On the Degrees of Freedom for Multi-Hop Wireless Networks under Layered TDD Constraint

Degrees of freedom (DoF) of a network build a new scaling law characterizing the scalability of capacity at high signal-to-noise region. In this paper, we extend our recent work from cascaded network to the general K-hop layered network. The main framework is based on the assumption of layered TDD, where all nodes at each layer work with the same on/off status. By this approach we decompose the DoF analysis into two steps: 1) apply the result of cascaded networks; 2) analyze / design the transmission of each hop. The upper and lower bounds on DoF are deduced. By viewing the network as cascaded X channels, we find an inner bound of the DoF region, applicable to many message topologies. The detail of message splitting is demonstrated. Finally ultimate analysis shows if the number of antennas/nodes at each relay layer goes to infinity, the lower bound reaches the upper bound. As a by-product, when K > 2 the network can alleviate the effect of TDD with the increase of relay antennas/nodes.