Digital Signal Processing Reference
In-Depth Information
Figure 2.11 Estimated source signal constellations obtained by jade (a) and GUT
method gut5 (b) for the data with four outliers. Signals that correspond to outliers are
marked by triangle. Robust GUT method gut5 is unaffected by outliers, which are
clearly detected in the plots whereas jade fails completely: outliers are able to
destroy the patterns of BPSK and 8-QAM signals.
To illustrate the reliable performance of the robut GUT matrices under contami-
nation, four observations were replaced by an outlier
z
out
generated as
z
out
¼
(
b
1
u
1
z
1, max
,
...
,
b
4
u
4
z
4, max
)
T
where
z
i
,max
is the element of the
i
th row of the sample data matrix
Z
n
¼
(
z
1
... z
n
)
[
C
kn
with largest modulus,
u
i
Unif(1,5) and
b
i
is a rva with a value of
2
1 or 1 with
equal probability
2
.Notethat
z
i
, out
¼ b
i
u
i
z
i
,max
points to the same or opposite direc-
tion as
z
i
,max
but its magnitude is at least as big, but at most 5 times larger than that
of
z
i
,max
. Note that only 0.2 percent (4 observations out of
n ¼
2000) of the data is
contaminated. Figure 2.11 depicts the estimated source signal constellations obtained
by
jade
and
gut5
. As can be seen, only
gut5
is able to separate the sources and is unaf-
fected by outliers, which are clearly detected in the plots.
jade
on the other hand fails
completely: BPSK and 8-QAM sources are no longer discernible in the plots. The
reliable performance of the robust ICA methods is evident in Table 2.2.: only the
robust GUT methods
gut4
and
gut5
and the robust DOGMA estimator
d1
are able
to separate the sources.
Table 2.3 gives average computation times. As can be seen
gut1
(i.e., the SUT) and
fobi
are the fastest to compute whereas
fica
is the slowest. To compute
fobi
we used the
Search WWH ::
Custom Search