On the geometry of wireless network multicast in 2-D

We provide a geometric solution to the problem of optimal relay positioning to maximize the multicast rate for low-SNR networks. The network we consider consists of a single source, multiple receivers and the only intermediate and locatable node as the relay. We construct network the hypergraph of the system nodes from the underlying information theoretic model of low-SNR regime that operates using superposition coding and FDMA in conjunction (which we call the “achievable hypergraph model”). We make the following contributions.

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