  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.
