Real-time tracking of linear processes over an AWGN channel without feedback: The MMSE optimality of the innovation encoder

We first present a formulation for the real-time tracking of a scalar continuous-time linear process over an Additive White Gaussian Noise (AWGN) channel without channel feedback and prove several results for minimum mean-squared error (MMSE) tracking. For the one-to-one channel case, we give an optimal encoder-decoder pair along with the optimal tracking performance. With the Gaussian distributed source innovation, one optimal form of the encoder is shown to be a linear innovation encoder, which scales the source innovation to match with the power constraint of the channel input. We then extend the formulation to the case where multiple source processes are tracked via a shared AWGN channel.