This paper considers a K-user multiple-input-multiple-output (MIMO)
interference channel (IC) where 1) the channel state information obtained by
the transmitters (CSIT) is completely outdated, and 2) the number of transmit
antennas at each transmitter, i.e., M, is greater than the number of receive
antennas at each user, i.e., N. The usefulness of the delayed CSIT was
firstly identified in a K-phase Retrospective Interference Alignment (RIA)
scheme proposed by Maddah-Ali et al for the Multiple-Input-Single-Output
Broadcast Channel, but the extension to the MIMO IC is a non-trivial step as
each transmitter only has the message intended for the corresponding user.
Recently, Abdoli et al focused on a Single-Input-Single-Output IC and solved
such bottleneck by inventing a K-phase RIA with distributed overheard
interference retransmission. In this paper, we propose two K-phase RIA
schemes suitable for the MIMO IC by generalizing and integrating some key
features of both Abdoli's and Maddah-Ali's works. The two schemes jointly yield
the best known sum Degrees-of-Freedom (DoF) performance so far. For the case
NM≥K, the achieved sum DoF is asymptotically given by
1564N when K→∞