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

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