This paper considers a K-user multiple-inputmultiple-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completely outdated, and 2) the number of transmit antennas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-SingleOutput
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 M
N ≥K, the achieved sum DoF
is asymptotically given by 64
15N when K→∞.