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.
L  10n log10 (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 gridbased 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
D  ( x1  x2 )2  ( y1  y2 )2
• to obtain distance distribution in three
cases
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