Differential Bi-Directional Relay Selection Using Analog Network Coding

In this paper, we consider a general bi-directional relay network with two sources and $N$ relays when neither the source nodes nor the relays know the channel state information~(CSI). A bi-directional relay selection scheme is proposed using differential analog network coding~(BRS-DANC), and a simple linear detector is given to recover the received signals. In the proposed scheme, we provide an optimal and a sub-optimal methods to select the relay node from a single source by minimizing the average symbol error rate~(SER). The performance of the proposed BRS-DANC scheme is analyzed, and a simple asymptotic SER expression is derived. It is shown that the SER performance of the proposed differential scheme is about 3 dB away from that of the coherent detection scheme.