Optimal Power Allocation between Training and Data for MIMO Two-Way Relay Channels

Power allocation between training and data in MIMO two-way relay systems is proposed, which takes into consideration both the symmetric and asymmetric cases of the two sources. For the former, we present a closed form for the optimal ratio of data energy to total energy, which is suitable for the single antenna case as well, and can be simplified when the number of antennas is large. We also show that the achievable rate is a monotonically increasing function of the data time. Concerning the asymmetric case, we prove that the difference of the two SNRs is either a concave or convex function of the energy ratio, depending on the imbalance between the two sources. Using this, the minimum SNR between the two sources is maximized.