Abstract
In this paper, we study how many different solutions exist for a feasible interference alignment (IA) problem. We focus on linear IA schemes without symbol extensions for the K-user multiple-input multiple-output (MIMO) interference channel. When the IA problem is feasible and the number of variables matches the number of equations in the polynomial system, the number of solutions is known to be finite. Unfortunately, the exact number of solutions is only known for a few particular cases, mainly single-beam MIMO networks. In this paper, we prove that the number of IA solutions is given by an integral formula that can be numerically approximated using Monte Carlo integration methods. More precisely, the number of solutions is the scaled average over a subset of the solution variety (formed by all triplets of channels, precoders and decoders satisfying the IA polynomial equations) of the determinant of certain Hermitian matrix related to the geometry of the problem. Our results can be applied to arbitrary interference MIMO networks, with any number of users, antennas and streams per user.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
