# Optimization in VHTS Satellite System Design with Irregular Beam Coverage for Non-Uniform Traffic Distribution

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## Abstract

**:**

## 1. Introduction

- Enhanced mobile broadband: addresses use cases centered on the human being to access multimedia content, services, and data.
- Ultra-reliable and low-latency communications: this service enabler has strict requirements for capabilities such as performance, latency, and availability. Examples include wireless control of industrial manufacturing or production processes, remote medical surgery, automation of distribution in an intelligent network, transport safety, etc.
- Massive machine-type communications: a large number of connected devices that normally transmit a relatively low volume of data not sensitive to delay. The devices are required to be low cost and have a long battery life.

- A new cost function is proposed to design VHTS satellite systems using irregular coverage that allows to simultaneously minimize the cost per Gbps in orbit, the Offered Capacity Error, and the Normalized Coverage Error, including traffic demand distribution. The multibeam coverage error study for regular and irregular beams size coverage is introduced for the first time as an optimization variable.
- A trade-off is presented that compares the offered satellite capacity, the effective coverage, area, and satellite cost per Gbps in orbit.
- In contrast to the state of the art, antenna design parameters are taken into account for system optimization.

## 2. System Model

#### 2.1. Offered Capacity and Distribution of Traffic Demand

_{b}is the bandwidth and the $S{E}_{b}$ is the spectral efficiency, both in the b-th beam. $S{E}_{b}$ is the spectral efficiency of the ModCod (Modulation and Coding) scheme of a commercial modem of the DVBS2-x standard [27]. Hence, the spectral efficiency in each beam depends on the Carrier to $CIN{R}_{b}$ in the same beam.

- Traffic model (required throughput density): this parameter represents the information on the customs and habits of users when they access the service. It is essential to know the connection habits of the users since it is possible to estimate the areas where more connections are produced, and therefore, more capacity is required; this variable is represented in bps/Km
^{2}. - Required Capacity: this parameter provides information on the data rate required per beam and will depend on the traffic model used (bps/Km
^{2}) and the area of the beam (Km^{2}).

^{2}. Thus, if we define $\Delta \Omega $ as a specific geographic area of one km

^{2}, ${r}_{\nabla \Omega}$ as the value of required throughput density per km

^{2}(in bps/km

^{2}) inside $\Delta \Omega $, ${r}_{b}$ as expected value over all the area inside b-th beam (in bps/km

^{2}) and ${A}_{b}$ as b-th beam area (in km

^{2}), then, the requested traffic for the b-th beam ${R}_{b}$ (in bps) is calculated as (1):

^{2}(${r}_{\nabla \Omega}$ depends on the throughput per user (${C}_{u}$, in bps/user), the population density (${D}_{\Delta \Omega}$

_{,}in inhabitant/km

^{2}), the penetration rate (${F}_{\Delta \Omega}$, in user/inhabitant), and the concurrence rate (${T}_{\Delta \Omega}),$hence:

#### 2.2. Technical and Commercial Requirements

_{GW}is the antenna diameter of the gateway. ${k}_{1}$ and ${k}_{2}$ are empirical constants to adjust the cost to monetary units [8]. The total cost of the ground segment is the sum of the cost of the gateways.

## 3. Problem Statement

#### 3.1. Coverage Model

_{o}and lon

_{o}are the geographical position references, where the satellite antenna points its first beam. The ${\mathsf{\theta}}_{3\mathrm{dB}}$ parameter is the half-power beamwidth and depends on the satellite antenna design. The inclination angle α represents the beam’s grid orientation concerning the equator, being positive from east to north. Finally, the coverage beam efficiency ${\eta}_{{a}_{x}}$ is the proportion of each beam inside the service area, and it must be greater or equal to the minimum required for each beam. In that sense, ${a}_{x}$ is the resulting service area, also known as satellite coverage (in square kilometers), and it is represented as the area occupied by the beams, considering overlapping. When any design parameters are changed, the satellite coverage is wholly modified, changing the number of beams required to cover the same service area.

#### 3.2. Coverage with Irregular Beams for Non-Uniform Traffic Distribution

#### 3.3. Cost Function for System Design Optimization

_{b}) average offered capacity in each beam and the (R

_{b}) average required capacity in each beam while also minimizing the (E) Normalized Coverage Error and the (Cost

_{Gbps}) cost per Gbps in orbit as explained in Section 2, Section 3.1 and Section 3.2.

## 4. Method: Optimization Methodology in VHTS Satellite System Design with Irregular Beam Coverage

_{b}, the capacity offered in each beam, the capacity provided of the overall satellite, and the three KPIs (capacity offered error, coverage normalized error, and cost of Gbps in orbit) to calculate the cost function (18) for the t-th possible configuration of the gird orientation.

- -
- MFB: this technology combines different feed horns of the cluster to form the appropriate illumination pattern to obtain a specific reflector pattern. This technology requires the use of a complex beamforming network (BFN) or limited butler matrix network with less flexibility. Usually, it is designed with passive waveguide technology to reduce losses; then, the cluster may be bulky.
- -
- Phased array feed: in this case, integrated RF circuits, ASICS, and active components are needed to implement this technology. The use of this technology results in more compact but complex antenna systems. This technology is also suitable for high-flexibility payload antennas in which the two colors can be implemented in one feed cluster.
- -
- SFB: using this technology, simple implementation can be completed but with a lack of flexibility. Furthermore, for a large service area and number of spots, several reflector antennas must be used.
- -
- Dichroic sub reflector: using any of the previous technologies, but to reduce the number of reflector antennas onboard the satellite, the use of dichroic multiband sub-reflector fed system is a promising option to locate many feeds using two different focal points of the reflector system (see Figure 10a). Note that depending on the feed cluster frequency, the volume needed may define the corresponding focal point to increase the clearance of the reflector antenna.
- -
- Polarization selective surfaces: to reduce the complexity and separate the colors at feed level, polarization-selective surfaces can also be implemented (see Figure 10b).

## 5. Results

#### 5.1. Case Study Analysis

#### 5.2. Optimization Methodology Performance

#### 5.3. Cluster Definition

_{0}orientation is set to spots 41 (the best) and to spot 7. Note that the minimum values are obtained for the spot b = 41.

_{0}oriented to spot b = 41 is about one order of magnitude less than the obtained to spot b = 7.

_{0}. In a real case, those can be north-, south-, east-, and west-oriented antennas. The impact of implementing those four different orientations will be observed in a different oriented separated cluster. Thus, in this proposal, it can be observed that the four colors clusters match with the whole cluster presented in Figure 17b. Furthermore, the resulted in focal distance $f=4m$, while the diameter of the reflector is $D=1.77m$, resulting in a $f/D=2.25$. The $f/D$ can be reduced if the minimum spot size is reduced.

## 6. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Nomenclature

$B$ | Number of beams |

$b$ | b-th beam |

${\mathsf{\theta}}_{3\mathrm{dB}}$ | One-sided half-power beamwidth |

$B{W}_{b}$ | Bandwidth in b-th beam |

${\theta}_{b}$ | b-th beamwidth |

$CIN{R}_{b}$ | Carrier to Interference plus ratio ratio in b-th beam |

${C}_{b}$ | Offered capacity in b-th beam |

$S{E}_{b}$ | Spectral efficiency in the b-th beam |

$\Delta \Omega $ | Specific geographic area of one km^{2} |

${r}_{\Delta \mathsf{\Omega}}$ | Throughput density per km^{2} |

${C}_{u}$ | Throughput per user |

${D}_{\Delta \Omega}$ | Population density |

${F}_{\Delta \Omega}$ | Penetration rate |

${T}_{\Delta \Omega}$ | Concurrence rate |

${r}_{b}$ | Expected value over all the area inside b-th beam |

${A}_{b}$ | Area of b-th beam |

${\cup}_{b}$ | Ratio between the satellite orbital position and the geographical coordinate of the center of the b-th beam |

$Cos{t}_{GW}$ | Cost per gateway |

${u}_{GW}$ | User beam per gateway |

${D}_{GW}$ | Antenna diameter of gateway |

${g}_{1}\left(\xb7\right)$ | Cost associate to ${u}_{GW}$ |

${g}_{2}\left(\xb7\right)$ | Cost associate to ${D}_{GW}$ |

$Cos{t}_{sat}$ | Satellite cost |

$Cos{t}_{Gbps}$ | Cost per Gbps in orbit |

$Cos{t}_{T}$ | Total system cost |

${C}_{sat}$ | Satellite capacity |

$E$ | Normalized error between the service area and the coverage area |

${a}_{x}$ | Coverage area |

${a}_{y}$ | Service area |

$\alpha $ | Beams grid orientation with respect to the equator |

${\eta}_{{a}_{x}}$ | Beam Coverage Efficiency |

$K$ | Number of regions |

${a}_{{y}_{k}}$ | Area of k-th region that depends on traffic distribution |

$({\mathrm{lat}}_{o},{\mathrm{lon}}_{o})$ | Geographic position reference for the coverage area |

$({\mathrm{lat}}_{{o}_{K}},{\mathrm{lon}}_{{o}_{K}})$ | Geographic position reference for the k-th coverage area |

${\theta}_{3d{B}_{K}}$ | Beamwidth of k-th region that depends on traffic distribution |

${\overline{A}}_{y}$ | Vector of size 1 × K containing the area of the K regions (${a}_{{y}_{1}}{a}_{{y}_{2}}\cdots {a}_{{y}_{K}}$) |

${\overline{A}}_{x}$ | Vector of size 1 × K containing the area of the K regions (${a}_{{x}_{1}}{a}_{{x}_{2}}\cdots {a}_{{x}_{K}}$) |

$\overline{LA{T}_{o}}$ | Vector of size 1 × K containing latitudes of the first beam in the K regions (${lat}_{{o}_{1}}{lat}_{{o}_{2}}\cdots {lat}_{{o}_{K}}$). |

$\overline{LO{N}_{o}}$ | Vector of size 1 × K containing longitudes of the first beam in the K regions (${lon}_{{o}_{1}}{lon}_{{o}_{2}}\cdots {lon}_{{o}_{K}}$). |

${\overline{\theta}}_{3dB}$ | Vector of size 1 × K containing the assigned beamwidth in the area of the K regions (${\theta}_{3d{B}_{1}}{\theta}_{3d{B}_{2}}\cdots {\theta}_{3d{B}_{K}}$). |

${F}_{1}$ | System cost function to optimize |

${h}_{1}$ | Weight of the capacity error in the cost function |

${h}_{2}$ | Weight of the normalized coverage error in the cost function |

${h}_{3}$ | Weight of the cost per Gbps in orbit in the cost function |

$M$ | Number of system constraints |

$S{C}_{m}$ | m-th system constraint |

${L}_{m}$ | m-th set of possible values to the m-th system constraint |

$T$ | Set size of grid inclination |

$D$ | Diameter of the satellite reflector antenna |

${D}_{f}$ | Diameter of the feed |

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**Figure 2.**Required traffic distribution in the service area. The traffic demand will depend on the beam area and the average required capacity per km

^{2}.

**Figure 3.**System parameters that influence the design of the multibeam coverage. ${a}_{y}$ is the required service area (in square kilometers). The pair of lat

_{o}and lon

_{o}are the geographical position references. The ${\mathsf{\theta}}_{3\mathrm{dB}}$ parameter is the half-power beamwidth. The inclination angle α represents the beam’s grid orientation.

**Figure 4.**Normalized coverage error of regular multibeam coverage for Portugal, Spain, and France with an orbital position of 9° E. (

**a**) θ

_{3dB}= 0.60° and α = 0°. (

**b**) θ

_{3dB}= 0.60° and α = 10°. (

**c**) θ

_{3dB}= 0.60° and α = 20°.

**Figure 5.**Different number of beams needed for the same service area depending on the configuration of the parameters. (

**a**) ${\mathsf{\theta}}_{3\mathrm{dB}}$ = 0.66° and $\mathsf{\alpha}$ = 20°: 13 beams. (

**b**) ${\mathsf{\theta}}_{3\mathrm{dB}}$ = 0.61° and $\mathsf{\alpha}$ = 18.6°: 12 beams.

**Figure 6.**CNR (Carrier to Noise Ratio), CIR (Carrier to Interference Ratio), and CINR (Carrier to Interference plus Noise Ratio) geographical maps in dB for the KaSat coverage and same number of beams but different beamwidths. (

**a**) CNR in dB using ${\mathsf{\theta}}_{3\mathrm{dB}}$ = 0.65°. (

**b**) CNR in dB using ${\mathsf{\theta}}_{3\mathrm{dB}}$ = 0.55°. (

**c**) CIR in dB using ${\mathsf{\theta}}_{3\mathrm{dB}}$ = 0.65°. (

**d**) CIR in dB using ${\mathsf{\theta}}_{3\mathrm{dB}}$ = 0.55°. (

**e**) CINR in dB using ${\mathsf{\theta}}_{3\mathrm{dB}}$ = 0.65°. (

**f**) CINR in dB using ${\mathsf{\theta}}_{3\mathrm{dB}}$ = 0.55°.

**Figure 7.**Study of the traffic demand in the service area to be divided into smaller areas according to the traffic demand based on population density [34].

**Figure 10.**Deployable multi-feed antenna dual reflector (compensated) systems using dichroic and polarization selective surfaces. (

**a**) Using dichroic sub reflector with any of the previous technologies, but to reduce the number of reflector antennas onboard the satellite. and (

**b**) Using polarization selective surfaces: to reduce the complexity and separate the colors at feed level.

**Figure 11.**Hypothetical distribution of traffic demand over the service area to evaluate the performance of the methodology.

**Figure 12.**Performance based on the number of regions into which the service area is divided and grid orientation: Normalized Coverage Error and Offered Capacity Error per beam.

**Figure 13.**Performance based on the number of regions into which the service area is divided and grid orientation: Satellite Capacity and Cost per Gbps in orbit.

**Figure 14.**Performance comparison of methodology on Very High Throughput Satellite (VHTS) affordability for throughput according to [9]. Note: the launch cost and the ground segment cost have been added.

**Figure 15.**Performance comparison of methodology on Very High Throughput Satellite (VHTS) according to previous methodology (FOM) [8].

**Figure 17.**(

**a**) Position of the spots centers and z-axis direction; (

**b**) Feeds positions with the antenna z-axis pointing to selected spot.

**Figure 18.**Four colors feed clusters for the four colors scheme. (

**a**) Blue, (

**b**) yellow, (

**c**) red, and (

**d**) green.

Parameter | Case Study |
---|---|

Service area | Europe and some specific cities in North Africa [36] |

Satellite position | 9° E |

Bandwidth per gateway (Q/V band) | 2.5 GHz |

Gateway antenna diameter | 9.1 m |

Bandwidth per beam (Ka band) | 250 MHz |

Power per beam | 15 dBW |

Frequency plan | 4 colors |

Maximum investment cost | 400 M€ |

Maximum satellite mass | 6700 Kg |

Maximum satellite antenna diameter (user link) | 2 m |

Maximum satellite mass | 6700 kg |

Possible beamwidths | [0.55° 0.60° 0.65] |

Possible orientation of the grid | [−10° 0° 10° 20°] |

A_{0} to Spot b = 41 (Selected) | A_{0} to Spot b = 7 (for Comparison) | ||
---|---|---|---|

$\overline{\sigma}$ | ${\overline{\sigma}}^{2}$ | $\overline{\sigma}$ | ${\overline{\sigma}}^{2}$ |

$2.09\times {10}^{-2}$ | $4.38\times {10}^{-4}$ | $2.20\times {10}^{-2}$ | $4.82\times {10}^{-4}$ |

**Table 3.**Mean of differences between the feed horns locations adjusted and original locations for both A

_{0}to the spots 41 and 7.

A_{0} to Spot b = 41 (Best) | A_{0} to Spot b = 7 | |
---|---|---|

$\overline{\left|{d}_{adj}-d\right|}$ | $7.95\times {10}^{-4}$ | $2.79\times {10}^{-3}$ |

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**MDPI and ACS Style**

Ortiz-Gomez, F.G.; Salas-Natera, M.A.; Martínez, R.; Landeros-Ayala, S.
Optimization in VHTS Satellite System Design with Irregular Beam Coverage for Non-Uniform Traffic Distribution. *Remote Sens.* **2021**, *13*, 2642.
https://doi.org/10.3390/rs13132642

**AMA Style**

Ortiz-Gomez FG, Salas-Natera MA, Martínez R, Landeros-Ayala S.
Optimization in VHTS Satellite System Design with Irregular Beam Coverage for Non-Uniform Traffic Distribution. *Remote Sensing*. 2021; 13(13):2642.
https://doi.org/10.3390/rs13132642

**Chicago/Turabian Style**

Ortiz-Gomez, Flor G., Miguel A. Salas-Natera, Ramón Martínez, and Salvador Landeros-Ayala.
2021. "Optimization in VHTS Satellite System Design with Irregular Beam Coverage for Non-Uniform Traffic Distribution" *Remote Sensing* 13, no. 13: 2642.
https://doi.org/10.3390/rs13132642