1. Towards a Widely Applicable SINR Model for Wireless Access Sharing Christian Scheideler University of Paderborn Joint work with Andrea Richa and Stefan Schmid 1WRAWN'13, Christian Scheideler

2. Motivation SINR model: considered good compromise between realistic modelling of interference and algorithm design and analysis Basic form: node v correctly receives message from node u if and only if P(u)/d(u,v)  N +  w  u,v P(w)/d(w,v)  ●P(u): transmission power of u ●d(u,v): distance between u and v ●N: background noise WRAWN'13, Christian Scheideler2   

3. Motivation Background noise hard to model: ●Temporary Obstacles ● Background noise ● Physical Interference ● Co-existing networks ● Jammer 3WRAWN'13, Christian Scheideler

4. Motivation Ideal world: Classical approach used in theory. 0 time Background noise : noise level 4WRAWN'13, Christian Scheideler

5. Motivation Ideal world: OR 0 time Background noise : noise level 5WRAWN'13, Christian Scheideler

6. Motivation Ideal world: OR Gaussian / predictable Classical approach used in systems. 0 time Background noise : noise level 6WRAWN'13, Christian Scheideler

7. Motivation Real world: How to model this??? 0 time background noise : noise level 7WRAWN'13, Christian Scheideler

8. Our Approach: Adversarial Noise Background noise (microwave, radio signal,...) Intentional jammer Temporary obstacles (cars...) Co-existing networks … X X X X X 8WRAWN'13, Christian Scheideler

9. Our Approach: Adversarial Noise ● Idea: model unpredictable behavior via adversary (i.e., adversarial noise)! X X X X X 9WRAWN'13, Christian Scheideler

10. Our Approach: Adversarial Noise ●(B,T)-bounded adversary: has an overall noise budget of BT for each time interval of length T and each node v that it can distribute among the time steps as it likes ●Node v correctly receives a message from u if and only if P(u)/d(u,v)  ADV(v) +  w  u,v P(w)/d(w,v)  ●ADV(v): adversarial noise at node v WRAWN'13, Christian Scheideler10   

11. Our Approach: Adversarial Noise ●Node v correctly receives a message from u if and only if P(u)/d(u,v)  ADV(v) +  w  u,v P(w)/d(w,v)  ●ADV(v): adversarial noise at node v Other benefit beyond general model for noise: ●softens strict “if and only if” condition of original SINR (adversary controls correct receipt within range) WRAWN'13, Christian Scheideler11   

12. WRAWN'13, Christian Scheideler12 Simple ADV-SINR Model ●single frequency (e.g., sensor nodes) ●at each time step, a node can transmit a packet, and the transmissions are synchronized ●a node may transmit or sense the channel at any time step (half-duplex) ●when sensing the channel with threshold S, a node v may –sense an idle channel whenever ADV(v) +  u  v P(u)/d(u,v)   < S –sense a busy channel otherwise

13. WRAWN'13, Christian Scheideler13 Simple ADV-SINR Model ●single frequency (e.g., sensor nodes) ●at each time step, a node can transmit a packet, and the transmissions are synchronized ●a node may transmit or sense the channel at any time step (half-duplex) ●in addition to sensing an idle or busy channel, a node v receives a message from u whenever the adversarial SINR formula holds Is it possible to design algorithms for this model?

14. WRAWN'13, Christian Scheideler14 Single-hop wireless network ●[Awerbuch, Richa, S. PODC’08] ●n reliable honest nodes and a jammer (adversary); all nodes within transmission range of each other and of the jammer jammer

15. WRAWN'13, Christian Scheideler15 Simple (yet powerful) idea ●each node v sends a message at current time step with probability p v ≤ p max, for constant 0 < p max << 1. p = ∑ p v (aggregate probability) q idle = probability the channel is idle q succ = probability that only one node is transmitting (successful transmission) ●Claim. q idle. p ≤ q succ ≤ (q idle. p)/ (1- p max ) if (number of times the channel is idle) = (number of successful transmissions) p = θ(1) q succ = θ(1) ! (what we want!) ~

16. WRAWN'13, Christian Scheideler16 Basic approach ●a node v adapts p v based only on steps when an idle channel or a successful message transmission are observed, ignoring all other steps (including all the blocked steps when the adversary transmits!) steps jammed by adversary idle steps successful transmissions steps where collision occurred but no jamming time

17. WRAWN'13, Christian Scheideler17 Basic approach ●a node v adapts p v based only on steps when an idle channel or a successful message transmission are observed, ignoring all other steps (including all the blocked steps when the adversary transmits!) steps jammed by adversary idle steps successful transmissions steps where collision occurred but no jamming time

18. WRAWN'13, Christian Scheideler18 Naïve protocol Each time step: ●Node v sends a message with probability p v. If v does not send a message then –if the wireless channel is idle then p v = (1+ γ ) p v –if v received a message then p v = p v /(1+ γ) (where γ = O(1/(log T + loglog n)) )

19. WRAWN'13, Christian Scheideler19 Problems ●Basic problem: Aggregate probability p could be too large. –all time steps blocked due to message collisions w.h.p. steps jammed by adversary idle steps successful transmissions steps where collision occurred but no jamming time

20. WRAWN'13, Christian Scheideler20 Problems ●Basic problem: Aggregate probability p could be too large. –all time steps blocked due to message collisions w.h.p. steps jammed by adversary idle steps successful transmissions steps where collision occurred but no jamming time

21. WRAWN'13, Christian Scheideler21 Problems ●Basic problem: Aggregate probability p could be too large. –all time steps blocked due to message collisions w.h.p. ●Idea: If more than T consecutive time steps without successful transmissions (or idle time steps), then reduce probabilities, which results in fast recovery of p. ●Problem: Nodes do not know T. How to learn a good time window threshold? –It turns out that additive-increase additive-decrease is the right strategy!

22. WRAWN'13, Christian Scheideler22 MAC Protocol for Single Hop ●each node v maintains –probability value p v, –time window threshold T v, and –counter c v ●Initially, T v = c v = 1 and p v = p max (< 1/24). ●synchronized time steps (for ease of explanation) ●Intuition: wait for an entire time window (according to current estimate T v ) until you can increase T v

23. WRAWN'13, Christian Scheideler23 MAC Protocol for Single Hop In each step: ●node v sends a message with probability p v. If v decides not to send a message then –if v senses an idle channel, then p v = min{(1+ γ ) p v, p max } –if v successfully receives a message, then p v = p v /(1+ γ ) and T v = max{T v - 1, 1} ●c v = c v + 1. If c v > T v then –c v = 1 –if v did not receive a message successfully in the last T v steps then p v = p v /(1+ γ ) and T v = T v +1

24. MAC Protocol for ADV-SINR MAC goal: successfully transmit messages Performance metric adopted from [Richa, S., Schmid, Zhang, DISC’10]: ●potentially busy step: ADV(v)  (1-  )S Goal: achieve constant throughput WRAWN'13, Christian Scheideler24 Throughput =

25. MAC Protocol for ADV-SINR Important prerequisites: ●For (B,T)-bounded adversary: B<(1-  )S (otherwise, all steps can be (potentially) busy) ●Area around each v suff. dense, i.e., there must be nodes within a transmission range of r where P/r    S ●  >2 WRAWN'13, Christian Scheideler25 r

26. MAC Protocol for ADV-SINR Initially, each node v sets T v :=1, c v :=1, p v :=p max, and  =O(1/(log T + loglog n)). In each round, every node v decides to transmit a message with probability p v. ●If v does not decide to send a message: –v receives a message: p v :=(1+  ) -1 p v –channel idle: p v :=min{(1+  )p v, p max }, T v :=max{1,T v -1} ●c v :=c v +1 ●If c v >T v then c v :=1, and if there was no idle step within T v steps then p v :=(1+  ) -1 p v, T v :=T v +2 WRAWN'13, Christian Scheideler26

27. WRAWN'13, Christian Scheideler27 Main Result ●Let N = max{T,n} ●Theorem. MAC protocol is 1/2  ((1/  ) 2/(  -2) ) -competitive under any ((1-ε)S,T)-bounded adversary if the protocol is executed for Ω((T log N)/ε + (log 4 N)/(ε γ 2 ) ) steps w.h.p., for any constant 0<ε<1 and any T.

28. Main Result Proof idea: 3 zones WRAWN'13, Christian Scheideler28 transmission zone interference zone outer zone

29. WRAWN'13, Christian Scheideler29 Main Result ●Let N = max{T,n} ●Theorem. MAC protocol is 1/2  ((1/  ) 2/(  -2) ) -competitive under any ((1-ε)S,T)-bounded adversary if the protocol is executed for Ω((T log N)/ε + (log 4 N)/(ε γ 2 ) ) steps w.h.p., for any constant 0<ε<1 and any T. In unit-disk model,  (1)-competitive possible!

30. Main Result ●((1-  )S,T)-bounded adversary,  0 WRAWN'13, Christian Scheideler30 transmission zone interference zone r=  ((1/  ) 1/(  -2) )

31. Main Result ●ideally, p=  (  2/(  -2) ) in each transmission zone WRAWN'13, Christian Scheideler31 transmission zone interference zone r=  ((1/  ) 1/(  -2) )

32. Main Result ●better: power control? WRAWN'13, Christian Scheideler32 transmission zone interference zone r=  ((1/  ) 1/(  -2) )

33. Other adversarial modeling in wireless networks ●Adversary: used to model external world ●More benign: –Control packet injection rates –Control mobility ●Intentionally disruptive: –jammers ●More disruptive: malicious adversaries –Undermine security –Control Byzantine nodes (introduce fake messages) WRAWN'13, Christian Scheideler33

34. Other adversarial modeling in wireless networks ●Adversarial packet injection/queueing: –[Chlebus, Kowalski, Rokicki, PODC’06], [Andrews, Jung, Stolyar, STOC’07], [Anantharamu, Chlebus, Rokicki, OPODIS’09], [Chlebus, Kowalski, Rokicki, Distributed Computing’09], [Lim, Jung, Andrews, INFOCOM’12] ●Multi-channel access with adversarial jamming: –[Dolev, Gilbert, Guerraoui, Newport, DISC’07], [Anantharamu, Chlebus, Kowalski, Rokicki, SIROCCO’11], [Dolev,Gilbert, Khabbazian, Newport, DISC’11], [Daum, Gilbert, Kuhn, Newport, PODC’12], [Ghaffari, Gilbert, Newport, Tan, OPODIS’12] WRAWN'13, Christian Scheideler34

35. Other adversarial modeling in wireless networks ●Broadcasting\Gossiping with adversarial jamming: –[Dolev, Gilbert, Guerraoui, Newport, DISC’07], [Dolev,Gilbert, Khabbazian, Newport, DISC’11], [Daum, Gilbert, Kuhn, Newport, PODC’12], [Ghaffari, Gilbert, Newport, Tan, OPODIS’12] ●Capacity Maximization with adversarial jamming: [Dams, Hoefer, Kesselheim, unpublished] ●Malicious adversary: –[Dolev, Gilbert, Guerraoui, Newport, DISC’07], [Gilbert, Young, PODC’12] ●Infection spreading with adversarial mobility: [Wang,Krishnamachari, ] ●Etc. WRAWN'13, Christian Scheideler35

36. 36 Future Work: Adversarial Jamming ●Jamming-resistant protocols with power control: –Increasing power increases chance that signal will overcome jamming activity, however… –Increasing power also generates more interference… –Also adapt noise threshold level? ●How about reactive jammers under SINR? ●Can the protocols be modified so that no rough bounds on n and T are required in  ? ●Stochastic/oblivious jammers: Simpler to handle? E.g., a constant  seems to work fine here. WRAWN'13, Christian Scheideler

37. Power Control Problem: many parameters (p v, T v, P v, S v ) ●VERY tricky to find setup that avoids any scenarios where protocol can get stuck ●Even much more tricky to prove that a correct protocol works WRAWN'13, Christian Scheideler37

38. WRAWN'13, Christian Scheideler38 Thank you! Questions?