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 ID: 1021550
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1. Barrier Coverage in Bistatic Radar Sensor Networks: Cassini Oval Sensing and Optimal PlacementXiaowen Gong, Junshan Zhang, Douglas Cochran, Kai XingArizona State UniversityUniversity of Science and Technology of ChinaMOBIHOC 2013 July 30th, 2013
2. OutlineIntroductionSocial Group Utility Maximization FrameworkRandom Access Control Game under SGUMPower Control Game under SGUMConclusion2
3. Radar: What and WhyPassive sensors: Detect radiation emitted or reflected by a targetRadars: Actively emit radio waves and collect the echo reflected by the targetNo reliance on external source of radiation Superior penetration capabilitytargetemitted signalecho signal3
4. Radar ApplicationsAir traffic controlEarthquake monitoring4
5. Radar Sensing ModelMonostatic radar (MR): co-located radar transmitter and receiverDisk sensing model (similar to passive sensors)Bistatic radar (BR): separated radar transmitter and receiverSNR (, : distance from transmitter, receiver to target) Radar constant captures physical characteristicsSensing region defined by a Cassini oval: Set of points with constant distance product to two fixed pointsBR can outperform MR due to the flexibility 5
6. Bistatic Radar NetworkBistatic radar network (BRN) of BR transmitters and BR receivers Transmitters operate on orthogonal radio resourcesA receiver can pair with all transmitters to form multiple BRs, and vice versa (can be relaxed)Transmitters and receivers are homogeneous, respectivelyTypically more receivers than transmitters 6
7. Network CoverageDeploy the BRN in a region for intruder detection Detectability of intrusion: Worst-case intrusion path Detectability of a point : The distance product from to its closest BR entrancedestination Detectability of an intrusion path : 7: all possible intrusion paths
8. Problem DefinitionP1 is difficult to solve in general (even under disk sensing model)The shape of region can be arbitraryThe feasible solution space is large PROBLEM 1 (P1): Optimize the placement locations of BR nodes in region to minimize the worst-case intrusion detectability: 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? 8
9. Placement for Barrier CoverageA barrier is a curve in region that intersects with any intrusion path Vulnerability of a barrier : Minimum detectability of all points in P1: find the optimal barrier : Minimum achievable vulnerability PROPERTY : 9: all possible barriers
10. Placement on Shortest BarrierShortcut barrier: The shortest barrier 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 The shortest barrier is not optimal in general 10THEOREM 1: The shortcut barrier is the optimal barrier to cover if it exists.
11. Optimal Placement on A Line SegmentP2 is an optimization problem PROBLEM 2 (P2): Optimize the placement locations of BRs on a line segment of length to minimize its vulnerability: 11Non-convex in general Optimization variables
12. Placement Order and Spacing Local placement order Local placement spacing Example:12A placement order with a placement spacing A placement on a line segment
13. Optimal Order . . . . . .. . .. . . for even for odd and . . . for odd and 13THEOREM 2: An order is optimal if and only if and . Example:
14. Optimal Spacing for even k 14Example:: unique solution of for equation . . . . . . THEOREM 3: For the optimal order , the optimal spacing is composed of , where can be characterized by , . . . . . . .. . .. . . . . .
15. Optimal Spacing (cont’d)15 for odd k Example: . . . . . . . . . . . .
16. Optimal Placement or is non-optimal
17. Heuristic Placement Heuristic 1: Heuristic 2: ( or ) 17 Optimal placement:
18. Numerical Results Optimal placement vs. heuristic placement on a line segmentBistatic radar network vs. monostatic radar network under optimal placement # of MRs 18
19. Related WorkWorst-case coverageFind the worst-case intrusion path for arbitrary deployed sensors [Meguerdichian, Mobicom01, Mobihoc01, Infocom01]Barrier coverageFind 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 systemsRadar sensor networkWaveform design [Liang, Secon06], radar scheduling [Hanselmann, Information Fusion10], radar management [Li, Sensys07]Doppler coverage for a network of monostatic radars[Gong, Infocom13]19
20. ConclusionContributionFormulated the worst-case coverage problem for a bistatic radar network based on the Cassini oval sensing modelShowed that it is not optimal in general to place BRs on the shortest barrier unless the shortcut barrier existsCharacterized 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 BRsImportance: Advantages of networked BRs over passive sensors and MRsChallenge: The Cassini oval sensing model and the coupling across BRs give rise to significant difficulty20
21. Thank You!21Please send any questions to the authors at xgong9@asu.edu