  In this paper, we investigate a multiuser relay system with simultaneous
wireless information and power transfer. Assuming that both base station (BS)
and relay station (RS) are equipped with multiple antennas, this work studies
the joint transceiver design problem for the BS beamforming vectors, the RS
amplify-and-forward transformation matrix and the power splitting (PS) ratios
at the single-antenna receivers. Firstly, an iterative algorithm based on
alternating optimization (AO) and with guaranteed convergence is proposed to
successively optimize the transceiver coefficients. Secondly, a novel design
scheme based on switched relaying (SR) is proposed that can significantly
reduce the computational complexity and overhead of the AO based designs while
maintaining a similar performance. In the proposed SR scheme, the RS is
equipped with a codebook of permutation matrices. For each permutation matrix,
a latent transceiver is designed which consists of BS beamforming vectors,
optimally scaled RS permutation matrix and receiver PS ratios. For the given
CSI, the optimal transceiver with the lowest total power consumption is
selected for transmission. We propose a concave-convex procedure based and
subgradient-type iterative algorithms for the non-robust and robust latent
transceiver designs. Simulation results are presented to validate the
effectiveness of all the proposed algorithms.
