Relay Selection for Two-way Relaying with Amplify-and-Forward Protocols

In this paper, we propose a relay selection amplify-and-forward (RS-AF) protocol in general bi-directional relay networks with two sources and $N$ relays. In the proposed scheme, the two sources first transmit to all the relays simultaneously, and then a single relay with a minimum sum symbol error rate (SER) will be selected to broadcast the received signals back to both sources. To facilitate the selection process, we propose a simple sub-optimal Min-Max criterion for relay selection, where a single relay which minimizes the maximum SER of two source nodes will be selected. Simulation results show that the proposed Min-Max selection has almost the same performance as the optimal selection with lower complexity. We also present a simple asymptotic SER expression and make comparison with the conventional all-participate amplify-and-forward (AP-AF) relaying scheme. The analytical results are verified through simulations. To improve the system performance, optimum power allocation (OPA) between the sources and the relay is determined based on the asymptotic SER. Simulation results indicate that the proposed RS-AF scheme with OPA yields considerable performance improvement over an equal power allocation (EPA) scheme, specially with large number of relay nodes.