  We address the problem of modulating a parameter onto a power-limited signal,
transmitted over a discrete-time Gaussian channel and estimating this parameter
at the receiver. Continuing an earlier work, where the optimal trade-off
between the weak-noise estimation performance and the outage probability
(threshold-effect breakdown) was studied for a single (scalar) parameter, here
we extend the derivation of the weak-noise estimation performance to the case
of a multi-dimensional vector parameter. This turns out to be a non-trivial
extension, that provides a few insights and it has some interesting
implications, which are discussed in depth. Several modifications and
extensions of the basic setup are also studied and discussed.
