Interference Models: Beyond the Unit-disk and Packet-Radio Models

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

2. 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 Andrea Richa

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

4. 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 Andrea Richa

5. 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 u' v Andrea Richa

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

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

8. PRN: What is the problem? ≥ rt v s ≤ rt ≤ rt t ≤ ri n-2 nodes • 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 Andrea Richa

9. Bounded Interference Models 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 • … u ri rt u' v w does not cause interference at u (even if all nodes outside transmit at the same time) may cause interference at u Andrea Richa

10. 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 Andrea Richa

11. SIT Model • SIT (Sensing - Interference - Transmission) • Separatetransmission 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 Andrea Richa

12. 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 Andrea Richa

13. Cost Function • Euclidean distance d(•,•) • Cost function c: • symmetric: c(u,v) = c(v,u) • d > 0,depends on the environment • c(u,v)Î [d(u,v)/(1+d), (1+d)d(u,v)] • c may not be ametric b u a v w Andrea Richa

14. Transmission and Interference Ranges • Transmission power P • Transmission range rt(P); Interference range ri(P) • A node v canonly cause interference at node v’ if c(v,v’)≤ ri(P), w.h.p. • If c(v,w) ≤rt(P)then v successfully receives a message from w provided no other node v' with c(v, v')≤ ri(P)also transmits at the same time, w.h.p. u ri(P) v c(v,w) £ rt(P) c(v,v') £ ri(P) v' rt(P) w Andrea Richa

15. 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 Andrea Richa

16. Physical Carrier Sensing • Carrier sense transmission (CST) range, denoted rst(T, P) • Carrier sense interference (CSI) range, denoted rsi(T, P) • Both ranges grow monotonically in both T and P. • We will assume that P is fixed, and omit this parameterin the remainder of this talk. rsi(T,P) c(w,v) £ rst(T, P) c(w, v') £ rsi(T, P) c(w, v'') ³ rsi(T, P) w v' rst(T,P) v v'' Andrea Richa

17. Carrier Sensing Ranges • If c(v,w) ≤ rst(T), then wsenses 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 thatc(v',w) ≤ rsi(T), w.h.p. • Nodes outside of rsi(T) cannot be sensed by node w, w.h.p. rsi(T) c(w,v) £ rst(T) c(w, v') £ rsi(T) c(w, v'') ³ rsi(T) w v' rst(T) v v'' Andrea Richa

18. 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 Andrea Richa

19. 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 • Constantsize messages • Broadcasting and information gathering: Use constant density spanner Andrea Richa

20. Dominating Sets Density = 3 • Dominating set (DS): a subset U ofnodes 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)≤rt) • Transmission graph Gt(V,Et): edge (u,v) Î Et iff c(u,v) ≤ rt • Density of U: maximum number of neighbors that a node has in U. • Seek for connected dominating set of constant density Dominator / Leader Andrea Richa

21. Constant Density Dominating Set • Our results:Locally self-stabilizing randomized protocol that converges to a constant density dominating set of the transmission graph Gtin O(log4n) steps w.h.p. • Uncertainties in our model make it harder! • Without any estimate on the size of network, we need toexploit physical carrier sensing! Andrea Richa

22. 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 1 Round 2 …. Round k Round 1 Round 2 …. Andrea Richa

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

24. 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 nodebecomesr-active r-active inactive changes from inactive to r-active in Step 1 Andrea Richa

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

26. 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. r-active inactive changes from r-active to inactive in Step 2 such conflicts will eventually be resolved Andrea Richa

27. Why k rounds (k-coloring)? Fact: In Gt,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 usekindependent sets(one for each color) to guarantee coverage! Andrea Richa

28. Different Sensing Ranges • E.g., an inactive nodev 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 no active node transmitting here in round r whp u ri rt if an active node transmitted here in a round other than r, v would have sensed whp Andrea Richa

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

30. Active node Inactive node Gateway node Gateway edge Other edges Constant Density Topologial Spanner • Our results: Our local self-stabilizing protocol achieves a constant density5-spanner of the transmission graph Gt,, inO(log4 n + (D log D)log n) time w.h.p. • D: density of the original network v u l' l s t Andrea Richa

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

32. SIT: What is the problem? 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 u ri rt could still interfere at u Andrea Richa

33. 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 Andrea Richa

34. 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) Andrea Richa

35. SINR Model • Signal-Interference-Noise-Ratio (SINR) condition:A message sent by nodeu 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 inS P/||w v|| Andrea Richa

36. 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 Andrea Richa

37. 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 Bounded interference model MAC Extended SINR model PHY Andrea Richa

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

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

40. Getting Down to Constant Density • Each node is initially inactive. • Each node v maintains a probability of transmission pv. Goal: For each transmission range Rv of node v, w in Rv pw = (1) bounded interference Andrea Richa

41. Getting Down to Constant Density Density Estimation: • Each node v chooses one of two time stepsuniformly at random, say step s(the other step iss): • Step s: vtransmits PING signal with probability pv • Step s: v senses channelChannel free:pv:=min{(1+)pv, pmax}Channel busy:pv:=max{(1-)pv, pmin}(>0 is a small constant) Multiplicative increase, multiplicative decrease scheme. Andrea Richa

42. 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. • thesubset 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. Andrea Richa

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

44. 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 Andrea Richa

45. 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) Andrea Richa

46. 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 Andrea Richa

47. Questions? Andrea Richa

48. 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. Andrea Richa

49. Log-Normal Shadowing • Received power at a distance of drelative to received power at reference distance d0 in dB is-10 log(d/d0) + X- : path loss coefficient- X: Gaussian variable with standard deviation  Andrea Richa

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