Outage Probability and Optimum Power Allocation for Analog Network Coding

We study the analog network coding (ANC), which is a well-known amplify-and-forward (AF)-based bidirectional protocol, for a bidirectional network consisting of two different sources and a relay. In this protocol, the two sources exchange information with the help of the relay during two time slots in a half-duplex mode. For this system, we first derive a tight lower bound of outage probability, which is very close to the exact outage probability in the whole signal-to-noise ratio (SNR) range irrespective of the values of channel variances. Using the tight lower bound, we obtain finite-SNR diversity-multiplexing tradeoff of the ANC protocol. Furthermore, we propose an optimum power allocation scheme, which simultaneously minimizes the outage probability and maximizes the total mutual information of the ANC protocol.