Grassmannian beamforming for MIMO amplify-and-forward relaying

In this paper, we consider the beamforming code-book design problem for the half-duplex MIMO amplify-and-forward relay channel with Rayleigh fading. The analysis is divided into two steps. First, we present the optimal beamforming scheme with full channel state information (CSI) and derive the optimal source and relay beamforming vectors. Next, we consider the beamforming problem with receiver CSI only and provide a beamforming vector quantization scheme. Based on the statistics of the optimal beamforming vectors, we show that Grassmannian codebooks minimize the upper bound for SNR loss caused by quantization, and therefore these codebooks are appropriate choices for quantizing the optimal beamforming vectors. The efficiency of the Grassmannian codebooks is verified by simulation results.