An Optimization-Based Wide-Beam Design for THz MIMO

Beam training is a promising scheme to realize the terahertz (THz) multiple-input multiple-output (MIMO) communication without leveraging the explicit channel state information (CSI). In this context, a crucial issue for THz MIMO is how to design the beam codewords for realizing any expected radiation pattern during the training. The narrow beams can be realized by array response vectors, whereas the wide-beam design is still an open problem. In this paper, we propose a novel optimization-based method for THz wide-beam design, which is referred to as successive convex approximation (SCA)-based auxiliary target pursuit (SCA-ATP). Specifically, we equivalently formulate the wide-beam design as a problem of pursuing the auxiliary target in Euclidean space. By lifting the optimization vector into a positive semidefinite matrix, we can tackle it with the SCA technique by iteratively solving a sequence of simplified subproblems.