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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)
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Introduction
Eigenbeamforming for Full-Duplex MIMO Relays – 2 / 26
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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
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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
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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
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System Model and Experimental Setups
Eigenbeamforming for Full-Duplex MIMO Relays – 6 / 26
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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
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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.
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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.
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Experimental Results on Natural Isolation
Eigenbeamforming for Full-Duplex MIMO Relays – 10 / 26
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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}
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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)
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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
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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
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Additional Isolation from Eigenbeamforming
Eigenbeamforming for Full-Duplex MIMO Relays – 15 / 26
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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
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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!
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Eigenbeamforming
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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
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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
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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}
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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
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Variation of Additional Isolation (2)
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• 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)
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Conclusion
Eigenbeamforming for Full-Duplex MIMO Relays – 23 / 26
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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])
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Conclusion
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• 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
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Eigenbeamforming for Full-Duplex MIMO Relays – 26 / 26