  This paper studies the decoupling principle of a linear vector channel, which
is an extension of CDMA and MIMO channels. We show that the scalar-channel
characterization obtained via the decoupling principle is valid not only for
collections of a large number of elements of input vector, as discussed in
previous studies, but also for individual elements of input vector, i.e. the
linear vector channel for individual elements of channel input vector is
decomposed into a bank of independent scalar Gaussian channels in the
large-system limit, where dimensions of channel input and output are both sent
to infinity while their ratio fixed.
