Information Theory of Cloud-based CooperativeInterference Management

Aly El Gamal

Joint work with Yasemin Karacora, Tolunay Seyfi, Manik Singhal,Meghana Bande (Illinois), Venu Veeravalli (Illinois)

Department of Electrical and Computer EngineeringPurdue University

EURECOM, July 4th, 2017University of Padova, July 11th, 2017

Huawei University Days, Aug. 4th, 2017

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Cloud-based Communication

Global Knowledge / Control available at Central nodes

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Cloud-based Coordinated Multi-Point (CoMP)

Enabling centralized approaches:

1 Cell association decisions

2 Transmission schedules

Enabling CoMP Gains for Cell Edge Users

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Locally Connected Interference Networks

M1 M̂1Tx1 Rx1

M2 M̂2Tx2 Rx2

M3 M̂3Tx3 Rx3

M4 M̂4Tx4 Rx4

Generic Time Varying Channel

Tx i connected to Rx {i, i+ 1, · · · , i+ L}Purdue ECE

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Locally Connected Interference Networks

M1 M1BS1 MT1

M2 M2BS2 MT2

M3 M3BS3 MT3

M4 M4BS4 MT4

BS: Base Station

MT: Mobile TerminalPurdue ECE

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Cloud-based Cell Associations

M1 M1BS1 MT1

M2 M2BS2 MT2

M3 M3BS3 MT3

Each Mobile Terminal can be associated with N Base Stations

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Degrees of Freedom (DoF)

DoF(K,N) = limSNR→∞

sum capacity(K,N, SNR)

log SNR

• Objective: Determine Per User DoF as a function of N .

PUDoF(N) = limK→∞

DoF(K,N)

K

What is the optimal cell association?

Downlink: PUDoFD(N), Uplink: PUDoFU (N)

Average: PUDoFUD(N)

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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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Justifying Choices: Network Topology

Cellular Network Model

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Justifying Choices: Network Topology

Solutions for L = 2 are applicablePurdue ECE

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Justifying Choices: Cooperation Constraint

Modelling a limited capacity backhaul:

• Each mobile terminal can be associated with N base stations

• Associations reflect the allocation of messages to transmitters inthe downlink

• In uplink, associations allow base stations to decode the mobileterminal’s message

Digital Backhaul in both Uplink and Downlink

Solutions can generalize to more practical constraints

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Justifying Choices: 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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Results: Downlink

Using One-Shot Zero-Forcing:

PUDoFZFD (N) =

2N

2N + L

≥ 12 ,∀N ≥

L2

Optimal for L = 1

Assigining Wi to Tx {i, i+ 1, · · · , i+N − 1} ⇒ NN+L

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Results: Downlink

Average Backhaul Load B (Associations per message):

PUDoFZFD (B,L = 1) = PUDoFD(B,L = 1) =

4B − 1

4B

Compare to 2N2N+1

Can achieve 12 using zero-forcing and B = 1 for L ≤ 6

Achieved using convex combination of N = 2B and N = 2B − 1

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Results: Downlink

One-shot Zero-forcing, No Extra Backhaul Load, PUDoF ≥ 12

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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,” submitted to Allerton ’17

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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

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Average Uplink-Downlink DoF

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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Average Uplink-Downlink DoF

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 no backhaul load

• 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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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 Erasures2

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

2 A. El Gamal, V. Veeravalli, “Dynamic Interference Management,”Asilomar ’13

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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 M̂1

M2 M̂2

M3 M̂3

M4 M̂4

M5 M̂5

Maximize probability of message delivery

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Cell Association (N = 1): Low Erasure Probability

Tx1 Rx1

Tx2 Rx2

Tx3 Rx3

M1 M̂1

M2 M̂2

M3 M̂3

Avoiding Interference

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Cell Association (N = 1): Low Erasure Probability

Tx1 Rx1

Tx2 Rx2

Tx3 Rx3

M1 M̂1

M2 M̂2

M3 M̂3

Avoiding Interference

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Cell Association (N = 1)

Tx1 Rx1

Tx2 Rx2

Tx3 Rx3

Tx4 Rx4

M1 M̂1

M2 M̂2

M3 M̂3

M4 M̂4

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 M̂1

M2 M̂2

M4 M̂4

M5 M̂5

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 M̂1

M2 M̂2

M3 M̂3

M4 M̂4

M5 M̂5

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 M̂1

M2 M̂2

M3 M̂3

M4 M̂4

M5 M̂5

Note that limp→1PUDoF(p,N=2)

1−p = 2

Role of Cooperation: CoveragePurdue ECE

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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)3

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?

3Y. Karacora, T. Seyfi, A. El Gamal, “The Role of Transmitter Cooperation inLinear Interference Networks with Block Erasures,” submitted Asilomar ’17

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Wyner’s Interference Networks

M1 M̂1Tx1 Rx1

M2 M̂2Tx2 Rx2

M3 M̂3Tx3 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 M̂1Tx1 Rx1

M2 Tx2 Rx2

M3 M̂3Tx3 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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Converse: Asymmetric Model

Tx1 Rx1

Tx2 Rx2

M3 Tx3 Rx3

Can this message assignment be Useful?

If no, then converse is not restricted to linear schemes

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Summary: Converse Argument

• Channel is time varying with joint pdf

• Once message is transmitted, all connected receivers have astatistically equivalent version

• Coordinated Multi-Point transmission cannot be used to cancelinterference

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Converse: Symmetric Model

Tx1

Tx2

Tx3

Tx4

Rx1

Rx3

Rx2

Rx4

M1

M3

Linear Cooperation over n time slots

nK2 equations in nK

2 variables

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Converse: Symmetric Model

Tx1

Tx2

Tx3

Tx4

Rx1

Rx3

Rx2

Rx4

M1

M3

nK2 equations in nK

2 variables

Equations linearly independent ⇒ PUDoF ≤ 12

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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 problem4

• Cloud communication can enable some of these ideas

4Noga Alon, Amotz Bar-Noy, Nathan Linial, David Peleg, “On the complexity ofradio communication”, 1987,1991

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Coordinated Learning of Network Topology

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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Coordinated Learning of Network Topology

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

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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Coordinated Learning of Network Topology

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

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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Converse?

• Mimic Probabilistic method for broadcast channel?

• Slight variation of Group Testing?

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Conclusions

Cloud-based Wireless Networks:

• Enabling centralized approaches

• new questions and conclusions

• Value of flexible cell association

• Significant CoMP gains

• Learning network topology?

• Benefit with no CSIT / Ad-hoc networks?

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Look for the book!

V. V. Veeravalli, A. El Gamal “Interference Management inWireless Networks: Fundamental Bounds and the Role of

Cooperation”, Cambridge University Press, Jan. 2018

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