Near-far robustness and optimal power allocation for two-way relaying with MIMO amplify and forward relays

In this paper we consider two-way relaying with a MIMO amplify and forward (AF) relay. Assuming single stream transmission and perfect channel state information (CSI) we are able to analytically express the signal to noise ratios (SNR) at the user terminals. These SNR expressions are first used to study the near-far robustness by analyzing their asymptotic behavior when the signal from one of the users is significantly stronger than the signal received from the other terminal. Subsequently we demonstrate how to achieve individual SNR targets for both terminals via a combined strategy of user power control and the algebraic norm-maximizing (ANOMAX) transmit strategy at the relay. We also derive a simple necessary and sufficient condition to guarantee that the region of achievable SNR targets is convex. At the end of the paper we demonstrate via numerical computer simulations that the weighting parameter in ANOMAX can be used to reduce the required transmit power for given SNR targets.