Digital Signal Processing Reference
In-Depth Information
messages, through the use of a clever backoff approach. This approach establishes
a tree from any sensor to a client. In this chapter a similar algorithm will be used
to propagate pathloss information from any receiver to any potential transmitter,
hence conceptually resulting in a forest of trees. The resulting flooding method as
detailed in Sect.
4.3.3
requires a number of packet forwardings close to the number
of nodes
N
.
4.3.1.3 Iterative Power Control
When each secondary transmitter knows its distance to the first transmitter's con-
tour, it can compute its maximal power as function of the interference margins and
a worst-case design time pathloss model as function of distance. From a secondary
transmitter's viewpoint, a worst-case pathloss model is a pessimistic one that as-
sumes that the power of the secondary transmitter decays slowly, resulting in maxi-
mal interference. Consequently, the computed power level will be much lower than
what could be tolerated in reality.
Using the approach of contour estimation and distance flooding, it is however
possible to iteratively adapt the distance between the two contours. While estimat-
ing the contour of the secondary transmitter, it is also possible to estimate a more re-
alistic pathloss model which in turn can be used to improve the power estimate. Key
here is to estimate the pathloss in the direction of the point closest to the first trans-
mitter's contour. Since the pathloss model can vary significantly as a function of the
exact path followed, this direction gives the best information for the targeted power
control. As will be shown in Sect.
4.3.4
, this iterative power adjustment algorithm
will converge in only a few steps and will require an order of
N
communications.
4.3.2 Local Channel Estimation
In this section, it is detailed how a smart secondary transmitter can locally smooth
the fast RSSI variations, without relying on a global trend or any prior informa-
tion, which allows robust inside/outside classification with respect to the threshold
contour.
Given a node
N
i
at location
x
i
, with received (noisy) power measure RSSI
i
,the
objective is to find the noise-reduced power
ˆ
RSSI
i
. Given a complete polynomial
1
x
...
x
n
T
, the cognitive transmitter tries to find the coefficient
basis
p
(
x
)
=[
]
vector
ˆ
a
i
which minimizes following weighted least squares objective function:
w
ij
(
a
T
p
(
x
j
)
RSSI
j
)
2
,
a
i
=
ˆ
arg min
a
−
(4.1)
j
where the summation is over
N
i
's neighboring nodes
N
j
(with positions
x
j
). Note
that
N
i
is contained in its own neighborhood. For example, the complete polynomial
basis of order
n
T
=
1 in two dimensions is
p
(
x
)
=[
1
xy
]
and the coefficient vector
