  Independent Vector Analysis (IVA) has emerged in recent years as an extension
of Independent Component Analysis (ICA) into multiple sets of mixtures, where
the source signals in each set are independent, but may depend on source
signals in the other sets. In a semi-blind IVA (or ICA) framework, information
regarding the probability distributions of the sources may be available, giving
rise to Maximum Likelihood (ML) separation. In recent work we have shown that
under the multivariate Gaussian model, with arbitrary temporal covariance
matrices (stationary or non-stationary) of the source signals, ML separation
requires the solution of a "Sequentially Drilled" Joint Congruence (SeDJoCo)
transformation of a set of matrices, which is reminiscent of (but different
from) classical joint diagonalization. In this paper we extend our results to
the IVA problem, showing how the ML solution for the Gaussian model (with
arbitrary covariance and cross-covariance matrices) takes the form of an
extended SeDJoCo problem. We formulate the extended problem, derive a condition
for the existence of a solution, and propose two iterative solution algorithms.
In addition, we derive the induced Cram\'er-Rao Lower Bound (iCRLB) on the
resulting Interference-to-Source Ratios (ISR) matrices, and demonstrate by
simulation how the ML separation obtained by solving the extended SeDJoCo
problem indeed attains the iCRLB (asymptotically), as opposed to other
separation approaches, which cannot exploit prior knowledge regarding the
sources' distributions.
