Control-Oriented Achievable Rates for Continuous-Time Gaussian Channels with Feedback

In this work, we revisit the problem of power-constrained transmission over continuous-time (CT) linear, time-invariant (LTI) channels with additive colored Gaussian noise, where channel output feedback is available at the transmitter. Although this model has been studied by several authors, previous work has primarily relied on a stochastic processes framework, which yields explicit achievable rates and capacity characterizations only for a limited class of channel models. Here, we adopt the control-theoretic framework, introduced by Elia in 2004 for the study of discrete-time feedback channels, and extend it to CT settings. We show how CT communications channels can be represented within this formulation, and illustrate the resulting coding scheme with an explicit example. It is observed that the rate achieved by the proposed feedback scheme is 30% higher than the capacity of the channel without feedback, attained by the waterfilling scheme. This work suggests a promising direction for developing communication schemes for additional important CT channel models that have not been studied previously.