Pushing IA to the(SNR) limit

M. Guillaud

Objectives

IA in theory...

... and in practiceVienna MIMO Testbed

IA Implementation

Performance Metrics

Measurement Results

Conclusion

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

Maxime Guillaudwith Martin Mayer, Gerald Artner, Martin Lerch, Gabor Hannak

Institute of TelecommunicationsVienna University of Technology

Vienna, Austriaguillaud@tuwien.ac.at

Scandinavian Workshop on Testbed-BasedWireless Research

KTH, Stockholm, November 27, 2013

institute oftelecommunications

1/20

Pushing IA to the(SNR) limit

M. Guillaud

Objectives

IA in theory...

... and in practiceVienna MIMO Testbed

IA Implementation

Performance Metrics

Measurement Results

Conclusion

Interference Alignment, Theory vs. Practice

Previous works on IA:I “simulated” IA [El Ayach,Peters,Heath 2009]I indoor, Ettus USRPs [Gollakota, Perli, Katabi, 2009]I indoor, Lyrtech [Gonzalez, Ramirez, Santamaria et al, 2011]I indoor, Ettus USRPs [Zetterberg, Moghadam, 2012]

Our objective: investigate the “fundamental” limits of IAI over-the-airI using lab-grade equipmentI in a standard-agnostic way

2/20

Pushing IA to the(SNR) limit

M. Guillaud

Objectives

IA in theory...

... and in practiceVienna MIMO Testbed

IA Implementation

Performance Metrics

Measurement Results

Conclusion

Interference Alignment, Theory vs. Practice

Previous works on IA:I “simulated” IA [El Ayach,Peters,Heath 2009]I indoor, Ettus USRPs [Gollakota, Perli, Katabi, 2009]I indoor, Lyrtech [Gonzalez, Ramirez, Santamaria et al, 2011]I indoor, Ettus USRPs [Zetterberg, Moghadam, 2012]

Our objective: investigate the “fundamental” limits of IAI over-the-airI using lab-grade equipmentI in a standard-agnostic way

2/20

Pushing IA to the(SNR) limit

M. Guillaud

Objectives

IA in theory...

... and in practiceVienna 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 6=kHkjxj + nk ∀k = 1 . . . K

3/20

Pushing IA to the(SNR) limit

M. Guillaud

Objectives

IA in theory...

... and in practiceVienna 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 6=kHkjxj + nk ∀k = 1 . . . K

3/20

Pushing IA to the(SNR) limit

M. Guillaud

Objectives

IA in theory...

... and in practiceVienna MIMO Testbed

IA Implementation

Performance Metrics

Measurement Results

Conclusion

Interference Alignment in Pictures

s1 H11

H21

H33

H23

n1

n2

n3

s2

s3

NT

NT

NT

NR

NR

NR

I Based on linear precoding: xi = Visi with si ∈ Cd

I Interference (in red) from multiple Tx aligns at the RxI Interference-free subspace used for communication

4/20

Pushing IA to the(SNR) limit

M. Guillaud

Objectives

IA in theory...

... and in practiceVienna MIMO Testbed

IA Implementation

Performance Metrics

Measurement Results

Conclusion

Mathematical formulation of IA1

I interference∑

j 6=i HijVjsj does not occupy all receivedimensions

I IA solution equivalent to finding matrices Vi and Ui

s.t.{

UHi HijVj = 0, ∀j 6= i

rank(UH

i HiiVi)

= di .

1K. Gomadam, V.R. Cadambe, S.A. Jafa, “A distributed numerical approach to interference alignment andapplications to wireless interference networks,” IEEE Trans. on Information Theory, June 2011.

5/20

Pushing IA to the(SNR) limit

M. Guillaud

Objectives

IA in theory...

... and in practiceVienna MIMO Testbed

IA Implementation

Performance Metrics

Measurement Results

Conclusion

Mathematical formulation of IA1

I interference∑

j 6=i HijVjsj does not occupy all receivedimensions

I IA solution equivalent to finding matrices Vi and Ui

s.t.{

UHi HijVj = 0, ∀j 6= i

rank(UH

i HiiVi)

= di .

1K. Gomadam, V.R. Cadambe, S.A. Jafa, “A distributed numerical approach to interference alignment andapplications to wireless interference networks,” IEEE Trans. on Information Theory, June 2011.

5/20

Pushing IA to the(SNR) limit

M. Guillaud

Objectives

IA in theory...

... and in practiceVienna MIMO Testbed

IA Implementation

Performance Metrics

Measurement Results

Conclusion

Why the hype ?

Some attractive properties

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

DoF = limSNR→+∞

Ci (SNR)

log SNR = d

BUT...I Extensive CSI requirements: Hij ∀j 6= iI What good is the DoF result at finite SNR ?

6/20

Pushing IA to the(SNR) limit

M. Guillaud

Objectives

IA in theory...

... and in practiceVienna MIMO Testbed

IA Implementation

Performance Metrics

Measurement Results

Conclusion

Why the hype ?

Some attractive properties

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

DoF = limSNR→+∞

Ci (SNR)

log SNR = d

BUT...I Extensive CSI requirements: Hij ∀j 6= iI What good is the DoF result at finite SNR ?

6/20

Pushing IA to the(SNR) limit

M. Guillaud

Objectives

IA in theory...

... and in practiceVienna MIMO Testbed

IA Implementation

Performance Metrics

Measurement Results

Conclusion

Why the hype ?

Some attractive properties

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

DoF = limSNR→+∞

Ci (SNR)

log SNR = d

BUT...I Extensive CSI requirements: Hij ∀j 6= iI What good is the DoF result at finite SNR ?

6/20

Pushing IA to the(SNR) limit

M. Guillaud

Objectives

IA in theory...

... and in practiceVienna MIMO Testbed

IA Implementation

Performance Metrics

Measurement Results

Conclusion

Why the hype ?

Some attractive properties

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

DoF = limSNR→+∞

Ci (SNR)

log SNR = d

BUT...I Extensive CSI requirements: Hij ∀j 6= iI What good is the DoF result at finite SNR ?

6/20

Pushing IA to the(SNR) limit

M. Guillaud

Objectives

IA in theory...

... and in practiceVienna MIMO Testbed

IA Implementation

Performance Metrics

Measurement Results

Conclusion

Why the hype ?

Some attractive properties

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

DoF = limSNR→+∞

Ci (SNR)

log SNR = d

BUT...I Extensive CSI requirements: Hij ∀j 6= iI What good is the DoF result at finite SNR ?

6/20

Pushing IA to the(SNR) limit

M. Guillaud

Objectives

IA in theory...

... and in practiceVienna MIMO Testbed

IA Implementation

Performance Metrics

Measurement Results

Conclusion

The Vienna MIMO Testbed Set-Up

I Replicate an urban outdoor-to-indoor and indoor-to-indoorscenario, with 3 Tx / 1 Rx

7/20

Pushing IA to the(SNR) limit

M. Guillaud

Objectives

IA in theory...

... and in practiceVienna MIMO Testbed

IA Implementation

Performance Metrics

Measurement Results

Conclusion

The Vienna MIMO Testbed Set-Up: Tx sideI 2 rooftop TX, Kathrein Scala Division XX-pol BTS antennas

I Indoor Tx, 2× Kathrein Scala Division X-pol directional ant.

8/20

Pushing IA to the(SNR) limit

M. Guillaud

Objectives

IA in theory...

... and in practiceVienna MIMO Testbed

IA Implementation

Performance Metrics

Measurement Results

Conclusion

The Vienna MIMO Testbed Set-Up: Rx side

I Rx using 4 custom-built λ2 dipoles in a laptop shell

I On a positioning table

9/20

Pushing IA to the(SNR) limit

M. Guillaud

Objectives

IA in theory...

... and in practiceVienna MIMO Testbed

IA Implementation

Performance Metrics

Measurement Results

Conclusion

Testbed Characteristics

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

LANI Center frequency 2.503 GHzI 200 MHz sampling rateI OFDM with 15.02 kHz subcarrier spacingI One instance of MATLAB at each node

10/20

Pushing IA to the(SNR) limit

M. Guillaud

Objectives

IA in theory...

... and in practiceVienna MIMO Testbed

IA Implementation

Performance Metrics

Measurement Results

Conclusion

IA-Specific Implementation Details

I Two additional “ghost” receivers to simulate the 3-user IC

I System dimensions allow IA with d = 2 streams per userI IA precoder computed in closed-form based on

eigendecompositionI Consider a single subcarrier to keep complexity low

11/20

Pushing IA to the(SNR) limit

M. Guillaud

Objectives

IA in theory...

... and in practiceVienna MIMO Testbed

IA Implementation

Performance Metrics

Measurement Results

Conclusion

Measurement Methodology

I Closed-loop system with periodic training sequences

(Tp ≈ 70ms)

12/20

Pushing IA to the(SNR) limit

M. Guillaud

Objectives

IA in theory...

... and in practiceVienna MIMO Testbed

IA Implementation

Performance Metrics

Measurement Results

Conclusion

Covariance-Based Performance Metrics

I Mutual informationI independent of the channel codeI upper bound for the achievable rate

I Consider the covariance at the receiver

E{

y1yH1}

= H11V1Qx1 VH1 HH

11︸ ︷︷ ︸desired signal

QS

+∑j=2,3

H1j Vj Qxj VHj HH

1j︸ ︷︷ ︸interference

QI

+ Qn1︸︷︷︸noiseQN

I Assuming Gaussian signals:

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

13/20

Pushing IA to the(SNR) limit

M. Guillaud

Objectives

IA in theory...

... and in practiceVienna MIMO Testbed

IA Implementation

Performance Metrics

Measurement Results

Conclusion

Covariance-Based Performance Metrics

I Mutual informationI independent of the channel codeI upper bound for the achievable rate

I Consider the covariance at the receiver

E{

y1yH1}

= H11V1Qx1 VH1 HH

11︸ ︷︷ ︸desired signal

QS

+∑j=2,3

H1j Vj Qxj VHj HH

1j︸ ︷︷ ︸interference

QI

+ Qn1︸︷︷︸noiseQN

I Assuming Gaussian signals:

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

13/20

Pushing IA to the(SNR) limit

M. Guillaud

Objectives

IA in theory...

... and in practiceVienna MIMO Testbed

IA Implementation

Performance Metrics

Measurement Results

Conclusion

Covariance-Based Performance Metrics

I Mutual informationI independent of the channel codeI upper bound for the achievable rate

I Consider the covariance at the receiver

E{

y1yH1}

= H11V1Qx1 VH1 HH

11︸ ︷︷ ︸desired signal

QS

+∑j=2,3

H1j Vj Qxj VHj HH

1j︸ ︷︷ ︸interference

QI

+ Qn1︸︷︷︸noiseQN

I Assuming Gaussian signals:

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

13/20

Pushing IA to the(SNR) limit

M. Guillaud

Objectives

IA in theory...

... and in practiceVienna MIMO Testbed

IA Implementation

Performance Metrics

Measurement Results

Conclusion

Covariance-Based Performance MetricsI Signal covariances estimated over the air

I With perfect CSIT: Qb=E{ybyHb }=[Ui U⊥

i ]diag(λ1,...,λ4)

[UH

i

U⊥i

H

]

14/20

Pushing IA to the(SNR) limit

M. Guillaud

Objectives

IA in theory...

... and in practiceVienna MIMO Testbed

IA Implementation

Performance Metrics

Measurement Results

Conclusion

Covariance-Based Performance MetricsI Signal covariances estimated over the air

I With perfect CSIT: Qb=E{ybyHb }=[Ui U⊥

i ]diag(λ1,...,λ4)

[UH

i

U⊥i

H

]

14/20

Pushing IA to the(SNR) limit

M. Guillaud

Objectives

IA in theory...

... and in practiceVienna MIMO Testbed

IA Implementation

Performance Metrics

Measurement Results

Conclusion

Spatial stationarity: 5 Rx positionsAligning interference from Tx2 and Tx3

15/20

Pushing IA to the(SNR) limit

M. Guillaud

Objectives

IA in theory...

... and in practiceVienna MIMO Testbed

IA Implementation

Performance Metrics

Measurement Results

Conclusion

Spatial stationarity: 5 Rx positionsCorresponding RSS for 5 positions

16/20

Pushing IA to the(SNR) limit

M. Guillaud

Objectives

IA in theory...

... and in practiceVienna MIMO Testbed

IA Implementation

Performance Metrics

Measurement Results

Conclusion

Spatial stationarity: 5 Rx positionsAligning interference from Tx1 and Tx2

17/20

Pushing IA to the(SNR) limit

M. Guillaud

Objectives

IA in theory...

... and in practiceVienna MIMO Testbed

IA Implementation

Performance Metrics

Measurement Results

Conclusion

Interference suppressionE{

λ3λ2

}for signal of interest from Tx 1, 2 and 3

signal/interference imbalance (PS /∑

PI ) [dB]

18/20

Pushing IA to the(SNR) limit

M. Guillaud

Objectives

IA in theory...

... and in practiceVienna 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

Pushing IA to the(SNR) limit

M. Guillaud

Objectives

IA in theory...

... and in practiceVienna 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

Pushing IA to the(SNR) limit

M. Guillaud

Objectives

IA in theory...

... and in practiceVienna MIMO Testbed

IA Implementation

Performance Metrics

Measurement Results

Conclusion

Conclusion

Experimental evidence (in our testbed) for

I Interference leakage (due to delayed CSI ? synchronization ?channel estimation noise ?)

Isupp ≈ 45− 50 dB at best

I Transmitter noise (below −20 dB SIR)

20/20

Pushing IA to the(SNR) limit

M. Guillaud

Thank you for your attention

Questions ?

21/20