Grassmannian Beamforming for MIMO Amplify-and-Forward Relaying

In this paper, we derive the optimal transmitter/ receiver beamforming vectors and relay weighting matrix for the multiple-input multiple-output amplify-and-forward relay channel. The direct link is considered in the problem model and the unquantized and quantized schemes are derived; then a modified quantizing scheme is presented which introduces a negligible degradation in the system performance but significantly reduces the required number of feedback bits,Finally,we carry out a reasonable improvement of the quantized and modified quantizing schemes .