Joint Source and Relay Precoding in Multiantenna Millimeter-Wave Systems

This paper considers the joint source and relay precoding design for millimeter-wave (mm-wave) systems under the assumption that the source, relay, and destination nodes are equipped with multiple antennas. We focus on the rate maximization problem with the per antenna power constraints at the source and relay while taking into account the computational complexity and sparse characteristics of mm-wave channels. We solve this problem as follows. First, the precoding problem is formulated by exploiting the sparse and low-rank structures of mm-wave channels which is nonconvex. Second, we reformulate this nonconvex problem into two semidefinite programming (SDP) subproblems, each having a rank one constraint. Third, we propose two algorithms to solve these two SDP subproblems: interior-point-based and low complexity algorithms. Finally, the original rate maximization problem is examined by iteratively utilizing the solutions of these SDP problems. The proposed interior-point-based method to solve the SDP problem uses the standard convex optimization tools followed by the random vector generation scheme to get the rank one solution. However, the proposed low complexity algorithm examines the SDP problem in one-dimensional spatial signal space (i.e., without rank relaxation) via a new augmented Lagrangian function method. Simulation results show that both algorithms achieve good performances, and the latter one is much faster than the former one with a slight decrease in performance. In addition, both algorithms achieve superior performances compared to the existing precoding design algorithms.