SIMULATION METRICS FOR WIRELESS SENSOR NETWORKS (WSN)
1. Energy Consumption
a. Theoretical background
 Radio model: The radio model is showed in Figure 1 (redrawn from
[1] page 2)
Figure 1: Radio model for WSN
The formula for sending (Figure 2) and receiving (Figure 3) a message
(redrawn from [1] page 2):
Figure 2: Energy consumption formula for sending a k-bit message to
a distance d
Figure 3: Energy consumption formula for receiving a k-bit message

Sensor board, CPU board, and Memory board: These boards work in
2 modes: full action and sleep. In the sleep mode, the energy
dissipation is almost zero. The full action consumes energy as
showed in Table 1 (redrawn from [2] page 21)
Table 1: Current of boards in sensor node MICA2DOT (MPR 500)

Calculations: We use the assumption of [1] to calculate the energy
dissipation:
Eelec = 50nJ/bit
amp = 100pJ/bit/m2 = 0.1nJ/bit/m2
Data rate = 2000bits/s
Data package size = 2000-bit
(Size of a data messages)
Signal package size = 64-bit
(Size of advertising, neighbor activation, or maintenance
messages)
From Table 1, we deduce that current of CPU board in full operation
is equal to Radio board in the receiving mode. And, the current of
sensor board in full operation is around 2/3 of current of the radio in
receiving mode. So:
ERx_data = Eelec* k-bit/message = 50nJ/bit * 2000
bits/message = 100 µJ/message
(Meaning: The radio board consumes 100 µJ for each received
data message)
ERx_signal = Eelec* k-bit/message = 50nJ/bit * 64
bits/message = 3.2 µJ/message ~ 3 µJ/message
(Meaning: The radio board consumes 3 µJ for each received
signal message)
ETx_data = Eelec* k-bit/message + amp*k*d^2 = 50 nJ/bit
* 2000 bits/message + 0.1 nJ/bit*2000 bits/message*d^2 =
(100 µJ + 200*d^2)/message
(Meaning: The radio board consumes (100 + 200*d^2) µJ for
transmitting a data message to a distance d)
ETx_signal = Eelec* k-bit/message + amp*k*d^2 = 50 nJ/bit
* 64 bits/message + 0.1 nJ/bit*64 bits/message*d^2 =
(3 µJ + 6.4*d^2)/message
(Meaning: The radio board consumes (3 + 64*d^2) µJ for
transmitting a signal message to a distance d)
We assume that, the optimized distance is 60m. So:
ETx_data = 2000(bit)*(50(nJ) + 0.1(nJ)*60*60) = 820
µJ/message
(Meaning: The radio board consumes 820 µJ for transmitting a
data message to a distance d<= 60m)
ETx_signal = 64(bit)*(50(nJ) + 0.1(nJ)*60*60) = 26.2
µJ/message ~ 26 µJ/message
(Meaning: The radio board consumes 26 µJ for transmitting a
data message to a distance d<= 60m)
ERadio = Eelec * data_rate = 50nJ/bit* 2000 bits/s = 100 µJ/s
(Meaning: if the radio board is in receive mode, it consumes
100 µJ at each second)
ESensor = ERadio * 2/3 = 66 µJ/s
(Meaning: if the sensor board is in full operation mode, it
consumes 66 µJ at each second)
In practical, the CPU is in sleep mode, it just switches to active
when having an external interrupt. So, in the simulation, we
assume that the processor is in sleep mode most of the time. It
turns to full operation when having an event. It means when
creating a new message, energy as follow is consumed:
ECPU_data = 2000(bit)*50(nJ) = 100 µJ/message
(Meaning: The CPU board consumes 100 µJ for creating a data
message)
ECPU_signal = 64(bit)*50(nJ) = 3.2 ~ 3 µJ/message
(Meaning: The CPU board consumes 3 µJ for creating a signal
message)
b. Summary Table
Table 2 is a summary of the calculations above
Create/Receive a data message
Create/Receive a signal message
Send a data message (d<= 60m)
Send a signal message (d<=60m)
Send a message (d > 60m)
Sensor board (full operation)
Radio board (idle/receive mode)
100 µJ
3 µJ
820 µJ
26 µJ
100 µJ + 0.1*d^2
66 µJ/s
100 µJ/s
Table 2: WSN Energy consumption summary table
c. Direct Communication Energy Consumption Model
In this method, the sensor boards of all nodes are in full operation.
When a node senses an object, it transmits the sensing information to
the base directly. Nodes don’t need to communicate together, so, the
radio boards are in sleep mode. The summary state of all nodes is as
follow:
o
o
o
Sensor board = Full operation
Radio board = Sleep, wake up for transmitting only.
CPU board = Sleep, wake up for creating messages only.
d. LEACH Energy Consumption Model
In this method, the sensor boards of all nodes are in full operation.
When a node senses an object, it transmits the sensing information to
its cluster head, then, the head forwards the information to the base
directly. Cluster heads need to receive messages from its clients, so,
the radio boards of the heads are in receiving mode. The radio boards
of other nodes are turned off (sleep mode). We know that one of the
weaknesses of LEACH is that nodes don’t always get invitation because
there are no cluster head in their zone (called wild nodes). So, in the
simulation scenario, I turn off the sensor board of nodes that didn’t
enroll in any cluster head. The summary state of nodes is as follow:
o
o
o
Cluster heads:
 Sensor board = Full operation.
 Radio board = Receive.
 CPU board = Sleep, wake up for creating messages only.
Client nodes:
 Sensor board = Full operation.
 Radio board = Sleep, wake up for transmitting only.
 CPU board = Sleep, wake up for creating messages only.
Wild nodes:
 Sensor board= Sleep after 10s of receiving no invitation.
 Radio board = Sleep.
 CPU board = Sleep.
Note: According to [1], the direct communication consumes less
energy than LEACH-based algorithm if and only if (Figure 4 – redrawn
from [1] page 3):
Figure 4: Condition for direct communication consume less energy
than LEACH
The n in Figure 4 is the number of hops - 1 from the destination to the
source. r is the distance among hops. In our LEACH simulation,
however, the distances among hops aren’t equal. So, from Figure 5,
the energy consumption for the LEACH and the direct communication
are as follow:
r
Source

r1
Destination
r2
Figure 5: LEACH and Direct Communication transmit model
ELEACH = k(bit)*(Eelec + amp* r1^2+ Eelec + amp* r2^2 + ERx)
EDIRECT = k(bit)*(Eelec + amp* r^2)
ELEACH < EDIRECT
 (Eelec + amp* r1^2+ Eelec + amp* r2^2 + ERx) < (Eelec +
amp* r^2) (1)
Because
Eelec = ERx = 50 µJ, amp = 0.1 µJ. So:
(1)  100+0.1(r1^2 + r2^2) < 0.1*r^2
 1000 + (r1^2 + r2^2) < r^2
r1, r2, and r are 3 edges of a triangle => r2^2 = r1^2 + r^2 2*r1*r*cos() [4]. Hence:
1000 + (r1^2 + r1^2 + r^2 - 2*r1*r*cos()) < r^2
 1000 + 2*r1^2 < 2*r1*r*cos() (2)
We assume r1= 60m. So:
(2) r > 68.3/cos()
To sum up, the simulation LEACH is more efficient than
the direct communication when the distances from nodes to the
base are greater than 68.3/cos() (m).
(Example: if 0<<45  0.707< cos() <1  r > 68.3/0.707~ 97.14
 A simulation result verified this.)
e. OCO Energy Consumption Model
In this method, nodes are categorized into 3 groups: border nodes,
forward nodes, and redundant nodes. In tracking mode, the sensor of
all border nodes is in full operation. The sensor boards of forwarding
nodes are in sleep mode. They just turned on only by their neighbors.
The redundant nodes have all boards in sleep mode. Actually, they just
wake up in a short time after each long period to get command from
the base because they are used as reservation. The summary state of
nodes is as follow:
o
o
o
Redundant nodes:
 Sensor board = Sleep.
 Radio board = Sleep.
 CPU board = Sleep.
Forwarding nodes:
 Sensor board = Sleep, wake up when receiving an
activation message and automatically turn to sleep after
an interval of sensing nothing.
 Radio board = Receive.
 CPU board = Sleep, wake up for creating messages only.
Border nodes:
 Sensor board = Full operation.
 Radio board = Receive.
 CPU board = Sleep, wake up for creating messages only.
2. Object Tracking Accuracy
a. Standard detected point
According to [3] (page 36), a sensor network with all nodes are
in tracking mode (sensor board is in full operation mode) is a useful
base for comparison because it provides the best possible quality of
tracking. So, we consider the total number of detected points in this
case is 100%, and called standard detected point.
b. Accuracy calculation
The accuracy of each method is a percent ratio between the
number of detected points of the method and the standard detected
point.
3. Cost per Detected Point
Cost per detected point is a ratio between the total energy dissipation
and the total number of detected points of the method.
4. References
[1] Wendi Rabiner Heinzelman, Anantha Chandrakasan, and Hari Balakrishnan
(2000). “Energy-Efficient Communication Protocol for Wireless Microsensor
Networks”. THE HAWAII INTERNATIONAL CONFERENCE ON SYSTEM SCIENCES,
JANUARY 4-7, 2000, MAUI, HAWAII. Retrieved 6/20/05 from
http://academic.csuohio.edu/yuc/mobile03/0403-heinzelman.pdf
[2] Rev B (2005). “MPR/ MIB User’s Manual”. DOCUMENT 7430-0021-06. Retrieved
7/10/05 from http://www.xbow.com/Support/Support_pdf_files/MPRMIB_Series_Users_Manual.pdf
[3] Sundeep Pattem, Sameera Poduri, and Bhaskar Krishnamachari (2003). “EnergyQuality Tradeoffs for Target Tracking in Wireless Sensor Networks”. DEPARTMENT
OF ELECTRICAL ENGINEERING AND DEPARTMENT OF COMPUTER
SCIENCE,UNIVERSITY OF SOUTHERN CALIFORNIA. Retrieved 7/10/05 from
http://www-scf.usc.edu/~pattem/PattemKrishnamachari_Tracking.pdf
[4] Math for Morons Like Us website (2005). “Algebra II: Equations and Triangles –
Law of Cosines”. Retrieved 7/10/05 from
http://library.thinkquest.org/20991/alg2/eqtri.html