Spectral Efficiency Improvement of 5G Massive MIMO Systems for High-Altitude Platform Stations by Using Triangular Lattice Arrays
<p>Examples of several scenarios where HAPSs can be exploited.</p> "> Figure 2
<p>Circular sector cell in the <span class="html-italic">u–v</span> plane within which the HAPS antenna array has to steer the main beam to serve the 5G users.</p> "> Figure 3
<p>Planar antenna array with a triangular lattice.</p> "> Figure 4
<p>Elements’ spacing (<span class="html-italic">d<sub>x</sub></span>, <span class="html-italic">d<sub>y</sub></span>), the antenna elements’ distance (<span class="html-italic">D</span>), and its minimum (<span class="html-italic">d</span><sub>0</sub>) as a function of the γ value for a triangular lattice array in the event of <span class="html-italic">R</span> = 1.1.</p> "> Figure 5
<p>RP in the case of an antenna array with 8 × 8 isotropic elements arranged in a triangular lattice in the event of (<b>a</b>) γ = 30°, and (<b>b</b>) γ = 60°. The red circle represents the visible region, whereas the black circle highlights the circular sector cell.</p> "> Figure 6
<p>Angular average gain (<span class="html-italic">η<sub>Gain</sub></span>) as a function of the γ value within the working frequencies (24.25 –29.5 GHz) in the case of a triangular lattice planar array of 8 × 8 elements.</p> "> Figure 7
<p>Array geometry of a planar array of 64 elements (8 × 8) in a triangular lattice (γ = 60°) and a square lattice.</p> "> Figure 8
<p>Gain in dBi of a planar array composed of 64 elements (8 × 8 array) as a function of the main beam steering inside the circular angular sector (−60°<math display="inline"><semantics> <mrow> <mo> </mo> <mo>≤</mo> <mo> </mo> </mrow> </semantics></math><span class="html-italic">θ<sub>0</sub></span><math display="inline"><semantics> <mrow> <mo> </mo> <mo>≤</mo> <mo> </mo> </mrow> </semantics></math> 60°<span class="html-italic">,</span> 0°<math display="inline"><semantics> <mrow> <mo> </mo> <mo>≤</mo> <mo> </mo> </mrow> </semantics></math> <span class="html-italic">ϕ<sub>0</sub></span><math display="inline"><semantics> <mrow> <mo> </mo> <mo>≤</mo> <mo> </mo> </mrow> </semantics></math> 180°). Equilateral triangular lattice at (<b>a</b>) 24.25 GHz, (<b>b</b>) 26.875 GHz, and (<b>c</b>) 29.5 GHz; square lattice at (<b>d</b>) 24.25 GHz, (<b>e</b>) 26.875 GHz, and (<b>f</b>) 29.5 GHz.</p> "> Figure 8 Cont.
<p>Gain in dBi of a planar array composed of 64 elements (8 × 8 array) as a function of the main beam steering inside the circular angular sector (−60°<math display="inline"><semantics> <mrow> <mo> </mo> <mo>≤</mo> <mo> </mo> </mrow> </semantics></math><span class="html-italic">θ<sub>0</sub></span><math display="inline"><semantics> <mrow> <mo> </mo> <mo>≤</mo> <mo> </mo> </mrow> </semantics></math> 60°<span class="html-italic">,</span> 0°<math display="inline"><semantics> <mrow> <mo> </mo> <mo>≤</mo> <mo> </mo> </mrow> </semantics></math> <span class="html-italic">ϕ<sub>0</sub></span><math display="inline"><semantics> <mrow> <mo> </mo> <mo>≤</mo> <mo> </mo> </mrow> </semantics></math> 180°). Equilateral triangular lattice at (<b>a</b>) 24.25 GHz, (<b>b</b>) 26.875 GHz, and (<b>c</b>) 29.5 GHz; square lattice at (<b>d</b>) 24.25 GHz, (<b>e</b>) 26.875 GHz, and (<b>f</b>) 29.5 GHz.</p> "> Figure 9
<p>ASLL statistical comparison of square and equilateral triangular lattices by considering the whole visible region.</p> "> Figure 10
<p>ASLL statistical comparison of square and equilateral triangular lattices by considering the circular sector cell.</p> "> Figure 11
<p>Planar array with 64 elements arranged with (<b>a</b>) an equilateral triangular lattice; and (<b>b</b>) a square lattice.</p> "> Figure 12
<p>Active <span class="html-italic">S<sub>ii</sub></span> CDF for square and equilateral triangular lattice planar arrays composed of 64 elements at 24.25 and 29.5 GHz.</p> "> Figure 13
<p>Matching efficiency (<span class="html-italic">η</span><sub>Γ</sub>) of a planar array composed of 64 elements (8 × 8) as a function of the main beam steering inside the circular angular sector (−60°<math display="inline"><semantics> <mrow> <mo> </mo> <mo>≤</mo> <mo> </mo> </mrow> </semantics></math><span class="html-italic">θ<sub>0</sub></span><math display="inline"><semantics> <mrow> <mo> </mo> <mo>≤</mo> <mo> </mo> </mrow> </semantics></math> 60°<span class="html-italic">,</span> 0°<math display="inline"><semantics> <mrow> <mo> </mo> <mo>≤</mo> <mo> </mo> </mrow> </semantics></math> <span class="html-italic">ϕ<sub>0</sub></span><math display="inline"><semantics> <mrow> <mo> </mo> <mo>≤</mo> <mo> </mo> </mrow> </semantics></math> 180°). Equilateral triangular lattice at (<b>a</b>) 24.25 GHz, (<b>b</b>) 26.875 GHz, and (<b>c</b>) 29.5 GHz; square lattice at (<b>d</b>) 24.25 GHz, (<b>e</b>) 26.875 GHz, and (<b>f</b>) 29.5 GHz.</p> "> Figure 13 Cont.
<p>Matching efficiency (<span class="html-italic">η</span><sub>Γ</sub>) of a planar array composed of 64 elements (8 × 8) as a function of the main beam steering inside the circular angular sector (−60°<math display="inline"><semantics> <mrow> <mo> </mo> <mo>≤</mo> <mo> </mo> </mrow> </semantics></math><span class="html-italic">θ<sub>0</sub></span><math display="inline"><semantics> <mrow> <mo> </mo> <mo>≤</mo> <mo> </mo> </mrow> </semantics></math> 60°<span class="html-italic">,</span> 0°<math display="inline"><semantics> <mrow> <mo> </mo> <mo>≤</mo> <mo> </mo> </mrow> </semantics></math> <span class="html-italic">ϕ<sub>0</sub></span><math display="inline"><semantics> <mrow> <mo> </mo> <mo>≤</mo> <mo> </mo> </mrow> </semantics></math> 180°). Equilateral triangular lattice at (<b>a</b>) 24.25 GHz, (<b>b</b>) 26.875 GHz, and (<b>c</b>) 29.5 GHz; square lattice at (<b>d</b>) 24.25 GHz, (<b>e</b>) 26.875 GHz, and (<b>f</b>) 29.5 GHz.</p> "> Figure 14
<p>Active <span class="html-italic">S<sub>11</sub></span> parameter related to the central array element as a function of beam steering for a planar array composed of 64 elements with (<b>a</b>) a triangular lattice; and (<b>b</b>) a square lattice.</p> "> Figure 15
<p>Simulated realized gain for a planar array composed of 64 elements at a broadside direction: (<b>a</b>) 24.25 GHz <span class="html-italic">ϕ</span> = 0°; (<b>b</b>) 24.25 GHz <span class="html-italic">ϕ</span> = 90°; (<b>c</b>) 29.5 GHz <span class="html-italic">ϕ</span> = 0°; and (<b>d</b>) 29.5 GHz <span class="html-italic">ϕ</span> = 90°.</p> "> Figure 16
<p>SE comparison for a planar array composed of 8 × 8 elements, in cases of square and triangular lattices, as a function of the <span class="html-italic">δ</span> ratio in dB in the event of 8 concurrent users.</p> "> Figure 17
<p>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.</p> "> Figure 18
<p>(<b>a</b>) SE comparison as a function of the number of users (<span class="html-italic">K</span>) between square and triangular lattice planar arrays composed of 64 elements; and (<b>b</b>) percentage SE improvement in the event of <span class="html-italic">δ</span> = 20 dB.</p> "> Figure 19
<p>Percentage SE improvement as a function of the number of users (<span class="html-italic">K</span>) between square and triangular lattice planar arrays composed of 64 elements in the event of (<b>a</b>) the same HAPS array gain for all of the frequencies for both lattices; and (<b>b</b>) an ideal planar array equipped with 64 elements without MC (w/o MC).</p> ">
Abstract
:1. Introduction
2. Triangular vs. Square Lattice Planar Arrays
3. Phased Array Comparison of Triangular and Square Lattices
4. Massive MIMO Performance Evaluation
5. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
References
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24.25 GHz | 26.875 GHz | 29.5 GHz | ||||
---|---|---|---|---|---|---|
Tri | Squ | Tri | Squ | Tri | Squ | |
ηGain | 21.38 | 20.77 | 22.18 | 21.57 | 22.87 | 22.28 |
σ2Gain | 0.89 | 0.83 | 0.97 | 0.9 | 1.12 | 0.99 |
minGain | 19.17 | 18.73 | 19.81 | 19.38 | 20.24 | 19.83 |
maxGain | 22.42 | 21.78 | 23.26 | 22.61 | 24.03 | 23.37 |
24.25 GHz | 26.875 GHz | 29.5 GHz | ||||
---|---|---|---|---|---|---|
Tri | Squ | Tri | Squ | Tri | Squ | |
ηSij | −48.6 | −42.52 | −49.35 | −44.8 | −50.74 | −46.2 |
Max(Sij) | −14.91 | −11.84 | −15.62 | −12.55 | −16.9 | −14.4 |
24.25 GHz | 26.875 GHz | 29.5 GHz | ||||
---|---|---|---|---|---|---|
Tri | Squ | Tri | Squ | Tri | Squ | |
ηSIR | 11.1 | 10 | 12 | 11.25 | 13.3 | 12.2 |
SIR90% | 0.4 | 0 | 0.9 | 0.5 | 1.4 | 1 |
Sector | Lattice | SE Improvement | ||
---|---|---|---|---|
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 % |
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Dicandia, F.A.; Genovesi, S. Spectral Efficiency Improvement of 5G Massive MIMO Systems for High-Altitude Platform Stations by Using Triangular Lattice Arrays. Sensors 2021, 21, 3202. https://doi.org/10.3390/s21093202
Dicandia FA, Genovesi S. Spectral Efficiency Improvement of 5G Massive MIMO Systems for High-Altitude Platform Stations by Using Triangular Lattice Arrays. Sensors. 2021; 21(9):3202. https://doi.org/10.3390/s21093202
Chicago/Turabian StyleDicandia, Francesco Alessio, and Simone Genovesi. 2021. "Spectral Efficiency Improvement of 5G Massive MIMO Systems for High-Altitude Platform Stations by Using Triangular Lattice Arrays" Sensors 21, no. 9: 3202. https://doi.org/10.3390/s21093202