Barrier Coverage in Bistatic Radar Sensor Networks: Cassini Oval Sensing and Optimal Placement

1. Barrier Coverage in Bistatic Radar Sensor Networks: Cassini Oval Sensing and Optimal Placement Xiaowen Gong, Junshan Zhang, Douglas Cochran, Kai Xing Arizona State University University of Science and Technology of China MOBIHOC 2013 July 30th, 2013

2. Outline • Introduction • Social Group Utility Maximization Framework • Random Access Control Game under SGUM • Power Control Game under SGUM • Conclusion

3. Radar: What and Why Passive sensors:Detect radiation emitted or reflected by a target emitted signal target echo signal • Radars:Activelyemit radio waves and collect the echo reflected by the target • No reliance on external source of radiation • Superior penetration capability

4. Radar Applications Air traffic control Earthquake monitoring

5. Radar Sensing Model • Monostatic radar (MR): co-located radar transmitter and receiver • Disk sensing model (similar to passive sensors) • Bistatic radar (BR): separated radar transmitter and receiver • SNR (, : distance from transmitter, receiver to target) • Radar constant captures physical characteristics • Sensing region defined by a Cassini oval:Set of points with constant distance product to two fixed points • BR can outperform MR due to the flexibility

6. Bistatic Radar Network • Bistatic radar network (BRN)of BR transmitters and BR receivers • Transmitters operate on orthogonalradio resources • A receiver can pair with all transmitters to form multiple BRs, and vice versa (can be relaxed) • Transmitters and receivers are homogeneous, respectively • Typically more receivers than transmitters

7. Network Coverage • Deploy the BRN in a region for intruder detection destination entrance Detectability of a point : The distance product from to its closest BR • Detectability of an intrusion path : Detectability of intrusion: Worst-case intrusion path : all possible intrusion paths

8. Problem Definition Question:How many transmitters and receivers are needed and where should they be placed in the region such that at least one BR can reliably detect the intruder (SNR ),regardless of the intruder’s path? PROBLEM 1 (P1): Optimize the placement locations of BR nodes in region to minimize the worst-case intrusion detectability: • P1 is difficult to solve in general (even under disk sensing model) • The shape of region can be arbitrary • The feasible solution space is large

9. Placement for Barrier Coverage • A barrier is a curve in region that intersects with any intrusion path Vulnerability of a barrier : Minimum detectability of all points in PROPERTY : : all possible barriers • P1: find the optimal barrier : • Minimum achievable vulnerability

10. Placement on Shortest Barrier • The shortest barrier is notoptimal in general • Shortcut barrier: The shortestbarrier if it is also the shortest line segment connecting boundaries and • It exists in many situations (e.g., when region is convex) shortcut barrier shortcut barrier shortest barrier THEOREM 1: The shortcut barrier is the optimal barrier to cover if it exists.

11. Optimal Placement on A Line Segment PROBLEM 2 (P2): Optimize the placement locations of BRs on a line segment of length to minimize its vulnerability: Non-convexin general  • P2 is an optimization problem Optimization variables

12. Placement Order and Spacing A placement on a line segment Aplacement order with a placement spacing Example: Local placement order Localplacement spacing

13. Optimal Order . . . . . . . . . . . . . . . THEOREM 2: An order is optimal if and only if and . Example: for even for odd and for odd and

14. Optimal Spacing . . . . . . . . . . . . . . . THEOREM 3: For the optimal order , the optimal spacing is composed of , where can be characterized by , . : unique solution of for equation Example: for even k . . . . . .

15. Optimal Spacing (cont’d) Example: for odd k . . . . . . . . . . . .

16. Optimal Placement oris non-optimal

17. Heuristic Placement Heuristic 1: Heuristic 2: ( or ) Optimal placement:

18. Numerical Results • Optimal placement vs. heuristic placement on a line segment • Bistatic radar network vs. monostatic radar network under optimal placement • #of MRs

19. Related Work • Worst-case coverage • Find the worst-case intrusion path for arbitrary deployed sensors [Meguerdichian, Mobicom01, Mobihoc01, Infocom01] • Barrier coverage • Find a covered barrier for arbitrary deployed sensors[Kumar, Mobicom05] , form a covered barrier under random deployment [Liu Mobihoc08], qualitative metric of barrier coverage [Chen, Mobihoc08] • Most radar literature focus on single radar systems • Radar sensor network • Waveform design [Liang, Secon06], radar scheduling [Hanselmann, Information Fusion10], radar management [Li, Sensys07] • Doppler coverage for a network of monostatic radars[Gong, Infocom13]

20. Conclusion • Contribution • Formulated the worst-case coverage problem for a bistatic radar network based on the Cassini oval sensingmodel • Showed that it is not optimal in general to place BRs on the shortest barrier unless the shortcut barrier exists • Characterized the optimal placement locations of BRs on a line segment by characterizing their optimal placement order and optimal placement spacing • Merits  • Novelty: The first to study the coverage problem for a network of BRs • Importance: Advantages of networked BRs over passive sensors and MRs • Challenge: The Cassini oval sensing model and the coupling across BRs give rise to significant difficulty

21. Thank You! Please send any questionsto the authors at xgong9@asu.edu