In this article, we explore the application of alignment matrices as applied to non-linear dimensionality reduction [1]-[3] in the analysis and solution of interference alignment schemes for wireless communications systems, with antennas sharing at the receivers. We propose an algorithm that aligns the interference when the antennas are shared in ring topology among three receivers. It is also shown that the degrees of freedom (DoF) of such an interfering channel can be characterized with the help of the dimension of the null space of the alignment matrix and a receiver chain alignment scheme is proposed.
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