Geometry of the 3-user MIMO interference channel

This paper studies vector space interference aligment for the three-user MIMO interference channel with i time or frequency diversity. The main result is a characterization of the feasibility of interference alignment in tl symmetric case where all transmitters have M antennas ai all receivers have N antennas. If N ≥ M and all users designed transmit dimensions, then alignment is feasible if and only (2r + 1)d ≤ max (rN, (r + 1)M) for all nonnegative integers The analogous result holds with M and N switched if M ≥ 1. It turns out that, just as for the 3-user parallel interference channel, the length of alignment paths captures the essen of the problem. In fact, for each feasible value of M and the maximum alignment path length dictates both the conver and achievability arguments. One of the implications of our feasibility criterion is th simply counting equations and comparing to the number variables does not predict feasibility. Instead, a more caret investigation of the geometry of the alignment problem is i quired. The necessary condition obtained by counting equatio is implied by our new feasibility criterion.