A novel method for turbulence compensation in atmospheric laser communication based on the Kolmogorov-Zakharov model

Abstract

A novel Kolmogorov-Zakharov model-based turbulence compensation method for atmospheric laser communication is presented, belonging to the field of atmospheric laser communication technology. This method addresses the technical problem of decreased compensation accuracy in strongly turbulent scenarios, which negatively impacts the transmission quality and stability of atmospheric laser communication. The method obtains the atmospheric refractive index structure constant by real-time acquisition of the laser signal's phase distribution and intensity fluctuations. The model parameters are then mapped to atmospheric laser communication physical quantities, and the model is updated based on this atmospheric refractive index structure constant. Next, based on the model and the Helmholtz equations for atmospheric laser transmission, a KZ turbulence stochastic matrix model for the atmospheric laser channel is obtained and solved to yield prediction results. Finally, dynamic turbulence compensation is performed based on these prediction results. This method is primarily used for turbulence compensation in atmospheric laser communication.

Description

Technical Field

[0001] This invention relates to the field of atmospheric laser communication technology, specifically to a method for turbulence compensation in atmospheric laser communication based on a novel Kolmogorov-Zakharov model. Background Technology

[0002] Atmospheric laser communication is a free-space optical communication method that uses a laser beam as a carrier to transmit information within an atmospheric channel. In the field of atmospheric laser communication, atmospheric turbulence is the core bottleneck causing performance degradation. This atmospheric turbulence is caused by irregular fluctuations in the refractive index due to random variations in atmospheric temperature, pressure, and humidity. Atmospheric turbulence induces phenomena such as intensity fluctuations, phase distortion, and beam drift in the laser beam, increasing the bit error rate and reducing the signal-to-noise ratio at the receiver, severely impacting signal transmission quality and stability.

[0003] Existing technologies typically employ software-based compensation methods based on signal processing, requiring no additional hardware. These methods largely rely on traditional turbulence statistical models, such as the Log-normal model and the Kolmogorov spectral model. However, these models are based on the assumption of weak turbulence and relatively smooth refractive index fluctuations, only describing the statistical characteristics of weak turbulence scenarios and failing to accurately depict the dynamic evolution of turbulence from weak to strong. In strong turbulence scenarios, more complex physical effects arise, significantly reducing compensation accuracy and making it difficult to meet the demands of high-bandwidth, low-latency atmospheric laser communication. Summary of the Invention

[0004] To overcome the technical problem that the compensation accuracy of existing technologies decreases in strong turbulence scenarios, thereby affecting the transmission quality and stability of atmospheric laser communication, this invention provides an atmospheric laser communication turbulence compensation method based on a novel Kolmogorov-Zakharov model (Random Matrix Model of Kolmogorov-Zakharov Turbulence, RMM of KZT).

[0005] This invention is achieved through the following technical solution:

[0006] A novel method for atmospheric laser communication turbulence compensation based on the Kolmogorov-Zakharov model includes:

[0007] S1: Based on the phase distribution and intensity fluctuations of the laser signal acquired in real time, the real-time atmospheric refractive index structure constant is obtained.

[0008] S2: Will The core parameters of the model are mapped to physical quantities of atmospheric laser communication, and then the atmospheric refractive index structure constant is used to... The model is updated;

[0009] S3: Based on the above Based on the model and the Helmholtz equations for atmospheric laser transmission, the KZ turbulent stochastic matrix model of the atmospheric laser channel is obtained.

[0010] S4: Solve the KZ turbulence stochastic matrix model of the atmospheric laser channel to obtain the prediction results;

[0011] S5: Perform dynamic turbulence compensation based on the prediction results.

[0012] This invention obtains the atmospheric refractive index structure constant by real-time acquisition of the phase distribution and intensity fluctuations of the laser signal in S1, combined with the data in S2. The mapping between model parameters and atmospheric laser communication physical quantities is based on model updates using the atmospheric refractive index structure constant, achieving model adaptation to the actual atmospheric environment. In S3, the Helmholtz equation is used to describe the fundamental wave equation for laser propagation in the atmosphere, accurately characterizing laser phase distortion, beam drift, and transmission characteristics. The model parameters conform to actual physical laws, and together with S1 and S2, they prevent the model from becoming disconnected from the physical scene. S4 and S5 utilize the... The model's predictions enable dynamic compensation for turbulence, enhancing the compensation effect and thus improving the transmission quality and stability of atmospheric laser communication.

[0013] The steps for obtaining the real-time atmospheric refractive index structure constant in S1 include:

[0014] The phase fluctuation variance is obtained based on the phase distribution, and the intensity fluctuation variance is calculated based on the light intensity. The phase fluctuation variance is verified using the intensity fluctuation variance. Then, the real-time atmospheric refractive index structure constant is calculated using the verified phase fluctuation variance. The calculation process satisfies the following formula:

[0015] ;

[0016] In the formula, Indicates the atmospheric refractive index structure constant; Indicates the variance of phase fluctuations; Indicates the wavenumber of the laser; Indicates the length of the communication link.

[0017] The method for calculating the atmospheric refractive index structure constant in this invention is based on real-time dynamic updates of atmospheric parameters, which closely matches the actual atmospheric conditions.

[0018] Furthermore, the aforementioned The rules for mapping the core parameters of the model to atmospheric laser communication physical quantities include:

[0019] Laser transmission mode mapping in atmospheric laser communication is Linear eigenmodes in the model;

[0020] Energy injection of atmospheric turbulence is mapped as Energy pump in the model;

[0021] The turbulent energy attenuation caused by atmospheric molecular scattering and absorption is mapped as follows: Energy dissipation in the model;

[0022] Atmospheric turbulence intensity mapped to Nonlinear coupling coefficients in the model.

[0023] By establishing The correlation between the model's core parameters and atmospheric laser communication physical quantities enables the model to conform to the actual atmospheric environment characteristics, providing a physical basis for the dynamic updating of the model.

[0024] Furthermore, the atmospheric laser channel KZ turbulence stochastic matrix model is as follows:

[0025] ;

[0026] In the formula, Indicates the imaginary root of the unit; Indicates the laser transmission mode; , , They represent the first The complex amplitude of each linear eigenmode; Indicates the first The eigenenergy of a linear eigenmode; Indicates the energy pumping / dissipation coefficient; This is the pump saturation coefficient; Represents the nonlinear coupling coefficient; express Four-wave interaction transition matrix elements; Represents a time variable; Indicates complex conjugation; It represents the complex conjugate of the complex amplitude of the laser transmission mode.

[0027] Furthermore, the solution to the atmospheric laser channel KZ turbulent stochastic matrix model described in S4 is performed using the fourth-order symplectic integral method.

[0028] The fourth-order symmetric integral method employed in this invention possesses the advantage of symmetric symmetry conservation, meaning that it can accurately conserve the total norm and energy even without pumping and dissipation. This method is well-suited to the Hamiltonian dynamics of the pump-dissipation relationship in atmospheric laser channels, avoiding energy distortion caused by non-symmetric methods. Even in non-symmetric systems, i.e., with pumping and dissipation, it maintains long-term integration without divergence, making it suitable for continuous dynamic compensation of atmospheric turbulence.

[0029] Furthermore, the iterative formula for solving the KZ turbulence stochastic matrix model of the atmospheric laser channel using the fourth-order symplectic integral method is as follows:

[0030] ;

[0031] ;

[0032] ;

[0033] ;

[0034] In the formula, The base of the logarithm of natural numbers. This represents the intermediate variable of the complex amplitude of the m-th laser transmission mode after the first linear transmission loss energy term. This represents the intermediate variable of the complex amplitude of the m-th laser transmission mode after turbulent energy pumping and pump saturation. This represents the intermediate variable of the complex amplitude of the m-th laser transmission mode after the interaction of the second linear transmission loss energy term and the nonlinear coupling term, which is ultimately used as the predicted result of the complex amplitude at that moment. The time window for predicting the complex amplitude of the laser mode.

[0035] Furthermore, the prediction results described in S4 include: laser transmission mode complex amplitude, phase distortion prediction value, intensity fluctuation prediction value, mode energy distribution, and chaotic state identifier.

[0036] Furthermore, the method for determining a chaotic state is as follows:

[0037] First, define the chaotic critical intensity of atmospheric turbulence. Then calculate the nonlinear coupling coefficients corresponding to the current turbulence. When the nonlinear coupling coefficient Greater than the critical strength of chaos When the current turbulence enters a chaotic state, it is determined that the current turbulence has entered a chaotic state; when the nonlinear coupling coefficient Less than the critical strength of chaos When the current turbulence is in a quasi-integrable state, it is determined that the current turbulence has entered a quasi-integrable state.

[0038] Furthermore, when the current turbulence is in a chaotic state, a phase conjugation algorithm with low-frequency harmonic compensation is adopted. Based on the predicted phase distortion value, local phase disturbances are canceled out through phase conjugation.

[0039] Furthermore, when the current turbulence is in a quasi-integrable state, the modulation order of the adaptive modulation and demodulation module is adjusted based on the intensity fluctuation prediction value; at the same time, based on the mode energy distribution, signal attenuation caused by energy cascading is suppressed.

[0040] By determining the chaotic state and implementing a case-by-case compensation mechanism, this invention can adapt to strong and weak turbulence scenarios. In complex environments with large day-night temperature differences and unstable airflow, it improves the stable operation time of the communication link compared to traditional compensation schemes.

[0041] The beneficial effects of this invention are:

[0042] This invention obtains the atmospheric refractive index structure constant by real-time acquisition of the phase distribution and intensity fluctuations of laser signals. The mapping between model parameters and atmospheric laser communication physical quantities is based on the atmospheric refractive index structure constant. Model update, achieving the above The model is adapted to the actual atmospheric environment; the Helmholtz equation is used to describe the fundamental wave equation of laser propagation in the atmosphere, resulting in a KZ turbulence stochastic matrix model of the atmospheric laser channel, which characterizes the energy cascade of atmospheric turbulence from a dynamic perspective; utilizing the aforementioned... The model's predictions enable dynamic compensation for turbulence, enhancing the compensation effect and thus improving the transmission quality and stability of atmospheric laser communication.

[0043] Compared to the traditional Log-normal model, the atmospheric laser channel KZ turbulent random matrix model constructed by the method of this invention has lower prediction errors for phase distortion and intensity fluctuations, and reduces the communication bit error rate. Attached Figure Description

[0044] 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 embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on the provided drawings without creative effort.

[0045] Figure 1 This is a schematic diagram illustrating the execution flow of one embodiment of the method of the present invention. Detailed Implementation

[0046] 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. Specific Implementation Method 1

[0048] refer to Figure 1This paper presents an implementation method for atmospheric laser communication turbulence compensation based on a novel Kolmogorov-Zakharov model, including the following steps:

[0049] Step S100: Deploy a wavefront detector and an intensity detector at the atmospheric laser communication receiver to collect phase distribution data and intensity data of the laser signal in real time, respectively; based on the phase distribution and intensity fluctuations of the laser signal collected in real time, obtain the real-time atmospheric refractive index structure constant.

[0050] The specific steps include:

[0051] Step S101: Using A pixel-scale wavefront detector acquires the phase distribution of the laser at the receiving end. And based on the phase distribution, the phase fluctuation variance is obtained. The calculation formula is as follows:

[0052] ;

[0053] In the formula, This indicates the average phase.

[0054] Step S102: Using A pixel-scale light intensity detector collects the intensity of the laser light received at the receiver. And calculate the intensity fluctuation variance based on the light intensity. The calculation formula is as follows:

[0055] ;

[0056] In the formula, This represents the average light intensity.

[0057] Step S103: Utilize the intensity fluctuation variance Verify the phase fluctuation variance Data reliability;

[0058] Specifically: First, utilize the aforementioned intensity fluctuation variance Inversely deriving the atmospheric refractive index structure constant Then, the atmospheric refractive index structure constant obtained by reverse calculation is obtained. Substituting the phase fluctuation theory formula into the turbulent scenario, we obtain the inversely derived phase fluctuation variance. Then, the phase fluctuation variance is obtained based on the phase distribution. and By comparison, if the relative error is within a preset range, the phase fluctuation variance can be determined. The data is reliable.

[0059] In practical applications, the preset range of the relative error can be set to less than 10% or less than 20%.

[0060] Step S104: Calculate the real-time atmospheric refractive index structure constant using the verified phase fluctuation variance; the calculation process satisfies the formula:

[0061] ;

[0062] In the formula, Indicates the atmospheric refractive index structure constant; Indicates the variance of phase fluctuations; Indicates the wavenumber of the laser; Indicates the length of the communication link.

[0063] Compared to existing technologies that directly measure the atmospheric refractive index structure constant using specialized turbulence analyzers such as scintillation meters or only use the Rytov approximation of light intensity fluctuations to calculate the atmospheric refractive index structure constant, the method of this invention combines phase distribution and light intensity fluctuation data and utilizes the communication system's own detector to measure the atmospheric refractive index structure constant.

[0064] The atmospheric refractive index structure constant calculation method in this invention eliminates the reliance on specialized instruments, reducing operating costs. Furthermore, the method of measuring the atmospheric refractive index structure constant using specialized instruments before transmitting the data to the communication system introduces a time delay. In contrast, this invention utilizes the communication system's own detector to measure the atmospheric refractive index structure constant, resulting in a shorter time delay compared to methods using specialized instruments. This allows for rapid response to dynamic changes in turbulence and is suitable for high-bandwidth, low-latency atmospheric laser communication scenarios.

[0065] Step S200: Map the core parameters of the RMM of the KZT model to the physical quantities of atmospheric laser communication, and then use the atmospheric refractive index structure constant to... The model is updated.

[0066] Step S201: The rules for mapping the core parameters of the RMM of KZT model to atmospheric laser communication physical quantities include:

[0067] In atmospheric laser communication, the laser transmission mode is mapped to the linear eigenmodes in the RMM of the KZT model; the laser transmission mode includes the base mode and higher-order transverse modes.

[0068] The energy injection of atmospheric turbulence is mapped to the energy pump in the RMM of the KZT model; the energy injection includes atmospheric temperature and airflow disturbance.

[0069] Energy pumping refers to the physical process by which atmospheric temperature gradients and airflow disturbances inject energy into a turbulent system. Energy pumping coefficient. In the RMM of KZT model, the mathematical parameters that quantify the intensity of the energy pumping process are used.

[0070] The intensity of the energy pumping process is quantitatively characterized by the energy pumping coefficient in the model: the energy pumping coefficient is determined by the total energy input intensity of the temperature gradient and the airflow disturbance. The values ​​of these parameters are positively correlated; that is, the greater the total energy input intensity, the higher the energy pumping coefficient. The larger the value, and When the temperature gradient is significant and the wind speed is high during the day, the total energy input is enhanced, and the energy pumping coefficient takes a larger value, corresponding to the strengthening of turbulent energy injection in the model. When the temperature gradient is gentle and the wind speed is low at night, the total energy input is weakened, and the energy pumping coefficient takes a smaller value, corresponding to the weakening of turbulent energy injection in the model. This achieves dynamic matching between the atmospheric turbulent energy input process and the model's energy pumping mechanism.

[0071] The turbulent energy attenuation caused by atmospheric molecular scattering and absorption is mapped to energy dissipation in the RMM of the KZT model. This energy dissipation is expressed through the energy dissipation coefficient in the model. Quantitative characterization.

[0072] The atmospheric refractive index structure constant is mapped to the nonlinear coupling coefficients in the RMM of the KZT model, allowing the model's nonlinear coupling coefficients to dynamically adapt to the atmospheric refractive index structure constant, rather than remaining fixed. The mapping formula is:

[0073] ;

[0074] In the formula, L represents the laser wave number, and L represents the communication link length.

[0075] Step S202: Using the atmospheric refractive index structure constant to... The model is updated.

[0076] Specifically, the atmospheric refractive index structure constant Input the KZ turbulent stochastic matrix model of the atmospheric laser channel and update the nonlinear coupling coefficients. Energy pump coefficient and pump saturation coefficient The updated atmospheric laser channel KZ turbulence stochastic matrix model is obtained. The formula is as follows:

[0077] ;

[0078] ;

[0079] .

[0080] Step S300: Based on the above Based on the model and the Helmholtz equations for atmospheric laser transmission, a KZ turbulent stochastic matrix model for the atmospheric laser channel is obtained.

[0081] The Helmholtz equation is the fundamental wave equation describing the propagation of laser light in the atmosphere. It accurately characterizes the propagation characteristics of laser light, such as phase distortion and beam drift, enabling... The model parameters conform to actual physical laws, avoiding a disconnect between the model and the physical scene; the Helmholtz equation describes the laser wavenumber. Link length The influence of macroscopic transmission patterns, etc. It describes the microscopic energy disturbance of turbulence on modes. Combining the two can construct a complete link between physical phenomena and model compensation, improving the compensation accuracy and real-time performance.

[0082] The mathematical expression for the atmospheric laser channel KZ turbulence stochastic matrix model is:

[0083] ;

[0084] In the formula, Indicates the imaginary root of the unit; Indicates the laser transmission mode; , , They represent the first The complex amplitude of each linear eigenmode is used to describe the energy occupancy level of the mode; Indicates the first The eigenenergy of a linear eigenmode corresponds to the energy characteristics of the mode itself; Indicates the energy pumping / dissipation coefficient, when Time represents the energy pumping coefficient; when and The time factor represents the energy dissipation coefficient, which is used to describe the replenishment and loss of modal energy factors by external effects such as scattering and absorption; This is the pump saturation coefficient, used to suppress the unlimited increase in amplitude caused by pumping and maintain the steady state of the system; This represents the nonlinear coupling coefficient, which is dimensionless and used to quantify the strength of the nonlinear interaction between linear eigenmodes. express The four-wave interaction transition matrix elements are approximately on the order of magnitude of... , For the system's degrees of freedom, describe the energy exchange paths between modes; Represents a time variable; Indicates complex conjugation; It represents the complex conjugate of the complex amplitude of the laser transmission mode.

[0085] Compared to existing models for atmospheric laser communication turbulence compensation—the physical quantities are mostly based on… Model, Spectral model, the present invention will By combining atmospheric laser communication and constructing a mapping relationship between atmospheric physical processes and the core parameters of the model, the traditional model can overcome the limitation of only being able to associate weak turbulence statistics, thus enabling adaptation to different turbulence scenarios and forming a customized model for cross-scenario transfer.

[0086] Step S400: Solve the KZ turbulence stochastic matrix model of the atmospheric laser channel to obtain the prediction results.

[0087] Step S401: Solve the updated atmospheric laser channel KZ turbulence stochastic matrix model using the fourth-order symplectic integral method. The iterative formula is as follows:

[0088] ;

[0089] ;

[0090] ;

[0091] ;

[0092] In the formula, The base of the logarithm of natural numbers. This represents the intermediate variable of the complex amplitude of the m-th laser transmission mode after the first linear transmission loss energy term. This represents the intermediate variable of the complex amplitude of the m-th laser transmission mode after turbulent energy pumping and pump saturation. This represents the intermediate variable of the complex amplitude of the m-th laser transmission mode after the interaction of the second linear transmission loss energy term and the nonlinear coupling term, which is ultimately used as the predicted result of the complex amplitude at that moment. The prediction time window for the complex amplitude of the laser mode corresponds to the laser propagation time difference from the current monitoring time to the compensation execution time, and its value is [value missing]. In this embodiment, in order to match the detector sampling frequency, .

[0093] Step S402: Obtain the prediction result using the above iterative formula.

[0094] The prediction results include: laser transmission mode complex amplitude, phase distortion prediction value, intensity fluctuation prediction value, mode energy distribution, and chaotic state identifier.

[0095] The laser transmission mode complex amplitude That is, the first The future complex amplitude of each mode is the basis for all predictions and is solved by fourth-order symplectic integrals.

[0096] The phase distortion prediction value Used for phase correction in weak turbulence, compensating for input. The calculation formula is:

[0097] .

[0098] The intensity fluctuation prediction value Used for adjusting the modulation order of strong turbulence, in W. The calculation formula is:

[0099] .

[0100] The modal energy distribution This refers to the mode occupancy probability, also known as energy distribution, used for strong turbulent mode diversity reception. The calculation formula is:

[0101] .

[0102] Nonlinear frequency shift Nonlinear frequency shift is used to characterize the disturbance intensity of nonlinear interactions in turbulence. The magnitude of the coefficient is related to the nonlinear coupling coefficient in the KZ turbulence stochastic matrix model of the atmospheric laser channel. Positively correlated with turbulent mode number They are negatively correlated, and the mathematical relationship can be simplified to: Linear performance level spacing Magnitude and turbulent mode number They are negatively correlated, and the mathematical relationship can be simplified to: .when Greater than When the system enters a chaotic state, the critical value of the chaotic state is derived based on the above relationship. .

[0103] When the actual nonlinear coupling coefficient greater than the critical value of the chaotic state At this point, nonlinear coupling violates the KAM integrability, leading to global chaotic attraction and the core characteristic of turbulence: energy propagation along modes from low to high. The main factor causing laser transmission distortion at this time is the cascading energy coupling between multiple modes, where the energy of low-energy modes such as the fundamental mode transitions through the four-wave interaction matrix elements. The rapid transmission to higher-order transverse modes and other high-energy modes causes violent fluctuations in the amplitude and phase of each mode, manifested as large intensity fluctuations and complex phase distortions. At this point, the turbulence is determined to be in a chaotic state.

[0104] When the actual nonlinear coupling coefficient Less than or equal to the critical value of the chaotic state At this time, the nonlinear coupling is weak, the KAM torus is not destroyed, the system phase space is dominated by integrable motion, and the energy fluctuates only within local modes without cross-mode cascading. At this time, the main factor of laser transmission distortion is the local phase perturbation within a single mode, such as the fundamental mode phase drift caused by the slow change of atmospheric refractive index. The intensity fluctuation is small, and the distortion is easier to correct. At this time, the turbulence is judged to be a quasi-integrable state.

[0105] The chaotic state identifier is used to mark the chaotic state of turbulence, including chaotic states and quasi-integrable states. The chaotic state represents strong turbulence, and the quasi-integrable state represents weak turbulence. It is used to trigger stratified compensation.

[0106] In this embodiment, the atmospheric refractive index structure constant is calculated once every 1 ms. The nonlinear coupling coefficients in the KZ turbulence stochastic matrix model of the atmospheric laser channel are also updated. Energy pump coefficient and pump saturation coefficient At the same time, it determines the chaotic characteristics of the turbulence.

[0107] Step S500: Perform turbulence dynamic compensation based on the prediction results.

[0108] Step S501: When the chaotic state is identified as chaotic, a phase conjugation algorithm with low-frequency harmonic compensation is used to cancel local phase disturbances through phase conjugation. Specific steps include:

[0109] First, the phase distribution at the current moment is acquired in real time. The future is obtained through the aforementioned steps of the present invention. Predicted phase distortion over time Then set the ideal phase as In this embodiment The actual future phase is: Therefore, the phase deviation that needs to be compensated for:

[0110] .

[0111] Then, the phase deviation that needs to be compensated is... Fourier decomposition is performed to extract low-frequency components, and the phase deviation to be compensated is generated using a liquid crystal spatial light modulator (LCo). Conjugate phase distribution.

[0112] Finally, the conjugate phase is loaded onto the phase equalizer to cancel out local phase disturbances in laser transmission and output the corrected laser signal.

[0113] Compared to traditional algorithms that "can only correct phase distortions that have already occurred and cannot cope with dynamic disturbances in real-time transmission", this invention predicts phase deviations using the KZ turbulence random matrix model of the atmospheric laser channel and then "compensates in advance" in a targeted manner.

[0114] Step S502: When the chaotic state is identified as a quasi-integrable state, based on the intensity fluctuation prediction value... Adjust the modulation order of the adaptive modulation and demodulation module; and simultaneously, based on the modal energy distribution... This suppresses signal attenuation caused by energy cascading.

[0115] Specifically, referring to Table 1, if the current turbulence state is strong turbulence, the QAM modulator is controlled to reduce the modulation order, thereby balancing high bandwidth and low bit error rate.

[0116] While adjusting the modulation order, a mode diversity reception mechanism is simultaneously activated to filter the mode energy distribution. The highest proportion of medium energy Each transmission mode is combined using the maximum ratio combining (MRC) algorithm to suppress signal attenuation caused by energy cascading.

[0117] The former There are 1 transmission mode, among which The numerical setting is taken from the modal energy distribution. The minimum number of modes with a cumulative energy share of 90% is selected. This allows the chosen modes to cover the vast majority of signal energy, thereby maximizing diversity reception gain. In this embodiment, .

[0118] In this embodiment, the receiving end of the atmospheric laser communication calculates the communication bit error rate every 10ms. If the bit error rate exceeds a preset threshold, it is fed back to the field-programmable gate array (FPGA) signal processing module to adjust the integration step size or compensation weight parameters of the matrix model, thereby optimizing the compensation effect. In this embodiment, the preset threshold for the bit error rate is set to... .

[0119] Table 1. Correspondence between intensity fluctuations, modulation order, and turbulence intensity

[0120]

[0121] Some other notes regarding this embodiment:

[0122] The transmitter of atmospheric laser communication adopts Narrow linewidth laser with output power of , matching support An adaptive modulator and fiber amplifier transmit the modulated laser signal to the atmospheric channel via a collimator.

[0123] The receiver of atmospheric laser communication includes four parallel photodetectors, each with a response bandwidth of [missing information]. Sampling frequency is The wavefront detector, sampling frequency is Light intensity detector, as well as field-programmable gate array (FPGA) signal processing module, digital signal processor (DSP) and compensation module.

[0124] The control unit uses an industrial-grade microcontroller to achieve coordinated control of the transmitting and receiving devices, as well as real-time scheduling of compensation parameters.

[0125] Before applying this implementation method, phase and intensity data of laser transmission are first collected in a standard turbulent environment. The four-wave interaction transition matrix elements and chaotic critical intensity in the model are fitted by the least squares method to establish an initial parameter library. Then, when the communication link is started, the receiver detector collects the laser signal data for the first 100ms, calculates the initial atmospheric refractive index structure constant, substitutes the atmospheric refractive index structure constant into the initial parameter library, determines the nonlinear coupling coefficient, energy pump coefficient, and pump saturation coefficient of the matrix model, and completes the initialization of the matrix model.

[0126] Finally, it should be noted that in this document, relational terms such as "first" and "second" are used only to distinguish one entity or operation from another, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Furthermore, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or apparatus. Without further limitations, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or apparatus that includes said element.

[0127] The above description of the disclosed embodiments enables those skilled in the art to make or use the invention. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the invention. Therefore, the invention is not to be limited to the embodiments shown herein, but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A method for atmospheric laser communication turbulence compensation based on a novel Kolmogorov-Zakharov model, characterized in that, include: S1: Based on the phase distribution and intensity fluctuations of the laser signal acquired in real time, the real-time atmospheric refractive index structure constant is obtained. S2: Will The core parameters of the model are mapped to physical quantities of atmospheric laser communication, and then the atmospheric refractive index structure constant is used to... The model is updated; S3: Based on the above Based on the model and the Helmholtz equations for atmospheric laser transmission, the KZ turbulent stochastic matrix model of the atmospheric laser channel is obtained. S4: Solve the KZ turbulence stochastic matrix model of the atmospheric laser channel to obtain the prediction results; S5: Perform dynamic turbulence compensation based on the prediction results; The The rules for mapping the core parameters of the model to atmospheric laser communication physical quantities include: Laser transmission mode mapping in atmospheric laser communication is Linear eigenmodes in the model; Energy injection of atmospheric turbulence is mapped as Energy pump in the model; The turbulent energy attenuation caused by atmospheric molecular scattering and absorption is mapped as follows: Energy dissipation in the model; Atmospheric turbulence intensity mapped to Nonlinear coupling coefficients in the model.

2. The atmospheric laser communication turbulence compensation method based on the novel Kolmogorov-Zakharov model according to claim 1, characterized in that, The steps for obtaining the real-time atmospheric refractive index structure constant in S1 include: The phase fluctuation variance is obtained based on the phase distribution, and the intensity fluctuation variance is calculated based on the light intensity. The phase fluctuation variance is verified using the intensity fluctuation variance. Then, the real-time atmospheric refractive index structure constant is calculated using the verified phase fluctuation variance. The calculation process satisfies the following formula: ； In the formula, Indicates the atmospheric refractive index structure constant; Indicates the variance of phase fluctuations; Indicates the wavenumber of the laser; Indicates the length of the communication link.

3. The atmospheric laser communication turbulence compensation method based on the novel Kolmogorov-Zakharov model according to claim 1 or 2, characterized in that, The atmospheric laser channel KZ turbulence stochastic matrix model is as follows: ； In the formula, Indicates the imaginary root of the unit; Indicates the laser transmission mode; , , They represent the first The complex amplitude of each linear eigenmode; Indicates the first The eigenenergy of a linear eigenmode; Indicates the energy pumping / dissipation coefficient; This is the pump saturation coefficient; Represents the nonlinear coupling coefficient; express Four-wave interaction transition matrix elements; Represents a time variable; Indicates complex conjugation; It represents the complex conjugate of the complex amplitude of the laser transmission mode.

4. The atmospheric laser communication turbulence compensation method based on the novel Kolmogorov-Zakharov model according to claim 3, characterized in that, The solution to the KZ turbulent stochastic matrix model of the atmospheric laser channel described in S4 is achieved using the fourth-order symplectic integral method.

5. The atmospheric laser communication turbulence compensation method based on the novel Kolmogorov-Zakharov model according to claim 4, characterized in that, The iterative formula for solving the KZ turbulence stochastic matrix model of the atmospheric laser channel using the fourth-order symplectic integral method is as follows: ； ； ； ； In the formula, The base of the logarithm of natural numbers. This represents the intermediate variable of the complex amplitude of the m-th laser transmission mode after the first linear transmission loss energy term. This represents the intermediate variable of the complex amplitude of the m-th laser transmission mode after turbulent energy pumping and pump saturation. This represents the intermediate variable of the complex amplitude of the m-th laser transmission mode after the interaction of the second linear transmission loss energy term and the nonlinear coupling term, which is ultimately used as the predicted result of the complex amplitude at that moment. The time window for predicting the complex amplitude of the laser mode.

6. The atmospheric laser communication turbulence compensation method based on the novel Kolmogorov-Zakharov model according to claim 5, characterized in that, The prediction results described in S4 include: laser transmission mode complex amplitude, phase distortion prediction value, intensity fluctuation prediction value, mode energy distribution, and chaotic state identifier.

7. The atmospheric laser communication turbulence compensation method based on the novel Kolmogorov-Zakharov model according to claim 6, characterized in that, The chaotic state identifier is used to mark the chaotic state of turbulence, including chaotic state and quasi-integrable state; The method for determining the chaotic state includes: First, define the chaotic critical intensity of atmospheric turbulence. Then calculate the nonlinear coupling coefficients corresponding to the current turbulence. When the nonlinear coupling coefficient Greater than the critical strength of chaos When the current turbulence enters a chaotic state, it is determined that the current turbulence has entered a chaotic state; when the nonlinear coupling coefficient Less than the critical strength of chaos When the current turbulence is in a quasi-integrable state, it is determined that the current turbulence has entered a quasi-integrable state.

8. The atmospheric laser communication turbulence compensation method based on the novel Kolmogorov-Zakharov model according to claim 7, characterized in that, When the current turbulence is in a chaotic state, a phase conjugation algorithm with low-frequency harmonic compensation is adopted. Based on the predicted phase distortion value, local phase disturbances are canceled by phase conjugation.

9. The atmospheric laser communication turbulence compensation method based on the novel Kolmogorov-Zakharov model according to claim 7, characterized in that, When the current turbulence is in a quasi-integrable state, the modulation order of the adaptive modulation and demodulation module is adjusted based on the intensity fluctuation prediction value; at the same time, based on the mode energy distribution, signal attenuation caused by energy cascading is suppressed.

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