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 an iterative algorithm based on block coordinate descent to minimize the IL cost function. A reformulation of the problem provides a geometric interpretation and shows interesting connections with envelope precoding and phase-only zero-forcing beamforming problems. As a result of this analysis, we derive a set of necessary (but not sufficient) conditions for a phase-optimized RIS to be able to perfectly cancel the interference on the $K$-user MIMO IC.

翻译：我们研究了可重构智能表面（RIS）辅助的K用户多输入多输出（MIMO）干扰信道（IC）中的干扰泄漏（IL）最小化问题。我们提出了一种基于块坐标下降的迭代算法，以最小化干扰泄漏代价函数。对问题的重新表述提供了几何解释，并揭示了与包络预编码和仅相位迫零波束成形问题之间的有趣联系。通过这一分析，我们推导出了一组必要条件（非充分条件），使得相位优化的RIS能够在K用户MIMO干扰信道上完美消除干扰。