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We address the problem of interference leakage (IL) minimization in the$K$-user multiple-input multiple-output (MIMO) interference channel (IC)assisted by a reconfigurable intelligent surface (RIS). We describe aniterative algorithm based on block coordinate descent to minimize the IL costfunction. A reformulation of the problem provides a geometric interpretationand shows interesting connections with envelope precoding and phase-onlyzero-forcing beamforming problems. As a result of this analysis, we derive aset of necessary (but not sufficient) conditions for a phase-optimized RIS tobe able to perfectly cancel the interference on the $K$-user MIMO IC.

Interference Leakage Minimization in RIS-assisted MIMO Interference Channels