On the Feasibility of Interference Alignment With Finite Channel Extensions for MIMO Interference Broadcast Channels With Common Messages

In this paper, we analyze the feasibility of interference alignment (IA) schemes with T finite channel extensions for multi-input-multi-output (MIMO) interference broadcast channel (IBC) with common messages, where each base station transmits one common single data stream to all users within its cell. We investigate necessary conditions of feasibility of the IA schemes for this network in three different scenarios, i.e., with no channel extensions (T = 1), with T (T ≥ 2) channel extensions for a positive measure of channel coefficients, and with T (T ≥ 2) dependent channel extensions. These necessary conditions impose constraints on system configurations, e.g., the number of users, the number of antennas, the number of cells, and the number of channel extensions, which must be satisfied when the IA schemes are feasible, and also implicitly provide constraints on the upper bound of degrees of freedom (DoF) with finite channel extensions.