Flexible Backhaul Design for Cellular Interference Management
Venu Veeravalli
Director, Illinois Center for Wireless Systems
Coordinated Science Lab
ECE Department University of Illinois at Urbana-Champaign
Interference in Cellular Networks
Interference Management is critical in dense wireless networks
Veeravalli – ICNC 2/18/15
K-User Interference Channel
Tx1 Rx1
Tx2
Txk
Rx2
Rxk
Veeravalli – ICNC 2/18/15
Information Theory & Interference Management
• Exact characterization of capacity o Very hard problem; still mostly
open
• Approximate characterization of capacity o Within constant number of bits/sec o Provides some architectural
insights
• Degrees of freedom (DoF) o Pre-log factor of sum-capacity in
high SNR regime o Number of interference free
sessions per channel use o Simplest of the three, but can
provide useful insights
Veeravalli – ICNC 2/18/15
Tx1 Rx1
Tx2
Txk
Rx2
Rxk
DoF and PUDoF for K-User IC
• User orthogonalization o Every user gets an
interference free channel once every K channel uses
o DoF = 1 or Per User DoF (PUDoF) = 1/K.
• Outer Bound on DoF [Host-Madsen, Nosratinia ‘05] o DoF ≤ K/2 or PUDoF ≤ 1/2
• Amazingly, this outer bound is
achievable via linear interference suppression!
Interference Alignment [Cadambe & Jafar ‘08]
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Tx1 Rx1
Tx2
Txk
Rx2
Rxk
Linear Transmit/Receive Strategies
Interference Channel
End-to-End matrix is Diagonal è No Interference!
# streams = Size of the Diagonal matrix
Channel
⎡ ⎤⎢ ⎥⎢ ⎥⎢ ⎥⎣ ⎦
[1,1] [1,2] [1,3]
[2,1] [2,2] [2,3]
[3,1] [3,2] [3,3]
H H H
H H H
H H H
Transmit Beams
⎡ ⎤⎢ ⎥⎢ ⎥⎢ ⎥⎣ ⎦
[1]
[2]
[3]
V 0 0
0 V 0
0 0 V
Receive Beams
U[1] 0 00 U[2] 00 0 U[3]
⎡
⎣
⎢⎢⎢⎢
⎤
⎦
⎥⎥⎥⎥
H
Veeravalli – ICNC 2/18/15
Interference Alignment with Symbol Extensions (Cadambe & Jafar)
Tx1
Tx2
Tx3
Rx1
Rx2
Rx3
3 Symbol Extensions
4 interference free streams è PUDoF = 4/9
Veeravalli – ICNC 2/18/15
Asymptotic Interference Alignment
# symbol extensions
PUDoF
PUDoF of 0.5 is achieved asymptotically
0 20 40 60 80 1000.44
0.45
0.46
0.47
0.48
0.49
0.5
Veeravalli – ICNC 2/18/15
Asymptotic Interference Alignment
# symbol extensions
PUDoF
0 200 400 600 800 1000 1200 14000.32
0.34
0.36
0.38
0.4
0.42
0.44
0.46
0.48
0.53 User
4 User
Choi, S.W. and Jafar, S.A. and Chung, S.Y. , “On the beamforming design for efficient interference alignment”, IEEE Communication Letters , 2009
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Interference Alignment: Summary
+ Achieves optimal PUDoF for fully connected channel
- Requires global channel state information (CSI)
- Requires large number of symbol extensions
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Tx Cooperation Through the Backhaul: DoF Analysis
Transmitter Cooperation – 2 Users
No Cooperation Per user DoF = 1/2
Time Sharing
Full Cooperation Per user DoF = 1
Zero-Forcing Tx beams
Tx1 W1
Tx2 W2 Rx2
Rx1 Tx1 W1
Tx2 W2 Rx2
Rx1
Backhaul
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Transmitter Cooperation – K Users
Per user DoF = 1/2 Interference Alignment
Per user DoF = 1 Zero-Forcing Tx beams
(Broadcast Channel)
• To achieve PUDoF of 1: o every message needs to be known at every Tx o Load on backhaul network increases by a factor of K
• What happens with partial cooperation?
K-User Interference Channel No Cooperation
K-User Interference Channel Full Cooperation
Veeravalli – ICNC 2/18/15
Cooperative Transmission with Transmit Set Size Constraint
• Each message is jointly transmitted using at most M transmitters (max backhaul
load factor = M )
• Message i transmitted
jointly using transmitters in set
• Consider all message
assignments satisfying cooperation constraint
Ti, |T
i| ≤ M
Veeravalli – ICNC 2/18/15
Backhaul
Tx1 W1
Tx2 W2 Rx2
Rx1
Tx3 W3 Rx3
Cooperative Transmission: Clustering
Clu
ster
1
Clu
ster
2
Per user DoF = 1/2
Achievable w/o any cooperation!
No Degrees of Freedom Gain!
Tx1 W1
Tx2 W2 Rx2
Rx1
Tx3 W3
Tx4 W4 Rx4
Rx3
Veeravalli – ICNC 2/18/15
Cooperative Transmission: Spiral Message Assignments
Wi is available at transmitters {i,i+1,…,i+M-1}
Tx1 W1
Tx2 W2 Rx2
Rx1
TxM WM
TxM+1 WM+1 RxM+1
RxM
Backhaul
Veeravalli – ICNC 2/18/15
Partial Cooperation: Matrix Interpretation
Channel
⎡ ⎤⎢ ⎥⎢ ⎥⎢ ⎥⎣ ⎦
[1,1] [1,2] [1,3]
[2,1] [2,2] [2,3]
[3,1] [3,2] [3,3]
H H H
H H H
H H H
Transmit Beams
⎡ ⎤⎢ ⎥⎢ ⎥⎢ ⎥⎣ ⎦
[1]
[2]
[3]
V 0 0
0 V 0
0 0 V
Receive Beams
U[1] 0 00 U[2] 00 0 U[3]
⎡
⎣
⎢⎢⎢⎢
⎤
⎦
⎥⎥⎥⎥
H[1] [3]1 2[1] [2]2 1
[2] [3]2 1
⎡ ⎤⎢ ⎥⎢ ⎥⎢ ⎥⎣ ⎦
V 0 V
V V 0
0 V V
M: # non-zero blocks in the columns of V
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Example: K=3, M=2
Each receiver chooses an interference direction Transmitters oblige the receivers
PUDoF of 2/3 with only 3 symbol extensions
Tx1 W1
Tx2 W2 Rx2
Rx1
Tx3 W3 Rx3
Veeravalli – ICNC 2/18/15
Spiral Message Assignment: Results [Annapureddy, El Gamal, VVV – IT’12]
• DoF with spiral message assignment satisfies:
• Proof of Achievability:
o First M-1 users enjoy interference-free communication
o Interference occupies half signal space at each other
receiver
Generalization of interference alignment scheme
Veeravalli – ICNC 2/18/15
K +M −1
2≤ DoF(K,M ) ≤dK +M −1
2e
Fully Connected IC with Cooperative Transmission: Summary
• Transmit cooperation constraint M < K
• Spiral assignment: backhaul load factor = M
• Interference alignment can be used to achieve DoF gains
• Symbol extension requirements less stringent
• As K is increased with M fixed, PUDoF è 1/2
No asymptotic PUDoF gain!
Veeravalli – ICNC 2/18/15
Backhaul
Tx1 W1
Tx2 W2 Rx2
Rx1
Tx3 W3 Rx3
Tx Cooperation in Locally (Partially) Connected Interference Networks
Interference in Cellular Networks
Locally (partially) connected interference channel!
Veeravalli – ICNC 2/18/15
Locally Connected IC Model
Wyner Model: L =1
Tx i is connected to receivers {i, i+1,…, i+L}
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Rx1 Tx1
Rx2 Tx2
Rx3 Tx3
Rx4 Tx4
Tx5 Rx5
L = 2
Rx1 Tx1
Rx2 Tx2
Rx3 Tx3
Rx4 Tx4
Tx5 Rx5
Results for Wyner Model [Lapidoth, Shamai, Wigger ‘07]
Rx2 Tx2
Rx3 Tx3
Rx4 Tx4
Tx1 Rx1
Rx5 Tx5
Rx6 Tx6
W2
W3
W4
W1
W5
W6
W2
W4
W1
W5
W1
W4
Backhaul load factor =1
PUDoF (L=1,M=2) = 2/3 > 1/2
Veeravalli – ICNC 2/18/15
Results for Wyner Model [Lapidoth, Shamai, Wigger ‘07]
• Spiral transmit sets
• PUDoF (L=1,M) = M/(M+1) Backhaul load factor = M/2
• Local cooperation can achieve PUDoF gains for locally connected channels
• Achievable scheme relies on only: o Zero-forcing transmit beamforming
o Local CSI
o Fractional reuse
• No interference alignment/symbol extensions
Is spiral message assignment optimal?
Veeravalli – ICNC 2/18/15
Example with M=1
Interference-aware message assignment + Fractional reuse
PUDoF(L =1,M =1) = 1
2 PUDoF(L =1,M =1) = 23
Veeravalli – ICNC 2/18/15
Rx1 Tx1
Rx2 Tx2
Rx3 Tx3
W1
W2
W3
Rx1 Tx1
Rx2 Tx2
Rx3 Tx3
W1
W2
W3
Example: Wyner Interference Model
Rx2 Tx2
Rx3 Tx3
Rx4 Tx4
Tx1 Rx1
Rx5 X5
W2
W4
W1
W2
W4
W1
W5
W1
W5
W3
W5
Veeravalli – ICNC 2/18/15
Backhaul load factor =6/5 PUDoF (L=1,M=2) = 4/5 > 2/3
Locally Connected IC with Cooperative Transmission [El Gamal, Annapureddy, VVV, IT ‘14]
• Result: Under cooperation constraint of M
• Corollary:
• With interference avoidance constraint:
2M
2M + L≤ PUDoF(L,M ) ≤ 2M + L −1
2M + L
PUDoF(L =1,M ) = 2M
2M +1
PUDoF(L,M ) = 2M
2M + L
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DoF Upper Bound: Useful Message Assignments
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Rx1 Tx1
Rx2 Tx2
Rx3 Tx3
Rx4 Tx4
W3
Assigning W3 to Tx1 not useful
Cooperative Transmission for IC: Summary
• Local Cooperation o no PUDoF gain for fully connected channel
o is optimal for locally connected channel
• Interference aware message assignments allow for higher throughput
• Fractional reuse and zero-forcing transmit beam-forming are sufficient to achieve PUDoF gains, without need for symbol extensions and interference alignment
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Tx Cooperation with Backhaul Load Constraint
Backhaul Load Constraint
• More natural cooperation constraint that takes into account overall backhaul load:
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|i∈[K ]∑ T
i|
K≤ B
• Solution under transmit set size constraint can be used to provide solutions under backhaul load constraint
Wyner’s Model with Backhaul Load Constraint
Result:
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PUDoF(B) = 4B −1
4B
Rx1 Tx1
Rx2 Tx2
Rx3 Tx3
Recall: PUDoF(M ) = 2M
2M +1
Coding Scheme for B=1
Veeravalli – ICNC 2/18/15
Rx2 Tx2
Rx3 Tx3
Rx4 Tx4
Tx1 Rx1
Rx5 X5
W2
W4
W1
W3
W5
Rx1 Tx1
Rx2 Tx2
Rx3 Tx3
W1
W2
W3
B = 2
3 PUDoF = 2
3
B = 6
5 PUDoF = 4
5
3K
8users
5K
8users
PUDoF (B =1) = 3
4
Application to L-connected network
Veeravalli – ICNC 2/18/15
Result: Using only zero-forcing transmit beamforming and fractional reuse:
Tx i is connected to receivers {i, i+1,…, i+L}
PUDoF(L,B =1) ≥ 1
2,∀L ≤ 6
without need for interference alignment and symbol extensions
Rx1 Tx1
Rx2 Tx2
Rx3 Tx3
Rx4 Tx4
Tx5 Rx5
L = 2
Interference in Cellular Networks
Locally (partially) connected interference channel!
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Interference Graph for Single Tier
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Tx,Rx pair
Interference Graph without Intrasector Interference
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Veeravalli – ICNC 2/18/15
Partition into Noninterfering Tx-Rx pairs
Rx2 Tx2
Rx3 Tx3
Rx4 Tx4
Tx1 Rx1
Rx5 Tx5
Rx6 Tx6
W2
W3
W4
W1
W5
W6
Veeravalli – ICNC 2/18/15
2
3 4 5
6
1
M=6
B = 6 × 6
9= 4; PUDoF = 6
9= 2
3
Rx2 Tx2
Rx3 Tx3
Rx4
Tx1
Rx5
Tx6 Rx6
Tx5
W3
Tx4
W5
W2
W4
W6
Rx1 W1
Veeravalli – ICNC 2/18/15
1
2
3 4 5
6
M=2
B = 6
9= 2
3; PUDoF = 4
9
PUDoF without Intrasector Interference
PUDoF = 7/15 with backhaul load factor B = 1
Veeravalli – ICNC 2/18/15
Cooperation through Backhaul
• Similar gains in DoF for other cellular interference models, with only zero-forcing and fractional reuse • Gains improve with asymmetric cooperation and
interference aware message assignment • Gains in DoF can also be obtained for uplink with
decoded messages being exchanged through backhaul [V. Ntranos, M. Maddah-Ali, G. Caire ‘14]
o Requires multiple antennas at both mobiles and basestations
o For same backhaul load factor, gain is smaller than on downlink with Tx cooperation
Veeravalli – ICNC 2/18/15
Summary
• Infrastructure enhancements in backhaul can be exploited through cooperative transmission to lead to significant rate gains o Minimal or no increase in backhaul load o Fractional reuse and zero-forcing transmit beam-
forming are sufficient to achieve rate gains o No need for symbol extensions and interference
alignment • Open Questions:
o Partial/unknown CSI o Network dynamics and robustness to link erasures o Joint design with message passing schemes for
uplink
Veeravalli – ICNC 2/18/15
References
• V. Cadambe and S. A. Jafar, “Interference Alignment and Degrees of Freedom of the K-User Interference Channel,” IEEE Trans. Inf. Theory, vol. 54, no. 8, pp. 3425 –3441, Aug. 2008.
• V. S. Annapureddy, A. El Gamal, and V. V. Veervalli, “Degrees of Freedom of Interference Channels with CoMP Transmission and Reception,” IEEE Trans. Inf. Theory, vol. 58, no. 9, pp. 5740-5760, Sep. 2012.
• A. Wyner, “Shannon-Theoretic Approach to a Gaussian Cellular Multiple-Access Channel,” IEEE Trans. Info Theory, vol. 40, no. 5, pp.1713 –1727, Nov. 1994.
• A. Lapidoth, S. Shamai (Shitz) and M. A. Wigger, “A linear interference network with local Side-Information,” in Proc. IEEE International Symposium on Information Theory (ISIT), Nice, Jun. 2007. Also in IEEE Trans. on Information Theory 2014.
• A. ElGamal, V.S. Annapureddy, and V.V. Veeravalli. “Interference Channels with CoMP: Degrees of Freedom, Message Assignment, and Fractional Reuse.” IEEE Transactions on Information Theory, 60(6): 3483-3498, June 2014.
• A. El Gamal, V. V. Veeravalli, ”Flexible backhaul design and degrees of freedom for linear interference networks,” in Proc. IEEE International Symposium on Information Theory (ISIT), pp.2694-2698, Hawaii, June-July 2014.
• V. Ntranos, M. A. Maddah-Ali, and G. Caire, “Cellular interference alignment,” CoRR, vol. abs/1402.3119, 2014. [Online]. Available: http://arxiv.org/abs/1402.3119
Veeravalli – ICNC 2/18/15