Network-Coded Bi-Directional Relaying for Amplify-and-Forward Cooperative Networks: A Comparative Study

In this paper, a comparative study of network-coded bi-directional amplify-and-forward (BD-AF) relaying is presented. In bi-directional relay networks, communication is performed over two phases: the broadcasting phase, and the cooperation phase. In the broadcasting phase, both source nodes broadcast their signals simultaneously to the N relay nodes, while in the cooperation phase, transmission is based on one of two modes: (1) time-division (TD), or (2) multiple-access (MA). In the TD-BD-AF scheme, each relay node is allocated a time-slot to transmit its processed signal, while in the MA-BD-AF scheme, all the N relay nodes simultaneously transmit network-coded signals to both source nodes, in a single time-slot. Moreover, a suboptimal relay selection (i.e. SRS-BD-AF) that approximately maximizes the sum-of-rates is proposed. Optimal and suboptimal sum-of-rates maximizing power allocations are studied under the TD-BD-AF and MA-BD-AF schemes, respectively, where it is shown that the MA-BD-AF scheme reduces to the SRS-BD-AF scheme. Symbol error rate performance analysis is provided, where it is shown that both the TD-BD-AF and SRS-BD-AF schemes achieve full diversity. Imperfect timing synchronization is analyzed and it is demonstrated that the SRS-BD-AF outperforms the other schemes in terms of the achievable rate. Simulation results are provided to complement the theoretical analysis.