1. 1 A General Algorithm for Interference Alignment and Cancellation in Wireless Networks Li (Erran) Li Bell Labs, Alcatel-Lucent Joint work with: Richard Alimi (Yale), Dawei Shen (MIT), Harish Viswanathan (Bell Labs), Richard Yang (Yale)

2. 22 Talk Outline Wireless mesh network design General interference alignment and cancellation (GIAC) problem  Design overview  Problem formulation  Computational complexity  Algorithm GNU radio testbed implementation Related work Conclusion and future work

3. 33 Limitation of Conventional Mesh Network Design Current mesh networks have limited capacity [dailywireless.org]  Increased popularity of video streaming and large downloads will only worsen congestion Network-wide transport capacity does not scale [Gupta and Kumar 2001] O( ) where n is the number of users Traditional design limitations:  Treats wireless transmission as a point-to-point link for unicast  Treats interference from other transmissions as noise

4. 44 A New Paradigm for Mesh Network Design Wireless networks propagate information rather than transporting packets  Physical layer: interference cancellation, zero forcing, interference alignment  Network coding Capacity scales better in this new paradigm  for α in [2,3) and random placement [Ozgur, Leveque and Tse, IEEE Trans. Info. Theory’07]  Optimal scaling requires cooperative transmission when node placements are “less regular” [Niesen, Gupta and Shah’08]

5. 55 GIAC Design Overview Goal: increase concurrency through interference cancellation techniques Design constraints and guidelines  Global cooperation not practical: cooperate locally  No explicit exchange of data packets for cooperation: exploit naturally occurring opportunities  Channel state information essential for any cooperative techniques: exchange only channel state information and necessary signaling messages

6. 66 GIAC Problem Formulation Objective: find the max number of simultaneous transmissions  Connectivity graph G=(V, E)  Interference graph G I =(V, E I )  A set of senders S V  A set of receivers R V  Receiver can be one or two hops away from sender  pkt i is destined to R i  Each node u has a packet pool L u which records overheard packets  Assume transmission rate is fixed at ρ  Assume channel matrix H is known Y = HX+N; X: input, Y: output, N: noise A snapshot of a local neighborhood SjSj RiRi h ij

7. 77 GIAC Problem Formulation (cont’d) How to enable simultaneous transmissions? Goal: where is a diagonal matrix Thus, y i =λ i x i +N i Sender pre- coding Receiver interference cancellation

8. 88 GIAC Problem Formulation (cont’d) Example:  u 1 has required channel state information  u 1 can trigger S 1 and S 2 to transmit simultaneously S1S1 R1R1 S2S2 R2R2 u1u1 u2u2 t=0

9. 99 GIAC Problem Formulation (cont’d) Example:  u 1 has required channel state information  u 1 can trigger S 1 and S 2 to transmit simultaneously S1S1 R1R1 S2S2 R2R2 u1u1 u2u2 t=1

10. 10 GIAC Problem Formulation (cont’d) Example:  u 1 has required channel state information  u 1 can trigger S 1 and S 2 to transmit simultaneously S1S1 R1R1 S2S2 R2R2 u1u1 u2u2 t=2

11. 11 Talk Outline Wireless mesh network design General interference alignment and cancellation (GIAC) problem  Design overview  Problem formulation  Computational complexity  Algorithm GNU radio testbed implementation Related work Conclusion and future work

12. 12 GIAC Complexity: Sender Side Computational complexity matters because algorithm runs in fast path The interference control problem is NP-hard  Consider a special case where the packet pool at each node is empty  Reduction from max independent set for each e=(v i, v j ), create a gadget with sender S i, S j, and receiver R i, R j where S i, S j has pkt i, pkt j SiSi SjSj RiRi RjRj

13. 13 GIAC Complexity: Receiver Side The problem is NP-hard  Reduction from clique: given G=(V,E), for each e=(v i, v j ), create a gadget with sender S i, S j, and receiver R i, R j where S i, S j has pkt i, pkt j and receiver R i, R j has pkt j, pkt i  Assume H has full rank (no channel alignments) SiSi SjSj RiRi RjRj

14. 14 GIAC: Optimal Algorithm for a Special Case Assumptions  No receiver-side cancellation  Channel matrix H has full rank (ignore channel alignment cases)  No power constraint Key intuition: for each transmitted packet pkt i, need an independent packet pkt i to cancel its interference at each receiver 1. Let PKT be the set of packets to be transmitted 2. For each pkt i, Let n i be the number of senders 3. While |PKT|>min{n i | pkt i PKT} 4. Let pkt be the one with minimal n i 5. PKT = PKT-{pkt} 6. done

15. 15 GIAC: Optimal Algorithm for a Special Case (cont’d) S1S1 S2S2 S4S4 R1R1 R2R2 S3S3 R3R3 pkt 1,pkt 2, pkt 3 : n 1, n 2, n 3 : 221 Example {pkt 1, pkt 2 } |{pkt 1, pkt2}| = min{n 1, n 2 } Stop! n 3 <|{pkt 1, pkt 2, pkt 3 }|

16. 16 GIAC Algorithm for One-Hop Opportunities Feasibility problem:  Given a set of packets and power constraint at each sender, can they be transmitted at the same time at a given rate? Yes, a feasible solution does not exist iff there exists W s.t. [ρ, …, ρ] W R

17. 17 GIAC Algorithm for One-Hop Opportunities (cont’d) Convex programming to compute feasibility Notation: H: channel matrix m: number of senders k: number of receivers Ф: coding coefficient matrix P: max power N i : noise at receiver R i

18. 18 GIAC Algorithm for One-Hop Opportunities (cont’d) 1. Let PKT be the set of packets to be transmitted 2. Create pseudo senders for any packet pkt a receiver has 3. While NotFeasible(PKT, H, ρ) 4. n i = maxNonIntR(PKT, H, i), i=1,2,…,|PKT| 5. Let pkt be the one with minimal n i 6. PKT = PKT-{pkt} 7. done 1. Let PKT be the set of packets to be transmitted 2. For each pkt i, Let n i be the number of senders 3. While |PKT|> min{n i | pkt i PKT} 4. Let pkt be the one with minimal n i 5. PKT = PKT-{pkt} 6. done Generalize the special case's optimal algorithm

19. 19 GIAC Algorithm for One-Hop Opportunities (cont’d) Computing max non-interfering receivers of pkt i : maxNonIntR(PKT, H, i)  Find the maximum matching M i between senders with pkt i and receivers in interference graph;  Let L i be the set of receivers not interfered by pkt i and not in the matching  maxNonIntR(PKT, H, i) = | M i | + | L i |

20. 20 GIAC Algorithm for One-Hop Opportunities (cont’d) Example S1S1 R1R1 S2S2 S3S3 R2R2 R3R3 Receivers not interfered by pkt 1 : {R 3 } Similarly, n 2 = |M 2 |+ |L 2 |=1+2=3 ; n 3 = |M 3 |+ |L 3 |=2+1=3 |M 1 |=2 |L 1 |=1 n 1 = |M 1 |+ |L 1 |= 3 S1S1 R1R1 S2S2 R2R2 Max matching of pkt 1

21. 21 GIAC Algorithm for One-Hop Opportunities (cont’d) Example 2 S1S1 R1R1 S2S2 R2R2 Create pseudo senders R1R1 R2R2 S1S1 S2S2 S3S3 S4S4

22. 22 GIAC Implementation in GNU Radio Time synchronization  Only need to synchronize within cyclic prefix  Sampling rate 500KHz Drift within 0.75 samples/sec

23. 23 GIAC Implementation in GNU Radio: (cont’d) Channel estimation and feedback  Need amplitude and phase offset  Stable phase offset estimate difficult in GNU radio Current estimation error: 15~20Hz Feedback delay: software processing delay, hardware-- software latency

24. 24 Related Work Practical interference cancellation techniques  Networked MIMO [Samardzija et al, Bell Labs Project 2005~now]  Physical/analog layer network coding [Zhang et al, MOBICOM’06, Katti et al, SIGCOMM’07]  Interference alignment and cancellation [Gollakota, Perli, Katabi, SIGCOMM’09]

25. 25 Conclusion and Future Work We have designed algorithms and protocols for opportunistic interference control Ongoing and future work  Implementation related Channel phase shift estimation and feedback Other implementation platforms, e.g. Bell Labs networked MIMO platform or MSR Sora?  How to solve the problem when there are multiple antennas?  Information theory related How much does dirty paper coding help? Can our interference control scheme achieve optimal capacity scaling in networks with “less regular” node deployments?

26. 26 Q and A Questions?

27. 27 MatrixNet Architecture Local Interference Graph Local Channel Information Base Estimated Local Node-pair Channels Routing Information Base Routing/flow Information Base Local Flows Fairness Policy Management Information Base Power Management Policy … Forwarding Queue Overheard Queue MatrixNet Routing MatrixNet MAC Concurrency Selection MatrixNet Encoding/Decoding Coordination Vectors MatrixNet Frame Queue

28. 28 Estimated local node-pair Channels (disseminate) Local Interference Graph MatrixNet Architecture Overheard packet cache Concurrency Algorithm & Scheduler Inferred local flows Pending packet queue Encoding & decoding vectors (disseminate) Coordinated transmission Routing