Date Added: Jan 2011
Degree of Freedom (DoF) region provides an approximation of capacity region in high Signal-to-Noise Ratio (SNR) regime, while sum DoF gives the scaling factor. In this correspondence, the authors analyze the DoF region and sum DoF for unicast layered multi-hop relay wireless networks with arbitrary number of source/destination/relay nodes, arbitrary number of hops and arbitrary number of antennas at each node. The result is valid for quite a few message topologies. They reveal the limitation on capacity of multi-hop network due to the concatenation structure and show the similarity with capacitor network. From the analysis on bound gap and optimality condition, the ultimate capacity of multi-hop network is shown to be strictly inferior to that of single-hop network.