Approximate Capacity of Fast Fading Interference Channels with No Instantaneous CSIT

TL;DR

This paper introduces a new fading model characterization called logarithmic Jensen's gap, enabling approximate capacity analysis of fast fading interference channels under various scenarios with finite gap bounds.

Contribution

It defines the logarithmic Jensen's gap for fading models and demonstrates its use in deriving approximate capacity regions for FF-IC with different feedback and CSIT conditions.

Findings

Finite logarithmic Jensen's gap for common fading models like Rayleigh and Nakagami.

Achieves constant capacity gap for FF-IC without feedback or instantaneous CSIT.

Provides approximate capacity bounds for fading 2-tap ISI and MAC channels.

Abstract

We develop a characterization of fading models, which assigns a number called logarithmic Jensen's gap to a given fading model. We show that as a consequence of a finite logarithmic Jensen's gap, approximate capacity region can be obtained for fast fading interference channels (FF-IC) for several scenarios. We illustrate three instances where a constant capacity gap can be obtained as a function of the logarithmic Jensen's gap. Firstly for an FF-IC with neither feedback nor instantaneous channel state information at transmitter (CSIT), if the fading distribution has finite logarithmic Jensen's gap, we show that a rate-splitting scheme based on average interference-to-noise ratio (inr) can achieve its approximate capacity. Secondly we show that a similar scheme can achieve the approximate capacity of FF-IC with feedback and delayed CSIT, if the fading distribution has finite logarithmic Jensen's gap. Thirdly, when this condition holds, we show that point-to-point codes can achieve approximate capacity for a class of FF-IC with feedback. We prove that the logarithmic Jensen's gap is finite for common fading models, including Rayleigh and Nakagami fading, thereby obtaining the approximate capacity region of FF-IC with these fading models. For Rayleigh fading the capacity gap is obtained as 1.83 bits per channel use for non-feedback case and 2.83 bits per channel use for feedback case. Our analysis also yields approximate capacity results for fading 2-tap ISI channel and fading interference multiple access channel as corollaries.