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On the Number of Interference Alignment Solutions for the <inline-formula> <tex-math notation="LaTeX">$K$ </tex-math></inline-formula>-User MIMO Channel With Constant Coefficients - MaRDI portal

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On the Number of Interference Alignment Solutions for the <inline-formula> <tex-math notation="LaTeX">$K$ </tex-math></inline-formula>-User MIMO Channel With Constant Coefficients

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Publication:2977115

DOI10.1109/TIT.2015.2482493zbMATH Open1359.94487arXiv1301.6196OpenAlexW2963809665MaRDI QIDQ2977115

Author name not available (Why is that?)

Publication date: 28 April 2017

Published in: (Search for Journal in Brave)

Abstract: In this paper, we study the number of different interference alignment (IA) solutions in a K-user multiple-input multiple-output (MIMO) interference channel, when the alignment is performed via beamforming and no symbol extensions are allowed. We focus on the case where the number of IA equations matches the number of variables. In this situation, the number of IA solutions is finite and constant for any channel realization out of a zero-measure set and, as we prove in the paper, it is given by an integral formula that can be numerically approximated using Monte Carlo integration methods. More precisely, the number of alignment solutions is the scaled average of the determinant of a certain Hermitian matrix related to the geometry of the problem. Interestingly, while the value of this determinant at an arbitrary point can be used to check the feasibility of the IA problem, its average (properly scaled) gives the number of solutions. For single-beam systems the asymptotic growth rate of the number of solutions is analyzed and some connections with classical combinatorial problems are presented. Nonetheless, our results can be applied to arbitrary interference MIMO networks, with any number of users, antennas and streams per user.


Full work available at URL: https://arxiv.org/abs/1301.6196




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