  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 interferences and improve system
performance. Most existing works on interference coordination require
significant CSI signaling overhead and are impractical in ultra-dense networks.
This paper investigate topological cooperation to manage interferences in
message sharing based only on network connectivity information. In particular,
we propose a generalized low-rank optimization approach to maximize achievable
degrees-of-freedom (DoFs). To tackle the challenges of poor structure and
non-convex rank function, we develop 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 Riemannian optimization
algorithms to solve the complex fixed-rank optimization problem by applying the
semidefinite lifting technique and Burer-Monteiro factorization approach.
Numerical results demonstrate the computational efficiency and higher DoFs
achieved by the proposed algorithms.
