On the Feasibility of Linear Interference Alignment for MIMO Interference Broadcast Channels with Constant Coefficients

TL;DR

This paper investigates the conditions under which linear interference alignment is feasible in MIMO interference broadcast channels with constant coefficients, providing necessary and sufficient criteria for specific cases.

Contribution

It establishes new necessary and sufficient conditions for linear IA feasibility in MIMO-IBC, especially when antenna numbers are divisible by data streams, and analyzes Jacobian matrix structures.

Findings

Proper systems with one data stream per user are feasible.

Necessary conditions include properness and an additional irreducible interference condition.

Symmetric MIMO-IBC has proper but infeasible antenna configurations.

Abstract

In this paper, we analyze the feasibility of linear interference alignment (IA) for multi-input-multi-output (MIMO) interference broadcast channel (MIMO-IBC) with constant coefficients. We pose and prove the necessary conditions of linear IA feasibility for general MIMO-IBC. Except for the proper condition, we find another necessary condition to ensure a kind of irreducible interference to be eliminated. We then prove the necessary and sufficient conditions for a special class of MIMO-IBC, where the numbers of antennas are divisible by the number of data streams per user. Since finding an invertible Jacobian matrix is crucial for the sufficiency proof, we first analyze the impact of sparse structure and repeated structure of the Jacobian matrix. Considering that for the MIMO-IBC the sub-matrices of the Jacobian matrix corresponding to the transmit and receive matrices have different repeated structure, we find an invertible Jacobian matrix by constructing the two sub-matrices separately. We show that for the MIMO-IBC where each user has one desired data stream, a proper system is feasible. For symmetric MIMO-IBC, we provide proper but infeasible region of antenna configurations by analyzing the difference between the necessary conditions and the sufficient conditions of linear IA feasibility.