Determining the feasibility conditions for vector space interference alignment in the K-user MIMO interference channel with constant channel coefficients has attracted much recent attention yet remains unsolved. The main result of this paper is restricted to the symmetric square case where all transmitters and receivers have N antennas, and each user desires d transmit dimensions. We prove that alignment is possible if and only if the number of antennas satisfies N ≥ d(K + 1)/2. We also show a necessary condition for feasibility of alignment with arbitrary system parameters. An algebraic geometry approach is central to the results. 978-1-4577-0437-6/11/$26.00
The authors of REF proposed a feasible condition for the case where all transmitters and receivers have the same number of antennas.
Feasibility of interference alignment for the MIMO interference channel: The symmetric square case
2011 IEEE Information Theory Workshop
2011 IEEE Information Theory Workshop
Mathematics Computer Science