Feasibility Test for Linear Interference Alignment

Introduction

We propose a test for checking the feasibility of linear interference alignment (IA) for multiple-input multiple-output (MIMO) channels with constant coefficients for any number of users, antennas and streams per user. We consider the compact complex manifold formed by those channels, precoders and decoders that satisfy the polynomial IA equations (the so-called solution variety), and study its projection onto the input space formed by the interference channels. When the derivative of this projection is surjective, namely when the tangent space of the solution variety is projected into the whole tangent space of the input space, the linear alignment problem is feasible; otherwise is infeasible. Building on these results, a general feasibility test, which amounts to check whether a given matrix is full-rank or not, is proposed.

Additional details can be obtained in the references below.

Source code

If you want to check the feasibility of your own systems, feel free to download the Matlab/Octave floating-point implementation of the test from Github.

Maintained by Óscar González. Any comment, suggestion, or bug report is welcome.

References

Ó. González, I. Santamaría, and C. Beltrán, "A general test to check the feasibility of linear interference alignment", IEEE International Symposium on Information Theory (ISIT 2012), Cambridge, MA, USA, July, 2012. PDF icon PDF Version (378.17 KB)
Ó. González, C. Beltrán, and I. Santamaría, "A Feasibility Test for Linear Interference Alignment in MIMO Channels with Constant Coefficients", IEEE Transactions on Information Theory., vol. 60, issue 3, pp. 1840-1856, March, 2014. PDF icon PDF Version (466.59 KB)