support only one-stream transmission and is not viable for multi-stream case [6]. To exploit the full potential of both spatial multiplexing and beamforming in a MIMO system, fully digital beamforming architecture is leveraged [7], [8]. Implementing a fully digital MIMO beamformer requires one radio frequency (RF) chain per antenna element. Due to the high number of power-hungry RF components, such as digital-to-analog converters (DACs), in conventional digital beamforming, the practical implementation of a massive MIMO system requires new approaches to be realized [2], [6]. As a solution, the combination of both digital and analog beamforming, using a limited number of RF chains, known as hybrid beamforming (HBF) has been considered.HBF splits the whole beamforming process into digital and analog parts, that enables multi-stream transmissions with a reduced complexity [6], [7]. Various HBF methods are proposed for fully and partially connected RF architectures in the literature [9]-[13], ranging from theoretical rate maximizing solutions to heuristic algorithms. In a fully connected HBF architecture, each RF chain is connected to all antennas [7], [10]. For a practical implementation of a mm-wave massive MIMO system, the fully connected structure may be too complex to be used due to very challenging and lossy RF signal division and combining processes. A more practical solution is to use partially connected RF architecture, in which each RF chain is connected only to a subset of the antenna array, called a sub-array [14], [15].Partially connected RF architecture itself can be divided into two categories, i.e., full-array-based and sub-array-based processing structures. In full-array-based processing, all data streams are conveyed to all sub-arrays. Thus, each stream is transmitted via its corresponding beam which is generated by using all sub-arrays and their antennas. This implies that full beamforming gain is potentially available. However, the directions of different beams are interdependent due to the partial connectivity. This sets restrictions to the beam generation and leads to suboptimal beam directions. In sub-array-based processing, each sub-array transmits only a single data stream. This leads to a more efficient and flexible beam design process. However, the beamforming gain is limited by the number of antennas per sub-array.Most of the HBF works in the literature use only phase shifting in the analog beamforming process [10]- [13]. However, employing analog amplitude control in addition to phase Abstract-Hybrid analog-digital beamforming has been recognized as a promising solution for a practical implementation of massive multiple-input multiple-output (MIMO) systems based on millimeter-wave technology. In this paper, three hybrid beamforming algorithms are proposed for single-user MIMO systems with partially connected radio frequency (RF) architecture, including a singular value decomposition (SVD) matching algorithm, an iterative orthogonalization algorithm, and a transmitreceive zero forcing (ZF...
