Interference Management in Wireless Networks

Interference Management in Wireless Networks Aly El Gamal Department of Electrical and Computer Engineering Purdue University Venu Veeravalli Coordinated Science Lab Department of Electrical and Computer Engineering University of Illinois at Urbana-Champaign

2 / 100 Just Published - Cambridge University Press

3 / 100 Part 1: Introduction

4 / 100 Explosion in Wireless Data Traffic How to accommodate exponential growth without new useful spectrum?

5 / 100 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!

6 / 100 By Adding More Basestations?

7 / 100 Through Improved Interference Management Several useful engineering solutions for managing interference But... What are fundamental limits?

8 / 100 References 1 T.S. Rappaport. Wireless communications: Principles and practice. New Jersey: Prentice Hall 1996. 2 A. J. Viterbi. CDMA: Principles of spread spectrum communication. Addison Wesley, 1995. 3 D. Tse and P. Viswanath. Fundamentals of wireless communication. Cambridge University Press, 2005. 4 E. Biglieri et al. Principles of Cognitive Radio. Cambridge University Press, 2012.

9 / 100 Part 2: Degrees of Freedom Characterization of Interference Channels

10 / 100 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 = sum capacity lim SNR 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

11 / 100 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

12 / 100 K-user (SISO) Interference Channel W 1 Tx1 Rx1 Ŵ 1 W 2 Tx2 Rx2 Ŵ 2 W 3 Tx3 Rx3 Ŵ 3 How many Degrees of Freedom (DoF)?

13 / 100 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

14 / 100 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 interference suppression! Interference Alignment [Cadambe & Jafar 08]

15 / 100 Linear Transmit/Receive Strategies Interference Channel with Tx/Rx Linear Coding U 1 0 0 H 1,1 H 1,2 H 1,3 V 1 0 0 0 U 2 0 H 2,1 H 2,2 H 2,3 0 V 2 0 0 0 U 3 H 3,1 H 3,2 H 3,3 0 0 V 3 }{{}}{{}}{{} Receive Beams Channel Transmit Beams End-to-End matrix is Diagonal = No Interference! # streams = Size of the Diagonal matrix

16 / 100 DoF of Linear Strategies U 1 0 0 H 1,1 H 1,2 H 1,3 V 1 0 0 0 U 2 0 H 2,1 H 2,2 H 2,3 0 V 2 0 0 0 U 3 H 3,1 H 3,2 H 3,3 0 0 V 3 (Symmetric) MIMO: N = # antennas H i,j : NT NT block-diagonal matrix Symbol Extensions (Time or Frequency) T = # symbol extensions DoF (T ) = (#streams)/t

17 / 100 Complexity of asymptotic Interference Alignment 0.5 0.49 PUDoF 0.48 0.47 0.46 0.45 0.44 0 20 40 60 80 100 # symbol extensions PUDoF of 0.5 is achieved asymptotically

18 / 100 Complexity of asymptotic Interference Alignment 0.5 0.48 3 User 0.46 PUDoF 0.44 0.42 0.4 4 User 0.38 0.36 0.34 0.32 0 200 400 600 800 1000 1200 1400 # symbol extensions [Choi, Jafar, and Chung, 09]

19 / 100 Interference Alignment Summary + Achieves optimal PUDoF for fully connected channel - Requires global channel state information (CSI) - Requires large number of symbol extensions

20 / 100 References 1 V.R. Cadambe and S.A. Jafar. Interference Alignment and Degrees of Freedom of the K-User Interference Channel. IEEE Trans. Inform. Theory, August 2008. 2 S. A. Jafar. Interference Alignment A New Look at Signal Dimensions in a Communication Network. In Foundations and Trends in Communications and Information Theory, NOW Publications, 2010. 3 A. Host-Madsen and A. Nosratinia, The multiplexing gain of wireless networks, in Proceedings of ISIT, 2005. 4 S.W. Choi, S.A. Jafar, and S.-Y. Chung. On the beamforming design for efficient interference alignment. IEEE Communications Letters, 2009.

21 / 100 Part 3: Coordinated Multi-Point Transmission

22 / 100 K-User Interference Channel Channel State Information known at all nodes. W 1 Tx1 Rx1 Ŵ 1 W 2 Tx2 Rx2 Ŵ 2 W 3 Tx3 Rx3 Ŵ 3

23 / 100 Coordinated Multi-Point (CoMP) Transmission Messages are jointly transmitted using multiple transmitters. W 1 Tx1 Rx1 Ŵ 1 W 2 Tx2 Rx2 Ŵ 2 W 3 Tx3 Rx3 Ŵ 3

24 / 100 CoMP Transmission Each message is jointly transmitted using M transmitters Message i is transmitted jointly using the transmitters in T i For all i [K], T i M We consider all message assignments that satisfy the cooperation constraint

25 / 100 Degrees of Freedom (DoF) DoF = sum capacity lim SNR log SNR Objective: Determine the DoF as a function of K and M DoF(K, M) PUDoF(M) = lim K K Is PUDoF(M)>PUDoF(1) for M > 1?

26 / 100 Example: Two-user Interference Channel W 1 Tx1 Rx1 Ŵ 1 W 2 Tx2 Rx2 Ŵ 2 No Cooperation, DoF=1, Time Sharing Full Cooperation, DoF=2, ZF Transmit Beamforming

27 / 100 No Cooperation (M = 1) For M = 1, outer bound = K/2 The outer bound can be achieved by jointly coding across multiple parallel channels [Cadambe & Jafar 08]: Corollary DoF(K, M = 1, L) DoF(K, M = 1) = lim = K/2 L L where L is the number of parallel channels Without cooperation, the Per User DoF number is given by PUDoF(M = 1) = 1 2

28 / 100 Full Cooperation (M = K) In this case, the channel is a MISO Broadcast channel. Each message is available at K antennas, and hence, can be canceled at K 1 receivers. Each user achieves 1 DoF, DoF(K, M = K) = K. What happens with partial cooperation (1 < M < K)?

29 / 100 Clustering W 1 Tx1 Rx1 Ŵ 1 W 2 Tx2 Rx2 Ŵ 2 W 3 Tx3 Rx3 Ŵ 3 W 4 Tx4 Rx4 Ŵ 4 No Degrees of Freedom Gain

30 / 100 Spiral Message Assignment T i = {i, i + 1,..., i + M 1} W 1 Tx1 Rx1 Ŵ 1 W 2 Tx2 Rx2 Ŵ 2 W 3 Tx3 Rx3 Ŵ 3

31 / 100 Spiral Message Assignment: Results Theorem The DoF of interference channel with a spiral message assignment satisfies K + M 1 K + M 1 DoF(K, M) 2 2 Proof of Achievability: First M 1 users are interference-free, and interference occupies half the signal space at each other receiver Generalizes the Asymptotic Interference Alignment scheme

32 / 100 Outline of the Achievable Scheme IA Encoder ZF Encoder Original Channel IA Decoder Derived Channel Approach: 1 ZF Step: Exploit cooperation to transform the interference channel into a derived channel (with single-point transmission) 2 IA Step: Use the known IA techniques to design beams for derived channel 3 Prove that the asymptotic IA step works for generic channel coefficients

33 / 100 DoF Outer Bound: Results Definition We say that a message assignment satisfies a local cooperation constraint if and only if r(k) = o(k), and for all K user channels, T i {i r(k), i r(k) + 1,..., i + r(k)}, i [K] Theorem With the restriction to local cooperation, PUDoF loc (M) = 1 2 Local cooperation cannot achieve a scalable Dof gain

34 / 100 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 scalable DoF gain

35 / 100 References 1 P. Marsch and G. P. Fettweis Coordinated Multi-Point in Mobile Communications: from theory to practice, First Edition, Cambridge, 2011. 2 A. Host-Madsen and A. Nosratinia, The multiplexing gain of wireless networks, in Proc. IEEE International Symp. Inf. Theory (ISIT), 2007. 3 V. Cadambe and S. A. Jafar, Interference alignment and degrees of freedom of the K-user interference channel, IEEE Trans. Inf. Theory, 2008. 4 V. S. Annapureddy, A. El Gamal, and V. V. Veeravalli, Degrees of Freedom of Interference Channels with CoMP Transmission and Reception, IEEE Trans. Inf. Theory, 2012. 5 A. El Gamal, V. S. Annapureddy, and V. V. Veeravalli, On Optimal Message Assignments for Interference Channels with CoMP Transmission, in Proc. CISS, 2012 6 C. Wilson and V. Veeravalli, Degrees of Freedom for the Constant MIMO Interference Channel with CoMP Transmission, IEEE Trans. Comm., 2014

36 / 100 Part 4: Locally Connected Networks

37 / 100 Locally Connected Model Tx i is connected to receivers {i, i + 1,..., i + L}. Tx 1 Rx 1 Tx 1 Rx 1 Tx 2 Rx 2 Tx 2 Rx 2 Tx 3 Rx 3 Tx 3 Rx 3 Tx 4 Rx 4 Tx 4 Rx 4 Tx 5 Rx 5 L = 2 Tx 5 Rx 5 Wyner Model: L =1

38 / 100 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

39 / 100 Justifying Choices: Network Topology Cellular Network Model

40 / 100 Justifying Choices: Network Topology Solutions for L = 2 are applicable

41 / 100 Results for Wyner Model [Lapidoth-Shamai-Wigger 07] W 1 Tx 1 Rx 1 W 1 W 2 Tx 2 Rx 2 W 2 W 3 Tx 3 Rx 3 W 4 Tx 4 Rx 4 W 4 W 5 Tx 5 Rx 5 W 5 W 6 Tx 6 Rx 6 Backhaul load factor =1 PUDoF (L=1,M=2) = 2/3 > 1/2

42 / 100 Example: No Cooperation W 1 Tx 1 Rx 1 W 1 Tx 1 Rx 1 W 2 Tx 2 Rx 2 W 2 Tx 2 Rx 2 W 3 Tx 3 Rx 3 W 3 Tx 3 Rx 3 PUDoF(L = 1,M = 1) = 1 2 PUDoF(L = 1,M = 1) = 2 3 Interference-aware message assignment + Fractional reuse

43 / 100 Locally Connected IC with CoMP: Main Result Theorem Under the general cooperation constraint T i M, i {1, 2,..., K}, 2M 2M + L 1 PUDoF(L, M) 2M + L 2M + L and the optimal message assignment satisfies a local cooperation constraint. Corollary PUDoF(L = 1, M) = 2M 2M + 1

44 / 100 DoF Achieving Scheme W 1 Tx 1 Rx 1 W 1 W 2 Tx 2 Rx 2 W 2 W 3 Tx 3 Rx 3 W 4 Tx 4 Rx 4 W 4 W 5 X 5 Rx 5 W 5 Backhaul load factor =6/5 PUDoF (L=1,M=2) = 4/5 > 2/3

45 / 100 DoF Outer Bound Have to consider all possible message assignments satisfying T i M, i [K] 1 First simplify the combinatorial aspect of the problem by identifying useful message assignments 2 Then derive an equivalent model with fewer receivers and same DoF

46 / 100 DoF Outer Bound: Useful Message Assignments An assignment of a message W x to a transmitter T y is useful only if one of the following conditions holds: 1 Signal delivery: T y is connected to the designated receiver R x 2 Interference mitigation: T y is interfering with another transmitter T z, both carrying the message W x

47 / 100 DoF Outer Bound: Useful Message Assignments Tx1 Tx2 Rx1 Rx2 W 3 Tx3 Rx3 Ŵ 3 Tx4 Rx4 Assigning W 3 to Tx1 is not useful.

48 / 100 DoF Outer Bound: Useful Message Assignments Corollary An assignment of a message W x to a transmitter T y is useful only if there exists a chain of interfering transmitters carrying W x that includes T y and another transmitter T z that is connected to R x Proves optimality of local cooperation

49 / 100 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 higher throughput Fractional reuse and zero-forcing transmit beam-forming are sufficient to achieve PUDoF gains, without need for symbol extensions and interference alignment

50 / 100 Uplink: Achieving Full DoF M 1 BS1 MT1 M 1 M 2 BS2 MT2 M 2 M 3 BS3 MT3 M 3 Associating each MT with two BSs connected to it Message Passing Decoding: Interference-free Degrees of Freedom

51 / 100 Results: Uplink 1 1 L + 1 N PUDoF ZF U (N) = N+1 L L+2 2 N L 2N 2N+L 1 N L 2 1 1 2, N L 2 Higher than Downlink Is Cooperation useful for N < L 2? 1 M. Singhal, A. El Gamal, Joint Uplink-Downlink Cell Associations for Interference Networks with Local Connectivity, Allerton 17

52 / 100 Average Uplink-Downlink DoF M 1 BS1 MT1 M 1 M 2 BS2 MT2 M 2 M 3 BS3 MT3 M 3 M 4 BS4 MT4 M 4 M 5 BS5 MT5 M 5 Downlink Associations Uplink Associations N = 3 PUDoF = 1+ 4 5 2 = 9 10

53 / 100 Average Uplink-Downlink DoF M 1 BS1 MT1 M 1 M 2 BS2 MT2 M 2 M 3 BS3 MT3 M 3 M 4 BS4 MT4 M 4 M 5 BS5 MT5 M 5 PUDoF UD (N, L = 1) = 4N 3 4N 2

54 / 100 Average Uplink-Downlink DoF For L 2: PUDoF ZF UD(N) 1 2 ( ( L 1 + 2N 2N+L 2 +δ+n (L+1) N )) L + 1 N 1 N L where δ = (L + 1) mod 2. For L + 1 N, scheme is different from both downlink and uplink

55 / 100 Summary of Insights Local cooperation is optimal for locally connected networks Significant DoF gains achieved with ZF and message passing decoding Limited cell associations Same for downlink and uplink Limited associations and no delay constraint CoMP useful?

56 / 100 Further Questions 1 General network topologies 2 When to simplify into optimizing for uplink / downlink only 3 Constrain average number of cell associations

57 / 100 References 1 V. S. Annapureddy, A. El Gamal, and V. V. Veeravalli, Degrees of Freedom of Interference Channels with CoMP Transmission and Reception, 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 cellular multiple-access channel, IEEE Trans. Inf. Theory, 1994. 4 S. Shamai and M. A. Wigger, Rate-limited Transmitter Cooperation in Wyner s Asymmetric Interference Network, in Proc. IEEE Int. Symp. Inf. Theory, 2014

58 / 100 Part 5: Cellular Network and Backhaul Load Constraint

59 / 100 Backhaul Load Constraint More natural cooperation constraint that takes into account overall backhaul load: i [K] T i B K Solution under transmit set size constraint T i M, i [M], can be used to provide solutions under backhaul load constraint

60 / 100 Wyner s Model with Backhaul Load Constraint Tx 1 Tx 2 Tx 3 Rx 1 Rx 2 Rx 3 Theorem Under cooperation constraint i [K] T i BK, PUDoF(B) = 4B 1 4B Recall that T i M, i [K] PUDoF(M) = 2M 2M+1

61 / 100 Coding Scheme: B = 1 W 1 Tx 1 Rx 1 W 1 Tx 1 Rx 1 W 2 Tx 2 Rx 2 W 2 Tx 2 Rx 2 W 3 Tx 3 Rx 3 W 3 Tx 3 Rx 3 W 4 Tx 4 Rx 4 B = 2 3 PUDoF = 2 3 W 5 X 5 Rx 5 3K B = 6 5 PUDoF = 4 5 8 users 5K 8 users PUDoF (B = 1) = 3 4

62 / 100 Application in Denser Networks Tx i is connected to receivers {i, i + 1,..., i + L}. Tx 1 Tx 2 Rx 1 Rx 2 Result: Using only zero-forcing transmit beamforming and fractional reuse: Tx 3 Rx 3 PUDoF(L, B = 1) 1, L 6. 2 Tx 4 Rx 4 Tx 5 Rx 5 L = 2 without need for interference alignment and symbol extensions

63 / 100 Application in Denser Networks PUDoF(M = 1) = 1 2 PUDoF(B = 1) 5 9

64 / 100 Interference in Cellular Networks Locally (partially) connected interference channel!

65 / 100 Interference Graph for Single Tier Tx,Rx pair Each node represents a Tx-Rx pair

66 / 100 No Intra-sector Interference

67 / 100 No Extra Backhaul Load B = 1, PUDoF= 1 2

68 / 100 Discussion: Cloud-based Communication Global Knowledge / Control available at Central nodes

69 / 100 Discussion: Understanding Network Topologies Centralized Solution Benchmark for Distributed Algorithms Enables Multi-RAT Networks Enables AI and Blockchain 2 2 A. El Gamal, H. El Gamal, A Blockchain Example for Cooperative Interference Management, submitted to WComm Letters.

70 / 100 Summary Infrastructure enhancements in backhaul can be exploited through cooperative 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

71 / 100 References 1 A. El Gamal and V. V. Veeravalli, Flexible Backhaul Design and Degrees 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 Backhaul Design with Cooperative Transmission in Cellular Interference Networks, in Proc. IEEE Int. Symp. Inf. Theory, 2015 3 V. Ntranos, M. A. Maddah-Ali, and G. Caire, Cellular Interference Alignment, arxiv, 2014. 4 V. Ntranos, M. A. Maddah-Ali, and G. Caire, On Uplink-Downlink Duality for Cellular IA, arxiv, 2014.

72 / 100 Part 6: Dynamic Interference Management

73 / 100 Application: Vehicle-to-Infrastructure (V2I) Networks Network with Dynamic Nature Delay Sensitive - Simple Coding Schemes Desired

74 / 100 Application: Vehicle-to-Infrastructure (V2I) Networks Associations between On-Board-Units and Road Side Units

75 / 100 Extensions 1 Interference Networks with Block Erasures 2 Interference Management with no CSIT 3 Fast Network Discovery

76 / 100 Deep Fading Block Erasures 3 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 13

77 / 100 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

78 / 100 Average Degrees of Freedom (DoF) DoF(K, N) = sum capacity(k, N, SNR) lim SNR log SNR DoF(K, N) PUDoF(N) = lim K K For dynamic topology: PUDoF is a function of p and N PUDoF(p, N) = E p [PUDoF(N)]

79 / 100 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

80 / 100 Cell Association (N = 1): Results PUDoFp(M=1)/(1 p) 1 0.9 0.8 0.7 0.6 0.5 (1) PUDoF p (2) PUDoF p (3) PUDoF p 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 p

81 / 100 Cell Association (N = 1): High Erasure Probability M 1 Tx1 Rx1 ˆM1 M 2 Tx2 Rx2 ˆM2 M 3 Tx3 Rx3 ˆM3 M 4 Tx4 Rx4 ˆM4 M 5 Tx5 Rx5 ˆM5 Maximize probability of message delivery

82 / 100 Cell Association (N = 1): Low Erasure Probability M 1 Tx1 Rx1 ˆM1 M 2 Tx2 Rx2 ˆM2 M 3 Tx3 Rx3 ˆM3 Avoiding Interference

83 / 100 Cell Association (N = 1): Low Erasure Probability M 1 Tx1 Rx1 ˆM1 M 2 Tx2 Rx2 ˆM2 M 3 Tx3 Rx3 ˆM3 Avoiding Interference

84 / 100 Cell Association (N = 1) M 1 Tx1 Rx1 ˆM1 M 2 Tx2 Rx2 ˆM2 M 3 Tx3 Rx3 ˆM3 M 4 Tx4 Rx4 ˆM4 Optimal at middle values of p

85 / 100 CoMP Transmission (N = 2): No Erasures M 1 Tx1 Rx1 ˆM1 M 2 Tx2 Rx2 ˆM2 Tx3 Rx3 M 4 Tx4 Rx4 ˆM4 M 5 Tx5 Rx5 ˆM5 PUDoF(p = 0, N = 2) = 4 5

86 / 100 Interference-Aware Message Assignment M 1 Tx1 Rx1 ˆM1 M 2 Tx2 Rx2 ˆM2 M 3 Tx3 Rx3 ˆM3 M 4 Tx4 Rx4 ˆM4 M 5 Tx5 Rx5 ˆM5 Note that lim p 1 PUDoF(p,N=2) 1 p = 8 5

87 / 100 High Erasure Probability: Ignoring Interference M 1 Tx1 Rx1 ˆM1 M 2 Tx2 Rx2 ˆM2 M 3 Tx3 Rx3 ˆM3 M 4 Tx4 Rx4 ˆM4 M 5 Tx5 Rx5 ˆM5 Note that lim p 1 PUDoF(p,N=2) 1 p = 2 Role of Cooperation: Coverage

88 / 100 CoMP Transmission in Dynamic Linear Network Definition A message assignment is universally optimal if it can be used to achieve PUDoF(p, N) for all values of p. Theorem For any value of N, there is no universally optimal message assignment. Knowledge of p is necessary to design the optimal scheme

89 / 100 CoMP Transmission (N = 2) 4 1 Identified optimal zero-forcing associations 2 As p goes from 1 to 0, role of cooperation shifts to interference management 3 As p goes from 0 to 1, role of cooperation shifts to coverage extension Knowledge of p is necessary Needed level of accuracy? 4 Y. Karacora, T. Seyfi, A. El Gamal, The Role of Transmitter Cooperation in Linear Interference Networks with Block Erasures, Asilomar 17

90 / 100 Wyner s Interference Networks M 1 Tx1 Rx1 ˆM1 M 2 Tx2 Rx2 ˆM2 M 3 Tx3 Rx3 ˆM3 Is Transmitter Cooperation with no CSIT useful?

91 / 100 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!

92 / 100 TDMA: Asymmetric Model M 1 Tx1 Rx1 ˆM1 M 2 Tx2 Rx2 M 3 Tx3 Rx3 ˆM3 Last transmitter inactive No inter-subnetwork interference

93 / 100 Converse: Asymmetric Model Tx1 Rx1 M 2 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

94 / 100 Converse: Asymmetric Model Tx1 Rx1 M 2 Tx2 Rx2 Tx3 Rx3 Knowing Rx1, Rx3, Rx4, Rx6,..., we reconstruct all messages PUDoF 2 3

95 / 100 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

96 / 100 Coordinated Learning of Network Topology Earlier work for the broadcast problem 5 Cloud communication can enable some of these ideas 5 Noga Alon, Amotz Bar-Noy, Nathan Linial, David Peleg, On the complexity of radio communication, 1987,1991

97 / 100 Coordinated Learning of Network Topology Lemma Let x 1,, x L K be L distinct integers, then for every 1 i L, there exists a prime p L log K such that, x i x j mod p, j {1,, L}, j i L : Connectivity parameter K : Number of users

98 / 100 Coordinated Learning of Network Topology Lemma Let x 1,, x L K be L distinct integers, then for every 1 i L, there exists a prime p L log K such that, x i x j mod p, j {1,, L}, j i 1 Let p 1,, p m be the prime numbers in {1,, L log K} 2 m phases of transmission 3 in i th phase, x j transmits in slot x j mod p i

99 / 100 Coordinated Learning of Network Topology Lemma Let x 1,, x L K be L distinct integers, then for every 1 i L, there exists a prime p L log K such that, x i x j mod p, j {1,, L}, j i 1 Let p 1,, p m be the prime numbers in {1,, L log K} 2 m phases of transmission 3 in i th phase, x j transmits in slot x j mod p i O(L 2 log 2 K) Communication rounds

100 / 100 Summary Exploiting infrastructure enhancements in backhaul to achieve rate gains No delay requirements (ZF Transmit Beamforming) No or minimal backhaul load Promising results for cellular networks