Optimal schedules for the D-node half duplex phase fading MRC

In this paper, we extend our previous work on the half duplex multiple-relay channel (MRC). A capacity upper bound based on the max-flow min-cut argument and achievable transmission rates based on the decode-forward coding strategy (DF) for the half duplex MRC have been shown to be functions of the schedule of the network, which is defined as the probability mass function of the transmit state vector (a description of which nodes transmit and which receive). Finding the optimal (rate-maximizing) schedule for DF can be formulated as a maximin optimization problem which is not easily solved in general. In our recent paper, we presented a technique to find optimal schedules for the 4-node MRC based on minimax hypothesis testing. Closed-form solutions were obtained for certain channel topologies. In this paper, we extend the technique to solve for optimal schedules for the general D-node half duplex MRC, where D ges 3.