Mean Square Capacity of Power Constrained Fading Channels with Causal Encoders and Decoders

TL;DR

This paper investigates the mean square stabilization of discrete-time LTI systems over power-constrained fading channels with causal encoders/decoders, providing new necessary and sufficient conditions and demonstrating less restrictive stabilizability criteria.

Contribution

It introduces the mean square capacity for channels with fading and noise under causal encoders/decoders, expanding beyond linear encoder assumptions and comparing with Shannon capacity.

Findings

Causal encoders/decoders improve stabilizability conditions.

Mean square capacity is smaller than Shannon capacity.

Numerical examples confirm less restrictive conditions.

Abstract

This paper is concerned with the mean square stabilization problem of discrete-time LTI systems over a power constrained fading channel. Different from existing research works, the channel considered in this paper suffers from both fading and additive noises. We allow any form of causal channel encoders/decoders, unlike linear encoders/decoders commonly studied in the literature. Sufficient conditions and necessary conditions for the mean square stabilizability are given in terms of channel parameters such as transmission power and fading and additive noise statistics in relation to the unstable eigenvalues of the open-loop system matrix. The corresponding mean square capacity of the power constrained fading channel under causal encoders/decoders is given. It is proved that this mean square capacity is smaller than the corresponding Shannon channel capacity. In the end, numerical examples are presented, which demonstrate that the causal encoders/decoders render less restrictive stabilizability conditions than those under linear encoders/decoders studied in the existing works.