User-fairness guaranteed low-cost satellite constellation design

DAI Cuiqin,DAI Chengwei

(School of Communication and Information Engineering,Chongqing University of Posts and Telecommunications,Chongqing 400065,P.R.China)

Abstract：In view of the challenges posed by the difference of user distribution and geographical environment to ensure user fairness under the service of satellite constellation,a LEO satellite constellation design scheme is proposed to guarantee the user fairness by comprehensively considering user demand,the level of communication development,and the level of disaster risk in different areas.The LEO Satellite Network model is established and the coverage performance of a single satellite is analyzed.The user fairness factor is defined,and the optimization problems for LEO satellite constellation are formulated by minimizing the constellation investment cost and maximizing the coverage rate while satisfying user fairness.The LEO satellite constellation design problem under the constraints of constellation capacity and constellation profit is solved using a Non-dominated Sorting Genetic Algorithm (NSGA-Ⅱ).Simulation results demonstrate that the designed satellite constellation can meet the requirements of user fairness in different areas with low satellite constellation investment cost,and simultaneously satisfy the coverage rate for the target area.

Keywords：satellite networks;satellite constellation design;user fairness;coverage performance;input cost

1 Introduction

Due to its advantages such as wide coverage,large capacity,flexible access,etc.,the Low Earth Orbit (LEO) satellite network has become the focus of academic and industrial attention[1-2].A basic but crucial issue to be considered in the deployment of LEO satellite network is the satellite constellation design[3].A well-designed LEO satellite constellation can effectively improve the system performance and reduce the system cost[4].

According to the coverage area of the satellite constellation,the existing workson LEO satellite constellation design can be divided into two categories：1) global satellite constellation design[5-8];2) regional satellite constellation design[9-16].For the global satellite constellation design,an ultra-dense LEO satellite constellation scheme has been proposed in[5] to meet the requirements of global seamless coverage and Quality of Service (QoS).In [6],a cube satellite constellation design scheme with Inter-Satellite Links (ISLs) was developed to provide global continuous communication coverage.In order to meet the requirements of global quadruple coverage,a global navigation satellite constellation design scheme based on the Walker constellation configuration was developed in [7].The aforementioned works have achieved effective results in meeting the requirements of global seamless coverage.However,due to the large number of satellites and the need for the deployment of ground stations around the world,this has been an economic burden and a territorial problem for many countries and regions.On the other hand,for the design of regional satellite system,the deployment of satellite system is relatively flexible and the number of satellite is low,which not only meets the target area coverage and user communication needs,but also has benefits on the investment cost of the system[8].

In general,regional satellite constellation can be designedby considering the system performance[9-12]and the system cost[13-16].From the perspective of system performance,various aspects have been considered in the existing research,such as coverage performance maximization[9-10],system capacity maximization[11],and user Quality-of-Experience(QoE) maximization[12].The Non-dominated Sorting Genetic Algorithm (NSGA-Ⅱ) was proposed to maximize the multiplicity coverage of target areas in [9].The Particle Swarm Optimization (PSO) algorithm was introduced in [10] to improve the coverage and detection performance in the military domain.On the premise of considering the coverage performance,the author was focused on the satellite constellation capacity maximization to meet user demands in [11].In [12],the author was concerned with optimizing QoE during the satellite constellation design process.However,the aforementioned works did not consider the effect of differentiated user distribution and geographical environment on system performance,which easily leads to less coverage resources available in user intensive areas and developed cities,while more coverage resources are available in user sparse areas and backward cities,which makes it difficult to guarantee the fairness of users in different areas under the satellite constellation coverage services.

From the perspective of system cost,it plays an important role in satellite constellation design due to increasing emphasis on constellation profitability[13-16].In [13],a flexible multi-stage constellation design scheme with minimum life cycle cost was proposed.Based on the reduction of the orbital altitude,[14] reduced the system cost by simplifying the satellite payload.In [15],the author designed a low system cost constellation by optimizing the orbital altitude and number of satellites.In order to minimize deployment costs,the author designed constellation with an optimal launch strategy in [16].However,the analysis of the profitability of the constellation was not considered in the aforementioned works.

In addition,satellite constellation design is a complex multi-parametric optimization process,which is difficult to be solved by traditional analytical methods.Therefore,modern optimization algorithms[17-18]have recently been proposed for the solution of the satellite constellation optimization design problem,and NSGA-Ⅱ has been widely used for its global optimization performance.In [19],the author used NSGA-Ⅱ to solve the constellation multi-objective optimization problem under practical constraints to maximize the system performance.In [20],the author used NSGA-Ⅱ to solve the multi-objective optimization design problem of hybrid constellation.

In this paper,the main contribution is a scheme ofLEO satellite constellation design,which aims to satisfy the user fairness in different areas with low investment cost under the constraints of constellation capacity and constellation profit,mainly in the following aspects.1) Based on the comprehensive consideration of the differentiated user distribution and communication environment in different areas,we define three user fairness factors：user demand,communication development level and natural disaster level,and calculate the user fairness value in different areas by comprehensive weighting.2) The lifecycle profitability of the satellite constellation is derived,and a constellation design problem is formulated with the objectives of ensuring user fairness,minimizing constellation investment cost,and maximizing coverage.

The rest of this paper is organized as follows.In SectionII,the LEO satellite network model is presented.In Section III,the user fairness factors are defined,and the value of user fairness is calculated.In Section IV,the details of the satellite constellation optimization design are presented.The simulation are provided in Section V,and the conclusion is drawn in Section VI.

2 System model

In this section,we describe the LEO satellite network,and present the ground coverage model of a single satellite.

2.1 Network model

As shown in Fig.1,we consider a LEO satellite network consisting of space layer and ground layer.The space layer consists of a constellation composed of multiple LEO satellites that can effectively cover urban hot areas and remote areas (e.g.,oceans,rural,forests).The LEO satellite transmits user data to ground stations via satellite-ground links or to another satellite via the ISLs,providing users with ubiquitous communication services.The ground layer consists of ground stations and mobile users.The ground stations can provide users with satellite network access services.

Fig.1 LEO satellite network model

2.2 Constellation coverage rate

The LEO satellite constellation aims to provide good communication services to the target area.The prerequisite for providing services to users is effective network coverage.Therefore,it is necessary to analyze the coverage performance of a single satellite,and the satellite coverage model is shown in Fig.2.WhereinRis the radius of the earth,his the satellite orbital altitude,Sis the sub-satellite point,θis the satellite half viewing angle,αis the half of geocentric angle,εis the communication elevation angle.

Fig.2 Satellite coverage model

According to the geometric relationship of satellite coverage,the formulas to calculateαandθare

(1)

(2)

where the sum ofα,θandεis 90°.

The coverage area of a satellite can be calculated by

Ssat=2πR2(1-cosα)

(3)

therefore,the area served by the satellite depends on the communication elevation angle and the orbital altitude.

The degree of coverage is the ratio of the area covered by the constellation to the total area of the target area.The gird point method is usually used to simplify the calculation[21].We assume that the latitude and longitude coordinates of grid pointGand sub-satellite pointSare (λg,φg),(λs,φs),respectively.Then the angle betweenGandScan be obtained

γ=arccos[sinλgsinλs+cosφgcosφscos(λg-λs)]

(4)

ifγ<α,Gcan be covered by the satellite,and ifγ>α,Gis not within the satellite coverage.In Fig.2,G1is covered by LEO satellite,andG2is not.WhetherGis covered by satellite can be expressed as

(5)

By comparing the covered grid points with the total grid points,the coverage of the satellite constellation can be determined

(6)

whereNgrepresents the total grid point number.

3 User fairness

In this section,three user equity factors are defined and calculated based on the distribution of users and the geography of each area.In order to estimate the level of coverage of the constellations in the various regions,an extensive weight formula is used.

3.1 User fairness factors

User fairness isthe most important criteria for satellite constellation to serve users.When satellite constellation design combines user fairness,reasonable allocation of constellation coverage resources according to the user fairness value requirements in different areas can bring better user services,cost-effective.

In order to comprehensively and accurately evaluate user fairness,three user fairness factors are defined andcalculated,namely,user demand,communication development level and natural disaster level.

Definition1User demand represents the number of users who can potentially communicate via satellite in an area.

Due to the different number of users in different areas,the user demands are also different.The greater the user demands,the more constellation coverage resources are required.If the satellite constellation cannot cover the area with high user demand,user fairness in the area with high user demand will be reduced.

After we divide the target area into several areas,the population density ofkarea can be expressed as

(7)

whereNkrepresents the population of areak,and theAkrepresents the area of areak.

In order to simplify the calculation,the population density is normalized,which can be obtained

(8)

whereNKdenotes the number of divided areas,which is introduced in the simulation parameter setting section in Section V.

Therefore,the user demand in areakcan be written as

Nuser(k)=NTotal×σuser×D(k)×σsat

(9)

whereNTotalrepresents the total population in the target area.σuserrepresents the proportion of communication users in the total population,σsatrepresents the proportion of satellite users in communication users.σuserandσsatmay change with the development of LEO satellite network.

Definition2The communication development level has a direct impact on user fairness,as the size of the communication market reflects the user’s communication consumption capacity.

According to the economic development and the regional userincome,the actual communication development level inkarea can be defined as

(10)

whereG(k) represents the GDP of thekarea,GTotalrepresents the GDP of the target area,ρcomrepresents the proportion of communication costs.

Definition3The natural disaster level refers to the average number of natural disasters occurring annually in an area,which reflects the communication environment of users in the area.

In areas prone to natural disasters,when ground communications are damaged,the demand for satellite communications is relatively high.Therefore,the level of natural disaster has a direct impact on user fairness.Areas prone to natural disasters should have relatively more constellation coverage than areas less prone to natural disasters.

Earthquakes and debris flows are selected as the criteria to quantify the level of natural disasters.Consequently,the natural disaster level inkarea can be defined as

E(k)=Ee(k)+Em(k)

(11)

whereEe(k) andEm(k) represent the annual average number of earthquakes and debris flows in areak,respectively.

3.2 User fairness function

In this section,the user fairness value is calculated by comprehensively considering the above three user fairness factors estimate the constellation coverage level of different areas.A comprehensive weighting strategy is used to calculate user fairness values in different areas,since the above user fairness factors have different importance for user fairness.

The user fairness value inkarea can be expressed as

(12)

whereNmax,MmaxandEmaxare respectively the maximum user demand,the maximum communication development level and the maximum natural disaster inNKareas.βN,βMandβEare the weight of user demand,communication development level and natural disaster level,and their sum is 1.

As the user fairness value is used to estimate the constellation coverage resources in different regions,the relationship between the user fairness value and thecoverage level is given.User fairness values range from 0 to 0.3,0.4 to 0.7,and 0.7 to 1,respectively,corresponding to coverage levels 2,3,and 4.

4 User-Fairness guaranteed LEO sate-llite constellation design

In this section,the problem of designing a satellite constellation to meet the equity of users in different regions under the satellite constellation service is first presented.Then,NSGA-Ⅱ is applied to solve the problem of optimising the design of satellite constellations.

4.1 Problem formulation with user fairness

In satellite constellation design,we aim to guaranteefairness in satellite constellation services for users in different areas at a minimum investment cost.More importantly,in this paper,the user fairness becomes a novel constraint.In addition,the capacity and profitability of the satellite constellation are analysed to ensure the quality of user services and the profitability of the constellation.Therefore,the optimization problem is represented as

max(-CTotal,SCOV)#

s.t.C1：F(k)≤Fr(k)k=1,2,…,NK#

C3：CTotal≤I

(13)

whereSCOVrepresents the satellite constellation coverage rate,Fr(k) represents the actual user fairness value inkarea.CTdenotes the constellation capacity,which measures the total number of users that the satellite network can serve.I andCTotalrepresent the normal predicted profit during the constellation life cycle and constellation investment cost respectively,and are given in detail in the introduction of constraint C3 below.

Constraint C1 indicates that the actual user fairness value in different regions should be greater than the calculated user fairness value to ensure user fairness.

Constraint C2 indicates that the constellation capacity should be greater than the total user demands to maintain the user’s QoS.The satellite constellation capacity will be introduced by the ratio of satellite transmitting power to user receiving power.Based on a single-user downlink,CTcan be expressed as

(14)

whereNrepresents the number of satellites in constellation.EIRPrepresents the equivalent full amplitude power,Guserrepresents the user gain,LfandLerespectively represent free space propagation loss and other link losses,SNRrepresents the signal-to-noise ratio,N0represents the power spectral density of thermal noise equal to the product Boltzmann constantKand the user terminal noise temperatureT,Ruseris the user terminal data rate.

Constraint C3 indicates that the benefits of the constellation should be greater than the investment cost to ensure that the constellation is profitable.As the predicted benefits over the life cycle of the satellite constellation are mainly derived from call revenues,call revenues are used to predict the benefits of the satellite constellation.The call revenue can be derived from the total paid communication minutes and the communication cost per minute over the life cycle of the satellite constellation.Accordingly,Ican be obtained by multiplying the satellite life,the number of communication minutes in a year and the communication cost per minute,which is expressed as

I=M×Cs×Ysat

(15)

(16)

whereMrepresents the communication minutes of the constellation in a year[22],CSrepresents the cost of constellation communication,with reference to Iridium constellation’s communication cost of USD 3 per minute,Erepresents the peak traffic load during satellite busy hours,ρrepresents the ratio of peak business demand to average,andYsatrepresents the satellite lifetime.

CTotalrefers to the model in [23],it can be expressed as

CTotal=Np×Nsat×(Csat+Claunch+Cinsurance)

(17)

whereCsatrepresents the satellite manufacturing cost,Claunchrepresents the launch cost,Cinsurancerepresents the insurance cost,NpandNsatrepresent the number of orbital planes and the number of satellites in each orbital plane,respectively.They can be expressed as

Csat=0.055×Wsat

(18)

Claunch=0.000 49×Wsat×h0.43

(19)

Cinsurance=a×(Csat+Claunch)

(20)

wherehrepresents the orbital altitude,Wsatrepresents the mass of the satellite,a represents the proportion of insurance cost.

4.2 LEO satellite constellation design with NSGA-II

According to the theoretical analysis and derivation in SectionIII and part 4.1,the satellite constellation design parameters closely related to user fairness,constellation capacity and constellation cost are selected,including orbital altitudeh,orbital inclinationi,number of satellites in each orbitNsatand number of orbital planesNp.For example,the number of satellites per orbit directly affects the satellite constellation capacity and the satellite constellation investment cost.As the number of satellites increases,the capacity of the satellite constellation increases and the investment cost of the satellite constellation increases.Therefore,satellite constellation design is a complex multi-parametric optimization problem.

NSGA-Ⅱ is a typical genetic algorithm that can solve the satellite constellation design problem well through non-dominated sorting,selection,crossover and mutation[9].In NSGA-I,we first encode the above-mentioned satellite constellation design parameters to be optimized into a chromosome,and the chromosome structure of each individual is specifically expressed as (21),then take the objective function as the fitness function,calculate the fitness of each individual in the iterative process of the algorithm,and constantly search for the optimal solution according to the optimization objectives and constraints,and finally obtain the optimal individual,that is,the optimal satellite constellation design parameters.The satellite constellation design process with NSGA-Ⅱ is shown in Fig.3,which mainly includes the following seven steps.

Fig.3 Constellation design process with NSGA-Ⅱ

Step1Determine and input the range of constellation design parameters,including orbit altitude,orbit inclination,number of satellites and number of satellites per orbit.

Step2The population set is initialized and the number of genetic iterations is 0.The four constellation design parameters are encoded in the chromosomes：orbital elevation,orbital inclination,number of orbital planes,and number of spacecraft per orbit.Then,the chromosome of each individual in the population is

x=[h/i/Nsat/Np]

(21)

Step3Calculate the -CTotal,SCOVof all individuals in the initial population,and calculate their non-dominated ranking and crowding distance.

Step4The parent individuals are selected,crossed and mutated to produce a new generation of the child population.Genetic manipulation makes it possible for the new generation population to produce better individuals.

Step5Extract the chromosomes of the individuals in the population,i.e.the satellite constellation design parameters,and complete constellation configuration in STK,and then determine whether it satisfies the user's fairness.If so,continue to execute the algorithm;If not,go to step 4 and repeat the whole process.

Step6Combine the parent and child populations,calculate the non-dominated ranking and the crowding distance to generate a new generation.The new population retains the better individuals in the parent and child.

Step7Determine whether the number of genetic iterations satisfies the termination conditions.If so,the algorithm terminates and obtains the optimal constellation design parameters;if not,go back to step 4 and repeat the whole process.

5 Simulation and discussion

The selection of the target area and the setting of the simulation parameters are presented in this section.Then the simulation results are discussed in terms of the coverage rate,the user fairness,the investment cost.

5.1 Simulation settings

In the paper,the longitude range 73°33′E to 135°05′E,and the latitude range 3°51′N to 53°33′N is the target area for LEO satellite constellation design.Consideringthe differences in user distribution and geographical environment in different areas,the target area can be geographically divided into seven areas：Northeast,Northwest,North,South,Southwest,Central and East.The user fairness values of different areas are calculated by (12).When calculating the coverage rate of the satellite constellation to the target area by (6),the target area is meshed by 3 degrees multiplied by 3 degrees.

In terms of satellite constellation configuration,Walker constellation ischosen in order to simplify the constellation design process and reduce the launch cost.In addition,to avoid the Van Allen belt and reduce atmospheric drag,the orbital altitude is set between 700 km and 1 500 km.The orbit inclination is usually chosen to be close to the maximum latitude of the target area,so the orbit inclination is limited to 38° and 52°.

Tab.1 indicates some key parameters.For the NSGA-Ⅱ,the population size,maximum number of iterations,crossover probability and mutation probability are set to 50,100,0.8,0.2,respectively.

Tab.1 Simulation settings

5.2 Results discussion

According to the simulation results,the designed satellite constellation consists of 4 orbital planes,with 9 satellites in each orbit plane.The orbital altitude is 1 050 km,and the orbital inclination is 48.8°.

Fig.4 displays the coverage rate of four satellite constellations：Designed Constellation,OneWeb,Global Star,and Iridium Next[12].It can be seen that the designed constellation and the OneWeb constellation and the Global Star constellation have 100% minimum,maximum,and average coverage rate over the target area compared to the Iridium Next constellation,while the Iridium Next constellation has only 94.19% minimum coverage rate at a given time.Therefore,the designed constellation does not only meet the required coverage but also offers advantages.

Fig.4 Comparison of constellation coverage rate

The following compares user fairness in different areas under the designed constellation,OneWeb,Global Star,and Iridium Next.The different geographical environments and the distribution of users in different areas require a more reasonable allocation of the constellation coverage resources in order to satisfy the user fairness in different areas in the satellite constellation services.The higher the value of regional user fairness,the higher the level of coverage will be.Through simulation,it can be seen that,the OneWeb constellation,the Global Star constellation and the Iridium Next constellation have a high coverage level in the target area,but the user fairness requirements for each target area are not met.In the designed constellation,the coverage level of the designed constellation is lower than the other three satellite constellations,but in terms of user fairness,the coverage level for areas with higher user fairness values (e.g.,Central,East) is higher,while the coverage level for areas with lower user fairness values (e.g.,Northeast,Northwest,Southwest) is relatively lower.Therefore,the proposed constellation can well meet the user fairness in different areas in constellation services.

Fig.5 compares the different cost under four constellations.The launch cost of a single satellite is lower than the satellite cost.In order to visually observe the difference between the launch costs,the launch cost in Fig.5 is the total launch cost of the satellite constellation.It can be observed that each part of the cost of the constellation designed in this paper is lower than that of the OneWeb constellation,the Global Star constellation and the Iridium Next constellation.The investment cost of satellite constellation consists of satellite cost,launch cost and insurance cost.Therefore,as shown in Fig.6,the total investment cost of the designed constellation is low.

Fig.5 Comparison of constellation cost composition

Fig.6 Comparison of constellation investment cost

6 Conclusion

In this paper,a LEO satellite constellation design scheme is proposed to satisfy user fairness in satellite constellation services.For user fairness,three user fairness factors are defined to evaluatethe user fairness according to the differences in user distribution and geographical environment.And the user fairness values in different areas are derived by the comprehensive weighting formula.The simulation results show that,in comparison with the traditional satellite constellations,the satellite constellation design scheme proposed in this paper can not only satisfy the user fairness in different areas,but also have a good performance in terms of constellation investment cost.