MIMO Y channel with imperfect CSI: Impact of training and feedback overhead

Signal space alignment with network coding (SSA-NC) is a cooperative transmission strategy that, under some conditions such as full channel state information (CSI), provides maximum degrees of freedom (DoF) in two-way relay networks. However, obtaining full CSI for SSA-NC requires a significant amount of training and feedback overhead. This paper focuses on the multiple-input multiple-output (MIMO) Y channel and explicitly considers the required training and feedback at the users and relay. We derive the optimum signaling overhead of this channel to maximize the effective sum-rate of the SSA-NC scheme. We further investigate an important question: under what conditions does the SSA-NC scheme have a better sum-rate performance compared to other popular schemes with lower complexity such as multi-user MIMO (MU-MIMO) and time division multiple access (TDMA)? Since different schemes require different amounts of training/feedback overhead, our result demonstrates how the channel coherence interval plays an important role in their relative performance. Specifically, the SSA-NC scheme outperforms the other schemes only when the coherence interval is sufficiently large. This result highlights the importance of properly taking the training and feedback overhead and channel coherence interval into account when designing the communication scheme for the MIMO Y channel.