Distributed Monitoring for Opportunistic Radios - Software Defined Radios - page 67

contour) which is closest to the primary contour and hence considered to give the
best estimate of α and β .
The distance d

from the secondary sender x s 2 to the footpoint f i
is used together with the estimated pathloss parameters to estimate an improved
transmission power:

= x s 2 − f i

+ β i , =

P interference +ˆ

P α i 10 log 10 (d) (4.6)

where P interference denotes the maximal interference that can still be tolerated at the
established contour of the first sender.
This process of power adaptation based on the estimated pathloss parameters
at the minimal contour-to-contour node can be iterated to further improve the sec-
ondary transmission power estimation. As can be seen in Fig. 4.7 , this requires only
a few iteration steps. In each step, one contour estimation and information propaga-
tion substep needs to be carried out, each with complexity of at most N messages.

4.3.4.2 The Decreasing Power Scenario

When the contours overlap, it will be required that the opportunistic transmitter de-
creases his transmission power. This however is relatively easy, since a node i inside
both contours will have an estimate of the received power from both transmitters,
and can hence easily determine the P i causing the overlap in contours. A node
noticing such an overlap simply communicates the P i to the second transmitter,
that follows the largest power adjustment reported. This case is very unlikely to
happen, but since we extrapolate an estimated pathloss model, we cannot avoid the
possibility.

4.3.5 Results

In this section, the simulation setup is introduced and some results discussed.

4.3.5.1 Simulation Model

In order to verify the approach on a data set that is not subject to measurement
errors, it is appropriate to set up a simulation model. The simulation scene consists
of a two-dimensional area in which buildings or obstacles result in shadowing losses
L S , on top of a general pathloss trend that varies with distance:
L = 10 α log 10 (d) + β + L S + X σ , (4.7)

where L is the total pathloss in dB ( α 40 dB for the simulations). Since

the measurement data shows a lot of variations in the measured RSSI, even for
a fixed position d and shadowing L S , zero-mean Gaussian distributed variations or

= 4 and β =