Critical Density Thresholds for Coverage in WirelessSensor NetworksSachin Adlakha Mani Srivastava Presented by : Abdulla Rasha Abu-samra

Outline of PresentationTalking about the definitions and model used.

Estimate number of sensor required for coverage.

Evaluate the radius of influence sensor nodes depending on their characteristic and the properties of the target.

Finding the radii of influence and critical density.

Verify our result by using matlab.

Coverage: is a measure of the Quality of service of a sensor network . Or how can the network observe (or cover) a given event? such as, intruder detection; animal or fire detection

Coverage depends upon:Range and sensitivity of sensing nodesLocation and density of sensing nodes in given region

Types of coverage

Worst-Case Coverage: Areas of breach (lowest coverage)

Can be used to determine if additional sensors needed

Best-Case Coverage: Areas of best coverage

Can be used by a friendly user to navigate in those areas

Sensor Model

Describe the signal strength received at the sensor node, depending on nature of sensors

Most types of sensors, sensing ability diminishes as distance increases

the signal would be detected ,if S(s, p) > F

ExposureIs the expected ability of observing a target in the sensor field

There are two models, Depending on the way a sensor detect:

Integrator model: This model related to sensors that are energy detectorsSuch as an acoustic sensorif exposure exceeds a threshold, the sensor detected the target

Derivative model:models for sensors that detect the changing in the signal strength . if the change is above threshold a detection is declared Such as a magnetic sensor

Detection Model

By using one of the exposure model , each sensor can make a decision to detect the event.

Individual Detection:

Cooperative Detection:

Target Characteristics

the target moving in straight line path constant speed 'v' from point 'a' to point 'b travel a distance ' '.

two radii associated with a given sensor:

Radius of complete influence ( )Radius of no Influence ( )

Finding the Radii of Influence and Critical Density

a single sensor located at originsensor model : sensing decreased as distance increasesdecay factor k= 2exposure model : integrator model The target is an object that moves in a straight-line path with speed v and travels a distance,Each sensor has a noise figure F and the threshold

The target is initially located at the signal strength received at the sensor at any time is

the total exposure as:

the exposure Using polar coordinates as:

maximum exposure at = 900

minimum exposure at = 00

( = 0.1, = 10m, v = 2m/sec)s

Finding the Maximum E the exposure is sum of exposures for two paths of length x and - x.

.

the maximum Es occurs for

radius of influence by equating the minimum Es to Ethreshold

Radius of no influence is found by equating the maximum Es to Ethreshold

the number of nodes required to cover this area is

r : is the sensing radius the number of sensors required to cover a given area A is the number of sensors required to cover a given area A is

SIMULATIONS

Random deployment over area ( 150m * 150m )k=2, 3, 4. = 0.1 Speed v=2m/sec distance = 10 m noise figure F = 0.0001

By using these values we can evaluate this equations

N = 244

Probability of Detection Vs. Number of Nodes

Variation of Number of Nodes with Target Speed

Variation of Number of Nodes with Threshold

Variation of Number of nodes for different K Cooperative Case

Probability of Detection Vs. Number of Node k =3 and k =4 cases

CONCLUSIONS

we evaluate the critical number of nodes required for target detection in a sensor network. We use both physical characteristics of sensors and target to derive an equation for effective of influence radius. Using this radius we estimate the critical density for coverage in sensor network..