## 1 Introduction  
The upcoming next generation (5G) of wireless communication networks is expected to drastically improve overall system performance, such as data throughput and energy efficiency [1, 2]. Currently, in most wireless communication systems, the users inside a sector cell are served through a base station, whose radiation pattern consists of a fixed broad main beam. In this scenario, the wireless communications system turns out to be inefficient from the energy point of view, since most of the base station (BS)'s radiated signal propagates towards directions in which there are no users [3]. The exploitation of larger frequency bandwidths and the deployment of more BSs to reduce the cell area are adopted in order to tackle the ever-increasing data throughput. On the other hand, in upcoming 5G wireless technology, improvement of the data throughput is guaranteed mainly by massive multiple-input and multiple-output (MIMO) technology [4, 5, 6], which is capable of serving multiple users simultaneously within the same time-frequency resource, through a multibeam radiation pattern with a consequent increase in the spectral efficiency (SE) of the system [2]. The coverage of users inside a sector cell is achieved through the deployment of phased arrays with a massive number of antennas. These arrays are able to provide advanced beamforming and beam tracking to generate multiple concurrent beams that send the different streams of data allocated on the same time-frequency resource to separate users [7]. In addition to radiation pattern optimization, a large-frequency spectrum is pivotal for supporting communication links with increased data transmission rates between the base station and the users. For this reason, the limited available spectrum below 6 GHz no longer satisfies the system's needs; consequently, the millimeter-wave (mmwave) band has recently drawn great attention for the next 5G wireless communications systems [8, 9, 10, 11]. The design of massive MIMO phased array antennas represents one of the most challenging aspects to tackle in order to guarantee reliable performance. In fact, the array performance in terms of gain, beam steering, peak sidelobe level (PSLL), antenna mutual coupling, and inter-element distance directly affects the quality of the overall wireless communication. Some examples of antenna arrays for mm-wave communication are reported in Reference [12]. In Reference [13], a 28 GHz phased array composed of 64 elements (8 \(\times\) 8) is described. Massive MIMO systems with 64 elements operating around 28 GHz and 40 GHz were designed with fully digital beamforming in References [14; 15]. Dual-polarized phased array transceivers able to provide two concurrent independent beams, and hence double the channel capacity, have also been proposed [16; 17]. However, some obstacles prevent the achievement of both seamless and ubiquitous wireless connectivity if only the terrestrial infrastructure is considered. In fact, terrestrial ground stations cannot be deployed in off-grid or inaccessible areas, such as rural zones, oceans, deserts, and generally harsh and remote environments. To this end, aerial wireless communication based on the employment of high-altitude platform stations (HAPSs) will play a paramount role in providing everywhere with access to the global network [18; 19; 20]. A HAPS consists of an unmanned aerial vehicle (UAV)--such as a gas-filled balloon, airship, or aircraft--operating in the stratosphere at an altitude of around 20 km [21] (Figure 1). HAPSs can be deployed in wireless communication networks with different topologies, within which they act mainly as aerial relays or aerial base stations to help improve the wireless communication [19]. In the former case, a HAPS collaborates with a ground BS by offering an alternative reliable link between it and a ground user by forwarding the data in case of a blockage between them.