# An Efficient Precoding Algorithm for mmWave Massive MIMO Systems
## 1 Introduction
The shared array architecture has complex hardware design and high-power consumption compared to the separate sub-array architecture, but it can fully exert the precoding performance and achieve better results. Therefore, the research in this paper is based on a shared array architecture. In the hybrid precoding study of millimeter-wave massive MIMO systems, the literature [18] uses the transmitter and receiver to jointly design the analog beamforming vectors under the multi-resolution codebook. Literature [19] introduces beam space multiple-input multiple-output, and uses a discrete Fourier transform (DFT) beamforming vector to direct the transmitted signal to a subspace with progressively maximized received signal power. Literature [20] converts the hybrid precoding problem into a sparse reconstruction problem based on the sparsity of the millimeter-wave channel. Under the condition of perfect known channel information, a low complexity hybrid precoding algorithm is proposed by using the concept of orthogonal matching pursuit. However, the design of RF precoding in [20] requires that the candidate matrix be selected from the candidate matrix to multiply the largest product by the inner product of the residual, and the construction of the candidate matrix requires high-precision channel estimation. Upon completion, it is necessary to estimate the signal emission angle and angle of arrival, which will cause system delay and consume system resources. At the same time, the algorithm uses the least-squares method to perform matrix inversion when updating the baseband precoding. The complexity of matrix inversion increases with the number of base vectors. High dimensional matrix inversion will lead to longer calculation delay and higher power consumption. The authors in [21] proposed a semidefinite relaxation algorithm by utilizing the idea of alternating minimization, which can provide substantial performance gains for phase shifters (PSs). However, while the PSs are studied substantially, there still exist an inevitable gap compared with the performance of PSs. The authors in [22] proposed an analog PSs and spatial multiplexing by utilizing multiple RF chains connected to a fixed subset of antenna elements. This algorithm is based on analog beamforming and therefore, it lacks the ability to provide the required precoding performance for mmWave massive MIMO systems. In [23], for single-stream single-user MIMO-OFDM systems, a hybrid precoding is proposed to maximize the received signal strength. Therefore, in view of the problems in [20; 21; 22], this proposed an efficient algorithm for effective precoding in mmWave massive MIMO systems. The novel contributions of this paper are as follows:  
* This study deploys bird swarm algorithm (BSA) to eliminate the need for the known candidate matrices in mmWave channel estimation as in the traditional algorithms. * The proposed algorithm uses the characteristics of BSA with global search optimal (GSO) value to search for the largest array response vector multiplied by the residual matrix, and uses the Banachiewicz-Schur (BS) block matrix generalized inverse to transform the high-dimensional matrix into a low-dimensional matrix, avoiding matrix inversion and reducing the amount of calculation. * It uses the results of each iteration to avoid matrix inversion and to simplify the computational complexity of the system. The rest of the paper is organized as follows. Section 2 described the system model. Section 3 explains the proposed algorithm. Section 4 gives the numerical simulation analysis while Section 5 concludes the paper.