Finite Feedback MIMO Precoding for the Two-Way Amplify-and-Forward Relay Network

We consider the finite feedback based pre-coding for the two-way amplify-and-forward (AaF) relay networks. Based on the channel information, the relay informs the pre-coder selection information to the two sources with finite bits of information. We present a set of precoder selection criteria and the code-book conditions to guarantee the full diversity order of M_r min{M₁, M₂}, where M_r is the number of antennas at the relay, M₁, M₂ are the numbers of antennas at the first source and the second source, respectively. The diversity performance is analyzed and numerically simulated in the symbol error rate sense and outage probability sense. Also, the impact of the distances between nodes on the individual outage is discussed.