COMPLEX-VALUED ADAPTIVE SIGNAL PROCESSING - Adaptive Signal Processing: Next Generation Solutions - page 79

eigenvalue spread of the augmented covariance matrix ¯ will always be greater
than or equal to that of the original covariance matrix C using the majorization
theorem [49].

1.10 In real-valued independent component analysis, separation is possible as long

as only one of the sources is Gaussian. In the complex case, however, as dis-
cussed in Section 1.6.4, Gaussian sources can be separated as long as they
are noncircular with unique spectral coefficients.
Show that the score function for Gaussian sources can be reduced to

4 s r þ j u i

u r

c n ( u ) ¼

4 s i
when we consider the scaling ambiguity for the complex case. Then, devise a
procedure for density (score function) matching for the estimation of complex
Gaussian sources.

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