Joint beamforming and transmit design for the non-regenerative MIMO broadcast relay channel

In this paper, we consider a multiple-input multiple-output (MIMO) broadcast relay channel (BRC), in which the communication of a multi-antenna base station (BS) with several multi-antenna mobile stations (MS) is assisted by a fixed half-duplex multi-antenna relay station (RS). Applying dirty paper coding (DPC) at the BS and beamforming at the RS, we jointly optimize the transmit covariance matrices at the BS and the beamforming matrix at the RS by maximizing the system sum rate, which is a nonconvex problem. To solve this problem, we resort to the more tractable sum rate maximization in the dual multiple access relay channel (MARC), which is still a nonconvex difference of convex functions (DC) programming problem. We develop an iterative algorithm, termed alternating matrix polynomial time DC (POTDC) algorithm, based on an alternating optimization of the beamforming matrix and the transmit covariance matrices. The resulting covariance matrices for the MARC are then mapped to the desired BRC covariance matrices. The sum rate performance of the proposed algorithm is demonstrated by simulations.