On the relay selection for cooperative wireless networks with physical-layer network coding

In this paper, we investigate a large cooperative wireless network with relay nodes, in which cooperation is enabled through physical-layer network coding (PLNC). Specifically, we study the impact of the relay selection on the network capacity with power constraints in two scenarios. First, we consider the basic PLNC model (a.k.a., the ARB model), in which one pair of source nodes (A, B) exchange messages via a selected relay node (R). Given the power constraint, we derive the optimal relay selection and power allocation that maximize the sum capacity, defined as the summation of the capacity for two source-destination channels. Based on results obtained above, we then consider a more general scenario with multiple pairs of source nodes. Assuming the constant power constraint, we derive the upper bound of the minimal sum capacity of any source pair. The optimal power allocation among multiple source pairs is also derived. To validate these theoretical results, we also provide two relay selection strategies: a modified optimal relay assignment strategy and a novel middle point strategy for maximizing the minimal sum capacity of any source pair.