  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the transmitters (CSIT) is completely outdated, and 2) the number of transmit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
$\frac{M}{N}{\geq}K$, the achieved sum DoF is asymptotically given by
$\frac{64}{15}N$ when $K{\to}\infty$.
