Topological Interference Management With User Admission Control via Riemannian Optimization

Topological interference management (TIM) provides a promising way to manage interference only based on the network connectivity information. Previous works on the TIM problem mainly focus on using the index coding approach and graph theory to establish conditions of network topologies to achieve the feasibility of topological interference management. In this paper, we propose a novel user admission control approach via sparse and low-rank optimization to maximize the number of admitted users for achieving the feasibility of topological interference management. However, the resulting sparse and low-rank optimization problem is non-convex and highly intractable, for which the conventional convex relaxation approaches are inapplicable, e.g., a simple ℓ
₁
-norm relaxation approach yields the objective unbounded and non-convex. To assist efficient algorithms design for the formulated rank-constrained (i.e., degrees-of-freedom (DoFs) allocation) ℓ
₀
-norm maximization (i.e., user capacity maximization) problem, we propose a novel non-convex but smoothed ℓ
₁
-regularized minimization approach to induce sparsity pattern with bounded objective values. We further develop a Riemannian trust-region algorithm to solve the resulting rank-constrained smooth non-convex optimization problem via exploiting the quotient manifold of fixed-rank matrices. Simulation results demonstrate the effectiveness and optimality of the proposed Riemannian algorithm to maximize the number of admitted users for topological interference management.