The Wiener filter is analyzed for stationary complex Gaussian signals from
an information-theoretic point of view. A dual-port analysis of the Wiener
filter leads to a decomposition based on orthogonal projections and results
in a new multistage method for implementing the Wiener filter using a nest
ed chain of scalar Wiener filters. This new representation of the Wiener fi
lter provides the capability to perform an information-theoretic analysis o
f previous, basis-dependent, reduced-rank Wiener filters. This analysis dem
onstrates that the recently introduced cross-spectral metric is optimal in
the sense that it maximizes mutual information between the observed and des
ired processes. A new reduced-rank Wiener filter is developed based on this
new structure which evolves a basis using successive projections of the de
sired signal onto orthogonal, lower dimensional subspaces. The performance
is evaluated using a comparative computer analysis model and it is demonstr
ated that the low-complexity multistage reduced-rank Wiener filter is capab
le of outperforming the more complex eigendecomposition-based methods.