Aiming at the problem of high computational complexity due to a large number of antennas deployed in mmWave massive multiple-input multiple-output (MIMO) communication systems, this paper proposes an efficient algorithm for optimizing beam control vectors with low computational complexity based on codebooks for millimeter-wave massive MIMO systems with split sub-arrays hybrid beamforming architecture. A bidirectional method is adopted on the beam control vector of each antenna sub-array both at the transmitter and receiver, which utilizes the idea of interference alignment (IA) and alternating optimization. The simulation results show that the proposed algorithm has low computational complexity, fast convergence, and improved spectral efficiency as compared with the state-of-the-art algorithms.2 of 15 constant constraint so the performance achieved by analog beamforming technology will be limited [6]. Simultaneous use of beamforming in the digital domain and the analog domain can reduce the overhead of the system and compensate for the defects of analog beamforming, making hybrid beamforming a first pre-coding technique [7][8][9][10][11][12][13][14][15][16]. It can be seen from literature [5] that the hybrid beamforming architecture includes a separate sub-array architecture and a shared architecture. The signal on each transmit antenna in the shared architecture is a hybrid superposition of signals on all RF links, and one RF link needs to drive all transmitting antenna. Compared with the shared architecture, one RF link in a separate sub-array architecture is connected to only one antenna sub-array, and each RF link only needs to drive a transmit antenna on the sub-array connected thereto, so the separate sub-array architecture system can effectively reduce energy consumption and hardware complexity. Literature [8] analyzed the relationship between digital beamforming and hybrid beamforming and compared its performance. In [9], an algorithm for determining the sub-array analog beam control vector based on the codebook matching beam pair is proposed for the separate sub-array architecture system. However, the algorithm requires more beam training times, so that it has a high degree of complexity. In [10], both the transmitting and receiving ends are shared hybrid beamforming architectures, and an orthogonal matching pursuit (OMP) algorithm for simultaneous beamforming and digital beamforming is proposed for hybrid beamforming architecture. In [12], based on the codebook with the maximum received power as the criterion, the beamforming method is used to solve the analog beamforming, and then the equivalent channel is used to solve the digital beamforming.Applying interference alignment ideas [17][18][19] in wireless networks can achieve higher system capacity. By integrating multiple interfering signals into a small subspace at the receiving end, maximizing the number of non-interfering dimensions remaining in the desired signal minimizes the impact of the interfering signal on the desired signal while maximizing...