Optimal precoding for a novel RF-MIMO scheme in transmit correlated Rayleigh channels

Recently, a novel MIMO transceiver architecture, which avoids the costly conversion to/from baseband through parallel RF chains, has been proposed. Despite its obvious advantages, the limitations of the analog combining architecture makes necessary to develop specific transmission schemes. For instance, in the case of perfect channel state information (CSI) at the receiver, and correlation CSI at the transmitter, the space and time encoders must operate separately (the former works in the RF domain and the latter works in baseband), and at different time scales: the spatial encoder or RF beamformer must remain fixed during the transmission of a probably large number of symbols, whereas the time encoder can work at the symbol rate. In this paper we propose a transmission scheme for this scenario with the goal of minimizing the pairwise error probability (PEP). In particular, with the proposed scheme the symbols are time-precoded with a unitary discrete Fourier transform (DFT) matrix, and then are successively transmitted using a set of RF weights (beamformers). The optimal spatial precoding matrix containing the RF beamformers is obtained by matching its left eigenspace with the eigenspace of the channel correlation matrix, applying standard power water-filling along these directions, and choosing its right eigenspace as any unitary matrix with unit-norm elements such as the DFT matrix. Numerical examples illustrate the good performance of the proposed scheme.