Throughput optimization method and system of deep space communication system

Abstract

The invention discloses a throughput optimization method and system for a deep space communication system, and relates to the technical field of deep space communication, and the method comprises the following steps: constructing an optimization problem; under a plurality of constraint conditions, randomly generating an initial population comprising a plurality of particles, and obtaining a fitness value of each particle; sorting each particle in the initial population according to the fitness values from large to small, and taking the first J particles as primary satellites of different sub-populations; performing multi-round iteration on the plurality of sub-populations; and after multiple rounds of iteration are completed, outputting optimal particles to obtain an optimal solution and a corresponding maximum throughput. According to the method, an initial population is divided into a plurality of sub-populations, and each sub-population is independently evolved by taking a primary satellite as a core; on the basis, each sub-population can carry out annular reconnaissance search in parallel, so that individuals can explore in multiple directions, and global search and local search strategies are further introduced, so that the population is balanced between global exploration and local development.

Description

A method and system for optimizing throughput in deep space communication systems Technical Field

[0001] This invention relates to the field of deep space communication technology, and in particular to a method and system for optimizing the throughput of a deep space communication system. Background Technology

[0002] With the increasing global demand for high-speed data transmission and reliable communication links, Low Earth Orbit (LEO) satellites, with their extensive coverage and high-capacity transmission capabilities, have become an important research direction in deep space communication. By networking LEO satellites to form a multi-satellite distributed system, continuous coverage, high-bandwidth data transmission, and high-performance networks can be provided for deep space exploration missions. Currently, deep space communication systems based on distributed LEO satellites have shown significant advantages in overcoming resource bottlenecks and link reliability, particularly in multi-satellite collaboration, resource sharing, dynamic scheduling, and high reliability. However, the deep space environment is complex and variable. For example, environmental factors such as coronal turbulence, pointing errors, and solar noise can cause severe signal attenuation. This requires deep space communication systems to maintain stability in extreme environments and effectively cope with complex interference.

[0003] In deep space communication systems, throughput is a crucial performance indicator for measuring link service capacity and resource utilization efficiency. It essentially reflects the actual rate of information successfully transmitted per unit bandwidth in each time block, under certain communication reliability and system availability conditions. Ensuring that the communication system maximizes throughput under strict constraints and improves system stability and adaptability remains a critical issue that urgently needs to be addressed. However, in deep space communication systems, multiple key parameters are interdependent and influenced by multiple constraints such as link reliability and orbital dynamics, leading to a highly nonlinear and complex optimization problem.

[0004] Existing methods for optimizing throughput in deep space communication systems primarily rely on traditional heuristic algorithms, such as the Proof-of-Action (POA) algorithm. In the traditional POA algorithm, the entire population is guided by a single host star, limiting the reconnaissance directions of particles and resulting in insufficient overall exploration capability, making it prone to getting trapped in local optima. Especially in the deep space communication throughput optimization problem, with its high-dimensional decision space and complex constraints, this global single-search mechanism struggles to balance search range and convergence efficiency, thus limiting the algorithm's ability to find the global optimum and leading to a non-optimal throughput. Summary of the Invention

[0005] In view of the defects of the existing technology, the present invention provides a throughput optimization method and system for deep space communication systems, which solves the existing problems.

[0006] The present invention adopts the following technical solution: Firstly, the present invention provides a throughput optimization method for a deep space communication system, comprising the following steps: modeling the throughput of the deep space communication system, taking maximizing throughput as the optimization objective, using transmission rate and minimum elevation angle of the ground terminal as joint optimization variables, and using satellite visibility constraints, average block error rate constraints, transmission rate constraints, and minimum elevation angle constraints as multiple constraints to construct an optimization problem; under multiple constraints, randomly generating an initial population including multiple particles, and obtaining the fitness value of each particle; wherein, each particle represents a candidate solution. Where R is the transmission rate. The minimum elevation angle is determined. Each particle in the initial population is sorted in descending order of fitness value. The top J particles are designated as the primary stars of different subpopulations, and the remaining particles are assigned to the subpopulation containing the nearest primary star based on Euclidean distance. Multiple iterations are performed on the multiple subpopulations. In each iteration, for all subpopulations, each particle searches along the rotation direction within a given plane, updating its position for the first time. After the first position update of all particles, if the distance between the current particle and the current globally optimal particle is greater than a set threshold, the current particle undergoes a second update using a global search method; otherwise, a second update is performed using a local search method. After multiple iterations, the optimal particle is output, yielding the optimal solution and the corresponding maximum throughput.

[0007] Preferably, each particle is searched along the rotation direction within a given plane, as shown below: In the formula, x i This represents the current position of the i-th particle. Let i be the position of the i-th particle after its first update. It is the current search direction vector of the i-th particle. Let θ be the angle of rotation around the origin of a certain decision space plane. h The rotation matrix is ​​given by t, where t is the number of iterations.

[0008] Preferably, the formula for the global search method is as follows: In the formula, Let be the position of the i-th particle after the second update in the global search. For weight parameters, For constant parameters, It is a random number. The globally optimal particle. Let be the local optimal position of the i-th particle. Let be the first intermediate variable; the specific formula for the local search method is shown below: In the formula, Let be the position of the i-th particle after the second update under the local search. For weight parameters, As the second intermediate variable, It follows a Gaussian distribution.

[0009] Preferably, the optimization problem is as follows: ; , In the formula, To constrain the optimization problem, R is the throughput, and R is the system's end-to-end effective transmission rate. Minimum elevation angle, The probability of at least one LEO satellite being visible is given by η1, where η1 is the visibility probability threshold for the serving satellite and η2 is the tolerance upper limit. For the transmission rate of the SR link, This represents the transmission rate of the RD link.

[0010] Preferably, the throughput modeling of the deep space communication system specifically includes the following steps: constructing a deep space communication system, which includes a probe S, distributed LEO satellites, and a ground terminal D, wherein the distributed LEO satellites are relay nodes R, the FSO signal of probe S is transmitted to the distributed LEO satellites through the SR link, and the distributed LEO satellites convert the FSO signal into an electrical signal and transmit it to the ground terminal D through the RD link; modeling multiple first key factors affecting the communication reliability of the SR link to obtain corresponding mathematical representations; modeling multiple second key factors affecting the communication reliability of the RD link to obtain corresponding mathematical representations; obtaining the average block error rate of the SR link based on the mathematical representations of the multiple first key factors, obtaining the average block error rate of the RD link based on the mathematical representations of the multiple second key factors, combining the average block error rates of the SR link and the RD link to obtain the end-to-end average block error rate of the deep space communication system; and obtaining the throughput of the deep space communication system based on the end-to-end average block error rate.

[0011] Preferably, the end-to-end average block error rate is as follows: In the formula, The average block error rate from end to end. The average block error rate of the SR link. The average block error rate of the RD link; the throughput of the deep space communication system is as follows: In the formula, This represents the throughput of deep space communication systems.

[0012] Preferably, the plurality of first key factors include fading behavior caused by coronal turbulence and pointing error, as well as phase fluctuations caused by coronal turbulence; the step of obtaining the average block error rate of the SR link based on the mathematical representation of the plurality of first key factors specifically includes the following steps: performing a joint representation of the mathematical representation of fading behavior caused by coronal turbulence and pointing error; obtaining the average bit error rate of the SR link; obtaining the average block error rate of the SR link based on the joint representation result, the mathematical representation of phase fluctuations caused by coronal turbulence, and the average bit error rate.

[0013] Preferably, the multiple second key factors include propagation loss and small-scale fading. The method for obtaining the average block error rate (BER) of the RD link based on the mathematical representation of these multiple second key factors specifically includes the following steps: dividing the distributed LEO satellites into a visible satellite set and an invisible satellite set based on the minimum elevation angle of the ground terminal; dividing the visible satellite set into a first visible satellite set with its main lobe facing the ground terminal and a second visible satellite set with its side lobes facing the ground terminal; obtaining the distance vectors (PDFs) between the first and second visible satellite sets and the ground terminal, respectively; obtaining the signal-to-noise ratio (SNR) of the RD link for the first and second visible satellite sets based on the mathematical representation of the multiple second key factors and the PDFs of the distances between the first and second visible satellite sets and the ground terminal; obtaining the service probability and the average BER of the RD link when the serving satellite is located in different visible areas; and obtaining the average block error rate of the RD link based on the SNR of the RD link for the first and second visible satellite sets, the service probability when the serving satellite is located in different visible areas, and the average BER of the RD link.

[0014] Secondly, the present invention provides a throughput optimization system for a deep space communication system, comprising: a construction module for modeling the throughput of the deep space communication system, with maximizing throughput as the optimization objective, transmission rate and minimum elevation angle of the ground terminal as joint optimization variables, and multiple constraints including satellite visibility constraint, average block error rate constraint, transmission rate constraint and minimum elevation angle constraint, to construct an optimization problem; and a generation module for randomly generating an initial population including multiple particles under multiple constraints, and obtaining the fitness value of each particle; wherein each particle represents a candidate solution. Where R is the transmission rate. The minimum elevation angle is defined by the following modules: A sorting module sorts each particle in the initial population according to its fitness value from largest to smallest, assigning the top J particles as the primary stars of different subpopulations, and distributing the remaining particles to the subpopulation containing the nearest primary star based on Euclidean distance; an iteration module performs multiple iterations on multiple subpopulations; in each iteration, for all subpopulations, each particle searches along the rotation direction in a given plane and updates its position for the first time; after the first position update of all particles, if the distance between the current particle and the current global best particle is greater than a set threshold, the current particle performs a second update using a global search method; otherwise, it performs a second update using a local search method; and an output module outputs the optimal particle, obtaining the optimal solution and the corresponding maximum throughput after multiple iterations.

[0015] Compared with existing technologies, the above-mentioned at least one technical solution adopted in this invention can achieve the following beneficial effects: This invention constructs an initial population by treating different key parameters in the deep space communication system as particles. Based on fitness ranking, the initial population is divided into multiple subpopulations, each of which evolves independently with a primary star as its core. This not only preserves more excellent individuals but also avoids the loss of diversity caused by a single primary star guidance in traditional POA (Programme of Availability). Furthermore, each subpopulation can conduct parallel circular reconnaissance searches, enabling individuals to explore in multiple directions, improving search accuracy while ensuring a uniform distribution of individuals in the decision space. This invention further introduces global and local search strategies, achieving a balance between global exploration and local development, thereby effectively suppressing premature convergence and ensuring optimal throughput of the deep space communication system under optimal key parameters. Attached Figure Description

[0016] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0017] Figure 1 is a flowchart of a throughput optimization method for a deep space communication system according to the present invention; Figure 2 is a signal flow diagram of the deep space communication system according to the present invention; Figure 3 is a model diagram of the deep space communication system according to the present invention; Figure 4 is a calculation principle diagram of the present invention; Figure 5 is an overall schematic diagram of the PB-POA framework of the present invention. Detailed Implementation

[0018] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0019] To address the above problems, this invention proposes a throughput optimization method for a deep space communication system based on distributed LEO satellite assistance. Its key feature is that during the signal transmission phase, the detector first transmits the encoded Free Space Optical (FSO) signal to the LEO satellite. Next, the LEO satellite's photoelectric converter converts the received FSO signal into an electrical signal, which is then relayed to the ground terminal node via radio frequency communication technology. At the ground terminal node, the received electrical signal undergoes interference cancellation processing to ensure signal purity. Finally, the ground terminal node successfully receives the transmitted signal and performs subsequent demodulation, decoding, and information restoration operations, thereby achieving efficient and reliable deep space communication network relay transmission with LEO satellite assistance. Referring to Figures 1-5, the method specifically includes the following steps:

[0020] S1: Construct a deep space communication system.

[0021] The LEO-assisted deep space communication system comprises a probe S, which transmits its signals to a ground terminal D via an LEO-assisted relay node R. The system is divided into two links: the probe-LEO satellite link (SR link) and the LEO satellite-Earth link (RD link). The SR link employs FSO technology, primarily due to its significant advantages in high bandwidth and low latency. For the RD link, radio frequency (RF) communication is used to ensure stable long-distance communication. Furthermore, the system utilizes the DF relay protocol. This protocol, by decoding the received signals on the LEO satellite, effectively suppresses noise and interference during signal transmission, thereby significantly improving transmission quality and reliability.

[0022] S2: Model the multiple primary key factors affecting the reliability of SR link communication and obtain their corresponding mathematical representations; model the multiple secondary key factors affecting RD link communication and obtain their corresponding mathematical representations.

[0023] The end-to-end signal-to-noise ratio of a deep space communication system based on the DF relay protocol. The definition is as follows: (1); where, and These are the signal-to-noise ratios for the SR link and the RD link, respectively.

[0024] In the S-R link, because the path traverses the deep space environment, solar activity significantly interferes with the propagation of the FSO signal. Particularly during the periodic occurrence of "solar intercourse," when the probe, the sun, and the LEO satellite are almost in a straight line, the SR link inevitably crosses the solar corona, causing the signal to encounter high-density plasma turbulence interference and resulting in severe signal attenuation. The distance r between the sun and the SR link... s This is called the solar radius distance, usually expressed as the solar radius R. sun The unit is denoted by . Using triangular relationships, the communication distance L of a deep space SR link is... FSO Represented as:

[0025] (2); where L se and L sp These represent the distance between the sun and the LEO satellite, and the distance between the sun and the probe, respectively. and β s Let S and P represent the angles of the Sun-LEO satellite-Probe (SEP) and the Sun-Probe-LEO satellite (SPE), respectively. According to formula (2), the SR link will pass through the solar corona, and its attenuation will be more severe as the SEP angle decreases. In addition, when the FSO signal passes through the coronal plasma, it will be subject to random phase fluctuations Δφ caused by turbulence, thus introducing additional phase errors. The system has a certain ability to compensate for this disturbance, and the actual total phase deviation κ is expressed as κ=Δψ−Δφ, where Δψ is the fixed phase offset compensated by the system, and Δφ is the actual phase disturbance value caused by turbulence. The actual total phase deviation κ will significantly weaken the coherent detection performance in the demodulation process, resulting in an increase in the Block Error Rate (BLER).

[0026] On the other hand, to ensure reliable data downlink, LEO satellites need to forward the received deep space probe signals to ground terminals via the RD link. This RD link uses Ka-band radio frequency communication, which has strong anti-interference capabilities and is suitable for ground reception. To simplify the modeling process, this invention assumes that the rain attenuation between all LEO satellites and ground terminals is the same, and models it uniformly as a constant g. RD This unified modeling approach, while ensuring model simplicity, can also reasonably characterize the power attenuation effect caused by atmospheric precipitation in Ka-band links.

[0027] Given the widespread distribution of relay satellites at low Earth orbit altitudes, their spatial layout significantly impacts the reachability and communication performance of ground terminals. Therefore, this invention models the spatial distribution of LEO satellites, assuming they are uniformly distributed in an area centered on the Earth with a radius of R. E +d min On the surface of a sphere, where R E Let d be the Earth's radius. min Let be the satellite's orbital altitude. This distribution can be modeled as a density of λ. s The binomial point process (BPP). This spherical region can be represented in spherical coordinates as follows: Where ρ, Φ, and φ represent radial distance, polar angle, and azimuth angle, respectively. Considering that ground terminals typically have a minimum elevation angle θ... min It can only establish communication with satellites whose viewing angle meets the requirements. Therefore, only satellites located within the visible area are considered usable relay nodes. According to the cosine theorem, the maximum communication distance d between the ground terminal and a visible satellite is... max It can be represented as:

[0028] (3); Based on the above constraints, the satellite Poisson point process Φ can be divided into two categories: the visible satellite set Φ vis With the set of invisible satellites Φ inv The visible satellite's location within the space region is a spherical cap region, represented in spherical coordinates as follows: Maximum polar angle Φ max It can be calculated using the Law of Cosines:

[0029] (4); In addition, the visible satellite set Φ vis It was further divided into two subsets: and These represent the sets of visible satellites facing the ground terminal from the main lobe and side lobes of a LEO satellite, respectively. Correspondingly, the areas potentially covered by the satellites in the main lobe and side lobes are denoted as follows: and Used to distinguish and Polar angle threshold Φ th The expression is as follows:

[0030] (5); where ω th The threshold angle between the main lobe and the side lobes. Region and They can be described as follows: and .

[0031] It is worth noting that although some satellites meet the visible geometry constraints, their antenna orientation may not cover the ground terminal. Therefore, it is necessary to further consider the antenna directivity characteristics of relay satellites. This invention assumes that LEO satellites use directional beamforming antennas with fixed beam directions, whose main lobe always points to the nadir point of the Earth. To characterize the actual beam characteristics, a conical aperture antenna is used to simulate the actual beam pattern of the satellite. However, for ease of modeling, this invention uses a simplified sector beam model. Let the visible satellites be l∈Φ. vis The angle between the line of sight and the ground terminal is ω. l Then its transmitting antenna gain is defined as:

[0032] (6); among which, and These represent the gains of the main lobe and side lobes, respectively. To simplify the modeling process, this invention ignores the mutual interference between the main lobe and side lobes, selecting the appropriate beam gain only based on the viewing angle position, without considering the interference effects between different beams.

[0033] Considering the high speed of LEO satellites and the frequent changes in communication link direction, to improve the link maintenance capability of ground terminals in complex dynamic environments, this invention assumes that the ground terminal is equipped with an omnidirectional antenna with a receiving gain of G. D Although the ground terminal attempts to track the trajectory of the currently serving satellite to achieve beam alignment, pointing errors may still occur in actual operation. e This refers to the deviation between the beam's main axis direction and the actual direction of the serving satellite. Therefore, its receiving antenna gain expression is:

[0034] (7); among which, This indicates the maximum receive gain.

[0035] This invention further focuses on the first key factor affecting the reliability of deep-space optical communication during the SCO period, including fading behavior caused by coronal turbulence and pointing errors, and phase fluctuations caused by coronal turbulence and solar noise. To analyze the impact of these factors on communication reliability in depth, it is necessary to first model the signal form received by the relay satellite. Specifically, the signal received by the LEO satellite is represented as:

[0036] (8); among which, P represents the response coefficient of a photodetector. S I is the transmit power of the FSO signal. SR Let denot be the signal strength of the SR link, Δψ−Δφ represent the phase deviation (including system compensation and turbulence disturbance), x(t) be the transmitted signal of the FSO signal, and n be the signal strength of the SR link. SR It has zero mean and variance. Additive white Gaussian noise (AWGN) is a significant factor in deep space optical communication. Due to the extremely long transmission distances and harsh environments, noise has a substantial impact on system performance. Generally, noise can be divided into two main categories: one is detector noise generated within the receiver, including thermal noise. and quantum noise Secondly, there is external environmental noise, including cosmic background noise. and solar noise The noise originates from residual cosmic radiation and solar activity, respectively. Therefore, the variance of the total noise is:

[0037] (9); among which, , , K B =1.38×10 -23 J / K is the Boltzmann constant, T is the receiver noise temperature, and R... b Symbol rate, It is the receiver responsivity, R L I0 is the equivalent resistance of the thermal noise source, I0 is the average received irradiance, q is the unit of elementary charge, and I0 is the equivalent resistance of the thermal noise source. bg It is the background irradiance.

[0038] The impact of solar noise is particularly critical. Solar noise mainly consists of two sources: diffuse solar reflection noise entering the detector's field of view (FoV), and solar noise originating from the primary mirror surface and directly scattered into the detector's FoV. Because diffuse light is highly scattered during propagation, very little energy actually enters the detector, resulting in limited interference with the received signal. Therefore, this invention focuses primarily on the latter, namely, solar noise directly scattered from the primary mirror surface. This noise is typically more intense and is affected by the surface roughness of the primary mirror. The influence of the relevant length τ is significant. Among them, Surface roughness describes the irregularity of an optical mirror at the microscopic scale; the larger the roughness, the more severe the scattering. This value is related to wavelength. The correlation is typically expressed as the standard deviation of the surface height. The correlation length τ represents the spatial distribution characteristics of the detector surface roughness, reflecting the focusing or diffusion properties of scattered light. The power spectral density of solar noise is expressed as:

[0039] (10); where D is the receiving aperture diameter, W is the spectral filter bandwidth, and θ FoV is the receiver's field of view, and m is the exponent of the accumulation function. It is worth noting that when... When τ < 10, it usually indicates a relatively smooth surface; while when τ > λ / α s When the correlation length is long, the gradient will be very large.

[0040] After the SR link completes relay, the signal will be transmitted to the ground terminal via the Ka-band RD link, i.e., the R-D link. The signal received by the ground terminal is represented as follows:

[0041] (11); where P RD e represents the transmit power of the RF signal. RD It has zero mean and variance. Additive white Gaussian noise, h RD Let represent the channel coefficient between the LEO satellite and the ground terminal, and s(t) be the transmitted RF signal.

[0042] In this invention, signal fading in the FSO channel due to turbulence and pointing errors is considered. Therefore, the signal strength of the SR link is expressed as I. SR =I t I p ...Among them, I t I represents the turbulence fading coefficient of the FSO channel. p This represents the pointing error coefficient.

[0043] In deep-space optical communication, coronal turbulence causes plasma inhomogeneity, which in turn induces scattering and refraction effects on the laser signal, leading to fluctuations in light intensity. This phenomenon can be measured by the scintillation index. Quantization is performed. To characterize the fading behavior caused by coronal turbulence, this invention uses the EW distribution to model it. This distribution model can effectively characterize the channel fading characteristics under different turbulence intensities, is applicable to various aperture sizes and turbulence conditions, and has strong modeling adaptability. Its probability density function (PDF) is expressed as:

[0044] (12); among which, Let be the probability density function of turbulence. It is related to the average irradiance The relevant scaling parameter, i, is the exponent of the accumulation function. and It is related to the flicker index Relevant shape parameters, This is a gamma function.

[0045] In terms of pointing error modeling, this invention introduces the Beckmann distribution to characterize the beam deflection at the receiver due to coronal turbulence and solar noise interference. This distribution considers the combined effects of receiver endpoint spread and random jitter, and its PDF expression is:

[0046] (13); among which, Let be the probability density function of the pointing error. This represents the ratio of the equivalent beam width to the standard deviation of the receiver pointing error. The equivalent beam width, , , and This represents the ratio between the equivalent beam radius at the receiving end and the standard deviation of the corresponding pointing error displacement (jitter). and These represent the proportional relationship between the pointing jitter in the horizontal and pitch directions and the radius of the receiving detector aperture, respectively. and These represent the ratios of the beam axis errors in the horizontal and elevation directions relative to the receiver's detection aperture radius on the receiving end plane, respectively. This represents the proportion of total power that can be received when the radial displacement is zero. , where a is the receiver aperture radius, ω z It is the beamwidth.

[0047] To comprehensively evaluate the actual performance of the communication system, phase fluctuations caused by coronal turbulence and solar noise need to be further considered. Based on the perturbation approximation theory, this invention models these phase fluctuations as a Gaussian distribution, with the probability density function PDF as follows:

[0048] (14); among which, This represents the phase variance, where κ = ∆ψ − ∆φ indicates the overall phase deviation, ∆ψ is the fixed phase offset compensated by the system, and ∆φ is the phase disturbance caused by coronal turbulence. The variance of the phase disturbance caused by coronal turbulence during the SCO period. The expression is as follows:

[0049] (15); where p is the non-Kolmogorov spectral index, r e It is the classical electron radius. For the gamma function, N e For solar wind plasma density, For the purpose of elevator degree, The plasma density perturbation factor, l oλ is the outer scale of coronal turbulence, and λ is the wavelength of the light signal. Furthermore, the model for solar wind plasma density is expressed as:

[0050] (16); where r s R is the distance between the sun and the FSO link. sun The radius is the radius of the sun.

[0051] Dielectric strength ε and electron density N e The fluctuation of (r) is related, and its expression is as follows: (17); In this invention, the Ka band is used in the R-D link to achieve higher communication bandwidth, lower signal latency, and better support for high-density data transmission between low-Earth orbit satellites and ground terminals. However, when operating in the Ka band, the signal transmission of the R-D link is susceptible to several secondary critical factors, including signal attenuation due to increased distance, signal weakening due to molecular absorption, and small-scale fading due to multipath effects and scattering. Therefore, the total fading coefficient of the R-D link can be modeled as h RD =h p h s , where h p h represents the propagation loss coefficient. s This represents the small-scale fading coefficient. The following describes the modeling of the two main fading factors:

[0052] 1) Propagation loss: Propagation loss coefficient h p This illustrates the power loss due to distance attenuation under free-space conditions. Its modeling is expressed using the Friis formula:

[0053] (18); where G R and G D Let W represent the gain of the satellite antenna in the direction r towards the ground terminal and in the opposite direction −r, respectively. Let W be the bandwidth and λ be the wavelength. d RD Let α be the R–D link distance. l G is the road loss index. RD K represents the rain attenuation factor. B =1.38×10 -23 J / K is the Boltzmann constant, and T is the receiver noise temperature.

[0054] 2) Small-scale fading: In this invention, small-scale fading in the R-D link is modeled using the SR distribution model. This distribution model is a composite fading model that can simultaneously characterize small-scale fading caused by multipath propagation and the shadowing effect on the dominant line-of-sight (LOS) component. The SR distribution, as a robust, practical, and widely applicable model, has been widely used for evaluating satellite propagation environment performance in different frequency bands. Therefore, the fading coefficient |h s | 2 The cumulative distribution function (CDF) and PDF are expressed as follows:

[0055] (19); (20); among which, The fading coefficient |h s | 2 The CDF, where n is the exponent of the accumulator function and x is the function variable. For the lower incomplete gamma function, , , , m RD The Nakagami-m fading parameter, whose value ranges from 0 to positive infinity, 2b RD Ω and Ω represent the average power of the multipath component and the LOS component, respectively.

[0056] S3: Obtain the average block error rate of the SR link based on the mathematical representation of multiple first key factors, obtain the average block error rate of the RD link based on the mathematical representation of multiple second key factors, and combine the average block error rates of the SR link and the RD link to obtain the end-to-end average block error rate of the deep space communication system.

[0057] In the constructed deep-space FSO communication channel, the signal strength I of the SR link SR Due to the combined effects of coronal turbulence and pointing error, the joint PDF can be expressed as: (21); Substituting formulas (12) and (13) into the above formula, the signal strength I of the SR link can be obtained. SR The PDF expression is as follows: (22); Using the generalized Newton's binomial theorem, the signal strength I is obtained. SR The PDF is: (23); where g is the exponent of the cumulative function.

[0058] By altering the integral term, we finally obtain I. SRThe PDF parsing expression is: (24); among which, , , , , For Meijer-G functions.

[0059] Integrating equation (24) yields the signal strength I of the SR link. SR CDF: (25); Transform the Meijer-G function to obtain I RD The CDF is: (26); among which, , For Meijer-G functions.

[0060] In order to obtain γ RD The CDF of this invention first provides the region where the main lobe covers the satellite. The CDF and PDF of the distance between the service satellite and the ground terminal are represented as follows: (27); (28); among which, and Located in the region covered by the main lobe satellite CDF and PDF between the service satellite and the ground terminal, d a For function variables, F D Let D be the distance function between the ground terminal and the nearest satellite, and let CDF and PDF be the distances between the ground terminal and the nearest satellite, respectively: (29); (30); where M l This refers to the number of LEO satellites.

[0061] Located in the area where the sidelobe covers the satellite The CDF and PDF of the distance between the service satellite and the ground terminal are represented as follows: (31); (32); For the proposed deep space communication system, the signal-to-noise ratio of the RD link. It can be represented as: (33); among which, It is the average signal-to-noise ratio, P RD It is the signal power received by the receiving end.

[0062] Furthermore, for a given service satellite s0∈ The signal-to-noise ratio γ of the RD link RD The CDF can be represented as: (34); among which, , , It is the antenna gain of the main lobe.

[0063] Substituting equations (19) and (28) into equation (34), we can obtain γ. RD The CDF is: (35); Using the binomial expansion formula and the definition of the lower incomplete gamma function, equation (35) can be rewritten as: (36); The integration region of equation (28) is transformed into subregions D1 and D2, which are defined as follows: and To compute the integral in equation (28), the double integral can be transformed into the sum of two integrals over subregions D1 and D2. The integral over D1 can be further decomposed into the product of two separate integrals with respect to x and t, expressed as:

[0064] (37); By changing the order of the integration variables, the integral over region D2 can be expressed as: (38); From equations (36) to (38), we can obtain, The final expression can be derived as: (39); Furthermore, for a given service satellite s0∈ The signal-to-noise ratio γ of the RD link RD The CDF can be represented as: (40); among which, , , It is the antenna gain of the sidelobe.

[0065] Similarly, when the serving satellite is located At that time, γ RD The CDF parsing expression is expressed as: (41); when the serving satellite is located At that time, γ RD The PDF parsing expression can be derived as: γ RD The PDF can be converted to γ ​​by CDF. RD Differentiation yields the result. For ease of calculation, the gamma function in equation (35) is first... For γ RD By differentiation, we obtain Then, equation (35) is applied to γ. RD By differentiation, we obtain γ RD The PDF parsing expression is:

[0066] (42); Similarly, when the serving satellite is located γRD The PDF parsing expression is represented as: (43); Average BLER is an important performance indicator for measuring the reliability of a communication system under given channel conditions. It represents the average proportion of erroneous coded blocks during transmission and reflects the system's ability to correctly receive data blocks throughout the entire transmission process. In relay mode using the DF forwarding protocol, the end-to-end average BLER can be expressed as:

[0067] (44); among which, and These represent the average BLER of the SR link and the RD link, respectively.

[0068] In SR links, due to the use of FSO technology, channel quality is affected by various factors, including coronal turbulence, pointing error, and phase fluctuations caused by turbulence. Based on these factors, the average BLER can be expressed as:

[0069] (45); among which, The average bit error rate of the SR link is expressed as: (46); among which, It is the Q function, represented as , , R is the average signal-to-noise ratio of the SR link. SR β is the transmission rate of the SR link. SR It is the code block length of the SR link, expressed as , It is the number of information bits in the SR link. This refers to the channel capacity of the SR link. The channel dispersion of the SR link is used to measure the random fluctuation of the channel relative to a deterministic channel at the same capacity.

[0070] Substituting equations (14), (24), and (46) into equation (45), and applying the generalized Newton binomial theorem and the Gauss-Chebyshev quadrature method, we can obtain... The final expression is as follows: (47); among which, , , , Let P be a Legendre polynomial defined on the interval [-1, 1]. n The i-th zero of (x) corresponds to the weight factor. y j Representing the Hermitian polynomial H tThe j-th zero of (y)(y=1,2,…,t), l j Then represents the corresponding weighting factor, expressed as , i represents the node index of the Gauss-Legend product ( ), j represents the node index of the Gaussian-Hermitian product ( ), where t is the order of the Gauss-Hermitian quadrature, and n is the order of the Gauss-Legendé quadrature.

[0071] For the RD link, i.e., the RD link from LEO satellite to the ground terminal, the distribution characteristics of the serving satellites in space must be considered first. Since LEO satellites are randomly distributed on the sphere, the ground terminal may encounter the following three service scenarios:

[0072] Case 1: The serving satellite is located in the main lobe visible region Sml vis; Case 2: The serving satellite is located in the side lobe visible region Ssl vis; Case 3: There is no serving satellite, that is, all satellites are in the invisible region.

[0073] Using the null probability principle of BPP (Block Probability of Particle Particles), i.e., the probability that no point exists within a specific region, the probabilities of the above three scenarios can be represented as follows: Main lobe service probability: (48); Sidelobe service probability: (49); Invisible probability (service interruption): (50); among which, This indicates the total number of LEO satellites.

[0074] Therefore, the probability that at least one visible satellite exists (i.e., the system is serviceable) is: .

[0075] Assuming the system is in a "serviceable" state, the average BLER of the RD link can be calculated by weighting the main lobe and side lobe service scenarios separately, as shown in the following expression: (51); among which, and These represent the average BLER when the serving satellite is in the main lobe and side lobe regions, respectively.

[0076] The BLER representation of an RD link is as follows: (52); where type={ml, sl}, represent the average block error rates corresponding to the main lobe (ml) and side lobes (sl), respectively, denoted as and . The average bit error rate of the RD link is expressed as:

[0077] (53); among them, , R is the average signal-to-noise ratio of the RD link. RD β is the transmission rate of the RD link. RD It is the code block length of the RD link, expressed as , It is the number of information bits in the RD link. It is the channel capacity of the RD link. This represents the channel dispersion of the RD link.

[0078] Substituting equations (48), (49), (50), and (52) into equation (51), and using the Gauss-Chebyshev quadrature method, the average BLER of the RD link can finally be expressed as: (54); Finally, substitute equations (47) and (54) into equation (44) to obtain the final end-to-end BLER analytical expression.

[0079] In deep space communication systems, throughput is a crucial performance indicator for measuring link service capacity and resource utilization efficiency. It essentially reflects the actual rate of information successfully transmitted per unit bandwidth in each time block, assuming certain communication reliability and system availability conditions, measured in bps / Hz. Considering the dynamic visibility of serving satellites and link quality fluctuations, this invention models system throughput as follows:

[0080] (55); among which, R represents the probability that at least one LEO satellite is visible, and R is the end-to-end effective transmission rate of the system, reflecting the maximum data rate that can be transmitted per unit time.

[0081] In this model, the choice of transmission rate R has a decisive impact on system throughput. On the one hand, if R is too low, although the block error rate is low and data reliability is high, the limited amount of data transmitted per unit time will directly limit the system throughput. On the other hand, if R is too high, although the theoretical transmission rate per unit time increases, the excessively high rate may exceed the channel's carrying capacity, leading to a significant increase in the block error rate, thus causing the actual effective throughput to decrease. Therefore, a trade-off must be struck between reliability and transmission rate. Furthermore, the minimum elevation angle θ... min The setting of θ also has a significant impact on system performance. Too low a θ... min While increasing the visibility range of serving satellites and improving availability can reduce link quality due to the longer communication distance between satellites and ground terminals and greater path loss, it can also lead to problems. minWhile link quality is improved, the number of visible satellites may decrease significantly, and there may even be periods when service satellites are "invisible," severely impacting system throughput. Therefore, throughput optimization must comprehensively consider both distance loss due to elevation angle and the impact of visibility.

[0082] Based on the above analysis, this invention constructs a joint optimization method for transmission rate R and minimum elevation angle θ. min The problem of maximizing system throughput, under the constraints of satellite visibility and average block error rate, is to maximize the system throughput T. D2D To achieve the optimal solution, the optimization problem can be expressed by the following mathematical model:

[0083] (56a); (56b); (56c); (56d); (56e); where, equation (56b) is the visibility constraint, requiring that the visibility probability of the system serving the satellite at any time is not lower than the threshold η1, to ensure the high availability of the system; equation (56c) is the reliability constraint, requiring that the average block error rate of the system not exceed the set tolerance upper limit η2, to ensure the accuracy of data transmission; equation (56d) is the transmission rate constraint, ensuring that the transmission rate does not exceed the maximum carrying rate of any link, where, This refers to the transmission rate of the SR link. It is the transmission rate of the RD link; Equation (56e) indicates that the elevation angle must be non-negative, which is a basic constraint in the actual physical scenario.

[0084] To efficiently solve the throughput maximization problem under multi-factor coupling conditions, this invention proposes a parallel-bounded planetary optimization algorithm (PB-POA) for throughput optimization in multi-LEO satellite-assisted deep space communication systems.

[0085] Figure 5 shows the overall schematic of the proposed PB-POA framework. Given the system parameters and the range of decision variables as input, the PB-POA algorithm mainly includes five steps: (1) population initialization and fitness evaluation, (2) distance-based population partitioning, (3) rotational search, (4) DGB-based particle update, and (5) periodic interaction. The algorithm executes these steps sequentially to search for high-quality solutions, ultimately outputting the system's maximum throughput and its corresponding optimal design parameters. The specific steps of PB-POA are explained below.

[0086] (1) Population initialization and fitness evaluation: Within the feasible decision space defined by constraints (56b)-(56e), an initial population of P particles is randomly generated. Each particle represents a candidate solution. The fitness value of each particle is calculated according to the objective function (55).

[0087] (2) Distance-based population partitioning: In the target space, particles spatially close to each other may correspond to different solution sets in the decision space. Directly grouping particles can easily lead to them being guided to local optima, thus reducing the diversity of the decision space. To avoid premature convergence, PB-POA adopts an improved grouping strategy: the top J particles with the best fitness values ​​are selected as the primary stars of the subpopulation, and the remaining particles are assigned to the subpopulation containing the nearest primary star based on Euclidean distance. The formula for calculating the distance between the optimal particle and other particles is:

[0088] (57); among which, This represents the value of the j-th optimal particle in the d-th dimension during the t-th iteration. This represents the value of the i-th particle in the d-th dimension parameter. It is the distance matrix between the host star and other planetary particles, where D is the parameter dimension and N is the total population size.

[0089] (3) Rotational Search: In high-dimensional decision spaces, the POA method updates particles only along a limited number of principal directions, resulting in low search efficiency in deep space communication optimization problems. To enhance the competitiveness of particles and increase their probability of reaching the global optimum, thereby improving overall search efficiency, this invention introduces a rotational search strategy. This strategy allows particles to explore along rotational directions within a given plane of the decision space, thereby enhancing search diversity and search space coverage. The particle update formula under this strategy is:

[0090] (58); where x i The vector representing the current position of the i-th particle. This is the updated location. It is the current search direction vector of the i-th particle. Let θ be the angle of rotation around the origin of a certain decision space plane. h The rotation matrix, angle θ h They are usually evenly distributed in the interval [0, 2π) to enable multi-directional search along the rotation trajectory.

[0091] The rotation angle is defined as: (59); where H represents the number of discrete directions of the rotational search, controlling the number and distribution density of search directions. By uniformly expanding the search in multiple rotational directions, PB-POA effectively overcomes the problem of limited search in traditional POA, improving the competitive ability of particles far from the host star and maintaining the diversity of the population in the decision space, thereby significantly enhancing the ability to discover the global optimal solution.

[0092] (4) Particle update strategy based on DGB (Dual-Guided Balance): In this stage, a DGB strategy is introduced to guide the search behavior of each particle. Specifically, the search pattern of a particle is determined by its distance from the optimal particle. At the t-th iteration, the distance d between particle i and particle j is... ij Defined as ,in, and Let represent the values ​​of particle i and particle j in the k-th dimension at the t-th iteration, respectively. Based on this distance metric, the distance between the optimal particle and particle i is calculated. and with the given minimum distance threshold Comparison. When When the particle is in a certain condition, it performs a global search; otherwise, it performs a local search.

[0093] The formula for the global search phase is: (60); among which, For constant parameters, , This represents the globally optimal particle. Represents particles The local optimal position, , Indicates the first In the next iteration, the globally optimal particle pair is... Gravity, This represents the maximum value of gravity in the current iteration. And satisfy .

[0094] In the local search phase, a dual approach of global optimum and neighborhood optimum is introduced, as shown in the formula: (61); among which, , This is used to provide strong initial exploration capabilities, and the value is gradually reduced with the number of iterations to promote algorithm convergence; This represents the current iteration number. Indicates the maximum number of iterations. It follows a Gaussian distribution; And satisfy .

[0095] (5) Periodic interaction: The periodic interaction mechanism allows subpopulations to exchange particles in a "best to worst" manner, thereby promoting the spread of superior genes and eliminating inferior solutions. This mechanism achieves a global balance between exploration and cooperation, effectively improving the convergence efficiency and solution diversity of the algorithm.

[0096] This invention is applicable to deep space communication scenarios based on distributed LEO satellites, and has significant application value, especially in deep space missions with high requirements for precision and reliability. For example, in fields such as deep space exploration, interplanetary communication, and deep space navigation, this invention can be used for modeling and optimizing deep space communication links. Compared with existing technologies, this invention has better scalability and adaptability, and can be widely applied to communication scenarios in different types of deep space missions and ground control terminals. At the same time, this invention exhibits a strong synergistic effect when combined with other advanced technologies, and is expected to further improve the overall performance of deep space communication technology. Through deep integration and innovation with existing technologies, this invention demonstrates enormous development potential in the field of deep space communication, continuously driving the field to higher levels. Looking to the future, this invention is expected to open new avenues for innovation in deep space communication technology, providing more advanced and reliable communication solutions for deep space exploration. These advancements will not only improve the execution efficiency and success rate of deep space missions, but also inject new vitality and possibilities into human space exploration.

[0097] Based on the same concept, the present invention also provides a throughput optimization system for a deep space communication system, including a construction module, a generation module, a sorting module, an iteration module, and an output module.

[0098] The building module is used to model the throughput of deep space communication systems. The optimization problem is constructed with the goal of maximizing throughput, the transmission rate and the minimum elevation angle of the ground terminal as joint optimization variables, and multiple constraints such as satellite visibility constraint, average block error rate constraint, transmission rate constraint and minimum elevation angle constraint.

[0099] The generation module is used to randomly generate an initial population consisting of multiple particles under multiple constraints, and to obtain the fitness value of each particle; where each particle represents a candidate solution. Where R is the transmission rate. This is the minimum elevation angle.

[0100] The sorting module is used to sort each particle in the initial population according to its fitness value from largest to smallest, and to assign the first J particles as the main stars of different subpopulations. The remaining particles are assigned to the subpopulation of the nearest main star according to the Euclidean distance.

[0101] The iteration module is used to perform multiple rounds of iteration on multiple subpopulations. In each round of iteration, for all subpopulations, each particle searches along the rotation direction in a given plane and updates its position for the first time. After all particles have completed the first position update, if the distance between the current particle and the current global best particle is greater than a set threshold, the current particle will be updated for the second time using a global search method; otherwise, it will be updated for the second time using a local search method.

[0102] The output module is used to output the optimal particle after multiple iterations, thus obtaining the optimal solution and the corresponding maximum throughput.

[0103] Although preferred embodiments of the invention have been described, those skilled in the art, upon learning the basic inventive concept, can make other changes and modifications to these embodiments. Therefore, the appended claims are intended to be interpreted as including both the preferred embodiments and all changes and modifications falling within the scope of the invention.

[0104] Obviously, those skilled in the art can make various modifications and variations to this invention without departing from its spirit and scope. Therefore, if these modifications and variations fall within the scope of the claims of this invention and their equivalents, this invention also intends to include these modifications and variations.

Claims

1. A method for optimizing throughput in a deep space communication system, characterized in that, Includes the following steps: The throughput of a deep-space communication system is modeled with maximizing throughput as the optimization objective. Transmission rate and minimum elevation angle of the ground terminal are used as joint optimization variables, and multiple constraints are imposed, including satellite visibility constraints, average block error rate constraints, transmission rate constraints, and minimum elevation angle constraints. An initial population of multiple particles is randomly generated under these constraints, and the fitness value of each particle is obtained. Each particle represents a candidate solution. Where R is the transmission rate. The minimum elevation angle is determined. Each particle in the initial population is sorted in descending order of fitness value. The top J particles are designated as the primary stars of different subpopulations, and the remaining particles are assigned to the subpopulation containing the nearest primary star based on Euclidean distance. Multiple iterations are performed on the multiple subpopulations. In each iteration, for all subpopulations, each particle searches along the rotation direction within a given plane, updating its position for the first time. After the first position update of all particles, if the distance between the current particle and the current globally optimal particle is greater than a set threshold, the current particle undergoes a second update using a global search method; otherwise, a second update is performed using a local search method. After multiple iterations, the optimal particle is output, yielding the optimal solution and the corresponding maximum throughput.

2. The throughput optimization method for a deep space communication system as described in claim 1, characterized in that, Each particle is searched along the rotation direction within a given plane, as detailed below: In the formula, x i This represents the current position of the i-th particle. Let i be the position of the i-th particle after its first update. It is the current search direction vector of the i-th particle. Let θ be the angle of rotation around the origin of a certain decision space plane. h The rotation matrix is ​​given by t, where t is the number of iterations.

3. The throughput optimization method for a deep space communication system as described in claim 2, characterized in that, The formula for the global search method is as follows: In the formula, Let be the position of the i-th particle after the second update in the global search. For weight parameters, For constant parameters, It is a random number. The globally optimal particle. Let be the local optimal position of the i-th particle. Let be the first intermediate variable; the specific formula for the local search method is shown below: In the formula, Let be the position of the i-th particle after the second update under the local search. For weight parameters, As the second intermediate variable, It follows a Gaussian distribution.

4. The throughput optimization method for a deep space communication system as described in claim 1, characterized in that, The optimization problem is as follows: ； ， In the formula, To constrain the optimization problem, R is the throughput, and R is the system's end-to-end effective transmission rate. Minimum elevation angle, The probability of at least one LEO satellite being visible is given by η1, where η1 is the visibility probability threshold for the serving satellite and η2 is the tolerance upper limit. For the transmission rate of the SR link, This represents the transmission rate of the RD link.

5. The throughput optimization method for a deep space communication system as described in claim 4, characterized in that, Modeling the throughput of the deep space communication system specifically includes the following steps: Constructing a deep space communication system comprising a probe S, distributed LEO satellites, and a ground terminal D, wherein the distributed LEO satellites are relay nodes R. The FSO signal from probe S is transmitted to the distributed LEO satellites via the SR link. The distributed LEO satellites convert the FSO signal into an electrical signal and transmit it to the ground terminal D via the RD link. Modeling multiple first key factors affecting the reliability of the SR link communication and obtaining corresponding mathematical representations; modeling multiple second key factors affecting the reliability of the RD link communication and obtaining corresponding mathematical representations; obtaining the average block error rate (BOR) of the SR link based on the mathematical representations of the first key factors; obtaining the average BOR of the RD link based on the mathematical representations of the second key factors; combining the average BOR rates of the SR link and the RD link to obtain the end-to-end average BOR rate of the deep space communication system; and obtaining the throughput of the deep space communication system based on the end-to-end average BOR rate.

6. The throughput optimization method for a deep space communication system as described in claim 5, characterized in that, The end-to-end average block error rate is as follows: In the formula, The average block error rate from end to end. The average block error rate of the SR link. The average block error rate of the RD link; the throughput of the deep space communication system is as follows: In the formula, This represents the throughput of deep space communication systems.

7. The throughput optimization method for a deep space communication system as described in claim 5, characterized in that, The first key factors include fading behavior caused by coronal turbulence and pointing error, as well as phase fluctuations caused by coronal turbulence; the method of obtaining the average block error rate of the SR link based on the data representation of the first key factors specifically includes the following steps: jointly representing the mathematical representation of fading behavior caused by coronal turbulence and pointing error; obtaining the average bit error rate of the SR link; and obtaining the average block error rate of the SR link based on the joint representation result, the mathematical representation of phase fluctuations caused by coronal turbulence, and the average bit error rate.

8. The throughput optimization method for a deep space communication system as described in claim 5, characterized in that, Several secondary key factors include propagation loss and small-scale fading. The method for obtaining the average block error rate (BER) of the RD link based on the mathematical representation of these secondary key factors specifically includes the following steps: dividing the distributed LEO satellites into a visible satellite set and an invisible satellite set based on the minimum elevation angle of the ground terminal; dividing the visible satellite set into a first visible satellite set with its main lobe facing the ground terminal and a second visible satellite set with its side lobes facing the ground terminal; obtaining the distance vectors (PDFs) between the first and second visible satellite sets and the ground terminal, respectively; obtaining the signal-to-noise ratio (SNR) of the RD link for the first and second visible satellite sets based on the mathematical representation of the secondary key factors and the PDFs of the distances between the first and second visible satellite sets and the ground terminal; obtaining the service probability and the average BER of the RD link when the serving satellite is located in different visible areas; and obtaining the average block error rate of the RD link based on the SNR of the RD link for the first and second visible satellite sets, the service probability when the serving satellite is located in different visible areas, and the average BER of the RD link.

9. A throughput optimization system for a deep space communication system, characterized in that, include: The construction module models the throughput of the deep space communication system, aiming to maximize throughput. It uses transmission rate and minimum elevation angle of the ground terminal as joint optimization variables, and employs multiple constraints including satellite visibility, average block error rate, transmission rate, and minimum elevation angle to construct the optimization problem. The generation module randomly generates an initial population of multiple particles under these constraints and obtains the fitness value of each particle. Each particle represents a candidate solution. Where R is the transmission rate. The minimum elevation angle is defined by the following modules: A sorting module sorts each particle in the initial population according to its fitness value from largest to smallest, assigning the top J particles as the primary stars of different subpopulations, and distributing the remaining particles to the subpopulation containing the nearest primary star based on Euclidean distance; an iteration module performs multiple iterations on multiple subpopulations; in each iteration, for all subpopulations, each particle searches along the rotation direction in a given plane and updates its position for the first time; after the first position update of all particles, if the distance between the current particle and the current global best particle is greater than a set threshold, the current particle performs a second update using a global search method; otherwise, it performs a second update using a local search method; and an output module outputs the optimal particle, obtaining the optimal solution and the corresponding maximum throughput after multiple iterations.

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