interference management in wireless networkselgamala/tutorial.pdf2 a. host-madsen and a. nosratinia,...

$: Interference Management in Wireless Networkselgamala/tutorial.pdf2 A. Host-Madsen and A. Nosratinia, \The multiplexing gain of wireless networks," in Proc. IEEE International Symp$
Interference Management in Wireless Networks

Aly El Gamal

Department of Electrical and Computer EngineeringPurdue University

Venu Veeravalli

Coordinated Science LabDepartment of Electrical and Computer Engineering

University of Illinois at Urbana-Champaign

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Just Published - Cambridge University Press

ECE Illinois & Purdue

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Part 1: Introduction


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Explosion in Wireless Data Traffic

How to accommodate exponential growth without new useful spectrum?


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Through Improved PHY?

• Point-to-Point wireless technology mature• Modulation/demodulation• Synchronization• Coding/decoding (near Shannon limits)• MIMO

• Centralized (in-cell) multiuser wireless technology also mature• Orthogonalize users when possible• Otherwise use successive interference cancellation

Spectral efficiency gains from further improvements in PHY are limited!


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By Adding More Basestations?


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Through Improved Interference Management

Several useful engineering solutions for managing interference

But...

What are fundamental limits?


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References

1 T.S. Rappaport. Wireless communications: Principles andpractice. New Jersey: Prentice Hall 1996.

2 A. J. Viterbi. CDMA: Principles of spread spectrumcommunication. Addison Wesley, 1995.

3 D. Tse and P. Viswanath. Fundamentals of wirelesscommunication. Cambridge University Press, 2005.

4 E. Biglieri et al. Principles of Cognitive Radio. CambridgeUniversity Press, 2012.


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Part 2: Degrees of Freedom Characterization ofInterference Channels


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Information Theory for IC: State-of-the-art

• Exact characterization• Very hard problem, still open even after > 30 years

• Approximate characterization• Within constant number of bits/sec• Provides some architectural insights

• Degrees of freedom (or multiplexing gain)

DoF = limSNR→∞

sum capacity

log SNR

• Pre-log factor of sum-capacity in high SNR regime• Number of interference free sessions per channel use• Simplest of the three, but can provide useful insight


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Degrees of Freedom

Advantages:

1 Simplicity

2 Captures the interference effect (without noise)

3 Highlights the combinatorial part of the problem

Drawbacks:

1 Insensitive to Gaussian noise

2 Insensitive to varying channel strengths


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K-user (SISO) Interference Channel

W1 W1Tx1 Rx1

W2 W2Tx2 Rx2

W3 W3Tx3 Rx3

How many Degrees of Freedom (DoF)?


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Degrees of Freedom with Orthogonalization

• One active user per channel use• Every user gets an interference free channel once every K channel

uses• DoF per user is 1/K; total DoF equals 1

• Special Case: K = 2• Can easily show that outer bound on DOF equals 1

=⇒ TDMA optimal from DoF viewpoint for K = 2


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Degrees of Freedom for general K

• Outer Bound on DoF [Host-Madsen, Nosratinia ’05]

• There are K(K− 1)/2 pairs and each user appears in (K− 1) pairs• Thus DoF ≤ K/2 or per user DoF ≤ 1/2

• Amazingly, this outer bound is achievable via linear interferencesuppression!

Interference Alignment [Cadambe & Jafar ’08]


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Linear Transmit/Receive Strategies

Interference Channel with Tx/Rx Linear CodingU1 0 00 U2 00 0 U3

†︸︷︷︸

Receive Beams

H1,1 H1,2 H1,3

H2,1 H2,2 H2,3

H3,1 H3,2 H3,3

︸︷︷︸

Channel

V 1 0 00 V 2 00 0 V 3

︸︷︷︸

Transmit Beams

End-to-End matrix is Diagonal =⇒ No Interference!

# streams = Size of the Diagonal matrix


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DoF of Linear Strategies

U1 0 00 U2 00 0 U3

† H1,1 H1,2 H1,3

H2,1 H2,2 H2,3

H3,1 H3,2 H3,3

V 1 0 00 V 2 00 0 V 3

H i,j : NT ×NT block-diagonal matrix

• (Symmetric) MIMO:N = # antennas

• Symbol Extensions (Time or Frequency)T = # symbol extensions

DoF (T ) = (#streams)/T


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Complexity of asymptotic Interference Alignment

# symbol extensions 0 20 40 60 80 100

0.44

0.45

0.46

0.47

0.48

0.49

0.5

PUDoF

PUDoF of 0.5 is achieved asymptotically


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Complexity of 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, Jafar, and Chung, ’09]


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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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References

1 V.R. Cadambe and S.A. Jafar. “Interference Alignment andDegrees of Freedom of the K-User Interference Channel.” IEEETrans. Inform. Theory, August 2008.

2 S. A. Jafar. “Interference Alignment – A New Look at SignalDimensions in a Communication Network.” In Foundations andTrends in Communications and Information Theory, NOWPublications, 2010.

3 A. Host-Madsen and A. Nosratinia, “The multiplexing gain ofwireless networks,” in Proceedings of ISIT, 2005.

4 S.W. Choi, S.A. Jafar, and S.-Y. Chung. “On the beamformingdesign for efficient interference alignment.” IEEE CommunicationsLetters, 2009.


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Part 3: Coordinated Multi-Point Transmission


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K-User Interference Channel

Channel State Information known at all nodes.

W1 W1Tx1 Rx1

W2 W2Tx2 Rx2

W3 W3Tx3 Rx3


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Coordinated Multi-Point (CoMP) Transmission

Messages are jointly transmitted using multiple transmitters.

W1 W1Tx1 Rx1

W2 W2Tx2 Rx2

W3 W3Tx3 Rx3


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CoMP Transmission

• Each message is jointly transmitted using M transmitters

• Message i is transmitted jointly using the transmitters in Ti

• For all i ∈ [K], |Ti| ≤M

• We consider all message assignments that satisfy the cooperationconstraint


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Degrees of Freedom (DoF)

DoF = limSNR→∞

sum capacity

log SNR

Objective: Determine the DoF as a function of K and M

PUDoF(M) = limK→∞

DoF(K,M)

K

Is PUDoF(M)>PUDoF(1) for M > 1?


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Example: Two-user Interference Channel

W1 W1Tx1 Rx1

W2 W2Tx2 Rx2

No Cooperation, DoF=1, Time Sharing

Full Cooperation, DoF=2, ZF Transmit Beamforming


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No Cooperation (M = 1)

• For M = 1, outer bound = K/2

• The outer bound can be achieved by jointly coding across multipleparallel channels [Cadambe & Jafar ’08]:

DoF(K,M = 1) = limL→∞

DoF(K,M = 1, L)

L= K/2

where L is the number of parallel channels

Corollary

Without cooperation, the Per User DoF number is given by

PUDoF(M = 1) =1

2


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Full Cooperation (M = K)

• In this case, the channel is a MISO Broadcast channel.

• Each message is available at K antennas, and hence, can becanceled at K − 1 receivers.

• Each user achieves 1 DoF,

DoF(K,M = K) = K.

What happens with partial cooperation (1 < M < K)?


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Clustering

W1 W1Tx1 Rx1

W2 W2Tx2 Rx2

W3 W3Tx3 Rx3

W4 W4Tx4 Rx4

No Degrees of Freedom Gain


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Spiral Message Assignment

Ti = {i, i+ 1, . . . , i+M − 1}

W1 W1Tx1 Rx1

W2 W2Tx2 Rx2

W3 W3Tx3 Rx3


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Spiral Message Assignment: Results

Theorem

The DoF of interference channel with a spiral message assignmentsatisfies

K +M − 1

2≤ DoF(K,M) ≤

⌈K +M − 1

2

⌉

Proof of Achievability: First M − 1 users are interference-free, andinterference occupies half the signal space at each other receiver

Generalizes the Asymptotic Interference Alignment scheme


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Outline of the Achievable Scheme

OriginalChannel

ZFEncoder

IAEncoder

IADecoder

Derived Channel

Approach:

1 ZF Step: Exploit cooperation to transform the interferencechannel into a derived channel (with single-point transmission)

2 IA Step: Use the known IA techniques to design beams forderived channel

3 Prove that the asymptotic IA step works for generic channelcoefficients


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DoF Outer Bound: Results

Definition

We say that a message assignment satisfies a local cooperationconstraint if and only if ∃r(K) = o(K), and for all K−user channels,

Ti ⊆ {i− r(K), i− r(K) + 1, . . . , i+ r(K)},∀i ∈ [K]

Theorem

With the restriction to local cooperation,

PUDoFloc(M) =1

2

Local cooperation cannot achieve a scalable Dof gain


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DoF Outer Bound: Results

Theorem

For M ≥ 2,

PUDoF(M) ≤ M − 1

M

Corollary

PUDoF(2) =1

2

Assigning each message to two transmitters cannot achieve a scalableDoF gain


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References

1 P. Marsch and G. P. Fettweis “Coordinated Multi-Point in MobileCommunications: from theory to practice,” First Edition,Cambridge, 2011.

2 A. Host-Madsen and A. Nosratinia, “The multiplexing gain ofwireless networks,” in Proc. IEEE International Symp. Inf. Theory(ISIT), 2007.

3 V. Cadambe and S. A. Jafar, “Interference alignment and degreesof freedom of the K-user interference channel,” IEEE Trans. Inf.Theory, 2008.

4 V. S. Annapureddy, A. El Gamal, and V. V. Veeravalli, “Degreesof Freedom of Interference Channels with CoMP Transmission andReception,” IEEE Trans. Inf. Theory, 2012.

5 A. El Gamal, V. S. Annapureddy, and V. V. Veeravalli, “OnOptimal Message Assignments for Interference Channels withCoMP Transmission,” in Proc. CISS, 2012

6 C. Wilson and V. Veeravalli, “Degrees of Freedom for theConstant MIMO Interference Channel with CoMP Transmission,”IEEE Trans. Comm., 2014


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Part 4: Locally Connected Networks


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Locally Connected Model

Tx i is connected to receivers {i, i+ 1, . . . , i+ L}.

Wyner Model: L =1

Rx1 Tx1

Rx2 Tx2

Rx3 Tx3

Rx4 Tx4

Tx5 Rx5

L = 2

Rx1 Tx1

Rx2 Tx2

Rx3 Tx3

Rx4 Tx4

Tx5 Rx5


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Justifying Choices: Network Topology

Local Connectivity:

• Reflects path loss

• Simplifies problem, only consider local cooperation

Large Networks:

• Understand scalability

• Derive insights

Solutions generalize to cellular network models


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Cellular Network Model


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Solutions for L = 2 are applicableECE Illinois & Purdue

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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

Backhaul load factor =1

PUDoF (L=1,M=2) = 2/3 > 1/2

W1

W2

W4

W5


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Example: No Cooperation

PUDoF(L =1,M =1) = 1

2 PUDoF(L =1,M =1) = 23

Rx1 Tx1

Rx2 Tx2

Rx3 Tx3

W1

W2

W3

Rx1 Tx1

Rx2 Tx2

Rx3 Tx3

W1

W2

W3

Interference-aware message assignment + Fractional reuse


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Locally Connected IC with CoMP: Main Result

Theorem

Under the general cooperation constraint |Ti| ≤M, ∀i ∈ {1, 2, . . . ,K},

2M

2M + L≤ PUDoF(L,M) ≤ 2M + L− 1

2M + L

and the optimal message assignment satisfies a local cooperationconstraint.

Corollary

PUDoF(L = 1,M) =2M

2M + 1


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DoF Achieving Scheme

Rx2 Tx2

Rx3 Tx3

Rx4 Tx4

Tx1 Rx1

Rx5 X5

W2

W4

W1

W2

W4

W1

W5

W3

W5

Backhaul load factor =6/5 PUDoF (L=1,M=2) = 4/5 > 2/3


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DoF Outer Bound

Have to consider all possible message assignments satisfying|Ti| ≤M, ∀i ∈ [K]

1 First simplify the combinatorial aspect of the problem byidentifying useful message assignments

2 Then derive an equivalent model with fewer receivers and sameDoF


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DoF Outer Bound: Useful Message Assignments

An assignment of a message Wx to a transmitter Ty is useful only ifone of the following conditions holds:

1 Signal delivery: Ty is connected to the designated receiver Rx

2 Interference mitigation: Ty is interfering with anothertransmitter Tz, both carrying the message Wx


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Tx1 Rx1

Tx2 Rx2

Tx3 Rx3

Tx4 Rx4

W3 W3

Assigning W3 to Tx1 is not useful.


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Corollary

An assignment of a message Wx to a transmitter Ty is useful only ifthere exists a chain of interfering transmitters carrying Wx thatincludes Ty and another transmitter Tz that is connected to Rx

Proves optimality of local cooperation


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CoMP Transmission for IC: Summary

• Local Cooperation• no PUDoF gain for fully connected channel• is optimal for locally connected channel

• Interference aware message assignments allow for higherthroughput

• Fractional reuse and zero-forcing transmit beam-forming aresufficient to achieve PUDoF gains, without need for symbolextensions and interference alignment


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Uplink: Achieving Full DoF

M1 M1BS1 MT1

M2 M2BS2 MT2

M3 M3BS3 MT3

Associating each MT with two BSs connected to it

Message Passing Decoding: Interference-free Degrees of Freedom


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Results: Uplink1

PUDoFZFU (N) =

1 L+ 1 ≤ NN+1L+2

L2 ≤ N ≤ L

2N2N+L 1 ≤ N ≤ L

2 − 1

≥ 12 ,∀N ≥

L2

Higher than Downlink

Is Cooperation useful for N < L2 ?

1M. Singhal, A. El Gamal, “Joint Uplink-Downlink Cell Associations forInterference Networks with Local Connectivity,” Allerton ’17ECE Illinois & Purdue

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Average Uplink-Downlink DoF

M1 M1BS1 MT1

M2 M2BS2 MT2

M3 M3BS3 MT3

M4 M4BS4 MT4

M5 M5BS5 MT5

Downlink Associations Uplink Associations

N = 3 PUDoF =1+ 4

52 = 9

10ECE Illinois & Purdue

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M1 M1BS1 MT1

M2 M2BS2 MT2

M3 M3BS3 MT3

M4 M4BS4 MT4

M5 M5BS5 MT5

PUDoFUD(N,L = 1) = 4N−34N−2


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For L ≥ 2:

PUDoFZFUD(N) ≥

12

(1 +

(dL2 e+δ+N−(L+1)

N

))L+ 1 ≤ N

2N2N+L 1 ≤ N ≤ L

where δ = (L+ 1) mod 2.

For L+ 1 ≤ N , scheme is different from both downlink and uplink


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Summary of Insights

• Local cooperation is optimal for locally connected networks

• Significant DoF gains achieved with ZF and message passingdecoding

• Limited cell associations ⇒ Same for downlink and uplink

• Limited associations and no delay constraint ⇒ CoMP useful?


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Further Questions

1 General network topologies

2 When to simplify into optimizing for uplink / downlink only

3 Constrain average number of cell associations


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References

1 V. S. Annapureddy, A. El Gamal, and V. V. Veeravalli, “Degreesof Freedom of Interference Channels with CoMP Transmission andReception,” IEEE Trans. Inf. Theory, 2012.

2 A. Lapidoth, N. Levy, S. Shamai (Shitz) and M. A. Wigger“Cognitive Wyner networks with clustered decoding,” IEEE Trans.Inf. Theory 2014

3 A. Wyner, “Shannon-theoretic approach to a Gaussian cellularmultiple-access channel,” IEEE Trans. Inf. Theory, 1994.

4 S. Shamai and M. A. Wigger, “Rate-limited TransmitterCooperation in Wyner’s Asymmetric Interference Network,” inProc. IEEE Int. Symp. Inf. Theory, 2014


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Part 5: Cellular Network and Backhaul Load Constraint


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Backhaul Load Constraint

More natural cooperation constraint that takes into account overallbackhaul load: ∑

i∈[K] |Ti|K

≤ B

Solution under transmit set size constraint |Ti| ≤M, ∀i ∈ [M ], can beused to provide solutions under backhaul load constraint


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Wyner’s Model with Backhaul Load Constraint

Rx1 Tx1

Rx2 Tx2

Rx3 Tx3

Theorem

Under cooperation constraint∑i∈[K] |Ti| ≤ BK,

PUDoF(B) =4B − 1

4B

Recall that |Ti| ≤M,∀i ∈ [K]⇒ PUDoF(M) = 2M2M+1


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Coding Scheme: B = 1

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

Rx2 Tx2

Rx3 Tx3

Rx4 Tx4

Tx1 Rx1

Rx5 X5

W2

W4

W1

W3

W5


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Application in Denser Networks

Tx i is connected to receivers {i, i+ 1, . . . , i+ L}.

Rx1 Tx1

Rx2 Tx2

Rx3 Tx3

Rx4 Tx4

Tx5 Rx5

L = 2

Result: Using only zero-forcing transmitbeamforming and fractional reuse:

PUDoF(L,B = 1) ≥ 1

2,∀L ≤ 6.

without need for interference alignmentand symbol extensions


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Application in Denser Networks

PUDoF(M = 1) = 12 PUDoF(B = 1) ≥ 5

9


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Interference in Cellular Networks

Locally (partially) connected interference channel!


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Interference Graph for Single Tier

Tx,Rx pair

Each node represents a Tx-Rx pair


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No Intra-sector Interference


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No Extra Backhaul Load

B = 1, PUDoF= 12


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Discussion: Cloud-based Communication

Global Knowledge / Control available at Central nodes


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Discussion: Understanding Network Topologies

• Centralized Solution Benchmark for Distributed Algorithms

• Enables Multi-RAT Networks

• Enables AI and Blockchain2

2A. El Gamal, H. El Gamal, “A Blockchain Example for Cooperative InterferenceManagement”, submitted to WComm Letters.ECE Illinois & Purdue

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Summary

• Infrastructure enhancements in backhaul can be exploited throughcooperative transmission to lead to significant rate gains

• Minimal or no increase in backhaul load• Fractional reuse and zero-forcing transmit beam-forming are

sufficient to achieve rate gains• No need for symbol extensions and interference alignment

• Open Questions:• Partial/unknown CSI• Network dynamics and robustness to link erasures• Joint design with message passing schemes for uplink


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References

1 A. El Gamal and V. V. Veeravalli, “Flexible Backhaul Design andDegrees of Freedom for Linear Interference Channels,” in Proc.IEEE Int. Symp. Inf. Theory, 2014.

2 M. Bande, A. El Gamal, and V. V. Veeravalli, “Flexible BackhaulDesign with Cooperative Transmission in Cellular InterferenceNetworks,” in Proc. IEEE Int. Symp. Inf. Theory, 2015

3 V. Ntranos, M. A. Maddah-Ali, and G. Caire, “CellularInterference Alignment,” arXiv, 2014.

4 V. Ntranos, M. A. Maddah-Ali, and G. Caire, “OnUplink-Downlink Duality for Cellular IA,” arXiv, 2014.


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Part 6: Dynamic Interference Management


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Application: Vehicle-to-Infrastructure (V2I) Networks

Network with Dynamic Nature

Delay Sensitive - Simple Coding Schemes Desired


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Application: Vehicle-to-Infrastructure (V2I) Networks

Associations between On-Board-Units and Road Side Units


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Extensions

1 Interference Networks with Block Erasures

2 Interference Management with no CSIT

3 Fast Network Discovery


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Deep Fading Block Erasures3

Communication takes place over blocks of time slots.

• Link block erasure probability p (long-term fluctuations).

• Non-erased links are generic (short-term fluctuations).

Maximize average performance

3 A. El Gamal, V. Veeravalli, “Dynamic Interference Management,”Asilomar ’13ECE Illinois & Purdue

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Dynamic Linear Interference Network

Tx i can only be connected to receivers {i, i+ 1}

Tx1 Rx1

Tx2 Rx2

Tx3 Rx3

Each of the dashed links can be erased with probability p


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Average Degrees of Freedom (DoF)

DoF(K,N) = limSNR→∞

sum capacity(K,N, SNR)

log SNR

PUDoF(N) = limK→∞

DoF(K,N)

K

• For dynamic topology: PUDoF is a function of p and N

PUDoF(p,N) = Ep [PUDoF(N)]


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Cell Association (N = 1)

Theorem

For the Cell Association problem in dynamic Wyner’s linear model,

PUDoF(p,N = 1) = max{

PUDoF(1)(p),PUDoF(2)(p),PUDoF(3)(p)}

PUDoF(1)(p): Optimal at high values of p

PUDoF(2)(p): Optimal at low values of p

PUDoF(3)(p): Optimal at middle values of p

Achievable through TDMA


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Cell Association (N = 1): Results

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10.5

0.6

0.7

0.8

0.9

1

p

PU

DoF

p(M

=1)

/(1−

p)

PUDoFp(1)

PUDoFp(2)

PUDoFp(3)


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Cell Association (N = 1): High Erasure Probability

Tx1 Rx1

Tx2 Rx2

Tx3 Rx3

Tx4 Rx4

Tx5 Rx5

M1 M1

M2 M2

M3 M3

M4 M4

M5 M5

Maximize probability of message delivery


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Cell Association (N = 1): Low Erasure Probability

Tx1 Rx1

Tx2 Rx2

Tx3 Rx3

M1 M1

M2 M2

M3 M3

Avoiding Interference


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Cell Association (N = 1): Low Erasure Probability

Tx1 Rx1

Tx2 Rx2

Tx3 Rx3

M1 M1

M2 M2

M3 M3

Avoiding Interference


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Cell Association (N = 1)

Tx1 Rx1

Tx2 Rx2

Tx3 Rx3

Tx4 Rx4

M1 M1

M2 M2

M3 M3

M4 M4

Optimal at middle values of p


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CoMP Transmission (N = 2): No Erasures

Tx1 Rx1

Tx2 Rx2

Tx3 Rx3

Tx4 Rx4

Tx5 Rx5

M1 M1

M2 M2

M4 M4

M5 M5

PUDoF(p = 0, N = 2) = 45


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Interference-Aware Message Assignment

Tx1 Rx1

Tx2 Rx2

Tx3 Rx3

Tx4 Rx4

Tx5 Rx5

M1 M1

M2 M2

M3 M3

M4 M4

M5 M5

Note that limp→1PUDoF(p,N=2)

1−p = 85


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High Erasure Probability: Ignoring Interference

Tx1 Rx1

Tx2 Rx2

Tx3 Rx3

Tx4 Rx4

Tx5 Rx5

M1 M1

M2 M2

M3 M3

M4 M4

M5 M5

Note that limp→1PUDoF(p,N=2)

1−p = 2

Role of Cooperation: CoverageECE Illinois & Purdue

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CoMP Transmission in Dynamic Linear Network

Definition

A message assignment is universally optimal if it can be used toachieve PUDoF(p,N) for all values of p.

Theorem

For any value of N , there is no universally optimal messageassignment.

Knowledge of p is necessary to design the optimal scheme


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CoMP Transmission (N = 2)4

1 Identified optimal zero-forcing associations

2 As p goes from 1 to 0, role of cooperation shifts tointerference management

3 As p goes from 0 to 1, role of cooperation shifts tocoverage extension

Knowledge of p is necessary

Needed level of accuracy?

4Y. Karacora, T. Seyfi, A. El Gamal, “The Role of Transmitter Cooperation inLinear Interference Networks with Block Erasures,” Asilomar ’17ECE Illinois & Purdue

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Wyner’s Interference Networks

M1 M1Tx1 Rx1

M2 M2Tx2 Rx2

M3 M3Tx3 Rx3

Is Transmitter Cooperation with no CSIT useful?


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Results: Full Transmitter Cooperation with no CSIT

Wyner’s Asymmetric Network:

PUDoF =2

3

Wyner’s Symmetric Network:

PUDoF =1

2

Achieved with no Cooperation and TDMA!


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TDMA: Asymmetric Model

M1 M1Tx1 Rx1

M2 Tx2 Rx2

M3 M3Tx3 Rx3

Last transmitter inactive ⇒ No inter-subnetwork interference


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Converse: Asymmetric Model

Tx1 Rx1

M2 Tx2 Rx2

Tx3 Rx3

Knowing Rx3, we obtain a statistically equivalent version of Tx2 as Rx2

Knowing Rx1, we obtain a statistically equivalent version of Tx1 as Rx2


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Converse: Asymmetric Model

Tx1 Rx1

M2 Tx2 Rx2

Tx3 Rx3

Knowing Rx1, Rx3, Rx4, Rx6, ... , we reconstruct all messages

PUDoF ≤ 23


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Next Tasks

• Can transmitter cooperation help in any network topology?

• Characterize DoF for general network topologies

• Extend to Dynamic Interference Networks

Coordinated Multi-Point can still improve Coverage


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Coordinated Learning of Network Topology

• Earlier work for the broadcast problem5

• Cloud communication can enable some of these ideas

5Noga Alon, Amotz Bar-Noy, Nathan Linial, David Peleg, “On the complexity ofradio communication”, 1987,1991ECE Illinois & Purdue

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Lemma

Let x1, · · · , xL ≤ K be L distinct integers, then for every 1 ≤ i ≤ L,there exists a prime p ≤ L logK such that,

xi 6= xj mod p,∀j ∈ {1, · · · , L}, j 6= i

L : Connectivity parameter K : Number of users


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Lemma


xi 6= xj mod p,∀j ∈ {1, · · · , L}, j 6= i

1 Let p1, · · · , pm be the prime numbers in {1, · · · , L logK}

2 m phases of transmission

3 in ith phase, xj transmits in slot xj mod pi


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Lemma


xi 6= xj mod p,∀j ∈ {1, · · · , L}, j 6= i

1 Let p1, · · · , pm be the prime numbers in {1, · · · , L logK}

2 m phases of transmission

3 in ith phase, xj transmits in slot xj mod pi

O(L2 log2K) Communication rounds


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Summary

• Exploiting infrastructure enhancements in backhaul to achieverate gains

• No delay requirements (ZF Transmit Beamforming)

• No or minimal backhaul load

• Promising results for cellular networks


interference management in wireless networkselgamala/tutorial.pdf2 a. host-madsen and a. nosratinia,...

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