When Target Motion Matters: Doppler Coverage in Radar Sensor Networks

Presenter: Yin Sun

Xiaowen Gong, Junshan Zhang, Douglas CochranSchool of Electrical, Computer, and Energy Engineering

Arizona State University

INFOCOM 2013, Apr. 17th, 2013

Outline

• Introduction• Doppler Coverage Model• Characterization of Doppler-Covered Regions• Critical Sensor Density for Doppler Coverage

under A Deployment Pattern• Conclusion

Passive Sensing vs. Active Sensing

• Passive sensors, such as thermal, seismic, optical, infrared sensors, detect natural radiation emitted or reflected by an object of interest (i.e., target)o Most sensor network literature consider passive sensors

• Radars are active sensors that actively emit radio waves and collect the echo reflected by the target (e.g. people, vehicles, aircrafts, ships)o Most radar literature focus on single radar systems

• Radars have a number of advantages over passive sensorso Typically have larger sensing rangeso Can work under severe conditions (e.g. darkness, haze, rain, snow)

Radar Sensing Model• Range-based sensing: SNR model

o Received target signal power: (SNR contour is circle) o Radar constant K captures physical characteristics (e.g., transmit power,

radar cross section)

𝑅

• Angle-based sensing: Doppler frequency shift (DFS) modelo DFS is the frequency difference between the emitted and received radar

signals due to the relative velocity between a radar and a moving target

𝑓 1> 𝑓 0 𝑓 1< 𝑓 0

𝑉 𝑉𝜑1 𝜑2

Δ

Clutter Spoils Radar Sensing

• Clutters are echoes from undesired objects (e.g., rocks, trees, clouds) o Can be much stronger in magnitude than that from a target o The magnitude depends on physical characteristics of undesired objects (e.g.,

material, shape) which may not be known o A salient challenge for radar compared to passive sensors

• Key observation: Clutter objects are typically stationary or slow-moving compared to the targeto DFS can be exploited for detection of moving target

Doppler Processing for Sensing • Moving target indication (MTI): An effective technique for exploiting the DFS

o 1. Apply high-pass filter in the DFS domain to suppress cluttero 2. Perform SNR-based detection (e.g. energy detection) in the filtered signal o Simple to implement with low computational costo The filtered signal contains the target signal if and only if Δis large enough (Δ)

clutter

noise

moving target

DFS

DFS

high-pass filtercutoff frequency

moving target

Networked Radars• Radar network is a promising paradigm for sensor network applications

o Networked radars offer diversity in both range (SNR) and angle (DFS) for potential better sensing capability

o Modern radar is becoming more affordable and more efficient, possible for larger-scale networked deployment

o Little attention has been paid to radar networks, especially coverage problems

𝑉 target detected!

no target

no target

• A coverage model is lacking for radar networks that exploit the DFSo Existing coverage model based on range (SNR) only: A point is covered by a

sensor if and only if is in the sensing range of (i.e., ) o DFS has been studied mostly for single radar systems but NOT for coverage of

radar networks

Doppler Coverage Model• We propose Doppler coverage model based on both range and angle

o If a target is Doppler-covered (D-covered), then there exists some radar that can observe both high SNR and large DFS

o Effective Doppler angle is determined by the cutoff frequency

DEFINITION: A target at a point moving in direction is Doppler-covered by a radar if and only if and or ; A point is Doppler-covered if and only if any direction from is Doppler-covered by some radar.

E.g.: is not D-covered

is down-D-covered

o New challenges: 1) The D-coverage depends on both distances and angular positions of radars from target 2) A radar can contribute two types of D-coverage: up-Doppler and down-Doppler

Coverage List

• How to check if a point is D-covered? Coverage list for a point o 1. Construct an image point for each in the set of sensors that cover

(“cover” in the range sense, i.e., ) such that o 2. Order all the points and based on their angular positions with respect to

LEMMA 1: A point is Doppler-covered by if and only if for any pair of neighbor points and in constructed from .

E.g.: , (or for short)

• Question 1: How to find all the Doppler-covered points (regions) for arbitrarily deployed sensors?

Safe/Complementary Safe Regions• How to check the condition in Lemma 1 for all points? Safe and complementary safe regions for a pair of radars

o Safe region: outside the circumscribed circles of where o Complementary safe (c-safe) region: inside the circumscribed circles of where

LEMMA 2: for any in the safe region of and ; for any in the complementary safe region of and .

Sub-Region Partition

• How to find a sub-region in which all points have the same coverage list? Sub-region partitiono Two points covered by the same set of sensors may have different coverage list

E.g.:

LEMMA 3: For a region covered by , is partitioned by all the lines each passing through a pair of sensors in into a set of sub-regions such that all the points in a sub-region have the same coverage list constructed from .

Doppler-Covered Regions• Answer 1: We develop an efficient method for characterizing Doppler-

covered regionso 1: Partition the entire region into sub-regions such that all points in a sub-

region have the same coverage listo 2: For each sub-region, construct safe or c-safe region for each pair of

neighbor points in its coverage list (construct safe region if both are non-image points or both are image points; otherwise, construct c-safe region)

, ,

The shaded regions are D-covered by }

Critical Sensor Density• Question 2: What is the critical sensor density (minimum number of sensors)

under a particular deployment pattern such that the entire region is Doppler-covered?o A natural question when we can control the deployment locationso Ignore boundary effect and focus on asymptotic case (typical in sensor coverage

literature)o Optimal deployment pattern is difficult to find even for passive sensor networks

• We consider a deployment pattern consisting of polygons (e.g., triangles, rectangles, hexagons) o There exists a unit region such that is D-covered if and only if the entire region is D-covered

Critical Sensing Range• Critical pattern size : maximum pattern size given and such that the unit

region is D-coveredo pattern size : a parameter characterizing the sensor density of a deployment

pattern (e.g., side length of a regular triangle for regular triangle pattern)o is increasing in and increasing in

• Critical sensor density critical pattern size critical sensing range o If we find the closed-form of as a function of parameterized by , then is the inverse function of

• Critical sensing range : minimum sensing range given and such that the unit region is D-coveredo is decreasing in and increasing in

• Answer 2: We design CSR Algorithm (find Critical Sensing Range): input output

Numerical Results• Doppler-covered percentage: percentage of D-covered areas

o An entire region of 100 X 100 under uniformly random deployment of sensorso Averaged results of 100 runso Sensing range (a) (b)

(𝑎) (𝑏)• We observe that 1) Performance is better for a larger 2) A larger sensing

range significantly improves performance

Conclusion

• Contributiono Introduced a novel Doppler coverage model to study the coverage of radar

networks that exploit both SNR and DFS for moving target detectiono Developed an efficient method for characterizing the Doppler-covered

regions for arbitrarily deployed sensors Can be used to evaluate the coverage of any deployed radar networks that

exploit DFS for moving target detectiono Designed CSR Algorithm for finding the critical sensor density for Doppler

coverage under a polygon deployment pattern Can be used to estimate the number of radars needed for Doppler coverage

• Future Worko Extending the coverage model: Barrier coverage, k-degree coverage …o Extending the Doppler model: Information of target’s motion … o Bistatic/multistatic radar networks

Thank You !

Please send any questions to the co-authors at xgong9@asu.edu; junshan.zhang@asu.edu

Questions ?

Range-based Detection: SNR Model

• Monostatic radar: co-located radar transmitter and receivero Received target signal power : (SNR contour is circle)o K: depends on physical layer characteristics, e.g., transmit power,

antenna gains, radar cross section

• Bistatic radar: separated radar transmitter and receivero Received target signal power :

radar Tx

𝑅

𝑅1❑

radar Rx

𝑅2❑

radar Tx and Rx

CSR Algorithm• CSR Algorithm (find Critical Sensing Range): input output

o Phase 1: coarse-grained search : lower bound of : upper bound of

: set of sensors that must cover all points in when : set of sensors that must or possibly cover some points in when : set of sensors that must not cover any points in when

o Phase 2: divide and conquer approach Split a coverage list into partial coverage lists

, ,

, , ,

Sub-routine PCSR Algorithm : PCSR[, ] finds the minimum sensing range required to Doppler-cover all the directions (if any) from any point and between and that can not be Doppler-covered by or

CSR Algorithm: Case Study

𝑟 𝜃1∗ =𝑙

))

𝑟 𝜃2

∗ =∥𝐸𝑀∥=𝑙√(√32 − 1sin 2𝜃

−1

tan 2𝜃 )2

+1

• CSR Algorithm applied for regular triangle patterno (a) (unit region) can be Doppler-covered by o (b) can be Doppler-covered by but not by