Low-Rank Optimization for Topological Interference Alignment in MIMO Networks

In dense networks, interference becomes the main bottleneck for achieving high data rates. Topological interference management (TIM) is proposed to manage interference only based on network topology information to reduce the system overhead. In this paper we study the TIM problem in the multiple-input multiple-output (MIMO) interference channel with only the network connectivity information. For the general asymmetric channel with
$M_{i}$
antennas at each transmitter and
$N_{i}$
antennas at each receiver, we provide a topological interference alignment condition via carefully designing the structured transceivers. It turns out that the achievable degrees-of-freedom (DoFs) for each user grow linearly with
$\min\{M_{i}, N_{i}\}$
. We further present a low-rank optimization approach to maximize the achievable DoFs, followed by developing a novel difference-of-convex programming algorithm with convergence guarantees. Numerical results demonstrate the effectiveness of the proposed methods for topological interference management in MIMO networks.