1. Andrea Richa1 Interference Models: Beyond the Unit-disk and Packet-Radio Models Andrea W. Richa Arizona State University

2. Andrea Richa2 Ad hoc Networks ●Wireless stations communicating over a wireless medium with no centralized infrastructure ●How to model ad hoc networks? –Need models that are close to reality, but which still allow for the design and formal analysis of algorithms

3. Andrea Richa3 Modeling Wireless Networks ●Wireless communication very difficult to model accurately: –Shape of transmission range –Interference –Mobility –Physical carrier sensing

4. Andrea Richa4 Outline Introduction → Simple Models of Wireless networks ●Bounded Interference Models ●SIT Model –What have we done? Leader Election; Constant Density Spanner ●Extended SINR Model ●Future Work and Conclusions

5. Andrea Richa5 Unit-Disk Graph ●Unit-Disk Graph (UDG) –Given a transmission radius R, nodes u, v are connected iff d(u,v) ≤ R –Too simple a model u R v u'

6. Andrea Richa6 ●Transmission range could be of arbitrary shape ●Does not consider interference R u UDG: What is the Problem? ●quasi-UDGs [Kuhn et al. 03]: - some uncertainty/non-uniformity in transmission, but still does not consider interference

7. Andrea Richa7 ●Can handle arbitrary transmission shapes ●Nodes u, v can communicate directly iff they are connected. ●Interference Model: –(interference range) = (transmission range) –too simplistic! u v w v' Packet Radio Network (PRN)

8. Andrea Richa8 ●While in the PRN model, s can send a message to t in 2 steps, no uniform protocol can successfully send a message in expected o(n) number of steps: linear slowdown PRN: What is the problem? v n-2 nodes s t ≤ r t ≤ r i ≥ r t

9. Andrea Richa9 Transmission and Interference Ranges: ●Separate values. ●Interference range constant times bigger than transmission range. Preliminary work: –most assume disk-shaped interference –[Adler and Scheideler '98]: too restrictive model for transmission –…–… Bounded Interference Models u rtrt v w u' riri does not cause interference at u (even if all nodes outside transmit at the same time) may cause interference at u

10. Andrea Richa10 Outline Introduction Simple Models of Wireless Networks Bounded Interference Models → SIT Model –What have we done: Leader Election; Constant Density Spanner ●Extended SINR Model ●Future Work and Conclusions

11. Andrea Richa11 SIT Model ●SIT (Sensing - Interference - Transmission) –Separate transmission and interference ranges via cost function –arbitrary, non-disk communication shapes –bounded interference ●Carrier sensing: –Physical carrier sensing: sense whether the channel is busy or not –Virtual carrier sensing ●fully probabilistic model

12. Andrea Richa12 Why Physical Carrier Sensing? ●Using physical carrier sensing, we can extract information from the network without relying on successful message transmissions –quite often it is enough just to know if at least one node is sending a message, rather than receiving the message –linear speedup ●It comes for “free” v

13. Andrea Richa13 Cost Function ●Euclidean distance d(,) ●Cost function c: –symmetric: c(u,v) = c(v,u) − , depends on the environment –c(u,v)  [ d(u,v)/(1+  ), (1+  ) d(u,v)] –c may not be a metric w u v a b

14. Andrea Richa14 Transmission and Interference Ranges ●Transmission power P ●Transmission range r t (P); Interference range r i (P) –A node v can only cause interference at node v’ if c(v,v’) ≤ r i (P), w.h.p. –If c(v,w) ≤r t (P) then v successfully receives a message from w provided no other node v' with c(v, v') ≤ r i (P) also transmits at the same time, w.h.p. w rt(P)rt(P) v' ri(P)ri(P) u v c(v,w)  r t (P) c(v,v')  r i (P)

15. Andrea Richa15 Physical Carrier Sensing ●Clear Channel Assessment (CCA) circuit: –Monitors the medium as a function of Received Signal Strength Indicator (RSSI) –Energy Detection (ED) bit set to 1 if RSSI exceeds a certain threshold –Has a register to set the threshold T in dB

16. Andrea Richa16 Physical Carrier Sensing ●Carrier sense transmission (CST) range, denoted r st (T, P) ●Carrier sense interference (CSI) range, denoted r si (T, P) ●Both ranges grow monotonically in both T and P. ●We will assume that P is fixed, and omit this parameter in the remainder of this talk. w v r st (T,P) v' v'' r si (T,P) c(w,v)  r st (T, P) c(w, v')  r si (T, P) c(w, v'')  r si (T, P)

17. Andrea Richa17 Carrier Sensing Ranges w v r st (T) v' v'' r si (T) c(w,v)  r st (T) c(w, v')  r si (T) c(w, v'')  r si (T) ●If c(v,w) ≤ r st (T), then w senses a transmission by node v, w.h.p. ●If w senses a transmission then there is at least one node v' transmitting a message such that c(v',w) ≤ r si (T), w.h.p. ●Nodes outside of r si (T) cannot be sensed by node w, w.h.p.

18. Andrea Richa18 Outline Introduction Simple Models of Wireless Networks Bounded Interference Models SIT Model → What have we done? Leader Election; Constant Density Spanner ●Extended SINR Model ●Future Work and Conclusions

19. Andrea Richa19 SIT:What have we done? ●Constant density dominating set and topological spanner: –Local-control –Self-stabilizing [Dijkstra '74], even in the presence of adversarial behavior –No knowledge (estimate) of the size or topology of the network –Nodes do not need globally distinct labels –Constant size messages ●Broadcasting and information gathering: Use constant density spanner

20. Andrea Richa20 Dominating Sets ●Dominating set (DS): a subset U of nodes such that each node v is either in U or has a node w in U within its transmission range (i.e., c(v,w) ≤ r t ) ●Transmission graph G t (V,E t ): edge (u,v)  E t iff c(u,v) ≤ r t ●Density of U: maximum number of neighbors that a node has in U. ●Seek for connected dominating set of constant density Dominator / Leader Density = 3

21. Andrea Richa21 Constant Density Dominating Set ●Our results: Locally self-stabilizing randomized protocol that converges to a constant density dominating set of the transmission graph G t in O(log 4 n) steps w.h.p. ●Uncertainties in our model make it harder! ●Without any estimate on the size of network, we need to exploit physical carrier sensing!

22. Andrea Richa22 Dominating Set Algorithm Basic principles: ●Nodes are either inactive or active (the potential leader nodes) and work in synchronous rounds ●Rounds organized into time frames of k rounds each (k sufficiently large constant). ●i-active node: active node that selected round i of the k rounds in a frame for its activities (like k-coloring) ●Initially, all nodes are 1-active ●Each round r of given frame consists of 2 steps: Round 1Round 2Round kRound 1Round 2 ….

23. Andrea Richa23 Step 1: “Waking up” nodes Step 1: ●Each r-active node transmits an ACTIVE signal. inactive r-active

24. Andrea Richa24 Step 1: “Waking up” nodes Step 1: ●Each r-active node transmits an ACTIVE signal. ●Each inactive node performs physical carrier sensing. No channel acitivity for last k rounds, including round r : inactive node becomes r-active inactive changes from inactive to r-active in Step 1 r-active

25. Andrea Richa25 Step 2: Leader Election Step 2: ●Each r-active node transmits a LEADER signal with probability p (for some constant p<1). inactive r-active

26. Andrea Richa26 Step 2: Leader Election Step 2: ●Each r-active node transmits LEADER signal with probability p (for some constant p<1). ●An r-active node not sending but either sensing or receiving a LEADER signal becomes inactive. inactive r-active changes from r-active to inactive in Step 2 such conflicts will eventually be resolved

27. Andrea Richa27 Why k rounds (k-coloring)? Fact: In G t,any Maximal Independent Set (MIS) is also a dominating set of constant density [Luby '85, Dubhashi et al., '03, Kuhn et al., '04, Gandhi and Parthasarathy '04] ●Given uncertainties in our model, we cannot guarantee that leader nodes will form an independent set without risking loss of coverage (i.e., having some inactive nodes not covered by any leader) Solution: we use k independent sets (one for each color) to guarantee coverage!

28. Andrea Richa28 Different Sensing Ranges ●E.g., an inactive node v uses different sensing ranges for the round r when it attempts to become active, and for other rounds. ●Interference-free communication among r-active (leader) nodes ●Coverage for all nodes u rtrt riri no active node transmitting here in round r whp if an active node transmitted here in a round other than r, v would have sensed whp

29. Andrea Richa29 Topological Spanners ●Definition: Given a graph G(V,E), find a subgraph H(V,E') such that d H (u,v) ≤ t d G (u,v) –Distances measured in number of edges (number of hops) –H is also called a t-spanner ●Previous Work (weaker models): [Alzoubi et. al., '03], [Dubhashi et. al., '03], …

30. Andrea Richa30 Constant Density Topologial Spanner ●Our results: Our local self-stabilizing protocol achieves a constant density 5-spanner of the transmission graph G t,, in O(log4 n + (D log D) log n) time w.h.p. –D: density of the original network u l l' v s t Active node Inactive node Gateway node Gateway edge Other edges

31. Andrea Richa31 Simulations ●90% of work through physical carrier sensing ●Performance comparable with other overlay network protocols (which need more assumptions, use simpler communication models)

32. Andrea Richa32 SIT: What is the problem? u rtrt riri Problem: Sharp threshold for transmission? –forward error correction Problem: Does not consider signal-to- noise ratio? –conservative model Problem: Does not consider unbounded (physical) interference!! –many transmitting nodes far away from u could still interfere at node u Solution: Extended SINR model could still interfere at u

33. Andrea Richa33 Outline Introduction Simple Models of Wireless Networks Bounded Interference Models SIT Model What have we done? Leader Election; Constant Density Spanner → Extended SINR Model ●Future Work and Conclusions

34. Andrea Richa34 Log-normal Shadowing ●Well-approximated by our cost model (SIT model) –irregular coverage area –sharp transmission threshold (forward error correction) ●when node u transmits with power P, received power at node v is  : path loss coefficient P c(u,v) 

35. Andrea Richa35 SINR Model ●Signal-Interference-Noise-Ratio (SINR) condition: A message sent by node u is received at node v iff - N: Gaussian variable for background noise - S: set of transmitting nodes -  : constant that depends on transmission scheme ●“Unbounded interference“ P/||u v||  N +  w in S P/||w v||  > 

36. Andrea Richa36 Extended SINR Model ●Extend SINR model to incorporate physical carrier sensing ●ED-bit set to 1 at v iff N +  w in S P/||w v||  >T

37. Andrea Richa37 Extended SINR Model Problem: Difficult to rigorously analyze routing protocols in this model! Solution: Reduce (extended) SINR model to bounded interference model with proper MAC scheme PHY MAC Extended SINR model Bounded interference model

38. Andrea Richa38 SINR X Bounded Interference Fact: If node distribution in ad hoc network is of constant density, then SINR simplifies to bounded interference. v transmission range interference range may cause interference does not cause interference

39. Andrea Richa39 SINR X Bounded Interference So how do we get from arbitrary distribution to constant density distribution of nodes??? v transmission range interference range may cause interference does not cause interference

40. Andrea Richa40 Getting Down to Constant Density ●Each node is initially inactive. ●Each node v maintains a probability of transmission p v. Goal: For each transmission range R v of node v,  w in R v p w =  (1) bounded interference

41. Andrea Richa41 Getting Down to Constant Density Density Estimation: ●Each node v chooses one of two time steps uniformly at random, say step s (the other step is s): –Step s: v transmits PING signal with probability p v –Step s: v senses channel Channel free: p v :=min{(1+  )p v, p max } Channel busy: p v :=max{(1-  )p v, p min } (  >0 is a small constant) Multiplicative increase, multiplicative decrease scheme.

42. Andrea Richa42 Algorithms for SINR Model ●W.h.p., in O(log n) time steps, our locally self- stabilizing algorithm converges to the right density estimates for all nodes. –the subset of nodes actively transmitting at any time step is of constant density, w.h.p. ●Current Work: Dominating set algorithm for extended SINR model is locally self-stabilizing and needs O(log n) time steps, w.h.p., to arrive at a stable constant density dominating set.

43. Andrea Richa43 SINR: What is the problem? Is the model sufficiently realistic?? ●Our interference model conservative: – signal cancellation – different signal strengths – bit recovery

44. Andrea Richa44 Self-Stabilization ●wireless communication too complex: no model will be able to accurately take into account all that can happen Problem: What happens if things deviate from proposed model? Solution: Protocols need to be self-stabilizing, i.e., they need to go back to a valid configuration for the model

45. Andrea Richa45 Collaborators ●Wireless Models: –Christian Scheideler (Technical U. of Munich), –Paolo Santi (U. of Pisa), –Kishore Kothapalli (IIIT), –Melih Onus (ASU) ●Simulations: –Martin Reisslein (ASU), –Luke Ritchie (ASU)

46. Andrea Richa46 More Future Work ●throughput ●power control ●future devices: MIMO (send/receive at same time), cognitive radio (continuous scan of available frequencies) ●alternatives to pure multihop ad-hoc networks? –wireless mesh networks: basestations form a mesh, everybody else ad-hoc ●energy-efficiency

47. Andrea Richa47 Questions?

48. Andrea Richa48 Publications ●K. Kothapalli, C. Scheideler, M. Onus, A.W. Richa. Constant density spanners for wireless ad-hoc networks. In Proceedings of the 17th ACM Symposium on Parallelism in Algorithms and Architectures (SPAA), pages 116-125, 2005. ●K. Kothapalli, M. Onus, A.W. Richa and C. Scheideler. Efficient Broadcasting and Gathering in Wireless Ad Hoc Networks. In Proceedings of the IEEE International Symposium on Parallel Architectures, Algorithms and Networks (ISPAN), pages 346-351, 2005. ●L. Ritchie, S. Deval, M. Onus, A. Richa, and M. Reisslein. Evaluation of Physical Carrier Sense Based Spanner Construction and Maintenance as well as Broadcast and Convergecast in Ad Hoc Networks. Submitted to IEEE Transactions on Mobile Computing. ●A.W. Richa, C. Scheideler, P. Santi. Leader Election Under the Physical Interference Model in Wireless Multi-Hop Networks. Manuscript.

49. Andrea Richa49 Log-Normal Shadowing ●Received power at a distance of d relative to received power at reference distance d 0 in dB is -10 log(d/d 0 )  + X  -  : path loss coefficient - X  : Gaussian variable with standard deviation 

50. Andrea Richa50 Topological Spanner Protocol ●Each round has time slots reserved for each phase of the protocol Three phase protocol: 1.Phase I: Dominating set 2.Phase II: Refined Distributed Coloring 3.Phase III: Gateway Discovery One round Ph. I Phase II Phase III Ph. I Phase IIPhase III Time

51. Andrea Richa51 Quasi-Unit Disk Graphs (q-UDG) [Kuhn et al’03] Given parameter 0<  modify UDG as follows: ●d(u,v)≤  successful transmission ●d(u,v)>1: v outside u’s transmission range ●  <d(u,v) ≤ 1: transmission may or may not be successful What is the problem? –model for transmission too conservative –does not model interference –green zone as “interference zone”? no interference within transm. range disk shaped interference u δ 1 ? ? ? ? ?

52. Andrea Richa52 –senses an ACTIVE signal with CSI range of r t ; if it did not sense any signal for the last k-1 rounds it senses with CST range of r i and if channel is clear, it becomes r-active

53. Andrea Richa53 Maximal Independent Sets Fact: In G t,any Maximal Independent Set (MIS) is also a dominating set of constant density –[Luby '85], [Dubhashi et. al., '03], [Kuhn et. al., '04], [Gandhi and Parthasarathy '04] ●Ideally, we would like to be able to show that the set of leader nodes form a MIS. However…