  This study proposes a novel precoding scheme for multiuser multiple-input
multiple-output (MIMO) relay systems in the presence of imperfect channel state
information (CSI). The base station (BS) and the MIMO relay station (RS) are
both equipped with the same codebook of unitary matrices. According to each
element of the codebook, we create a latent precoding matrix pair, namely a BS
precoding matrix and an RS precoding matrix. The RS precoding matrix is formed
by multiplying the appropriate unitary matrix from the codebook by a power
scaling factor. Based on the given CSI and a block of transmit symbols, the
optimum precoding matrix pair, within the class of all possible latent
precoding matrix pairs derived from the various unitary matrices, is selected
by a suitable selection mechanism for transmission, which is designed to
minimize the squared Euclidean distance between the pre-estimated received
vector and the true transmit symbol vector. We develop a minimum mean square
error (MMSE) design algorithm for the construction of the latent precoding
matrix pairs. In the proposed scheme, rather than sending the complete
processing matrix, only the index of the unitary matrix and its power scaling
factor are sent by the BS to the RS. This significantly reduces the overhead.
Simulation results show that compared to other recently reported precoding
algorithms the proposed precoding scheme is capable of providing improved
robustness against the effects of CSI estimation errors and multiuser
interference.
