Information Theory of Cloud-based Cooperative Interference ...elgamala/Padova2017.pdf · Achieved...
Transcript of Information Theory of Cloud-based Cooperative Interference ...elgamala/Padova2017.pdf · Achieved...
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
10Purdue ECE
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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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