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On the Capacity Improvement of Ad Hoc Wireless Networks Using Directional Antennas

Explore how directional antennas enhance network capacity in ad-hoc wireless setups. Learn about interference models, hybrid antenna approaches, and capacity gain factors for random networks.

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On the Capacity Improvement of Ad Hoc Wireless Networks Using Directional Antennas

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  1. On the Capacity Improvement of Ad Hoc Wireless Networks Using Directional Antennas Su Yi (RPI) Yong Pei (Univ. of Miami) Shivkumar Kalyanaraman (RPI) MobiHoc’03

  2. Outline • Related work • Capacity improvement of arbitrary networks using directional antennas • Capacity improvement of random networks using directional antennas • Hybrid antenna model • Conclusion and future work MobiHoc’03

  3. Scaling Laws under Interference Model • Theorems (Gupta/Kumar 2000) • Disk of area A square meters • n nodes • Each can transmit W bits/sec • Best case: Network can transport Θ bit-meters/sec • Square root law • Transport capacity doesn’t scale linearly, but only like square-root • Each node gets bit-meters/sec • Random case: Each node can obtain a throughput Θ bit-meters/sec MobiHoc’03

  4. r2 r1 Δr1 Δr2 Tx1 Tx2 Sender-based Interference Model |Tx1-Tx2| ≥(1 + ∆)(r1+r2) Interference Zone:transmission area MobiHoc’03

  5. Omni-directional Antenna Case Interference Zone: The first “1” – the hth hop of bit b is over subchannel m in slot t The second “1” – the unit area Transport capacity: MobiHoc’03

  6. Case1: Directional transmission and Omni-directional reception (DO) Sender-based Interference Zone: area of sector MobiHoc’03

  7. Case 2: Directional transmission and Directional reception (DD) Interference No interference Conditional Interference Zone: sender-based IZ, scaled by the probability that the receiver is pointing at the sender MobiHoc’03

  8. Feasible Capacity Improvement due to Directional Antennas • Dir Tx Omni Rv (DO) • Omni Tx Dir Rv (OD) • Dir Tx Dir Rv (DD) Intuition: Network capacity is related to inverse square root of the interference zone MobiHoc’03

  9. What If Beamwidths ( and ) Become Very Small? The formula: will become invalid for very small , ; and per-node capacity will tend to W/2 MobiHoc’03

  10. Capacity Gain Factor for Random Networks Voronoi Tessellation: • Partition of a plane with n points into n convex polygons (cells) • Each polygon contains one point • Every point in a polygon is closer to its central point than to any central point of other polygons MobiHoc’03

  11. 2(n) What’s Interesting about the Voronoi Tessellation Vn ? • Every Voronoi cell contains a disk ofarea 100log n/n. • Let (n) := radius of this disk • Every Voronoi cell is also contained in a disk of radius 2ρ(n) (n) MobiHoc’03

  12. What’s Interesting about the Voronoi Tessellation Vn ? (cont.) • Each Voronoi cell contains at least one node • We can choose the range r(n) of each transmission such that r(n)=8ρ(n) 2(n) 8(n) 2(n) MobiHoc’03

  13. Interfering Neighbors Concept • Definition: • There is a point in one cell which is within a distance 2(1+Δ)r(n) of some point in the other cell • Recall sender-based interference model: r(n) r(n) Tx2 Tx1 MobiHoc’03

  14. Interfering Neighbors Concept (cont.) • Lemma: • Omni-directional case (OO): every cell in Vn interferes with no more than cOOneighbors. • cOO depends only on Δ and grows no faster than linearly in (1+ Δ)2 MobiHoc’03

  15. How to Get the Number of Interfering Neighbors in Directional Antenna Case? • Key Idea:number of neighbors which see interference (from a node) … … is proportional to the area of the interference zone (of that node) • So we still use the concept of interference zone, and use the scaling factors derived earlier! MobiHoc’03

  16. Capacity Improvement (Random Networks) • Dir Tx Omni Rv • Omni Tx Dir Rv • Dir Tx Dir Rv Note: there is no square root! MobiHoc’03

  17. Hybrid Antenna Model • Main lobe: sector • Sidelobes and backlobe: circle MobiHoc’03

  18. Capacity Gain • Dir Tx Omni Rv (DO) • Omni Tx Dir Rv (OD) • Dir Tx Dir Rv (DD) MobiHoc’03

  19. Conclusions • Directional Antennas can reduce interference zones and improve network capacity • We provide expressions for capacity improvement with directional antennas relative to the traditional omni-directional antennas • Arbitrary networks: • reduction of the transmission area (a.k.a interference zone) and reduced probability of two neighbors pointing at each other • Random networks: • reduction of number of interfering neighbors, leading to capacity gain • Extension of results to approximately model the sidelobes and backlobes of real directional antennas (hybrid antenna model) MobiHoc’03

  20. Future work • Check if current directional antenna related MAC/routing protocols indeed achieve the maximum possible capacity improvements • Develop and Analyze MAC/routing protocol that actually achieve such capacity gains MobiHoc’03

  21. References • P.Gupta and P.R.Kumar. The capacity of wireless networks. IEEE Transaction on Information Theory, IT-46(2):388-404, March 2000 • J.J. Carr. Directional or Omnidirectional Antenna?Http://www.dxing.com/tnotes/tnote01.pdf • J.D.Kraus and R.J.Marhefka. Antennas: for All Applications, 3rd Ed. McGraw-Hill, New York, 2002 • R.Ramanathan. On the performance of ad hoc networks using beamforming antennas. In ACM MobiHoc’01, October 2001 MobiHoc’03

  22. Thank you! • For more information: yis@rpi.edu MobiHoc’03

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