Progressive hybrid precoder design for packet retransmissions in large-scale MIMO systems

We consider progressive hybrid precoder design for packet retransmissions in large-scale multiple-input multiple-output (MIMO) systems with perfect channel state information (CSI) knowledge at the transmitter. To exploit time diversity provided by packet retransmissions, we propose a two-step approach to optimize both the radio-frequency (RF) precoder and the corresponding baseband precoder with the objective of maximizing the mutual information. During each retransmission attempt, we choose the RF precoder matrix columns from the set of transmit array response vectors. For a given RF precoder, we show that the optimal baseband precoder is a function of the generalized eigen-matrix of the Gram matrices of the effective channel matrix and the RF precoding matrix. The optimal baseband precoder for each transmission round includes appropriate power loading, selection and reverse pairing of the singular values of the previous transmission attempts with the ratio of the elements obtained by the diagonalization of the Gram matrices of the effective channel matrix and the RF precoding matrix using a generalized eigen-matrix. Illustrative results show that the proposed progressive hybrid precoder design achieves a performance close to that of the optimal progressive digital precoder (OPDP).