with Probabilistic Distance

workablejeansMobile - Wireless

Nov 21, 2013 (3 years and 11 months ago)

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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


Advantage:


Simple and feasible

Advantage of the grid
-
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.”

Disadvantage of average distance


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


Heavy load of traffic


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