ROBUST ESTIMATION TECHNIQUES FOR COMPLEX-VALUED RANDOM VECTORS - Adaptive Signal Processing: Next Generation Solutions - page 122

as the plug-in estimator. The optimal weight at F S employs the MLE of S (i.e.,
w¼ w ml , where w ml is given by (2.23)) and is hereafter denoted by w mle .

B EXAMPLE 2.9
Our simulation setting is as follows. A k ¼ 4 sensor ULA with l= 2 spacing
received two ( d ¼ 2) uncorrelated circular Gaussian signals of equal variance s s
with DOAs at 10 8 (SOI) and 15 8 (interferer). In the first setting (A), noise n
has circular Gaussian distribution CN k ( s n I ), and in the second setting (B), noise
has circular Cauchy distribution CT k ,1 ( s n I ). Note that the Cauchy distribution
does not have finite variance and s n is the scale parameter of the distribution. In
both A and B, the SNR (dB) is defined using scale parameters as
10 log 10 [ s s =s n ] ¼ 15 dB. The number of snapshots is n ¼ 500.
Figure 2.8 depicts the estimated w -MVDR beampatterns for look direction 10 8
for settings A and B averaged over 100 realizations. Also plotted are the estimated
spectrums. The employed M -estimators are the SCM [i.e., HUB(1)], MLT(1) and
HUB(0.9). In the Gaussian noise case (setting A), the beampatterns are similar, in

Figure 2.8 Averaged w-MVDR beampatterns (a) and spectrums (b) for setting A and B
(n ¼ 500, SOI at 10 ). In Gaussian noise, all estimators perform

comparably. In Cauchy noise, SCM fails, but robust HUB(0.9) and MLT(1) estimators
perform very well.

8 , interferer at 15 8