Optimal state scheduling for three-hop directed cascaded networks with time division duplexing (invited paper)

Three-hop cascaded directed wireless relay network is considered, where relay nodes work in time division duplexing (TDD) mode. We investigate the optimal scheduling for capacity achieving with decode-and-forward (DF) strategy. By defining feasible network state (FNS), we formulate the problem into linear program, which schedules the activeness of all FNSs. Closed-form solution is obtained for general three-hop configuration, showing that DF is optimal to achieve the network capacity min{C 1 C 2 /C 1 +C 2 } = min(C 1 , C 3 )C 2 /min(C 1 , C 3 )+C 2 , where C k is the link capacity of the hop k. We also give the scheduling demonstration. Performance analyses are provided, including the degree of freedom (DoF) in multiple-input multiple-output (MIMO) scenario. Moreover, if extra single-hop message is allowed the network can support a higher DF rate as max(C 1 , C 3 )C 2 /min(C 1 , C 3 )+C 2 . The ultimate results with infinite relay capability are further deduced, which shows that the three-hop network can be superior to the corresponding two-hop scenario and indicates that the massive MIMO technique can be applied at the relay nodes to overcome the bottleneck of half duplexing constraint.