# with Probabilistic Distance

Mobile - Wireless

Nov 21, 2013 (4 years and 7 months ago)

99 views

Minimizing Energy Consumption
with Probabilistic Distance
Distributions in Wireless Sensor
Networks

Authors: Yanyan Zhuang,
Jianping Pan, Lin Cai

University of Victoria

Problem:

Prolong lifetime of wireless sensor network

Minimize energy cost in wireless sensor
network

The main part of energy cost in wireless
sensor network is cost by sensor
communication

Problem:

How to minimum communication cost in
wireless sensor network

How to measure energy cost by sensor
communication

Solution

Grid
-
based clustering model

Calculating average distance between two
communicating sensors

Simple and feasible

-
based model

“Once the grid structure is established
nodes can communicate locally with their
grid head and reach the data processing
center, or the sink node, through neighbor
grids.”

Disregard the super
-
linear path loss
exponent of over
-
the
-
air wireless
transmissions.

Existed models disregard the path loss of
wireless communication signals.

Path loss

When radiowave transmitted in space, it
will be absorbed or diffracted and causes
propagation loss.

10
10 log ( )
L n d c
 

Path loss is a major component in the
analysis and design of telecommunication
system.

Energy cost obtained from average
distance between two sensors is not
accurate

Find a more accurate calculation model

Key point

Reflect path loss on communication
distance

background

Clustering scheme

Equal
-
divided grid clustering

Variable size clustering

Distance distribution model

Based on geometric properties of grid
-
based clustering

Three steps

Step 1

Classify transceiver locations for a
wireless transmission

(1)two random nodes in the same grid

(2)two random nodes in diagonal neighbor
grids

(3)two random nodes in parallel neighbor
grids

Step 2

Find coordinate distribution of those nodes
in the three cases by the Heaviside Step
Function on unit square grids.

Step function:

Unit step function

The Heaviside step function, H, also called the unit step function, is a discontinuous
function whose value is zero for negative argument and one for positive argument. It
seldom matters what value is used for H(0), since H is mostly used as a distribution.

Dirac delta function

a 'function' δ(x) that has the value zero
everywhere except at x = 0 where its value
is infinitely large in such a way that its total
integral is 1.

Step 3

Apply coordinate distribution on the
distance calculating formula

to obtain distance distribution in three
cases

2 2
1 2 1 2
( ) ( )
D x x y y
   
Distance distribution

Distance distribution

Simulation

(1)distance verification

Compare results of their distance
distribution function to the output of
cumulative distribution function

Simplify integral calculation

Use high
-
degree polynomial functions by
Least Squares Fitting to approximate the
distribution functions.

Simulation

(2)compare one
-
hop energy cost

Result: error of energy calculation of
average distance model will increase
exponentially as the path loss exponent

grows

Simulation

(3) compare network energy cost of
“simulation”

, distance distribution model and average
distance model with varied grid length.

Result: there is an optimal grid size

Grid size

The closer to the sink the smaller of the
cluster

Sensors around the sink consume much
more energy than sensors located far from
the sink in the same time duration

Conclusion

Traditional energy cost calculating model based
on average communication distance between
two sensors in grid
-
based sensor network can
not reflect the accurate value for out of
consideration of path loss

Distance distribution model is more accurate
and useful in finding a suitable grid length to
further optimize energy efficiency