CN110266362B - Millimeter wave based interference suppression method for constellation multi-beam reception - Google Patents
Millimeter wave based interference suppression method for constellation multi-beam reception Download PDFInfo
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- H—ELECTRICITY
- H04—ELECTRIC COMMUNICATION TECHNIQUE
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- H04B7/00—Radio transmission systems, i.e. using radiation field
- H04B7/02—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas
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- H04B7/06—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas at the transmitting station
- H04B7/0613—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas at the transmitting station using simultaneous transmission
- H04B7/0615—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas at the transmitting station using simultaneous transmission of weighted versions of same signal
- H04B7/0617—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas at the transmitting station using simultaneous transmission of weighted versions of same signal for beam forming
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- H04B7/08—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas at the receiving station
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Abstract
The invention provides an interference suppression method for multi-beam reception of a star group based on millimeter waves, which is used in a star group communication system based on millimeter waves. The method adjusts the beam direction of the satellite according to the position information of all satellites in the constellation, so that only one transmitting satellite or receiving satellite exists in the coverage range of each beam, and the problem of mutual interference among links between the satellites is solved. The invention executes beam bias in the associated beam forming training A-BFT time slot of the beacon interval; beam offset is the addition of a beam offset angle in the beam direction at which the satellite is currently aligned; the beam offset angle is such as to maximize the achievable rate of the constellation network, obtained by an optimized genetic algorithm. The invention manages the limited wave beam resources on the satellite in the angle of resource management, calculates the optimal direction of each wave beam through an optimized genetic algorithm, realizes wave beam bias, and solves the problem of mutual interference between inter-satellite links caused by the millimeter wave technology in the satellite mobile communication.
Description
Technical Field
The invention belongs to the technical field of inter-satellite link mutual interference suppression, and relates to a method for inter-satellite link interference suppression in millimeter wave constellation multi-beam reception.
Background
The millimeter wave refers to electromagnetic waves with the frequency of 30 GHz-300 GHz and the wavelength range of 1-10 mm. With the large bandwidth in the millimeter wave band, a transmission rate of gigabits per second can be provided, making it possible to meet bandwidth intensive multimedia applications. The inter-satellite link formed by the millimeter waves has the characteristics of large communication capacity, strong anti-interference capability and relatively sufficient frequency spectrum resources. Millimeter wave communication is therefore considered to be the most promising technology in satellite networks. The small satellite constellation is a satellite system composed of two types of satellites, namely a main satellite located at the center of the satellite constellation and auxiliary satellites distributed around the main satellite. The small satellites forming the constellation can finish conventional tasks such as communication, navigation, remote sensing and the like independently or cooperatively, and can enhance the coverage of hot spots through scheduling to realize the maximization of resource utilization. Compared with the traditional single large satellite complex manufacturing process, high manufacturing cost and long development period, the constellation system formed by a plurality of small satellites can realize the same function as the large satellite through inter-satellite cooperation, meanwhile, each small satellite forming the constellation can enhance the flexibility, reliability and anti-interference capability of a satellite network in a mutually-substituted and complementary emission mode, and has the advantages which are incomparable to the single large satellite. In order to compensate for the high loss in the millimeter wave band transmission process, the satellite uses the directional narrow beam generated by the satellite-borne phased array antenna to perform inter-satellite communication. The directional transmission introduced into the millimeter wave constellation can greatly avoid the interference problem caused by the fact that the satellites work in the same frequency band, so that the millimeter wave constellation can meet the requirement of a plurality of constellations through frequency spectrum sharing, and the satellites share the same frequency band, so that the problem of frequency spectrum resource shortage is relieved. However, communication systems that support multiple satellites simultaneously introduce new problems. Due to the dynamic change of the constellation topology and the randomness of the messages sent by the satellites. A constellation may have multiple satellites moving into the same sector of a satellite and simultaneously transmitting messages to the satellite. At this time, the overlapping of multiple transmission beams occurs at the receiving satellite, which causes the problem of mutual interference between inter-satellite links, and greatly reduces the communication efficiency and network performance of the constellation, so the interference suppression technology is required to be provided for the satellites in the constellation, and the interference suppression technology provided for the satellites should be implemented from the perspective of resource management due to the limited resources on the satellites.
In the aspect of interference suppression, at present, no research directly aiming at a millimeter wave constellation scene exists, and the research of an interference suppression technology of a ground communication system (a vehicle networking scene, a D2D scene, a 5G scene and the like) is relatively mature. The applicability of the technology applied in the ground scene in the millimeter wave satellite network is limited only because the satellite communication has the characteristics of long communication distance, dynamic change of network topology, limited resources and power and the like. Reference 1(Cristina Perfect, Javier Del Ser, Muhammad Ikram Ashraf, et al. Beam width Optimization in Millimeter Wave Networks with delay Nodes: A Swarm Intellight Approach [ J ] European Wireless 2016:101-106.) proposes a beam width Optimization scheme based on a meta-heuristic algorithm. However, the scenario of the scheme is a cellular system, and compared with the communication environment among satellites studied by the invention, the distance between base stations is relatively short and the distribution is dense, and for the satellites in long-distance communication, the beam width needs to be narrower to reduce the interference degree, so that further consideration needs to be made in the aspect of reasonably selecting the beam width. Reference 2(Ghaith Hattab, EugeneVisotsky, Mark Cudak, et al. interference cancellation via Beam Range Biasing for5G mm wave Coexistence with Incumbents. [ J ]. IEEE 5G World Forum (5GWF) -SiliconValley, CA, USA.2018: 210-. Reference 3(Yu Li, Zufan Zhang, WeiWang, et al. conservation Transmission Based Game for D2 communication in mmWave Networks. [ J ]. IEEE International Conference communication.2017.) proposes a time domain resource sharing scheme Based on the starberg Game from the perspective of the time domain. The scheme only verifies the performance of the time domain resource sharing scheme in the end-to-end static communication, and further research is needed for the communication among the satellites with dynamically changed network topologies.
In summary, for designing an interference suppression technology applied to a constellation scene, the characteristics of a satellite, the computation complexity of the technology, the effectiveness of resource utilization, the accuracy of a result and the instantaneity of application should be considered. Therefore, due to the dynamic change of the constellation topology and the randomness of message sending among satellites, inter-constellation link mutual interference exists among the constellations, and the interference suppression technology is an important problem to be solved urgently in the constellation communication system.
Disclosure of Invention
The invention provides an interference suppression scheme based on beam domain beam bias for solving the problem of inter-satellite link interference suppression in millimeter wave multi-beam reception, the scheme can bias an aligned beam according to interference-causing satellite information in a beam forming stage, and utilizes an optimized genetic algorithm from the angle of beam resource management to improve the efficiency and accuracy of beam bias angle calculation, thereby providing an effective solution and thought for the interference problem existing in the inter-satellite link of a constellation in a millimeter wave multi-beam reception scene.
Specifically, the invention provides an interference suppression method based on millimeter wave constellation multi-beam reception, which is used for a constellation communication system under a millimeter wave multi-beam reception scene. In a millimeter wave based constellation communication system, each sector antenna of a primary satellite located at the center of the constellation is equipped with multiple beams, and when multiple satellites move into the coverage area of the same sector of a primary satellite and send messages to the primary satellite, beam overlap occurs at the primary satellite. The method adjusts the beam direction of the satellite according to the position information of each satellite in the constellation, so that only one transmitting satellite or receiving satellite exists in the coverage range of each beam.
The invention comprises the following steps:
performing beam biasing in an associated beamforming training A-BFT timeslot of a beacon interval;
the beam offset is to add a beam offset angle in the beam direction currently aligned with the satellite, that is, to add a transmission offset angle to the transmitting satellite and to add a reception offset angle to the receiving satellite.
The beam offset angle is used for enabling the reachable speed of the constellation network to be maximum, and the beam offset angle is obtained through an optimized genetic algorithm.
The optimized genetic algorithm takes the reachable rate of the constellation network as a fitness function, individuals in the population are beam offset angles of transmitting satellites or beam offset angles of receiving satellites, the number A of the individuals in the population is 2I, and I is the number of the transmitting satellites in the constellation network; repeatedly executing the genetic algorithm Q times, wherein Q is A; and (3) obtaining an optimal population every time the genetic algorithm is executed, repeating the genetic algorithm for Q times to obtain Q optimal populations, and selecting an optimal result from the Q optimal populations to be used as a final beam offset angle scheme.
And initializing the population each time the genetic algorithm is executed, selecting the population according to the fitness, performing cross and variation operation on the individuals in the population to generate a new population, wherein the optimal solution refers to the population with the maximum fitness value.
The method of the invention is based on the interference suppression technology of the beam bias of the beam domain, manage the limited beam resource on the satellite in the angle of resource management; the optimal direction of each beam is calculated through an optimized genetic algorithm, beam offset is realized, and the problem of mutual interference between inter-satellite links caused by the millimeter wave technology in the satellite group mobile communication is solved. Compared with the prior art, the invention has the following advantages:
(1) according to the invention, a beam offset method is adopted in a beam domain, so that only one transmitting satellite is ensured to be communicated with each beam coverage range of the receiving satellite, and only one receiving satellite is ensured to be communicated with each beam coverage range of the transmitting satellite, thereby solving the problem of mutual interference between inter-satellite links;
(2) the beam bias method provided by the invention is completed in each A-BFT period, has real-time performance, and simultaneously provides guarantee for normal and efficient communication among satellites in the subsequent DTI period;
(3) the invention effectively utilizes the limited beam resources on the satellite, improves the calculation speed of the beam offset scheme and the accuracy of the result by combining the optimized genetic algorithm from the resource management perspective, and ensures the utilization rate of the resources.
Drawings
Fig. 1 is a schematic diagram of the structure of a beacon interval BI;
fig. 2 is a model diagram of communication between the constellation using beam bias in a millimeter wave multi-beam scene according to an embodiment of the present invention;
FIG. 3 is a schematic flow chart of obtaining the offset angle by using the optimized genetic algorithm according to the embodiment of the present invention.
Detailed Description
The present invention will be described in further detail and with reference to the accompanying drawings so that those skilled in the art can understand and practice the invention.
Under a millimeter wave multi-beam receiving scene, the problem of inter-satellite link interference caused by topology dynamic change and message sending randomness existing in a constellation communication system. In order to facilitate the integration of millimeter wave communication and multi-beam reception with a constellation communication system, the invention provides an interference suppression method for constellation multi-beam reception based on millimeter waves. The method adjusts the beam direction of the satellites of both communication sides from the angle of the beam domain, and plays a role in inhibiting interference; and executing a beam bias scheme at a beam forming stage in each beacon interval, ensuring that the beam bias scheme can be periodically executed, and meeting the requirement of satellite communication real-time. The method also realizes the beam offset scheme by utilizing the optimized genetic algorithm so as to ensure that the beam resource is effectively utilized, shorten the operation time and improve the accuracy of the result.
As shown in fig. 1, for a Beacon Interval (BI) in millimeter wave communication, a transmission protocol divides transmission time into multiple BIs, and performs timeslot allocation using the multiple BIs as a basic unit, and the transmission time is divided into four types of sub-intervals according to different access rules: BTI, A-BFT, ATI and DTI. In the millimeter wave multi-beam receiving scene, BTI (beacon transmission interval) is a beacon transmission interval period, and a main satellite transmits a beacon frame to a satellite in the coverage area of the main satellite in the beacon transmission interval period. A-BFT (Association Beamforming Training, A-BFT) is an associated Beamforming Training period, and the invention executes beam offset in the time slot period. Ati (authorization Transmission Interval) is a notification Transmission interval period, and completes the service of authentication and association between satellites. Dti (data Transmission interval) is a data Transmission interval period during which data interaction between satellites can be performed.
As can be seen from fig. 1, the a-BFT is located before the DTI, and the beam biasing of the present invention is performed at the a-BFT, which provides for normal and efficient communication between subsequent satellites. Meanwhile, each main satellite sends BI at fixed time, so that beam offset can be periodically executed, and the optimal beam direction of each beam can be calculated in real time according to the change of the satellite position caused by the dynamic change of the satellite topology. In the embodiment of the present invention, a BI of 102.4ms is used, i.e., the beam offset is updated every 102.4 ms.
In a constellation communication system, the coverage area of a main satellite positioned at the center of a constellation is divided into 36 sectors, and the width of each sectorEach sector antenna is provided with 4 beams, each having a main lobe width thetaml5 deg. is equal to. The transmission power of each satellite is the same and the operation mode is half duplex. The transmission or reception gain in dB per beamCan be represented by the following formula:
wherein the content of the first and second substances,an offset angle indicating transmission or reception of a line connecting the transmission satellite i and the reception satellite j with respect to their respective directions of lines of sight, which will be referred to as a transmission offset angle and a reception offset angle, respectively, hereinafter;t represents transmission and r represents reception. Theta-3dBAngle, θ, representing half power beamwidthmlAnd theta-3dBIs in a relation ofml=2.6·θ-3dB。G0Maximum gain of the antenna, GslIndicating the side lobe gain.The value of (a) is the target that the genetic algorithm optimized by the present invention needs to search for.
Maximum gain G of antenna0The calculation formula of (a) is as follows:
side lobe gain GslThe calculation formula of (a) is as follows:
Gsl=-0.4111·ln(θ-3dB)-10.579 (3)
due to the dynamic change of the constellation topology, a situation that a plurality of satellites move to the coverage area of the same sector of a certain main satellite occurs, and the transmission of satellite messages is random, and it cannot be determined when a message needs to be sent, so that a situation that a plurality of satellites send messages to a certain main satellite at the same time exists. If multiple satellites move into the same sector of the same primary star and send messages to the primary star simultaneously. Beam overlap will occur at the primary satellite at this time, resulting in inter-satellite link interference. Therefore, the beam pointing directions of the satellites need to be reasonably adjusted according to the position information of all the satellites in the constellation, and only one transmitting satellite or receiving satellite in the coverage range of each beam is ensured to be communicated with the beam pointing directions, so that the problem of interference among inter-satellite links is effectively avoided.
One scenario for introducing a beam bias scheme in a millimeter wave multi-beam reception scenario is shown in fig. 2. In fig. 2, MS1 represents the central primary in constellation 1, CS1, CS2 are the secondary in constellation 1, and MS2 is the central primary in constellation 2. CS1, CS2, and MS2 are all located within the same sector coverage of a central master MS1 in constellation 1 and simultaneously send messages to MS1 and MS1 receives messages.Represents the receive bias angle between CS1 and MS1, which as shown is the angle between the line of sight of MS1 and the line of sight of MS1 and CS 1;represents the transmit bias angle between CS1 and MS1, which as shown in the figure is the angle between the line of sight of CS1 and the line of sight of CS1 and MS 1;represents the receive bias angle between CS2 and MS 1;represents the transmit bias angle between CS2 and MS 1;represents the receive bias angle between MS1 and MS 2;indicating the transmit bias angle between MS1 and MS 2. After the beam offset angle is obtained, the satellite adjusts the beam direction by utilizing the offset angle in the A-BFT time slot, and adds the beam offset value to the originally aligned beam direction, so that the beam is not aligned with the transmitting satellite or the receiving satellite any more, and the existing interference is reduced or inhibited.
The interference suppression method based on millimeter wave constellation multi-beam reception calculates the offset angle through an optimized genetic algorithm, so that the constellation network can reach the maximum reachable rate.
The final purpose of eliminating interference is to improve the performance of the constellation network, so the invention takes the maximum achievable rate of the constellation network as the realization target of the invention, and the specific analysis process is as follows:
let C represent the Set of Satellites (SS),represents a set of Master Stars (MS),represents a set of Transmitting Satellites (TS),represents a collection of receiving satellites (RMS), whereinReceived power of satellite jCan be composed ofCalculated as:
wherein the content of the first and second substances,respectively representing a transmitting offset angle and a receiving offset angle between a transmitting satellite i and a receiving satellite j; k is a radical of0=(λ/4π)2Is constant, λ is the millimeter wave wavelength, Pi tIs the transmission power of the satellite i and,representing the gain of a transmitting antenna of a transmitting satellite i under a receiving satellite j;is the receive antenna gain of the receiving satellite j under the transmitting satellite i; di,jRepresenting the transmission distance between satellites i and j,the path loss of the transmitting satellite i and the receiving satellite j is shown, n is a path loss index, and n is set to be 2 in the embodiment of the invention.
Is provided withC (j) andrespectively, the set of TS, SS and MS under the coverage of the receiving satellite j. Interference power at satellite jThe calculation is as follows:
wherein the content of the first and second substances,an offset angle representing the direction of reception of the interfering satellite z from the receiving satellite j;an offset angle representing the transmission direction of the interfering satellite z and the receiving satellite j;is the transmit power of the satellite z;a transmit antenna gain representing an interfering satellite z under satellite j;represents the receive antenna gain of the receiving satellite j under the interfering satellite z;representing the path loss of the interfering satellite z and the receiving satellite j.
The interference at satellite j is caused by the other secondary and primary satellites, as shown in equation (6),is the interference power caused by the satellite c,indicating the offset angle of the transmitting satellite c from the receive direction of the receiving satellite j,an offset angle representing the transmission direction of the transmitting satellite c and the receiving satellite j;is the interference power caused by the master satellite m,representing the offset angle of the transmitting master satellite m from the receiving direction of the receiving satellite j,indicating the offset angle of the transmitting master satellite m from the transmitting direction of the receiving satellite j.The transmission power of the satellite c and the transmission power of the satellite m are respectively;represents the transmit antenna gain of the transmitting satellite c under satellite j;the gain of the receiving antenna of the receiving satellite j under the sending satellite c is shown;represents the transmitting antenna gain of the transmitting main satellite m under the satellite j;the gain of a receiving antenna of a receiving satellite j under a sending main satellite m is shown;representing the path loss of the transmitting satellite c and the receiving satellite j;representing the path loss of the transmitting master satellite m and the receiving satellite j.
According to shannon's theorem, the achievable rate at the receiving satellite j is calculated by the ratio (SINR) of the received useful signal power to the interference plus noise power, and the SINR calculation formula of the receiving satellite j is as follows:
wherein the content of the first and second substances,SINR for the receiving satellite j; collectionRepresents the SS and MS transmitting messages while causing interference at satellite j; n is a radical of0Representing the power spectral density of Gaussian noise, taking N0=-174dBm/Hz;BmmWRepresenting the channel bandwidth, take BmmW=1200MHz。
in the beam offset scheme, the maximum achievable rate of the constellation network versus the offset angle can be represented by the following equation:
wherein the content of the first and second substances,the beam offset angles of the transmitting satellite TS and the receiving satellite RMS are respectively expressed, the above formula is the target to be realized by the beam offset scheme, and the offset angle is the object to be searched by the genetic algorithm.Representing the beam width. N represents the number of beams.
Equation (10) represents the determination of the beam offset angles for the transmitting satellite and the receiving satellite that maximize the achievable rate for the constellation network. Due to the limited resources in the satellite communication environment and the sensitivity to time delays. Therefore, when the beam offset scheme is realized, the low calculation complexity, the high calculation speed and the high accuracy of the calculation result must be ensured, and the effective utilization of the calculation resources is ensured. The intelligent algorithm can well meet the requirements, and particularly, the genetic algorithm is very suitable for solving complex optimization problems, is not limited by problem conditions, and has strong search capability and environmental adaptability of the global optimal solution. The problem is solved by an optimized genetic algorithm to obtain the offset angle, and a flow of the method is shown in fig. 3, and the corresponding implementation steps are described below.
And 2, calculating the fitness of the population. Using the reachable speed of the whole star swarm network as the fitness functionCalculation the fitness value of each population is obtained as shown in equation (9). A larger fitness value indicates a better population of individuals.
Step 3, selecting excellent populations from the current generation population to form a new generation populationIs selected probability paCan be expressed as:
Let the number of populations to be kept from the current generation population be N1Is represented asThen the remaining M-S-N1Individuals in the individual population will result from crossover and mutation operations of the genetic algorithm.
For the kth individual theta in a certain population of the current generation populationkAnd the first individual thetalBy a crossover operation at the g-th bit, θ is obtainedkgAnd thetalgThe following are:
θkg=θkg(1-b)+θlgb (12)
θlg=θlg(1-b)+θkgb (13)
wherein, thetakgDenotes the kth individual thetakThe g-th bit; thetalgDenotes the l-th individual thetalThe g-th bit; b is [0,1 ]]Random number of intervals. Generating new individuals through cross operation, and setting the number of populations generated by the cross operation as M1Is shown as
For the g gene theta of a population in the a individualagThe operation method for carrying out mutation comprises the following steps:
wherein, thetamaxIs gene θagUpper bound of (theta)minIs gene θagLower boundary of (f), (u) ═ r2(1-o/Kmax)2R is a random number, o is the current iteration number, KmaxIs the maximum number of evolutions, r is [0,1 ]]Random number of intervals. Generating new individuals through mutation operation, and setting the number of populations generated by the mutation operation as M2Is shown asM=M1+M2。
Step 4, selecting the obtainedObtained by cross-over operationAnd obtained by mutation operationsThe new generation group is formed together and the obtained new generation group is taken as the current generation group. Judging whether the current algebra K is larger than the set maximum iteration number KmaxIf so, stopping iteration and outputting the current optimal populationObtaining an optimal offset angle for each beam; otherwise, continuing to execute the step 2.
In the method, the steps 1-4 are repeatedly executed for Q times, an optimal solution is obtained every time, Q optimal solutions are obtained after Q times of repetition, and an optimal result is selected from the optimal solutions to serve as a final beam offset scheme.
Genetic algorithms are widely used as a stochastic approach to solve complex optimization problems and achieve significant results. However, it still has inherent disadvantages based on random optimization, for example, the genetic algorithm has weak local search capability and has a certain risk of premature convergence. In practical applications, it is inevitable to run the genetic algorithm multiple times on the same problem to find a better solution. Along the thought, the invention optimizes the adopted genetic algorithm and carries out optimization on the genetic algorithm in the same constellation networkAnd carrying out multiple solving, and selecting an optimal result from a plurality of generated results as a global optimal solution to solve the limitation of jumping out a local optimal solution.
The embodiment of the invention provides an interference suppression method suitable for a constellation communication system in a millimeter wave multi-beam receiving scene, which ensures that only one transmitting satellite is communicated with each beam coverage range of a receiving satellite and only one receiving satellite is communicated with each beam coverage range of the transmitting satellite by providing a beam bias scheme in a beam domain, thereby solving the problem of mutual interference between inter-satellite links.
It is to be understood that the described embodiments are merely exemplary of the invention, and not restrictive of the full scope of the invention. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
Claims (1)
1. An interference suppression method based on millimeter wave constellation multi-beam reception is disclosed, and the application scene is as follows: in a millimeter wave based constellation communication system, each sector antenna of a main satellite positioned in the center of a constellation is provided with a plurality of beams, and when a plurality of satellites move to the coverage range of the same sector of one main satellite and send messages to the main satellite, beam overlapping occurs at the main satellite; the method is characterized in that the beam pointing directions of the satellites are adjusted according to the positions of all the satellites in the constellation, so that only one transmitting satellite or receiving satellite exists in the coverage range of each beam; the method comprises the following steps:
performing beam biasing in an associated beamforming training A-BFT timeslot of a beacon interval;
the beam offset is to add a beam offset angle in the beam direction at which the satellite is currently aligned; the beam offset angle is obtained through a genetic algorithm so as to maximize the reachable speed of the constellation network;
the achievable rate of the constellation network is obtained by summing the achievable rates of the receiving satellites, and is expressed as follows:
wherein the content of the first and second substances,the achievable rate of the constellation network,representing a set of receiving satellites that are to be received,to receive the achievable rate for satellite j,representing the transmit offset angle between the transmitting satellite i and the receiving satellite j,respectively representing the receiving offset angles between a transmitting satellite i and a receiving satellite j;
maximizing the achievable rate of the constellation network is expressed as follows:
wherein, thetamlRepresenting the main lobe width of the beam of the receiving satellite,represents the width of the sector of the receiving satellite, N represents the number of beams;
the genetic algorithm is as follows:
step 1, initializing an individual; it is assumed that S populations are initially generated randomly by a genetic algorithm, each population includes A individuals, and each individual is a beam offset angle of a transmitting satellite or a receiving satellite and is expressed asThe set of individuals is represented asWherein A is 2I, and I is the groupThe number of satellites in the satellite(s),is a set of transmitting satellites, and S is the scale of each generation;
step 2, calculating the fitness of the population; using the reachable speed of the whole star swarm network as the fitness functionCalculating to obtain the fitness value of each population as shown in formula (1);
step 3, selecting excellent populations from the current generation population to form a new generation populationIs selected probability paCan be expressed as:
let the number of populations to be kept from the current generation population be N1Is represented asThen the remaining M-S-N1Individuals in the individual population will result from crossover and mutation operations of the genetic algorithm;
for the kth individual theta in a certain population of the current generation populationkAnd the first individual thetalBy a crossover operation at the g-th bit, θ is obtainedkgAnd thetalgThe following are:
θkg=θkg(1-b)+θlgb (4)
θlg=θlg(1-b)+θkgb (5)
wherein, thetakgDenotes the kth individual thetakThe g-th bit; thetalgDenotes the l-th individual thetalThe g-th bit; b is [0,1 ]]A random number of intervals; generating new individuals through cross operation, and setting the number of populations generated by the cross operation as M1Is shown as
For the g gene theta of a population in the a individualagThe operation method for carrying out mutation comprises the following steps:
wherein, thetamaxIs gene θagUpper bound of (theta)minIs gene θagLower boundary of (f), (u) ═ r2(1-o/Kmax)2R is a random number, o is the current iteration number, KmaxIs the maximum number of evolutions, r is [0,1 ]]A random number of intervals; generating new individuals through mutation operation, and setting the number of populations generated by the mutation operation as M2Is shown asM=M1+M2;
Step 4, selecting the obtainedObtained by cross-over operationAnd obtained by mutation operationsForming a new generation group together, and taking the obtained new generation group as a current generation group; judging whether the current algebra k is larger than the set maximum iterationNumber of times KmaxIf so, stopping iteration and outputting the current optimal populationObtaining an optimal offset angle for each beam; otherwise, continuing to execute the step 2;
and (3) repeatedly executing the steps 1-4 for Q times, obtaining an optimal solution every time, obtaining Q optimal solutions after repeating the Q times, and selecting an optimal result from the optimal solutions to serve as a final beam offset scheme.
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