Hierarchical Codebook based Multiuser Beam Training for Millimeter Massive MIMO

In this article, multiuser beam training based on hierarchical codebook for millimeter wave massive multi-input multi-output is investigated, where the base station (BS) simultaneously performs beam training with multiple user equipments (UEs). For the UEs, an alternative minimization method with a closed-form expression (AMCF) is proposed to design the hierarchical codebook under the constant modulus constraint. To speed up the convergence of the AMCF, an initialization method based on Zadoff-Chu sequence is proposed. For the BS, a simultaneous multiuser beam training scheme based on an adaptively designed hierarchical codebook is proposed, where the codewords in the current layer of the codebook are designed according to the beam training results of the previous layer. The codewords at the BS are designed with multiple mainlobes, each covering a spatial region for one or more UEs. Simulation results verify the effectiveness of the proposed hierarchical codebook design schemes and show that the proposed multiuser beam training scheme can approach the performance of the beam sweeping but with significantly reduced beam training overhead.