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Wireless Communication Using Directional Antennas: Strong Connectivity and Plane Coverage

Explore the use of directional antennas to focus energy for desired communication points, fulfilling requirements for strong connectivity and hop spanners in wireless communication networks.

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Wireless Communication Using Directional Antennas: Strong Connectivity and Plane Coverage

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  1. Wireless Communication using Directional Antennas

  2. Directional Antennas • Focus the energy in a desired direction: Desired Communication Point Antenna Array • Geometric representation: r a

  3. Communication Links A

  4. Requirement #1 Strong Connectivity B A

  5. Requirement #2 HopSpanner B A |AB| ≤ 1: minpath(A, B) has a constant #hops.

  6. Requirements #3 MinimumRadius A B

  7. How can A reach B? A B

  8. Problem Statement • Given: • plane point set S, fixed angle a • one a-antenna per point • Find: • orientations of a-antennas • a minimum radiusr • such that the induced communication graph is a strongly connected hop spanner.

  9. Case a = 180o EuclideanMST R A B

  10. 180o Antennas - Clustering BFS Traversal R Select non-adjacent edges of the MST.

  11. 180o Antennas - Clustering BFS Traversal R Select non-adjacent edges of the MST.

  12. 180o Antenna Orientations R

  13. Basic Observation R

  14. Basic Observation R A B

  15. 180o Antennas of Radius 2 R A B

  16. How can A reach B now? A B

  17. (180o, 2)-Communication Graph CommunicationGraph for: a = 180oRadius = 2Strongly connectedHop factor = 3 R

  18. What about a < 180o ? • Next: a≥ 120o

  19. 120o Antennas – 3 Point Connectivity K K 2 1 Want: Strong Connectivity Plane Coverage C A B

  20. 120o Antennas – 3 Point Connectivity Want: Strong Connectivity Plane Coverage C A B Radius = Maximum Pairwise Distance C A B

  21. 120o Antennas – 3 Point Connectivity Radius = Maximum Pairwise Distance ≤ 2 C A B Observation: Radius = 3 also covers the unit disk around each point C A B

  22. 120o Antennas – 3 Point Connectivity Radius = Maximum Pairwise Distance ≤ 2 C A B Observation: Radius = 3 also covers the unit disk around each point C A B

  23. 120o Antennas – 3 Point Connectivity Radius = Maximum Pairwise Distance ≤ 2 C A B Observation: Radius = 3 also covers the unit disk around each point C A B

  24. Connecting 3-Point Clusters Z X Y C A B Assumption: Clusters at unit distance. C A B Z Y X

  25. Connecting 3-Point Clusters Z X Y C A B Assumption: Clusters at unit distance. C A B Z Y X

  26. Connecting 3-Point Clusters Z X Y C A B Assumption: Clusters at unit distance. C A B Z Y X

  27. 120o Antennas - Clustering EuclideanMST(S) R Partition S intoclusters of ≥ 3 nodes

  28. (120o, 5)-Communication Graph r = 5:Each cluster isstrongly connectedand covers the enclosing unit halo R

  29. (120o, 5)-Communication Graph r = 5:Each cluster isstrongly connectedand covers the enclosing unit halo R A B

  30. 120o Antennas - Summary of Results • Given: • plane point set S • fixed angle a ≥ 120o • There exist • orientations of a-antennas • Such that • radius r = 5 establishes a communication graph that is a strongly connected, 5-hop spanner. • Lower bound:r = 2

  31. a ≥ 90o : Similar Approach K K K K A C 1 2 3 4 B • 4 Point Connectivity D

  32. a ≥ 90o : Similar Approach Communication Graph D K K K K A A C C 3 2 4 1 B B Radius = Second longest pairwise distance • 4 Point Connectivity D

  33. a ≥ 90o : Similar Approach A C B • Radius + 1: Unit halo coverage D • Allows us to connect clusters at unit distance

  34. 90o Antennas - Clustering EuclideanMST R Partition S intoclusters of ≥ 4 nodes

  35. (90o, 7)-Communication Graph r = 7:Each cluster isstrongly connectedand covers the enclosing unit halo R A B

  36. 90o Antennas - Summary of Results • Given: • plane point set S • fixed angle a ≥ 90o • There exist • orientations of a-antennas • Such that • radius r = 7 establishes a communication graph that is a strongly connected, 6-hop spanner. • Lower bound:r = 2

  37. OPEN Restriction too strong! • What about a < 90 ? • This approach does not work: • Strong connectivity: • each antenna must cover at least one point • Plane coverage: • some antennas cover no points • Conflicting criteria!

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