Finite-SNR Diversity-Multiplexing Tradeoff and Optimum Power Allocation   in Bidirectional Cooperative Networks
  This paper focuses on analog network coding (ANC) and time division broadcasting (TDBC) which are two major protocols used in bidirectional cooperative networks. Lower bounds of the outage probabilities of those two protocols are derived first. Those lower bounds are extremely tight in the whole signal-to-noise ratio (SNR) range irrespective of the values of channel variances. Based on those lower bounds, finite-SNR diversity-multiplexing tradeoffs of the ANC and TDBC protocols are obtained. Secondly, we investigate how to efficiently use channel state information (CSI) in those two protocols. Specifically, an optimum power allocation scheme is proposed for the ANC protocol. It simultaneously minimizes the outage probability and maximizes the total mutual information of this protocol. For the TDBC protocol, an optimum method to combine the received signals at the relay terminal is developed under an equal power allocation assumption. This method minimizes the outage probability and maximizes the total mutual information of the TDBC protocol at the same time. 
Zhihang Yi and Il-Min Kim