Capacity of Fading Channels without Channel Side Information

TL;DR

This paper investigates the capacity of fading channels without channel side information using a Gaussian-Markov model, revealing a fundamental structure linking user and channel information rates and analyzing their behavior with respect to channel coherence.

Contribution

It introduces a unified model for slow and fast fading channels without side information and derives a new capacity formula showing the relationship between user and channel information rates.

Findings

Channel information rate is a non-increasing function of the coherence coefficient α.

User information rate exhibits asymptotic monotonic behavior with respect to α at high SNR.

The monotonic behavior of user information rate with respect to α is conjectured to be universal.

Abstract

There are currently a plurality of capacity theories of fading channels, including the ergodic capacity for fast fading channels and outage capacity for slow fading channels. However, analyses show that the outage capacity is a misconception. In this paper we use the 1st order Gaussian-Markov process with coherence coefficient $\alpha$ as the unified model for slow and fast fading channels, the capacity of which without channel side information is studied. We demonstrate that the information rate of a fading channel has a structure that the rate of user message is always accompanied by a rate of channel information. The formula for the channel information rate is derived and turns out to be a non-increasing function of $\alpha$. We prove that there is an asymptotically monotonic behavior of the user information rate with respect to $\alpha$ when the input is independent, identically distributed and Gaussian in the high signal to noise ratio regime. It is further conjectured that the monotonic behavior of the user information rate with respect to $\alpha$ is universal.