Analysis of Maximal Topologies and Their DoFs in Topological Interference Management

Topological interference management (TIM) can obtain degrees of freedom (DoF) gains with no channel state information at the transmitters (CSIT) except topological information of network in the interference channel. It was shown that TIM achieves symmetric DoF 1/2 when internal conflict does not exist among messages [7]. However, it is difficult to assure whether a specific topology can achieve symmetric DoF 1/2 without scrutinizing internal conflict. It is also hard to derive a specific topology directly from the conventional condition for symmetric DoF 1/2. Even except for the topology achieving symmetric DoF 1/2, topology achieving specific DoF less than 1/2 is not well known. With these problems in mind, we propose a method to derive all maximal topologies directly in TIM, named as alliance construction in K-user interference channel. That is, it is proved that a topology is maximal if and only if it is derived from alliance construction. Further we translate a topology design by alliance construction in the alignment-conflict graph into topology matrix and propose conditions for maximal topology matrix (MTM). Moreover, we propose a generalized alliance construction that derives topologies achieving DoF 1/n for n ≥ 3 by generalizing sub-alliances. A topology matrix can also be used to analyze topologies with DoF 1/n .