  In this work, we consider the design of hybrid analog-digital (HAD)
multi-carrier MIMO-OFDM two-way relaying systems, where the relay station is
equipped with a HAD amplify-and-forward architecture and every mobile station
is equipped with a fully-digital beamforming architecture. We propose a
sub-optimal solution by reformulating the original non-convex problem as a
constrained Tucker2 decomposition with the objective of minimizing the sum
Euclidean-norm between the HAD amplification matrices and their fully-digital
counterparts. For the fully-digital amplification matrix design, we use a
Frobenius-norm maximization of the effective channels on every subcarrier and
propose an effective solution applicable for multi-stream communication
scenarios. After that, we propose an alternating maximization (AltMax) HAD
solution by exploiting the tensor structure of the reformulated problem.
Simulation results are provided, where we show that the proposed fully-digital
and AltMax-based HAD amplification matrix designs outperform some benchmark
methods, especially for multi-stream communication scenarios.
