Topological Interference Alignment via Generalized Low-Rank Optimization with Sequential Convex Approximations

Abstract

In this paper, we consider solving the topological interference management (TIM) problem by using a generalized low-rank matrix completion (LRMC) model, thereby maximizing the achievable degrees of freedom (DoF) only based on the network connectivity information. The LRMC problem is NP-hard due to the nonconvex rank objective function. The nuclear norm relaxation fails as it always returns a full-rank matrix in our model. Another approach named Riemannian Pursuit (RP) is often inefficient for finding highly accurate feasible solutions. We thus propose a novel Generalized Low-Rank Optimization along with the Difference of Convex Algorithm (GLRO-DCA), which aims to find a low-rank solution while always keeping the feasiblity. The GLRO-DCA increases the rank consecutively and solves the associated fixed-rank LRMC problem, where the generalized fixed-rank LRMC problem is reformulated by minimizing the difference between the nuclear norm and the Ky Fan norm and solved by the DCA. We accelerate the DCA by applying extrapolation techniques to improve the computational efficiency. Numerical results exhibit the ability of our proposed GLRO-DCA for the TIM problem to find low-rank solutions, which is superior to the existing nuclear norm relaxation approach and the RP approach.