Digital Signal Processing Reference
In-Depth Information
5.5.2 Numerical Results
The statistical features (best, mean, and standard deviation values) of the best fea-
sible solutions obtained after 30 independent runs for each case study are used to
evaluate the performance of the competing algorithms.
Table
5.1
shows a comparison of the performances of the competing algorithms
for different values of
ε
and
L
in the uncorrelated case (
ρ
0). We can see that the
CBBO-DE algorithm emerged the best candidate algorithm for
L
=
=
50
sensors in terms of the best “mean” results. For the 20 sensors case, the 2-Stage-
CBBO-DE produces the best “mean” results. In terms of the “best” fitness function
values, it can be inferred that the CBBO-DE algorithm outperformed the other com-
peting algorithms in the case of a large number of sensors for the different values of
error probability at the fusion center. For
L
10 and
L
=
=
20, better “best” results were found
by CPSO in two cases and by CGA in one case.
Table
5.2
shows a comparison of the numerical results of the competing algo-
rithms when the observations are correlated in the case of
L
10 sensors for differ-
ent values of the fusion error probability
ε
and the degree of correlation
ρ
. As illus-
trated in this table, CBBO-DE is found to be the best performing algorithm since it
produced better “mean” results in 7 cases out of a total of 12. In terms of the “best”
fitness function value, out of these 12 test cases, the CGA algorithm could achieve
the best results in 5 cases, while the CBBO-DE, 2-Stage-CBBO-DE, and CPSO al-
gorithms obtained the “best” fitness function value in 2 cases and the CBBO-DE in
3 cases. In the case of small probability of error at the fusion center
(ε
=
0
.
001
)
,the
CGA algorithm emerged as the best performer for the different values of
ρ
.
For
L
=
=
20 sensors, as shown in Table
5.3
, CBBO-DE emerged as the best per-
former in terms of the best “mean” and the “best” fitness function values.
The results for
L
=
50 sensors, in the case of correlated observations, are pre-
sented in Table
5.4
. The CBBO algorithm has emerged as the best performer since
it obtained the best “mean” results in 10 cases out of a total of 12.
From these sets of performance evaluations, it can be generally concluded that,
when the observations are correlated (Tables
5.2
,
5.3
, and
5.4
), the performance
improvement for the CBBO-DE algorithm, compared to the other competing algo-
rithms, was larger for
L
=
10 and
L
=
20 sensors than for
L
=
50 sensors, where
the solution quality of CBBO is superior.
Table
5.5
shows the amplifier gain allocated to each sensor for
L
10 sensors.
The second column of this table gives the analytical optimal schedule for i.i.d. obser-
vations (
ρ
=
0), where 0 means a node should remain inactive in order to provide
significant system power savings. These analytical results are obtained using the
method of Lagrange multipliers [
27
]. From these results, one can observe that more
power is distributed to sensors with good channel fading coefficients and less power
is allocated to sensors with poor channels. Consequently, one can decide whether a
sensor is in transmit mode or in silent mode.
=
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