A Riccati-Lyapunov Approach to Nonfeedback Capacity of MIMO Gaussian Channels Driven by Stable and Unstable Noise

TL;DR

This paper characterizes the nonfeedback capacity of MIMO Gaussian channels with nonstationary, unstable noise using Riccati and Lyapunov equations, linking asymptotic limits to finite block capacities.

Contribution

It introduces a novel Riccati-Lyapunov framework to analyze nonfeedback capacity in challenging nonstationary, unstable noise conditions for MIMO Gaussian channels.

Findings

Capacity characterized by generalized Riccati and Lyapunov equations.

Conditions established for asymptotic equivalence of capacities.

Finite block capacity limits derived from Riccati and Lyapunov equations.

Abstract

In this paper it is shown that the nonfeedback capacity of multiple-input multiple-output (MIMO) additive Gaussian noise (AGN) channels, when the noise is nonstationary and unstable, is characterized by an asymptotic optimization problem that involves, a generalized matrix algebraic Riccati equation (ARE) of filtering theory, and a matrix Lyapunov equation of stability theory of Gaussian systems. Furthermore, conditions are identified such that, the characterization of nonfeedback capacity corresponds to the uniform asymptotic per unit time limit, over all initial distributions, of the characterization of a finite block or transmission without feedback information (FTwFI) capacity, which involves, two generalized matrix difference Riccati equations (DREs) and a matrix difference Lyapunov equation.