Shaping-power-constrained transceiver designs for MIMO AF relaying systems with direct link

In this paper, we propose new relay transceiver designs based on the minimum mean square error (MMSE) criterion for amplify-and-forward multiple-input-multiple-output (MIMO) relaying systems with direct link. Since each antenna element is equipped with its own power amplifier, a norm power constraint, which restricts the transmit power with the expected norm of the transmit signal vector, is not suitable for practical systems. Therefore, we consider a shaping constraint (SC), which imposes a limit on the shape of the transmit covariance matrix. The SC includes several power constraints such as the peak power constraint and the per-antenna power constraint as special cases. To this end, we first derive the optimal structure of the MMSE relay transceiver under the SC. Then, by introducing an upper bound of the mean square error, we provide closed-form relay transceiver solutions. Due to limited bandwidth of the feedback channel, perfect channel knowledge at the transmitter may not be feasible. Thus, we also propose a quantized relay transceiver design based on Grassmannian codebooks for a limited-feedback scenario. From simulation results, it is confirmed that the proposed relay transceiver techniques demonstrate a significant performance improvement compared with conventional schemes.