Weak-Noise Modulation-Estimation of Vector Parameters

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 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 has some interesting implications. Several modifications and extensions of the basic setup are also studied and discussed.