Assignment of hybrid laser and microwave inter-satellite links for navigation satellite systems

Abstract

A hybrid network comprising both laser and microwave inter-satellite links (ISLs) has been established within navigation satellite constellations. Leveraging the flexible construction of microwave links and the high ranging accuracy and communication efficiency of laser links, a collaborative link scheme was proposed. With Position Dilution of Precision (PDOP) and communication delay serving as performance indices, multi-objective optimization models for hybrid ISLs were established, incorporating complex constraints. Assignment algorithms based on Non-dominated Sorting Genetic Algorithm II (NSGA-II) and the standard Genetic Algorithm (GA) were proposed. The effectiveness of the collaborative link scheme and the assignment algorithms was evaluated through simulations. The results indicated that each satellite could establish 18.4 ISLs per minute on average. The average PDOP of hybrid links for geosynchronous orbit (GEO) / inclined geosynchronous orbit (IGSO) and medium Earth orbit (MEO) satellites were 1.5 and 1.1, respectively. The average communication delay from overseas to anchor satellites via pure laser links was approximately 0.15 s. When some laser links were unavailable, the remaining available laser ISLs could collaborate with microwave ISLs to provide a transmission route with a maximum delay of 3.2 s. It was demonstrated that the collaborative link scheme and assignment algorithms effectively addressed the hybrid link assignment problem, considering both inter-satellite ranging and communication.

Introduction

Major navigation satellite systems currently in operation include the United States Global Positioning System (GPS), Russia’s Global Navigation Satellite System (GLONASS), Europe’s Galileo system, and China’s BeiDou Satellite Navigation System (BDS). At the same time, Japan and India have gradually established the regional navigation satellite systems. These systems have realized the core capabilities of global or regional positioning, navigation and timing services to a certain degree. Precision orbit determination and time synchronization, control instruction upload and operation information download are the basis for stable operation of navigation satellite systems. In the early stage of the system construction, the measurement and control of the space segment are all realized by the ground station. However, with the continuous development of the system, the scale of the navigation constellation composed of satellites that maintain a certain space-time relationship with each other has become larger, and the limited ground measurement and control resources are gradually unable to undertake the management task. In particular, with the limitation of the regional distribution of BDS ground stations, the tracking arc of the space segment of the ground operation control system is limited, which greatly limits the improvement of the global service capability of the system. In order to improve the measurement accuracy of space-time and communication efficiency, Inter-satellite Link (ISL) technology has been introduced in navigation satellite systems.

Different from the single communication function of ISLs in communication satellite system, navigation ISLs also take into account the function of inter-satellite or satellite-ground measurement. The GPS Block IIR satellite, representing the second generation of GPS satellites, utilizes a time-division microwave ISL with a wide-beam in the Ultra High Frequency (UHF) band¹. Specifically, each Block IIR satellite broadcasts information to other satellites within each designated timeslot. The inter-satellite ranging and communication across the entire constellation are achieved through a process of multiple timeslot polling. In order to improve ranging accuracy and communication efficiency, and to overcome the disadvantages such as poor anti-interference ability of wide-beam in UHF band, GPS III is planning to use microwave ISLs with narrow-beams in higher frequency band². At present, the BeiDou-3 Global System has adopted the microwave ISL with narrow-beam in Ka-band, and the Galileo system is also planning to adopt the narrow-beam microwave ISL^3,4. The phased array antenna of microwave ISL with the narrow beam requires a large number of transceiver modules and phase controllers. Limited by the satellite platform, the majority of navigation satellites are equipped with only one phased array antenna, and can only build a link with one satellite at the same time. Therefore, the space-division time-division duplex mechanism is adopted for narrow beam microwave ISLs. The flexible pointing of phased array antennas is utilized to realize the rapid switching of microwave ISLs between different targets, which brings a problem of optimization for link assignment⁵. Yang⁶ and Yan⁷ proposed a link slot allocation method based on intelligent optimization algorithm to reduce communication delay and increase the number of ranging links. Hou⁸ described the information transfer process of directional time-division navigation ISLs based on the directed graph theory, and proposed the shortest route determination method based on the Dijkstra algorithm. Sun⁹ optimized the topology and routing of ISLs with the goal of minimizing the delay of communication to ground, and used the Position Dilution of Precision (PDOP) as an evaluation index of inter-satellite ranging geometry for ranging link assignment.

At present, the majority of navigation satellite systems use microwave ISLs for networking. In order to achieve higher ranging accuracy and communication efficiency, laser ISLs are gradually introduced into navigation satellite systems. Compared with communication in the Radio Frequency (RF), wireless optical communication of the laser ISL has the advantages of high transmission rate, high security, low power consumption, and strong anti-interference ability. Laser ISLs have been verified by many tests on communication satellites^10,11. However, due to the extremely small divergence angle of the beam, the establishment of ISLs requires a time-consuming Acquisition, Tracking and Pointing (ATP) process¹². Because the link cannot be switched as quickly as the traditional microwave ISL, the laser ISL cannot provide the ranging information needed for precise orbit determination with different satellites although its ranging accuracy is higher. Therefore, laser ISLs cannot completely replace microwave ISLs under the requirements of inter-satellite ranging and communication. It is an important stage of system development to gradually introduce laser ISL into the existing microwave ISL network of navigation satellites, so as to form a hybrid network of laser and microwave ISLs.

Currently, the laser ISL technology for satellite navigation systems is still in the experimental phase¹³. Preliminary research has been conducted on the assignment of hybrid laser and microwave ISLs. In the hybrid laser and microwave ISL network, the process of inter-satellite ranging and communication is restricted not only by the number of ISL devices on board and inter-satellite visibility, but also by two different link systems. Aiming at the ISL assignment of laser/microwave hybrid network in navigation constellation, Tian¹⁴ proposed a grouping topology assignment algorithm for hybrid ISLs of high, medium, and low Earth orbit navigation constellations. However, the assignment process only considered the data transmission needs of the constellation and did not take into account the inter-satellite ranging requirements. Zhang¹⁵ proposed a collaborative ranging scheme for laser and microwave links in navigation constellations and demonstrated through simulation that the addition of laser inter-satellite links can significantly improve the inter-satellite ranging PDOP based on microwave links. Liu¹⁶ and Ding¹⁷ proposed network assignment algorithms based on the simulated annealing algorithm, which simultaneously address the needs of inter-satellite ranging and communication. However, laser links and microwave links adopted time-division independent assignment schemes, with insufficient collaboration between the two different types of links. Additionally, the existing studies only consider the initial phase of laser link construction, when some satellites carry laser link devices. With the extensive application of laser ISLs in low-orbit communication constellations and the development of technology, navigation constellations will gradually complete the deployment of the entire network of laser devices, and realize the connectivity and high-speed communication based on laser links of the whole network. We propose a hybrid link collaborative construction scheme by integrating the high ranging accuracy and communication efficiency of laser links with the flexible establishment of microwave links. This scheme simultaneously addresses the needs of inter-satellite ranging and communication, achieving complementary strengths of different link systems. And on the basis of this scheme, a collaborative assignment model and algorithm for the links have been established.

According to the characteristics of laser links, the process of laser link establishment is divided into a transition state and a steady state. In the steady state, the navigation constellation forms a high-speed communication network through laser links. In the transition state, the microwave ISL provides a temporary communication path. The inter-satellite ranging required for precise orbit determination is mainly realized by microwave links, supplemented by a small amount of high-precision laser ranging information. In the second part, the system of laser and microwave links is introduced. The multi-layer static processing is carried out according to the link maintenance and switch, and the collaborative construction scheme of laser and microwave links is proposed. In the third part, considering the requirements of ranging and communication, multi-objective optimization models with complex constraints of the link system, the number of link devices and inter-satellite visibility are established. Hybrid link assignment algorithms based on the Non-dominated Sorting Genetic Algorithms-II (NSGA-II) algorithm and the standard Genetic Algorithm (GA) are proposed in the fourth part. In the fifth part, the ISL assignment simulation is carried out to evaluate the performance of collaborative link scheme and the effectiveness of link assignment algorithms.

Hybrid link scheme

The system of ISLs

Microwave ISLs with narrow beams

The narrow-beam microwave ISL adopts a phased array antenna which can realize narrow-beam scanning, and achieves Effective Isotropic Radiated Power (EIRP) of the beam with low power consumption. Due to the beamwidth limitation, a link device can only establish a link with one another device. Phased array antennas require a large number of transceiver modules and phase controllers, and navigation satellites usually carry only one phased array antenna due to the limited satellite platform.

In order to realize the whole network measurement and communication of the navigation constellation with constraints of the number of link devices, the Concurrent Spatial Time Division Duplexing (CSTDD) system is adopted in the microwave ISL. The single link works in the half-duplex mode. Forward and backward links are distinguished by time separation to realize inter-satellite bidirectional measurement and communication. Multiple links are multiplexed in space through the narrow beam pointing switch of the phased array antenna to complete the link construction with different satellites, as shown in Fig. 1.

Fig. 1.

Establishment and switching of narrow beam microwave ISLs based on CSTDD.

In the CSTDD system, the timeslot is the basic unit of link construction and maintenance. The satellite can establish a bidirectional link with a visible satellite at each timeslot. Its link target is switched at the next timeslot to link with multiple visible satellites. The assignment problem of microwave ISLs is to select the link target of each satellite at different timeslots.

Laser ISLs

In a satellite network built with laser ISLs, the laser device converts the data into an optical signal, which is then transmitted to the target satellite. After the device on the target receives the optical signal, it is converted into an electrical signal, which is decoded and processed, and finally the original data is obtained. Laser links can communicate at a rate of hundreds of Gbit/s in free space and have higher ranging accuracy than microwave links^16,18. In addition, the energy density of laser communication is higher and the mass of laser devices is smaller. Using laser ISLs can effectively reduce satellite energy consumption and the requirements on satellite platform capacity, so that a satellite can carry multiple laser devices^10,19.

Different from traditional RF ISLs, the laser signal is highly directional, and the extremely narrow divergence angle of the beam results in the signal being received only by the receiver in the path of the laser beam, so the laser link can only be built point-to-point between satellites. In addition, the higher alignment and tracking accuracy requirements at both ends of the link require a time-consuming ATP process to establish a reliable and stable laser ISL, which makes it impossible to achieve frequent link switching like microwave links²⁰. Therefore, the laser ISL network of the navigation constellation is established with the Finite State Automaton (FSA) system²¹. The operation mechanism is to divide the constellation operation process into several laser link cycles, which are much larger than the microwave link timeslot. The link cycle is the basic unit of laser link establishment and maintenance. Each cycle includes the transition state and steady state of the link. The transition state mainly completes the ATP process, while the steady state of the link maintains the fixed topology of the laser network. In the next laser link cycle, the topology structure is reconstructed according to this process, as shown in Fig. 2. In the transition state, the link in the ATP process has not been established stably, so it does not have the function of inter-satellite measurement and communication.

Fig. 2.

Establishment and switching of laser ISLs based on FSA.

Static processing of link topology

The high-speed motion of navigation satellite constellations in space determines that ISLs cannot maintain a fixed topological structure over extended periods, but rather exhibit dynamic changes. However, based on the microwave and laser link systems introduced earlier, the timeslot of the microwave link and the cycle of the laser link are the basic units for link establishment and maintenance. Within the unit, satellites maintain a fixed link topology. The link topology is dynamically restructured when entering the next unit. Therefore, during the duration of each link unit, both the microwave link and laser link topologies can be regarded as static structures.

Due to the periodicity of the movement and covering the Earth of the navigation constellation, the system operation time can be divided into several cycles. When satellite-ground communication needs to be considered, the operation cycle is the regression cycle of the constellation. The relative orientation of satellites and ground stations in space is repeatable in each operation cycle, so the same topology structure can be used to establish ISLs.

Although the number of instantaneous link construction is limited, thanks to the flexible link switching ability, navigation satellites can obtain the inter-satellite ranging information required for orbit determination and realize the inter-satellite data transmission through the microwave link switching at multiple timeslots. Accordingly, microwave link assignment and performance evaluation need to be combined with the topology of multiple timeslots. The time interval of assignment and evaluation is the superframe of microwave links. As shown in Fig. 3, the operation cycle of the system can be divided into superframes of equal length of time. Each superframe is the basic unit of link assignment and performance evaluation and is composed of timeslots. The timeslot is the basic unit of microwave link establishment and maintenance. Each satellite can establish a link with a visible satellite (, is the total number of microwave links established by a satellite in a superframe) at each timeslot, and the link target can be switched between timeslots. Therefore, the microwave link topology of the whole constellation formed at each timeslot maintains a static structure.

Fig. 3.

Static disposal of microwave link of a satellite.

The advantage of laser links over microwave links is that each satellite can carry multiple laser link devices, so it is possible to establish links with multiple satellites at the same time. However, due to the complexity of ATP process, laser links need to be maintained for a long time once established. The time it takes for a link topology to be established and maintained is the laser link cycle. As shown in Fig. 4, the system operation time is divided into laser link cycles of equal length of time. This cycle is the basic unit of laser link assignment and performance evaluation. In each laser cycle, each satellite’s laser device is linked to a target device (, is the total number of laser links established of a satellite in a laser cycle and is the total number of laser devices on each satellite) of a visible satellite. Therefore, the laser link topology formed by the whole constellation in each link cycle maintains a static structure.

Fig. 4.

Static disposal of laser link of a satellite.

Collaborative construction scheme of laser and microwave links

Laser ISL can provide more accurate inter-satellite ranging and more efficient inter-satellite communication than microwave links, but due to the limitation of link construction process, it is impossible to realize flexible link switching to meet the requirement of precision orbit determination. At the same time, the ATP process of link establishment makes the transition state link unavailable. The microwave ISL can be constructed between different visible satellites through flexible beam switching to provide rich ranging information, but the ranging accuracy and communication efficiency are lower than that of laser links. In order to realize the complementary advantages of two type of links with different systems, a collaborative construction scheme of laser and microwave links is proposed.

As shown in Fig. 5, a constellation regression period contains laser link cycles. Each laser link cycle has the same length with superframe of microwave links, and is composed of two link states: transition state and steady state. The steady-state duration of the laser link is equal to superframes of microwave links. The laser link in steady state constitutes the backbone communication network of the constellation, which completes the inter-satellite data transmission and provides a small amount of high-precision inter-satellite ranging information. A large amount of inter-satellite ranging information is provided simultaneously by the microwave link in the superframes. The transition-state duration of the laser link is equal to superframes of microwave links. And the laser link without switching can still be used as the inter-satellite communication link. The communication path of the laser backbone network is reduced due to the unavailability of the link in the transition state. The microwave link is used as the supplement to form a temporary communication path and jointly provides inter-satellite ranging information.

Fig. 5.

Laser/microwave cooperative scheme of link establishment.

Assignment model of hybrid ISLs

Inter-satellite visibility

The basic premise of establishing ISLs between satellites is that they can be visible to each other. Factors affecting inter-satellite visibility mainly include Earth shelter on the signal propagation path and beam scanning range of link devices, as shown in Fig. 6. The specific criteria can be found in²².

Fig. 6.

Visibility between satellites. The ISL antenna is mounted towards the center of the earth with a scanning angle and is the Earth radius.

Based on the static processing of the dynamic establishment process of laser/microwave links, the laser cycle and microwave superframe are the basic units of link assignment, so the inter-satellite visibility is required to remain constant within the assignment unit. Symmetric visibility matrices and are respectively used to describe the visibility between laser link devices and microwave link devices in each assignment unit. When the two satellites and are continuously visible in the whole assignment unit, the two satellites are considered to be visible, and the corresponding visibility matrix elements and , meetting the conditions for the establishment of laser links and microwave links respectively. Otherwise, it is not visible between the two satellites, and , . Because of the difference in durations of laser cycles and microwave superframes, the device visibility of the two ISLs needs to be determined separately.

Link assignment matrix

After the dynamic establishment process of laser/microwave links is statically processed, the static topology of lasers and microwave links is maintained in their link cycle and link timeslot respectively.

The laser link topology for each link cycle is described by an assignment matrix ( is the total number of satellites in the constellation). The row elements of the assignment matrix are the link targets of each device of the satellite . The element represents the device of satellite is linked with satellite . Under the constraint of the bidirectional link system, a laser device of satellite is also linked with satellite and . indicates that the device of satellite is idle.

According to the laser link assignment matrix, the link topology can be equivalent described by a symmetric adjacency matrix . Matrix element represents satellite and to establish a laser link. Correspondingly, and . indicates that no laser link has been established between satellite i and j in the current cycle. Constrained by the number of laser devices on each satellite, the symmetric adjacency matrix further meets and .

The microwave link topology at timeslot k in a superframe is described by an assignment vector . Vector element is the link target of satellite at timeslot . indicates that satellite is idle at the current timeslot. indicates that the satellite and build a link at timeslot . With the constraint of bidirectional system, . The assignment vectors of K timeslots together constitute the microwave link assignment matrix of the superframe .

Each microwave link topology at each timeslot can be equitably described as a symmetric adjacency matrix . Matrix element represents satellite and to establish a microwave link, correspondingly, and . indicates that no microwave link is established between the two satellites at the current timeslot. Constrained by the number of microwave devices on each satellite, the adjacency matrix further meets and .

Optimization model of link assignment

In addition to finally realizing the autonomous operation of the navigation satellite constellation, the important function of the ISL in the conventional operation mode is to realize the inter-satellite ranging and the rapid return of operation data under the restriction of regional ground monitoring stations. Therefore, the goal of link assignment is to give full play to its measurement and communication functions.

Inter-satellite ranging performance

With the dual one-way ISL system, the decoupling of spatial information and clock deviation information can be achieved. Therefore, ISLs can provide inter-satellite geometric distance information free of clock deviations for precise orbit determination. Precise orbit determination is equivalent to the inverse process of spatial positioning, and its accuracy is influenced by the precision, quantity, and geometric configuration of the ranging links. The PDOP can be used to comprehensively evaluate the performance of the ranging links^9,21,23.

The PDOP of all ranging links established by the satellite in a link assignment unit is

1

Where, the measurement matrix.

2

is the spatial position coordinate of satellite , ( is the number of links) is the coordinate of the satellite linked with the satellite . is the inter-satellite geometric distance and is the trace operation of the matrix.

A smaller value indicates superior performance of inter-satellite ranging links established by satellite within the link assignment unit, consequently enabling higher orbit determination accuracy. Therefore, the assignment requirement of laser/microwave hybrid ISLs for inter-satellite ranging can be precisely formulated as

3

That is to minimize the maximal PDOP of inter-satellite ranging links of satellites in the constellation.

Inter-satellite communication performance

The data return delay is a key index to measure the efficiency of satellite-to-ground communication, including inter-satellite transmission delay and satellite-ground transmission delay. The satellite-ground transmission delay does not occupy ISL resources, so the ISL assignment only considers the inter-satellite transmission delay. The satellites that can be monitored by regional ground stations are called anchor satellites. The data return of anchor satellites utilizes the satellite-ground link rather than the inter-satellite link, resulting in zero intersatellite transmission delay. Satellites that cannot be monitored by ground stations are called overseas satellites, whose data return requires a joint of ISLs and satellite-ground links.

The delay of inter-satellite transmission is limited by the ISL system. Under the premise that the whole network is connected through laser links, data transmission is not limited by the switching cycle of laser links, and the delay is determined by the inter-satellite distance, data volume and link bandwidth. The data volume varies significantly among different types of services, and the link bandwidth allocation is dynamically adjusted according to service priorities and network conditions during actual operation. Most importantly, the propagation delay determined by the inter-satellite distance is usually the main source of delay in inter-satellite communication. Therefore, only the laser link communication delay caused by the inter-satellite distance is considered.

4

Where, represents the spatial distance between any two satellite and , and denotes the speed of light in a vacuum.

In the time-division system of microwave links, there is no end-to-end real-time path between satellites, and multi-point communication needs to be achieved through link switching. This factor results in the inter-satellite communication delay is determined by the ISL switching cycle, that is, the timeslot. The communication between overseas satellites and anchor satellites can be realized through at least one microwave ISL, and the corresponding transmission delay is at least 1 timeslot length .

The inter-satellite communication delay for any satellite in the constellation to realize data return through hybrid laser/microwave links is.

5

Where, and are respectively the number of laser links and microwave links included in the transmission path with the minimum delay from satellite S to an anchor satellite, and the delay of laser links is determined by (4).

In a hybrid laser/microwave link topology, the data return delay of each satellite in the constellation varies. Performance evaluation index such as the average delay or maximum delay of the constellation can be used. Focusing solely on the average delay of the constellation may overlook delay issues in extreme cases. The maximum communication delay of the constellation reflects the system’s performance under the most adverse conditions. For satellite navigation systems, the real-time performance of information transmission between satellites and the ground stations directly affects the accuracy and safety of the system’s services. By optimizing the maximum communication delay, it can be ensured that even in the worst-case scenario, data return can meet the basic requirements for real-time performance. Therefore, the assignment requirements for communication efficiency in a hybrid laser/microwave ISL network can be described as

6

That is to minimize the maximal ISL delay to anchor satellites of satellites in the constellation.

Optimization model

Laser and microwave ISLs have different construction systems and different assignment units, which cannot be described with a unified assignment model. Therefore, a step-by-step assignment scheme is adopted. The laser ISLs constitute the backbone network of the navigation constellation. Firstly, the laser links are assigned to achieve the optimal performance of inter-satellite communication and ranging. Based on the laser backbone network, the microwave link assignment is carried out to further optimize the network performance, and emergency communication links are provided in the transition state of the laser link.

Based on the model of inter-satellite visibility and assignment matrices established above, and considering the inter-satellite communication and ranging requirements of navigation constellations, the optimal model of laser ISL assignment under the constraint of ISL system can be described as follows.

7

Among them, the first constraint is the visibility constraint between two linked satellites. The second is the bidirectional link constraint. The third and fourth items are that the number of links built for each satellite does not exceed the number of laser devices carried.

Based on the backbone network established by laser links, the topology configuration of microwave links is optimized to further improve the communication and ranging performance. In the microwave superframe within the transition state of laser links, due to the unavailability of some laser communication links, the microwave link needs to provide both ranging and communication links. The optimal model can be described as follows.

8

Among them, the first constraint is the inter-satellite visibility constraint. The second constraint is bidirectional link system. And the third constraint is that each satellite can only establish one link in a single timeslot at most.

In the steady state of laser links, the laser link provides the inter-satellite communication link, and the microwave link only provides the ranging information. The optimization model (8) only considers the optimization objective .

Assignment algorithm of hybrid ISLs

Algorithm flow

The problem of microwave link assignment within the steady state of laser links is a single-objective optimization problem of minimizing the PDOP of ranging links, which can be solved using the standard Genetic Algorithm (GA). The algorithm achieves population evolution through three standard genetic operations of selection, crossover and mutation, and iteratively updates the optimal solution. The basic flow of the algorithm is shown in Fig. 7.

Fig. 7.

Calculation process of GA. Variable is the current evolutionary population whose maximum is set as .

Laser link assignment and microwave link assignment within the transition state of laser links are both multi-objective optimization problems. The Non-dominated Sorting Genetic Algorithm-II (NSGA-II) with the elite strategy has been widely used in multi-objective optimization problems because of its high computational speed and high population diversity. Before the standard genetic operations of selection, crossover and variation, NSGA-II added the combination of parent and progeny populations, as well as the hierarchical operation based on inter-individual domination, and finally obtained the Pareto optimal solution^24,25. The basic calculation process of the algorithm is shown in Fig. 8, which mainly includes the following four parts:

Fig. 8.

Calculation process of NSGA-II. Variable is the current evolutionary population whose maximum is set as .

(1) Pretreatment: A random strategy is used to generate the initial parent population of size , and the progeny population of size is generated based on selection, crossover and mutation genetic operators.

(2) Non-dominated sorting and crowding calculation: The parent population and the progeny population are merged into a mixed population of size . The mixed population is non-dominated sorted and the crowding degree is calculated.

(3) Population evolution: According to the calculation results of non-dominated sorting and crowding degree of the mixed population, the first individuals in the crowding order are taken as the new parent population, as shown in Fig. 9. Selection, crossover and mutation are further implemented on the new parent population to produce a new progeny population.

Fig. 9.

Generating the new parent population through non-dominated and crowding distance sorting.

(4) Evolutionary termination determination: If the current evolutionary generation does not reach the maximum, return to step (2), otherwise the evolutionary is terminated.

The algorithm involves the core steps such as non-dominant sorting, crowding calculation, selection, crossover and mutation. The implementation of crossover and mutation is consistent with the standard GA.

Standard genetic operation

Standard genetic operations include selection, crossover and mutation. For the single-objective optimization problem of microwave links, the roulette strategy is used to implement the selection operation. The specific implementation of standard genetic operations in microwave link assignment is referred to the author’s previous work²⁶.

For multi-objective optimization problems, NSGA-II uses a binary tournament as a selection operation. In each generation, two individuals are first randomly selected from the current population using a binary tournament selection operation, and then the one with a lower non-dominant level or a bigger crowding is selected. In addition, due to the differences between laser link assignment problem and microwave link assignment problem in terms of individual coding methods and constraints, crossover and mutation operations cannot be fully implemented using the methods described in [26].

The genetic crossover in laser link assignment takes the adjacency matrix as the operation object. Figure 10 shows the crossover process of the laser link topology formed by four satellites, each carrying two laser link devices. The process consists of two steps, link interchange and topology repair.

1. Link interchange. Two genetic individuals and are randomly selected and all the elements in row () and column of the corresponding link adjacency matrix and are interchanged. The link interchange process can ensure that the newly generated adjacency matrix and still satisfy the bidirectional link constraint and the visibility constraint.

2. Topology repair. The above link interchange process may lead to the number of built links of a single satellite exceeding the number of devices, so the link topology needs to be repaired. For satellites i with excessive links, set element 1 of the row i and column i of the adjacency matrix to 0, that is, remove redundant links one by one, until the repaired adjacency matrix elements meet the requirements and . The criterion for removing links is that the number of links of the object is the maximum. As shown in Fig. 10, in the laser link topology defined by the adjacency matrix after link interchange, there are three links for satellite 4, and one redundant link needs to be removed. The links that can be removed include satellite 4-satellite 1 and satellite 4-satellite 3. The link satellite 4 - satellite 1 should be removed based on the principle that the number of links of satellite 1 is larger than that of satellite 3.

Fig. 10.

The individual crossover based on the laser adjacency matrix. The links in yellow and green are selected to be interchanged between individuals, the links in red are dismantled because of the number limitation of the link devices.

The genetic mutation also takes the adjacency matrix as the operating object. Randomly select an element of the adjacency matrix and meet , reset the adjacency matrix element and . After the mutation, the topology is repaired according to the previous method to meet the constraint on the number of link devices.

Non-dominated sorting

The non-domination sorting of the NSGA-II algorithm is based on the Pareto domination relationship of population individuals. Set three parameters 、 and for any individual in the individual collection , where is the number of individuals in the collection those dominate individual , is the number of individuals in the collection those are dominated by individual , and is the non-dominated level of individual . The process of non-dominated sorting is

1. Initialize the current level , and calculate the and of each individual in the collection .

2. Storing the individual whose from the unsorted individual collection into the collection .

3. For each individual in the collection , each individual of its , let .

4. Set the collection as the th level of non-dominated individual collection. Make non-dominated level for all the individuals in the collection and update the individual collection .

5. If the collection of individuals not sorted , the sorting ends. Otherwise, let , return to step (2).

Pareto domination relationship between population individuals is defined as: for two optimization objectives in link assignment problems and , any two optimization variables and , the situation dominate is defined as satisfies ; weakly dominate is defined as satisfies and satisfies ; and do not dominate each other is defined as satisfies , and satisfies .

The above non-dominated sorting process results in different Pareto level collection , ,…, ( is the total levels) of population individuals as shown in Fig. 11, and the individuals in the collection are not dominated by the individuals in ().

Fig. 11.

Genetic individuals are divided into different Pareto levels through non-dominated sorting.

Calculation and sorting of crowding

The crowding degree represents the spatial density of individuals. The crowding degree of any individual is defined as the side length of the largest rectangle that contains the individual itself but no other individuals in the same Pareto level.

For individuals with smaller crowding degree, their surroundings are more crowded. In order to maintain population diversity and ensure that the algorithm can converge to an evenly distributed Pareto level, it is necessary to sort individuals according to crowding degrees, so that individuals with bigger crowding degree have higher retention priority.

After the non-dominated sorting and crowding calculation, each individual in the population has two attributes, non-dominated level and crowding degree . Define retention priorities of individuals: when two individuals and meet , or meet and , then . The individuals are sorted in descending order of priority, and the ones at the top are retained first. That is, if the non-dominated level of two individuals is different, the individual with smaller non-dominated level will be retained. When two individuals are in the same non-dominated level, the one with the bigger crowding degree is chosen.

Simulation and evaluation of link assignment

Simulation condition

Taking a global navigation satellite constellation equipped with both laser and microwave ISL devices as the object, the assignment simulation of hybrid laser/microwave ISLs is carried out based on the model and algorithm proposed. The satellite constellation is a hybrid constellation consisting of 24 medium earth orbit (MEO) satellites, 3 geosynchronous orbit (GEO) satellites and 3 inclined geosynchronous orbit (IGSO) satellites. Constellation parameters are shown in Table 1. Three ground monitoring stations are located in Beijing (40.09°N, 116.23°E), Xi’an (34.51°N, 109.21°E) and Sanya (18.27°N, 109.18°E). The minimum elevation angle of the ground station is 5 °. The ISL device is pointed to the Earth center with a half-scanning angle of 60 °.

Table 1.

Orbit parameters of global satellite constellation.

Satellite ID	Orbit type	Orbit height (km)	Orbital inclination (°)	Distribution of orbital planes
1 ~ 3	GEO	35,786	0	3 satellites are positioned above the equator at longitudes of 80°, 110.5°, and 140°.
4 ~ 6	IGSO	35,786	55	3 satellites are distributed among 3 orbital planes, with a phase difference of 120°.
7 ~ 30	MEO walker constellation	21,528	55	24 satellites are evenly distributed among 3 orbital planes, with a phase difference of 120° between each pair of orbital planes.

The simulation duration is 7 days, which is approximately a regression cycle of the navigation constellation. The length of microwave ISL timeslot is 3 s. A superframe lasts 1 min, including 20 timeslots. The length of the laser ISL cycle is 1 h, that is, the laser link network maintains a fixed topology during the 1 h, in which the former 10 min is the transition state, and the latter 50 min is the steady state. The size of the genetic population is 60 and the maximum evolutionary generation is 100.

According to the orbit of the constellation and the space position of the ground station, the visibility between satellites and between satellites and ground stations is calculated. Figure 12 shows the visible arcs of each satellite to the ground station. During the whole regression cycle, the number of satellites visible to ground stations is 13 to 18. Among them, three GEO satellites and three IGSO satellites are continuously visible to ground stations. All the MEO satellites are not continuously visible to the ground station. Therefore, the MEO satellite needs to use ISLs to achieve information return to the ground station in its overseas arc.

Fig. 12.

Visibility between the satellites and ground stations.

Microwave link superframes and laser link cycles, as their own link assignment units, have different time lengths. In the static processing of link topology, two satellites are only visible when the device of the ISL is continuously visible throughout the assignment unit. Therefore, there is a difference in visibility between the laser link and the microwave link devices of the two satellites.

Taking GEO satellite #1, IGSO satellite #4 and MEO satellite #7 as examples, Figs. 13 and 14 respectively show the number of satellites visible to their respective laser and microwave link devices. The number of visible satellites of GEO, IGSO and MEO microwave devices is 11 ~ 15, 10 ~ 16 and 15 ~ 23, respectively, and the number of visible satellites to laser devices is 10 ~ 13, 8 ~ 14 and 13 ~ 21, respectively. Due to the longer static processing time, laser links have a more stringent definition of inter-satellite visibility, resulting in loss of visibility. However, because the relative orientation between the satellites changes slowly during the static processing period of 1 h, the number of visible satellites lost by the laser device is only 1 to 2 compared with the microwave device.

Fig. 13.

The number of visible satellites through the microwave link device.

Fig. 14.

The number of visible satellites through the laser link device.

Configuration of laser link devices

The phased array antenna employed in microwave ISLs presents significant implementation challenges due to its narrow-beam characteristics, which necessitate the integration of numerous transceiver modules and precision phase-shifting controllers. Current navigation satellite constellations face critical operational limitations as most platforms, constrained by stringent mass/power budgets and spatial restrictions, can only accommodate a single phased array antenna system. Therefore, each satellite is equipped with only one microwave ISL device in the simulation.

Benefiting from the miniaturization and low power consumption of laser ISL devices, each satellite is capable of carrying multiple link devices. The varying number of devices results in different numbers of links that each satellite can establish, which also leads to differences in ranging and communication performance of the link network. To analyze the impact of the number of laser devices on each satellite on the performance of the link network, each satellite is initially equipped with 3 to 5 laser link devices and link assignment simulations are conducted for several selected laser link cycles (Listed in Table 2) with varying numbers of anchor satellites and average visible satellite counts in the constellation. Since the primary role of laser ISLs is to form the backbone communication network, the solution with the minimum communication delay in the optimal solution set is selected as the final solution.

Table 2.

Parameters of the selected laser link cycles for simulation.

Link cycle	The number of anchor satellites	The average number of visible satellites in the constellation
1	18 (The maximum within the constellation’s regression cycle)	15.80
6	13 (The minimum within the constellation’s regression cycle)	15.33
51	16	16.33 (The maximum within the constellation’s regression cycle)
143	15	15.27 (The minimum within the constellation’s regression cycle)

The maximal data return delay and ranging PDOP of the constellation with different numbers of laser link devices on each satellite are shown in the Figs. 15 and 16. When the number of laser devices on each satellite increases from 3 to 4, both the maximal return delay and ranging PDOP of the constellation are significantly improved. For link cycle #6, since the number of anchor satellites is the smallest in this cycle, further increasing the number of devices allows the anchor satellite to establish data links with more overseas satellites, thereby further improving the return delay. In other cycles, further increasing the number of devices results in less significant performance improvements. According to the calculation results, as the number of laser devices increases, both the ranging and communication performance of the constellation improve. When the number of devices is 4, the maximal delay in each cycle is less than 0.2 s. Considering the cost-effectiveness of the system, each satellite will be configured with four sets laser devices in the following parts.

Fig. 15.

The maximal return delay of the constellation when each satellite is configured with different numbers of laser link payloads.

Fig. 16.

The maximal ranging PDOP of the constellation when each satellite is configured with different numbers of laser link payloads.

Performance evaluation of laser ISLs

Based on the above configuration of the satellite constellation and ISL devices, the multi-objective optimization algorithm proposed is firstly used to assign the laser ISLs within 168 link cycles in the regression cycle. In the steady state of the laser link, the navigation constellation is provided with inter-satellite route by laser links. Figure 17 shows the statistical results of communication delay between overseas satellites and anchor satellites in each link cycle. Relying only on the laser ISL, the average communication delay of overseas satellites is about 0.15 s, the minimum delay is smaller than 0.1 s, and the maximum time delay is slightly greater than 0.25 s, indicating that the laser ISL can provide efficient data return paths for the navigation constellation.

Fig. 17.

Statistical results of full constellation delay for overseas data return via steady-state laser links in each cycle.

Figure 18 shows the PDOP of the inter-satellite laser ranging link, with an average PDOP of about 3. However, due to the limitation of the number of laser link devices and link system, each satellite can only establish four laser ranging links at most in each link cycle. Too few links cause PDOP to be sensitive to the relative geometry between satellites. With the change of inter-satellite geometry caused by the constellation operation, the minimum PDOP of the constellation is better than 2, while the maximum PDOP is more than 13.3, there is a significant performance difference. Therefore, compared with microwave ISL, laser ISL has higher ranging accuracy, but it cannot provide sufficient inter-satellite ranging information because it cannot realize flexible link switching.

Fig. 18.

Statistical results of full constellation PDOP for inter-satellite ranging via steady-state laser links in each cycle.

The establishment of the laser ISL needs to go through the ATP process, so each cycle is divided into a transition state and a steady state. The new link of each cycle is not available in the transition state, so its measurement and communication performance will be affected in a network built with pure laser links. Taking GEO satellite #1, IGSO satellite #4 and MEO satellite 7 as examples, Fig. 19 shows the number of laser links established by each satellite in the transition state and steady state within each cycle. In the steady state, all the devices of each satellite are linked in more than 90% link cycles, and the minimum number of links is 3. However, in order to maximize the measurement and communication benefits of each cycle, there are frequent link reconstructions between link cycles. The number of available laser links in transition states is 0 in exceeding 20% link cycles, indicating that all links need to be rebuilt. In this state, the laser ISL cannot provide effective inter-satellite communication route and ranging information.

Fig. 19.

The number of laser links in the steady and transition state.

According to the analysis results of the visibility between satellites and ground stations, GEO and IGSO satellites are always visible to the ground station, so there is no communication delay of the laser ISL. Taking MEO satellites #7, #15 and #23 located in three orbital planes as examples, Fig. 20 shows the communication delay in the transition state and steady state respectively. When the satellite is visible to stations, the link delay required for inter-satellite communication is 0, and is not affected by the link status. When the satellite operates overseas, all the three satellites can communicate with anchor satellites within 0.25 s in the steady state. However, in the link transition state, a large number of links are unavailable due to the link reconstruction between cycles. In the transition state of more than 20% link cycles, there is no laser communication path to the anchor satellite for the three satellites and the communication delay is infinite. In the transition state of the remaining link cycles, there is also a significant increase in communication delay to the anchor satellite, reaching 0.38 ns.

Fig. 20.

The communication delay to anchor satellites in the steady and transition state.

Based on the above analysis, the laser ISL can provide an efficient data transmission path for inter-satellite communication when it is established stably. However, in the transition state, the number of available laser links is significantly reduced, resulting in some overseas satellites unable to communicate with anchor satellites. On the other hand, although the ranging accuracy of laser links is significantly better than that of microwave links, it is limited by the number of devices and the link cannot be flexibly switched, resulting in less ranging information provided during the link cycle. Therefore, it is necessary to further use microwave ISLs to obtain more abundant inter-satellite ranging information and provide temporary inter-satellite communication path in the transition state of laser links.

Performance evaluation of hybrid ISLs

On the basis of the backbone network composed of laser ISLs, the assignment of microwave ISLs is further carried out to build a hybrid laser/microwave ISL network.

Each satellite carries only one microwave link device, and can only link to one visible satellite per timeslot. However, the microwave link can be flexibly switched, so it can be used to establish the ranging link with different satellites in space by time-division, and provides rich inter-satellite ranging information combined laser links. Figure 21 shows the number of hybrid inter-satellite ranging links. The number of laser/microwave ranging links established by each satellite is greater than 12 per minute, and up to 24 ranging links can be established, with an average of 18.4. Compared with the pure laser link, the addition of microwave links can significantly increase the information of inter-satellite ranging.

Fig. 21.

The number of hybrid ISLs constructed for each satellite.

Figure 22 statistics the PDOP of hybrid ranging links for each satellite. The PDOP is significantly improved with the addition of the microwave ranging links on the basis of the laser ranging links. Compared with pure laser links, the sensitivity of PDOP to the relative azimuth change of satellites is reduced. In the whole regression cycle, the PDOP of hybrid ranging links of GEO and IGSO satellites ranges from 1 to 2.1, with an average of 1.5. The PDOP of MEO satellites ranges from 0.7 to 1.7, with an average of 1.1.

Fig. 22.

PDOP statistics for each satellite with hybrid ISLs.

In the steady state of the laser link, the microwave link only provides ranging information. However, in the transition state, because some overseas satellites do not have a laser path to the anchor satellites, it is necessary to provide communication routes by microwave links, so as to form a communication network composed of laser links and microwave links. Figure 23 shows the communication delay between three MEO satellites and the anchor satellites with the support of laser/microwave hybrid links. In the whole regression cycle, the communication route between the overseas satellites and the anchor satellites is mainly provided by the laser link, and the communication delay is less than 0.4 s. In the laser link transition state, the microwave link provides a temporary communication path for part of the time, and the inter-satellite communication is realized. Due to the limitation of time-division system of microwave ISLs, the minimum delay of inter-satellite microwave communication is one timeslot, which is 3 s in this simulation. Therefore, in the case of hybrid links, the communication delay of MEO satellites to anchor satellites in some overseas periods is slightly greater than 3 s, and the maximum delay is about 3.2 s. Because the time delay does not exceed 2 microwave timeslots, it indicates that only one microwave link is used for hybrid inter-satellite routes.

Fig. 23.

The communication delay to anchor satellites via hybrid ISLs comparing to only laser ISLs. (a) Delay of MEO #7. (b) Delay of MEO #15. (c) Delay of MEO #23.

Conclusion

To fully leverage the advantages of different ISLs in satellite navigation systems, we propose a collaborative construction scheme for laser and microwave links. Firstly, a backbone communication network is established through laser ISLs, which simultaneously provides high-precision inter-satellite ranging information for the system. When some laser links are unavailable due to the ATP process, microwave links serve as temporary communication links and provide abundant inter-satellite ranging information throughout all stages of constellation operation, ensuring the normal functioning of the entire system. Based on this collaborative scheme, we further consider the requirements of inter-satellite ranging and communication, and establish hybrid link assignment models according to the constraints of different system operation stages (including link systems, number of devices, and visibility). Link assignment algorithms based on the GA and the NSGA-II are designed. Finally, a simulation of hybrid laser/microwave ISL assignment is implemented for a global navigation satellite constellation equipped with both laser and microwave link devices. According to the simulation results, each satellite can establish an average of 18.4 ISLs per minute, with a maximum of 24 links. In the hybrid ranging links of GEO and IGSO satellites, the average PDOP is 1.5; for MEO satellites, the average PDOP is only 1.1. In the steady state of laser ISLs, the average communication delay for overseas satellites to transmit data to the anchor satellite through the laser link is about 0.15 s, with the minimum delay better than 0.1 s and the maximum delay slightly higher than 0.25 s. In the transition state where some laser links are interrupted, the laser link can collaborate with the microwave link to provide a transmission path, with the maximum delay about 3.2 s. The results demonstrate that the proposed collaborative construction scheme for laser and microwave links fully exploits the synergistic advantages of the two different types of links, effectively compensating for the shortcomings of laser links, such as large dispersion of ranging quality, and the low communication efficiency of microwave links. The established hybrid link assignment model and optimization algorithms are capable of comprehensively considering the measurement and communication requirements of the navigation constellation, achieving optimized link assignment under complex constraints.

The inter-satellite communication delay is affected by inter-satellite distance, data volume, and link bandwidth. Considering the propagation delay determined by the inter-satellite distance is usually the main source of laser link delay, only the communication delay of laser links caused by inter-satellite distance is considered in the hybrid ISL assignment model. The actual laser communication delay in operation will be slightly larger than the assessment result. Moreover, we assume that the communication delay between two satellites connected by a microwave link is one timeslot, that is, it requires that the inter-satellite distance, link bandwidth, and data volume can meet the restriction of completing communication within one timeslot. The design of link timeslot length represented by the microwave ISL of the BDS can meet this requirement. However, during actual operation, there may be cases where inter-satellite communication cannot be completed within one timeslot. We will consider the actual inter-satellite transmission data volume and dynamic bandwidth allocation in the constellation operation, and further carry out research on the hybrid ISL assignment problem. Furthermore, both the duration of the microwave link superframe and the laser link cycle, and the constellation configuration significantly impact the determination of inter-satellite visibility, thereby influencing the feasible solution space for link topology optimization. Analyzing the effects of these factors on inter-satellite visibility and link topology performance is a necessary task in the next step.

Author contributions

N. W. and L. S. concepted and designed the study. Y. F. and Z. L. acquired the data. Q. D. and C. W. analyzed data. N. W. and L. S. drafted the manuscript. W. H. Revised the manuscript critically for important intellectual content. All authors reviewed the manuscript.

Funding

This research was funded by Nanning Outstanding Youth Science and Technology Innovation and Entrepreneurship Talent Cultivation Project, grant number RC20210102.

Data availability

The datasets used and/or analyzed during the current study are available from the corresponding author upon reasonable request.

Declarations

Competing interests

The authors declare no competing interests.