  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. To assist efficient algorithms design for the
formulated rank-constrained (i.e., degrees-of-freedom (DoF) allocation) l0-norm
maximization (i.e., user capacity maximization) problem, we propose a
regularized smoothed l1- norm minimization approach to induce sparsity pattern,
thereby guiding the user selection. We further develop a Riemannian
trust-region algorithm to solve the resulting rank-constrained smooth
optimization problem via exploiting the quotient manifold of fixed-rank
matrices. Simulation results demonstrate the effectiveness and near-optimal
performance of the proposed Riemannian algorithm to maximize the number of
admitted users for topological interference management.
