1. Link Layer: Wireless Mesh Networks Capacity Y. Richard Yang 11/13/2012

2. 2 Outline r Admin. and recap r Wireless mesh network capacity r Maximize mesh capacity

3. Admin. r Exam m Average (mean): 68.6; max = 74 r Project check point 1 m Sending email to cs434ta@cs.yale.edu m Includes contents on references setting 3

4. 4 Recap: Wireless Link Access Control r Problem: single shared medium, hence if two transmissions overlap on all dimensions [time, space, frequency, and code], then it is a collision Slotted ALOHA Ethernet Hidden-terminal Collision detection/ prevention Zigzag decoding

5. 5 Recap: 802.11 CSMA/CA data wait B1 = 5 B2 = 15 B1 = 25 B2 = 20 data wait B1 and B2 are backoff intervals at nodes 1 and 2 cw = 31 B2 = 10 busy

6. Recap: ZigZag Decoding Exploits 802.11’s behavior r Retransmissions  Same packets collide again r Senders use random jitters  Collisions start with interference-free bits ∆1 ∆2 PaPa PbPb PaPa PbPb Interference-free Bits

7. ZigZag Algorithm ∆1 ∆2 while (exists a chunk that is interference-free in one collision and has interference in the other) { decode and subtract from the other collision } 1 1 ∆1 ≠∆2 1 1

8. ∆2 1 1 2 2 1 1 ∆1 How Does ZigZag Work? ∆1 ≠∆2 while (exists a chunk that is interference-free in one collision and has interference in the other) { decode and subtract from the other collision }

9. ∆2 1 1 2 2 2 2 ∆1 How Does ZigZag Work? 3 3 ∆1 ≠∆2 while (exists a chunk that is interference-free in one collision and has interference in the other) { decode and subtract from the other collision }

10. ∆2 1 1 2 2 4 4 ∆1 How Does ZigZag Work? 3 3 3 3 ∆1 ≠∆2 while (exists a chunk that is interference-free in one collision and has interference in the other) { decode and subtract from the other collision }

11. ∆2 1 1 2 2 4 4 4 4 ∆1 How Does ZigZag Work? 3 3 5 5 ∆1 ≠∆2 while (exists a chunk that is interference-free in one collision and has interference in the other) { decode and subtract from the other collision }

12. ∆2 1 1 6 6 ∆1 How Does ZigZag Work? 3 3 5 5 5 5 2 2 4 4 ∆1 ≠∆2 while (exists a chunk that is interference-free in one collision and has interference in the other) { decode and subtract from the other collision }

13. ∆2 1 1 6 6 6 6 ∆1 How Does ZigZag Work? 2 2 4 4 3 3 5 5 7 7 ∆1 ≠∆2 while (exists a chunk that is interference-free in one collision and has interference in the other) { decode and subtract from the other collision }

14. ∆2 1 1 6 6 8 8 ∆1 How Does ZigZag Work? 2 2 4 4 3 3 5 5 7 7 7 7 ∆1 ≠∆2 Delivered 2 packets in 2 timeslots As efficient as if the packets did not collide while (exists a chunk that is interference-free in one collision and has interference in the other) { decode and subtract from the other collision }

15. Implementation USRP Hardware GNURadio software Carrier Freq: 2.4-2.48GHz BPSK modulation

16. USRPs Testbed 10% HT, 10% partial HT, 80% perfectly sense each other 802.11a

17. Throughput Comparison 802.11 Throughput CDF of concurrent flow pairs Hidden Terminals Partial Hidden Terminals Perfectly Sense

18. Throughput Comparison ZigZag Throughput CDF of concurrent flow pairs 802.11 Hidden Terminals get high throughput ZigZag Exploits Capture Effect

19. Capture Effect r Subtract Alice and combine Bob’s packet across collisions to correct errors ∆1 ∆2 P a1 PbPb P a2 PbPb 3 packets in 2 time slots  better than no collisions

20. 20 Summary r Basic lesson: m Traditional thinking was on avoiding collisions m Zigzag changed the way of thinking: decoding collisions r Many extensions of the Zigzag idea: decoding collisions, instead of avoiding collisions m See Remap in Backup Slides

21. 21 Infrastructure Mode Wireless AP wired network AP: Access Point Problems of infrastructure mode wireless networks? 802.11 by default operates in infrastructure mode.

22. 22 Mesh Networks ad-hoc (mesh) mode AP wired network AP: Access Point m fast and low-cost deployment m no central point of failure m no APs overhead for users who can reach each other

23. 23 Outline r Admin. and recap r Wireless mesh network capacity

24. 24 Capacity of Mesh Networks r The question we study: how much traffic can a mesh wireless network carry, assuming an oracle to avoid the potential overhead of distributed synchronization (MAC)? r Why study capacity? m learn the fundamental limits of mesh wireless networks m separate the spatial reuse perspective and system design perspective m gain insight for designing effective wireless protocols

25. 25 Mesh Transmission Constraints  transmission successful if there are no other transmitters within a distance (1+  )r of the receiver receiver sender r (1+  )r Interference constraint r a single half-duplex transceiver at each node: m either transmits or receives m transmits to only one receiver m receives from only one sender Radio interface constraint

26. 26 Model r Domain is a disk of unit area r There are n nodes in the domain r The transmission rate is W bits/sec

27. 27 Capacity of Mesh Wireless Network r Consider two types of networks m arbitrary networks: place nodes optimally to derive overall upper bound m random network: nodes are placed randomly

28. Outline r Admin r Wireless mesh network capacity m setting m arbitrary networks: place nodes optimally to derive overall upper bound 28

29. 29 Transmission Model: Bit-time Perspective r Chop time into a total of WT bit-times in T seconds r The transmission decision is made for each bit bit time 2bit time tbit time WTbit time 1 1 2 3 5 4 1 2 3 5 4

30. 30 Transmission Model: End-to-end Perspective r Assume the network sends a total of T end-to-end bits in T seconds r Assume the b-th bit makes a total of h(b) hops from the sender to the receiver r Let r b h denote the hop-length of the h-th hop of the b-th bit 2 1 2 T

31. 31 Hop-Count Constraint Since there are a total of WT bit-times, and during each bit-time there are at most n/2 simultaneous transmissions, we have 2

32. 32 m k (1+  )r’ r’r’ Area Constraint r Consider two simultaneous transmissions at a bit-time i j (1+  )r r D jm + r >= D im >= (1+  )r’  D jm >= (r+r’)  /2 D jm + r’ >= D jk >= (1+  )r ½  r ½  r’

33. 33 Area Constraint r For each transmission with distance r from sender to receiver, we draw a circle with radius ½  r r These circles do not overlap

34. 34 Area Constraint: Global Picture 2

35. 35 Area Constraint: Global Picture sum over all circles, since each circle has at least ¼ of its area in the unit disk, 2

36. 36 Summary: Two Constraints  transmission successful if there are no other transmitters within a distance (1+  )r of the receiver Interference constraint r a single half-duplex transceiver at each node Radio interface constraint receiver sender r (1+  )r

37. 37 Capacity Bound Note: Let L be the average (direct-line) distance for all T end-to-end bits. Discussion: what does the result mean?

38. 38 Discussion r L depends on m traffic pattern (who needs to talk to whom) and m positions of the end-to-end (application-level) senders and (application-level) receivers r If end-to-end senders and receivers are spread out throughout the network, L is large m per node capacity r Otherwise, L will be small as network becomes denser

39. 39 Achieving Capacity: Example r n/2 senders and receivers: r L=

40. 40 Results: Arbitrary Networks Protocol Model

41. Outline r Admin r Wireless mesh capacity m setting m arbitrary networks: place nodes optimally to derive overall upper bound m random networks: uniform distribution of nodes and senders/receivers 41

42. 42 Uniform Random Networks r Uniform distribution of n nodes r n origin-destination (OD) pairs r Each node chooses same power level P, and thus equal radius r(n) r Equal throughput (n) bits/sec for all OD pairs

43. 43 Random Networks: Required Bits r Assume: average length of each OD pair is L r Average number of hops:  Total required bit transmissions per second to support (n) :

44. 44 Random Networks: Offered Bits r Required bit transmissions per second: r What is the maximum number of transmissions (of bits) in one second? m space used per transmission (interference limited): at least ¼  r(n)/2] 2 =  2 r 2 (n)/16 m number of simultaneous transmissions at most (interference limited): m total bits per second

45. 45 Random Networks: Capacity Required ≤ offered  

46. 46 Connectivity Constraint r Need routes between origin-destination pairs - places a lower bound on transmit range r(n) Not connected Connected A D A D To maintain connectivity with a high probability, requires r(n) on the order:

47. 47 Random Networks: Capacity Required ≤ offered   

48. 48 Measurement r Measured scaling law: throughput declines worse with n than theoretically predicted: 1/n 1.68 r Remaining story line m wireless mesh networks may have low scalability, and need techniques to increase capacity

49. 49 Improving Wireless Mesh Capacity  transmission successful if there are no other transmitters within a distance (1+  )r of the receiver Interference constraint r a single half-duplex transceiver at each node Radio interface constraint rate*distance capacity: Reduce LIncrease W Approx. optimal Multiple transceivers Reduce interf. area

50. 50 Outline r Admin. and recap r Wireless mesh network capacity r Maximize mesh capacity m Reduce L

51. 51 Change Traffic Pattern: Reduce L r Reduce L => make communications local m node placement: change the demand patterns (thus L) e.g. base stations/access points with high-speed backhaul F E A BC D BS1BS2 S T infrastructure

52. 52 Change Traffic Pattern: Reduce L r Reduce L => make communications local by being patient and wait in a mobile network

53. 53 Outline r Admin. and recap r Wireless mesh network capacity r Maximize mesh capacity m Reduce L m Reduce interference

54. 54 Reduce Interference Footprint r Antenna design: steered/switched directional antennas A D C B A B D C

55. Backup Slides 55

56. 56 802.11g Overlapping-Channel Collision Bob AP a on channel C a Collision! Alice AP b on channel C b Collision! Chuck

57. 57 802.11g Overlapping-Channel Collision Bob AP a on channel C a More Collision! Alice AP b on channel C b More Collision! Chuck Retransmission

58. 58 Remap Basic Idea: Structured Permutation Subcarrier Group G1G1 G2G2 G3G3 G4G4 A1A1 A2A2 A3A3 A4A4 Mapping π 1 A4A4 A3A3 A2A2 A1A1 Mapping π 2 A2A2 A1A1 A4A4 A3A3 Mapping π 3 A3A3 A4A4 A1A1 A2A2 Mapping π 4

59. 59 How Permutation Helps r Non-matching collisions on adjacent channels C 1 and C 2 Subcarrier Group G1G1 G2G2 G3G3 G4G4 A1A1 A2A2 A3A3 A4A4 1 st transmission 2 nd transmission A4A4 A3A3 A2A2 A1A1 A2A2 A1A1 A4A4 A3A3 3 rd transmission A3A3 A4A4 A1A1 A2A2 4 th transmission

60. 60 How Permutation Helps (cont’d) r Non-matching collisions on non-adjacent channels C 1 and C 3 Subcarrier Group G1G1 G2G2 G3G3 G4G4 A1A1 A2A2 A3A3 A4A4 1 st transmission 2 nd transmission A4A4 A3A3 A2A2 A1A1

61. 61 Remap Basic Idea: Matching-collision setting Collision! Alice Bob Collision! AP a on channel C a AP b on channel C b Matching collisions on adjacent channels

62. 62 Remap for Matching Collisions r collisions at adjacent channels C 1 and C 2 : a time and frequency view PbPb ∆1∆1 ∆2∆2 A1A1 A2 A2 A3A3 A4A4 S1S1 S2S2 SnSn Time Freq PaPa B5B5 B2 B2 B3B3 B4B4 A4A4 A3 A3 A2A2 A1A1 S1S1 S2S2 SnSn B2B2 B5 B5 B4B4 B3B3 P′bP′b P′aP′a G1G1 G3G3 G2G2 G5G5 G4G4 G2G2 1 5 9 13 4 10 14 3 7 11 2 6 8 12