Satellite constellation design and radio resource management using genetic algorithm

Satellite constellation design and radio resource management using genetic algorithm M. Asvial, R. Tafazolli and B.G. Evans Abstract: Novel strategies for automatic satellite constellation design with satellite diversity and radio resource management are proposed. The automatic satellite constellation design means that some parameters of satellite constellation design can be determined simultaneously. The total number of satellites, the altitude of a satellite, the angle between planes, the angle shift between satellites and the inclination angle are considered in the design. Satellite constellation design is modelled using a multiobjective genetic algorithm. This method is applied to low Earth orbit (LEO), medium Earth orbit (MEO) and hybrid constellations. The use of a genetic algorithm allows automatic satellite constellation design while achieving dual satellite diversity statistics. Furthermore, a strategy for dynamic channel allocation is proposed that uses a genetic algorithm for use in mobile satellite systems (MSS) networks. The main idea behind this algorithm is to use the minimum cost as a metric to provide optimum channel solutions for specified interference constraints. The simulation is designed for a MEO satellite constellation. Using this algorithm, the proposed model outperforms conventional dynamic channel assignment (DCA) schemes in terms of call blocking and call dropping probability. Generally, genetic algorithms are robust to dynamic variations in satellite constellation design and provide resource allocation improvements in DCA in MSS networks. 1 Introduction The multiobjective genetic algorithm (GA) has been introduced as a robust technique to solve many multivariable problems [1, 2]. Simulated annealing and GAs have been proposed for satellite constellation design in order to achieve the optimal discontinuous coverage and satellite constellation geometries [3, 4]. The discrete time-step coverages that provide the same value of the maximum revisit time in different designs have been evaluated. Furthermore, the optimisation of channel assignment in mobile satellite system (MSS) networks is key to efficient radio resource management. The main goal is to serve the maximum number of users with a limited number of frequencies or channels. Channel assignment methods have already been developed, such as fixed channel assignment (FCA), dynamic channel assignment (DCA) and hybrid channel assignment for MSS networks in low Earth orbit (LEO) and medium Earth orbit (MEO) constellations [5, 6]. The possibility of frequency reuse between spotbeams (cells) and the traffic load for each spotbeam in MSS networks is continuously changing. DCA schemes have been used to address the dynamics in order to achieve better channel utilisation than FCA. Also, DCA has been shown to be more flexible than FCA in terms of traffic variations. GAs r IEE, 2004 IEE Proceedings online no. 20040291 doi:10.1049/ip-com:20040291 Paper first received 9th January and in revised form 22nd December 2003. Originally published online 24th May 2004 M. Asvial is with the Center for Information and Communication Engineering Research, Electrical Engineering Department, University of Indonesia, Kampus UI, Depok 16424, Indonesia R. Tafazolli and B.G. Evans are with the Centre for Communication System Research, University of Surrey, Guildford, Surrey GU2 7XH, UK have also been used to good effect as robust algorithms to optimise channel planning in cellular networks [7]. We will first consider a GA for use in the design of the automatic satellite constellation for non-geo circular orbits with dual satellite diversity and the hybrid satellite constellation. The objective of the algorithm is to jointly optimise parameters of the satellite constellation for both the single layer and the hybrid lower/upper layers. The optimised parameters include the total number of satellites, the satellite maximum altitude, the angle shift between satellites, the angle between planes and the inclination angle. The results of the satellite constellation design using the GA show that the total number of satellites can be reduced while achieving dual satellite diversity statistics. We will also consider the use of a GA for DCA in MSS networks. The main idea behind this algorithm is to use the minimum cost as a metric to provide optimum channel solutions for specified interference constraints. The combination of traffic load for each spotbeam and interference limited DCA are represented as a chromosome structure within a GA environment. As an example of the technique, we demonstrate the automatic design of a satellite constellation while also improving the dual satellite diversity statistics. 2 Satellite constellation type The constellation is assumed to be the circular orbits of both the LEO and MEO constellations. The circular constellations tend to have maximum satellite diversity in the latitude region surrounding the latitude corresponding to the inclination angle. A common orbital period and the same inclination angle for all satellites are applied to different planes of the satellite constellation. Each orbital plane contains an equal number of satellites. The coverage feature of this constellation is assumed to be 204 IEE Proc.-Commun., Vol. 151, No. 3, June 2004

circular. The constellation is proposed since it offers global coverage with a trade-off between diversity and minimum elevation angle. The contiguous coverage is provided by the dynamic overlap between satellites in different planes. A circular orbit is proposed for GEO which places it on the equatorial plane. The satellite constellations for LEO and MEO are designed using the GA so as to have a resonant orbit with a repetitive ground track whilst also avoiding the Van Allen radiation belts. The angle between planes and the angle shift between satellites are used as important parameters for positioning purposes. The angle shift between satellites is defined in [8] as the angle travelled by one satellite in its plane measured from the line of nodes until the satellite in the other plane passes through this same reference line. A high value for the angle between planes and a small angle shift between satellites are required for a high positioning accuracy. 3 Satellite constellation design using the GA The parameters of the satellite constellation are represented as a chromosome structure in the GA process. The parameters include the number of satellites, the altitude of satellite s orbit, the angle between planes, the angle shift between satellites, and the inclination angle. In the simulation, each chromosome for each variable is assumed to have the same length. An individual is represented by the total chromosome length and used in the further stages of the GA, such as selection, crossover and mutation. The chromosome structure of the satellite constellation design suing a GA is shown in Fig. 1. A fitness function for all the parameters of an element of the dual satellite diversity is evaluated for each generation. The interpolation between the best and worst Pareto ranks is then examined for each fitness value. The same weighting factor (o) for all objective functions is determined to control the optimal solution. The fitness function of this algorithm can be expressed as: Fj l 1 ¼ 1 þ ððjoe ðs;h;y;j;iþ2satdiv min ðs; h; yþjþ=ðjoe max ðj; iþþ ð1þ where j is the generation number, l ¼ 1, y, N is the identification index for each individual and a is the scaling factor. Satellite parameters for both LEO and MEO are represented as s, h, y, j and i for the number of satellites, the altitude of the satellite, the angle shift between satellites, the angle between planes and the inclination angle. E mink ð:þ and E maxk ð:þ are the expectation operators of the parameters with minimising and maximising values, respectively. The scaling factor is varied, so as to examine its effect on the robustness of each generation to map the fitness values in 10010001 01000101 00100111 10001101 100100010100010100100111 10001101. 111000110101101111100001 11111101 individual N Fig. 1 total chromosome length. chromosome for each parameter individual 1 Genetic satellite constellation chromosome structure the range 0 and 1. All parameters retain the satellite diversity condition (SatDiv). The fitness of the offspring, depends on the parents through the crossover and mutation processes. The best fitness for each chromosome according to the satellite diversity for all parameters is then selected. The concept of selection is based on a random roulette wheel process. The probability of any individual being selected from the population is defined as: P s ðjþ ¼ ðf jþ r 1 ð2þ ðf sum Þ r 1 where P s (j) is the probability of the selection of individual j of the previous generation. The individual with index j is selected, if: X j D ðf i Þ r 1 ðf sum Þ r 1 z ð3þ i¼1 where z is a real random number between zero and one. Two randomly selected parents are used in the crossover and mutation processes. Multipoint crossover and nonuniform mutation processes are used in the algorithm. The process is carried out on a group of the fittest individuals that represent all parameters of the satellite constellation. The chromosome matrix output of the genes of the satellite constellations can be written as: max :gen c max;min ¼ mat fp maxk ; p minl gl ð4þ where p maxk and p minl are the chromosome for the maximum and the minimum of the objective function with the best fitness for the satellite constellation, and mat[] is the row matrix of the offspring vector and i is the generation number. For the hybrid satellite constellation, the parameters of both layers are represented as the hybrid chromosome structure. The fitness function in (1) is extended to the hybrid constellation case andcanbeexpressed as: Fj l ¼ ðs;h;y;j;iþ2satdiv 1 1 þ ððjo Q 2 k¼1 E min k ðs; h; jþjþ=ðjo Q 2 k¼1 E ð5þ max k ðj; iþþ where k is the number of layers in the hybrid constellation. The selection process is based on a non-dominated sorting GA that has been discussed in [2]. The crossover and mutation operators remain as those proposed to model a single layer of the genetic satellite constellation. For the hybrid constellation, (4) can be rewritten as: c ¼½p1 m;...; pn 1 ; pm 2 ;...; pn 2Š for m ¼ð1;...nÞ ð6þ where p1or2 m are the parameters of the hybrid satellite constellations that are proposed in the GA. The GA process can be stopped after an optimum number of generations. We need to make some final remarks concerning the different parameters of the GA such as population size, number of mutations and number of selected parents. The best fitness is then chosen by ranking them from one to the maximum number of generations and then stopping the process of selection, crossover and mutation. 4 Satellite constellation simulation results For the example satellite constellation the population size is chosen to be 350 and the maximum number of generations as 550. The value of the crossover probability and the mutation probability are chosen to be 0.6 and 0.025 as IEE Proc.-Commun., Vol. 151, No. 3, June 2004 205

suggested in [1]. The satellite s altitude is chosen to be 700 1700 km for LEO, 8000 17 000 km for MEO and 36 000 km for geostationary Earth orbit (GEO). In this simulation, dual satellite diversity is employed for LEO, MEO and the hybrid orbits. Simulation results for the single-layer case are shown in Table 1 and for the hybrid case in Table 2. From the Tables it can be clearly seen that the number of satellites for the hybrid satellite constellation is smaller than in the single-layer case. Also, the maximum satellite altitude for the hybrid constellation for both LEO and MEO are lower than for the single layer satellite constellation. The optimised inclination angle of both the LEO and MEO constellations is in the range of 501 551. An orbit inclination in this range can optimise the coverage area and diversity over a predefined range of latitudes. In associated work [8], an inclination angle of around 551 has been shown to be optimum in avoiding positioning errors introduced by a satellite drift from its true orbit as a consequence of an asymmetric gravitational field. Thus, the results for the genetic satellite constellation design and the hybrid constellations are highly suitable for mobile communications applications, which require a fast and accurate user location from the constellation. The angle between planes and the angle shift between satellites for the single layer and the hybrid LEO/MEO are close to 901 and 01 respectively. These are also close to the optimum values for use in communications with mobile terminal positioning [8]. Maximising the angle between planes and minimising the angle shift between satellites gives the best accuracy for positioning errors. The most important result of the satellite constellation designed using the GA is the achievement of dual satellite diversity statistics as shown in Figs. 2 and 3. The results are compared to Globalstar for LEO and to ICO for MEO. Furthermore, the dual satellite diversity statistics are fully available down to a 141 minimum elevation angle for the hybrid constellation as shown in Table 2. Comparing the single MEO and LEO constellation results as shown in percentage of time, % 100 80 60 40 20 Fig. 2 100 GA for LEO Globalstar 0 0 10 20 30 40 50 60 70 80 90 latitude, deg Dual satellite diversity statistics for LEO constellation Table 1: Genetic satellite constellation parameters Constellation parameters LEO MEO Number of satellites 45 8 Number of planes 5 2 Number of satellites per 9 4 plane Orbital altitude, km 1656 10 948 Orbit inclination, deg 52 53 Angle between planes, deg 70 85 Angle shift between satellites, deg 10 8 Apogee/perigee inc. circular orbit inc. circular orbit percentage of time, % Fig. 3 80 60 40 20 GA for MEO ICO 0 0 10 20 30 40 50 60 70 80 90 latitude, deg Dual satellite diversity statistics for MEO constellation Table 2: Genetic hybrid satellite constellation design parameters Constellation parameters Hybrid LEO/MEO Hybrid LEO/GEO Hybrid MEO/GEO LEO MEO LEO GEO MEO GEO Number of satellites 30 6 28 1 8 1 Number of planes 5 2 4 1 2 1 Number of satellites per planes 6 3 7 1 4 1 Orbital altitude, km 1334 10 216 1428 35 788 10 348 35 798 Orbit inclination, deg 52 51 54 0 55 0 Angle between planes, deg 76 80 80 86 Angle shift between satellites, deg 8 6 7 5 Orbital type circular orbit circular orbit Visibility of dual satellite diversity, % 100 100 100 206 IEE Proc.-Commun., Vol. 151, No. 3, June 2004

Table 1, the results for the hybrid constellation show a marked improvement in terms of the dual satellite diversity statistics and also the total number of satellites for LEO and MEO can be reduced. 5 Dynamic channel allocation for MSS networks We consider an example MSS spotbeam coverage in which the frequency reuse between two spotbeams is determined if the mobile terminal position is not within the overlapped coverage region. The frequency reuse condition for all spotbeams is investigated as a function of time. The update interval time and the sampling time are introduced in order to track the varying time coefficients and constraints of the algorithm. The update interval time is used to cope with the dynamically changing conditions of the channel within the spotbeams and also depends on the traffic load and the possibility of frequency reuse. The continuously changing traffic load and frequency reuse conditions between update times are reflected by the sampling time. Traffic distribution is determined within a 51 51 mesh element on the Earth s surface. The rush hour traffic is always determined for each locality using the local traffic profile. In this case, we assume that the load ratio of the local traffic profile for voice or telephone traffic for each spotbeam reaches its maximum between 10.00 and 12.00 (rush hour) and its minimum between 23.00 and 6.00, as shown in Fig. 4. Channel requirements are defined by the Erlang B formula from the traffic load for each spotbeam at the update interval and sampling time. 100 A set of spotbeam numbers is denoted by n and represented in a square matrix of (n, n). The elements of this matrix are denoted as x i,k, (i,k ¼ 1,2,y, n), which represent the possibility of frequency reuse between channels assigned to spotbeams i and k respectively. Using this notation, each element of x i,k is equal to one, if spotbeams i and k can reuse a channel. Otherwise, x i,k is assumed to be zero. Consider a set matrix (n, z) oftypef i, j, where z is the dynamic number of channels that are available at the update interval and sampling times. The elements of this matrix are equal to one if the jth channel is assigned to a frequency in the ith spotbeam and zero otherwise. The interference constraints used in the algorithm include the co-site interference, the co-spotbeam interference, and the adjacent co-spotbeam interference. The total interference needs to be minimised. Depending on the above conditions, the fitness function of the DCA obtained using the GA can be written as: F ¼ Xn X t i i¼1 k¼1 D i;k þ Xn X t i X z X t j i¼1 k¼1 j¼1 I¼1 I i;j ðtþc i;k ðtþc j;l ðtþ ð7þ where D i,k is the assigned channel configuration from evaluation of calls at the update and sampling time, I i,j (t)is the co-site interference, C i,k (t) is the co-channel interference and C j,l (t) is the adjacent co-channel interference. 6 DCA obtained from GA BasedontheformulationoftheDCArulein[5] which is referred to as a conventional DCA, all channels in the spotbeams have the same opportunity to be used. The traffic condition for each spotbeam needs to be evaluated at the update interval times, and we now propose the use of an evolutionary GA for these calculations. For each gene in the chromosome, a service is assigned from the evaluation of the calls and channel interferences for each spotbeam. The chromosome structure of the genetic DCA is shown in Fig. 5. The dynamic length of the chromosome is determined by the total number of spotbeams (Sb) and the number of channels (C st ) for each spotbeam. n Cl = Σ Sb i i =1 ΣC Sb1 ΣC Sb2 ΣC Sbi ΣC Sbn Sb 1 Sb 2 Sb n 80 Fig. 5 Chromosome structure of the genetic DCA traffic load, % Fig. 4 60 40 20 0 0 4 8 12 16 20 24 time, h Local traffic profile The initial population size of the genetic DCA is generated and denotes the service allocation for each gene in the chromosome. The fitness of each chromosome is calculated using to the fitness function described in (7). During the evolutionary process, the values of the genes are changed in order to improve the fitness value. Assuming that the current generation of individuals is q, the probability of any individual being selected from the population can be defined as: P m ðqþ¼ PM 1 Q¼0 F r 1ðqÞ F r 1 ðqþ ð8þ where M is the population size and q is the index of the individual. The best pair of genes is carried over to the next population. Two chromosomes are selected from the original population for the crossover process and are then subjected to a mutation process before the new offspring are passed to the next generation. The selection criteria are based on a random roulette wheel selection. The sum of the fitness values for all the existing individuals is then calculated from: S r 1 ¼ XM 1 F r 1 ðqþ ð9þ q¼0 The mutation point and the crossover point are selected randomly. This procedure is repeated until the maximum population size is searched. The selected solution vector is used to find an optimum for the channel allocation and to IEE Proc.-Commun., Vol. 151, No. 3, June 2004 207

minimise the interference effect. Here, the calls exchange the composition position of a chromosome within the call list. The selected block calls are used to improve the bit string position within the call list by a random value. The chromosome fitness can be written as: chromosome fitness ¼ Xmax j¼1 F l j ð10þ where j is the generation number and l ¼ 1, y, N is the identification index for each individual. If the current number of generations is less than the maximum number of generations, the process returns to the first step. After the maximum number of generations, the best chromosome is selected which then represents the best channel allocation for the specified conditions. At the end of each optimisation process, the program reports the individual with the best fitness. The graph in Fig. 6 shows an example of the progress of the optimisation process carried out in this algorithm. fitness 0.72 0.70 0.68 average population fitness maximum population fitness 0.66 0 100 200 300 400 500 generations Fig. 6 Genetic DCA fitness value as a function of generation number 7 DCA simulation results As the simulation example we have chosen a S-UMTS configuration based on the MEO constellation with ten satellites that are distributed into two planes with five satellites in each plane. The altitude of the satellites is 10 355 km. The update interval time is chosen to be 15 min and the sampling time is 1 min. The simulation is proposed only for the best effort traffic class without any specific requirements. Experiment 1: This experiment is performed to evaluate the call dropping probability. The call dropping probabilities for the genetic DCA and conventional DCA are shown in Fig. 7. The call dropping probability reflects the limited number of channel measurements that the mobile terminal can make on a satellite link before trying another satellite. In this simulation, the use of single-channel receivers is assumed. This value has to be kept low to prevent long interruptions at handover and therefore the call dropping probability curves reflect the capacity limitation of this single-channel receiver scheme. The maximum number of generations is chosen to be 550 with 0.01 as the mutation probability and 0.6 as the crossover probability. In this experiment, the population sizes of the genetic DCA are chosen to be 100 and 250. The results show that the performance of the genetic DCA is better than the dropping call probability Fig. 7 10 2 10 3 10 4 10 5 10 6 0 2 4 6 8 10 12 request call conventional DCA for simple conditions and without realtime requirements. As illustrated in Fig. 7, the call dropping probability of the genetic DCA model tends to decrease as the population size increases. This indicates that a large part of the population of the genetic algorithm expect to find the best genes and it is more adaptable to changes in the traffic load. This is because, as the population is increased, the probability to select the best genes for the lower traffic load channel assignment should also increase. Experiment 2: We evaluate the call blocking probability for 61 spotbeams per satellite. The maximum number of generations is chosen to be 500 with 0.01 as the mutation probability and 0.6 as the crossover probability. In this experiment the population size of the genetic DCA is chosen to be 150. The performances of the call blocking probability for the genetic DCA and the conventional DCA are shown in Fig. 8. The results show that the call blocking probability of the genetic DCA model tends to decrease more rapidly as the traffic intensity decreases and has a marked improvement compared to the conventional DCA. call blocking probability Fig. 8 10 0 10 1 10 2 10 3 10 4 Call dropping probability 8 Conclusions conventional DCA genetic DCA with 100 population size genetic DCA with 250 population size genetic DCA conventional DCA 0 50 100 150 200 250 mean request calls Call blocking probability GAs for satellite constellation design and DCA for MSS networks have been proposed and evaluated. As an example of the technique, we have presented the automatic design of LEO, MEO and hybrid constellations while still being able to provide the dual satellite diversity statistics. 208 IEE Proc.-Commun., Vol. 151, No. 3, June 2004

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