Joint source and relay beamforming design for general MIMO relaying broadcast channels

The design of proper precoders enables the spectral efficiency for multiple-input multiple-output relaying broadcast channels (MIMO-RBC). In this work, a general MIMO-RBC is considered with two types of users (relay users and direct users) and the base station (BS) can send information continuously to the users during two phases. We then present a communication scheme that achieves the full number of degrees of freedom (DoF) of the channel with a sophisticated precoding strategy to overcome the relay station (RS) half-duplex constraint, by a well designed precoding matrix (PM) and beamforming matrix (BM) for BS and RS, respectively. The throughput criteria within the sophisticated precoding strategy is addressed for PM and BM designs in the considered communication scheme, and we show that this problem is non-linear non-convex and the optimal solutions remain unsolved. In order to find an efficient solution, we first convert it into a series of tractable subproblems, and then an iterative design algorithm is proposed based on alternative optimization, which can obtain the optimal matrices for BS and RS. Our numerical results obtained through simulations show the advantages of the proposed scheme.