Topological interference management (TIM) allows studying the degrees of freedom (DoF) of partially connected linear interference communication networks, where the channel state information at the transmitters (CSIT) is restricted to the topology of the network, i.e., a knowledge of which interference links are weak and which are strong. In this paper, we consider TIM for an infinite downlink cellular network in the onedimensional (1D) linear and the two-dimensional (2D) hexagonal models. We consider uniformly distributed users in each cellular cell, effectively creating a continuous distribution of users, aiming to study user classes based on different interference profiles rather than on actual individual users' positions. We also consider the construction of the TIM network topology by analyzing different interference thresholds. Unlike previous works, we use TIM at the user class level to find the system's DoF independent of the actual user position. Finally, after proposing a fractional coloring scheme that can achieve the optimal DoF solution, a trade-off between DoF and SIR is given.

This paper presents a new formulation to build an interference topology for the multiuser unicast Topological Interference Management (TIM) based wireless network problem. Based on our interference topology formulation, we are able to evaluate the achievable rate's theoretical limit, in the asymptotic signal to noise ratio (SNR) regime, for the underlying wireless network and not just for its topological interference representation. This new formulation allows us to cope with the finite SNR regime and not just with the asymptotic SNR regime with the Degrees of Freedom (DoF) analysis. A new SNR independent interference threshold parameter is proposed and we evaluate the achievable symmetric rates of the wireless network in both the finite SNR regime and the asymptotic SNR regime. Finally, we present outer bound solutions on the new normalized interference threshold parameter for interference topologies with half-DoF-feasibility, considering both an orthogonal resource allocation and Interference Alignment (IA). These bounds specify if a given half-DoF-feasible interference topology can be, in terms of the achievable rate, the best topology or not. Using this result, we limit the search space in the normalized interference threshold parameter range, to find half-DoF-feasible interference topologies having the possibility to be the best topologies in terms of the achievable rate.

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