Coherent free space optical communication system based on RBMGC optimization algorithm

Abstract

The invention relates to a coherent free space optical communication system based on an RBMGC optimization algorithm, belongs to the technical field of optical communication, and solves the problem of poor high-order aberration correction effect caused by insufficient high-order phase aberration correction capability of an existing SLAO system optimization algorithm under a complex atmospheric turbulence condition. The SLAO system comprises a high-speed camera, a wavefront controller and a wavefront corrector, an RBMGC optimization algorithm is operated in the wavefront controller to generate an optimal voltage control signal of the wavefront corrector, and the RBMGC optimization algorithm adopts a self-adaptive step length updating mode established based on a gradient correction mechanism to update the position in an exploration stage and a development stage. Therefore, the search process is optimized. The RBMGC optimization algorithm has better convergence rate, correction precision and robustness when correcting the high-order aberration under the complex turbulence condition, the correction effect of the SLAO system on the high-order aberration is improved, and the communication performance of the CFSOC system is improved.

Description

Technical Field

[0001] The present invention relates to the technical field of optical communications, and in particular to a coherent free-space optical communication system based on an RBMGC optimization algorithm. Background Art

[0002] In recent years, coherent free-space optical communication (CFSOC), owing to its spectrum-free nature, gigabit-class transmission rates, and strong anti-interference capabilities, has been widely used in scenarios such as wireless video surveillance, drone swarm networks, and low-orbit satellite communications. Researchers are exploring the wider application of CFSOC technology in practical engineering to promote the development of next-generation wireless communications. However, when laser signals are transmitted through atmospheric channels, they are affected by atmospheric turbulence, resulting in intensity flicker and wavefront aberrations in the beam. This ultimately reduces CFSOC's mixing efficiency (ME), increases the bit error rate (BER), and significantly degrades communication performance.

[0003] Adaptive optics (AO) systems used at the receiving end of CFSOC systems can correct for the effects of atmospheric turbulence in real time. The large size and complex structure of AO systems with wavefront sensors significantly limit their potential applications. Therefore, using a sensorless AO (Sensor-Less Adaptive Optics (SLAO) system to compensate for aberrations in communications is more beneficial for the application of CFSOC systems in various scenarios. The existing Stochastic Parallel Gradient Descent (SPGD) algorithm has been widely used in SLAO due to its simple model, small number of parameters, and easy implementation. The core idea of the SPGD algorithm is to make small random perturbations to the model parameters at each iteration. The algorithm then determines whether these perturbations improve the model performance based on CFSOC system performance metrics (such as mixing efficiency (ME) and bit error rate (BER). If performance improves, the changes are retained; otherwise, they are discarded. In this way, the algorithm gradually finds the model parameters that minimize the CFSOC system performance metrics. Another commonly used algorithm is the Optimized Equilibrium Optimizer algorithm using Linear Population Size Reduction (LOEO), which optimizes algorithm parameters through dynamic gradient descent and combines it with the Linear Population Size Reduction (LPSR) strategy to improve the correction speed of the algorithm. It also adjusts the algorithm's search framework to ensure algorithm convergence and its ability to withstand complex atmospheric turbulence.

[0004] However, the optimization algorithms in the above two existing SLAO systems have the disadvantage of insufficient ability to correct high-order phase aberrations under complex atmospheric turbulence conditions. They also have problems such as slow convergence speed, low accuracy and poor stability. Therefore, the communication performance of the CFSOC system is restricted and its application has certain limitations. Summary of the Invention

[0005] To address the problem that the optimization algorithm in the existing SLAO system has insufficient ability to correct high-order phase aberrations under complex atmospheric turbulence conditions, resulting in poor correction effect for high-order aberrations, as well as shortcomings such as slow convergence speed, low precision, and poor stability, which limits the communication performance of the CFSOC system, the present invention provides a coherent free-space optical communication system based on the RBMGC optimization algorithm. The system introduces a Red-billed Blue Magpie Optimizer based on a Gradient Correction mechanism (RBMGC) into the SLAO system to measure the wavefront aberrations generated by atmospheric turbulence interference in the CFSOC system. Because the RBMGC optimization algorithm has the advantages of fast convergence speed, high precision, and strong robustness, the SLAO system has better correction capabilities for high-order phase aberrations generated by complex atmospheric turbulence interference, thereby significantly reducing the bit error rate of the CFSOC system, improving mixing efficiency, and enhancing the communication performance of the CFSOC system.

[0006] In order to solve the above problems, the present invention adopts the following technical solutions:

[0007] A coherent free-space optical communication system based on an RBMGC optimization algorithm includes a wavefront sensorless adaptive optical system for correcting wavefront distortion, wherein the wavefront sensorless adaptive optical system includes:

[0008] a high-speed camera, configured to obtain wavefront distortion information of the transmission light beam and transmit the wavefront distortion information to a wavefront controller;

[0009] a wavefront controller, running an RBMGC optimization algorithm to generate an optimal voltage control signal for a wavefront corrector based on the wavefront distortion information, wherein the RBMGC optimization algorithm is an improvement on the RBMO algorithm framework, retaining the random perturbation strategy in the RBMO algorithm search framework and adopting an adaptive step size update method based on a gradient correction mechanism to update the position in the exploration and development phases to optimize the search process;

[0010] The wavefront corrector receives the optimal voltage control signal, performs wavefront distortion correction, and outputs a corrected optical signal.

[0011] Beneficial effects of the present invention:

[0012] This paper applies the RBMGC optimization algorithm to the SLAO system to correct for high-order wavefront aberrations under complex atmospheric turbulence, thereby further improving the mixing efficiency and reducing the bit error rate of the CFSOC system. The RBMGC optimization algorithm inherits the random perturbation strategy in the original search framework of the Red-billed Blue Magpie Optimizer (RBMO) algorithm to ensure diversity in the global search and prevent premature entrapment in local optima. Furthermore, a gradient correction mechanism is introduced during the exploration and development phases of the RBMO algorithm. Based on this gradient correction mechanism, a new adaptive step-size update method is established to update the position and optimize the search process. This improved RBMGC optimization algorithm achieves faster convergence, higher correction accuracy, and better robustness when correcting for high-order aberrations under complex turbulence conditions. This improves the SLAO system's correction of high-order aberrations and further enhances the communication performance of the CFSOC system. BRIEF DESCRIPTION OF THE DRAWINGS

[0013] Figure 1 It is a structural diagram of the CFSOC system with the SLAO system;

[0014] Figure 2 The flowchart of the RBMGC optimization algorithm in the wavefront controller;

[0015] Figure 3 This is the structural design diagram of the 32-unit adaptive DM;

[0016] Figure 4 Two sets of Zernike polynomials are created for strong turbulence and weak turbulence conditions;

[0017] Figure 5 The original wavefront plane and the wavefront plane after 35 and 70 iterations under strong turbulence and weak turbulence conditions;

[0018] Figure 6 The original point spread function and the point spread function after 35 and 70 iterations under strong and weak turbulence conditions are shown in Figure 2.

[0019] Figure 7 The curves of the RMS value changing with the number of iterations under strong turbulence and weak turbulence conditions;

[0020] Figure 8 The curves of mixing efficiency changing with the number of iterations under strong turbulence and weak turbulence conditions;

[0021] Figure 9 The curves of bit error rate changing with the number of iterations under strong turbulence and weak turbulence conditions;

[0022] Figure 10The curves showing the change of the normalized RMS value with the number of iterations during the correction process for the RBMGC optimization algorithm and the SPGD algorithm are shown;

[0023] Figure 11 The curves showing the change of the normalized mean mixing efficiency with the number of iterations during the correction process of the RBMGC optimization algorithm and the SPGD algorithm are shown;

[0024] Figure 12 The curves of the mean bit error rate changing with the number of iterations during the correction process of the RBMGC optimization algorithm and the SPGD algorithm are shown;

[0025] Figure 13 The curves showing the change of the mean RMS value with the number of iterations during the correction process of the RBMGC optimization algorithm, RBMO algorithm and LOEO algorithm under strong turbulence and weak turbulence conditions respectively;

[0026] Figure 14 The curves showing the variation of the mean mixing efficiency with the number of iterations during the correction process of the RBMGC optimization algorithm, RBMO algorithm and LOEO algorithm under strong turbulence and weak turbulence conditions respectively;

[0027] Figure 15 The curves showing the variation of the mean bit error rate with the number of iterations during the correction process of the RBMGC optimization algorithm, RBMO algorithm and LOEO algorithm under strong turbulence and weak turbulence conditions respectively;

[0028] Figure 16 This is a diagram showing the correction effect of the RBMGC optimization algorithm implemented on the experimental platform. DETAILED DESCRIPTION

[0029] The technical solution of the present invention will be described in detail below with reference to the accompanying drawings and preferred embodiments.

[0030] The principle of existing coherent detection technology is that the information waveform is modulated onto an optical carrier by amplitude, frequency, or phase. The optical signal is then transmitted through an atmospheric channel to the receiver. At the receiver, the optical signal is shaped and collected by an optical system. A coherent receiver then mixes the optical signal with the local oscillator (LO) light. The coherent receiver then detects the signal's amplitude and phase information to recover the original transmitted signal. Coherent detection can suppress background noise and intentional interference, improving the system's spectral frequency. Therefore, coherent detection technology is considered an effective means of improving receiver sensitivity in FSOC systems. However, during actual transmission, atmospheric turbulence can distort the coherence of the received signal, leading to wavefront mismatch between the input optical signal and the LO, thereby reducing received power. To compensate for this phase distortion, a SLAO system is used to correct for wavefront aberrations.

[0031] Figure 1A schematic diagram of a CFSOC system with a SLAO system is presented. In the CFSOC system, an optical signal emitted by a laser source at the transmitting end is amplified by a modulator and an optical amplifier before being transmitted through an atmospheric channel. During transmission, the optical signal is affected by atmospheric turbulence, which causes changes in its phase and amplitude, resulting in wavefront distortion. To compensate for the effects of atmospheric turbulence, a SLAO system is introduced at the receiving end to correct for this wavefront distortion. The SLAO system primarily consists of a high-speed camera, a wavefront controller, and a wavefront corrector (usually a deformable mirror (DM)). The SLAO system corrects the distorted laser signal using the principle of interferometry. The core function of the high-speed camera is to acquire wavefront distortion information of the transmitted beam and transmit this information to the wavefront controller. The wavefront controller then runs the RBMGC optimization algorithm to generate the optimal voltage control signal for the wavefront corrector based on the wavefront distortion information transmitted by the high-speed camera. This signal is then output to the wavefront corrector. The RBMGC optimization algorithm is an improvement on the RBMO algorithm framework. It retains the random perturbation strategy of the RBMO algorithm search framework and uses an adaptive step-size update method based on a gradient correction mechanism to update the position during the exploration and development phases to optimize the search process. The wavefront corrector receives the optimal voltage control signal and performs wavefront distortion correction based on the optimal voltage control signal to obtain a corrected optical signal. This corrected optical signal is combined with the local oscillator beam. The mixed laser beam is then transmitted through a reflector, lens, photodetector, and optical amplifier to a demodulator for demodulation. The optical signal is then converted to a digital signal in a digital signal processor, and finally converted into data output.

[0032] The effectiveness of the CFSOC system is evaluated using three metrics: mixing efficiency (ME), root mean square (RMS), and bit error rate (BER). These metrics are of great significance for the measurement analysis and performance fitness determination of the SLAO system.

[0033] 1) Mixing efficiency (ME).

[0034] Because the optical signal is affected by factors such as atmospheric turbulence before mixing with the LO light, ME becomes a key evaluation metric for CFSOC systems. It is numerically quantified as the Strehl ratio (SR) of the far-field focal plane image. The SR can be calculated to analyze the ME changes in a CFSOC system using homodyne detection before and after phase distortion compensation.

[0035] In a CFSOC system using homodyne detection, assuming that the LO light is a plane wave, the optical signal intensity is constant, and ME can be expressed as:

[0036] (1)

[0037] In formula (1), the variable and represent the amplitudes of the optical signal and LO light, respectively; , and represent the wavefront phases of the optical signal and LO light respectively; U represents the incident field of the photodetector.

[0038] 2) Root mean square value (RMS).

[0039] The RMS value is a mathematical measure that is the square root of the average value of the input wavefront phase aberrations and the average value of the square root of the deviations. The RMS value can be expressed as follows:

[0040] (2)

[0041] In formula (2), is the variance of the phase difference.

[0042] 3) Bit error rate (BER).

[0043] The bit error rate is an important indicator for measuring the communication performance of the CFSOC system. Under atmospheric turbulence interference conditions, the bit error rate of the binary phase shift keying (BPSK) receiving system is mathematically expressed as:

[0044] (3)

[0045] In formula (3), represents the quantum efficiency of the detector, represents the number of photons received by a single bit, represents the mixing efficiency of the system, represents the complementary error function.

[0046] The RBMGC optimization algorithm is an improvement of the RBMO algorithm. Here we first introduce the principle of the RBMO algorithm.

[0047] The RBMO algorithm operates in four phases: population initialization, exploration, exploitation, and storage of optimal solutions. Initially, the RBMO algorithm randomly generates candidate solutions and updates them after each iteration. Subsequently, red-billed blue magpies operate in small groups (2 to 5) or clusters (10 or more) to improve their search efficiency.

[0048] In the exploration phase, the RBMO algorithm initially searches for the optimal solution. When the red-billed blue magpie acts in a group search mode, the search strategy of formula (4) is adopted, and when the red-billed blue magpie acts in a cluster search mode, the search strategy of formula (5) is adopted.

[0049] (4)

[0050] (5)

[0051] In formula (4) and formula (5), Indicates the current iteration number; Indicates the New search agent locations; and represents the number of red-billed blue magpies randomly selected from all search individuals; Indicates the number of randomly selected Individuals, Indicates the number of randomly selected Individuals, Represents a randomly selected search individual in the current iteration. and Represents a randomly generated number between 0 and 1.

[0052] During the development phase, the RBMO algorithm searches for the optimal solution. When the red-billed blue magpie is searching in a small group, the search strategy of formula (6) is used to find the optimal solution. When the red-billed blue magpie is searching in a cluster, the search strategy of formula (7) is used to find the optimal solution.

[0053] (6)

[0054] (7)

[0055] In formula (6) and formula (7), Represents the location of the food at the current iteration; is the convergence factor, which is used to control the step size of the development phase, where Indicates the maximum number of iterations for the algorithm to run; and Represents random numbers used to generate a standard normal distribution.

[0056] After the RBMO algorithm finds the optimal solution at the current iteration, it compares and updates it with the optimal solution from the previous iteration, obtains a better solution in the next iteration, and stores this better solution. After reaching the target number of iterations, the algorithm obtains the optimal solution, as shown in Formula (8).

[0057] (8)

[0058] In formula (8), Indicates the optimal solution stored by the current algorithm, represents the new optimal solution.

[0059] In 1997, Wolpert DH et al. proposed the No Free Lunch Theorems for Optimization (NFL), an important theory in the field of machine learning. This theorem states that for all possible optimization problems, the average performance of any two optimization algorithms is equal. This means that no algorithm can comprehensively outperform other algorithms in all performance metrics (such as convergence speed, global search capability, and versatility). Therefore, any optimization algorithm has room for improvement. Although the exploration and development phases of the RBMO algorithm have given it powerful local search capabilities, when faced with more complex search spaces, especially when correcting high-order phase aberrations under complex atmospheric turbulence conditions, the RBMO algorithm is prone to premature convergence to a local optimum. To address this problem, the present invention proposes an RBMO algorithm based on a gradient correction mechanism, namely the RBMGC optimization algorithm. The RBMGC optimization algorithm is an improvement on the original RBMO algorithm framework. The RBMGC optimization algorithm incorporates gradient information and incorporates a gradient correction mechanism to design a new adaptive step-size update method. This method is applied to the exploration and development phases of the original RBMO algorithm. By changing the position update method of the original RBMO algorithm, the search process is optimized, thereby accelerating the algorithm's convergence. At the same time, the RBMGC optimization algorithm retains the random perturbation strategy of the original RBMO algorithm in the exploration and development phases to maintain global search diversity and prevent the algorithm from prematurely falling into local optimality, thereby improving the algorithm's overall optimization performance.

[0060] The gradient correction mechanism is as follows:

[0061] In the RBMGC optimization algorithm, the gradient and the square of the gradient are weighted averaged to obtain the first-order moment estimate (mean) and second-order moment estimate (variance) of the gradient, refer to formulas (9)-(10).

[0062] (9)

[0063] (10)

[0064] In formula (9) and formula (10), is the first-order moment estimate of the gradient at the current moment, is the first-order moment estimate of the gradient at the previous moment, is the second-order moment estimate of the gradient at the current moment, is the second-order moment estimate of the gradient at the previous moment. is the gradient value at the current moment. and are smoothing factors, used to update and The exponential moving average of controls the impact of historical gradients on the current estimate.

[0065] Since communication in a complex transmission environment such as the atmospheric channel will cause the algorithm to have deviations in the estimation of the gradient at the initial moment, in order to prevent over-adjustment caused by the initial deviation of the gradient, the correction terms of the gradient first-order moment estimation and second-order moment estimation formulas (11)-(12) are used to obtain a smooth and stable gradient update method, refer to formula (13).

[0066] (11)

[0067] (12)

[0068] (13)

[0069] In formula (11), formula (12) and formula (13), represents the corrected gradient, represents the first-order moment estimate of the corrected gradient, represents the corrected second moment estimate of the gradient. Represents the standard deviation of the corrected gradient, which is used to measure the magnitude of the gradient change. is the stability constant, which is a very small value (usually set to 10 -10 ) to prevent numerical problems caused by division by zero errors. and are smoothing factors, used to update and .

[0070] The step size update of the RBMGC optimization algorithm is as follows:

[0071] Based on the above-mentioned gradient correction mechanism, the present invention proposes a new adaptive step size update method, see formula (14).

[0072] (14)

[0073] in, is the step size update amount, is the learning rate. This new step-size update method can adaptively reduce the update step size in areas with drastic gradient changes and increase the step size in areas with gentle gradients. This prevents instability caused by excessively large step sizes when the gradient is large, while also maintaining sufficient update amplitude to accelerate convergence when the gradient is small. This new adaptive step-size update method is applied to the exploration and development phases of the original RBMO algorithm, resulting in a new search strategy for the exploration phase, see formulas (15)-(16), and a new search strategy for the development phase, see formulas (17)-(18).

[0074] (15)

[0075] (16)

[0076] In formula (15) and formula (16), and Represents a randomly generated number between 0 and 1.

[0077] (17)

[0078] (18)

[0079] In formula (17) and formula (18), and Represents random numbers used to generate a standard normal distribution.

[0080] Subtract the new update step size from the tail of the search strategy formula in the exploration and development phases of the RBMGC optimization algorithm This means that each step in the exploration and exploitation phases of the algorithm follows the direction of fastest descent of the objective function. This step-size update method provides a clearer descent direction for parameter updates, accelerating convergence. Furthermore, the RBMGC optimization algorithm retains the random perturbation strategy of the original RBMO algorithm in the exploration and exploitation phases to maintain global search diversity and prevent the algorithm from prematurely falling into local optima, thereby improving overall optimization performance.

[0081] Finally, the optimal solution is updated according to formula (8). If the RBMGC optimization algorithm generates an update to the optimal solution, the gradient parameters at this time are saved and used for the next algorithm execution. The cycle realizes the process of gradient storage and update.

[0082] As a swarm intelligence optimization algorithm, the RBMGC optimization algorithm boasts strong global optimization capabilities and algorithmic convergence. However, this type of algorithm requires several SLAO systems operating in parallel to achieve maximum effectiveness. To verify the algorithm's feasibility, this invention uses a single wavefront controller to serially traverse all individuals for the optimization process, thereby reducing equipment costs. When using the RBMGC optimization algorithm, to reduce computation time, the voltage vector matrix can be mapped to a Zernike coefficient matrix, thereby reducing the search dimension and ensuring algorithm performance.

[0083] In the RBMGC optimization algorithm, appropriate parameter design can, under certain circumstances, reduce hardware costs and improve algorithm performance. The parameters relevant to the performance of the RBMGC optimization algorithm include the initial search individual, learning rate, smoothing factor, stability constant, and decision probability threshold. The data values of the relevant parameters used in this embodiment are shown in Table 1.

[0084] Table 1 RBMGC optimization algorithm parameters

[0085]

[0086] Among the parameters shown in Table 1, increasing the initial search individuals is beneficial to improving the iterative convergence effect of the RBMGC optimization algorithm. Considering that the search individuals will also affect the timeliness of the algorithm, blindly increasing the population size will make the algorithm lose real-time performance. The setting of the learning rate enables the new adaptive step size update method to adaptively reduce the update step size in the area where the gradient changes drastically, and increase the step size in the area where the gradient is flat. This can prevent instability caused by excessive step size when the gradient is large, and can also maintain sufficient update amplitude to accelerate convergence when the gradient is small. A suitable learning rate is conducive to finding a more accurate solution. The smoothing factor is mainly used to update , and , The exponential moving average of controls the influence of historical gradients on the current estimate. A stability constant is used to prevent numerical issues caused by division by zero errors. The decision probability threshold, an idea proposed by the original RBMO algorithm authors, is set to keep the total number of groups and clusters similar, balancing the decision probabilities of group and cluster searches.

[0087] The operation flow chart of the RBMGC optimization algorithm in the wavefront controller is as follows: Figure 2 As shown, the specific process is as follows:

[0088] Step 1: After obtaining the relevant parameters of the RBMGC optimization algorithm, initialize the voltage vector matrix;

[0089] Step 2: Randomly generate N groups of voltage vector matrices within the set range as the solution space of the RBMGC optimization algorithm;

[0090] Step 3: Determine whether the current number of iterations is less than the maximum number of iterations. If so, proceed to step 4; if not, proceed to step 5;

[0091] Step 4: Perform a loop of the exploration phase and the development phase, and update the voltage control signal through iterations of the exploration phase and the development phase;

[0092] Step 5: If the number of iterations reaches the maximum number of iterations, the iteration is stopped, and the optimal solution of the voltage control signal, that is, the optimal voltage control signal, is output, and the algorithm is completed.

[0093] Furthermore, the cycle of exploration and development in step 4 includes the following processes:

[0094] Step 4.1: Enter the exploration phase;

[0095] Step 4.1.1: Calculate the gradient parameters , , , and the corrected gradient ;

[0096] Step 4.1.2: Randomly generate a number between 0 and 1 and compare the generated random number with the decision probability threshold. Based on the comparison result, determine whether the search strategy in the exploration phase is a group search strategy or a cluster search strategy:

[0097] If the generated random number is less than the decision probability threshold, the group search strategy shown in formula (15) is adopted;

[0098] If the generated random number is greater than or equal to the decision probability threshold, the cluster search strategy shown in formula (16) is adopted;

[0099] Step 4.2: Enter the development phase;

[0100] Step 4.2.1: Calculate the gradient parameters , , , and the corrected gradient ;

[0101] Step 4.2.2: Randomly generate a number between 0 and 1 and compare the generated random number with the decision probability threshold. Based on the comparison result, determine whether the search strategy in the development phase is a group search strategy or a cluster search strategy:

[0102] If the generated random number is less than the decision probability threshold, the group search strategy shown in formula (17) is adopted;

[0103] If the generated random number is greater than or equal to the decision probability threshold, the cluster search strategy shown in formula (18) is adopted;

[0104] Step 4.3: Update the stored optimal solution according to formula (8): After finding the optimal solution in the current iteration, compare it with the optimal solution generated in the previous iteration. If a better solution is obtained within the current iteration, store the better solution and use it to update the stored optimal solution.

[0105] Step 4.4: Determine whether the optimal solution has been updated. If so, proceed to step 4.5. If not, return to step 3.

[0106] Step 4.5: Store the gradient value at the current iteration and return to step 3.

[0107] The present invention will first combine the RBMO algorithm with the gradient correction mechanism to establish a new adaptive step-size update method, and apply it to the exploration stage and development stage of the RBMO algorithm. At the same time, the RBMGC optimization algorithm retains the random perturbation strategy in the search framework of the original RBMO algorithm to ensure the diversity of the global search and prevent the algorithm from falling into the local optimum too early. This improved method greatly improves the convergence speed and convergence accuracy of the algorithm. The present invention applies the RBMGC optimization algorithm to the SLAO system, and verifies through simulation experiments that the RBMGC optimization algorithm has excellent correction capabilities when facing high-order aberrations under complex atmospheric turbulence conditions. The results show that the SLAO system based on the RBMGC optimization algorithm can effectively improve the mixing efficiency of the CFSOC system and reduce the bit error rate.

[0108] In order to verify the application effect of the RBMGC optimization algorithm in the SLAO system, the present invention uses the MATLAB software platform for simulation analysis. During the simulation analysis, the continuous surface DM is used as the wavefront corrector, and the shape of the DM is changed by controlling the voltage to achieve the purpose of wavefront correction. The RBMGC optimization algorithm is used as the control algorithm to change the voltage of each actuator in the DM. Assume that the initial wavefront aberration of the laser after transmitting through the atmospheric channel is , the solution vector is obtained through the RBMGC optimization algorithm , this solution is the control voltage of each DM mirror actuator. The algorithm continuously updates the solution and generates the compensation phase The residual phase aberration can be obtained by the difference between the initial phase and the compensation phase. In the simulation process, it is assumed that the laser wavelength is , the ratio of the diameter of the optical lens to the focal length is 1, the number of photons in a single bit is 10, and the radius of the Airy mode is , the quantum efficiency of the detector is 1, and a 32-unit adaptive DM is used as the wavefront corrector. Its structural design is shown in the figure below. Figure 3 In this 32-unit adaptive DM, the cross-link value of the actuator is 0.2, the normalized distance coefficient between actuators is 0.392, and the Gaussian function is 2, where the initial voltage of each driver is set to 0.

[0109] Usually the parameters to quantify the intensity of atmospheric turbulence, where represents the aperture size of the receiving system, is the Fried parameter that characterizes the atmospheric coherence characteristics. In order to further explore the influence of atmospheric turbulence on wavefront aberration, we adjust The values of are used to simulate Zernike polynomial aberrations of different orders. Zernike polynomials decompose the phase of the distorted wavefront into the sum of a series of weighted orthogonal polynomials, each of which represents a specific aberration. Normalized atmospheric turbulence intensity is usually divided into three main levels: under weak turbulence conditions, is about 2; under moderate turbulence conditions, it is about 10; and under strong turbulence conditions, Greater than 15. In order to evaluate the correction performance of the RBMGC optimization algorithm under different turbulence conditions, Set to 5 and 20 respectively to simulate the performance under weak turbulence and strong turbulence conditions. It can be expressed as:

[0110] (19)

[0111] in, is the piston term coefficient, which corresponds to the constant term of the Zernike polynomial and represents the overall axial translation of the wavefront. It does not change the relative shape of the wavefront, but only shifts the overall wavefront phase by a constant value. For the

[0112] The coefficient of a Zernike polynomial mode reflects the weight of the corresponding mode in the wavefront phase distribution. The larger the coefficient, the more significant the contribution of the wavefront distortion corresponding to the mode. For the Zernike polynomials are a set of orthogonal polynomials defined on the unit circle (normalized), with different Corresponding to different wavefront distortion modes, by combining different and coefficients Can fit complex wavefront phase distribution.

[0113] The Zernike coefficient represents the size of the wavefront aberration. The larger the coefficient, the larger the aberration. In the Zernike polynomial, the first three terms represent the piston aberration, the tilt aberration along the X direction, and the tilt aberration along the Y direction, respectively. These aberrations can be directly corrected by the beam steering unit (BSU). In the actual communication process, the atmospheric transmission environment is very complex. The use of Zernike polynomials of order 4-36 can simulate the wavefront aberration more realistically. Therefore, in the simulation analysis, according to Roddier's method (see "RODDIER N. Atmospheric wavefront simulation usingZernike polynomials [J]. Optical Engineering, 1990, 29(10):1174-1180."), the Zernike coefficient and the aberration are mapped to a mathematical relationship, from Initial Zernike coefficients are randomly generated, and the 4th to 36th Zernike polynomials are used to construct higher-order aberrations. Figure 4 The first and second columns of give the Zernike polynomials created under strong turbulence and weak turbulence conditions, respectively.

[0114] Next, we will verify in detail the ability of the RBMGC optimization algorithm to correct wavefront aberrations. Figure 4 The 4th to 36th order modes of the Zernike polynomials in the figure plot the original wavefront plane and original point spread function (PSF) under strong turbulence and weak turbulence respectively, as shown in Figure 5 and Figure 6 The RBMGC optimization algorithm was performed for 35 and 70 iterations under two turbulence conditions (strong and weak turbulence), respectively. The residual wavefront aberration and PSF generated after the iteration are shown in the first column of Figure 5 and Figure 6 The initial ME under strong and weak turbulence conditions are 0.0004 and 0.5055, respectively.

[0115] Figure 5 and Figure 6 The first row shows that under strong turbulence conditions, the ME value of the RBMGC optimization algorithm increases from 0.0004 to 0.8930 after 35 iterations, and from 0.0003 to 0.9998 after 70 iterations. Figure 5 and Figure 6The second row depicts the wavefront aberration phase plane and corresponding PSF plots after 35 and 70 iterations of the RBMGC optimization algorithm under weak turbulence conditions. Under these conditions, the ME value increases from 0.5055 to 0.9567 after 35 iterations, and to 0.9999 after 70 iterations. As can be seen from the figure, most of the wavefront distortion is substantially compensated after 35 iterations, and the RBMGC optimization algorithm continues to compensate for aberrations in subsequent iterations, achieving even higher accuracy.

[0116] In order to further verify the generalization ability of the RBMGC optimization algorithm, 100 independent repeated simulations were performed under strong and weak turbulence conditions respectively. Figures 7 to 9 The RMS, ME, and BER curves for 100 simulations under strong and weak turbulence conditions are shown. The black curve represents the variation in a single experiment, and the red curve represents the average curve corresponding to the 100 simulations.

[0117] like Figure 7 As shown in the figure, under both turbulence conditions, the RBMGC optimization algorithm can effectively reduce aberrations, with a trend of continuous convergence in each iteration. Under strong turbulence conditions, the RBMGC optimization algorithm requires at least 37 iterations and a maximum of 45 iterations to reduce the RMS value to below 0.1. After 70 iterations, the average RMS value is reduced to 0.0108. Under weak turbulence conditions, the RBMGC optimization algorithm requires at least 23 iterations and a maximum of 31 iterations to reduce the RMS value to below 0.1. After 70 iterations, the average RMS value is reduced to 0.0009.

[0118] like Figure 8 As shown in the figure, under both turbulence conditions, the ME value can be improved to 0.8 or above in each experiment. When the ME is greater than 0.8, a minimum of 22 iterations and a maximum of 47 iterations are required under strong turbulence conditions. A minimum of 6 iterations and a maximum of 15 iterations are required under weak turbulence conditions. After 70 iterations of RBMGC correction, the final ME is approximately equal to 1.

[0119] like Figure 9 As shown in the figure, it can be seen from the mean curve under strong turbulence conditions that the BER drops from 0.4938 to From the mean curve under weak turbulence conditions, it can be seen that after 19 iterations, the BER decreases from Down to The above data demonstrates that applying the RBMGC optimization algorithm to the SLAO system can effectively correct the wavefront distortion of optical signals, significantly reducing the bit error rate of the CFSOC communication system and improving the system's communication performance. Overall, 100 repeated experiments have verified that the performance of the RBMGC optimization algorithm is unaffected by random factors, producing stable and statistically significant results across multiple experiments, demonstrating high stability, robustness, and reliability.

[0120] In order to evaluate the improvement effect and performance of the RBMGC optimization algorithm, the present invention also uses the RBMGC optimization algorithm, SPGD algorithm, RBMO algorithm and LOEO algorithm to correct the aberrations generated under two turbulent conditions to compare their correction effects. Taking into account that the SPGD algorithm performs poorly when dealing with strong atmospheric turbulence, the RBMGC optimization algorithm is only compared with the SPGD algorithm under weak turbulence conditions. In the comparison process, a normalized comparison method was adopted for ME and RMS. The RMS value is optimized to 0.5 and the ME value is optimized to 0.8 as the scale for normalized comparison, so that the properties of the algorithm can be observed more intuitively. The two algorithms were repeated 100 times, and the normalized root mean square value and the mean curve of ME are shown as follows. Figure 10 and Figure 11 As shown in the figure, the mean curve of the bit error rate is as follows Figure 12 As shown. The positive gain coefficient of the SPGD algorithm , random disturbance voltage amplitude .

[0121] exist Figure 10 In the processing, the starting RMS value of 0.8254 under weak turbulence conditions is normalized to the starting point 1, and the optimized target RMS value of 0.5 is proportionally scaled to 0.01 to observe the optimization effect of the algorithm. As can be seen from the figure, the RBMGC optimization algorithm only needs 9 iterations to reach the target, while the SPGD algorithm needs 125 iterations to reach the target. Figure 11 As shown in the figure, in the comparison of normalized ME, the RBMGC optimization algorithm reaches the target after 10 iterations, and the SPGD algorithm reaches the target after 247 iterations. Figure 12 This means that after 30 iterations, the RBMGC optimization algorithm reduces the bit error rate of the CFSOC system from Reduce to , and after 250 iterations, the system’s bit error rate was reduced to These experimental data show that, compared with the SPGD algorithm, the RBMGC optimization algorithm uses fewer iterations to achieve the same goal. This shows that using the RBMGC optimization algorithm to correct high-order aberrations in the SLAO system is more effective.

[0122] Next, the RBMGC optimization algorithm, RBMO algorithm, and LOEO algorithm were used to correct high-order aberrations under strong turbulence conditions and weak turbulence conditions respectively. The experiment was repeated 100 times for each algorithm. The changes in the RMS, ME, and BER mean curves of the three algorithms after completing the iteration are shown in the figure below. Figure 13-15 shown.

[0123] from Figure 13 As can be seen in the figure, under strong turbulence conditions, the LOEO algorithm requires 50 iterations to reduce the RMS value to below 1.06, after which the algorithm becomes stuck in a local optimum and is unable to further correct the aberrations. The RBMO and RBMGC optimization algorithms require only 20 iterations to reduce the RMS value to below 1.06, a 60% reduction in iterations compared to the LOEO algorithm. The RBMO algorithm reduces the RMS value to 0.54 by the 40th iteration before becoming stuck in a local optimum. The RBMGC optimization algorithm, on the other hand, requires only 29 iterations to achieve this goal, and the algorithm shows a trend of continuous convergence. By the 59th iteration, the RBMGC optimization algorithm reduces the RMS value to below 0.01. Under weak turbulence conditions, the LOEO algorithm requires 40 iterations to reduce the RMS value to below 0.2, which has some effect on correcting the aberrations, but then becomes stuck in a local optimum. The RBMO algorithm requires 27 iterations to reach this goal, while the RBMGC optimization algorithm requires 20 iterations to converge the RMS value to less than 0.2, which is 50% fewer iterations than the LOEO algorithm and 35% fewer iterations than the RBMO algorithm. It continues to converge in subsequent iterations, reducing the RMS value to below 0.01 at the 34th iteration.

[0124] It can be seen that under strong turbulence conditions, the LOEO algorithm converges faster than the RBMO and RBMGC algorithms in the early stages. After the sixth iteration, the RBMO algorithm converges faster than the LOEO and RBMGC algorithms, and after the 20th iteration, the RBMGC algorithm's overall convergence speed is better than that of the RBMO and LOEO algorithms. Under weak turbulence conditions, the LOEO algorithm converges faster than the RBMGC and RBMO algorithms before the 10th iteration, after which the RBMGC algorithm exhibits even better convergence speed. Overall, the RBMGC algorithm performs best, and the RBMO algorithm outperforms the LOEO algorithm.

[0125] like Figure 14As shown in the figure, with an ME of 0.9 as the target, the RBMGC optimization algorithm requires 31 iterations to reach the target under strong turbulence conditions, and the ME shows a continuous upward trend. After 50 iterations, the RBMGC optimization algorithm has approximately improved the ME to 1. However, the RBMO and LOEO algorithms cannot reach the target within 70 iterations. After 70 iterations, the RBMO algorithm has achieved a maximum ME of 0.74, while the LOEO algorithm has only improved its ME to 0.32. Both algorithms subsequently fall into local optima. Under weak turbulence conditions, the RBMGC optimization algorithm requires 15 iterations to reach the target. After 28 iterations, the RBMGC optimization algorithm has achieved an ME of approximately 1. However, the RBMO and LOEO algorithms require 18 iterations to reach the target. After 70 iterations, the MEs of the two algorithms have increased to 0.97 and 0.96, respectively. It is clear that the RBMGC optimization algorithm has higher mixing efficiency under both turbulence conditions.

[0126] like Figure 15 As shown, in some basic communication scenarios, the bit error rate is usually required to be lower than Under strong turbulence conditions, the RBMGC optimization algorithm is used as the control algorithm in the SLAO system, which reduces the bit error rate of the CFSOC system from 0.49 to The use of LOEO algorithm can reduce the bit error rate of CFSOC system to , both algorithms have effectively reduced the bit error rate of the CFSOC system; the RBMO algorithm cannot reduce the bit error rate to The initial bit error rate of the CFSOC system under weak turbulence conditions is However, in special communication scenarios such as low-orbit satellite intersatellite links, the bit error rate is usually required to be lower than It can be seen that the three algorithms can effectively reduce the bit error rate of the CFSOC system. The RBMGC optimization algorithm needs 17 iterations to reduce the BER to , the RBMO algorithm requires 22 times, while the LOEO algorithm requires 27 times. The RBMGC optimization algorithm reduces the number of iterations by 22.7% and 37% compared with the RBMO algorithm and LOEO algorithm, respectively.

[0127] The above experiments consistently demonstrate that the RBMGC algorithm significantly outperforms the RBMO, LOEO, and SPGD algorithms in correcting higher-order aberrations under complex turbulence, both under strong and weak turbulence conditions. It converges faster and achieves better correction results. Specifically, the SPGD algorithm is unable to effectively correct aberrations under strong turbulence, and under weak turbulence, requires a significant number of iterations to achieve the same performance as the RBMGC algorithm. The RBMO algorithm is slightly better than the LOEO algorithm in correcting higher-order aberrations under both turbulence conditions, but the final correction effect is inferior to that of the RBMGC algorithm.

[0128] To verify the ability of the SLAO system, based on the RBMGC optimization algorithm, to correct actual aberrations, the present invention also collected wavefront aberration data on the original experimental platform for subsequent testing experiments. After constructing the experimental platform, the Greenwood frequency was varied by adjusting the rotation speed of the phase screen during the experiment. The laser was collimated by the phase screen and lens, then corrected by the SLAO system. A wave splitting receiver split the beam into two parts: one for imaging and the other for measuring wavefront aberration data.

[0129] like Figure 16 As shown, the system's initial ME value was 0.0311. After iterative correction using the RBMGC optimization algorithm, the ME value increased to 0.2489 at the 10th iteration. At the 20th iteration, the ME value increased to 0.5928. At the 30th iteration, the ME value increased to 0.8020. In computationally resource-constrained scenarios like experimental platforms, the gradient correction mechanism provides optimization direction, reduces blind searches, and improves convergence efficiency. Experimental data demonstrates that using RBMGC as a control algorithm can improve the communication performance of the experimental system under limited computing resources, which has profound implications for the application of the RBMGC optimization algorithm.

[0130] The above simulation results show that the RBMGC optimization algorithm has a stronger ability to process high-order phase aberrations under complex turbulence conditions than the SPGD algorithm and LOEO algorithm. Applying the RBMGC optimization algorithm to the SLAO system can effectively improve the performance of the coherent free-space optical communication system.

[0131] The present invention first proposes a red-billed blue magpie optimization algorithm (RBMGC) based on a gradient correction mechanism, connects the RBMGC algorithm to the SLAO system, and analyzes the feasibility of applying the RBMGC algorithm to the CFSOC system. Then, based on relevant principles, high-order phase aberrations are generated under complex atmospheric turbulence conditions. Numerical simulations verify the RBMGC algorithm's excellent correction capability for high-order wavefront aberrations under strong and weak turbulence conditions, as well as its effect on improving communication system performance during the aberration correction process. Finally, using an experimental platform equipped with the SLAO system, the collected actual aberration data is corrected using the RBMGC algorithm, and the optimization of the mixing efficiency is analyzed. The results show that the SLAO system based on the RBMGC optimization algorithm can effectively improve the mean error (ME) and reduce the bit error (BER). The present invention can provide a new high-order wavefront aberration correction method for the SLAO system in the design of the CFSOC system.

[0132] The technical features of the above-mentioned embodiments can be combined arbitrarily. In order to make the description concise, not all possible combinations of the technical features in the above-mentioned embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0133] The above-described embodiments merely illustrate several implementations of the present invention, and while their descriptions are relatively specific and detailed, they should not be construed as limiting the scope of the patent. It should be noted that a person skilled in the art would be able to make numerous variations and improvements without departing from the spirit of the present invention, all of which fall within the scope of protection of the present invention. Therefore, the scope of protection of the patent for this invention shall be determined by the appended claims.

Claims

1. A coherent free-space optical communication system based on the RBMGC optimization algorithm, characterized in that: A wavefront sensorless adaptive optical system for correcting wavefront distortion is provided, the wavefront sensorless adaptive optical system comprising: a high-speed camera, configured to obtain wavefront distortion information of the transmission light beam and transmit the wavefront distortion information to a wavefront controller; a wavefront controller, running an RBMGC optimization algorithm to generate an optimal voltage control signal for a wavefront corrector based on the wavefront distortion information, wherein the RBMGC optimization algorithm is an improvement on the RBMO algorithm framework, retaining the random perturbation strategy in the RBMO algorithm search framework and adopting an adaptive step size update method based on a gradient correction mechanism to update the position in the exploration and development phases to optimize the search process; The wavefront corrector receives the optimal voltage control signal, performs wavefront distortion correction, and outputs a corrected optical signal.

2. The coherent free-space optical communication system based on the RBMGC optimization algorithm according to claim 1, characterized in that: The operation process of the RBMGC optimization algorithm in the wavefront controller includes: Step 1: After obtaining the relevant parameters of the RBMGC optimization algorithm, initialize the voltage vector matrix; Step 2: randomly generate N groups of voltage vector matrices as the solution space of the RBMGC optimization algorithm; Step 3: Determine whether the current number of iterations is less than the maximum number of iterations. If so, proceed to step 4; if not, proceed to step 5; Step 4: Perform a loop of the exploration phase and the development phase, and update the voltage control signal through iterations of the exploration phase and the development phase; Step 5: Output the optimal solution of the voltage control signal, that is, the optimal voltage control signal.

3. The coherent free-space optical communication system based on the RBMGC optimization algorithm according to claim 2, characterized in that: The exploration and development cycle includes the following processes: Step 4.1: Enter the exploration phase; Step 4.1.1: Calculate the gradient parameters and the corrected gradient; Step 4.1.2: Randomly generate a number between 0 and 1 and compare it with the decision probability threshold. Determine the search strategy for the exploration phase based on the comparison result. Step 4.2: Enter the development phase; Step 4.2.1: Calculate the gradient parameters and the corrected gradient; Step 4.2.2: Randomly generate a number between 0 and 1 and compare it with the decision probability threshold. Determine the search strategy for the development phase based on the comparison result. Step 4.3: After finding the optimal solution in the current iteration, compare it with the optimal solution produced by the previous iteration. If a better solution is obtained within the current iteration, store the better solution and update the stored optimal solution with the better solution. Step 4.4: Determine whether the optimal solution has been updated. If so, proceed to step 4.5; if not, return to step 3; Step 4.5: Store the gradient value at the current iteration and return to step 3.

4. The coherent free-space optical communication system based on the RBMGC optimization algorithm according to claim 3, characterized in that: In the exploration phase, when the randomly generated number is less than the decision probability threshold, the group search strategy shown in formula (15) is adopted, otherwise the cluster search strategy shown in formula (16) is adopted; （15） （16） in, For the New search agent locations; The first randomly selected individual; The first randomly selected individual; is the search individual randomly selected in the current iteration; and is the number of red-billed blue magpies randomly selected from all search individuals; and A randomly generated number between 0 and 1; is the learning rate; is the corrected gradient.

5. The coherent free-space optical communication system based on the RBMGC optimization algorithm according to claim 3, characterized in that: In the development phase, when the randomly generated number is less than the decision probability threshold, the group search strategy shown in formula (17) is adopted, otherwise the cluster search strategy shown in formula (18) is adopted; （17） （18） in, For the New search agent locations; is the location of the food at the current iteration; is the convergence factor, is the maximum number of iterations of the algorithm under the current experiment; The first randomly selected individual; is the search individual randomly selected in the current iteration; and is the number of red-billed blue magpies randomly selected from all search individuals; and is a random number used to generate a standard normal distribution; is the learning rate; is the corrected gradient.

6. The coherent free-space optical communication system based on the RBMGC optimization algorithm according to claim 4 or 5, characterized in that: Corrected gradient The calculation formula is as follows: （13） in, is the first-order moment estimate of the corrected gradient; is the second-order moment estimate of the corrected gradient; is the stability constant.

7. The coherent free-space optical communication system based on the RBMGC optimization algorithm according to any one of claims 3 to 5, characterized in that: The gradient parameters include the first-order moment estimate of the gradient at the current moment, the second-order moment estimate of the gradient at the current moment, the first-order moment estimate of the gradient after correction, and the second-order moment estimate of the gradient after correction.

8. The coherent free-space optical communication system based on the RBMGC optimization algorithm according to any one of claims 2 to 5, characterized in that: The RBMGC optimization algorithm maps the voltage vector matrix to a Zernike coefficient matrix.

9. The coherent free-space optical communication system based on the RBMGC optimization algorithm according to any one of claims 2 to 5, characterized in that: The relevant parameters include: the initial search individuals are 30, the learning rate is 0.01, the smoothing factor for updating the first-order moment estimate and the second-order moment estimate of the current gradient is 0.9, the smoothing factor for updating the first-order moment estimate and the second-order moment estimate of the corrected gradient is 0.999, and the stability constant is 10 -10 , the decision probability threshold is 0.

5.

10. The coherent free-space optical communication system based on the RBMGC optimization algorithm according to any one of claims 1 to 5, characterized in that: The performance indicators include mixing efficiency, root mean square value and bit error rate.

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