## 1 Introduction  
One of the key technologies employed in 5G communication to realize high data rates of up to 10 Gbps is the massive multiple-input multiple output (MIMO) system, which benefits from the use of a large number of antennas [1; 2]. In a conventional fully digital precoding architecture for MIMO systems, each RF chain is connected to a single antenna, which is a challenge from the viewpoint of massive MIMO systems. Specifically, a large number of RF chains can increase power consumption substantially in fully digital MIMO systems [3; 4; 5; 6]. To resolve this problem, hybrid beamforming (HBF) architectures, which consist of analog and digital beamforming, have been proposed [3; 4; 6; 7; 8]. Hybrid beamforming architectures can be classified into two types: fully connected hybrid beamforming (FC-HBF) [9; 10; 11; 12] and partially connected hybrid beamforming (PC-HBF) [13; 14; 15]. The number of required variable phase shifters (VPS) in a fully connected architecture is \(N_{t}N_{RF}\), where \(N_{t}\) is the number of antennas, and \(N_{RF}\) is the number of RF chains. According to [8], the power consumption of one VPS is 30 mW, which can contribute significantly to the power consumption of a massive MIMO system in a collective manner.  
To reduce total power consumption, the PC-HBF architecture has been considered. Compared with the FC-HBF architecture, the number of required phase shifters is reduced to \(N_{t}\) in the PC-HBF architecture, which reduces hardware complexity and lowers power consumption. Another advantage of the PC-HBF architecture is that it typically requires substantially lower computational complexity than the FC-HBF architecture because of the reduced number of signal processing paths. Furthermore,in the PC-HBF architecture, a single subarray can transmit a data stream, which provides flexibility when choosing the beam direction [14; 15].  
In [15], an infinite-resolution phase shifters and a switch network are used for PC-HBF, whereas analog precoders are found through mutual information maximization in a multi-user MIMO system. In [16], the employment of phase over-samplers (POSs) and a switch network for analog precoding is introduced. In [16], the researchers also propose a PC-HBF scheme, which employs POSs, but an evaluation of its performance is left for future work. In [13], the researchers demonstrate that CPSs and switches can be used for analog beamforming to reduce power consumption because a CPS consumes approximately 83.3% less power than a VPS [8].  
Motivated by the low power consumption property of CPSs/switches and the relatively higher spectral efficiency of VPS-based HBF, we propose a new PC-HBF architecture that employs both VPSs and CPSs to harness the advantages of both types of phase shifters. The proposed architecture poses a combinatorial optimization problem that must be solved to allocate VPSs and CPSs to appropriate antennas such that the system sum-rate can be maximized. We formulate a system sum-rate optimization problem for analog beamforming design. Exhaustive search can find the ideal solution to this combinatorial problem. However, given the excessively large number of combinations, exhaustive search is impractical in the context of massive MIMO systems. To resolve this problem, we propose a near-optimal greedy algorithm that optimizes the system sum-rate heuristically.  
The remainder of this paper is organized as follows. Section 2 briefly describes the system model, whereas the proposed architecture and the developed algorithm are discussed in Section 3. Section 4 describes simulation results. Finally, our conclusions are given in Section 5.