Topological Interference Management for Hexagonal Cellular Networks

We consider the topological interference management problem for a downlink hexagonal cellular network, where the channel state information at the transmitters is limited to just the network topology. Recent work by Jafar showed that if interference is limited to only near the cell boundary, then, an aligned frequency reuse pattern achieves the optimal value of 6/7 degrees of freedom (DoF) per cell, as opposed to the conventional frequency reuse baseline of 1/3 DoF per cell. We generalize the setting to include interference from multiple layers of adjacent cells and characterize how the gains of the optimal solution over basic frequency reuse diminish with increasing number of interference layers. Next, we focus on single-layer interference and explore the sensitivity of the idealized assumptions behind the connectivity model of Jafar, which achieves higher DoF but only at the cost of a higher effective noise floor than the baseline, and under idealized placements of users. A modified connectivity model that operates at a comparable noise-floor to the baseline is then studied, and its DoF are shown to be bounded above by 6/11 and below by 1/2. Through numerical simulations, we compare the solutions that achieve 6/7, 1/2, and 1/3 DoF per cell and find that, while both the 6/7 and the 1/2 DoF solutions beat the baseline 1/3 figure, between them, the 1/2 DoF aligned frequency reuse pattern is more robust for small cell networks particularly for random users' distribution on the cell boundaries.