On Necessary and Sufficient Conditions of Interference Alignment Feasibility in a MIMO Interference Channel

  • Kosar Ghorbani
  • Abolfazl FalahatiEmail author


One of the major problems of applying interference alignment (IA) for handling interference in a multi-user MIMO interference channel, with constant coefficients over time and without symbol extension is the feasibility problem. The feasibility of IA is to determine whether an IA is capable to omit all interferer signals or not, when the parameters of the system such as the number of users and the number of antennas are fixed. Comparing the Ruan sufficient condition of feasibility with González feasibility test, their corresponding matrices are shown to have the same structure in this paper. We claim the row rank fullness of Ruan and González matrices with generic channel matrices satisfy properness condition, which are necessary condition of IA feasibility. Other necessary conditions are extracted by investigating row rank fullness of these matrices. An optimization problem based on the extracted conditions is introduced to obtain the maximum sum degrees of freedom (DoF). The simulation results reveal an upper bound on the sum DoF with the optimization subject to the point to point constraint, the two-user information theory constraint and the extracted constraints.


Interference alignment MIMO interference channel Feasibility condition Degrees of freedom (DoF) 



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© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of Electrical EngineeringUniversity of Science and Technology (DCCS Lab)TehranIran

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