Robust Signal Space Inequalities from Aligned Image Sets

Abstract

The past decade has shown that the most promising avenue for understanding the approximate capacity of MIMO interference networks is through the pursuit of generalized degrees of freedom (GDoF) characterizations. The GDoF framework is capable of addressing critical aspects of MIMO interference networks - such as the interplay of spatial dimensions with channel strengths and channel uncertainty levels. However, conventional approaches have repeatedly found GDoF (even DoF) characterizations intractable, especially under channel uncertainty. Against this background, a recent approach based on a combinatorial accounting of the size of aligned image sets (AIS) under finite precision channel knowledge shows promise. This talk will explain the AIS approach, present examples of signal space inequalities that are obtained using this approach, and show how these inequalities may be used to obtain new GDoF characterizations.