Achievable and Crystallized Rate Regions of the Interference Channel with Interference as Noise

TL;DR

This paper characterizes the achievable rate region of the interference channel when interference is treated as noise, introducing the concept of crystallized rate regions formed by binary power control and time-sharing.

Contribution

It extends the analysis of the interference channel to n users, introducing the crystallized rate region concept based on binary power control and convex hull operations.

Findings

Most of the rate region can be achieved with simple binary power control.

The crystallized rate region offers a new geometric perspective.

Time-sharing enhances achievable rates depending on hyper-surface convexity.

Abstract

The interference channel achievable rate region is presented when the interference is treated as noise. The formulation starts with the 2-user channel, and then extends the results to the n-user case. The rate region is found to be the convex hull of the union of n power control rate regions, where each power control rate region is upperbounded by a (n-1)-dimensional hyper-surface characterized by having one of the transmitters transmitting at full power. The convex hull operation lends itself to a time-sharing operation depending on the convexity behavior of those hyper-surfaces. In order to know when to use time-sharing rather than power control, the paper studies the hyper-surfaces convexity behavior in details for the 2-user channel with specific results pertaining to the symmetric channel. It is observed that most of the achievable rate region can be covered by using simple On/Off binary power control in conjunction with time-sharing. The binary power control creates several corner points in the n-dimensional space. The crystallized rate region, named after its resulting crystal shape, is hence presented as the time-sharing convex hull imposed onto those corner points; thereby offering a viable new perspective of looking at the achievable rate region of the interference channel.