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 inputs 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 [1] and [2]. Furthermore, the reader is invited to test the proposed algorithm online in the following section.
For describing the K-user assymmetric interference channel we adhere to the notation
where , and are the number of transmit antennas, receive antennas and number of streams of the k-th user, respectively. Here, we show several examples:
You can also enter your own system in the following box:
Disclaimer: Due to limited server resources this demo is constrained to a total number of 200 antennas and 50 streams. Depending on the server workload these limits can sometimes be more restrictive.
