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

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 co...

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Bibliographic Details
Published in:	IEEE transactions on signal processing 2013-05, Vol.61 (9), p.2178-2191
Main Authors:	Liu, Tingting, Yang, Chenyang
Format:	Article
Language:	eng
Subjects:	Algorithms Antennas Applied sciences Broadcasting Channels Degrees of freedom (DoF) Detection, estimation, filtering, equalization, prediction Electromagnetism Exact sciences and technology Feasibility Information, signal and communications theory Interference interference alignment feasibility interference broadcast channel Jacobi matrix method Jacobian matrices Jacobian matrix Matrix converters MIMO multi-input-multi-output (MIMO) Receiving antennas Signal and communications theory Signal, noise Sparse matrices Streams Studies Telecommunications and information theory
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Summary:	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.
ISSN:	1053-587X 1941-0476