#### Retrospective Interference Alignment for the 3-user MIMO Interference Channel with delayed CSIT

##### Marc Torrellas, Adrian Agustin, Josep Vidal

The degrees of freedom (DoF) of the 3-user multiple input multiple output interference channel (3-user MIMO IC) are investigated where there is delayed channel state information at the transmitters (dCSIT). We generalize the ideas of Maleki et al. about {\it Retrospective Interference Alignment (RIA)} to be applied to the MIMO IC, where transmitters and receivers are equipped with $(M,N)$ antennas, respectively. We propose a two-phase transmission scheme where the number of slots per phase and number of transmitted symbols are optimized by solving a maximization problem. Finally, we review the existing achievable DoF results in the literature as a function of the ratio between transmitting and receiving antennas $\rho=M/N$. The proposed scheme improves all other strategies when $\rho \in \left(\frac{1}{2}, \frac{31}{32} \right]$.

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