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Towards a Widely Applicable SINR Model for Wireless Access Sharing

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

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Towards a Widely Applicable SINR Model for Wireless Access Sharing

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

  2. Motivation SINR model: consideredgoodcompromisebetweenrealisticmodellingofinterferenceandalgorithm design andanalysis Basic form:nodevcorrectlyreceivesmessagefromnodeuifandonlyif P(u)/d(u,v)a N + Swu,v P(w)/d(w,v)a • P(u): transmission power ofu • d(u,v): distancebetweenuandv • N: backgroundnoise  b WRAWN'13, Christian Scheideler

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

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

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

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

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

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

  9. Our Approach: Adversarial Noise • Idea: model unpredictablebehavior via adversary (i.e., adversarialnoise)! X X X X X WRAWN'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)a ADV(v) + Swu,vP(w)/d(w,v)a • ADV(v): adversarial noise at node v  b WRAWN'13, Christian Scheideler

  11. Our Approach: Adversarial Noise • Node v correctly receives a message from uif and only if P(u)/d(u,v)a ADV(v) + Swu,vP(w)/d(w,v)a • 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)  b WRAWN'13, Christian Scheideler

  12. 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 thresholdS, a node v may • sense an idle channel wheneverADV(v) + Suv P(u)/d(u,v)a< S • sense a busy channel otherwise WRAWN'13, Christian Scheideler

  13. 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 vreceives a message from u wheneverthe adversarial SINR formula holds Is it possible to design algorithms for this model? WRAWN'13, Christian Scheideler

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

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

  16. Basic approach • a node v adapts pv 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!) time idle steps successful transmissions steps jammed by adversary steps where collision occurred but no jamming WRAWN'13, Christian Scheideler

  17. Basic approach • a node v adapts pv 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!) time idle steps successful transmissions steps jammed by adversary steps where collision occurred but no jamming WRAWN'13, Christian Scheideler

  18. Naïve protocol Each time step: • Node vsends a message with probability pv . If v does not send a message then • if the wireless channel is idle then pv= (1+ γ) pv • if vreceived a message thenpv= pv/(1+ γ) (whereγ = O(1/(log T + loglog n))) WRAWN'13, Christian Scheideler

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

  20. Problems • Basic problem:Aggregateprobability pcould be too large. • all time steps blocked due to message collisions w.h.p. time idle steps successful transmissions steps jammed by adversary steps where collision occurred but no jamming WRAWN'13, Christian Scheideler

  21. Problems • Basic problem:Aggregateprobability p could be too large. • all time steps blocked due to message collisions w.h.p. • Idea: If more than T consecutive time stepswithout 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! WRAWN'13, Christian Scheideler

  22. MAC Protocol for Single Hop • each node vmaintains • probability valuepv, • time window thresholdTv, and • countercv • Initially, Tv = cv = 1andpv = pmax (< 1/24). • synchronized time steps (for ease of explanation) • Intuition:wait for an entire time window (according to current estimate Tv) until you can increase Tv WRAWN'13, Christian Scheideler

  23. MAC Protocol for Single Hop In each step: • node v sends a message with probability pv . If v decides not to send a message then • if v senses an idle channel, then pv= min{(1+γ)pv , pmax} • if vsuccessfully receives a message, then pv= pv /(1+ γ)and Tv= max{Tv - 1, 1} • cv= cv + 1. If cv> Tvthen • cv= 1 • ifvdidnot receive a messagesuccessfullyin thelast Tv steps thenpv= pv /(1+ γ)andTv= Tv +1 WRAWN'13, Christian Scheideler

  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-e)S Goal: achieve constant throughput Throughput = WRAWN'13, Christian Scheideler

  25. MAC Protocol for ADV-SINR Importantprerequisites: • For(B,T)-boundedadversary: B<(1-e)S(otherwise, all stepscanbe (potentially) busy) • Area aroundeachvsuff. dense, i.e., there must benodeswithin a transmissionrangeofrwhere P/ra bS • a>2 r WRAWN'13, Christian Scheideler

  26. MAC Protocol for ADV-SINR Initially, eachnodevsetsTv:=1, cv:=1,pv:=pmax, andg=O(1/(log T + loglog n)). In eachround, everynodevdecidestotransmit a messagewithprobabilitypv. • Ifvdoes not decideto send a message: • vreceives a message: pv:=(1+g)-1 pv • channelidle: pv:=min{(1+g)pv, pmax}, Tv:=max{1,Tv-1} • cv:=cv+1 • Ifcv>Tvthencv:=1, andifthere was noidlestepwithinTvstepsthenpv:=(1+g)-1 pv, Tv:=Tv+2 WRAWN'13, Christian Scheideler

  27. Main Result • Let N = max{T,n} • Theorem. MAC protocol is 1/2Q((1/e)2/(a-2))-competitive under any ((1-ε)S,T)-bounded adversary if the protocol is executed for Ω((T log N)/ε+ (log4N)/(εγ2))steps w.h.p., for any constant 0<ε<1and anyT. WRAWN'13, Christian Scheideler

  28. Main Result Proofidea: 3 zones interferencezone outerzone transmission zone WRAWN'13, Christian Scheideler

  29. Main Result • Let N = max{T,n} • Theorem. MAC protocol is 1/2Q((1/e)2/(a-2))-competitive under any ((1-ε)S,T)-bounded adversary if the protocol is executed for Ω((T log N)/ε+ (log4N)/(εγ2))steps w.h.p., for any constant 0<ε<1and anyT. In unit-disk model, Q(1)-competitive possible! WRAWN'13, Christian Scheideler

  30. Main Result • ((1-e)S,T)-boundedadversary, e0 interferencezone r=W((1/e)1/(a-2)) transmission zone WRAWN'13, Christian Scheideler

  31. Main Result • ideally, p=Q(e2/(a-2)) in eachtransmissionzone interferencezone r=W((1/e)1/(a-2)) transmission zone WRAWN'13, Christian Scheideler

  32. Main Result • better: power control? interferencezone r=W((1/e)1/(a-2)) transmission zone WRAWN'13, Christian Scheideler

  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 Scheideler

  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 Scheideler

  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 Scheideler

  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 g? • Stochastic/oblivious jammers: Simpler to handle? E.g., a constant g seems to work fine here. WRAWN'13, Christian Scheideler

  37. Power Control Problem:manyparameters (pv, Tv, Pv, Sv) • VERY trickyto find setupthatavoidsanyscenarioswhereprotocolcanget stuck • Even muchmoretrickytoprovethat a correctprotocolworks WRAWN'13, Christian Scheideler

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

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