Two-Unicast Wireless Networks: Characterizing the Degrees-of-Freedom

The authors consider two-source two-destination (i.e., two-unicast) multi-hop wireless networks that have a layered structure with arbitrary connectivity. They show that, if the channel gains are chosen independently according to continuous distributions, then, with probability 1, two-unicast layered Gaussian networks can only have 1, 3=2 or 2 sum degrees-of-freedom1. They provide sufficient and necessary conditions for each case based on network connectivity and a new notion of source-destination paths with manageable interference. The achievability scheme is based on forwarding the received signals at all nodes, except for a small fraction of them in at most two key layers.