Reconfigurable Intelligent Surface for Interference Alignment in MIMO Device-to-Device Networks

In multiple-input multiple-output (MIMO) device-to-device (D2D) networks, interference and rank-deficient channels are the critical bottlenecks for achieving high degrees of freedom (DoFs). In this paper, we propose a reconfigurable intelligent surface (RIS) assisted interference alignment strategy to simultaneously mitigate the co-channel interference and cope with rank-deficient channels, thereby improving the feasibility of interference alignment conditions and in turn increasing the achievable DoFs. The key enabler is a general low-rank optimization approach that maximizes the achievable DoFs by jointly designing the phase-shift and transceiver coding matrices. To address the unique challenges of the rank objective function, the unit modulus constraints, and the bilinear constraint resulting from coupled optimization variables, we develop a block-structured Riemannian pursuit method by solving fixed-rank and unit modulus constrained least square subproblems along with rank increase. Finally, to achieve good DoF performance, we develop unified Riemannian conjugate gradient algorithms to alternately optimize the fixed-rank transceiver matrix and the unit modulus constrained phase shifter by exploiting the non-compact Stiefel manifold and the complex circle manifold, respectively. Numerical results demonstrate the effectiveness of deploying an RIS and the superiority of the proposed block-structured Riemannian pursuit method in terms of the achievable DoFs compared to the state-of-the-art methods.