Full-duplex MIMO: Spatial Processing and Characterization Alexios - - PowerPoint PPT Presentation

Telecommunications Circuits Laboratory

Full-duplex MIMO:

Spatial Processing and Characterization

Alexios Balatsoukas-Stimming, Pavle Belanovic, Konstantinos Alexandris, Raffael Hochreutener, Andreas Burg

Telecommunications Circuits Laboratory (TCL) École Polytechnique Fédérale de Lausanne (EPFL) CTW, May 26, 2014

Introduction Full-Duplex MIMO Full-Duplex MIMO Testbed Self-interference Characterization

What is ahead of us?... The capacity challenge

• Number of subscribers

saturates at a penetration slightly above 100

• Usage changes: from voice to

data

158 103

20 40 60 80 100 120 140 160 180

Netherlands Sweden

Example for growith of voice and data in % per year ‘08

• ’09

Voice Data

20 40 60 80 100 120 140

2010 2015 2020

Total mobile data traffic [Exa Bytes per year]

Source: UMTS Forum Report 44 forecasts 2010-2020 report

30X

Expect huge increase in mobile traffic

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Introduction Full-Duplex MIMO Full-Duplex MIMO Testbed Self-interference Characterization

Future networks will rely on small (femto) cells and WiFi offload

FD relay covers indoor area

WiFi offload

HD type

• 1 relay

extends coverage

Femto cells Micro cell Strong need for flexible short range links with high capacity, flexible spectrum usage, and for efficient relaying.

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Introduction Full-Duplex MIMO Full-Duplex MIMO Testbed Self-interference Characterization

Bi-directional wireless communications

Half-duplex (HD) - all wireless communication systems use this

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Introduction Full-Duplex MIMO Full-Duplex MIMO Testbed Self-interference Characterization

Bi-directional wireless communications

Half-duplex (HD) - all wireless communication systems use this

Time-division duplexing (TDD)

Wasted time resources: switching interval

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Introduction Full-Duplex MIMO Full-Duplex MIMO Testbed Self-interference Characterization

Bi-directional wireless communications

Half-duplex (HD) - all wireless communication systems use this

Time-division duplexing (TDD)

Wasted time resources: switching interval

Frequency-division duplexing (FDD)

Wasted frequency resources: guard bands

3/31

Introduction Full-Duplex MIMO Full-Duplex MIMO Testbed Self-interference Characterization

Bi-directional wireless communications

Half-duplex (HD) - all wireless communication systems use this

Time-division duplexing (TDD)

Wasted time resources: switching interval

Frequency-division duplexing (FDD)

Wasted frequency resources: guard bands

Full-duplex (FD) - a new and efficient alternative

Up to twice the throughput! No additional transmit power or bandwidth No wasted time or frequency resources

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Introduction Full-Duplex MIMO Full-Duplex MIMO Testbed Self-interference Characterization

Improved relaying

HD relay needs to alternate between reception and transmission

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Introduction Full-Duplex MIMO Full-Duplex MIMO Testbed Self-interference Characterization

Improved relaying

HD relay needs to alternate between reception and transmission FD relay provides continuous reception and transmission

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Introduction Full-Duplex MIMO Full-Duplex MIMO Testbed Self-interference Characterization

How to compare HD and FD

Transmit power allocation is critical

• Higher transmit power in HD simply improves the quality of the link
• In FD, with higher transmit power we get:

improved forward link higher self-interference

• Need to determine the best transmit power to use in FD

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Introduction Full-Duplex MIMO Full-Duplex MIMO Testbed Self-interference Characterization

A look at the capacities

fast link C FD node 1 FD node 2

1

slow link C

2

• Optimization problem:

max

P1,P2

(1 + α) C1 s.t. C2 = αC1 P1 ≤ P/2 P2 ≤ P/2 where: C1 = W log2

• 1 +

δP2 N0 + βP1

• , C2 = W log2
• 1 +

δP1 N0 + βP2

• W : bandwidth, δ : path loss, β : suppression, P1, P2: transmit power

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Introduction Full-Duplex MIMO Full-Duplex MIMO Testbed Self-interference Characterization

Comparing HD and FD: capacity

10 10

1

10

2

1 2 3 4 5 6 7 8 x 10

8

Distance (m) Capacity (bits/channel use)

β=−80dB, FD β=−90dB, FD β=−100dB, FD HD

FD can provide better capacity than HD! More self-interference suppression (β) ⇒ higher FD gain

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Introduction Full-Duplex MIMO Full-Duplex MIMO Testbed Self-interference Characterization

Comparing HD and FD: energy efficiency

10 10

1

10

2

0.5 1 1.5 2 2.5 3 3.5 4 x 10

8

Distance (m) Efficiency (bits/channel use/mW)

β=−80dB, FD β=−90dB, FD β=−100dB, FD HD

FD can provide better efficiency than HD! More self-interference suppression (β) ⇒ higher FD gain

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Introduction Full-Duplex MIMO Full-Duplex MIMO Testbed Self-interference Characterization

Outline

1 Introduction 2 Full-Duplex MIMO 3 Full-Duplex MIMO Testbed 4 Residual MIMO Self-interference Characterization

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Introduction Full-Duplex MIMO Full-Duplex MIMO Testbed Self-interference Characterization

Digital construction of cancelation signal

A flexible (and well-suited for MIMO) way of achieving cancellation

• Cancellation signal constructed

in the digital domain

• Uses an additional transmitter
• First built using WARP boards

(photo: A. Sahai et al./Rice University)

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Introduction Full-Duplex MIMO Full-Duplex MIMO Testbed Self-interference Characterization

A note on phase noise

• Phase noise: limiting factor in FD radios (Sahai 2013, Syrjala 2014)

[1]

• A. Sahai, G. Patel, C. Dick, A. Sabharwal, “On the Impact of Phase Noise on Active Cancelation in Wireless

Full-Duplex,” IEEE Trans. Vehicular Commun., 2013 [2]

• V. Syrjala, M. Valkama, L. Anttila, T. Riihonen, D. Korpi, “Analysis of Oscillator Phase-Noise Effects on

Self-Interference Cancellation in Full-Duplex OFDM Radio Transceivers,” IEEE Trans. Wireless Commun., 2014 11/31

Introduction Full-Duplex MIMO Full-Duplex MIMO Testbed Self-interference Characterization

A note on phase noise

• Phase noise: limiting factor in FD radios (Sahai 2013, Syrjala 2014)
• We are interested in the relative phase noise between Tx and Cx

[1]

• A. Sahai, G. Patel, C. Dick, A. Sabharwal, “On the Impact of Phase Noise on Active Cancelation in Wireless

Full-Duplex,” IEEE Trans. Vehicular Commun., 2013 [2]

• V. Syrjala, M. Valkama, L. Anttila, T. Riihonen, D. Korpi, “Analysis of Oscillator Phase-Noise Effects on

Self-Interference Cancellation in Full-Duplex OFDM Radio Transceivers,” IEEE Trans. Wireless Commun., 2014 11/31

Introduction Full-Duplex MIMO Full-Duplex MIMO Testbed Self-interference Characterization

A note on phase noise

• Phase noise: limiting factor in FD radios (Sahai 2013, Syrjala 2014)
• We are interested in the relative phase noise between Tx and Cx

Solution: share carrier between Cx and Tx → similar phase noise

Shared reference Shared carrier

[1]

• A. Sahai, G. Patel, C. Dick, A. Sabharwal, “On the Impact of Phase Noise on Active Cancelation in Wireless

Full-Duplex,” IEEE Trans. Vehicular Commun., 2013 [2]

• V. Syrjala, M. Valkama, L. Anttila, T. Riihonen, D. Korpi, “Analysis of Oscillator Phase-Noise Effects on

Self-Interference Cancellation in Full-Duplex OFDM Radio Transceivers,” IEEE Trans. Wireless Commun., 2014 11/31

Introduction Full-Duplex MIMO Full-Duplex MIMO Testbed Self-interference Characterization

A note on phase noise

• Phase noise: limiting factor in FD radios (Sahai 2013, Syrjala 2014)
• We are interested in the relative phase noise between Tx and Cx

Solution: share carrier between Cx and Tx → similar phase noise

Shared reference Shared carrier

The same approach can reduce the impact of sampling clock jitter

[1]

• A. Sahai, G. Patel, C. Dick, A. Sabharwal, “On the Impact of Phase Noise on Active Cancelation in Wireless

Full-Duplex,” IEEE Trans. Vehicular Commun., 2013 [2]

• V. Syrjala, M. Valkama, L. Anttila, T. Riihonen, D. Korpi, “Analysis of Oscillator Phase-Noise Effects on

Self-Interference Cancellation in Full-Duplex OFDM Radio Transceivers,” IEEE Trans. Wireless Commun., 2014 11/31

Introduction Full-Duplex MIMO Full-Duplex MIMO Testbed Self-interference Characterization

Cancelation results

20 MHz BW, 4 dBm transmit power

−10 −5 5 10 −120 −100 −80 −60 −40 −20 20 PowerpldBm) FrequencyplMHz) Txpl4dBm) Rxpl−14dBm) RFpSup.plsharedpref.)pl−51dBm) NoisepFloorpl−85dBm)

• Passive analog: -18 dB
• Active analog

Linear: -37 dB

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Introduction Full-Duplex MIMO Full-Duplex MIMO Testbed Self-interference Characterization

Cancelation results

20 MHz BW, 4 dBm transmit power

−10 −5 5 10 −120 −100 −80 −60 −40 −20 20 PowerpldBm) FrequencyplMHz) Txpl4dBm) Rxpl−14dBm) RFpSup.plsharedpref.)pl−51dBm) RFpSup.plsharedposc.)pl−62dBm) NoisepFloorpl−85dBm)

• Passive analog: -18 dB
• Active analog

Linear: -37 dB

• Red. phase noise: -11 dB

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Introduction Full-Duplex MIMO Full-Duplex MIMO Testbed Self-interference Characterization

Cancelation results

20 MHz BW, 4 dBm transmit power

−10 −5 5 10 −120 −100 −80 −60 −40 −20 20 PowerpgdBm3 FrequencypgMHz3 Txpg4dBm3 Rxpg−14dBm3 RFpSup.pgsharedpref.3pg−51dBm3 RFpSup.pgsharedposc.3pg−62dBm3 Dig.pSup.pg−63dBm3 NoisepFloorpg−85dBm3

• Passive analog: -18 dB
• Active analog

Linear: -37 dB

• Red. phase noise: -11 dB
• Total: -67 dB

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Introduction Full-Duplex MIMO Full-Duplex MIMO Testbed Self-interference Characterization

Cancelation results

20 MHz BW, 4 dBm transmit power

−10 −5 5 10 −120 −100 −80 −60 −40 −20 20 PowerpgdBm3 FrequencypgMHz3 Txpg4dBm3 Rxpg−14dBm3 RFpSup.pgsharedpref.3pg−51dBm3 RFpSup.pgsharedposc.3pg−62dBm3 Dig.pSup.pg−63dBm3 NoisepFloorpg−85dBm3

• Passive analog: -18 dB
• Active analog

Linear: -37 dB

• Red. phase noise: -11 dB
• Total: -67 dB
• Residual power: -63 dBm

12/31

Introduction Full-Duplex MIMO Full-Duplex MIMO Testbed Self-interference Characterization

Full-Duplex MIMO

• No cancellation:

y = Hx + Htxt + nr

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Introduction Full-Duplex MIMO Full-Duplex MIMO Testbed Self-interference Characterization

Full-Duplex MIMO

• No cancellation:

y = Hx + Htxt + nr

• Cancellation signal xc:

Hcxc = −Htxt

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Introduction Full-Duplex MIMO Full-Duplex MIMO Testbed Self-interference Characterization

Full-Duplex MIMO

• No cancellation:

y = Hx + Htxt + nr

• Cancellation signal xc:

Hcxc = −Htxt

• In practice, transmitted signals are affected by non-idealities:

˜ xt = xt + nt, ˜ xc = xc + nc

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Introduction Full-Duplex MIMO Full-Duplex MIMO Testbed Self-interference Characterization

Full-Duplex MIMO

• No cancellation:

y = Hx + Htxt + nr

• Cancellation signal xc:

Hcxc = −Htxt

• In practice, transmitted signals are affected by non-idealities:

˜ xt = xt + nt, ˜ xc = xc + nc

• Cancellation under transmit impairments:

y = Hx + Ht˜ xt + Hc˜ xc + nr = Hx + Htnt + Hcnc + nr

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Introduction Full-Duplex MIMO Full-Duplex MIMO Testbed Self-interference Characterization

Full-Duplex MIMO

• No cancellation:

y = Hx + Htxt + nr

• Cancellation signal xc:

Hcxc = −Htxt

• In practice, transmitted signals are affected by non-idealities:

˜ xt = xt + nt, ˜ xc = xc + nc

• Cancellation under transmit impairments:

y = Hx + Ht˜ xt + Hc˜ xc + nr = Hx + Htnt + Hcnc + nr Effective noise: neff Htnt + Hcnc + nr

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Introduction Full-Duplex MIMO Full-Duplex MIMO Testbed Self-interference Characterization

2 × 2 Full-Duplex MIMO Testbed hardware

• We wish to characterize the effective noise neff to:

1 Better understand transmit impairments → improved cancellation

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Introduction Full-Duplex MIMO Full-Duplex MIMO Testbed Self-interference Characterization

2 × 2 Full-Duplex MIMO Testbed hardware

• We wish to characterize the effective noise neff to:

1 Better understand transmit impairments → improved cancellation 2 Assess whether neff follows usual assumptions → better receivers

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Introduction Full-Duplex MIMO Full-Duplex MIMO Testbed Self-interference Characterization

2 × 2 Full-Duplex MIMO Testbed hardware

• We wish to characterize the effective noise neff to:

1 Better understand transmit impairments → improved cancellation 2 Assess whether neff follows usual assumptions → better receivers

• National Instruments

PXIe-1082

4× NI 5791R RF transceivers Circulator-based anntena front-end

14/31

Introduction Full-Duplex MIMO Full-Duplex MIMO Testbed Self-interference Characterization

2 × 2 Full-Duplex MIMO Testbed hardware

• We wish to characterize the effective noise neff to:

1 Better understand transmit impairments → improved cancellation 2 Assess whether neff follows usual assumptions → better receivers

• National Instruments

PXIe-1082

4× NI 5791R RF transceivers Circulator-based anntena front-end

• 1× Desktop PC

Runs Windows with LabVIEW

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Introduction Full-Duplex MIMO Full-Duplex MIMO Testbed Self-interference Characterization

Measurement setup

• 2.45 GHz carrier, 0 dBm transmit power

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Introduction Full-Duplex MIMO Full-Duplex MIMO Testbed Self-interference Characterization

Measurement setup

• 2.45 GHz carrier, 0 dBm transmit power
• 15 cm antenna spacing

15/31

Introduction Full-Duplex MIMO Full-Duplex MIMO Testbed Self-interference Characterization

Measurement setup

• 2.45 GHz carrier, 0 dBm transmit power
• 15 cm antenna spacing
• 10 MHz bandwidth, 256 OFDM carriers, QPSK modulation

15/31

Introduction Full-Duplex MIMO Full-Duplex MIMO Testbed Self-interference Characterization

Measurement setup

• 2.45 GHz carrier, 0 dBm transmit power
• 15 cm antenna spacing
• 10 MHz bandwidth, 256 OFDM carriers, QPSK modulation
• Nf = 100 OFDM frames consisting of 40 OFDM symbols

15/31

Introduction Full-Duplex MIMO Full-Duplex MIMO Testbed Self-interference Characterization

Measurement setup

• 2.45 GHz carrier, 0 dBm transmit power
• 15 cm antenna spacing
• 10 MHz bandwidth, 256 OFDM carriers, QPSK modulation
• Nf = 100 OFDM frames consisting of 40 OFDM symbols
• Remote signal x is absent (Rx at max. sensitivity)

15/31

Introduction Full-Duplex MIMO Full-Duplex MIMO Testbed Self-interference Characterization

Measurement setup

• 2.45 GHz carrier, 0 dBm transmit power
• 15 cm antenna spacing
• 10 MHz bandwidth, 256 OFDM carriers, QPSK modulation
• Nf = 100 OFDM frames consisting of 40 OFDM symbols
• Remote signal x is absent (Rx at max. sensitivity)
• Channel estimation is performed with a “very long” aperiodic

sequence to minimize error

15/31

Introduction Full-Duplex MIMO Full-Duplex MIMO Testbed Self-interference Characterization

Measurement setup

• 2.45 GHz carrier, 0 dBm transmit power
• 15 cm antenna spacing
• 10 MHz bandwidth, 256 OFDM carriers, QPSK modulation
• Nf = 100 OFDM frames consisting of 40 OFDM symbols
• Remote signal x is absent (Rx at max. sensitivity)
• Channel estimation is performed with a “very long” aperiodic

sequence to minimize error

• Residual noise recorded in 2 × N matrix N

15/31

Introduction Full-Duplex MIMO Full-Duplex MIMO Testbed Self-interference Characterization

Measurement setup

• 2.45 GHz carrier, 0 dBm transmit power
• 15 cm antenna spacing
• 10 MHz bandwidth, 256 OFDM carriers, QPSK modulation
• Nf = 100 OFDM frames consisting of 40 OFDM symbols
• Remote signal x is absent (Rx at max. sensitivity)
• Channel estimation is performed with a “very long” aperiodic

sequence to minimize error

• Residual noise recorded in 2 × N matrix N
• Statistical metrics used for effective noise characterization:

15/31

Introduction Full-Duplex MIMO Full-Duplex MIMO Testbed Self-interference Characterization

Measurement setup

• 2.45 GHz carrier, 0 dBm transmit power
• 15 cm antenna spacing
• 10 MHz bandwidth, 256 OFDM carriers, QPSK modulation
• Nf = 100 OFDM frames consisting of 40 OFDM symbols
• Remote signal x is absent (Rx at max. sensitivity)
• Channel estimation is performed with a “very long” aperiodic

sequence to minimize error

• Residual noise recorded in 2 × N matrix N
• Statistical metrics used for effective noise characterization:

1 Autocorrelation per receiver (to assess memory)

15/31

Introduction Full-Duplex MIMO Full-Duplex MIMO Testbed Self-interference Characterization

Measurement setup

• 2.45 GHz carrier, 0 dBm transmit power
• 15 cm antenna spacing
• 10 MHz bandwidth, 256 OFDM carriers, QPSK modulation
• Nf = 100 OFDM frames consisting of 40 OFDM symbols
• Remote signal x is absent (Rx at max. sensitivity)
• Channel estimation is performed with a “very long” aperiodic

sequence to minimize error

• Residual noise recorded in 2 × N matrix N
• Statistical metrics used for effective noise characterization:

1 Autocorrelation per receiver (to assess memory) 2 Pseudo-variance and correlation between real and imaginary parts (to

assess circularity)

15/31

Introduction Full-Duplex MIMO Full-Duplex MIMO Testbed Self-interference Characterization

Measurement setup

• 2.45 GHz carrier, 0 dBm transmit power
• 15 cm antenna spacing
• 10 MHz bandwidth, 256 OFDM carriers, QPSK modulation
• Nf = 100 OFDM frames consisting of 40 OFDM symbols
• Remote signal x is absent (Rx at max. sensitivity)
• Channel estimation is performed with a “very long” aperiodic

sequence to minimize error

• Residual noise recorded in 2 × N matrix N
• Statistical metrics used for effective noise characterization:

1 Autocorrelation per receiver (to assess memory) 2 Pseudo-variance and correlation between real and imaginary parts (to

assess circularity)

3 Histograms (to assess distribution)

15/31

Introduction Full-Duplex MIMO Full-Duplex MIMO Testbed Self-interference Characterization

Measurement setup

• 2.45 GHz carrier, 0 dBm transmit power
• 15 cm antenna spacing
• 10 MHz bandwidth, 256 OFDM carriers, QPSK modulation
• Nf = 100 OFDM frames consisting of 40 OFDM symbols
• Remote signal x is absent (Rx at max. sensitivity)
• Channel estimation is performed with a “very long” aperiodic

sequence to minimize error

• Residual noise recorded in 2 × N matrix N
• Statistical metrics used for effective noise characterization:

1 Autocorrelation per receiver (to assess memory) 2 Pseudo-variance and correlation between real and imaginary parts (to

assess circularity)

3 Histograms (to assess distribution) 4 Spatial covariance matrix (to assess spatial correlation)

15/31

Introduction Full-Duplex MIMO Full-Duplex MIMO Testbed Self-interference Characterization

Autocorrelation

• The autocorrelation of each element of neff is estimated as

ˆ Ri,j =

   N−j−1

k=0

Ni,j+kN∗

i,k,

j ≥ 0, ˆ R∗

i,−j,

j < 0,

16/31

Introduction Full-Duplex MIMO Full-Duplex MIMO Testbed Self-interference Characterization

Autocorrelation

• The autocorrelation of each element of neff is estimated as

ˆ Ri,j =

   N−j−1

k=0

Ni,j+kN∗

i,k,

j ≥ 0, ˆ R∗

i,−j,

j < 0,

−100 −50 50 100 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Lags Autocorrelation

Time domain Frequency domain

• Time domain: neff has non-negligible memory

16/31

Introduction Full-Duplex MIMO Full-Duplex MIMO Testbed Self-interference Characterization

Autocorrelation

• The autocorrelation of each element of neff is estimated as

ˆ Ri,j =

   N−j−1

k=0

Ni,j+kN∗

i,k,

j ≥ 0, ˆ R∗

i,−j,

j < 0,

−100 −50 50 100 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Lags Autocorrelation −100 −50 50 100 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Autocorrelation Lags

Time domain Frequency domain

• Time domain: neff has non-negligible memory
• Frequency domain: neff is practically memoryless

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Introduction Full-Duplex MIMO Full-Duplex MIMO Testbed Self-interference Characterization

Pseudo-variance

• For each chain i, the pseudo-variance is defined as:

τ 2

i E

• n2

eff,i

• 17/31

Introduction Full-Duplex MIMO Full-Duplex MIMO Testbed Self-interference Characterization

Pseudo-variance

• For each chain i, the pseudo-variance is defined as:

τ 2

i E

• n2

eff,i

• A smaller pseudo-variance indicates a more circular random

variable

17/31

Introduction Full-Duplex MIMO Full-Duplex MIMO Testbed Self-interference Characterization

Pseudo-variance

• For each chain i, the pseudo-variance is defined as:

τ 2

i E

• n2

eff,i

• A smaller pseudo-variance indicates a more circular random

variable

• We empirically estimate τ 2

i as

ˆ τ 2

i = 1

N

N

• j=1

N2

i,j

17/31

Introduction Full-Duplex MIMO Full-Duplex MIMO Testbed Self-interference Characterization

Pseudo-variance

• For each chain i, the pseudo-variance is defined as:

τ 2

i E

• n2

eff,i

• A smaller pseudo-variance indicates a more circular random

variable

• We empirically estimate τ 2

i as

ˆ τ 2

i = 1

N

N

• j=1

N2

i,j

• Time domain: |ˆ

τ 2

1 | ≈ 10−3

• Frequency domain: |ˆ

τ 2

1 | ≈ 10−5 → more circular

17/31

Introduction Full-Duplex MIMO Full-Duplex MIMO Testbed Self-interference Characterization

Histograms

• Joint histogram of R(N1,j) and I(N1,j)

Time domain Frequency domain

• Time domain: R(N1,j) and I(N1,j) are strongly correlated

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Introduction Full-Duplex MIMO Full-Duplex MIMO Testbed Self-interference Characterization

Histograms

• Joint histogram of R(N1,j) and I(N1,j)

Time domain Frequency domain

• Time domain: R(N1,j) and I(N1,j) are strongly correlated
• Freq. domain: R(N1,j) and I(N1,j) are practically uncorrelated

18/31

Introduction Full-Duplex MIMO Full-Duplex MIMO Testbed Self-interference Characterization

Histograms

• Histogram of R(N1,j)

−0.2 −0.15 −0.1 −0.05 0.05 0.1 0.15 0.2 2 4 6 8 10 12 Data Density Histogram t Location−Scale Normal

Time domain Frequency domain

• Time domain: Not Gaussian (Student’s t-distribution is good fit)

19/31

Introduction Full-Duplex MIMO Full-Duplex MIMO Testbed Self-interference Characterization

Histograms

• Histogram of R(N1,j)

−0.2 −0.15 −0.1 −0.05 0.05 0.1 0.15 0.2 2 4 6 8 10 12 Data Density Histogram t Location−Scale Normal −0.2 −0.1 0.1 0.2 1 2 3 4 5 6 7 8 9 10 Data Density Histogram t Location−Scale Normal

Time domain Frequency domain

• Time domain: Not Gaussian (Student’s t-distribution is good fit)
• Frequency domain: Gaussian (central limit theorem)

19/31

Introduction Full-Duplex MIMO Full-Duplex MIMO Testbed Self-interference Characterization

Spatial covariance matrices

• Spatial covariance matrix: K E
• (neff − E[neff]) (neff − E[neff])H

Measurements are specific to our setup. However, the variance of ˆ Ktime over time and ˆ Kfreq

• ver the frequency tones is small compared to the magnitude of the entries.

20/31

Introduction Full-Duplex MIMO Full-Duplex MIMO Testbed Self-interference Characterization

Spatial covariance matrices

• Spatial covariance matrix: K E
• (neff − E[neff]) (neff − E[neff])H
• We empirically estimate K as ˆ

K = 1

N (N − m) (N − m)H

• mi = 1

N

N

k=1 Ni,k, i = 1, 2, is the ML estimate of E[neff] Measurements are specific to our setup. However, the variance of ˆ Ktime over time and ˆ Kfreq

• ver the frequency tones is small compared to the magnitude of the entries.

20/31

Introduction Full-Duplex MIMO Full-Duplex MIMO Testbed Self-interference Characterization

Spatial covariance matrices

• Spatial covariance matrix: K E
• (neff − E[neff]) (neff − E[neff])H
• We empirically estimate K as ˆ

K = 1

N (N − m) (N − m)H

• mi = 1

N

N

k=1 Ni,k, i = 1, 2, is the ML estimate of E[neff]

• Time domain:

ˆ Ktime =

• 0.0067

−0.0013 − 0.0031i −0.0013 + 0.0031i 0.0053

• Measurements are specific to our setup. However, the variance of ˆ

Ktime over time and ˆ Kfreq

• ver the frequency tones is small compared to the magnitude of the entries.

20/31

Introduction Full-Duplex MIMO Full-Duplex MIMO Testbed Self-interference Characterization

Spatial covariance matrices

• Spatial covariance matrix: K E
• (neff − E[neff]) (neff − E[neff])H
• We empirically estimate K as ˆ

K = 1

N (N − m) (N − m)H

• mi = 1

N

N

k=1 Ni,k, i = 1, 2, is the ML estimate of E[neff]

• Time domain:

ˆ Ktime =

• 0.0067

−0.0013 − 0.0031i −0.0013 + 0.0031i 0.0053

• Frequency domain:

ˆ Kfreq =

• 0.0070

−0.0013 − 0.0039i −0.0013 + 0.0039i 0.0057

• Measurements are specific to our setup. However, the variance of ˆ

Ktime over time and ˆ Kfreq

• ver the frequency tones is small compared to the magnitude of the entries.

20/31

Introduction Full-Duplex MIMO Full-Duplex MIMO Testbed Self-interference Characterization

Spatial covariance matrices

• Spatial covariance matrix: K E
• (neff − E[neff]) (neff − E[neff])H
• We empirically estimate K as ˆ

K = 1

N (N − m) (N − m)H

• mi = 1

N

N

k=1 Ni,k, i = 1, 2, is the ML estimate of E[neff]

• Time domain:

ˆ Ktime =

• 0.0067

−0.0013 − 0.0031i −0.0013 + 0.0031i 0.0053

• Frequency domain:

ˆ Kfreq =

• 0.0070

−0.0013 − 0.0039i −0.0013 + 0.0039i 0.0057

• Spatial correlation remains in frequency domain

Measurements are specific to our setup. However, the variance of ˆ Ktime over time and ˆ Kfreq

• ver the frequency tones is small compared to the magnitude of the entries.

20/31

Introduction Full-Duplex MIMO Full-Duplex MIMO Testbed Self-interference Characterization

Summary of residual noise properties

• Time domain:

✗ Not memoryless

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Introduction Full-Duplex MIMO Full-Duplex MIMO Testbed Self-interference Characterization

Summary of residual noise properties

• Time domain:

✗ Not memoryless ✗ Not Gaussian

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Introduction Full-Duplex MIMO Full-Duplex MIMO Testbed Self-interference Characterization

Summary of residual noise properties

• Time domain:

✗ Not memoryless ✗ Not Gaussian ✗ Not circular symmetric

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Introduction Full-Duplex MIMO Full-Duplex MIMO Testbed Self-interference Characterization

Summary of residual noise properties

• Time domain:

✗ Not memoryless ✗ Not Gaussian ✗ Not circular symmetric ✗ Spatially colored

21/31

Introduction Full-Duplex MIMO Full-Duplex MIMO Testbed Self-interference Characterization

Summary of residual noise properties

• Time domain:

✗ Not memoryless ✗ Not Gaussian ✗ Not circular symmetric ✗ Spatially colored

Traditional receiver assumptions do not hold

21/31

Introduction Full-Duplex MIMO Full-Duplex MIMO Testbed Self-interference Characterization

Summary of residual noise properties

• Time domain:

✗ Not memoryless ✗ Not Gaussian ✗ Not circular symmetric ✗ Spatially colored

• Frequency domain:

✓ Memoryless

Traditional receiver assumptions do not hold

21/31

Introduction Full-Duplex MIMO Full-Duplex MIMO Testbed Self-interference Characterization

Summary of residual noise properties

• Time domain:

✗ Not memoryless ✗ Not Gaussian ✗ Not circular symmetric ✗ Spatially colored

• Frequency domain:

✓ Memoryless ✓ Gaussian

Traditional receiver assumptions do not hold

21/31

Introduction Full-Duplex MIMO Full-Duplex MIMO Testbed Self-interference Characterization

Summary of residual noise properties

• Time domain:

✗ Not memoryless ✗ Not Gaussian ✗ Not circular symmetric ✗ Spatially colored

• Frequency domain:

✓ Memoryless ✓ Gaussian ✓ Circular symmetric

Traditional receiver assumptions do not hold

21/31

Introduction Full-Duplex MIMO Full-Duplex MIMO Testbed Self-interference Characterization

Summary of residual noise properties

• Time domain:

✗ Not memoryless ✗ Not Gaussian ✗ Not circular symmetric ✗ Spatially colored

• Frequency domain:

✓ Memoryless ✓ Gaussian ✓ Circular symmetric ✗ Spatially colored

Traditional receiver assumptions do not hold

21/31

Introduction Full-Duplex MIMO Full-Duplex MIMO Testbed Self-interference Characterization

Summary of residual noise properties

• Time domain:

✗ Not memoryless ✗ Not Gaussian ✗ Not circular symmetric ✗ Spatially colored

• Frequency domain:

✓ Memoryless ✓ Gaussian ✓ Circular symmetric ✗ Spatially colored

Traditional receiver assumptions do not hold OFDM: Need to study and undo effects of colored noise

21/31

Introduction Full-Duplex MIMO Full-Duplex MIMO Testbed Self-interference Characterization

Impact of colored noise on ZF and ML receivers

• Zero-forcing (ZF) receiver: ˆ

xZF = D

H−1y

• 22/31

Introduction Full-Duplex MIMO Full-Duplex MIMO Testbed Self-interference Characterization

Impact of colored noise on ZF and ML receivers

• Zero-forcing (ZF) receiver: ˆ

xZF = D

H−1y

• Maximum-likelihood (ML) receiver: ˆ

xML = arg minx∈OM y − Hx

22/31

Introduction Full-Duplex MIMO Full-Duplex MIMO Testbed Self-interference Characterization

Impact of colored noise on ZF and ML receivers

• Zero-forcing (ZF) receiver: ˆ

xZF = D

H−1y

• Maximum-likelihood (ML) receiver: ˆ

xML = arg minx∈OM y − Hx

5 10 15 20 25 30 10

−5

10

−4

10

−3

10

−2

10

−1

10 SNR (dB) FER ZF ML ZF (w. self−interference) ML (w. self−interference)

22/31

Introduction Full-Duplex MIMO Full-Duplex MIMO Testbed Self-interference Characterization

Impact of colored noise on ZF and ML receivers

• Zero-forcing (ZF) receiver: ˆ

xZF = D

H−1y

• Maximum-likelihood (ML) receiver: ˆ

xML = arg minx∈OM y − Hx

5 10 15 20 25 30 10

−5

10

−4

10

−3

10

−2

10

−1

10 SNR (dB) FER ZF ML ZF (w. self−interference) ML (w. self−interference)

Colored noise → ∼3 dB worse performance

22/31

Introduction Full-Duplex MIMO Full-Duplex MIMO Testbed Self-interference Characterization

Noise whitening

• Whitening filter: W = K−1/2

23/31

Introduction Full-Duplex MIMO Full-Duplex MIMO Testbed Self-interference Characterization

Noise whitening

• Whitening filter: W = K−1/2

ZF receiver: ˆ xZF = D (H−1W−1Wy) = D (H−1y)

23/31

Introduction Full-Duplex MIMO Full-Duplex MIMO Testbed Self-interference Characterization

Noise whitening

• Whitening filter: W = K−1/2

ZF receiver: ˆ xZF = D (H−1W−1Wy) = D (H−1y) ML receiver: ˆ xML = arg minx∈OM Wy − WHx

23/31

Introduction Full-Duplex MIMO Full-Duplex MIMO Testbed Self-interference Characterization

Noise whitening

• Whitening filter: W = K−1/2

ZF receiver: ˆ xZF = D (H−1W−1Wy) = D (H−1y) ML receiver: ˆ xML = arg minx∈OM Wy − WHx

5 10 15 20 25 30 10

−5

10

−4

10

−3

10

−2

10

−1

10 SNR (dB) FER ZF ML ZF (w. self−interference) ML (w. self−interference) ZF (w. self−interference whitening) ML (w. self−interference whitening)

23/31

Introduction Full-Duplex MIMO Full-Duplex MIMO Testbed Self-interference Characterization

Noise whitening

• Whitening filter: W = K−1/2

ZF receiver: ˆ xZF = D (H−1W−1Wy) = D (H−1y) ML receiver: ˆ xML = arg minx∈OM Wy − WHx

5 10 15 20 25 30 10

−5

10

−4

10

−3

10

−2

10

−1

10 SNR (dB) FER ZF ML ZF (w. self−interference) ML (w. self−interference) ZF (w. self−interference whitening) ML (w. self−interference whitening)

ML: Noise whitening → ∼1 dB reclaimed

23/31

Introduction Full-Duplex MIMO Full-Duplex MIMO Testbed Self-interference Characterization

Estimation of covariance matrix

• Whitening filter requires knowledge of covariance matrix K

24/31

Introduction Full-Duplex MIMO Full-Duplex MIMO Testbed Self-interference Characterization

Estimation of covariance matrix

• Whitening filter requires knowledge of covariance matrix K
• K can be estimated in training phase

We have observed that K does not vary significantly with low mobility

24/31

Introduction Full-Duplex MIMO Full-Duplex MIMO Testbed Self-interference Characterization

Estimation of covariance matrix

• Whitening filter requires knowledge of covariance matrix K
• K can be estimated in training phase

We have observed that K does not vary significantly with low mobility

• Since the setup is highly static, we can attempt to build a model to

predict K

No need to estimate K Possibility of optimizing the setup to reduce coloring

24/31

Introduction Full-Duplex MIMO Full-Duplex MIMO Testbed Self-interference Characterization

Setup

• Two RF chains, antenna distance d

25/31

Introduction Full-Duplex MIMO Full-Duplex MIMO Testbed Self-interference Characterization

Setup

• Two RF chains, antenna distance d
• Cancellation channel:

Hc =

• hCX1,RX1

hCX2,RX2

• 25/31

Introduction Full-Duplex MIMO Full-Duplex MIMO Testbed Self-interference Characterization

Setup

• Two RF chains, antenna distance d
• Cancellation channel:

Hc =

• hCX1,RX1

hCX2,RX2

• Self-interference channel

Ht =

• hTX1,RX1

hTX1,RX2 hTX1,RX2 hTX2,RX2

• 25/31

Introduction Full-Duplex MIMO Full-Duplex MIMO Testbed Self-interference Characterization

Setup

• Two RF chains, antenna distance d
• Cancellation channel:

Hc =

• hCX1,RX1

hCX2,RX2

• Self-interference channel

Ht =

• hTX1,RX1

hTX1,RX2 hTX1,RX2 hTX2,RX2

• 25/31

Introduction Full-Duplex MIMO Full-Duplex MIMO Testbed Self-interference Characterization

Covariance matrix model

• Assumption: Single frequency fc

26/31

Introduction Full-Duplex MIMO Full-Duplex MIMO Testbed Self-interference Characterization

Covariance matrix model

• Assumption: Single frequency fc
• Cancellation channel Hc is constant → modeled as constant gain

α and constant phase φα: Hc =

• αejφα

αejφα

• 26/31

Introduction Full-Duplex MIMO Full-Duplex MIMO Testbed Self-interference Characterization

Covariance matrix model

• Assumption: Single frequency fc
• Cancellation channel Hc is constant → modeled as constant gain

α and constant phase φα: Hc =

• αejφα

αejφα

• Self-interference channel from transmitter i to receiver i is constant

→ modeled as constant gain β and constant phase φβ: Ht =

• βejφβ

? ? βejφβ

• 26/31

Introduction Full-Duplex MIMO Full-Duplex MIMO Testbed Self-interference Characterization

Covariance matrix model

• Self-interference channel from transmitter i to receiver j → wireless

channel of distance d

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Introduction Full-Duplex MIMO Full-Duplex MIMO Testbed Self-interference Characterization

Covariance matrix model

• Self-interference channel from transmitter i to receiver j → wireless

channel of distance d

• Can be modeled as gain γ(d) and phase φγ(d):

γ(d) =

λ

4πd

2

φγ(d) = 2πd λ

27/31

Introduction Full-Duplex MIMO Full-Duplex MIMO Testbed Self-interference Characterization

Covariance matrix model

• Self-interference channel from transmitter i to receiver j → wireless

channel of distance d

• Can be modeled as gain γ(d) and phase φγ(d):

γ(d) =

λ

4πd

2

φγ(d) = 2πd λ

• Model for self-interference channel:

Ht =

• βejφβ

γ(d)ejφγ(d) γ(d)ejφγ(d) βejφβ

• 27/31

Introduction Full-Duplex MIMO Full-Duplex MIMO Testbed Self-interference Characterization

Covariance matrix model

• Recall that: neff Htnt + Hcnc + nr

28/31

Introduction Full-Duplex MIMO Full-Duplex MIMO Testbed Self-interference Characterization

Covariance matrix model

• Recall that: neff Htnt + Hcnc + nr
• Assume that nt, nc, nr are independent and Knt = Knc = I and

Knr = σ2I

28/31

Introduction Full-Duplex MIMO Full-Duplex MIMO Testbed Self-interference Characterization

Covariance matrix model

• Recall that: neff Htnt + Hcnc + nr
• Assume that nt, nc, nr are independent and Knt = Knc = I and

Knr = σ2I

• Then, we get

Ky(d) =

• A(d)

B(d) B(d) A(d)

• ,

where A(d) = α2 + β2 + γ(d)2 + σ2 and B(d) = βγ(d)

• ej(φγ(d)−φβ) + e−j(φγ(d)−φβ)

28/31

Introduction Full-Duplex MIMO Full-Duplex MIMO Testbed Self-interference Characterization

Avoiding colored noise

• Optimal distance d∗ to minimize off-diagonal elements (i.e.,

minimize spatial correlation): d∗ = arg min

d

γ(d)

• ej(φγ(d)−φβ) + e−j(φγ(d)−φβ)

29/31

Introduction Full-Duplex MIMO Full-Duplex MIMO Testbed Self-interference Characterization

Avoiding colored noise

• Optimal distance d∗ to minimize off-diagonal elements (i.e.,

minimize spatial correlation): d∗ = arg min

d

γ(d)

• ej(φγ(d)−φβ) + e−j(φγ(d)−φβ)
• Using Euler’s formula, we get:

d∗ =

2k + 1

4 − φβ 2π

• λ,

k ∈ Z, which gives B(d∗) = 0!

29/31

Introduction Full-Duplex MIMO Full-Duplex MIMO Testbed Self-interference Characterization

Avoiding colored noise

• Optimal distance d∗ to minimize off-diagonal elements (i.e.,

minimize spatial correlation): d∗ = arg min

d

γ(d)

• ej(φγ(d)−φβ) + e−j(φγ(d)−φβ)
• Using Euler’s formula, we get:

d∗ =

2k + 1

4 − φβ 2π

• λ,

k ∈ Z, which gives B(d∗) = 0!

• Suitably chosen antenna spacing eliminates coloring

29/31

Introduction Full-Duplex MIMO Full-Duplex MIMO Testbed Self-interference Characterization

Covariance matrix model verification

• Carrier frequency: 2.40 GHz, signal bandwidth: 10 KHz

30/31

Introduction Full-Duplex MIMO Full-Duplex MIMO Testbed Self-interference Characterization

Covariance matrix model verification

• Carrier frequency: 2.40 GHz, signal bandwidth: 10 KHz

6 8 10 12 14 16 18 1 2 x 10

−4

Antenna distance (cm) Covariance between y(1) and y(2)

Measurements Model

30/31

Introduction Full-Duplex MIMO Full-Duplex MIMO Testbed Self-interference Characterization

Covariance matrix model verification

• Carrier frequency: 2.40 GHz, signal bandwidth: 10 KHz

6 8 10 12 14 16 18 1 2 x 10

−4

Antenna distance (cm) Covariance between y(1) and y(2) 6 8 10 12 14 16 18 0.01 0.02 0.03 0.04 0.05 0.06 Antenna distance (cm) Covariance between y(1) and y(2)

Measurements Model

30/31

Introduction Full-Duplex MIMO Full-Duplex MIMO Testbed Self-interference Characterization

Covariance matrix model verification

• Carrier frequency: 2.40 GHz, signal bandwidth: 10 KHz

6 8 10 12 14 16 18 1 2 x 10

−4

Antenna distance (cm) Covariance between y(1) and y(2) 6 8 10 12 14 16 18 0.01 0.02 0.03 0.04 0.05 0.06 Antenna distance (cm) Covariance between y(1) and y(2)

Measurements Model

• Initial measurements indicate good agreement

30/31

Introduction Full-Duplex MIMO Full-Duplex MIMO Testbed Self-interference Characterization

Conclusions

• Effective noise in time domain behaves very differently than

thermal noise

31/31

Introduction Full-Duplex MIMO Full-Duplex MIMO Testbed Self-interference Characterization

Conclusions

• Effective noise in time domain behaves very differently than

thermal noise

• Effective noise in frequency domain is more conventional

31/31

Introduction Full-Duplex MIMO Full-Duplex MIMO Testbed Self-interference Characterization

Conclusions

• Effective noise in time domain behaves very differently than

thermal noise

• Effective noise in frequency domain is more conventional
• Spatial correlation of effective noise affects conventional receivers

31/31

Introduction Full-Duplex MIMO Full-Duplex MIMO Testbed Self-interference Characterization

Conclusions

• Effective noise in time domain behaves very differently than

thermal noise

• Effective noise in frequency domain is more conventional
• Spatial correlation of effective noise affects conventional receivers
• Noise whitening using the estimated covariance matrix reduces

effect of correlation

31/31

Introduction Full-Duplex MIMO Full-Duplex MIMO Testbed Self-interference Characterization

Conclusions

• Effective noise in time domain behaves very differently than

thermal noise

• Effective noise in frequency domain is more conventional
• Spatial correlation of effective noise affects conventional receivers
• Noise whitening using the estimated covariance matrix reduces

effect of correlation

• Due to static nature of the setup correlation can be captured by a

simple geometric model

31/31

Introduction Full-Duplex MIMO Full-Duplex MIMO Testbed Self-interference Characterization

Conclusions

• Effective noise in time domain behaves very differently than

thermal noise

• Effective noise in frequency domain is more conventional
• Spatial correlation of effective noise affects conventional receivers
• Noise whitening using the estimated covariance matrix reduces

effect of correlation

• Due to static nature of the setup correlation can be captured by a

simple geometric model

• Antenna position can be optimized to reduce correlation (for

narrowband signals)

31/31