Routing and Power Allocation in Asynchronous Gaussian Multiple-Relay Channels

: We investigate the cooperation efficiency of the multiple-relay channel when carrier-level synchronization is not available and all nodes use a decode-forward scheme. We show that by using decode-forward relay signaling, the transmission is effectively interference-free even when all communications share one common physical medium. Furthermore, for any channel realization, we show that there always exist a sequential path and a corresponding simple power allocation policy, which are optimal. Although this does not naturally lead to a polynomial algorithm for the optimization problem, it greatly reduces the search space and makes finding heuristic algorithms easier. To illustrate the efficiency of cooperation and provide prototypes for practical implementation of relay-channel signaling, we propose two heuristic algorithms. The numerical results show that in the low-rate regime, the gain from cooperation is limited, while the gain is considerable in the high-rate regime.