## 1 Introduction  
Fifth-generation (5G) wireless communication can now operate in the millimetre-wave (mm-Wave) frequency range 2 (FR2), which spans from 24 GHz to about 70 GHz [1] and will almost certainly play a vital role in future generations such as sixth-generation (6G) systems [2]. However, the mm-Wave approach suffers from significant path loss in propagation from a communication point of view. This issue can be solved by effectively implementing mm-Wave technology with massive MIMO systems employing large antenna arrays with convenient beamforming techniques to mitigate the effect of path loss [2, 3]. Furthermore, cell-free systems are accomplished by deploying many geographically distributed access points (APs) over the coverage area without cell boundaries [4]. These APs are linked to a central processing unit (CPU) via high-speed fibre or wireless backhaul/fronthaul links to simultaneously serve user equipment (UE) and time-frequency resources [5]. From these aspects, cell-free massive MIMO systems can provide a good quality of service (QoS) to all UEs in the coverage area compared to distributed massive MIMO systems [6, 7]. Power consumption and hardware cost of mm-Wave systems are significantly higher when completing the entire process in the digital domain with a large number of antennas. A more convenient solution is to adopt a hybrid analog/digital design as a more cost-effective option [8]. A large number of antennas are connected to a small number of radio frequency (RF) chains that perform analog-to-digital conversion via an analog front-end (implemented using phase shifters) [9, 10]. The hybrid analog/digital approach has two main schemes: fully connected and partially connected. The fully connected way is when each RF chain is connected to all of the antennas, and the partially connected scheme is when each RF chain is connected to some of the antennas [8, 11, 12, 13]. The authors in [14] proposed the hybrid analog/digital structure by employing constant phase shifters (CPSs) instead of using variable phase shifters (VPSs) due to huge power consumption and hardware complexity in the case of the fully connected scheme with a large number of antennas. They also utilized switches in the design of the analog beamforming. Thus, their proposed method achieved better energy efficiency and a slight loss in spectral efficiency using low-power CPSs. Additionally, the authors in [15] used the same structure as in [14] and maximized the signal-to-interference-plus-noise ratio (SINR) by presenting novel algorithms based on quasi-orthogonal combining. However, depending on channel conditions, when signals received at many antennas are aggregated at the RF chain, a subset of antennas may contribute more to interference than to the desired signal power, resulting in SINR loss. To enhance energy efficiency, a zero-forcing precoding technique was presented in [16] with a low complexity power control scheme for cell-free massive MIMO systems. The performance of cell-free mm-Wave massive MIMO systems was studied using a hybrid beamforming technique with limited fronthaul capacity, in which precoders and combiners were created using an Eigen beamforming scheme [17]. The authors in [18] proposed adaptive RF chain activation (ARFA) to reduce power consumption in uplink cell-free mm-Wave massive MIMO systems, where the fully connected hybrid analog/digital approach is individually created at each AP using known channel state information (CSI). However, the phase shifters in this technique are huge due to the vast number of antennas at each AP, resulting in high hardware implementation costs and power consumption. A hybrid beamforming technique with fixed phase shifters based on an alternating minimization algorithm for the uplink cell-free massive MIMO systems was presented in [19]. They also employed fixed phase shifters with dynamic cascade switches at each AP to avoid the performance loss caused by erroneous fluctuation of the adaptive fixed number of phase shifters with channel conditions.