Optimal partial feedback design for MIMO block fading channels with feedback capacity constraint

In this paper, we focus in investigating the optimal MIMO transmission and the optimal feedback strategies for MIMO link capacity when the feedback link is causal and has a capacity constraint. We show that the design of the optimal feedback scheme is identical to the design of vector quantizer (Lloyd's algorithm) with a modified distortion measure. In the general case, the optimal feedback strategy has a general form of power water-filling cascaded with beamforming matrix as well.