Image Processing Reference
In-Depth Information
maximum width of the resulting overlapping region
A
is
l
. According to the figure, the transmission
range
r
is equal to
l
+(
d
/
)
.
d
=
(
r
−
l
)
(.)
In an ideal environment, both sensor nodes
S
and
S
transmit a message. This message can be
received within the radius
r
around the nodes. In the overlapping region
A
(dashed region), all
n
A
enclosed sensor nodes receive both messages. These sensor nodes
S
i
(
n
A
)areneighborsof
both sending nodes. Due to the uniform distribution of nodes, the number of nodes
n
in range of
onesensornode(
A
TR
=
i
=
r
) is constant. Since the node density µ is constant in the whole network,
the following equation is formed:
=
π
⋅
n
A
A
=
n
n
A
TR
µ
=
r
=
(.)
π
⋅
and results in
n
A
n
⋅
π
r
A
=
(.)
The calculation of width
l
can be approximated by
√
√
r
π
r
r
sin
⎛
⎝
arcsin
(
(
A
−
)/
)
⎞
⎠
l
=
r
+
⋅
(.)
After calculation of
l
,thedistance
d
can be determined by Equation .. ..The achieved accuracy
of NIDES oscillates between .
r
and .
r
.
6.2.9 Received Signal Strength
In vacuum, a radio signal of a circular source propagates circularly. Generally, the transmission of
radio signals is adherent with the transport of energy into the surrounding of the sender. This en-
ergy level is flatten with the distance
d
to the sender, but it can be detected by a receiver. In several
publications, this method to detect the energy level is called received signal strength (RSS).
Friis presented an equation to compute the distance based on transmission power
P
TX
,received
power
P
RX
,antennagains(
G
TX
,
G
RX
), system losses
L
,andthewavelengthλ
provided ideal
conditions (no reflection, no diffraction, no obstacles, etc.) are met [Fri].
P
RX
P
TX
=
G
RX
G
TX
L
λ
π
d
)
(
(.)
If a sensor node
S
is able to detect the received power
P
RX
of a message, the distance between the
transmitting node
S
and
S
canbecalculatedbyrearrangingEquation..
According to Equation ., wave length λ
and distance
d
affect
P
RX
quadratically [Rap]. he
attenuation of a signal is defined as path loss (PL) which is the logarithm of transmitting power to
received power in decibel.
log
P
TX
G
RX
G
TX
L
λ
π
d
)
PL
(
dB
)=
P
RX
=−
log
(
(
)
(.)
To detect a signal of a transmitting node at a receiving node correctly, the receiver sensitivity PL
max
must be higher than the PL depending on the specific distance
d
between both nodes. For instance,
