Method for expanding a coherent free-space optical communication system

Abstract

The present application relates to a coherent free space optical communication system expansion method, and belongs to the field of optical communication, which solves the problem of poor correction effect of existing systems under strong turbulence and mobile platform adaptability. The transmitting end adopts circular polarization SPPSK modulation, divides the static wavefront into N independent regions, each region maps bit information with orthogonal circular polarization state, generates a spatial polarization beam and sends it to the receiving end; the V-AO system of the receiving end adopts the EPSA-DE algorithm, generates control voltage through iterative optimization, and drives the correction element to jointly correct the phase and polarization aberrations caused by atmospheric turbulence; the corrected beam is mixed and demodulated to recover the original data. The present application does not need strict alignment between the transmitting end and the receiving end through circular polarization SPPSK modulation, is suitable for mobile platforms, and improves the correction effect and stability under strong turbulence through the EPSA-DE algorithm, significantly expanding the communication capacity of the system.

Description

Technical Field

[0001] This invention relates to the field of optical communication technology, and in particular to a method for expanding the capacity of a coherent free-space optical communication system. Background Technology

[0002] Free-space optical communication, with its strong anti-interference capability, high transmission rate, and large signal bandwidth, is widely used in the field of communication. In recent years, the study of the spatial structure characteristics of light has become a hot topic in the field of optical communication research. Thanks to this characteristic, researchers can use coding methods in the spatial dimension, opening up a new dimension for information transmission. This makes it possible to establish high-capacity, long-distance free-space optical communication systems. Without increasing the physical bandwidth of the optical channel, it significantly enhances the system's data carrying capacity and spectral efficiency. Multiplexing technology is a common means of increasing the capacity of communication systems. Multiple independent data channels are multiplexed in the communication system, and parallel transmission is achieved, thereby significantly improving the capacity. Key examples include frequency, polarization and wavelength division multiplexing in radio frequency and optical systems, and orbital angular momentum modes. However, in free-space optical communication links, atmospheric turbulence can cause serious interference to the light beam because fluctuations in the spatial refractive index can change the phase distribution and intensity distribution of the light beam. This, in turn, reduces the signal-to-noise ratio of the system, increases the bit error rate, and thus reduces the system's communication capacity. Adaptive optics has been used as an effective means to correct real-time wavefront distortion of the light beam. However, compensating for wavefront distortion caused by strong and higher-order turbulence or beam distortion with polarization state fluctuations remains a challenge.

[0003] Polarization, as a degree of freedom in beam information transmission, has found extensive practical applications in optics. At the forefront of communication science, Polarization Shift Keying (PolSK) technology, with its superior polarization modulation capabilities, has become a key application in fiber optic and free-space optical communication systems. This technology achieves efficient signal encoding and transmission by precisely manipulating the polarization state of light waves. Its verification and deployment in practical applications not only confirm its theoretical feasibility but also highlight its practical utility and value in modern communication technology. With its high stability and anti-interference capabilities during signal transmission, PolSK technology provides solid technical support for high-speed data transmission and has become a vital force driving progress in the field of communication.

[0004] However, current spatial polarization phase shift keying (SPPSK) systems based on linear polarization have an inherent limitation: the transmitter and receiver require strict coordinate axis alignment. When the system is mounted on a mobile platform (such as a drone or satellite), the transmitter and receiver are prone to relative rotation, causing polarization axis angular shifts and placing them outside the same coordinate system, severely impacting communication quality. Furthermore, current optimization algorithms for wavefront correction, such as stochastic parallel gradient descent (SPGD), are prone to getting trapped in local optima and exhibit poor correction performance under strong turbulence conditions.

[0005] Therefore, there is an urgent need for a coherent free-space optical communication capacity expansion method that can adapt to mobile platforms, has stronger anti-interference capabilities, and can more effectively correct the effects of atmospheric turbulence. Summary of the Invention

[0006] To address the issues of poor adaptability to mobile platforms and inadequate correction performance under strong turbulence in existing coherent free-space optical communication systems, this invention provides a method for expanding the capacity of a coherent free-space optical communication system.

[0007] The technical solution adopted in this invention is as follows:

[0008] A method for expanding the capacity of a coherent free-space optical communication system, applied to a coherent free-space optical communication system, the system including a transmitter and a receiver, the receiver being equipped with a vector adaptive optics system, the method comprising the following steps:

[0009] Step 1: At the transmitting end, the data is encoded and modulated using circular polarization SPPSK modulation to generate a spatially polarized beam, and the spatially polarized beam is transmitted to the receiving end via an atmospheric channel;

[0010] The encoding and modulation process includes: dividing a single static wavefront of the light beam into N independent regions, each region corresponding to a data transmission channel; mapping the N bits of data to be transmitted to the N regions, each bit corresponding to one region; and characterizing the information of the bit by loading a specific circular polarization state on each region, wherein two orthogonal circular polarization states are used to map binary values ​​"0" and "1" respectively.

[0011] Step 2: At the receiving end, the vector adaptive optics system uses the EPSA-DE algorithm as the control algorithm. Through iterative optimization, a control voltage is generated, and the correction element in the vector adaptive optics system is driven according to the control voltage to maximize the system's performance evaluation index and realize the joint correction of the beam affected by atmospheric turbulence. The joint correction includes compensating for the phase aberration and polarization aberration of the beam simultaneously.

[0012] Step 3: Mix the corrected beam with the local oscillator beam, and after demodulation and digital signal processing, recover the original data.

[0013] This invention proposes a modulation scheme based on circularly polarized SPPSK and uses it as the system's communication protocol. Simultaneously, a differential evolution enhanced PID search optimization algorithm (hereinafter referred to as EPSA-DE algorithm) is introduced as the control algorithm for the vector adaptive optics system to correct beam polarization fluctuations and phase distortions caused by atmospheric turbulence interference. Compared with existing technologies, this invention has the following advantages:

[0014] (1) Capacity enhancement: Spatial multiplexing based on wavefront polarization state is achieved by circularly polarized SPPSK modulation, which enhances the information carrying capacity of the beam, increases the number of bits per unit bandwidth, and significantly expands the capacity of coherent free space optical communication system.

[0015] (2) Adaptability to mobile platforms: The use of circular polarization state for information representation fundamentally solves the problem that the transmitter and receiver need to be strictly aligned in the linear polarization system. Since the present invention does not require strict coordinate axis alignment between the transmitter and receiver, the coherent free space optical communication system can work stably on a mobile platform where the transmitter and receiver are relatively rotated. While having low bit error rate characteristics, it has stronger anti-interference ability and stronger adaptability to mobile platforms.

[0016] (3) Excellent correction effect: The EPSA-DE algorithm is used as the control algorithm for the vector adaptive optics system. It not only has a better correction effect than the traditional SPGD algorithm under weak turbulence, but also has excellent correction performance under strong turbulence and shows stronger stability. Simulation results show that the algorithm can effectively suppress atmospheric turbulence, improve the mixing efficiency of the system, and reduce the bit error rate. Attached Figure Description

[0017] Figure 1 This is a flowchart of the coherent free-space optical communication system expansion method according to an embodiment of the present invention;

[0018] Figure 2 This is a block diagram illustrating the principle of circularly polarized SPPSK modulation.

[0019] Figure 3This is a block diagram of a V-AO-based CFSOC system.

[0020] Figure 4 A simplified structural diagram of a V-AO-based CFSOC system;

[0021] Figure 5 This is a schematic diagram of the polarization correction principle of the V-AO system on the Poincaré sphere.

[0022] Figure 6 This is the initial Zernike coefficient diagram used in the simulation of this invention;

[0023] Figure 7 This is the initial wavefront aberration diagram used in the simulation of this invention;

[0024] Figure 8 This is a comparison of polarization aberrations in 19 channel regions before and after correction in the simulation of the V-AO system of this invention;

[0025] Figure 9 This is a comparison of polarization aberrations before and after channel 3 correction in the simulation of this invention;

[0026] Figure 10 This is a comparison of polarization aberrations before and after channel 9 correction in the simulation of this invention;

[0027] Figure 11 This refers to the phase aberration of the V-AO system after correction in the simulation of this invention;

[0028] Figure 12 This is a graph showing the variation of the mixing efficiency of the EPSA-DE algorithm under different turbulence conditions with the number of iterations in the simulation of this invention.

[0029] Figure 13 This is a graph showing the change in bit error rate of the EPSA-DE algorithm under different turbulent conditions with the number of iterations in the simulation of this invention;

[0030] Figure 14 This is a performance comparison chart of the EPSA-DE algorithm and the PSA algorithm under strong turbulence in the simulation of this invention. Detailed Implementation

[0031] The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments. This embodiment is implemented based on the technical solution of the present invention, and provides detailed implementation methods and specific operating procedures; however, the scope of protection of the present invention is not limited to the following embodiments.

[0032] like Figure 1As shown, this embodiment provides a method for expanding the capacity of a coherent free space optical communication system based on circularly polarized SPPSK modulation and EPSA-DE algorithm. This method is applied to a coherent free space optical communication (CFSOC) system, which mainly includes a transmitter and a receiver, and the receiver is equipped with a vectorial adaptive optics (V-AO) system.

[0033] The specific implementation steps of the coherent free-space optical communication system expansion method based on circularly polarized SPPSK modulation and EPSA-DE algorithm proposed in this embodiment are as follows:

[0034] Step 1: At the transmitting end, the data is encoded and modulated using circular polarization SPPSK modulation to generate a spatially polarized beam, which is then transmitted to the receiving end via an atmospheric channel.

[0035] The process of encoding and modulating the data includes: dividing a single static wavefront of the beam into N independent regions, each region corresponding to a data transmission channel; mapping the N bits of data to be transmitted to the N regions, each bit corresponding to one region; and characterizing the information of the bit by loading a specific circular polarization state on each region, wherein two orthogonal circular polarization states are used to map the binary values ​​"0" and "1" respectively.

[0036] Step 2: At the receiving end, the vector adaptive optics system uses the EPSA-DE algorithm as the control algorithm. Through iterative optimization, a control voltage is generated, and the correction element in the vector adaptive optics system is driven according to the control voltage to maximize the system's performance evaluation index and realize the joint correction of the beam affected by atmospheric turbulence. The joint correction includes compensating for the phase aberration and polarization aberration of the beam at the same time.

[0037] Step 3: Mix the corrected beam with the local oscillator beam, and after demodulation and digital signal processing, recover the original data.

[0038] Specifically, Figure 2This diagram illustrates the SPPSK transmission principle employing circular polarization modulation and a V-AO system. The circular polarization state of the beam is used as a means of information transmission. During SPPSK data transmission, a single static wavefront region of the beam is divided into N regions. Two polarization states with orthogonal characteristics are mapped to binary values ​​"0" and "1," respectively. In the transmitted data, N bits of data are encoded into spatially distributed polarization states. Based on the transmitted bitstream, a large number of polarization states mapping to that bit data are distributed in the corresponding regions. After encoding and modulation, the beam enters the atmospheric channel from the transmitter. After traveling a certain distance, the polarization state distribution within these independent channels is scrambled. When the beam reaches the receiver, it preferentially passes through the V-AO system. The beam is corrected or compensated within the V-AO system. Finally, at the receiver, the beam's polarization channel is accurately identified, and data is extracted through demultiplexing.

[0039] However, due to the influence of atmospheric turbulence, these independent states of polarization (SOPs) and phase channels are significantly disturbed, leading to polarization fluctuations and phase distortion. To extract data from the beam, all SOPs and phase channels must be accurately identified. To achieve this, polarization and phase interference caused by turbulence must be compensated for. For this purpose, the V-AO system in this invention can simultaneously correct polarization and phase aberrations, effectively compensating for polarization fluctuations and phase distortion. This demonstrates that multiplexed data transmission of SOPs and phase channels through atmospheric turbulence channels is feasible.

[0040] Unlike other modulation schemes, SPPSK, as a novel polarization modulation technique, achieves spatial multiplexing based on the polarization state within the wavefront. SPPSK requires spatial modulation of the polarization state of the entire beam at any given moment, meaning that different regions within the wavefront exhibit different polarization states. The static pattern of the wavefront is divided into discrete regions or points, each modulated with a unique polarization state code to transmit information. These different regions or points can be considered independent discrete channels. Each independent region defined on the wavefront corresponds to an additional parallel transmission channel, doubling the system capacity. Therefore, after dividing the wavefront into N regions, the system can simultaneously transmit N parallel data streams, increasing the total communication capacity to N times its original value. This method can be seen as a form of polarization state spatial multiplexing. Furthermore, SPPSK integrates Binary Phase Shift Keying (BPSK). This integration requires adding a polarization modulation component to the original BPSK-based CFSOC system, where BPSK is implemented in the beam phase, polarization state modulation occurs on the wavefront, and spatial multiplexing is applied. Circularly polarized SPPSK modulation enhances the information carrying capacity of a light beam by multiplexing the polarization degrees of freedom of light, increasing the number of bits per unit bandwidth and significantly expanding the capacity of coherent free-space optical communication systems. Compared to orbital angular momentum, it does not require a set of vector vortex beams with orthogonal spatial properties, but instead uses a single vector beam to transmit a large amount of information. The phase and polarization state of this vector beam are used as a way to characterize the information.

[0041] like Figure 3 As shown, in a V-AO-based CFSOC system, the laser emitted by the laser is modulated into a carrier signal by a modulator employing SPPSK. The beam then travels through an atmospheric communication link and reaches the receiver. Due to atmospheric turbulence, the phase and polarization state of the beam are distorted. To compensate for these distortions, a V-AO system is introduced at the receiver, including a V-AO corrector, a V-AO controller, a wavefront sensor (or CCD), and a beam splitter. Subsequently, the laser and the local oscillator signal are mixed by a beam combiner to generate an intermediate frequency (IF) signal. After being received by the detector, the signal is processed using a demodulator and a digital signal processor.

[0042] Figure 4 The diagram shows a simplified structural schematic of a CFSOC system based on V-AO. In this system, the laser emitted by the laser source passes sequentially through a half-wave plate 1, two mirrors (M), a polarizer, and a beam expander before exiting. After being affected by atmospheric turbulence, the laser enters the V-AO system.

[0043] The V-AO system mainly consists of the following components arranged sequentially along the optical path: a first liquid crystal spatial light modulator (SLM1), a second liquid crystal spatial light modulator (SLM2), a half-wave plate 2, a deformable mirror (DM), a high-speed camera (CCD), and a controller. SLM1, SLM2, and DM are all correction elements. The V-AO system achieves joint correction of polarization and phase aberrations through feedback control. The liquid crystal spatial light modulators affect both the polarization and phase of the beam. Polarization aberration is primarily corrected by the two liquid crystal spatial light modulators. The deformable mirror only affects the beam phase. Therefore, the deformable mirror is placed after the two liquid crystal spatial light modulators to correct accumulated phase aberration.

[0044] At the output of the V-AO system, the beam is split into two beams by an inverted beam splitter. One beam, after passing through a lens and optical fiber, is used as the system output. The other beam, after passing through a reflector (M) and a lens, is focused onto the CCD. The CCD converts the acquired image information into electrical signals, which are transmitted to the controller (i.e., the V-AO controller). The controller activates its built-in EPSA-DE algorithm, and after numerous iterations of optimization, generates three voltage signals (corresponding to...). The system transmits three voltage signals to two liquid crystal spatial light modulators and a deformable mirror, respectively. Upon receiving the electrical signals, the two liquid crystal spatial light modulators and the deformable mirror change their internal structures, thereby influencing the light beam. Since the correction of polarization aberration depends on the effectiveness of phase correction, the performance of the controller's built-in control algorithm has a decisive impact on the correction effect.

[0045] The correction principle of the V-AO system is explained below.

[0046] Under atmospheric channel conditions, turbulence in the gaseous medium causes fluctuations in the beam's polarization state and phase distortion. Although turbulence disturbs the polarization state, these disturbances are usually small and negligible for the entire beam in conventional polarization shift keying (PSK) techniques. However, for SPPSK modulation, because it distinguishes the polarization state space of the beam wavefront region and divides it into N distinct polarization regions, treating each region as an independent data transmission channel, turbulence-induced polarization interference has a more significant impact on the N polarization regions in SPPSK compared to conventional systems due to the differentiation effect. Therefore, polarization perturbation is an important consideration in SPPSK modulation and cannot be ignored. To improve communication quality and reduce the system's bit error rate (BER), the impact of polarization perturbation on the entire communication link must be mitigated.

[0047] To reduce BER, the V-AO system is designed to correct both phase and polarization aberrations simultaneously. See also... Figure 3 The V-AO system uses two liquid crystal spatial light modulators for polarization aberration correction and one DM for phase aberration correction. To provide a comprehensive description of the optical link system, before iterative optimization using the EPSA-DE algorithm, a mathematical model of the optical link is first established based on the Jones matrix, i.e., mathematical modeling of the beam and its components. The optical link mathematical model models the influence of each component in the V-AO system on the beam as a corresponding Jones matrix, and then obtains the complete optical link expression from the transmitter to the receiver through matrix multiplication and concatenation.

[0048] Specifically, each element in the optical link is modeled as a Jones matrix ( The SOP and phase of a single point in the pupil are modeled as Jones vectors. Then calculate the SOP and phase effect of each element on a single point.

[0049]

[0050] in, For the initial Jones vector, This is the Jones vector after the influence of the component.

[0051] If only the delay and phase modulation of the fully polarized beam are considered, then The value can be represented as follows:

[0052]

[0053] in, It is a scalar phase; The imaginary part in the complex form; It is a special unitary matrix describing the change of SOP, which can also be represented as:

[0054]

[0055] in, It is the applied delay; It is an identity normal matrix, that is , , The specific value can be flexibly selected according to the specific application scenario, provided that the condition is met. It is a 2×2 identity matrix. , , It is the Pauli matrix:

[0056]

[0057] In the above modeling process, special unitary matrices The physical meaning is the change of SOP, which can be viewed as the rotation of SOP on the Poincaré sphere, where It is a rotating axis. It is the rotation angle.

[0058] For a given Jones vector You can find its corresponding Stokes vector. The formula is:

[0059]

[0060] Where † denotes conjugate transpose.

[0061] Next, we will create a mathematical model of the entire optical link.

[0062] for Figure 2 and Figure 3 The Jones vector at position b, affected by atmospheric turbulence, is expressed by the formula:

[0063]

[0064] in, For scalar phase, For the axis of rotation, The rotation angle is... For the corresponding Figure 2 and Figure 3 Jones vector at position a in the middle.

[0065] For the corresponding Figure 3 The Jones vector at position c represents the Jones vector generated by the SLM1 effect, and is expressed by the formula:

[0066]

[0067] in, The rotation angle when SLM1 is applied. , .

[0068] For the corresponding Figure 3 The Jones vector at position d, representing the Jones vector processed by half-wave plate 2, is expressed by the formula:

[0069]

[0070] in,

[0071] For the corresponding Figure 3The Jones vector at position e in the middle represents the Jones vector after the influence of SLM2, and is expressed by the formula:

[0072]

[0073] in, This is the rotation angle when SLM2 is applied.

[0074] For the corresponding Figure 3 The Jones vector at position f represents the Jones vector after the influence of DM, and is expressed by the formula:

[0075]

[0076] in, Phase compensation during DM operation.

[0077] From the perspective of input and output, the mathematical model of the entire optical link is expressed as follows:

[0078]

[0079] To observe the correction principle of the V-AO system, the influence of other factors is excluded, and only the components of the V-AO system are retained. The initial Jones vector is assumed to be... The Jones vector after reflection by SLM2 is .So Figure 3 The mathematical representation of polarization correction is as follows:

[0080]

[0081] Now, assuming the Jones vector [1;1] Corresponding Stokes vector Then it can be obtained through formula (5). Therefore, it can be obtained by... as well as The value is set to obtain the desired result. The value of, i.e. .

[0082] Based on the established optical link mathematical model, the polarization state change caused by atmospheric turbulence is mapped to rotation on the Poincaré sphere. The effects of SLM1, half-wave plate 2, and SLM2 on the polarization state are mapped to rotation on the Poincaré sphere about the corresponding rotation axis, respectively. The rotation angles of SLM1 and SLM2 required to restore the polarization state to the desired circular polarization state are solved, and the rotation angles are converted into the initial voltages of SLM1 and SLM2 to provide initialization parameters for the EPSA-DE algorithm.

[0083] Figure 5 This demonstrates the implementation of the V-AO system's correction principle on a Poincaré sphere. In the diagram, V, Q, and U represent the coordinate axes of the solid, while a, b, c, and d represent the names of four sub-figures and also indicate the overall sequence of changes: from a to b, then to c, and finally to d. and The axis of rotation is represented by equation (7) and equation (8) for specific definitions. Represents the initial Stokes vector. The Stokes vector after SLM1 is applied. The Stokes vector after being acted upon by half-wave plate 2. This is the Stokes vector after SLM2 processing, which is the desired Stokes vector. The V-AO system can generate any SOP. For example, (a) assumes... The initial state has a value of ,and (a) The Stokes vector corresponding to any desired SOP; (b) SLM1 acts on the beam, the process of which is modeled as along Axis rotation Then, after rotating it another 180°, we get... (c) This stage is the process of the half-wave plate 2 being affected, and it is modeled as a process of... After rotating the axis 180°, we get (d) Similarly, SLM2 acts on the beam, and this process is modeled as first rotating around... Axis rotation After rotating 180°, the desired state is achieved. .

[0084] In this embodiment, the disturbance caused by atmospheric turbulence is modeled as Therefore, we can see that there are three unknowns in the equation, namely... (Scalar phase) (rotation axis) (Rotation angle). Here Calibration is performed using a native wavefront-less AO (Sensor-Less Adaptive Optics, SLAO) system. Furthermore, to simplify calculations, [the following is introduced]. Prior knowledge, i.e., assumptions This is known a priori. Furthermore, for ease of analysis, atmospheric turbulence is usually considered as a single-axis isotropic medium within a certain range, where its optical properties are assumed to be uniform in all directions. From this, we can obtain... .

[0085] The SOP needs to be corrected. and The value must be determined, and Corrected by a wavefront-free optimization system, therefore It can also be determined through iterative optimization, for example, by using Zernike polynomials. ,Right now:

[0086]

[0087] in, The radius is in polar coordinates. For polar coordinates, Let Zernike be the order of the polynomial. Represents the coefficients of the i-th Zernike polynomial. Let be the i-th order Zernike polynomial.

[0088] To correct the SOP, it is necessary to calculate the complex conjugate Jones vector of the SOP perturbation component. The formula is:

[0089]

[0090] in, .

[0091] The corresponding Stokes vector can be calculated using equation (5):

[0092]

[0093] therefore, and The value of can be determined by the following equation:

[0094]

[0095] Then and The values ​​are converted into corresponding control voltage data, and then input as parameters into SLM1 and SLM2 respectively to facilitate SOP calibration.

[0096] The V-AO system is a correction system based on SLAO. It adds a polarization correction element (i.e., a liquid crystal spatial light modulator) to the original SLAO system, achieving beam compensation through joint feedback correction of phase and polarization aberrations. The presence of the V-AO system greatly reduces the influence of atmospheric turbulence on the beam polarization state and phase. The rotation angle of the polarization correction element in the V-AO system is controlled by a control algorithm. The V-AO system uses a deformable mirror and a liquid crystal spatial light modulator as the means of phase correction and polarization correction, respectively. Beam compensation is achieved by changing the shape of the deformable mirror and the arrangement of liquid crystal molecules inside the liquid crystal spatial light modulator through control voltage. In this invention, the V-AO system uses the EPSA-DE algorithm as the control algorithm, and the solution of the control algorithm is the control voltage of each correction element. The Strehl ratio (SR) is used as the fitness; the algorithm optimizes SR to the desired value, thereby obtaining the optimal control voltage of the system.

[0097] Optionally, in this embodiment, the specific parameters of the EPSA-DE algorithm are as follows: the number of initial control voltages N=30; the maximum number of iterations T=50; the proportional adjustment coefficient Kp is 1; the integral adjustment coefficient Ki is 0.5; the differential adjustment coefficient Kd is 1.2; the scaling factor H is 1; and the current crossover rate CR is 0.8.

[0098] The EPSA-DE algorithm introduces the concept of differential evolution into the original PID-based Search Algorithm (PSA). Differential evolution guides the population towards a positive outcome through three basic evolutionary operators: mutation, crossover, and selection, until the algorithm's termination condition is met. While retaining the original mechanisms of the PSA algorithm, the EPSA-DE algorithm further enhances its optimization capabilities by introducing mutation, crossover, and selection during subsequent developments of the PSA algorithm.

[0099] In the V-AO system of this invention, the EPSA-DE algorithm is used to jointly optimize the control voltage of the phase correction element (i.e., deformable mirror) and the polarization correction element (i.e., liquid crystal spatial light modulator), thereby improving the compensation effect of the system. The iterative optimization process of the EPSA-DE algorithm includes the following steps:

[0100] Step 2.1, Initialization:

[0101] Within the allowable voltage range of the correction elements, N sets of control voltage vectors U are randomly generated. Each set of control voltage vectors contains the voltage parameters of all correction elements, forming the initial population of the algorithm.

[0102]

[0103] in, Representing the The first individual dimension; and They are the first Upper and lower limits of each variable (dimension); It is a random number between 0 and 1. , This parameterized design ensures the algorithm's ability to explore the solution space uniformly.

[0104] Step 2.2, Fitness Calculation:

[0105] The control voltage vector U is loaded into the V-AO system, and the corresponding system performance evaluation index value is obtained, which is used as the fitness of the control voltage vector U.

[0106] Optionally, the system performance evaluation metric is the Strehl ratio (SR). SR, as a fitness function value, is used to evaluate the compensation effect of the control voltage vector U. In a CFSOC system employing zero-difference detection, the mixing efficiency (ME) can be approximated by the Strehl ratio (SR) of the far-field spot. ME is an important evaluation metric for optical communication quality, reflecting the degree of matching between the signal light and the local oscillator light. A larger ME value indicates smaller wavefront phase distortion of the signal light and higher CFSOC communication quality, while a smaller ME value indicates lower quality.

[0107] Step 2.3, System Deviation and PID Adjustment:

[0108] The system deviation is calculated based on the difference between the historical best fitness value and the current fitness value, and the voltage increment is adjusted using a PID controller. This step ensures the stability and convergence speed of the voltage update process. The voltage increment generated by the PID controller... Determined by the following formula:

[0109]

[0110] in, , and It is a vector of n rows and 1 column containing random numbers from 0 to 1; , and These are the adjustment factors for proportional, integral, and derivative equations, respectively, for example, set to 1, 0.5, and 1.2.

[0111] For the first The overall deviation at the next iteration is calculated using the following formula:

[0112]

[0113] Among them, the number of iterations The best individual These are particles that correspond to the overall historical minimum. It is the number of iterations. Particles at that location.

[0114] It can be represented as:

[0115]

[0116] in, For the first Overall deviation at the next iteration; Number of iterations The particle at that location corresponds to the overall historical minimum. Number of iterations The particle at that location corresponds to the overall historical minimum.

[0117] Step 2.4, Differential Evolution Operation:

[0118] Based on PID control, three types of differential evolution operators are introduced: mutation operator, crossover operator, and selection operator, to generate new candidate solutions.

[0119] The mutation operator is used to generate new candidate solutions based on the voltage vector differences between different particles. Specifically, three distinct particles are selected from the parent generation, and the following mutation operation is performed to generate a new mutation vector:

[0120]

[0121] in, , , The three selected particles are respectively. This is the difference scaling factor.

[0122] The crossover operator is used to partially exchange candidate solutions with the current solution to form a trial solution. Specifically, it transforms the mutation vector... The particles are mixed with the original particles according to the crossover probability to generate experimental vectors. Furthermore, the crossover operator can generate test vectors using binomial crossover operations.

[0123]

[0124] in, For the test vector The Dimensional components; For the mutation vector The Dimensional components; This is the original solution; In order to target the A dimension component is generated independently in Random numbers within the interval; It is an integer randomly selected from a preset range; This represents the crossover probability.

[0125] The selection operator is used to compare the experimental solution with the original solution based on the fitness value and retain the better solution. Here, a greedy selection strategy is adopted, which selects the best particle based on the fitness value evaluation.

[0126]

[0127] in, To select the best particle, Mutant particles, For primordial particles, This represents the fitness function.

[0128] Step 2.5, Updates and Iterations:

[0129] Re-drive DM, SLM1, and SLM2 using the updated control voltage vector, and recalculate the fitness value. Repeat steps 2.2 to 2.4 until the fitness value reaches a preset threshold or the number of iterations reaches the maximum number of iterations. The particle position update formula in this step is:

[0130]

[0131] in, For the first The position of the substitute particle. To prevent the algorithm from getting trapped in local optima, a zero-output conditional factor for Lévy flight is added. Its expression is:

[0132]

[0133] in, This represents the current iteration number; This represents the maximum number of iterations. A vector of n rows and 1 column containing random numbers from 0 to 1; Representing Levi's flight; This is the adjustment factor, and its calculation formula is as follows:

[0134]

[0135] It is an n x 1 matrix, and its calculation formula is as follows:

[0136]

[0137] in, A vector of n rows and 1 column containing random numbers from 0 to 1.

[0138] Through steps 2.1-2.5 above, the EPSA-DE algorithm achieves dynamic optimization of the voltages of the deformable mirror and the two liquid crystal spatial light modulators, enabling the V-AO system to simultaneously correct the phase aberration and polarization aberration of the beam, ultimately improving the link transmission performance.

[0139] This invention, based on spatial polarization phase-shift keying (SPPSK), achieves spatial multiplexing of the polarization state in the wavefront through circular polarization SPPSK modulation. This enhances the information carrying capacity of the beam, increases the number of bits per unit bandwidth, and significantly expands the capacity of coherent free-space optical communication systems. The invention uses circular polarization for information representation, fundamentally solving the problem of strict alignment between the transmitter and receiver in linearly polarized systems. Because circular polarization is used as the information transmission method, strict coordinate axis alignment between the transmitter and receiver is not required. Therefore, the coherent free-space optical communication system can operate stably on a mobile platform where the transmitter and receiver rotate relative to each other. It possesses low bit error rate characteristics, stronger anti-interference capabilities, and greater adaptability to mobile platforms.

[0140] To enhance the beam correction capability of vector adaptive optics systems, this invention proposes a novel PSA-based control algorithm, the EPSA-DE algorithm. This algorithm incorporates mutation, crossover, and selection concepts from the Differential Evolution Algorithm (DE) into the position update process of the PSA algorithm, thereby strengthening its optimization capabilities. Furthermore, the introduction of the DE algorithm effectively balances the exploration and development aspects of the algorithm's iteration process. Through the deep integration of the PSA algorithm's group collaboration and the DE algorithm's differential perturbation, the EPSA-DE algorithm demonstrates significant advantages in both theoretical convergence and practical optimization efficiency. It outperforms the traditional SPGD algorithm under weak turbulence and exhibits excellent correction performance under strong turbulence, while also demonstrating greater stability. This invention also includes theoretical research and numerical simulations to verify the correction effect of the EPSA-DE algorithm under different turbulence levels, comparing its performance with that of the PSA and SPGD algorithms. Experimental verification of the EPSA-DE algorithm's ability to effectively suppress atmospheric turbulence is also conducted. The results show that the EPSA-DE algorithm can effectively correct phase aberrations and polarization aberrations, thereby improving the communication performance of the system.

[0141] To verify the effectiveness of this invention, numerical simulation is performed below.

[0142] In the CFSOC system, Zernike polynomials are typically used to describe various aberrations caused by atmospheric turbulence. In this simulation, Zernike polynomials are also used to simulate polarization aberrations, with the initial 15th order of the Zernike polynomial used to characterize wavefront aberrations, thereby improving fitting accuracy and more realistically simulating the effects of atmospheric turbulence. The simulation parameters are set as follows: beam wavelength is 1.55 μm, the mode radius of the Airy disk is assumed to be 1, the ratio of lens diameter to focal length is 1, each qubit receives 20 photons, and the detector's quantum efficiency is 1. The generation of wavefront aberrations depends on the intensity of turbulence. Two sets of wavefront aberrations with Zernike coefficients are randomly generated to simulate weak and strong turbulence conditions, respectively. The initial Zernike coefficients corresponding to weak and strong turbulence are as follows: Figure 6 As shown, Figure 6 (a) in the text corresponds to weak turbulence. Figure 6 (b) in the diagram corresponds to strong turbulence. (and) Figure 6 The corresponding initial wavefront aberrations are as follows Figure 7 As shown, Figure 7 (a) in the text corresponds to weak turbulence. Figure 7 (b) in the text corresponds to strong turbulence.

[0143] Due to the characteristics of circularly polarized SPPSK modulation technology, the CFSOC system can independently modulate the wavefront polarization state and beam phase, thereby realizing the simulation of multi-channel parallel transmission. In phase-modulated transmission, wavefront aberrations are corrected using a traditional SLAO, while polarization aberrations in polarization-modulated transmission are compensated by the polarization correction elements of the V-AO system.

[0144] In the simulation, the polarization state (SOP) of the beam is first characterized using the Jones vector. Then, the EPSA-DE algorithm is used to optimize the V-AO system. Based on the iterative results, the Zernike mode data of the wavefront is determined and converted into voltage data. This voltage data is then applied to the deformable mirror and the liquid crystal spatial light modulator to achieve joint aberration correction. Prior knowledge of Q is introduced into the simulation. Theoretically, the entire wavefront of light can be divided into an infinite number of regions. However, considering the basic communication requirements of optical communication systems, and balancing the bit error rate requirements with computational efficiency, this simulation divides the wavefront of light into 19 independent regions.

[0145] For the 19 divided channel regions, the polarization aberration comparison before and after correction is as follows: Figure 8 As shown, where, Figure 8 In the diagram, (a) represents the polarization aberration before correction. Figure 8In the diagram, (b) represents the corrected polarization aberration. To more clearly demonstrate the correction effect, channels 3 and 9 are selected for comparative analysis, with the polarization aberrations of channel 3 before and after correction shown below. Figure 9 As shown, the polarization aberrations of channel 9 before and after correction are as follows: Figure 10 As shown, where, Figure 9 and Figure 10 In the image, (a) shows the polarization aberrations of channels 3 and 9 before correction, respectively. Figure 9 and Figure 10 In Figure (b), the polarization aberrations after correction are shown for channels 3 and 9, respectively. The phase aberration correction results are as follows: Figure 11 As shown, where, Figure 11 In the diagram, (a) represents the corrected phase aberration corresponding to weak turbulence. Figure 11 In the diagram, (b) represents the corrected phase aberration corresponding to strong turbulence.

[0146] To simulate the signal transmission process, a 19-bit bitstream was allocated to each of the 19 regions, with each region carrying 1 bit of data, to simulate the parallel transmission of static data in multiple channels. Subsequently, polarization disturbances caused by atmospheric turbulence were simulated based on Zernike polynomial data, and the V-AO system underwent 50 iterations of optimization to achieve joint polarization and phase correction. Ten independent experiments were repeated, and the mixing efficiency (ME) and BER of the V-AO system as a function of iteration number were statistically obtained. The ME curves under weak and strong turbulence conditions are shown below. Figure 12 As shown, where, Figure 12 (a) in the text corresponds to strong turbulence. Figure 12 (b) in the figure corresponds to weak turbulence. The BER curves under weak and strong turbulence conditions are shown in the figure. Figure 13 As shown, where, Figure 13 (a) in the text corresponds to strong turbulence. Figure 13 (b) in the text corresponds to weak turbulence.

[0147] Figure 14 The graph shows a performance comparison between the EPSA-DE algorithm and the original PSA algorithm in the CFSOC system. Figure 14 In the figure, (a) is the curve showing the change of root mean square error (RMS) with the number of iterations. Figure 14 In Figure (b), the mixing efficiency (ME) varies with the number of iterations. Figure 14 As can be seen, the EPSA-DE algorithm has a faster convergence speed than the PSA algorithm. In the CFSOC system, after multiple repeated experiments, the EPSA-DE algorithm can achieve an ME of 0.8 in an average of 15 iterations, while the original PSA algorithm requires 24 iterations to reach the same level.

[0148] The simulation results above show that:

[0149] (1) SPPSK modulation based on circular polarization can increase the communication capacity of the CFSOC system from 1 bit per unit bandwidth to 20 bits per unit bandwidth, which significantly expands the system capacity.

[0150] (2) As the control algorithm of V-AO system, EPSA-DE algorithm has better correction effect than traditional SPGD algorithm under weak turbulence. Under strong turbulence, EPSA-DE algorithm not only has better correction effect than traditional SPGD algorithm, but also shows better stability. Simulation verification shows that EPSA-DE algorithm has excellent performance in CFSOC system.

[0151] (3) By adopting circularly polarized SPPSK modulation and EPSA-DE algorithm, this invention effectively solves the problems of the system being unable to adapt to mobile platforms and the algorithm correction effect being poor in the prior art, and significantly improves the communication capacity and reliability of CFSOC.

[0152] The technical features of the above embodiments can be combined in any way. For the sake of brevity, not all possible combinations of the technical features in the above 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.

[0153] The embodiments described above are merely illustrative of several implementations of the present invention, and while the descriptions are relatively specific and detailed, they should not be construed as limiting the scope of the invention patent. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of the present invention, and these all fall within the protection scope of the present invention. Therefore, the protection scope of this invention patent should be determined by the appended claims.

Claims

1. A method for expanding the capacity of a coherent free-space optical communication system, applied to a coherent free-space optical communication system, the system comprising a transmitter and a receiver, the receiver being equipped with a vector adaptive optics system, characterized in that, The method includes the following steps: Step 1: At the transmitting end, the data is encoded and modulated using circular polarization SPPSK modulation to generate a spatially polarized beam, and the spatially polarized beam is transmitted to the receiving end via an atmospheric channel; The encoding and modulation process includes: dividing a single static wavefront of the light beam into N independent regions, each region corresponding to a data transmission channel; mapping the N bits of data to be transmitted to the N regions, each bit corresponding to one region; characterizing the information of the bit by loading a specific circular polarization state on each region, wherein two orthogonal circular polarization states are used to map binary values ​​"0" and "1" respectively. Step 2: At the receiving end, the vector adaptive optics system uses the EPSA-DE algorithm as the control algorithm. Through iterative optimization, a control voltage is generated, and the correction element in the vector adaptive optics system is driven according to the control voltage to maximize the system's performance evaluation index and realize the joint correction of the beam affected by atmospheric turbulence. The joint correction includes compensating for the phase aberration and polarization aberration of the beam simultaneously. Step 3: Mix the corrected beam with the local oscillator beam, and after demodulation and digital signal processing, recover the original data.

2. The method according to claim 1, characterized in that, The vector adaptive optics system includes a first liquid crystal spatial light modulator, a half-wave plate, a second liquid crystal spatial light modulator, and a deformable mirror arranged sequentially along the optical path. The two liquid crystal spatial light modulators, serving as correction elements, are used to correct the polarization aberration of the light beam, and the deformable mirror, serving as a correction element, is used to correct the phase aberration of the light beam.

3. The method according to claim 1 or 2, characterized in that, The iterative optimization process of the EPSA-DE algorithm includes the following steps: Step 2.1 Initialization: Within the allowable voltage range of the correction element, randomly generate N sets of control voltage vectors to form the initial population; Step 2.2, Fitness Calculation: Input each group of control voltage vectors and obtain the corresponding system performance evaluation index value, which is used as the fitness of the group of control voltage vectors. Step 2.3, PID control: Based on the deviation between the historical best fitness value and the current fitness value, a PID controller is used to generate the voltage increment; Step 2.4, Differential Evolution Operation: Based on PID control, the mutation operator, crossover operator, and selection operator of the differential evolution algorithm are introduced to generate new candidate solutions; Step 2.5, Update and Iteration: Re-drive the correction element using the updated control voltage vector, and repeat steps 2.2 to 2.4 until the fitness value reaches the preset threshold or the number of iterations reaches the maximum number of iterations.

4. The method according to claim 3, characterized in that, In step 2.3, the voltage increment generated by the PID controller Determined by the following formula: in, , , These are the adjustment factors for proportional, integral, and derivative equations, respectively. , and It is a vector of n rows and 1 column containing random numbers from 0 to 1; For the first Overall deviation at the next iteration.

5. The method according to claim 3, characterized in that, In step 2.4, the differential evolution operation specifically includes: Mutation operator: Select three distinct particles from the parent generation and perform the following mutation operation to generate a new mutation vector. : in, , , The three selected particles are respectively. It is the difference scaling factor; Crossover operator: transforms the mutation vector The particles are mixed with the original particles according to the crossover probability to generate experimental vectors; Selection operator: Compare the fitness values ​​of the trial vectors with the current solutions, and retain the better ones for the next generation.

6. The method according to claim 5, characterized in that, The crossover operator generates test vectors using a binomial crossover operation.

7. The method according to claim 3, characterized in that, In step 2.5, the particle position update formula is: in, For the first The position of the substitute particle; To introduce the zero-output condition factor for Lévy flight; in, This represents the current iteration number; This represents the maximum number of iterations. A vector of n rows and 1 column containing random numbers from 0 to 1; Representing Levi's flight; It is an adjustment factor. .

8. The method according to claim 3, characterized in that, The system performance evaluation metric is the Strehl ratio.

9. The method according to claim 2, characterized in that, Before iterative optimization using the EPSA-DE algorithm, mathematical modeling is performed based on the Jones matrix and Poincaré sphere theory, specifically including: A mathematical model of the optical link is established based on the Jones matrix. The mathematical model of the optical link models the influence of each component in the vector adaptive optics system on the beam as a corresponding Jones matrix. The complete optical link expression from the transmitter to the receiver is obtained by matrix multiplication and concatenation. Based on the aforementioned optical link mathematical model, the polarization state change caused by atmospheric turbulence is mapped as a rotation on a Poincaré sphere. The effects of the first liquid crystal spatial light modulator, the half-wave plate, and the second liquid crystal spatial light modulator on the polarization state are respectively mapped as rotations on the Poincaré sphere about the corresponding rotation axes. The rotation angles of the first and second liquid crystal spatial light modulators required to restore the polarization state to the desired circular polarization state are calculated, and the rotation angles are converted into the initial voltages of the first and second liquid crystal spatial light modulators to provide initialization parameters for the EPSA-DE algorithm.

10. The method according to claim 9, characterized in that, The rotation angles of the first liquid crystal spatial light modulator and the second liquid crystal spatial light modulator are determined by the following equation: in, The rotation angle of the first liquid crystal spatial light modulator; This refers to the rotation angle of the second liquid crystal spatial light modulator; The Stokes vector corresponding to the desired circularly polarized state.

Images