Compute-and-forward in the two-hop multi-antenna X-channel

We utilize the compute-and-forward and inverse compute-and-forward schemes in a two-hop multi-antenna X-channel. We introduce the beamforming problems and compare numerical results to a network coding scheme with decode-and-forward. Furthermore, we derive conditions under which compute-and-forward and inverse compute-and-forward achieve higher sum rate than network coding and decode-and-forward. Finally, we illustrate the results by numerical simulations.