On the Degrees of Freedom of Asymmetric MIMO Interference Broadcast Channels

TL;DR

This paper investigates the degrees of freedom in asymmetric MIMO interference broadcast channels, establishing necessary and sufficient conditions for interference alignment feasibility and deriving the maximal achievable DoF per user.

Contribution

It introduces the irreducible condition for IA feasibility in asymmetric MIMO-IBC and characterizes the maximal DoF per user for both asymptotic and linear IA.

Findings

Irreducible condition is necessary for IA feasibility.

In certain cases, the irreducible condition is also sufficient.

Derived upper bounds for DoF per user in asymmetric MIMO-IBC.

Abstract

In this paper, we study the degrees of freedom (DoF) of the asymmetric multi-input-multi-output interference broadcast channel (MIMO-IBC). By introducing a notion of connection pattern chain, we generalize the genie chain proposed in [11] to derive and prove the necessary condition of IA feasibility for asymmetric MIMO-IBC, which is denoted as irreducible condition. It is necessary for both linear interference alignment (IA) and asymptotic IA feasibility in MIMO-IBC with arbitrary configurations. In a special class of asymmetric two-cell MIMOIBC, the irreducible condition is proved to be the sufficient and necessary condition for asymptotic IA feasibility, while the combination of proper condition and irreducible condition is proved to the sufficient and necessary condition for linear IA feasibility. From these conditions, we derive the information theoretic maximal DoF per user and the maximal DoF per user achieved by linear IA, and these DoFs are also the DoF per user upper-bounds of asymmetric G-cell MIMO-IBC with asymptotic IA and linear IA, respectively.