Optimal eigenbeamforming for suppressing self-interference in full-duplex MIMO relays

Optimal Eigenbeamforming for Suppressing

Self-Interference in Full-Duplex MIMO Relays

Taneli Riihonen†, Arun Balakrishnan†, Katsuyuki Haneda†,

Shurjeel Wyne∗, Stefan Werner†, and Risto Wichman†

†Aalto University School of Electrical Engineering, Finland∗COMSATS Institute of Information Technology, Pakistan

Session WP2 “Beamforming”, March 23, 201145th Conference on Information Sciences and Systems (CISS 2011)

Introduction

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Half-Duplex Relaying: The Prevalent Concept

Eigenbeamforming for Full-Duplex MIMO Relays – 3 / 26

• Two-hop MIMO relay links have been a hot research topic recently

• Most of the literature assumes half-duplex relaying mode

. Different time slots or frequency bands for relay Rx and Tx− Disadvantage: ∼ 50% loss in system spectral efficiency

. Inevitable choice for relays with single antenna array: Weakerdesired signal would be drowned by strong self-interference

Full-Duplex Relaying: Better Spectral Efficiency!

Eigenbeamforming for Full-Duplex MIMO Relays – 4 / 26

• MIMO relay with separated receive and transmit antenna arrays

• It may be viable to choose the full-duplex mode, and avoid the lossof spectral efficiency which is inherent for the half-duplex mode

• Technical challenge: To keep residual self-interference minimal

. Natural isolation facilitates the usage of signal processingtechniques to provide additional isolation

In Our Paper

Eigenbeamforming for Full-Duplex MIMO Relays – 5 / 26

• Most earlier papers on full-duplex relays pay little attentionto the existence of self-interference

. We model explicitly the inevitable self-interference signaland study how to suppress it

• The SVD of the self-interference channel is previously exploitedonly in a suboptimal manner

. We apply optimal eigenbeam selection and minimize thepower of the self-interference

• Some earlier studies only simulate the performance of full-duplexMIMO relay links with self-interference

. We evaluate the performance of the system using real-worldchannel measurement data

System Model and Experimental Setups

Eigenbeamforming for Full-Duplex MIMO Relays – 6 / 26

Signal Model

Eigenbeamforming for Full-Duplex MIMO Relays – 7 / 26

S

Rrx Rtx

DxS

yR xR

yD

HSR HRD

HSD

HRR

• Two-hop transmission through a full-duplex MIMO relay

. Simultaneously, the source and the relay transmit

xS ∈ CNS×1 and xR ∈ C

Ntx×1

. and the relay and the destination receive

yR = HSRxS + HRRxR + nR ∈ CNrx×1

yD = HRDxR + HSDxS + nD ∈ CND×1

Experimental Antenna Arraysfor Full-Duplex MIMO Relay ∗

Eigenbeamforming for Full-Duplex MIMO Relays – 8 / 26

• Design goals:

1. Compact size but high isolation2. 2.6GHz ± 100MHz operation band3. Multiple Rx and Tx antenna elements

• Nrx = Ntx = 4 in all numerical results!∗Further details are provided in [EuCAP’10]:

K. Haneda et al., “Measurement of loop-back interference channels for outdoor-to-indoor full-duplex radio relays,” April 2010.

Channel Measurement Campaignfor Outdoor-to-Indoor Relaying Scenarios ∗

Eigenbeamforming for Full-Duplex MIMO Relays – 9 / 26

Compact array configuration• Arrays attached side-by-side (2cm)• Small box like a Wi-Fi router• Several positions next to windows

Separate array configuration• Four Tx antenna orientations• LOS: Tx in the same room as Rx• NLOS: Tx in the adjacent corridor

∗Further details are provided in [EuCAP’10]:K. Haneda et al., “Measurement of loop-back interference channels for outdoor-to-indoor full-duplex radio relays,” April 2010.

Experimental Results on Natural Isolation

Eigenbeamforming for Full-Duplex MIMO Relays – 10 / 26

Natural Isolation

Eigenbeamforming for Full-Duplex MIMO Relays – 11 / 26

Relay

yR xR

HRR

Proc

essi

ng

• The power of the undesired self-interference term is

PI = E{‖HRRxR‖22} = tr{HRRRxR

HHRR} where RxR

= E{xRxHR }

• Next slides: Analysis of experimental natural isolation given by

Ptx/PI = 1/‖HRR‖2F when RxR

= PtxI

. Distribution of natural isolation: FPtx/PI(·)

. Average natural isolation: E{Ptx/PI}

Variation of Natural Isolation (1)

Eigenbeamforming for Full-Duplex MIMO Relays – 12 / 26

• Empirical cumulative distributionfunction of natural isolation

• Channel samples from measure-ments over different frequencybins and antenna locations

• Comparison of the configurations

−3 −2 −1 0 1 2 30

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Compact arraysSeparate arrays (NLOS)Separate arraysSeparate arrays (LOS)Simulated Rayleigh channel

FP

tx/P

I(x)

x − E{Ptx/PI} [dB]

• Variance around the average isolation:Compact arrays > Separate arrays > Rayleigh channel

• LOS channels vary less than NLOS channels (this is intuitive)

Variation of Natural Isolation (2)

Eigenbeamforming for Full-Duplex MIMO Relays – 13 / 26

• Empirical cumulative distributionfunction of natural isolation

• Channel samples from measure-ments over different frequencybins and antenna positions

• Comparison of the orientations

1

2

3 4Rrx Rtx

−3 −2 −1 0 1 2 30

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Orientation 1Orientation 2Orientation 3Orientation 4

FP

tx/P

I(x)

x − E{Ptx/PI} [dB]

• Tx array orientation affects significantly the natural isolation, whilewe will see that the additional isolation due to eigenbeamformingis quite the same with all orientations

Average Natural Isolation

Eigenbeamforming for Full-Duplex MIMO Relays – 14 / 26

• For compact array configuration,E{Ptx/PI} = 36.2dB

• For separate array configuration,E{Ptx/PI} is directly proportionalto antenna separation (2–3dB/m)

1

2

3 4dRR

Rrx Rtx

0 2 4 6 8 10 1250

55

60

65

70

75

80

85

Orientation 1Orientation 2Orientation 3Orientation 4

line-o

f-sight (LOS)

non-line-o

f-sight (N

LOS)

E{P

tx/P

I}[d

B]

dRR [m]

• 20dB isolation from window glass for separate array configuration• Mere natural isolation may not be sufficient which motivates us to

obtain additional isolation with signal processing

Additional Isolation from Eigenbeamforming

Eigenbeamforming for Full-Duplex MIMO Relays – 15 / 26

Spatial Suppression

Eigenbeamforming for Full-Duplex MIMO Relays – 16 / 26

Relay

yR yR xR xR

Grx Gtx

HRR

Proc

essi

ng

• Received and transmitted signals with spatial filters:

yR = GrxyR and xR = GtxxR

. With successful mitigation, any MIMO relaying protocol couldbe used for generating xR ∈ C

Ntx×1 based on yR ∈ CNrx×1

• Filter design such that GrxHRRGtx ≈ 0 in

yR = Grx(HSRxS + nR) + GrxHRRGtxxR

Motivation for Eigenbeamforming

Eigenbeamforming for Full-Duplex MIMO Relays – 17 / 26

• Channel condition number

κ{HRR} = ‖HRR‖2 · ‖H−1

RR‖2

=σRR[1]

σRR[min{Nrx, Ntx}]

1

2

3 4Rrx Rtx

0 2 4 6 8 10 12 14 16 18 200

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Compact arraysSeparate arraysSeparate arrays (Orientation 1)Separate arrays (Orientation 2)Separate arrays (Orientation 3)Separate arrays (Orientation 4)Simulated Rayleigh channel

Fκ{H

RR}(x

)

x

• For measured channels, rk{HRR} = min{Nrx, Ntx} (full rank)but still κ{HRR} > 1 (non-uniform eigenmodes)

. Idea: The relay could point interfering transmit and receivebeams to the minimum eigenmodes!

Eigenbeamforming

Eigenbeamforming for Full-Duplex MIMO Relays – 18 / 26

Relay

yR yR xRxR

UHRR VRRS

Trx Stx

HRR

Proc

essi

ng

• Let us choose the receive and transmit filters as

Grx = STrxU

HRR and Gtx = VRRStx

. SVD of the self-interference channel: HRR = URRΣRRVHRR

. Generic row and column subset selection matrices:ST

rx ∈ {0, 1}Nrx×Nrx , Stx ∈ {0, 1}Ntx×Ntx

• Eigenbeamforming yields a sparse residual interference channel:GrxHRRGtx = ST

rx(UHRR

URR)ΣRR(VHRR

VRR)Stx = STrxΣRRStx

Optimal Beam Selection

Eigenbeamforming for Full-Duplex MIMO Relays – 19 / 26

Relay

yR xR

STrx Stx

ΣRR

Proc

essi

ng

• Minimize ‖STrxΣRRStx‖

2F to suppress self-interference efficiently

and ‖ΣRRStx‖2F to reduce the risk of Rx front-end saturation

⇒ Example solution

STrx =

[

INtx−Ntx

0 0

0 0 INrx+Ntx−Ntx

]

and Stx =

[

0

INtx

]

• Residual interference power: PI = Ptx

∑min{Nrx,Ntx}

n=Nrx+Ntx−(Nrx+Ntx)+1σ2

RR[n]

. Sum of Nrx + Ntx − max{Nrx, Ntx} smallest singular values

Special Case: Null-Space Projection

Eigenbeamforming for Full-Duplex MIMO Relays – 20 / 26

Relay

yR xR

STrx Stx

ΣRR

Proc

essi

ng

• Transmission and reception in orthogonal subspaces• Optimal beam selection yields ST

rxΣRRStx = 0, i.e., PI = 0, if

Nrx + Ntx ≤ Nrx + Ntx − rk{HRR}

. But measurements indicate that rk{HRR} = min{Nrx, Ntx}

• In practice, the condition becomes

Nrx + Ntx ≤ max{Nrx, Ntx}

Variation of Additional Isolation (1)

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• Isolation improvement

∆PI =‖HRR‖

2

F

‖STrxΣRRStx‖2

F

• Comparison of the configurations

0 5 10 15 20 25 300

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Compact arraysSeparate arraysRayleigh channel

Nrx + Ntx = 567

F∆

PI(x)

x [dB]

• The separate array configuration seems to benefit more fromeigenbeamforming than the compact array configuration

• Rayleigh model is in between the two measured configurations

Variation of Additional Isolation (2)

Eigenbeamforming for Full-Duplex MIMO Relays – 22 / 26

• Isolation improvement

∆PI =‖HRR‖

2

F

‖STrxΣRRStx‖2

F

• Comparison of the orientations

1

2

3 4Rrx Rtx

0 5 10 15 20 25 300

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Orientation 1Orientation 2Orientation 3Orientation 4

Nrx + Ntx = 567

F∆

PI(x)

x [dB]

• Tx array orientation affects little the additional isolation• The difference between LOS and NLOS channels is even smaller

than the differences between the orientations (not shown here)

Conclusion

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Total Isolation

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Natural isolationE{Ptx/PI}

0 2 4 6 8 10 1250

55

60

65

70

75

80

85

Orientation 1Orientation 2Orientation 3Orientation 4

line-o

f-sight (LOS)

non-line-o

f-sight (N

LOS)

E{P

tx/P

I}[d

B]

dRR [m]

+ Additional isolationE{∆PI}

Nrx + Ntx Compact arrays Separate arrays Rayleigh channel2 ∞ ∞ ∞3 ∞ ∞ ∞4 ∞ ∞ ∞

5 24.8dB 26.5dB 26.3dB6 10.2dB 10.9dB 10.4dB7 4.8dB 4.6dB 4.3dB8 0dB 0dB 0dB

• 2–4 streams: null-space projection• 5–7 streams: eigenbeamforming• 8 streams: no additional isolation

• In practice, total isolation is also limited by imperfections in theside information needed for suppression (see [ACSSC’09, ACSSC’10])

Conclusion

Eigenbeamforming for Full-Duplex MIMO Relays – 25 / 26

• Full-duplex relaying could offer significantly improved spectralefficiency w.r.t. conventional half-duplex relaying

• Main technical problem: self-interference in the relay

. Separated Rx and Tx antenna arrays for natural isolation

. Signal processing for additional isolation− In this paper: optimal eigenbeamforming

• We investigated how much isolation could be achieved in practice

. Design and manufacturing of prototype antenna arrays

. Channel measurement campaign for outdoor-to-indoorrelaying scenarios at 2.6GHz band

. Analysis of achievable total (= natural + additional) isolation

Eigenbeamforming for Full-Duplex MIMO Relays – 26 / 26