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Abstract
Low earth orbit satellite laser communication has become an important part of communications due to its large capacity and low latency. The lifetime of the satellite mainly depends on the recharge and discharge cycles of the battery. The low earth orbit satellites frequently recharge under sunlight and discharge in the shadow, which leads satellites to age quickly. This paper studies the energy-efficient routing problem for satellite laser communication and builds the satellite ageing model. Based on the model, we propose an energy-efficient routing scheme based on the genetic algorithm. Compared with shortest path routing, the proposed method improves the satellite lifetime by about 300%, and the performances of the network are only slightly degraded, the blocking ratio increases by only 1.2%, and the service delay increases by 1.3 ms.
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1. Introduction
Satellite communication has become an important part of the communication network. Specially, the low earth orbit (LEO) satellite network, with its better coverage and lower transmission delay, has gradually become the development trend of the next generation of satellite communication. Iridium has built a network of 66 LEO satellites that can cover the earth [1]. OneWeb has launched more than 400 satellites [2]. Starlink plans to launch 42,000 low-orbit satellites, and more than 3710 satellites have been launched by January 2023 [3].
A stable and sufficient power supply is required for satellites to work in orbit, perform various tasks such as orbit change, altitude adjustment, and communication. There are two main sources of power for satellites: solar panels and batteries. When satellites are in the sunlight, solar panels absorb solar energy and convert it into electrical energy, and charge the battery. When satellites are in the eclipse periods, satellites can only rely on the battery for energy supply. The life of the battery largely determines the life of the satellite [4]. There are many studies to improve battery life from battery materials and structures [5]. After a satellite is launched, the parameters of the battery are fixed. At this time, the life of the battery is affected by factors such as temperature, discharge rate, depth of discharge (DOD), etc. [6]. The DOD refers to the ratio of the current battery power consumption to the total battery power [7], which is an important factor affecting battery life. Take the lithium-ion battery commonly used in satellites as an example, in order to obtain 100% energy of the battery, instead of discharging the battery from 100% to 0% (where DOD is 100%), it is better to discharge the battery from 100% to 50% (where DOD is 50%), and recharge it to 100%, and discharge it to 50% again [8]. Keeping the battery at a lower DOD, results in a longer life of battery.
Routing refers to calculating and allocating a path for transmitting service. In satellite networks, satellites take on the role of routers [9]. Prior studies explore the routing problem in the satellite network from the perspective of improving network capacity, reducing transmission delay, etc. [10–12]. However, these routing schemes do not take into account the energy consumption caused by routing. Unrestrained use of satellites with high DOD leads to satellites aging quickly. As shown in Fig. 1, with the same power consumed, using satellites with higher DOD for routing purpose will result in more battery life reduction.
The researches on energy-efficient routing of terrestrial Internet do not consider the battery life [13,14], so existing approaches cannot be applied in satellite networks. The satellite energy-efficient routing problem was first proposed by Yang in 2016 [15]. The paper analyzes the relationship between routing and battery DOD, then it proves the energy-efficient routing problem in satellite networks is NP-hard, finally it proposes an energy-efficient routing scheme, GreenSR. GreenSR pre-calculates the shortest path of all services and cuts the set of nodes included in the path into a minimum spanning tree (MST). Then GreenSR selects the rest of nodes to join the MST to obtain a new topology. In the new topology, the paths of all services are recalculated until all nodes are traversed. When calculating the routing path, the satellite battery DOD is added to the edge as a weight to ensure that the routing consumes less battery life. Liu [16] proposes a satellite energy-efficient routing scheme, DRL-ER. The routing path of the service is obtained through reinforcement learning, which decreases the life consumption of the satellite network by 55% and ensures that the service delay is within the specified range. Chou [17] proposes a network architecture in which GEO and LEO satellites work together. Under the architecture, EDCA algorithm was proposed to predict the number of LEO satellites skipped when traffic passes through high-orbit satellites, thereby improving network life.
GreenSR needs to calculate the MST of the satellite topology in advance. When the scale of the satellite network is large and the ground nodes are dense, the MST is too small and a large number of nodes needs to traverse, which is time-consuming and may not be able to search for the optimal solution. When using DRL-ER, each service uses the reinforcement learning model to output the routing path, the routing calculation is inefficient. EDCA utilizes the architecture of multi-layer satellite network to realize energy-efficient routing, which has strong constraints and cannot be used in a single-layer satellite network. Previous researches on satellite energy-efficient routing have their own limitations. Besides, they assume that the inter-satellite link using microwaves. The algorithms improve the life of the satellite network based on the idea of load balancing to distribute traffic. With the development of optical devices and acquisition, tracking and pointing (ATP) technology, using lasers inter-satellite links to build the satellite optical networks is an inevitable trend [18]. Starlink has successively activated inter-satellite laser links since October 2022. In the satellite optical network, the inter-satellite link is the laser, which is different from the microwave link. The power of the laser terminal is less, and the transmission power is less fluctuated by service changes. Therefore, the energy-efficient routing based on load balancing cannot effectively reduce the power consumption in the satellite optical network. To solve the above problems, this paper proposes an energy-efficient routing scheme for satellite optical networks, using genetic algorithms (GA) to select satellites that perform communication tasks, and satellites that do not perform communication tasks to enter a low-power sleep state, to save energy. The GA-based scheme does not traverse the entire network nodes, so routing strategy is obtained more efficiently. Moreover, after obtaining the routing planning, within a period, all services can be routed through basic routing algorithms such as the shortest path, which reduces the route calculation time. The main contributions of the work are as follows:
- • Based on the energy-efficient routing model in satellite networks, a satellite optical network energy-efficient routing model is proposed.
- • A representation for satellite optical network suitable for genetic algorithm is proposed.
- • A genetic algorithm-based energy-efficient scheme in satellite optical networks is proposed, which improves the life of the satellite optical network while ensuring that the network capacity does not decrease below a certain threshold.
- • We compare the performances of blocking ratio and service transmission delay after using energy-efficient routing, which were not analyzed in previous studies.
2. Satellite ageing model
This section introduces the power supply mode and power consumption model of the satellite. Based on the models, the relationship between the satellite life and the battery depth of discharge is analyzed, which provides a theoretical basis for the energy-efficient routing model for satellite optical networks.
2.1 Power supply for satellites
Typically, there are two sources of power in a satellite, solar panels and batteries. In the sun, the solar panels absorb solar energy and convert it into electrical energy to support the work of the satellite and charge the battery at the same time. During the earth shadow period, the satellite can only rely on the battery for power supply. The satellite moves around the earth, and the distance and angle between the satellite and the sun constantly change. Even if the solar panel is designed to rotate toward the sun, the solar power that the satellite can receive changes. When the satellite completely enters into the shadow, it cannot be powered by solar energy.
Typical satellite solar panel systems use single-axis solar tracking, which always maximizes the angle between the solar panel and the sunlight. The axis of the solar panel coincides with the roll axis (longitude axis). We use $\alpha$ to represent the angle between the orbit plane and the sun, and $\omega$ to represent the angular velocity of the satellite (i.e., radians per second), then the orbital period of the satellite is t, and $0 \le t \le 2\pi /\omega$. Assuming that the distance between the satellite and the sun is the largest at time ${t_0}$, then at any time, t, the satellite rotates in an arc of $\theta = (t - {t_0})\omega$. We define $\beta$ as the angle between the normal of solar panel and the sunlight, and our goal is to minimize $\beta$ through rotation. Then we can get ${\beta _m} = \arccos \sqrt {1 - {{\cos }^2}\alpha {{\cos }^2}\theta }$. According to the [15], the output power of the solar panel can be expressed by Eq. (1):
where $\gamma$ represents the total amount of solar radiation received by the solar panel, $\eta$ indicates photoelectric conversion efficiency, S is the area of the solar panel. We set the satellite orbit altitude to 1050 km, RAAN to 0, inclination angle to 89 degrees, S to 15.43${\textrm{m}^2}$ and $\eta$ to 1, and using the satellite simulation system for verification. The obtained solar output power is shown in Fig. 2:From Fig. 2, it can be seen that the periodic change of the output power of the satellite solar panel is consistent with the model we established (the difference is from the influence of the space environment), and the solar power is zero during the earth shadow period.
2.2 Power consumption of satellites
Power consumption of the communication satellite in satellite optical networks can be divided into four parts. First, the consumption of basic functions ${P_{base}}$, such as maintaining altitude and rotating solar panels. This work mainly discusses the power consumption of communication, so the basic power consumption is regarded as a constant. Second, the consumption of laser terminals ${P_{ISL}}$ for building inter-satellite laser links. Third, the consumption of microwave communication antennas ${P_{GSL}}$ for building ground-satellite links. Fourth, the power consumption of the on-board processor for processing traffic ${P_{prs}}$. We assume that the traffic flow through the i-th satellite ${v_i}$ is ${T_i}$, where ${T_i}$ can be expressed by the Eq. (2):
According to [19–21], ${P_{ISL}}$ and ${P_{GSL}}$ have a linear relationship with the traffic flow, and ${P_{prs}}$ have an exponential relationship with the traffic flow. Then $P_i^{ISL} = P_i^{OT} + \alpha \sum {T_i^{ISL}}$, $P_i^{OT}$ is the basic power of the satellite laser terminal, which is used for acquisition, aiming and tracking, etc. $P_i^{GSL} = P_i^{RA} + \beta \sum {T_i^{GSL}}$, $P_i^{RA}$ is the fundamental power of the microwave antenna. $P_i^{prs} = \xi {({T_i})^\lambda }$. Then the power consumption of the satellite is Eq. (3):
Satellites generally have two working modes, work mode and sleep mode, such as remote sensing satellites. In work mode, the satellite performs various tasks. In sleep mode, only the basic functions are reserved to maintain the operation of the satellite. It is generally recognized that communication satellites do not sleep in order to ensure the communication needs, whereas, with the increase in the number of LEO satellites and the use of inter-satellite laser links, not all satellites need to perform communication tasks. In this work, we assume that when the communication satellite is asleep, only the basic functions of the satellite are retained without any transmission. The power consumption model for satellites is shown as Eq. (4):
2.3 Ageing model of satellites
The aging of satellites is caused by many factors, such as the aging of mechanical parts, high-energy particle radiation, battery aging, and so on. Battery aging is a major factor affecting the life of satellites. Presently, there are many risks for using nuclear batteries in satellites, the most widely used in satellites are rechargeable batteries. For rechargeable batteries, the life of the battery can be expressed by the battery cycle life (or the number of cycles), and one cycle represents the discharge of the battery from 100% capacity to 0%. When the battery exceeds the number of cycles, the battery enters a state of strong loss, and its performance drops significantly. For lithium-ion battery cells that are commonly used in satellites, the battery cycle life is closely related to the material and design of the structure. When the basic parameters of the battery are set, the cycle life of the battery is mainly related to the depth of discharge, discharge rate, temperature, etc. This work focus on the depth of discharge (DOD). DOD refers to the ratio of the current power consumption of the battery to the total power of the battery, as shown in Eq. (5):
${L_{t1t2}}$ is the life of the battery consumed. Figure 3 shows the curve of $f(D)$.
The gray area is ${L_{t1t2}}$. It can be seen from the figure that the integral area is Area1 when the DOD is from 20% to 40%, and the integral area is Area2 when the DOD is from 60% to 80%, Area1 < Area2. We can see the different DODs have different effects on the battery life even if the same power is consumed. The smaller the DOD, the slower the battery life ages.
3. Problem statement
In this section, we build the satellite optical network model and traffic model, specify the problem of energy-efficient routing in satellite optical networks, and analyze that the problem cannot be solved by solving equations.
3.1 Satellite optical network model
A system composed of multiple satellites working cooperatively is called a satellite constellation [24]. A satellite constellation describes the topology of a satellite network from a geometric perspective. We describe the satellite network as G(V, E), V is the set of all satellites and E is the set of all inter-satellite links (ISLs).
Satellite networks dynamically change, which is embodied in two aspects, 1) the distance change of inter-satellite links in the different orbits, 2) the position change between satellites and the earth surface. To route in the dynamic satellite networks, the routing scheme based on virtual topology is proposed and widely used [25]. The virtual topology refers to fixing the satellite network topology as a snapshot at different time points. The topology in the snapshot is considered static. It can reflect the actual satellite network topology by combining the multiple snapshots. Assume the snapshot duration is from t1 to t2, then the goal of this study is to minimize the cycle lifetime consumption of the satellite network within each snapshot.
3.2 Gravity traffic model
The traffic in the satellite network comes from the ground, and the intensity of the ground traffic varies according to the population and development of the region. We divide the earth surface into 12${\times}$24 = 288 regions and set the traffic intensity according to the real number of Internet users in these regions [26]. The flow of traffic between different regions is then modeled according to the gravity model [27]. Let Ti represent the traffic request of region i, and Tij represents the flow from region i to region j, then Tij can be expressed by Eq. (10):
The lenij indicates the distance between Ti and Tj. In this work, we aim to reduce the satellite network life consumption without affecting the network capacity, so the goal of energy-efficient routing is to minimize the network blocking ratio $\min B(Tij)$, $B({\cdot} )$ is the network blocking ratio.
3.3 Energy-efficient routing in satellite optical networks
In this research, we only consider satellites using rechargeable batteries. Satellites move around the earth and are alternately in sunlight and shadow. From 2.1, it can be seen that satellites in shadow can only be powered by batteries. The orbital period of the LEO satellite is short (about 2 hours), so satellites are frequently alternated in shadow and sunlight, and the battery discharges frequently. From 2.3, we know the cycle life consumption is quite different under different DOD, even if the battery discharge same energy. The satellite ages quickly in a state of low DOD for a long time, which affects the structure of the entire satellite network.
The energy-efficient routing problem considered in this work is how to select satellites for routing with more suitable DOD. The goal is to reduce the overall life consumption of the satellite network without affecting the network capacity.
The ${L_{t1t2}}$ is the lifetime consumption of the satellite network, and B is the network blocking ratio. From the Eq. (4), (7), (8), the formula (12) can be obtained, where T is the traffic, D is the DOD, and P is the power consumption:
Due to the uneven distribution of the traffic and various nonlinear effects that affect the satellite cycle life, how to reduce the consumption of the satellite life as much as possible while ensuring that the network blocking ratio does not increase has become a nonlinear combinational optimization problem, so the optimal solution of energy-efficient routing in satellite optical networks cannot be obtained by solving equations.
4. Genetic algorithm-based energy-efficient routing
In section 3, we model the energy-efficient routing problem in satellite optical networks. We analyze that using energy-efficient routing strategies can improve the overall lifetime of the network without reducing network capacity. Due to the nonlinear relationship between the life consumption and the DOD, the problem cannot obtain optimal solutions by solving equations. Therefore, in this work, we use the heuristic algorithm, genetic algorithm, to search for the optimal solution. The genetic algorithm is used to select which satellites are on standby and which satellites are used for communication, then using the shortest path algorithm to calculate among the working satellites.
4.1 Genetic algorithm
Genetic algorithm [28] is a kind of evolutionary algorithm, which is a random search strategy based on the theory of biological evolution. Genetic algorithm simulates the evolution process of organisms in the computer, and can be used to solve tasks that are difficult to model mathematically. The steps of genetic algorithm are: 1) chromosome representation: a feasible solution in the problem is defined as a chromosome, and the variables in the solution are called genes; 2) initialization: select some chromosomes as the initial population; 3) calculate the fitness: evaluate the pros and cons of chromosomes through the defined fitness function; 4) selection: select chromosomes for inheritance according to rules; 5) crossover: exchange genes on two chromosomes; 6) mutation: randomly modify genes on chromosomes. By iterating steps 3-6, the genes of the chromosomes in the population are updated, so that the fitness reaches the expected goal, and the optimal solution to the problem is quickly found by simulating the search strategy of natural selection.
4.2 Chromosome representation of satellite optical networks
The basic and key step that using genetic algorithm to solve problems is to represent the feasible solution into chromosomes. In this work, we represent all satellites in the shadow period as a chromosome, and satellites exist in two states, work mode and standby mode. In the work mode, the satellite can use the GSL or the ISL for service transmission. In the standby mode, the satellite only provides the power to maintain the basic work of the satellite without any service transmitting. The length of the chromosome is the number of satellites in the shadow, where 0 means sleep mode and 1 means work mode. As shown in Fig. 4.
4.3 Genetic algorithm-based energy-efficient routing
The genetic algorithm-based energy-efficient routing (GA-EER) proposed is based on the virtual topology routing [29], i.e., the changing satellite network topology is divided into static topology snapshots according to time intervals, and the services are routed in each snapshot. In this work, the satellite network is divided into snapshots at 5-minute intervals. For each snapshot, we first use the genetic algorithm to obtain the optimal satellite topology for communication, then the shortest path computation (i.e., Dijkstra algorithm) under the topology. Specific steps are as follows:
- 1) Initialization: Determine the set of satellites in the earth shadow period, first set the initial state of all satellites as sleep status, and then randomly select a certain number of satellites to be the work mode. In this work, the number of satellites in the earth shadow period is about 230, we set the number of sleep satellites is 110. In this way, a chromosome is initialized. A chromosome is a sub-topology, which is expressed as an energy-efficient topology below. Next, use the same method to establish an initial population with 50 chromosomes;
- 2) Routing: In each energy-efficient topology, perform routing to obtain two indicators of satellite network, life consumption ${L_{t1t2}}$ and blocking ratio B;
- 3) Fitness calculation: The weighted sum of the life consumption and blocking ratio is used as the fitness, $F({\cdot} ) = m{L_{t1t2}} + nB$. The expected goal of fitness is that the satellite life consumption is reduced, and the network blocking ratio is reduced. Set the fitness threshold. When the fitness reaches the threshold or the fitness convergence, stop the iteration. If the requirements are not met, the GA-EER continues to iterate;
- 4) Selection: Use roulette to select two parent chromosomes from the initial population, that is, the smaller the fitness, the greater the probability of being selected;
- 5) Crossover: One-point crossover is used on the two parent chromosomes according to the probability, that is, a point on the chromosome is randomly selected, and then part of the chromosomes of the two parents are exchanged at this point. Crossover aims to increase the diversity of the next generated chromosomes, in this work, the crossover probability is 70%.
- 6) Mutation: According to the set mutation probability, the value of a gene on the chromosome is randomly changed. In this work, the mode of the satellite is switched, and the corresponding gene changes from 0→1 or from 1→0. The mutation operation is also used to increase the diversity of chromosomes in the new population. In this work, the mutation probability is 5%.
The process of the GA-EER is shown in Fig. 5. The yellow module in the figure represents the basic operation of the genetic algorithm, and the red module combines the unique operations of the energy-efficient routing task, and the outputs is the optimal energy-efficient routing scheme under the current snapshot. Taking the right side of Fig. 5 as an example, all the satellites under the sun maintain the work mode, and the satellites in the shadow are selected to work or sleep through the genetic algorithm. The optimal solution obtained by the GA-EER can ensure that the network performance is hardly degraded while improve the overall life of the satellite network.
5. Simulation results and analysis
5.1 Simulation settings
To guarantee global coverage, we use the polar orbit constellation with an inclination of 89 degrees. The orbital height is 1050 km, which is typical for LEO satellites. In order to verify the effectiveness of the proposed scheme in a large-scale satellite network, we construct the constellation containing 1152 satellites. The constellation has 24 orbits with 48 satellites in each orbit, which can achieve more uniform coverage of the ground. We simulate the satellite network to work 24 hours in 10 hours simulation runtime. The duration of snapshots is a fixed interval, which is 5 minutes. We set the parameters of satellite battery and power consumption according to [20,29]. In this work, we assume that the satellite in sunlight does not use batteries. The service traffic is based on real Internet data [26] and gravity models [27]. We divide the surface of earth into 12${\times}$24 = 288 regions, and set the traffic intensity according to the number of Internet users in these regions. Table 1 shows the parameters for the simulation. Pbase, POT, PRA, $\alpha$, $\beta$, $\xi$, $\lambda$ are the parameters of power consumption in Eq. (3).
Table 1. Simulation settings
5.2 Numerical results and analysis
The goal of energy-efficient routing is to reduce the life consumption of the satellite optical network without reducing the network throughput. In this work, we mainly consider two performance index, blocking ratio and life consumption, and weight them as the loss of the genetic algorithm. Figure 6 is the normalized loss curve of GA-EER under different service numbers. It can be seen that under different service numbers, the losses decrease and tend to converge, indicating that GA-EER has found the optimal solution. From Fig. 6, it can be seen that when the service numbers are 3000 and 4000, it starts to converge around the fifth iteration, and the loss is reduced by about 50%. Under the service numbers of 7000 and 8000, the losses drop slower and fluctuate. Because a fixed number of satellites are selected for sleeping, when the network is overloaded, the number of satellites that need to transmit services increases, and the search for optimal solution becomes more difficult. Future work can explore this problem by dynamically adjusting the number of sleep satellites.
Figure 7 shows the lifetime consumption of the satellite optical network L (defined in Eq. (7)). The benchmarks are Dijkstra shortest path (SP) without considering energy, and the existing energy-efficient routing algorithm GreenSR [15]. It can be seen from Fig. 7 that compared with the SP, GA-EER can effectively reduce the satellite network life consumption by an average of 67%. Compared with GreenSR, the life consumption reduces by about 52%. We convert the service life consumption into the cycle life of the satellite optical network.
Assuming that under the SP algorithm, the cycle life of the network is 5 years, then GA-EER can increase the cycle life to 15.4 years, as shown in Fig. 8.
The cost of the energy-efficient routing is that it affects the performance of the network, such as network capacity and service transmission delay. Figure 9 shows the blocking ratio of different algorithms under different service numbers. The network is blocked at the number of services is 6500 with GA-EER, and the number of services is 7400 with SP and GreenSR. After the number of services is 7400, the blocking ratio increases by an average of 1.2%. That means the GA-EER reduces the network capacity when the network is overloaded.
From Fig. 10, it can be seen that the service transmission delays of the energy-efficient routing are higher than that of SP. This is because energy-efficient routing bypasses some services in order to increase the satellite network life. When the number of services is greater than 7500, the delay tends to be flat. This is because more services are blocked, less delays are counted. From Fig. 10, it can be seen that when the number of services is less than 6500, the average delay of GA-EER is 1.4 ms higher than that of SP. When the number of services is from 6500 to 8000, the average delay of GA-EER is 2.3 ms higher than that of SP and 1.2 ms higher than that of GreenSR. It can be seen that GA-EER brings the cost of increased delay, and the increment reduces as the number of services increases. This is because when the network is overloaded, the routing paths obtained by SP and GA-EER overlap more.
The figures below show the life consumption, blocking ratio and transmission delay of different algorithms in each snapshot when the network is lightly loaded (4000 service number) and the network is heavily loaded (8000 service number). Figure 11 is the life consumption of 100 snapshots, Fig. 12 is the blocking ratio of 100 snapshots, and Fig. 13 is the delay of 100 snapshots. The overall trend of the three indicators is consistent with the above conclusions, which proves that this algorithm can be applied to dynamic satellite optical network scenarios.
We compare the current energy-efficient routing schemes in satellite networks. It can be seen from Table 2 that although the simulation settings of different papers are different, GA-EER is better on reducing the life consumption from the absolute value compared with SP.
Table 2. Performance comparison of different energy-efficient routing algorithms in satellite networks
6. Conclusions
In this paper, we study the problem of energy-efficient routing for satellite laser communication. We propose a novel energy-efficient routing model. We analyze the research problem as a nonlinear combinatorial optimization problem, and propose a genetic algorithm-based energy-efficient routing scheme (GA-EER). The simulation results show that compared with the shortest path algorithm, the proposed scheme can reduce the life consumption by 66.4%, the blocking ratio is 0, and the transmission delay increases by 1.3 ms when the network is lightly loaded. The life consumption is reduced by 65.5%, the blocking ratio is increased by 1.6%, the transmission is increased by 1.8 ms when the network is heavily loaded. The increase of transmission delay is due to the energy-efficient routing selecting satellites with lower DOD through detours. The increase of blocking ratio under heavy load is because a fixed number of satellites are selected for routing in this work. If the number of services is high, the proposed scheme cannot provide enough bandwidth of inter-satellite links. Therefore, future works can consider dynamically selecting different numbers of satellites for routing according to the traffic, to ensure that the network blocking ratio increases less or even does not increase under heavy load conditions.
Funding
National Natural Science Foundation of China (62021005, 62101063).
Acknowledgments
The authors thank the National Natural Science Foundation of China (62021005, 62101063) for supporting this work.
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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