Joint Symbol Level Precoding and Receive Beamforming Optimization for Multiuser MIMO Downlink

Consider a multi-casting system where a multi-antenna base station (BS) sends multiple data streams to multiple users via symbol-level precoding (SLP). Unlike most of the existing literature which assume single-antenna users, we consider joint SLP and linear receive beamforming (SLP-RBF) design, to investigate the performance boost brought by multi-antenna users. The SLP-RBF problem minimizes the total transmission power subject to the user symbol error probability (SEP) constraints. It turns out that, due to the RBF, the problem involves a large number of non-convex bilinear terms and is much more challenging to handle. In this paper, our goal is to develop computationally efficient algorithms to tackle the SLP-RBF problem. We first introduce several convex approximation forms for the bilinear terms and develop a successive convex approximation (SCA) based algorithm. Furthermore, by exploiting the problem structure and a rank-reduction transformation (RDT), we equivalently write the problem as a dimension-reduced problem with simple box constraints. The reformulated problem enables us to develop a highly efficient iterative algorithm based on accelerated gradient descent methods. We also extend the study to the SLP-RBF problem with one-bit transmission constraints. Since the RDT is no longer applicable, we develop an algorithm based on successive upper-bound minimization (SUM) and alternating direction method of multipliers (ADMM). Simulation results show that the joint SLP-RBF design offers significant power efficiency gains over SLP methods, and the proposed algorithms is time efficient and can handle a large scale system.