Computation of Feedback Capacity of Single User Multi-Antenna Stationary Gaussian Channel

Abstract

In this paper, we consider the single user communications through multiple transmitting and receiving antennas over the additive stationary Gaussian channel under input power constraints. We consider the problem of finding the feedback capacity of the aforementioned channel by utilizing the control theoretic interpretation of feedback communications. We connect the problem of finding the strictly causal filter to achieve the feedback capacity with the problem of finding stabilizing feedback controllers with maximum reliable transmission rate over Youla parameters. We then evaluate the asymptotic capacity achieving upper bounds by solving finite dimensional dual optimization problem. Optimal filter obtained from dual problem is then used to derive the sequence of lower bounds. Numerical example shows that the sequence of lower bounds and upper bounds are capacity achieving.