## 1 Introduction
In the latter case, the HAPS acts as an aerial base station by offering wide wireless connectivity between ground users and the core network in the event of an inadequate terrestrial network or temporary ground station malfunction or maintenance. Moreover, thanks to their rapid deployment, HAPSs can assist in readily deploying communication networks after catastrophic events, such as earthquakes [22; 23]. Furthermore, HAPSs can act as reliable relays between terrestrial users and CubeSats [24; 25]--low Earth orbit (LEO) satellites--in order to form an airborne communication network (ACN) [26; 27]. The antenna system certainly represents one of the most important factors for HAPSs where reliable performance is concerned [28]. In Reference [29] a multibeam lens antenna for a HAPS operating at L/S band is presented. A Ka-band phased array composed of  
Figure 1: Examples of several scenarios where HAPSs can be exploited. 256 open-ended substrate-integrated square waveguides and a 4-channel beamformer circuit produced by Anokiwave was described in Reference [30]. In addition to the above-mentioned critical phased array aspects, another meaningful parameter that has to be accurately investigated for large phased arrays at mm-wave is the thermal aspect [31]. From the electromagnetic perspective, the most straightforward way of improving the cooling performance to dissipate heat is to increase the distance between the array elements. However, increasing the minimum distance between the single radiators too much can degrade the PSLL, with the appearance of grating lobes inside the visible region. This is detrimental to the signal-to-interference ratio (SIR) in massive MIMO systems with multiuser communication within the same time-frequency resource. Recently, a solution based on aperiodic antenna element arrangement capable of reducing the PSLL inside a defined sector cell for massive MIMO systems has been proposed in Reference [32]. However, the array aperiodicity considerably increases the design complexity of the feeding network, as well as complicating the array calibration. Most of the designed phased arrays with uniform lattices rely on square or rectangular element grids, although a triangular lattice allows for an increase in the minimum antenna distance, avoiding the onset of grating lobes [33; 34]. Few examples of triangular lattice 5G phased arrays are reported in the literature [35; 36]. However, a comprehensive analysis addressing the overall performance of massive MIMO systems, including SE and SIR, has not been yet presented, although some recent studies have proven the advantages of triangular lattice arrays over square and rectangular ones for 5G massive MIMO system ground stations [37]. The previous mm-wave 5G phased antenna arrays were designed to operate in one specific band, even if there are different frequency bands allocated to 5G mm-wave world-wide. For this reason, it is advantageous to design phased arrays that can operate over a wide band in order to allow for multistandard operation or exploit interband carrier aggregation (CA) to enhance spectral efficiency [38]. In this paper, the beneficial effects of adopting a triangular lattice rather than a square one are described and tested on a phased array for HAPS communications within both the 5G New Radio (NR) n258 (24.25-27.5 GHz) and NR n257 (26.5-29.5 GHz) bands. A thorough analysis of the overall system performance--including array gain, average sidelobe level (ASLL), signal-to-interference ratio (SIR), and spectral efficiency (SSE)--is carried out in order to demonstrate the effects of the employed array lattice. Furthermore, the comparison to a planar array of 8\(\times\)8 elements in terms of array gain, the minimum distance between elements, and ASLL is presented in Section 2. Section 3 is devoted to highlighting the superior robustness of triangular lattices for the antenna elements' impedance variation during beam steering inside the sector when compared to square lattices, via full-wave electromagnetic simulations.