Relay Selection with ANC and TDBC Protocols in Bidirectional Relay Networks

We study relay selection (RS) with the analog network coding (ANC) and time division broadcast (TDBC), which are two major amplify-and-forward (AF)-based protocols in bidirectional relay networks. We consider a bidirectional network consisting of two different end-sources and multiple relays, where each terminal has a single antenna and operates in a half-duplex mode. In this network, a single best relay is selected depending on channel conditions to help bidirectional communication between the two end-sources. Specifically, we first consider RS schemes for the ANC and TDBC protocols based on a max-min criterion to minimize the outage probabilities. Then, for the RS in the ANC protocol, we derive a closed-form expression of the outage probability; for the RS in the TDBC protocol, we derive a one-integral form of the outage probability and its lower bound in closed-form. Numerical results confirm that the closed-form expression of the ANC protocol and the one-integral form of the TDBC protocol are very accurate, and that the closed-form lower bound of the TDBC protocol is also tight.