Spectral Efficiency Improvement of 5G Massive MIMO Systems For

sensors

Article Spectral Efﬁciency Improvement of 5G Massive MIMO Systems for High-Altitude Platform Stations by Using Triangular Lattice Arrays

Francesco Alessio Dicandia * and Simone Genovesi

Dipartimento di Ingegneria dell’Informazione, University of Pisa, 56122 Pisa, Italy; [email protected] * Correspondence: [email protected]

Abstract: The beneficial effects of adopting a triangular lattice on phased arrays with regular and periodic grids for high-altitude platform station (HAPS) systems are presented in the scenario of massive MIMO communications operating within the 5G NR n257 and n258 frequency bands. Assessment of a planar array with 64 elements (8 × 8) is provided for both a triangular lattice and a square one in terms of array gain, average sidelobe level (ASLL), and mutual coupling. Particular attention is devoted to illustrating the impact of the antenna array lattice at the system level by evaluating its significant merits, such as its spectral efficiency (SE) and signal-to-interference ratio (SIR). The better performance exhibited by the triangular lattice array in comparison to the square one makes it appealing for the 5G massive MIMO paradigm.

Keywords: phased array; massive MIMO; 5G; wideband array; triangular grid

Citation: Dicandia, F.A.; Genovesi, S. Spectral Efficiency Improvement of 5G Massive MIMO Systems for 1. Introduction High-Altitude Platform Stations by The upcoming next generation (5G) of wireless communication networks is expected Using Triangular Lattice Arrays. to drastically improve overall system performance, such as data throughput and energy Sensors 2021, 21, 3202. https:// efficiency [1,2]. Currently, in most wireless communication systems, the users inside a doi.org/10.3390/s21093202 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 Academic Editors: Giuseppe Piro and inefficient from the energy point of view, since most of the base station (BS)’s radiated Naser Ojaroudi Parchin 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 Received: 13 March 2021 are adopted in order to tackle the ever-increasing data throughput. On the other hand, Accepted: 3 May 2021 in upcoming 5G wireless technology, improvement of the data throughput is guaranteed Published: 5 May 2021 mainly by massive multiple-input and multiple-output (MIMO) technology [4–6], which is capable of serving multiple users simultaneously within the same time–frequency resource, Publisher’s Note: MDPI stays neutral through a multibeam radiation pattern with a consequent increase in the spectral efficiency with regard to jurisdictional claims in published maps and institutional affil- (SE) of the system [2]. The coverage of users inside a sector cell is achieved through the iations. 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 Copyright: © 2021 by the authors. rates between the base station and the users. For this reason, the limited available spectrum Licensee MDPI, Basel, Switzerland. below 6 GHz no longer satisfies the system’s needs; consequently, the millimeter-wave (mm- This article is an open access article wave) band has recently drawn great attention for the next 5G wireless communications distributed under the terms and conditions of the Creative Commons systems [8–11]. Attribution (CC BY) license (https:// The design of massive MIMO phased array antennas represents one of the most creativecommons.org/licenses/by/ challenging aspects to tackle in order to guarantee reliable performance. In fact, the array 4.0/). performance in terms of gain, beam steering, peak sidelobe level (PSLL), antenna mutual

Sensors 2021, 21, 3202. https://doi.org/10.3390/s21093202 https://www.mdpi.com/journal/sensors Sensors 2021, 21, x FOR PEER REVIEW 2 of 20

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 × 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]. Sensors 2021, 21, 3202However, some obstacles prevent the achievement of both seamless and ubiquitous2 of 20 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, coupling, and inter-element distance directly affects the quality of the overall wireless com- oceans, deserts, and generally harsh and remote environments. To this end, aerial wireless munication. Some examples of antenna arrays for mm-wave communication are reported communication basedin Reference on the [ 12employment]. In Reference of [h13igh], a- 28altitude GHz phased platform array station composeds (HAPSs) of 64 elements will play a paramount(8 role× 8) in is described.providing Massive everywhere MIMO systemswith access with 64to elementsthe global operating network around [18– 2820] GHz. A HAPS consists andof an 40 u GHznmanned were designed aerial v withehicle fully (UAV) digital— beamformingsuch as a gas in References-filled balloon,[14,15] .air- Dual- ship, or aircraft—polarizedoperating phased in the array stratosphere transceivers at able an to altitude provide twoof around concurrent 20 independentkm [21] (Error! beams, and hence double the channel capacity, have also been proposed [16,17]. Reference source notHowever, found.) some. HAPSs obstacles can prevent be deployed the achievement in wireless of both communication seamless and ubiquitous networks with differentwireless topologies connectivity, within if only thewhich terrestrial they infrastructureact mainly as is considered. aerial relays In fact, or terrestrialaerial base stations to helpground improve stations the cannot wireless be deployed communication in off-grid or [19] inaccessible. In the form areas,er such case, as a rural HAPS zones, collaborates withoceans, a ground deserts, BS and by generally offering harsh an andalternative remote environments. reliable link To between this end, aerial it and wireless a communication based on the employment of high-altitude platform stations (HAPSs) will ground user by forwarding the data in case of a blockage between them. In the latter case, play a paramount role in providing everywhere with access to the global network [18–20]. the HAPS acts asA an HAPS aerial consists base of anstation unmanned by offering aerial vehicle wide (UAV)—such wireless asconnectivity a gas-ﬁlled balloon, between airship, ground users andor the aircraft—operating core network inin the the stratosphere event of an at aninadequate altitude of aroundterrestrial 20 km network [21] (Figure or1 ). temporary groundHAPSs station can bemalfunction deployed in or wireless maintenance. communication Moreover networks, thanks with different to their topologies, rapid deployment, HAPSswithin can which assist they in act readily mainly deploying as aerial relays communication or aerial base stations networks to help after improve cata- the wireless communication [19]. In the former case, a HAPS collaborates with a ground BS strophic events, suchby offering as earthquakes an alternative [22,23] reliable. Furthermore, link between itHAPSs and a ground can act user as reliable by forwarding relays the between terrestrialdata users in case and of CubeSat a blockages [24,25] between— them.low Earth In the o latterrbit (LEO) case, the satellite HAPS actss—in as order an aerial to form an airbornebase communication station by offering n wideetwork wireless (ACN) connectivity [26,27]. between ground users and the core The antennanetwork system incertainly the event represents of an inadequate one of terrestrial the most network important or temporary factors groundfor HAPSs station malfunction or maintenance. Moreover, thanks to their rapid deployment, HAPSs can where reliable performanceassist in readily is concerned deploying communication [28]. In Reference networks [29] aftera multibeam catastrophic lens events, antenna such as for a HAPS operatingearthquakes at L/S [band22,23]. is Furthermore, presented. HAPSsA Ka-band can act phased as reliable array relays composed between terrestrialof 256 open-ended substrateusers- andintegrated CubeSats square [24,25]—low waveguide Earth orbits and (LEO) a satellites—in4-channel beamformer order to form an circuit airborne produced by Anokiwavecommunication was described network (ACN) in Reference [26,27]. [30].

HAPS-satellite communications

Maritime Communications Inter-HAPS communications

Rural areas

Disaster Ground station managment Crop monitoring

Figure 1. ExamplesFigure of several 1. Examples scenarios of several where scenarios HAPSs where can HAPSs be exploited. can be exploited.

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

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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 8×8 elements in terms of array gain, the minimum distance between elements, and ASLL is presented in Section2. Section3 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. This represents a step forward with respect to Reference [37], since it better quantifies the effects of mutual coupling and matching efficiency (ηΓ). Massive MIMO metrics, such as SE and SIR, are evaluated in Section4, whilst conclusions are summarized in Section5.

2. Triangular vs. Square Lattice Planar Arrays The radiation pattern (RP) generated by a planar array with N×M elements in the event of uniform amplitude excitation, and when neglecting the mutual coupling, is equal to [39]: N−1 M−1 jϕ jβF RP(θ, φ) = ∑ ∑ e nm Enm(θ, φ) e n=0 m=0 (1) F = xnm sin(θ) cos(φ) + ynm sin(θ) sin(φ)

where β = 2π/λ0 is the phase constant; Enm(θ,φ) represents the elements’ radiation pattern; and ϕnm represents the phase associated with the (n,m)-th element necessary to steer the main beam toward the desired direction (u0, v0), which depends on the element’s Sensors 2021, 21, x FOR PEER REVIEW 4 of 20

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(xnm, ynm) within the employed lattice. The relation between the phase nm and the element’s position (positionxnm, ynm) is (x givennm, ynm by) within the following the employed equation lattice.: The relation between the phase ϕnm and the element’s position (xnm, ynm) is given by the following equation: nm=+ ( x nmu0 y nm v0 ) ϕnm = β(xnmu0 + ynmv0) u0 = sin() 0 cos() 0 (2) u0 = sin(θ0) cos(φ0) (2) v0 = sin()()0v0 sin= sin0(θ0) sin(φ0)

0 The minimumThe minimum distance between distance elements between elements(d ) is a fundamental (d0) is a fundamental parameter parameter for array for array 0 radiation radiationperformance. performance. Furthermore Furthermore,, d shouldd0 beshould selected be selected in order in to order avoid to avoidthe appear- the appearance ance of gratingof grating lobes lobes within within the visible the visible region region during during the thebeam beam steering steering inside inside the theangular angular sector sector selectedselected to serve to serve the theusers. users. In fact, In fact, high high lateral lateral lobes lobes do not do notonly only provide provide a consid- a considerable erable reductionreduction in inthe the maximum maximum array array gain gain,, but but also also produce produce interference interference for forall allother other users users servedserved with withinin the same the same time time–frequency–frequency resource. resource. In general, In general, the maximum the maximum value value of of the the minimumminimum distance distance between between the antenna the antenna elements elements depends depends on the on maximum the maximum steering steering angle angle necessarynecessary to cover to cover the thearea area of interest of interest.. The HAPSThe scenario HAPS differs scenario from differs thatfrom of a 5G that ground of a 5G BS ground—whose BS—whose coverage coveragespans 30° spans 30◦ in elevationin elevationand 120° andin azimuth 120◦ in [37,40] azimuth—since [37,40 a]—since circular ascan circular area scanturns area out turnsto be outmore to be more appropriateappropriate [18]. Therefore, [18]. Therefore, it is assume it isd assumedto cover an to coverangular an sector angular with sector a maximum with a maximum ◦ ◦ ◦ steering anglesteering of 60° angle off ofbroadside 60 off broadside (–60 ≤ 0 (–60≤ 60°)≤ θ for0 ≤ all60 ) angles for all (0φ angles≤ 0 ≤ (0 180°)≤ φ0, as≤ 180 ), as shown in shownError! Reference in Figure2 sourcein the u–vnot plane.found. in the u–v plane.

v=sin()sin() 1 sin(60°)

-1 0 1 u= sin()cos()

-1

Figure 2. CircularFigure 2.sectorCircular cell sectorin the u cell–v inplane the withinu–v plane which within the whichHAPS theantenna HAPS array antenna has to array steer has to steer the the main beammain to beam serve to the serve 5G theusers. 5G users.

As stated Asbefore, stated most before, of the most designed of the designed phased arrays phased with arrays uniform with uniformlattices rely lattices upon rely upon a a square arrangementsquare arrangement of the antenna of the antenna elements. elements. In this case, In this the case, condition the condition on d0 for on avoid-d0 for avoiding ing the appearancethe appearance of grating of grating lobes lobesinside inside the visible the visible region region is given is given by: by:  λ d ≤HF HF (3) d0  0 (3) R + sin(θmax) R + sin (max )

where λHF represents the wavelength evaluated at the highest frequency (i.e., 29.5 GHz); where HF represents the wavelength evaluated at the highest frequency◦ (i.e. 29.5 GHz); θmax is the maximum antenna array steering angle, which is 60 for the considered circular max is the maximum antenna array steering angle, which is 60° for the considered circular angular sector shown in Figure2; and R is a real number that represents the distance in angular sector shown in Error! Reference source not found.; and R is a real number that the u–v plane between the closest grating lobes and the center of the visible region (u = 0, represents the distance in the u–v plane between the closest grating lobes and the center v = 0). Therefore, in order to guarantee the absence of undesirable high lobes inside the of the visible region (u = 0, v = 0). Therefore, in order to guarantee the absence of undesir- visible region, R has to be set to greater than 1. able high lobes inside the visible region, R has to be set to greater than 1. In the case of an antenna array with uniform spacing but with a triangular grid, the In the case of an antenna array with uniform spacing but with a triangular grid, the spacing dx and dy—namely, the height and the base of the triangle (Figure3)—are related spacing dxto and the dγy—anglenamely by, thethe followingheight and equations: the base of the triangle (Error! Reference source not found.)—are related to the  angle by the following equations: d = D sin(γ) x (4) dy = 2D cos(γ)

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Sensors 2021, 21, 3202 5 of 20 dDx = sin ( ) (4) dDy = 2 cos( ) where D is the distance between the (n,m)-th element and the (n+1,m)-th, as depicted in whereFigure3 D. is the distance between the (n,m)-th element and the (n+1,m)-th, as depicted in Error! Reference source not found.. y

FigureFigure 3.3. PlanarPlanar antenna antenna array array with with a triangular a triangular lattice. lattice.

Differently from a square lattice, there are different choices of grid spacing (dx, dy) in Differently from a square lattice, there are different choices of grid spacing (dx, dy) in an array with a triangular grid, which are able to guarantee the absence of grating lobes. In anthis array case thewith grating a triangular lobes are grid avoided, which if the are following able to equationsguarantee are the satisﬁed: absence of grating lobes. In this case the grating lobes are avoided if the following equations are satisfied: 2 2 λHF ∗ λHF ∗ 2 − u + 2 − v ≥ R 2 2dx 0 dy 0 2λHF * * 2 HF− sin(θmax) ≥ HFR dy −u00 + − v  R λ  (5) 2ddHFxy− sin(θ ) ≥ R dx max u∗ = ( ) ( ) 20 sin θmax cos γ v∗HF= ( ) ( ) 0 −sinsinθmax( sin) γ R d max * * y where u0 and v0 represent the u–v plane coordinates where the grating lobes can appear. (5) It is worthwhile to note that the previousHF grating lobes absence equations are only valid for equilateral or isosceles triangular lattices.−sin Scalene(max ) latticesR have not been considered since dx they provide a lower value for d0. Equation (5) was used to understand the effect of γ on * Sensors 2021, 21, x FOR PEER REVIEW the element spacing in a circular scan sector. The elements’ spacing (dx, dy), along with the 6 of 20 u0= sin( max ) cos( ) minimum distance between them, were evaluated for γ within the interval [20◦,80◦] in the * event of R = 1.1. The plot summarizingv0= sin the( results max ) sin is( shown) in Figure4.

where u0* and v0* represent the u–v plane coordinates where the grating lobes can appear. It is worthwhile to note that the previous grating lobes absence equations are only valid for equilateral or isosceles triangular lattices. Scalene lattices have not been considered since they provide a lower value for d0. Equation Error! Reference source not found. was used to understand the effect of  on the element spacing in a circular scan sector. The elements’ spacing (dx, dy), along with the minimum distance between them, were evaluated for  within the interval [20°,80°] in the event of R = 1.1. The plot summarizing the results is shown in Figure 4.

FigureFigure 4. 4. Elements’Elements’ spacing spacing (dx ,(dyx),, d they), antennathe antenna elements’ elements’ distance distance (D), and its (D minimum), and its (d minimum0) as a (d0) as a functionfunction of of thetheγ value value for for a triangular a triangular lattice lattice array inarray the event in the of Revent= 1.1. of R = 1.1.

It is apparent that the  value has a considerable effect on d0. Specifically,  = 30° and  = 60° provide the largest minimum distance between elements, which is equal to 5.97 mm (0.587 HF) in the addressed scenario. Moreover, Figure 4 emphasizes how the triangular lattice provides the designer more degrees of freedom due to different possible combinations of element spacing (dx, dy). For example, let us consider the RP of an 8×8 array of isotropic elements (i.e. Enm(,) = 1) when the main beam is steered along one of the  directions where there are grating lobes and when  = 60°. Figure 5 illustrates the outcomes for two values of , namely, 30° and 60°. It is apparent that the different antenna element spacing (Figure 4) determines a different pattern shape, although the minimum distance remains the same. In particular, in the event of  = 30° (Figure 5a), the antenna array presents a superior spatial resolution along the v plane, whereas the equilateral triangular lattice ( = 60°) provides an almost circular footprint in the u–v plane. Moreover, in both cases the grating lobe is evidently outside the visible region (red circle), located at a distance of R = 1.1 from the center (u = 0, v = 0), as expected. Therefore, according to the desired spatial resolution in the u–v plane, it is possible to select the proper  value.

(a) (b)

Figure 5. RP in the case of an antenna array with 8 × 8 isotropic elements arranged in a triangular lattice in the event of (a)  = 30°, and (b)  = 60°. The red circle represents the visible region, whereas the black circle highlights the circular sector cell.

In order to find the most suitable triangular lattice grid—and hence, the  value—the angular average gain (Gain), namely, the mean value of the gain attained during the beam steering inside the all-circular sector, in the case of a planar array composed of 8 × 8 elements, was evaluated as a function of the  value within the addressed bandwidth (24.25– 29.5 GHz), and by considering the beam scan within the circular sector cell, as shown in Error! Reference source not found.. An element pattern shape equal to E(,) = cos( ),

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Figure 4. Elements’ spacing (dx, dy), the antenna elements’ distance (D), and its minimum (d0) as a function of the  value for a triangular lattice array in the event of R = 1.1. Sensors 2021, 21, 3202 6 of 20

It is apparent that the  value has a considerable effect on d0. Specifically,  = 30° and  = 60° provide the largest minimum distance between elements, which is equal to 5.97 ◦ mm (0.587 HF) in the addressedIt is apparent scenario that the. Moreover,γ value has aFigure considerable 4 emphasizes effect on dhow0. Speciﬁcally, the trian-γ = 30 ◦ gular lattice providesand theγ designer= 60 provide more the degrees largest minimumof freedom distance due to between different elements, possible which com- is equal to 5.97 mm (0.587 λHF) in the addressed scenario. Moreover, Figure4 emphasizes how binations of elementthe spacing triangular (dx, latticedy). For provides example the, designerlet us consider more degrees the RP of of freedom an 8×8 due array to differentof isotropic elements (i.e.possible Enm( combinations,) = 1) when of elementthe main spacing beam (d isx, dsteeredy). For example,along one let usof considerthe  di- the RP rections where thereof are an 8grating× 8 array lobesof isotropic and when elements  = 60° (i.e.,. EFigurenm(θ,φ) 5= illustrates 1) when the the main outcomes beam is steered ◦ for two values of , namelyalong one, 30° of the andφ directions60°. It is whereapparent there that are gratingthe different lobes and antenna when θ element= 60 . Figure 5 illustrates the outcomes for two values of γ, namely, 30◦ and 60◦. It is apparent that the spacing (Figure 4) determines a different pattern shape, although the minimum distance different antenna element spacing (Figure4) determines a different pattern shape, although remains the same. Inthe particular, minimum distancein the event remains of the  = same. 30° ( InFigure particular, 5a), in the the antenna event of γ array= 30◦ (pre-Figure5a ), sents a superior spatialthe antenna resolution array along presents the a superior v plane spatial, whereas resolution the equilateral along the v plane, triangular whereas the ◦ lattice ( = 60°) providesequilateral an almost triangular circular lattice footprint (γ = 60 ) providesin the u an–v almostplane.circular Moreover, footprint in both in the u–v cases the grating lobeplane. is evident Moreover,ly inoutside both cases the the visible grating region lobe is evidently(red circle) outside, located the visible at a regiondis- (red circle), located at a distance of R = 1.1 from the center (u = 0, v = 0), as expected. Therefore, tance of R = 1.1 fromaccording the cente to ther desired(u = 0, spatialv = 0) resolution, as expected. in the u–v Therefore,plane, it is possibleaccording to select to thethe proper desired spatial resolutionγ value. in the u–v plane, it is possible to select the proper  value.

(a) (b)

FigureFigure 5. RP5. RP in the in casethe ofcase an antennaof an antenna array with array 8 × 8 with isotropic 8 × elements8 isotropic arranged elements in a triangular arranged lattice in a in triangular the event of (a) γlattice= 30◦, andin the (b) γevent= 60◦ .of The (a red)  = circle 30°, represents and (b)  the = 60°. visible The region, red whereascircle represents the black circle the highlightsvisible region, the circular sector cell.whereas the black circle highlights the circular sector cell. In order to find the most suitable triangular lattice grid—and hence, the γ value—the  In order to findangular the most average suitable gain triangular (ηGain), namely, lattice the grid mean— valueand hence of the, gainthe attained value— duringthe the angular average gainbeam (Gain steering), namely inside, the the mean all-circular value sector, of the in gain the caseattained of a planar during array the composed beam of steering inside the all8 ×-circular8 elements sector,, was evaluated in the case as a functionof a planar of the arrayγ value composed within the addressed of 8 × 8 bandwidthele- ments, was evaluated(24.25–29.5 as a function GHz), and of the by considering  value within the beam the scan addressed within the bandwidth circular sector (24.25 cell, as– shown in Figure2. An element pattern shape equal to E(θ,φ) = cos(θ), with a half-power beamwidth 29.5 GHz), and by considering(HPBW) of 90 ◦the, was beam assumed scan as within the element the factorcircular during sector the averagecell, as gain shown evaluation. in Error! Reference sourceFrom not thefound. color map. An of element Figure6 it pattern can be concluded shape equal that ηGain to alwaysE(,) increases= cos( with), frequency, although it exhibits higher value ﬂuctuations with respect to the γ value, especially ◦ in the lower band. Furthermore, ηGain grows almost linearly up to γ = 30 , then gradually decreases with the increase of the γ value up to around γ = 45◦, where a reversal of the ◦ trend occurs. Subsequently, the angular average gain reaches the second peak at γ = 60 , after which it quickly drops again. Therefore, by considering the minimum element spacing (Figure4) and the angular average gain (Figure6), it is possible to infer that with a circular sector cell there are two optimal γ values in cases of triangular grids, namely, γ = 30◦ and γ = 60◦. In fact, these values ensure the largest minimum antenna element distance and, Sensors 2021, 21, x FOR PEER REVIEW 7 of 20

with a half-power beamwidth (HPBW) of 90°, was assumed as the element factor during the average gain evaluation. From the color map of Figure 6 it can be concluded that Gain always increases with frequency, although it exhibits higher value fluctuations with respect to the  value, especially in the lower band. Furthermore, Gain grows almost linearly up to  = 30°, then gradually decreases with the increase of the  value up to around  = 45°, where a reversal of the trend occurs. Subsequently, the angular average gain reaches the second peak at  = 60°, after which it quickly drops again. Therefore, by considering the minimum element spacing (Figure 4) and the angular average gain (Figure 6), it is possible to infer that with a circular sector cell there are two optimal  values in cases of triangular grids, namely,  = 30° and  = 60°. In fact, these values ensure the largest minimum antenna element dis-

Sensors 2021, 21, 3202 tance and, hence, the lowest performance degradation 7due of 20 to the elements’ mutual coupling [41,42], in addition to having the highest angular average gain as a function of the

frequency.hence, the lowest performance degradation due to the elements’ mutual coupling [41,42], in addition to having the highest angular average gain as a function of the frequency.

Figure 6. Angular average gain (η ) as a function of the γ value within the working frequencies Figure 6. Angular averageGain gain (Gain) as a function of the  value within the working frequencies (24.25 –29.5 GHz) in the case of a triangular lattice planar array of 8 × 8 elements. (24.25 –29.5 GHz) in the case of a triangular lattice planar array of 8 × 8 elements. In view of highlighting the impact of the antenna array lattice, two 8 × 8 planar arrays were considered—the former with elements arranged on a square lattice, and the latter onIn an equilateralview of triangular highlighting (γ = 60◦) grid. the It impact is worth noting of the that, antenna as stated before, array in a lattice, two 8 × 8 planar arrays triangular lattice placement of the elements there are two most suitable values, namely, wereγ = considered 30◦ and γ = 60◦. However,—the informer the following with performance elements comparison, arranged it was decided on a to square lattice, and the latter on use an equilateral triangular lattice due to its more uniform footprint in the u–v plane, as an equilateralshown in Figure5 b.triangular By considering ( the = Equations 60°) grid. (3)–(5), withIt isR worth= 1.1, for anoting square lattice that, as stated before, in a trian- gulard0 turns lattice out to placement be 5.17 mm (0.508 ofλHF the), whereas elements the equilateral there triangular are two grid exhibitsmost asuitable values, namely,  = 30° minimum element distance of 5.97 mm (0.587 λHF), hence offering a 13.5% improvement. andIt  is = worth 60° observing. However, that values in oftheR greater following than 1 assure performance the absence of grating comparison, lobes it was decided to use an equilateralduring the beam triangular steering inside lattice the circular due sector to [ 43its]. Themore same Runiformvalue for both footprint lattices in the u–v plane, as shown provides the same distance in the u–v plane between the closest grating lobes and the in centerFigure of the 5 visibleb. By region considering (u = 0, v = 0), and hence, the theEquations same PSLL value Error! as a function Reference source not found.– of the beam steering inside the circular sector cell. Furthermore, PSLL is around –13.3 dB Error!at the Reference broadside, whereas source with the not increase found. in the θ, steeringwith angle,R = 1.1 PSLL, for degrades a square up to lattice d0 turns out to be 5.17 ◦ mmaround (0.508 –9 dB  forHFθ),= whereas60 due to the the cosine-shaped equilateral elements’ triangular radiation pattern. gr Theid largerexhibits a minimum element dis- minimum distance obtained via a triangular lattice arrangement allows us to achieve a tancelower of level 5.97 of mutual mm coupling (0.587 among HF antenna), hence elements offering by ensuring a greater13.5% robustness improvemen of t. It is worth observing the active impedance of the array elements along the beam steering, a superior linearity of thatthe values employed of power R greater ampliﬁers than (PAs), and 1 assure a general improvementthe absence of the of massive grating MIMO lobes during the beam steering insideperformance the circular [41]. The wider sector element [43] distance. The offered same by the R triangular value lattice for can both be also lattices provides the same dis- considered advantageous for the thermal aspect, by helping the cooling system of the tancetransceiver, in the which u–v is plane critical in between large mm-wave the phased closest arrays grating [31]. The overlapped lobes and array the center of the visible region (u =geometry 0, v = of0), triangular and hence and square, the lattices same is illustrated PSLL in value Figure7. as a function of the beam steering inside the circular sector cell. Furthermore, PSLL is around –13.3 dB at the broadside, whereas with the increase in the  steering angle, PSLL degrades up to around –9 dB for  = 60° due to the cosine-shaped elements’ radiation pattern. The larger minimum distance obtained via a triangular lattice arrangement allows us to achieve a lower level of mutual coupling among antenna elements by ensuring greater robustness of the active impedance of the array elements along the beam steering, a superior linearity of the employed power am- plifiers (PAs), and a general improvement of the massive MIMO performance [41]. The

Sensors 2021, 21, x FOR PEER REVIEW 8 of 20

wider element distance offered by the triangular lattice can be also considered advantageous for the thermal aspect, by helping the cooling system of the transceiver, which is critical in large mm-wave phased arrays [31]. The overlapped array geometry of triangu- Sensors 2021, 21, 3202 lar and square lattices is illustrated in Figure 7. 8 of 20 Sensors 2021, 21, x FOR PEER REVIEW 8 of 20

wider element distance offered by the triangular lattice can be also considered advantageous for the thermal aspect, by helping the cooling system of the transceiver, which is critical in large mm-wave phased arrays [31]. The overlapped array geometry of triangular and square lattices is illustrated in Figure 7.

FigureFigure 7. 7.ArrayArray geometry geometry of ofa planar a planar array array of of 64 64 elements elements (8 (8 × ×8) 8)in ina triangular a triangular lattice lattice ( ( γ= 60°)= 60 ◦and) and Figurea square 7. Arraylattice. geometry of a planar array of 64 elements (8 × 8) in a triangular lattice ( = 60°) and a square lattice. a square lattice. TheThe larger larger array array area area of of the the triangular triangular element element arrangement arrangement also also guarantees guarantees a abetter better angularangular resolution resolution and, and, in ina amassive massive MIMO MIMO scenario, scenario, a areduced reduced angular angular interval interval within within whichwhichThe users userslarger cannot cannot array be be spatially spatially area resolved resolved of the[2] [2. ]. triangular element arrangement also guarantees a better TheThe array array gain gain as as a afunction function of of the the main main beam beam direction direction ( (θ0,0 , φ) 0for) for both both arrays arrays of of angularFigureFigure 7resolution 7is is illustrated illustrated in in Figure and, Figure 88 by byin considering considering a massive an an element element MIMO pattern pattern scenario,equal equal to to E(E(,θ,)φ =a) cos( = reducedcos().θ ). angular interval within whichIt Itcan canusers be be not noteded cannot that, that, although although be spatiallythe the employed employed resolvedarray array lattices lattices present[2] present. similar similar trend trendss during during beambeam steering, steering, the the triangular triangular lattice outperformsoutperforms thethe square square one one due due to to a highera higher array array gain. ◦ gain.Furthermore,The Furthermore array the , gain the gain value as value presents a presentsfunction the highestthe highest of value thevalue along alongmain the broadsidethe beambroadside (θ0 =direction ( 00 =), 0°) then, (0, ) for both arrays of thdecreasesen decreases during during the the main main beam beam steering steering due due to to beam beam widening widening and and the the approaching approaching of Figureofthe the 7 gratinggrating is illustrated lobeslobes insideinside the in visible Figure region 8 [39] [ 39by].. For Forconsidering a a more more comprehensive comprehensive an element analysis, analysis, the the pattern equal to E(,) = cos(). impactimpact of of the the employed employed lattice lattice on on the the array array gain gain was was also also examined examined from from a statistical a statistical point point It can be noted that, although the employed2 array lattices present similar trends during ofof view view,, by by calculating calculating the the mean mean value value ( (ηGainGain), ),the the variance variance ( (σGainGain), ),the the minimum minimum value value beam(min(min steering,GainGain), and), and the the maximum maximumthe triangular value value (max (maxGainGain). Thelattice). The results results outperformsreported reported in inTable Table 1 1emphasize emphasizethe square that that one due to a higher array thethe triangular triangular lattice lattice enables enables the the attain attainmentment of of an an average average linear linear array array gain gain improvement improvement 0 gain.ofof aroundFurthermore around 13 13 % %,, when when compared, comparedthe gain to to a asquarevalue square lattice lattice.presents. Moreover, Moreover, the as as visible highest visible fr fromom the value the color color along the broadside ( = 0°), thenmaps mapsdecreases of ofFigure Figure 8,8 during,the the use use of of a athetriangular triangular main lattice lattice beam provides provides steering both both a asuperior superior due m minimumtoinimum bea valuem value widening and the approaching (min ) and maximum value (max ) to those of a square grid. of the(min gratingGainGain) and maximum lobes value inside (maxGain theGain) to those visible of a square region grid. [39]. For a more comprehensive analysis, the impact of the employed lattice on the array gain was also examined from a statistical point  of view, by calculating the mean value (Gain), the variance ( Gain), the minimum value (minGain), and the maximum value (maxGain). The results reported in Table 1 emphasize that the triangular lattice enables the attainment of an average linear array gain improvement of around 13 %, when compared to a square lattice. Moreover, as visible from the color

maps of Figure 8, the use of a triangular lattice provides both a superior minimum value (a() minGain) and maximum(b )value (maxGain) to those (cof) a square grid.

Figure 8. Cont.

(a) (b) (c)

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(d) (e) (f)

FigureFigure 8. 8.GainGain in indBi dBi of a of planar a planar array array composed composed of 64 of elements 64 elements (8 × 8 (8 array)× 8 array)as a function as a function of the main of the beam main steering beamsteering inside ≤ 0 ≤ ◦ ≤ 0 ≤ ◦ ◦ ◦ theinside circular the angular circular sector angular (−60° sector (−6060°,≤ 0°θ0 ≤ 60180°)., 0 Equilateral≤ φ0 ≤ 180 triangular). Equilateral lattice triangularat (a) 24.25 lattice GHz, ( atb) ( a26.875) 24.25 GHz, GHz, and(b) ( 26.875c) 29.5 GHz,GHz; andsquare (c) 29.5lattice GHz; at (d square) 24.25 lattice GHz, at(e) ( d26.875) 24.25 GHz, GHz, and (e) ( 26.875f) 29.5 GHz,GHz. and (f) 29.5 GHz.

TableTable 1. 1. StatisticalStatistical comparison comparison between between the the g gainain (dBi) (dBi) of of a a square square lattice lattice and an equilateral triangulartriangular lattice for an 8 × 8 array evaluated within the circular scan sector. lattice for an 8 × 8 array evaluated within the circular scan sector.

24.2524.25 GHz GHz 26.875 26.875 GHz GHz 29.5 29.5 GHz GHz TriTri Squ Squ Tri Tri Squ Squ Tri Tri Squ Squ ηGain 21.38 20.77 22.18 21.57 22.87 22.28 Gain2 21.38 20.77 22.18 21.57 22.87 22.28 σ Gain 0.89 0.83 0.97 0.9 1.12 0.99 2 minGainGain 0.8919.17 0.83 18.73 0.97 19.81 0.9 19.38 1.12 20.24 0.99 19.83 maxGain 22.42 21.78 23.26 22.61 24.03 23.37 minGain 19.17 18.73 19.81 19.38 20.24 19.83

maxSinceGain the user’s22.42 interference21.78 plays a23.26 key role in massive22.61 MIMO24.03 systems, the23.37 impact of the employed array lattice on the average sidelobe level (ASLL) was evaluated from a statisticalSince the point user’s of view. interference For the plays ASLL a evaluation, key role in themassive addressed MIMO region systems, was the selected impact for ofeach the employed main beam array pointing lattice at aon user the byaverage the following sidelobe ellipse level (ASLL) equation: was evaluated from a statistical point of view. For the ASLL evaluation, the addressed region was selected for each (u−u0) (v−v0) main beam pointing at a user by the following2 + ellipse2 > equation:1 ru rv λ λ (6) ru = 1.2 , rv = 1.2 (u−− u) Lx ( v v ) Ly 00+1 where L and L represent the array22 side length along the x and y directions; λ is the x y rruv wavelength; (u ,v ) the desired direction in the u–v planein which to steer the main beam;(6) 0 0  and ru and rv identify the main beam in the u and v planes, respectively. Once the sidelobe rruv==1.2 , 1.2 region has been selected for a desired (u0,vLL0xy) direction, the ASLL is calculated by averaging all of the array’s radiation pattern values inside the sidelobe region. Moreover, since the wherearray L canx and steer Ly represent the main beamthe array inside side a length circular along area (Figurethe x and2), y we direction decideds; to is evaluate the wave- the length; (u0,v0) the desired direction in the u–v plane in which to steer the main beam; and ru ASLL mean (ηASLL), minimum (minASLL), and maximum (maxASLL) values by considering and rv identify the main beam in the u and v planes, respectively. Once the sidelobe region different scan angles (Nθ = 15, Nφ = 91) uniformly distributed inside the circular sector hasthrough been selected the following for a desired equations: (u0,v0) direction, the ASLL is calculated by averaging all of the array’s radiation pattern values inside the sidelobe region. Moreover, since the array can steer the main beam inside a circular area (FigureNθ N2φ), we decided to evaluate the ASLL mean η = 1 ∑ ∑ ASLL(i, j) (ASLL), minimum (minASLL), and maximumASLL N θ(Nmaxφ ASLL) values by considering different scan an- i=1 j=1 (7) gles (N = 15, N = 91) uniformly distributed inside the circular sector through the following minASLL = min{ASLL(i, j)} , i = 1, 2, 3, . . . , Nθ, j = 1, 2, 3, . . . , Nφ equations: maxASLL = max{ASLL(i, j)} , i = 1, 2, 3, . . . , Nθ, j = 1, 2, 3, . . . , Nφ

N N where ASLL(i,j) represents1 the ASLL when the array main beam direction is toward the ASLL = ASLL( i, j) direction identiﬁed byNN (i,j). Theij==11 calculated ASLL mean (ηASLL), minimum (minASLL), and maximum (maxASLL) values are illustrated in Figures9 and 10. Speciﬁcally, Figure9 high-(7) minASLL = minASLL( i , j) , i = 1,2,3,..., N , j = 1,2,3,..., N lights the ASLL statistical comparison in the event that the sidelobe region is represented by the intersectionmax betweenASLL = max EquationASLL( i (6) , j) and , i = the 1,2,3,...,u–v points N , j inside = 1,2,3,..., the unit N radio’s circle, whereas the ASLL assessment of Figure 10 takes into account a sidelobe region represented

SensorsSensors 20212021,, 2121,, xx FORFOR PEERPEER REVIEREVIEWW 1010 ofof 2020

wherewhere ASLL(ASLL(ii,,jj)) representsrepresents thethe ASLLASLL whenwhen thethe arrayarray mainmain beambeam directiondirection isis towardtoward thethe directiondirection identifiedidentified byby ((ii,,jj).). TheThe calculatedcalculated ASLLASLL meanmean ((ASLLASLL),), minimumminimum ((minminASLLASLL)),, andand max-max- imumimum ((maxmaxASLLASLL)) valuesvalues areare illustratedillustrated inin FigureFiguress 99 andand 1010.. SpecificallySpecifically,, FigureFigure 99 highlightshighlights thethe ASLLASLL statisticalstatistical comparisoncomparison inin thethe eventevent thatthat thethe sidelobesidelobe regionregion isis representedrepresented byby thethe Sensors 2021, 21, 3202 10 of 20 intersectionintersection betweenbetween EEquationquation Error!Error! ReferenceReference sourcesource notnot found.found. andand thethe uu––vv pointspoints insideinside thethe unitunit radioradio’’ss circle,circle, whereaswhereas thethe ASLLASLL assessmentassessment ofof FigureFigure 1010 takestakes intointo accountaccount aa side-side- lobelobe region region represented represented by by the the intersection intersection between between equation equation Error!Error!by the ReferenceReference intersection sourcesource between notnot found.found. Equation andand (6) thethe and uu––vv the pointspointsu–v pointsinsideinside the insidethe circularcircular the circular sectorsector cellcell sector shownshown cell ininshown Error!Error! in ReferenceReference Figure2. sourcesource notnot found.found...

FigureFigureFigure 9.9. 9. ASLLASLLASLL statisticalstatistical statistical comparisoncomparison of of square square andand equilateralequilateral triangulartriangular lattices latticeslattices by byby considering consideringconsidering the thethewhole wholewhole visible visiblevisible region. region.region.

FigureFigureFigure 10.10. 10. ASLLASLLASLL statisticalstatistical statistical comparisoncomparison comparison ofof of squaresquare square andand and equilateralequilateral equilateral triangulartriangular triangular latticeslattices lattices byby by consideringconsidering considering thethethe circularcircular circular sectorsector sector cell.cell. cell.

ByByBy lookinglooking looking atat at FigureFigure Figuresss 99 andand 1010 itit is isis evident evidentevident thatthat thethe useuse ofof triangulartriangular latticeslattices inin planarplanar antennaantennaantenna arraysarrays outperforms outperforms thatthat ofof squaresquaresquare ones onesones from fromfrom a aa statistical statisticalstatistical point pointpoint of ofof view, view,view, in inin terms termsterms of ASLL. The better performance of triangular lattices is highlighted by a lower ASLL mean ofof ASLL.ASLL. TheThe betterbetter performanceperformance ofof triangulartriangular latticeslattices isis highlightedhighlighted byby aa lowerlower ASLLASLL value, a reduced minimum value, and a similar maximum value. Speciﬁcally, triangular meanmean value,value, aa reducreduceded minimumminimum value,value, andand aa similarsimilar maximummaximum value.value. Specifically,Specifically, trian-trian- lattices allow for a percentage reduction of the ASLL mean value (ηASLL) of 1–2% within the gulargular lattices lattices allow allow for for a a percentagepercentage reductionreduction ofof the the ASLLASLL meanmean valuevalue ((ASLLASLL)) ofof 11––2%2% desired bandwidth, compared to square lattices, when considering the whole visible region. withinwithin thethe desireddesired bandwidth,bandwidth, comparedcompared toto squaresquare lattices,lattices, whenwhen consideringconsidering thethe wholewhole The ASLL superiority of triangular lattices is further conﬁrmed by taking into account only visiblevisible region.region. TheThe ASLLASLL superioritysuperiority ofof triangulartriangular latticeslattices isis furtherfurther confirmedconfirmed byby takingtaking the investigated circular sector cell (Figure 10). Indeed, the ASLL mean value percentage intointo accountaccount onlyonly thethe investigatedinvestigated circularcircular sectorsector cellcell ((FigureFigure 1010).). Indeed,Indeed, thethe ASLLASLL meanmean reduction in triangular lattices compared to square lattices turns out to be between 3.5% valuevalue percentagepercentage reductionreduction inin triangulartriangular latticeslattices comparedcompared toto squaresquare latticeslattices turnsturns outout toto and 4.5%. This feature is attractive for 5G massive MIMO systems, since it allows for a bebe betweenbetween 3.5%3.5% andand 4.5%.4.5%. ThisThis featurefeature isis attractiveattractive forfor 5G5G massivemassive MIMOMIMO systems,systems, sincesince reduction in both the intra-cell and inter-cell interference. Since lateral lobes related to itit allowsallows forfor aa reductionreduction inin bothboth thethe intraintra--cellcell andand interinter--cellcell interference.interference. SinceSince laterallateral lobeslobes the main beam pointing at one user generate interference for all other users served within relatedrelated toto thethe mainmain beambeam pointingpointing atat oneone useruser generategenerate interferenceinterference fforor allall otherother usersusers the same time–frequency resource, the lower ASLL guaranteed by a triangular lattice is served within the same time–frequency resource, the lower ASLL guaranteed by a trian- servedappealing within for the use same in a HAPS time– 5Gfrequency massive resource, MIMO system. the lower ASLL guaranteed by a trian- gulargular latticelattice isis appealingappealing forfor useuse inin aa HAPSHAPS 5G5G massivemassive MIMOMIMO system.system. 3. Phased Array Comparison of Triangular and Square Lattices In this section, a planar array composed of 64 elements (8 × 8) is analyzed to better emphasize the advantages of using a triangular lattice. The full-wave electromagnetic simulations were carried out using Ansys HFSS [44]. Each single element consists of a square patch antenna printed on a 0.7 mm thick grounded dielectric layer (RO5880), fed through a coaxial cable. As mentioned in the previous section, the minimum antenna element spacing Sensors 2021, 21, x FOR PEER REVIEW 11 of 20

3. Phased Array Comparison of Triangular and Square Lattices In this section, a planar array composed of 64 elements (8 × 8) is analyzed to better emphasize the advantages of using a triangular lattice. The full-wave electromagnetic simulations were carried out using Ansys HFSS [44]. Each single element consists of a square patch antenna printed on a 0.7 mm thick grounded dielectric layer (RO5880), fed through Sensors 2021, 21, 3202 11 of 20 a coaxial cable. As mentioned in the previous section, the minimum antenna element spacing for a square lattice is 5.17 mm (0.508 HF), whereas the equilateral triangular grid provides a minimum element distance of 5.97 mm (0.587 HF). Since antennafor array a square design lattice is isbeyond 5.17 mm the (0.508 scopeλHF of), whereasthis paper, the equilateralthe lattice triangularcomparison grid provides a minimum element distance of 5.97 mm (0.587 λ ). as a function of frequency was pursued by tuning the antennaHF array elements to be Since antenna array design is beyond the scope of this paper, the lattice comparison as matched in one narrowbanda function of frequency was band pursued at time by. tuningThe finite the antenna array with array 64 elements elements to be, matched with the antenna elementsin one narrowband tuned to frequency29.5 GHz, band is illustrated at time. The in Figure ﬁnite array 11. Specifically, with 64 elements, the with the x–z plane representsantenna the E elements-plane of tuned the array to 29.5, whereas GHz, is illustrated y–z represents in Figure the 11 H.- Speciﬁcally,plane. At the the x–z plane beginning, the mutualrepresents coup theling E-plane (Sij) among of the array,antenna whereas elementsy–z represents was addressed. the H-plane. The Atsimu- the beginning, lated mutual couplingthe mutual average coupling value (S (ij)Sij among) among antenna antenna elements elements was addressed., and the Themaximum simulated mutual mutual coupling ascoupling a function average of valuethe frequency (ηSij) among, are antenna illustrated elements, in Table and the 2. maximum It can be mutual seen coupling that a triangular latticeas a function enables of us the to frequency, considerably are illustratedreduce both in Tablethe mutual2. It can coupling be seen that aver- a triangular lattice enables us to considerably reduce both the mutual coupling average value and the age value and the maximum mutual coupling. For instance, the peak mutual coupling maximum mutual coupling. For instance, the peak mutual coupling achieved at the highest achieved at the highestfrequency frequency (29.5 GHz) (29.5 with GHz) a square with latticea square (−14.4 lattice dB) turns(–14.4 out dB) to turns be worse out than to the peak be worse than the mutualpeak mutual coupling coupling achieved achieved at the lowest at the frequency lowest frequency (24.25 GHz) (24.25 for theGHz) triangular for lattice the triangular latticeplanar planar array array (−14.91 (−14.91 dB). IndB). general, In general, the mutual the mutual coupling coupling difference difference between triangular between triangularand and square square lattices lattice iss more is more pronounced pronounced at the at lowest the lowest frequencies, frequencies and then, and the coupling then the coupling differencedifference tends tend tos to reduce reduce with with the increasethe increas in frequency.e in frequency.

(a) (b)

FigureFigure 11. 11.Planar Planar array array with with 64 elements 64 elements arranged arranged with (a) with an equilateral (a) an equilateral triangular triangular lattice; and lattice; (b) a square and lattice.(b) a square lattice. Table 2. Simulated mutual coupling average values (ηSij) among antenna elements and the maximum value comparison in dB between triangular and square lattice planar arrays composed of 64 elements Table 2. Simulated mutual coupling average values (Sij) among antenna elements and the maxi- (8 × 8). mum value comparison in dB between triangular and square lattice planar arrays composed of 64 elements (8 × 8). 24.25 GHz 26.875 GHz 29.5 GHz Tri Squ Tri Squ Tri Squ 24.25 GHz 26.875 GHz 29.5 GHz ηSij −48.6 −42.52 −49.35 −44.8 −50.74 −46.2 TriMax( Sij) Squ− 14.91 Tri−11.84 −Squ15.62 −12.55Tri −16.9Squ −14.4

Sij −48.6 −42.52 −49.35 −44.8 −50.74 −46.2 One of the detrimental effects of mutual coupling is the variation of the antenna Max(Sij) −14.91elements’ input−11.84 impedance −15.62 during beam−12.55 steering. The−16.9 impact of the−14.4 employed array lattice on active Sii parameters (i = 1, ... ,64) was evaluated from a statistical point of view One of the detrimentalthrough the effects cumulative of mutual distribution coupling function is the (CDF) variation of the of active the antennaSii of all ofele- the antenna ments’ input impedancearray elements during during beam thesteering. coverage. The From impact Figure of the12, aemployed better statistical array behaviorlattice of active on active Sii parametersSii parameters (i = 1,…,64) in triangular was evaluated lattice than from in a square statistical one ispoint clearly of recognizable.view through Indeed, the the cumulative distributiontriangular lattice,function thanks (CD toF) a of lower the active mutual S couplingii of all of (Table the antenna2), provides array an averageele- value of the active S of around 13.8 dB within the investigated frequencies, whereas the square ments during the coverage. Fromii Figure 12, a better statistical behavior of active Sii pa- one is characterized by a mean value between −11.8 dB and −12.5 dB. rameters in triangular lattice than in square one is clearly recognizable. Indeed, the triangular lattice, thanks to a lower mutual coupling (Table 2), provides an average value of

Sensors 2021, 21, x FOR PEER REVIEW 12 of 20

the active Sii of around 13.8 dB within the investigated frequencies, whereas the square Sensors 2021, 21, 3202 one is characterized by a mean value between −11.8 dB and 12−1 of2.5 20 dB. Sensors 2021, 21, x FOR PEER REVIEW 12 of 20

the active Sii of around 13.8 dB within the investigated frequencies, whereas the square one is characterized by a mean value between −11.8 dB and −12.5 dB.

Figure 12. Active Sii CDF for square and equilateral triangular lattice planar arrays composed of 64 Figure 12. Active Sii CDF for square and equilateral triangular lattice planar arrays composed of elementsFigure at 12.24.25 Active and 29.5 SGHz.ii CDF for square and equilateral triangular lattice planar arrays composed of 64 64 elements at 24.25 and 29.5 GHz. elements at 24.25 and 29.5 GHz. ToTo further further emphasize emphasize the the superior superior robustness robustness of of the the antenna antenna elements’ elements’ impedance impedance  variationvariation when when using using a triangular a triangular lattice, lattice, the the simulated simulated array array matching matching efficiency efficiency ( (η)Γ was) was evaluatedevaluatedTo for forfurther all all of of the the investigatedemphasize investigated steering steering the anglessuperior angles by, by, using using robustness the the following following of equation: equation: the antenna elements’ impedance variation when using a triangular64 lattice, the simulated array matching efficiency () was 64 2 1− S 2 evaluated for all of the investigated∑ (1 − |S iisteeringii| ) angles by, using the following equation: i=i=1 (8) ηΓ== (8) 6464 64 2 The color maps of Figure 13 confirm the advantages of adopting triangular lattices in The color maps of Figure 13 confirm the advantages of adopting1− triangularSii lattices in planar arrays, rather than square ones, in that they provide higher( efficiency) values for all planar arrays, rather than square ones, in that they provide higheri=1 efficiency values for all (8) investigated frequencies (24.25–29.5 GHz). Specifically, the triangular lattice provides a investigated frequencies (24.25–29.5 GHz). Specifically, the= triangular lattice provides a higherhigher match matchinging efficiency efficiency value value than than the the square square lattice lattice for for all all of of the the64 investigated investigated steering steering ◦ ◦ angles,angles, except except around around  φ= 90°= 90 planeplane (H (H-plane-plane of ofthe the array) array) for for  θanglesangles greater greater than than 40°. 40 In. In particular,particular,The the the color triangular triangular maps lattice lattice of shows showsFigure a better a better 13 matchingconfirm matching efficiency efficiencythe advantages in inapproxim approximatelyately of adopting90% 90% triangular lattices in of the covered area within the addressed frequency band. ofplanar the covered arrays, area within rather the addressedthan square frequency ones, band. in that they provide higher efficiency values for all investigated frequencies (24.25–29.5 GHz). Specifically, the triangular lattice provides a higher matching efficiency value than the square lattice for all of the investigated steering angles, except around  = 90° plane (H-plane of the array) for  angles greater than 40°. In particular, the triangular lattice shows a better matching efficiency in approximately 90% of the covered area within the addressed frequency band.

(a) (b) (c)

Figure 13. Cont.

(a) (b) (c)

Sensors 2021, 21, x FOR PEER REVIEW 13 of 20

Sensors 2021, 21, 3202 13 of 20 Sensors 2021, 21, x FOR PEER REVIEW 13 of 20

(d) (e) (f)

Figure 13. Matching efficiency () of a planar array composed of 64 elements (8 × 8) as a function of the main beam (d) (e) (f) steering inside the circular angular sector (−60° ≤ 0 ≤ 60°, 0° ≤ 0 ≤ 180°). Equilateral triangular lattice at (a) 24.25 GHz,

(b) 26.875 GHz, and Figure(cFigure) 29.5 13. GHz; 13. MatchingMatching square efficiency lattice efﬁciency at ( ( (dη)) Γ of24.25) ofa planar a GHz, planar array (e array) 26.875 composed composed GHz, of and of64 64 elements(f elements) 29.5 GHz. (8 (8 × × 8) 8)as asa function a function of ofthe the main main beam beam steering inside the circular angular sector (−60°◦ ≤ 0 ≤ 60°, ◦0° ≤◦ 0 ≤ 180°). Equilateral◦ triangular lattice at (a) 24.25 GHz, steering inside the circular angular sector (−60 ≤ θ0 ≤ 60 , 0 ≤ φ0 ≤ 180 ). Equilateral triangular lattice at (a) 24.25 GHz, (b()b 26.875) 26.875 GHz, GHz,The and and main (c ()c 29.5) 29.5reason GHz; GHz; squarethe square triangular lattice lattice at at (d lattice ()d 24.25) 24.25 ’sGHz, GHz,matching (e ()e 26.875) 26.875 efficiency GHz, GHz, and and (undergoesf ()f 29.5) 29.5 GHz. GHz. a value reduction in the principal planes for  angles close to 60° at the highest frequency is due to scan TheThe main main reason reason the the triangular triangular lattice lattice’s’s matching matching efficiency efﬁciency undergoes undergoes a value a valuereduc- re- blindness onset. This phenomenon can be observed through the active S11 parameter re- tionduction in the inprincipal the principal planes planes for  angles for θ angles close to close 60° toat the 60◦ highestat the highest frequency frequency is due isto duescan to lated to the array’s central element at the highest frequency (29.5 GHz), as a function of blindnessscan blindness onset. onset.This phenomenon This phenomenon can be can observed be observed through through the active the active S11 parameterS11 parameter re- the beam steeringlatedrelated shown to the to in thearray Figure array’s’s central 14 central. To elem emphasize elementent at the at the highest highestscan frequency blindness frequency (29.5 onset, (29.5 GHz) GHz), the, asactive asa function a function of of S11 parameter wasthethe considered beam beam steering steering during shown shown beam inin Figure steering Figure 14 14. Towithin. To emphasize emphasize the whole the the scan visible scan blindness blindness region. onset, More onset, the the active active in detail, the colorS11S maps11parameterparameter highlight was was considered that considered the triangular during during beam beam lattice steering steering does within not within avoid the the whole the whole scan visible visible blind- region. region. More More ness onset—characterizedinin detail, detail, the theby color colora strong maps maps antennahighlight highlight elementthat that the the triangular mismatch triangular lattice— latticebut does only does not reduces not avoid avoid the it the byscan scan blind- blind- pushing the involvednessness onset angular onset—characterized—characterized sector a bit by further by a strong a strong [43] antenna. antenna In fact, element elementby considering mismatch mismatch—but —thebut simulated only only reduces reduces it itby by pushingpushing the the involved involved angular angular sector sector a abit bit further further [43] [43. ].In In fact, fact, by by considering considering the the simulated simulated phased array in the event of beam steering, the square lattice provides an active S11 higher phasedphased array array in in the the event event of of beam beam steering steering,, the the square square lattice lattice provides provides an an active active S11S11 higherhigher than –dB within the angular ranges || > 60°,  < 60°, and◦  > 120◦ ° (Figure 14◦b). On thanthan – –10dBdB within within the the angular angular range rangess | |θ|0| > >60 60°, , φ <0 <60 60°, and, and φ >0 120> 120° (Figure(Figure 14 14b).b). On On the other hand, the triangular lattice presents a milder mismatch of the central element for thethe other other hand hand,, the the triangular triangular lattice lattice presents presents a milder a milder mismatch mismatch of of the the central central element element for for || > 60°,  < 30°,  >150°◦, and 80°<◦  < 100°◦ (Figure◦ 14a). Moreover,◦ by considering the |||θ 0>| 60° > 60, , <φ 300 <°,30  >150, φ0 >150°, and, 80°< and 80 << 100°φ0 < ( 100Figure(Figure 14a). Moreover,14a). Moreover, by considering by considering the  ◦ angular sector withangularthe | angular| sector > 60° sector —withhence | with|, >outside | 60°θ0|— >hence 60 the—hence, ,desired outside outside scanthe desired angle the desired scanarea angle scan(highlighted angle area ( areahighlighted by (highlighted by dashed red linesdashed)—bythe dashed redtriangular lines red) lines)—the— thelattice triangular presents triangular lattice an lattice Spresents11 central presents an array S11 ancentral elementS11 central array higher element array than element higher higherthan −dB in 40 % of− casesthandB in−, whereas10dB 40 % inof 40cases the % ofsquare, whereas cases, lattice whereas the square does the solattice square in 50 does lattice % ofso does cases.in 50 so % inof 50cases. % of cases.

(a) (b) (a) (b) Figure 14. Active S11 parameter related to the central array element as a function of beam steering for a planar array composed of 64 elements with (a) a triangular lattice; and (b) a square lattice. FigureFigure 14. Active 14. ActiveS11 parameter S11 parameter related related to the central to the arraycentral element array element as a function as a offunction beam steering of beam for steering a planar array for a planar array composed of 64 elements with (a) a triangular lattice; and (b) a square lattice. composed of 64 elements with (Witha) a triangular the aim lattice;of evaluating and (b) a the square impact lattice. of the antenna array lattice on the radiation  patternWith shape, the the aim realized of evaluating gain as the a function impact of of the the antenna angle arrayat a broadside lattice on thedirection radiation is With the aimreported of evaluating in Figure the15. impact of the antenna array lattice on the radiation pattern shape, thepattern realized shape, gain the as realizeda function gain of as the a function  angle of at the a θbroadsideangle at a direction broadside is direction is reported in Figure 15. reported in Figure 15.

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(a) (b)

FigureFigure 15. Simulated 15. Simulated realized realized gain for gain a planar for a arrayplanar composed array composed of 64 elements of 64 atelements a broadside at a broadside direction: ( adi-) 24.25 GHz φ = 0◦rection:;(b) 24.25 (a) GHz 24.25φ =GHz 90◦;( c =) 29.50°; ( GHzb) 24.25φ = 0GHz◦; and  (=d 90°;) 29.5 (c GHz) 29.5φ =GHz 90◦ . = 0°; and (d) 29.5 GHz  = 90°.

Figure 15 conﬁrms that a triangular lattice provides a narrower main beam in the Figure 15 confirms ◦that a triangular lattice provides a narrower main beam in the = 90° plane, thus providingφ = 90 plane,a higher thus maximum providing gain a higher and better maximum angular gain resolution. and better Moreo- angular resolution. Moreover, a triangular lattice leads to comparable cross-polar levels to square one in ver, a triangular lattice leads to comparable cross-polar levels to square one in the  = 90° the φ = 90◦ plane, whereas it introduces a slight degradation in the E-plane of the array plane, whereas it (Figureintroduces 15a,c)—although a slight degradation a cross-polar in level the E of-plane about of 50 the dB around array ( theFigure mean beam is 15a,c)—although astill cross guaranteed.-polar level of about 50 dB around the mean beam is still guaranteed. 4. Massive MIMO Performance Evaluation 4. Massive MIMO PerformanceThe comparison Evaluation of triangular and square lattices was carried out in terms of array S The comparisongain, of ASLL, triangular active andii parameters, square lattice and matchings was carried efﬁciency, out byin consideringterms of array a circular sector in which to serve users. However, one of the key factors that will allow us to drastically gain, ASLL, active Sii parameters, and matching efficiency, by considering a circular sector improve the data throughput of the upcoming 5G wireless technology will be the use in which to serve users.of massive However, MIMO one technology of the key capable factors of servingthat will different allow us users to drastically within the same time– improve the data throughputfrequency resource of the through upcomin multibeamg 5G wireless radiation technology patterns. In will general, be the various use of beamforming massive MIMO technologymethods are cap availableable of forserv theing achievement different users of a multibeam within the system same [10 time,45,46–fre-]. quency resource throughLet multibeam us consider aradiation HAPS equipped pattern withs. In an general, array of Mvarious= 64 (8 beamforming× 8) antenna elements that methods are availableserves forK theconcurrent achieve groundment o users,f a multibeam equipped withsystem a single [10,45,46] isotropic. antenna, located inside Let us considerthe a above-mentionedHAPS equipped circular with an angular array sectorof M = (Figure 64 (8 2×), 8) through antenna a multibeamelements radiation that serves K concurrentpattern ground in a line-of-sight users, equipped (LOS) scenario. with a Thesingle assumption isotropic of antenna a LOS channel, located is consistent since, at mm-wave, the LOS ray represents the predominant mode of propagation between inside the above-mentioned circular angular sector (Error! Reference source not found.), the base station (BS) and the users, due to large path loss as well as the use of high- through a multibeamgain radiation antennas pattern [47,48]. Furthermore,in a line-of-sight the LOS(LOS) channel scenario condition. The assumption turns out to be further of a LOS channel isemphasized consistent since, in the caseat mm of- HAPSwave, wireless the LOS communication ray represents [49 the]. predominant mode of propagation betweenThe received the signal-to-interference-plus-noisebase station (BS) and the users ratio, due (SINR) to large for the pathnth userloss in case of a as well as the use ofmulti-user high-gain scenario antennas can be[47,48] written. Furthermore, as [40,50,51]: the LOS channel condition turns out to be further emphasized in the case of HAPS wireless communication [49]. δηΓ(θn, φn)G(θn, φn) SINR = th (9) The received signal-to-interference-plus-noisen ratioK (SINR) for the n user in case of 2 a multi-user scenario can be written as [40,50,51]: δ ∑ G(θi, φi)|hi ∗ Wn| + 1 i=1

 ( n,,  n)G(  n  n ) SINRn = K 2 (9) G( i,  i) h i * W n + 1 i=1

where G(n,n) represents the HAPS array’s gain toward the nth user located at (n,n);  represents the ratio between the transmitted power (Pt) and the noise power (0); hn ϵ 1×M

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(n = 1,2,..,K) corresponds to the channel propagation between the nth user and the HAPS Sensors 2021, 21, 3202 antenna array; and wn ϵ M×1 consists of the precoding vector that, in general,15 depends of 20 on the selected beamforming method. It is worth noting that, differently from Reference [37], the simulated matching efficiency () was included in th Error!where ReferenceG(θn,φn) represents source not the found. HAPS array’s in order gain to toward achieve the a nmoreuser accurate located SINR at (θn, φestimaten); δ . To evaluaterepresents the the system ratio between quality the of transmitted service, powera maximum (Pt) and r theatio noise (MR) power precodi (σ0);nghn technique1×M [2] with(n = 1,2,..,a perfectK) corresponds channel s totate the i channelnformation propagation (CSI) was between assumed the nth inuser the and following the HAPS analysis. However,antenna array; it is andworthwn notingM×1 consiststhat more of the efficient precoding precoding vector that, and in combining general, depends algorithms on able tothe reduce selected interference beamforming could method. be exploited It is worth [52] noting but, that, in general, differently they from require Reference more [37 complex-], the simulated matching efficiency (η ) was included in (9) in order to achieve a more ity and turn out to be more sensitiveΓ to channel estimation error. Additionally, since array accurate SINR estimate. To evaluate the system quality of service, a maximum ratio (MR) elementsprecoding’ mutual technique coupling [2] with (MC) a perfect under channelmines state the informationMIMO performance (CSI) was [53] assumed due to in the unwantedthe following correlation analysis. among However, elements, it is worththe channel noting matri that morex H is efficient modelled precoding as [54]: and combining algorithms able to reduce interference could beH exploited [52] but, in general, they require more complexity and turnH=− out H to0 ( beImxm more SS sensitive) to channel estimation (10) error. Additionally, since array elements’ mutual coupling (MC) undermines the MIMO whereperformance H0 ϵ K [ 53× ]M due denotes to the unwantedthe complex correlation channel among gain elements,among the the users channel and matrix the HAPSH an- tennais modelled elements as [54 in]: the absence of antenna mutual coupling; Im×m is an identity matrix; and H S ϵ M×M corresponds to the scatteringH = H0 parametersImxm − SS matrix of the HAPS planar (10)array. Un- like [37], the channel matrix was evaluated by taking into account in where H K × M denotes the complex channel gain among the users and the HAPS Error! Reference0 source not found. the full-wave simulation of the planar array, and not antenna elements in the absence of antenna mutual coupling; Im×m is an identity matrix; justand theS antennaM×M corresponds element distance to the scattering. Once the parameters SINR is matrixknown, of the the HAPSmaximum planar achievable array. bi- trateUnlike over [37 ],1 Hz the channelof bandwidth matrix wasfor the evaluated nth user, by which taking is into the account spectral in e (10)fficiency the full-wave (SE) per user, is:simulation of the planar array, and not just the antenna element distance. Once the SINR is known, the maximum achievable bitrate over 1 Hz of bandwidth for the nth user, which is the spectral efficiency (SE) per user, is:SEnn=+log2 ( 1 SINR ) (11) = ( + ) For the SE assessment bothSE nthe logsimulated2 1 SINR arrayn gain and the S-matrix of (11)the planar arrayFors shown the SE in assessment Figure 11 bothwere the used. simulated Furthermore array gain, 10 and,000 thesetSs -matrixof K-concurrent of the planar users ran- domlyarrays showndistributed in Figure inside 11 thewere circular used. Furthermore,sector were 10,000adopted. sets It of isK -concurrentworth observing users that a smartrandomly user’s distributed selection inside inside the the circular sectorsector can improve were adopted. the massive It is worth MIMO observing performance that and thea smart energy user’s efficiency selection of inside the wireless the sector communication can improve the [55] massive. However, MIMO this performance aspect was ne- glectedand the, energysince the efficiency main goal of the of wireless the paper communication is to highlight [55]. the However, performance this aspect difference was s be- tweenneglected, square since and the triangular main goal lattice of thes paper. The achievable is to highlight SE as the a performancefunction of the differences  value, which between square and triangular lattices. The achievable SE as a function of the δ value, is the ratio between the transmitted power (Pt) and the noise power (0), is reported in P Figurewhich is16 the for ratio both between square the and transmitted triangular power lattice ( ts) andin the the event noise powerof eight (σ 0simultaneous), is reported users in Figure 16 for both square and triangular lattices in the event of eight simultaneous users inside the investigated circular sector. inside the investigated circular sector.

FigureFigure 16. 16. SESE comparison forfor a a planar planar array array composed composed of 8of× 8 8× elements,8 elements, in casesin cases of square of square and and triangulartriangular lattices,lattices, as as a a function function of of the theδ ratio  ratio in dB in indB the in event the event of 8 concurrent of 8 concurrent users. users.

It can be seen that the triangular lattice deployment of the array antenna elements allows for the achievement of a considerable improvement in the SE. The SE starts to grow

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It can be seen that the triangular lattice deployment of the array antenna elements almost linearlyalmostallows with the forlinearly increase the achievement with in the the  value,increase of a after considerable in which the  value,it reaches improvement after a superior which in theitlimit reaches SE. due The a SEsuperior starts tolimit due to the SIR, andtogrow the the system almostSIR, and becomes linearly the system withinterference the becomes increase limited. ininterferencethe Therefore,δ value, lonceimited. after the which Therefore,upper it reaches SE once a superior the upper SE boundary is reached,boundarylimit due further to is thereached, increasing SIR, and further the the transmitted system increasing becomes power the interferencetransmitteddoes not represent limited. power an does Therefore, effi- not represent once the an efficient way of improvingcientupper way SE the boundary of SE. improving The is improved reached, the SE. furtherSE Thein the increasingimproved triangular the SE lattice transmitted in the array triangular is power apparentdoes lattice not array represent is apparent from looking atfroman the efﬁcient lookingstatistical way at behaviorof the improving statistical of the the CDF behavior SE. of The the improved ofSIR the (Figure CDF SE 17 inof), the theand triangular SIR both ( Figurethe lattice 17), array and isboth the average SIR (SIRapparent) and 90% from of lookingthe SIR atoccurrence the statistical (SIR behavior90%), as highlighted of the CDF in of Table the SIR 3. (Figure 17), and both average SIR (SIR) and 90% of the SIR occurrence (SIR90%), as highlighted in Table 3. the average SIR (ηSIR) and 90% of the SIR occurrence (SIR90%), as highlighted in Table3.

Figure 17. SIR CDF comparison for a planar array composed of 8x8 elements, in cases of square and triangular lattices, in the event of 8 concurrent users. FigureFigure 17. SIRSIR CDFCDF comparison comparison for for a planar a planar array array composed composed of 8x8 of elements, 8x8 elements, in cases in of squarecases of and square Table 3. Simulatedandtriangular average triangular lattices, SIR lattices,(SIR in) thein dB eventin theand of event SIR 8 concurrent90% of across 8 concurrent triangular users. users. and square lattice planar arrays composed of 64 elements (8 × 8), in the event of 8 served users inside the circular sector.

Table 3. Simulated average SIR (SIR) in dB and SIR90% across triangular and square lattice planar Table24.25 3. Simulated GHz average SIR (η26.875SIR) in dBGHz and SIR90% across29.5 triangular GHz and square lattice planar arrayarrayss composed of of 64 64 elements elements (8 ×(8 8),× 8) in, thein the event event of 8 of served 8 served users users inside inside the circular the circular sector. sector. Tri Squ Tri Squ Tri Squ 24.2524.25 GHz GHz 26.87526.875 GHz GHz 29.5 GHz29.5 GHz SIR 11.1 10 12 11.25 13.3 12.2 Tri Squ Tri Squ Tri Squ SIR90% 0.4 0 Tri 0.9 Squ 0.5 Tri 1.4 Squ 1 Tri Squ ηSIR 11.1 10 12 11.25 13.3 12.2 SIRSIR90% 0.411.1 010 0.912 0.511.25 1.413.3 1 12.2 Since to improve the SE it is better to serve more users inside the predefined sector SIR90% 0.4 0 0.9 0.5 1.4 1 cell rather than increasingSince to the improve transmitted the SE itpower is better, the to SE serve is plot moreted users as a inside function the predeﬁnedof the sector cell number of usersrather (K) thanfor both increasing triangular the transmittedand square power,lattices the in SEthe is event plotted of asa a function= 20 dB of the number (Figure 18). of usersSince (K )to for improve both triangular the SE and it is square better lattices to serve in themore event users of a insideδ = 20 dBthe (Figure predefined 18). sector cell rather than increasing the transmitted power, the SE is plotted as a function of the number of users (K) for both triangular and square lattices in the event of a  = 20 dB (Figure 18).

(a) (b)

Figure 18. (Figurea) SE comparison 18. (a) SE comparison as a function as ofa function the number of the of number users (K )of between users (K square) between and square triangular and latticetriangu- planar arrays composed oflar 64 lattice elements; planar and arrays (b) percentage composed SEof 64 improvement elements; and in the(b) eventpercentage of δ = SE 20 improvement dB. in the event of  = 20 dB. (a) (b)

Figure 18. (a) SE comparison as a function of the number of users (K) between square and triangular lattice planar arrays composed of 64 elements; and (b) percentage SE improvement in the event of  = 20 dB.

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The remarkable advantage of using a triangular lattice arrangement of the array elements instead of a square one is confirmed by observing the SE in Figure 18a. To emphasize the SE comparison, the percentage SE improvement is calculated and reported in Figure 18b. As can be seen, the achievable SE between the two lattices turns out to be comparable for few users, even if the triangular lattice’s SE is somewhat higher due to a superior array gain value (Figure8). Conversely, with the increase in the number of concurrent users, the SE improvement guaranteed by the triangular lattice array grows continuously, and reaches a value between 8.5% and 12 % in the event of 20 simultaneous users inside the sector. In view of highlighting the advantageous impact of the triangular lattice on planar arrays in massive MIMO systems, the percentage SE improvement of the most suitable triangular lattice, compared to rectangular or square lattices, is reported in Table4 for a case of 20 concurrent users deployed inside the different sector cells. Table4 confirms that, although with some performance differences, the triangular lattice turns out to be the most efficient array grid regardless of the sector cell or the adopted frequency within the considered range. It is worth observing that, in practice, a minimum user distance within the same time–frequency resource is required in order to avoid high SIR and, hence, increase the SE. However, SE improvement between triangular and square lattices remains substantially unchanged. A further analysis aimed at understanding the role of array gain and the elements’ mutual coupling (MC) was performed. The SE improvement between triangular and square lattices, as shown in Figure 18b, was recalculated under the hypothesis of having the same array gain (or the same received signal) for both of the employed lattices (20 dBi for all the frequencies), and in the case of an ideal array without MC (w/o MC).

Table 4. Percentage SE improvement offered by the most suitable triangular lattice, compared to rectangular/square lattices, in the case of planar arrays composed of 64 elements (8 × 8) for 20 served users inside the different sector cells.

SE Improvement Sector Lattice 24.25 GHz 29.5 GHz [37] Rectangular γ = 36.6◦ vs Rect 14 % 10 % This Paper Circular γ = 60◦ vs Squ 12 % 8.5 %

Figure 19a highlights how the higher array gain values, as a function of the steering angles obtained in the case of the triangular lattice planar array (Figure8), allow for an increase in the SE for just a few users (up to three). In fact, the SE improvement with the same array gain in the case of just a single user is equal to zero at all frequencies, whereas by increasing the number of concurrent users the curves are overlapped to the case of different gain values. Therefore, the higher SE provided by the triangular lattice in the event of many users is due to the better interference robustness guaranteed by the superior angular resolution. The SE improvement comparison of Figure 19b emphasizes how the MC effects contribute to a further increase in the percentage SE improvement of the triangular lattice compared to the square lattice, mainly at the lowest frequency (24.25 GHz). Conversely, the MC effect on percentage SE improvement gradually vanishes as the frequency increases, and becomes irrelevant at the highest frequency (29.5 GHz). Sensors 2021, 21, xSensors FOR PEER2021 REVIE, 21, 3202W 18 of 20 18 of 20

(a) (b)

Figure 19. PercentageFigure 19. SEPercentage improvement SE improvement as a function as of a the function number of of the users number (K) between of users square (K) between and triangular square lattice planar and triangular lattice planar arrays composed of 64 elements in the event of (a) the same HAPS arrays composed of 64 elements in the event of (a) the same HAPS array gain for all of the frequencies for both lattices; and array gain for all of the frequencies for both lattices; and (b) an ideal planar array equipped with (b) an ideal planar array equipped with 64 elements without MC (w/o MC). 64 elements without MC (w/o MC). 5. Conclusions 5. Conclusions An extensive analysis of HAPS massive MIMO systems employing triangular lattices An extensive analysis of HAPS massive MIMO systems employing triangular lattices has been presented within the 5G NR n257 and n258 frequency bands (24.25–29.5 GHz). has been presentedThe noteworthy within the 5G massive NR n257 MIMO and performance n258 frequency improvement bands (24.25 when–29.5 adopting GHz). a triangular The noteworthylattice massive arrangement MIMO performance of the array improvement elements instead when of adopting a square onea triangular in a planar array with lattice arrangementa regular of the lattice array haselements been instead highlighted. of a square Specifically, one in a a planar triangular array lattice with a allows for the regular lattice hasachievement been highlighted. of a superior Specifically, array gain a triangular and ASLL lattice reduction, allows as for well theas achiev greatere- robustness of ment of a superiorthe antenna array gain elements’ and ASLL impedance reduction variation, as well during as greater beam steeringrobustness by exploitingof the lower MC antenna elementslevels.’ impedance Moreover, variation the larger during minimum beam distance steering betweenby exploiting elements lower in MC the caselev- of a triangular els. Moreover, gridthe larger guarantees minimum a better distance angular between resolution elements that, in in the a massive case of a MIMO triangular scenario, provides grid guaranteessuperior a better interference angular resolution robustness that, and, in a hence,massive higher MIMO SE. scenario, The advantages provides offered by the superior interferenceregular robustness and periodic and triangular, hence, latticehigher arrangement SE. The advantages of antenna offered elements by makethe it appealing regular and periodicfor 5G triangular massive MIMO lattice applications.arrangement of antenna elements make it appealing for 5G massive MIMO applications. Author Contributions: Conceptualization, F.A.D.; validation, F.A.D. and S.G.; investigation, F.A.D. Author Contributionand S.G.;s: Conceptualization, writing—original F.A. draftD. preparation,; validation, F.A.D. F.A.D.; and writing—review S.G.; investigation, and editing, F.A.D. F.A.D. and S.G. and S.G.; writingAll—original authors draft have preparation, read and agreed F.A.D. to the; writing published—review version and ofediting, the manuscript. F.A.D. and S.G. All authors have read and agreed to the published version of the manuscript. Funding: Work partially supported by the Italian Ministry of Education and Research (MIUR) in the Funding: Work frameworkpartially supported of the CrossLab by the projectItalian Ministry (Departments of Education of Excellence). and Research (MIUR) in the framework of the CrossLab project (Departments of Excellence). Institutional Review Board Statement: Not applicable. Institutional Review Board Statement: Not applicable. Informed Consent Statement: Not applicable. Informed Consent Statement: Not applicable. Data Availability Statement: Not applicable. Data Availability Statement: Not applicable. Conflicts of Interest: The authors declare no conflict of interest. Conflicts of Interest: The authors declare no conflict of interest. References References 1. Larsson, E.G.; Edfors, O.; Tufvesson, F.; Marzetta, T.L. Massive MIMO for next Generation Wireless Systems. IEEE Commun. Mag. 1. Larsson, E.G.; Edfors,2014, 52 O.;, 186–195. Tufvesson, [CrossRef F.; Marzetta,] T.L. Massive MIMO for next Generation Wireless Systems. IEEE Commun. Mag. 2014, 2.52, 186Björnson,–195, doi:10.1109/MCOM.2014.6736761. E.; Hoydis, J.; Sanguinetti, L. Massive MIMO Networks: Spectral, Energy, and Hardware Efficiency. Found. 2. Björnson, E.; Hoydis,Trends®Signal J.; Sanguinetti, Process. L.2017 Massive, 11, 154–655. MIMO Networks: [CrossRef] Spectral, Energy, and Hardware Efficiency. Found. Trends® Signal Process.3. 2017Millimeter-Wave, 11, 154–655, Circuitsdoi:10.1561/2000000093. for 5G and Radar, 1st ed.; Hueber, G.; Niknejad, A.M. (Eds.) Cambridge University Press: Cambridge, UK, 3. Millimeter-Wave 2019;Circuits ISBN for 978-1-108-68639-6.5G and Radar, 1st ed.; Hueber, G., Niknejad, A.M., Eds.; Cambridge University Press Cambridge , UK, 2019; ISBN4. Lu,978- L.;1-108 Li,- G.Y.;68639 Swindlehurst,-6. A.L.; Ashikhmin, A.; Zhang, R. An Overview of Massive MIMO: Benefits and Challenges. IEEE J. 4. Lu, L.; Li, G.Y.; Swindlehurst,Sel. Top. Signal A.L.; Process. Ashikhmin,2014, 8, 742–758. A.; Zhang, [CrossRef R. An ]Overview of Massive MIMO: Benefits and Challenges. IEEE J. Sel. Top. Signal5. Dicandia, Process. 2014 F.A.;, 8 Genovesi,, 742–758, doi:10.1109/JSTSP.2014.2317671. S.; Monorchio, A. Analysis of the Performance Enhancement of MIMO Systems Employing Circular 5. Dicandia, F.A.; Genovesi,Polarization. S.; Monorchio,IEEE Trans. A. Antennas Analysis Propag. of the2017 Performance, 65, 4824–4835. Enhancement [CrossRef of] MIMO Systems Employing Circular Polarization. IEEE Trans. Antennas Propag. 2017, PP, 1–1, doi:10.1109/TAP.2017.2723083.

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