNR) limit

  • M. Guillaud

Objectives IA in theory... ... and in practice

Vienna MIMO Testbed IA Implementation Performance Metrics Measurement Results

Conclusion

Pushing IA to the (SNR) Limit: Experimental Results from the Vienna MIMO Testbed

Maxime Guillaud

with Martin Mayer, Gerald Artner, Martin Lerch, G´ abor Hann´ ak Institute of Telecommunications Vienna University of Technology Vienna, Austria guillaud@tuwien.ac.at

Scandinavian Workshop on Testbed-Based Wireless Research KTH, Stockholm, November 27, 2013

institute of telecommunications

1/20

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SLIDE 2

Pushing IA to the (SNR) limit

  • M. Guillaud

Objectives IA in theory... ... and in practice

Vienna MIMO Testbed IA Implementation Performance Metrics Measurement Results

Conclusion

Interference Alignment, Theory vs. Practice

Previous works on IA:

◮ “simulated” IA [El Ayach,Peters,Heath 2009] ◮ indoor, Ettus USRPs [Gollakota, Perli, Katabi, 2009] ◮ indoor, Lyrtech [Gonz´

alez, Ramirez, Santamaria et al, 2011]

◮ indoor, Ettus USRPs [Zetterberg, Moghadam, 2012]

Our objective: investigate the “fundamental” limits of IA

◮ over-the-air ◮ using lab-grade equipment ◮ in a standard-agnostic way

2/20

slide-3
SLIDE 3

Pushing IA to the (SNR) limit

  • M. Guillaud

Objectives IA in theory... ... and in practice

Vienna MIMO Testbed IA Implementation Performance Metrics Measurement Results

Conclusion

Interference Alignment, Theory vs. Practice

Previous works on IA:

◮ “simulated” IA [El Ayach,Peters,Heath 2009] ◮ indoor, Ettus USRPs [Gollakota, Perli, Katabi, 2009] ◮ indoor, Lyrtech [Gonz´

alez, Ramirez, Santamaria et al, 2011]

◮ indoor, Ettus USRPs [Zetterberg, Moghadam, 2012]

Our objective: investigate the “fundamental” limits of IA

◮ over-the-air ◮ using lab-grade equipment ◮ in a standard-agnostic way

2/20

slide-4
SLIDE 4

Pushing IA to the (SNR) limit

  • M. Guillaud

Objectives IA in theory... ... and in practice

Vienna MIMO Testbed IA Implementation Performance Metrics Measurement Results

Conclusion

K-user MIMO Interference Channel

Tx 1 Tx K Tx 2 Tx 3 Rx 1 Rx K Rx 2 Rx 3 yk = Hkkxk +

K

  • j=1,j=k

Hkjxj + nk ∀k = 1 . . . K

3/20

slide-5
SLIDE 5

Pushing IA to the (SNR) limit

  • M. Guillaud

Objectives IA in theory... ... and in practice

Vienna MIMO Testbed IA Implementation Performance Metrics Measurement Results

Conclusion

K-user MIMO Interference Channel

Tx 1 Tx K Tx 2 Tx 3 Rx 1 Rx K Rx 2 Rx 3 yk = Hkkxk +

K

  • j=1,j=k

Hkjxj + nk ∀k = 1 . . . K

3/20

slide-6
SLIDE 6

Pushing IA to the (SNR) limit

  • M. Guillaud

Objectives IA in theory... ... and in practice

Vienna MIMO Testbed IA Implementation Performance Metrics Measurement Results

Conclusion

Interference Alignment in Pictures

s 1

H11 H21 H33 H23

n1 n2 n3 s 2 s 3

NT NT NT NR NR NR

◮ Based on linear precoding: xi = Visi with si ∈ Cd ◮ Interference (in red) from multiple Tx aligns at the Rx ◮ Interference-free subspace used for communication

4/20

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SLIDE 7

Pushing IA to the (SNR) limit

  • M. Guillaud

Objectives IA in theory... ... and in practice

Vienna MIMO Testbed IA Implementation Performance Metrics Measurement Results

Conclusion

Mathematical formulation of IA1

◮ interference

j=i HijVjsj does not occupy all receive

dimensions

◮ IA solution equivalent to finding matrices Vi and Ui

s.t.

  • UH

i HijVj

= 0, ∀j = i rank

  • UH

i HiiVi

  • =

di.

  • 1K. Gomadam, V.R. Cadambe, S.A. Jafa, “A distributed numerical approach to interference alignment and

applications to wireless interference networks,” IEEE Trans. on Information Theory, June 2011. 5/20

slide-8
SLIDE 8

Pushing IA to the (SNR) limit

  • M. Guillaud

Objectives IA in theory... ... and in practice

Vienna MIMO Testbed IA Implementation Performance Metrics Measurement Results

Conclusion

Mathematical formulation of IA1

◮ interference

j=i HijVjsj does not occupy all receive

dimensions

◮ IA solution equivalent to finding matrices Vi and Ui

s.t.

  • UH

i HijVj

= 0, ∀j = i rank

  • UH

i HiiVi

  • =

di.

  • 1K. Gomadam, V.R. Cadambe, S.A. Jafa, “A distributed numerical approach to interference alignment and

applications to wireless interference networks,” IEEE Trans. on Information Theory, June 2011. 5/20

slide-9
SLIDE 9

Pushing IA to the (SNR) limit

  • M. Guillaud

Objectives IA in theory... ... and in practice

Vienna MIMO Testbed IA Implementation Performance Metrics Measurement Results

Conclusion

Why the hype ?

Some attractive properties

◮ Low-complexity processing, just linear filters ◮ Achieves the full channel degrees of freedom at high SNR

DoF = lim

SNR→+∞

Ci(SNR) log SNR = d

BUT...

◮ Extensive CSI requirements: Hij ∀j = i ◮ What good is the DoF result at finite SNR ?

6/20

slide-10
SLIDE 10

Pushing IA to the (SNR) limit

  • M. Guillaud

Objectives IA in theory... ... and in practice

Vienna MIMO Testbed IA Implementation Performance Metrics Measurement Results

Conclusion

Why the hype ?

Some attractive properties

◮ Low-complexity processing, just linear filters ◮ Achieves the full channel degrees of freedom at high SNR

DoF = lim

SNR→+∞

Ci(SNR) log SNR = d

BUT...

◮ Extensive CSI requirements: Hij ∀j = i ◮ What good is the DoF result at finite SNR ?

6/20

slide-11
SLIDE 11

Pushing IA to the (SNR) limit

  • M. Guillaud

Objectives IA in theory... ... and in practice

Vienna MIMO Testbed IA Implementation Performance Metrics Measurement Results

Conclusion

Why the hype ?

Some attractive properties

◮ Low-complexity processing, just linear filters ◮ Achieves the full channel degrees of freedom at high SNR

DoF = lim

SNR→+∞

Ci(SNR) log SNR = d

BUT...

◮ Extensive CSI requirements: Hij ∀j = i ◮ What good is the DoF result at finite SNR ?

6/20

slide-12
SLIDE 12

Pushing IA to the (SNR) limit

  • M. Guillaud

Objectives IA in theory... ... and in practice

Vienna MIMO Testbed IA Implementation Performance Metrics Measurement Results

Conclusion

Why the hype ?

Some attractive properties

◮ Low-complexity processing, just linear filters ◮ Achieves the full channel degrees of freedom at high SNR

DoF = lim

SNR→+∞

Ci(SNR) log SNR = d

BUT...

◮ Extensive CSI requirements: Hij ∀j = i ◮ What good is the DoF result at finite SNR ?

6/20

slide-13
SLIDE 13

Pushing IA to the (SNR) limit

  • M. Guillaud

Objectives IA in theory... ... and in practice

Vienna MIMO Testbed IA Implementation Performance Metrics Measurement Results

Conclusion

Why the hype ?

Some attractive properties

◮ Low-complexity processing, just linear filters ◮ Achieves the full channel degrees of freedom at high SNR

DoF = lim

SNR→+∞

Ci(SNR) log SNR = d

BUT...

◮ Extensive CSI requirements: Hij ∀j = i ◮ What good is the DoF result at finite SNR ?

6/20

slide-14
SLIDE 14

Pushing IA to the (SNR) limit

  • M. Guillaud

Objectives IA in theory... ... and in practice

Vienna MIMO Testbed IA Implementation Performance Metrics Measurement Results

Conclusion

The Vienna MIMO Testbed Set-Up

◮ Replicate an urban outdoor-to-indoor and indoor-to-indoor

scenario, with 3 Tx / 1 Rx

7/20

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SLIDE 15

Pushing IA to the (SNR) limit

  • M. Guillaud

Objectives IA in theory... ... and in practice

Vienna MIMO Testbed IA Implementation Performance Metrics Measurement Results

Conclusion

The Vienna MIMO Testbed Set-Up: Tx side

◮ 2 rooftop TX, Kathrein Scala Division XX-pol BTS antennas ◮ Indoor Tx, 2× Kathrein Scala Division X-pol directional ant.

8/20

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SLIDE 16

Pushing IA to the (SNR) limit

  • M. Guillaud

Objectives IA in theory... ... and in practice

Vienna MIMO Testbed IA Implementation Performance Metrics Measurement Results

Conclusion

The Vienna MIMO Testbed Set-Up: Rx side

◮ Rx using 4 custom-built λ

2 dipoles in a laptop shell

◮ On a positioning table

9/20

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SLIDE 17

Pushing IA to the (SNR) limit

  • M. Guillaud

Objectives IA in theory... ... and in practice

Vienna MIMO Testbed IA Implementation Performance Metrics Measurement Results

Conclusion

Testbed Characteristics

◮ 4 nodes (3 Tx + 1 Rx), 4 antennas per node ◮ Rubidium-synchronized clocks ◮ No duplexing, but high-speed feedback over dedicated fiber

LAN

◮ Center frequency 2.503 GHz ◮ 200 MHz sampling rate ◮ OFDM with 15.02 kHz subcarrier spacing ◮ One instance of MATLAB at each node

10/20

slide-18
SLIDE 18

Pushing IA to the (SNR) limit

  • M. Guillaud

Objectives IA in theory... ... and in practice

Vienna MIMO Testbed IA Implementation Performance Metrics Measurement Results

Conclusion

IA-Specific Implementation Details

◮ Two additional “ghost” receivers to simulate the 3-user IC ◮ System dimensions allow IA with d = 2 streams per user ◮ IA precoder computed in closed-form based on

eigendecomposition

◮ Consider a single subcarrier to keep complexity low

11/20

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SLIDE 19

Pushing IA to the (SNR) limit

  • M. Guillaud

Objectives IA in theory... ... and in practice

Vienna MIMO Testbed IA Implementation Performance Metrics Measurement Results

Conclusion

Measurement Methodology

◮ Closed-loop system with periodic training sequences (Tp ≈ 70ms)

12/20

slide-20
SLIDE 20

Pushing IA to the (SNR) limit

  • M. Guillaud

Objectives IA in theory... ... and in practice

Vienna MIMO Testbed IA Implementation Performance Metrics Measurement Results

Conclusion

Covariance-Based Performance Metrics

◮ Mutual information

◮ independent of the channel code ◮ upper bound for the achievable rate

◮ Consider the covariance at the receiver

E

  • y1yH

1

  • = H11V1Qx1VH

1 HH 11

  • desired signal

QS

+

  • j=2,3

H1jVjQxj VH

j HH 1j

  • interference

QI

+ Qn1

  • noise

QN

◮ Assuming Gaussian signals:

I(x1; y1) = log det (QI + QN + QS) − log det (QI + QN)

13/20

slide-21
SLIDE 21

Pushing IA to the (SNR) limit

  • M. Guillaud

Objectives IA in theory... ... and in practice

Vienna MIMO Testbed IA Implementation Performance Metrics Measurement Results

Conclusion

Covariance-Based Performance Metrics

◮ Mutual information

◮ independent of the channel code ◮ upper bound for the achievable rate

◮ Consider the covariance at the receiver

E

  • y1yH

1

  • = H11V1Qx1VH

1 HH 11

  • desired signal

QS

+

  • j=2,3

H1jVjQxj VH

j HH 1j

  • interference

QI

+ Qn1

  • noise

QN

◮ Assuming Gaussian signals:

I(x1; y1) = log det (QI + QN + QS) − log det (QI + QN)

13/20

slide-22
SLIDE 22

Pushing IA to the (SNR) limit

  • M. Guillaud

Objectives IA in theory... ... and in practice

Vienna MIMO Testbed IA Implementation Performance Metrics Measurement Results

Conclusion

Covariance-Based Performance Metrics

◮ Mutual information

◮ independent of the channel code ◮ upper bound for the achievable rate

◮ Consider the covariance at the receiver

E

  • y1yH

1

  • = H11V1Qx1VH

1 HH 11

  • desired signal

QS

+

  • j=2,3

H1jVjQxj VH

j HH 1j

  • interference

QI

+ Qn1

  • noise

QN

◮ Assuming Gaussian signals:

I(x1; y1) = log det (QI + QN + QS) − log det (QI + QN)

13/20

slide-23
SLIDE 23

Pushing IA to the (SNR) limit

  • M. Guillaud

Objectives IA in theory... ... and in practice

Vienna MIMO Testbed IA Implementation Performance Metrics Measurement Results

Conclusion

Covariance-Based Performance Metrics

◮ Signal covariances estimated over the air ◮ With perfect CSIT: Qb=E{ybyH

b }=[UiU⊥ i ]diag(λ1,...,λ4)

  • UH

i

U⊥

i H

  • 14/20
slide-24
SLIDE 24

Pushing IA to the (SNR) limit

  • M. Guillaud

Objectives IA in theory... ... and in practice

Vienna MIMO Testbed IA Implementation Performance Metrics Measurement Results

Conclusion

Covariance-Based Performance Metrics

◮ Signal covariances estimated over the air ◮ With perfect CSIT: Qb=E{ybyH

b }=[UiU⊥ i ]diag(λ1,...,λ4)

  • UH

i

U⊥

i H

  • 14/20
slide-25
SLIDE 25

Pushing IA to the (SNR) limit

  • M. Guillaud

Objectives IA in theory... ... and in practice

Vienna MIMO Testbed IA Implementation Performance Metrics Measurement Results

Conclusion

Spatial stationarity: 5 Rx positions

Aligning interference from Tx2 and Tx3

15/20

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SLIDE 26

Pushing IA to the (SNR) limit

  • M. Guillaud

Objectives IA in theory... ... and in practice

Vienna MIMO Testbed IA Implementation Performance Metrics Measurement Results

Conclusion

Spatial stationarity: 5 Rx positions

Corresponding RSS for 5 positions

16/20

slide-27
SLIDE 27

Pushing IA to the (SNR) limit

  • M. Guillaud

Objectives IA in theory... ... and in practice

Vienna MIMO Testbed IA Implementation Performance Metrics Measurement Results

Conclusion

Spatial stationarity: 5 Rx positions

Aligning interference from Tx1 and Tx2

17/20

slide-28
SLIDE 28

Pushing IA to the (SNR) limit

  • M. Guillaud

Objectives IA in theory... ... and in practice

Vienna MIMO Testbed IA Implementation Performance Metrics Measurement Results

Conclusion

Interference suppression

E λ3

λ2

for signal of interest from Tx 1, 2 and 3

signal/interference imbalance (PS/ PI) [dB] 18/20

slide-29
SLIDE 29

Pushing IA to the (SNR) limit

  • M. Guillaud

Objectives IA in theory... ... and in practice

Vienna MIMO Testbed IA Implementation Performance Metrics Measurement Results

Conclusion

Noise & Interference vs. Tx Power

Relative Tx power [dB]

Transmitter noise becomes significant at high Tx power!

19/20

slide-30
SLIDE 30

Pushing IA to the (SNR) limit

  • M. Guillaud

Objectives IA in theory... ... and in practice

Vienna MIMO Testbed IA Implementation Performance Metrics Measurement Results

Conclusion

Noise & Interference vs. Tx Power

Relative Tx power [dB]

Transmitter noise becomes significant at high Tx power!

19/20

slide-31
SLIDE 31

Pushing IA to the (SNR) limit

  • M. Guillaud

Objectives IA in theory... ... and in practice

Vienna MIMO Testbed IA Implementation Performance Metrics Measurement Results

Conclusion

Conclusion

Experimental evidence (in our testbed) for

◮ Interference leakage (due to delayed CSI ? synchronization ?

channel estimation noise ?) ¯ Isupp ≈ 45 − 50 dB at best

◮ Transmitter noise (below −20 dB SIR)

20/20

slide-32
SLIDE 32

Pushing IA to the (SNR) limit

  • M. Guillaud

Thank you for your attention

Questions ?

21/20