Generalized Low-Rank Optimization for Topological Cooperation in Ultra-Dense Networks

Abstract

Network densification is a natural way to support dense mobile applications under stringent requirements, such as ultra-low latency, ultra-high data rate, and massive connecting devices. Severe interference in ultra-dense networks poses a key bottleneck. Sharing channel state information (CSI) and messages across transmitters can potentially alleviate the interferences and improve the system performance. Most existing works on interference coordination require significant CSI signaling overhead and are impractical in the ultra-dense networks. This paper investigates the topological cooperation to manage interferences in message sharing based only on the network connectivity information. In particular, we propose a generalized low-rank optimization approach in a complex field to maximize the achievable degrees of freedom (DoFs) by establishing interference alignment conditions for the topological cooperation. To tackle the challenges of poor structure and non-convex rank function, we develop the Riemannian optimization algorithms to solve a sequence of complex fixed-rank subproblems through a rank growth strategy. By exploiting the non-compact Stiefel manifold formed by the set of complex full column rank matrices, we develop the Riemannian optimization algorithms to solve the complex fixed-rank optimization problem by applying the semidefinite lifting technique and the Burer–Monteiro factorization approach. The numerical results demonstrate the computational efficiency and higher DoFs achieved by the proposed algorithms.