Joint power allocation and relay selection strategies for wireless multi-unicast network-coded systems

In this paper, we study physical-layer network coding (PNC) in a multi-unicast system considering the network coding (NC) noise issue, which is due to unavoidable imperfect cancellation of interfering signals from unwanted sources. Our contributions to address this challenging problem are the following power allocation algorithms with the objective of maximization of the minimum average achievable rate among all the users. (1) Source and relay transmission power allocation subject to individual source and relay power constraints. We show that this approach is scalable and yields to a power assignment algorithm that exhibits the same optimization complexity for any number of sources in the network. (2) Relay signal power allocation, which is used to combine the received signals from different sources at the relay. This approach leads to a simple closed-form solution for two-unicast NC-CC system. An effective numerical algorithm for the multi-unicast case is also proposed. We further develop two joint power allocation and relay selection schemes to extend our results to general network topologies. We show that the joint optimization can be divided into two problems: optimal power allocation and optimal relay selection, where the latter can be performed in a decentralized manner. The proposed power allocation and relay selection schemes only rely on long-term channel statistics. Nevertheless, they are shown to be effective and close to optimal solutions. We conclude that the proposed algorithms largely combat the adverse effects of NC noise while improving fairness of user data rates.