Diversity analysis for generalized MIMO two-way x relay channel

We study the performance of a generalized multiple-input multiple-output (MIMO) two-way X relay channel, where there are two groups of K source nodes and one relay node, and each source node in one group exchanges independent messages with all the source nodes in the other group via the relay node. It is assumed that every source node is equipped with M antennas while the relay is equipped with N antennas. We adopt a signal alignment based transmission protocol where all the information exchanges among the two groups of source nodes are accomplished in two time slots. Through analyzing the information outage probability, we prove that the diversity order of the generalized MIMO two-way X relay channel with random signal alignment is one. Further, we prove that the diversity order can be improved to 2M - N when the signal alignment vectors are carefully selected.