Method for determining FSO system performance under weak turbulence condition based on OAM factor
阅读说明：本技术 基于oam因子的弱湍条件下fso系统性能的确定方法 (Method for determining FSO system performance under weak turbulence condition based on OAM factor ) 是由 王平 潘宇婷 王炜 张婷 庞维娜 李爽 于 2020-06-08 设计创作，主要内容包括：本发明公开了一种基于OAM因子的弱湍条件下FSO系统性能的确定方法,包括：基于大气湍流传输模型,得到计算OAM因子的表达式；给出FSO系统中OAM因子统计分布的概率密度函数,给出FSO系统中OAM因子的统计模型；基于最小二乘法,给出求解FSO系统中OAM因子的统计模型参数的优化问题和优化算法,求解FSO系统中OAM因子的统计模型参数,再验证FSO系统中OAM因子的统计模型的可靠性；基于FSO系统中OAM因子的统计模型,结合QPSK调制OAM复用FSO系统传输模型,推导系统误码率表达式,对比不同湍流强度对系统性能的影响。该方法将概率密度函数参数用湍流强度定量表示,能适用于更多的应用环境。(The invention discloses a method for determining the performance of an FSO system under a weak turbulence condition based on an OAM factor, which comprises the following steps: obtaining an expression for calculating the OAM factor based on the atmospheric turbulence transmission model; giving a probability density function of OAM factor statistical distribution in the FSO system, and giving a statistical model of the OAM factor in the FSO system; based on a least square method, an optimization problem and an optimization algorithm for solving the statistical model parameters of the OAM factors in the FSO system are given, the statistical model parameters of the OAM factors in the FSO system are solved, and then the reliability of the statistical model of the OAM factors in the FSO system is verified; based on a statistical model of OAM factors in the FSO system, a QPSK modulation OAM multiplexing FSO system transmission model is combined to deduce a system error rate expression, and the influence of different turbulence intensities on the system performance is compared. The method quantitatively expresses the probability density function parameters by the turbulence intensity, and can be suitable for more application environments.)
1. The method for determining the performance of the FSO system under the weak turbulence condition based on the OAM factors is characterized by comprising the following steps:
1) calculating an OAM factor in an FSO system by carrying out filtering decomposition on the received LG light based on an atmospheric turbulence transmission model, carrying out simulation for many times, and calculating an empirical probability density function based on nonparametric estimation of probability density;
2) giving a probability density function of OAM factor statistical distribution in the FSO system; fitting probability density functions of OAM factor statistical distribution in the FSO system proposed under different transfer intervals, OAM modes and turbulence conditions to obtain influences of parameters on the statistical distribution, and establishing a quantitative relation between probability density function parameters and turbulence intensity in a certain turbulence condition range to obtain a statistical model of the OAM factors in the FSO system;
3) based on a least square method, an optimization problem and an optimization algorithm for solving the statistical model parameters of the OAM factors in the FSO system are given, the statistical model parameters of the OAM factors in the FSO system are solved, and the reliability of the statistical model of the OAM factors in the FSO system under different OAM transfer intervals, OAM modes and turbulence conditions is verified through a back substitution result;
4) based on a statistical model of OAM factors in the FSO system, combining a QPSK modulation OAM multiplexing FSO system transmission model, deducing a system error rate expression, simulating and verifying the practicability of the statistical model of the OAM factors in the FSO system, bringing turbulence intensity into the obtained error rate expression, and comparing the influence of different turbulence intensities on the system performance.
2. The method for determining the performance of the FSO system under the weak turbulence condition based on the OAM factors as claimed in claim 1, wherein, in the step 1), the OAM attenuation and crosstalk factors are calculated by the following method:
1a) giving a light source expression;
1b) and based on the atmospheric turbulence transmission model, performing inner product calculation on the light field obtained by transmission to obtain OAM attenuation and crosstalk factors.
3. The method for determining the performance of the FSO system under the weak turbulence condition based on the OAM factors as claimed in claim 1, wherein the step 2) of giving the probability density function of the statistical distribution of the OAM factors in the FSO system comprises the following steps:
2a) the probability density function for uniformly describing the statistical distribution of the OAM factors in the FSO system is an EGG function
Wherein the content of the first and second substances,represents the OAM factor, a, b, c, theta,
2b) the method comprises the following steps of providing a simplified form of a probability density function of OAM factor statistical distribution in an FSO system under different OAM transfer interval conditions;
when m-n is more than or equal to 1, attenuating to probability density function of OAM factor statistical distribution in FSO system of GGD
Wherein | m-n | is an OAM transfer interval;
when m-n is more than or equal to 2, attenuating to probability density function of OAM factor statistical distribution in FSO system of exponential distribution
4. The method for determining the performance of the FSO system under the weak turbulence condition based on the OAM factors as claimed in claim 3, wherein in the step 2), a quantitative relation between a probability density function parameter and turbulence intensity is established in a certain turbulence condition range, so as to obtain a statistical model of the OAM factors in the FSO system, and the method is realized by the following steps:
2c) and (3) in a certain turbulence condition range, giving a quantitative expression of an atmospheric refractive index structure constant representing turbulence intensity, and determining a statistical model of the OAM factor of the FSO system by combining the uniformly-described probability density function of OAM factor statistical distribution in the FSO system attenuated to GGD and exponential distribution obtained in the steps 2a) and 2 b).
5. The method for determining the performance of the FSO system under the weak turbulence condition based on the OAM factors as claimed in claim 1, wherein the quantitative relation between the probability density function parameters and the turbulence intensity is established in a certain turbulence condition range, and a statistical model of the OAM factors in the FSO system is obtained as follows:
when m-n is 0, the quantitative relational expression between the probability density function parameter and the turbulence intensity is:
where m is the number of OAM modes before transmission, am,
when the m-n is equal to 0, the formula (1) and the formulas (4) to (8) form a statistical model of OAM factors in the FSO system;
when the probability density function of OAM factor statistical distribution in the FSO system is attenuated to GGD and | m-n | ≧ 1, the quantitative relational expression between the probability density function parameter and the turbulence intensity is:
wherein n is the OAM mode number after transmission, am→n,Is a quantitative expression parameter;
the formula (2) and the formulas (9) to (11) form a statistical model of the OAM factors in the FSO system when the probability density function of the OAM factor statistical distribution in the FSO system is attenuated to GGD and | m-n | ≧ 1;
when the probability density function of OAM factor statistical distribution in the FSO system is attenuated to exponential distribution, the quantitative relational expression between the probability density function parameter and the turbulence intensity is as follows:
wherein the content of the first and second substances,is a quantitative expression parameter;
the formula (3) and the formula (12) form a statistical model of the OAM factors in the FSO system when the probability density function of the OAM factor statistical distribution in the FSO system is attenuated to exponential distribution.
6. The method for determining FSO system performance under weak turbulence conditions based on OAM factors as claimed in claim 4, wherein in step 2c), a certain turbulence range is calculated as refractive index structure constant under weak turbulence conditionsAnd dividing the range by orders of magnitude.
7. The method for determining the performance of the FSO system under the weak turbulence condition based on the OAM factors as claimed in claim 1, wherein in the step 3), an optimization problem and an optimization algorithm for solving the statistical model parameters of the OAM factors in the FSO system are given, and the statistical model parameters of the OAM factors in the FSO system are solved by the following method:
3a) according to the empirical probability density function generated in the step 1), combining the statistical model of the OAM factors in the FSO system in a certain turbulence condition range in the step 2), and based on a least square method, giving out the optimization problem of solving the statistical model parameters of the OAM factors in the FSO system under the conditions of probability density function types of OAM factor statistical distribution in different FSO systems and OAM transfer intervals;
3b) decomposing the optimization problem of solving the statistical model parameters of the OAM factors in the FSO system in the step 3a) under the conditions of the probability density function types of the OAM factor statistical distribution and the OAM transfer intervals in different FSO systems, and providing an optimization algorithm for solving the statistical model parameters of the OAM factors in the FSO system and solving the optimization algorithm.
8. The method for determining the performance of the FSO system under the weak turbulence condition based on the OAM factors according to claim 7, wherein the step 3a) of solving the optimization problem of the statistical model parameters of the OAM factors in the FSO system under the conditions of the type of the probability density function of the statistical distribution of the OAM factors in different FSO systems and the OAM transfer interval comprises the following steps:
when | m-n | ═ 0, the optimization problem of solving the statistical model parameters of the OAM factors in the FSO system is as follows:
wherein the values of a, b, c, theta,determined by equations (4) - (8);to represent
when the probability density function of OAM factor statistical distribution in the FSO system is attenuated to GGD and | m-n | ≧ 1, the optimization problem of solving the statistical model parameters of the OAM factor in the FSO system is as follows:
wherein a, b, c are determined by the formulae (9) to (11),to represent
when the probability density function of OAM factor statistical distribution in the FSO system is attenuated to exponential distribution, the optimization problem of the statistical model parameters of the OAM factor in the FSO system is solved as follows:
wherein b is determined by the formula (12),parameters of a statistical model of the OAM factors in the FSO system when a probability density function of the statistical distribution of the OAM factors in the FSO system is attenuated to an exponential distribution,
9. The method for determining the performance of the FSO system under the weak turbulence condition based on the OAM factors as claimed in claim 8, wherein in the step 3b), the optimization algorithm for solving the statistical model parameters of the OAM factors in the FSO system is as follows:
when | m-n | ≧ 0, when the probability density function of the statistical distribution of the OAM factors in the FSO system decays to GGD and | m-n | ≧ 1, and when the probability density function of the statistical distribution of the OAM factors in the FSO system decays to exponential distribution, the optimization problem of solving the statistical model parameters of the OAM factors in the FSO system according to equations (13), (14), and (15), respectively, can be decomposed into a two-part simplified optimization problem, and an optimization algorithm based on the two-part simplified optimization problem is given and solved.
10. The method for determining the performance of the FSO system under the weak turbulent condition based on the OAM factors according to claim 1, wherein in the step 4), the transmission model of the QPSK modulation OAM multiplexing FSO system is as follows:
let s (t) be the transmission signal, g (t) be the reception signal, QPSK modulation OAM multiplexing FSO system
wherein the content of the first and second substances,
Technical Field
The invention belongs to the technical field of wireless optical communication, and particularly relates to a method for determining the performance of a research system based on a statistical model of an OAM factor of an FSO system quantitatively expressed by turbulence intensity under the condition of weak turbulence in atmosphere.
Background
Free Space Optical Communication (FSO Free Space Optical Communication) is a transmission Communication technique in which laser is used as a carrier and air is used as a transmission medium. This technology interest is multiplied by the combination of the high bandwidth of optical communications and the flexibility of wireless technology. Meanwhile, an Orbital Angular Momentum (OAM Orbital Angular Momentum) mode provides a new degree of freedom for light, which can further improve the capacity of a communication system in an FSO link. However, the light intensity and phase of the light beam may be affected by atmospheric turbulence, causing distortion and distortion of the OAM pattern. Therefore, in order to deepen understanding of the communication system, various statistical models are proposed by researchers to describe OAM mode attenuation and inter-mode crosstalk caused by atmospheric turbulence.
The energy of the vortex light in free space will remain in the OAM eigenstates, but as turbulence increases, the energy in the eigenstates will gradually leak into other OAM modes. The energy attenuation ratio in eigenstates is described by an OAM attenuation factor, and the energy ratio transferred to other OAM modes is described by an OAM crosstalk factor, which may be collectively referred to as an OAM factor. To date, various mathematical models have been proposed to describe the probability density Function (PDF probability density Function) with respect to OAM attenuation and crosstalk factors. Among them, Johnson SBThe probability density function and the exponential distribution function were first proposed to describe the statistical properties of the attenuation and crosstalk factors, respectively. Recently, e.m. amoud et al proposed a novel mathematical model describing vortex optical power attenuation caused by turbulence and crosstalk between OAM modes-Generalized gamma distribution function (GGD Generalized gamma distribution), which is suitable for various turbulence conditions and provides excellent fitting to simulated data of Laguerre-Gaussian (LG) and can study the influence of the performance of an FSO system based on LG light.
The current problems are as follows: all known statistical distributions related to attenuation and crosstalk factors need to be subjected to multiple experiments and then calculated to obtain PDF parameters, in an environment with changing turbulence conditions, an accurate PDF cannot be directly obtained by an existing mathematical model, and a statistical model with a quantitative relation between the PDF parameters related to OAM factors and turbulence intensity is not reported. Therefore, the research of the performance of the FSO system based on the statistical model describing OAM eigen-state mode attenuation and OAM mode crosstalk caused by atmospheric turbulence and the quantitative representation of PDF parameters by refractive index structure constants belongs to the current very important research direction.
Disclosure of Invention
The invention aims to establish a probability density function for uniformly describing the influence of atmospheric turbulence on vortex optical power of different OAM modes, and quantitatively express the parameters of the distribution function by the intensity of the turbulence to obtain a specific statistical model. Based on a trust domain algorithm in the optimization method, the optimization algorithm is designed to calculate the statistical model parameters, and then the performance of the OAM multiplexing communication system under different turbulence conditions is researched. Because the trust domain algorithm has integral convergence, the invention can calculate the system performance based on the model by expressing the fitting problem as the optimization problem and adjusting the optimization algorithm to effectively calculate the quantitative relation.
The invention is realized by the following technical scheme.
The method for determining the performance of the FSO system under the weak turbulence condition based on the OAM factors comprises the following steps:
1) calculating an OAM factor in an FSO system by carrying out filtering decomposition on the received LG light based on an atmospheric turbulence transmission model, carrying out simulation for many times, and calculating an empirical probability density function based on nonparametric estimation of probability density;
2) giving a probability density function of OAM factor statistical distribution in the FSO system; fitting probability density functions of OAM factor statistical distribution in the FSO system proposed under different transfer intervals, OAM modes and turbulence conditions to obtain influences of parameters on the statistical distribution, and establishing a quantitative relation between probability density function parameters and turbulence intensity in a certain turbulence condition range to obtain a statistical model of the OAM factors in the FSO system;
3) based on a least square method, an optimization problem and an optimization algorithm for solving the statistical model parameters of the OAM factors in the FSO system are given, the statistical model parameters of the OAM factors in the FSO system are solved, and the reliability of the statistical model of the OAM factors in the FSO system under different OAM transfer intervals, OAM modes and turbulence conditions is verified through a back substitution result;
4) based on a statistical model of OAM factors in the FSO system, combining a QPSK modulation OAM multiplexing FSO system transmission model, deducing a system error rate expression, simulating and verifying the practicability of the statistical model of the OAM factors in the FSO system, bringing turbulence intensity into the obtained error rate expression, and comparing the influence of different turbulence intensities on the system performance.
In the above technical solutions, the present invention also has a further defined solution:
further, in the step 1), the OAM attenuation and the crosstalk factor are calculated by the following method:
1a) giving a light source expression;
1b) and based on the atmospheric turbulence transmission model, performing inner product calculation on the light field obtained by transmission to obtain OAM attenuation and crosstalk factors.
Further, in the step 2), a probability density function describing the statistical distribution of OAM attenuation and crosstalk factors in the FSO system is given by the following steps:
2a) giving a probability density function for uniformly describing OAM attenuation and crosstalk factors in the FSO system;
2b) and (3) giving a simplified form of a probability density function of OAM factor statistical distribution in the FSO system under different OAM transfer interval conditions.
Further, in the step 2), a quantitative relation between a probability density function parameter and turbulence intensity is established within a certain turbulence condition range to obtain a statistical model of the OAM factor in the FSO system, which is given by the following steps:
2c) and (3) in a certain turbulence condition range, giving a quantitative expression of an atmospheric refractive index structure constant representing turbulence intensity, and determining a statistical model of the OAM factor of the FSO system by combining the uniformly-described probability density function of OAM factor statistical distribution in the FSO system attenuated to GGD and exponential distribution obtained in the steps 2a) and 2 b).
In the step 2C), the certain turbulence range is the refractive index structure constant C under the condition of
Further, in the step 3), an optimization problem and an optimization algorithm for solving the statistical model parameters of the OAM factors in the FSO system are given, and the optimization is realized by the following steps:
3a) and (2) according to the empirical probability density function generated in the step 1), combining the statistical model of the OAM factors in the FSO system in a certain turbulence condition range in the step 2), and providing the optimization problem of solving the statistical model parameters of the OAM factors in the FSO system under the conditions of probability density function types of OAM factor statistical distribution in different FSO systems and OAM transfer intervals.
3b) Decomposing the optimization problem of solving the statistical model parameters of the OAM factors in the FSO system in the step 3a) under the conditions of the probability density function types of the OAM factor statistical distribution and the OAM transfer intervals in different FSO systems, and providing an optimization algorithm for solving the statistical model parameters of the OAM factors in the FSO system and solving the optimization algorithm.
Further, in the step 4), the QPSK modulation OAM multiplexing FSO system bit error rate expression is implemented by the following steps:
4a) providing a signal-to-noise ratio expression of a QPSK modulation OAM multiplexing FSO system considering noise influence;
4b) and giving an error rate expression.
The invention has the following advantages:
the invention firstly provides a statistical model for describing OAM attenuation and crosstalk factors in an FSO system under the atmospheric weak turbulence condition, and probability density function parameters in the statistical model can be expressed by turbulence intensity. Furthermore, after the statistical model is obtained, the statistical information of OAM attenuation and crosstalk factors can be directly obtained through the statistical model, and multiple times of simulation calculation are not needed. Therefore, the method provides great convenience for researching the performance of the FSO system related to OAM.
Drawings
Fig. 1 is an OAM multiplexing transport model of an FSO communications system;
fig. 2a), 2b) and 2c) are comparison graphs of probability distribution and exponential distribution fitting of the GGD fitting based on OAM attenuation and crosstalk factors under the atmospheric turbulence condition of the FSO communication system under three different OAM transfer interval conditions, respectively;
3a), 3b) and 3c) are respectively a comparison graph of probability density functions and probability distributions obtained by data based on OAM attenuation and crosstalk factors under atmospheric turbulence conditions of an FSO communication system, which are obtained by model calculation under three different OAM transfer interval conditions;
fig. 4a) and 4b) are respectively a comparison graph of error rates of different channels of an OAM multiplexing FSO communication system under two different turbulence conditions;
fig. 5a) and 5b) are respectively comparison graphs of different channel error rates of the OAM multiplexing FSO communication system under two different average signal-to-noise ratios.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the following detailed description is further provided in conjunction with the accompanying drawings and the detailed description. The present embodiment is merely illustrative of the principles of the present invention and does not represent any limitation of the present invention.
The invention discloses a calculation method for researching the turbulence intensity influence system performance based on atmospheric weak turbulence, which is characterized by comprising the following steps:
step 1: and on the basis of an atmospheric turbulence transmission model, computing an OAM factor in the FSO system by performing filter decomposition on the received LG light, performing simulation for many times, and computing an empirical probability density function of the LG light on the basis of nonparametric estimation of probability density.
The OAM factor is calculated by the following method:
1a) giving an expression of LG in a light source
1b) The OAM factor calculation expression from M to n is as follows:
wherein
Step 2: giving a probability density function of OAM factor statistical distribution in the FSO system; fitting probability density functions of OAM factor statistical distribution in the FSO system proposed under different transfer intervals, OAM modes and turbulence conditions to obtain influences of parameters on the statistical distribution, and establishing a quantitative relation between probability density function parameters and turbulence intensity in a certain turbulence condition range to obtain a statistical model of the OAM factors in the FSO system;
the probability density function for describing OAM factor statistical distribution in the FSO system is given by the following steps:
2a) unified OAM factor statistics in description FSO systemThe probability density function of the cloth is a mixture index Generalized Gamma distribution function (EGG the mixed Exponential-Generalized Gamma distribution)
Wherein the content of the first and second substances,which represents the OAM factor, is the value of,
2b) The method comprises the following steps of providing a simplified form of a probability density function of OAM factor statistical distribution in an FSO system under different OAM transfer interval conditions;
when m-n is more than or equal to 1, attenuating to probability density function of OAM factor statistical distribution in FSO system of GGD
Wherein | m-n | is an OAM transfer interval;
when m-n is more than or equal to 2, attenuating to probability density function of OAM factor statistical distribution in FSO system of exponential distribution
Further, establishing a quantitative relation between the probability density function parameter and the turbulence intensity within a certain turbulence condition range to obtain a statistical model of the OAM factor in the FSO system:
2c) and (3) in a certain turbulence condition range, giving a quantitative expression of an atmospheric refractive index structure constant representing turbulence intensity, and determining a statistical model of the OAM factor of the FSO system by combining the uniformly-described probability density function of OAM factor statistical distribution in the FSO system attenuated to GGD and exponential distribution obtained in the steps 2a) and 2 b).
The above-mentioned certain turbulence range means: calculating the refractive index structure constant under weak turbulence conditionAnd dividing the range by orders of magnitude.
When m-n is 0, the quantitative relational expression between the probability density function parameter and the turbulence intensity is:
wherein m is the number of OAM modes before transmission,
When the probability density function of OAM factor statistical distribution in the FSO system is attenuated to GGD and | m-n | ≧ 1, the quantitative relational expression between the probability density function parameter and the turbulence intensity is:
wherein n is the OAM mode number after transmission,
When the probability density function of OAM factor statistical distribution in the FSO system is attenuated to exponential distribution, the quantitative relational expression between the probability density function parameter and the turbulence intensity is as follows:
wherein the content of the first and second substances,is a quantitative expression parameter; the formula (3) and the formula (12) form a statistical model of the OAM factors in the FSO system when the probability density function of the OAM factor statistical distribution in the FSO system is attenuated to exponential distribution.
And step 3: based on a least square method, an optimization problem and an optimization algorithm for solving the statistical model parameters of the OAM factors in the FSO system are given, the statistical model parameters of the OAM factors in the FSO system are solved, and the reliability of the statistical model of the OAM factors in the FSO system under different OAM transfer intervals, OAM modes and turbulence conditions is verified through a back substitution result;
the optimization problem and the optimization algorithm for solving the statistical model parameters of the OAM factors in the FSO system are given, the statistical model parameters of the OAM factors in the FSO system are solved, and the method comprises the following steps:
3a) according to the empirical probability density function generated in the step 1), combining the statistical model of the OAM factors in the FSO system in a certain turbulence condition range in the steps 2a) to 2c), and providing the optimization problem of solving the statistical model parameters of the OAM factors in the FSO system under the probability density function types of the OAM factor statistical distribution in different FSO systems and different OAM transfer interval conditions based on the least square method:
when | m-n | ═ 0, the optimization problem of solving the statistical model parameters of the OAM factors in the FSO system is as follows:
wherein the content of the first and second substances,
When the probability density function of OAM factor statistical distribution in the FSO system is attenuated to GGD and | m-n | ≧ 1, the optimization problem of solving the statistical model parameters of the OAM factor in the FSO system is as follows:
wherein a, b, c are determined by the formulae (9) to (11),
When the probability density function of OAM factor statistical distribution in the FSO system is attenuated to exponential distribution, the optimization problem of the statistical model parameters of the OAM factor in the FSO system is solved as follows:
wherein b is determined by the formula (12),namely, equation (3).
3b) Decomposing the optimization problem of solving the statistical model parameters of the OAM factors in the FSO system in the step 3a) under the probability density function type condition of the OAM factor statistical distribution in different FSO systems, and providing an optimization algorithm for solving the statistical model parameters of the OAM factors in the FSO system and solving the optimization algorithm.
When | m-n | ═ 0, the optimization problem of solving the statistical model parameters of OAM factors in the FSO system according to equation (13) can be decomposed into two parts:
a first part:
whereinjc＝1,2,...,NcProbability density function parameter for OAM factor statistical distribution in FSO system
A second part:
and when the | m-n | ═ 0, solving an optimization algorithm of the statistical model parameters of the OAM factors in the FSO system:
according to the formula (16), firstly, calculating
In the formula (16), settingAnd calculatejc＝1,2,...,NcThen calculated according to (21)
In the formula (16), setting
In the formula (16), settingAndand calculatejc＝1,2,...,NcThen calculated according to the formulas (18) and (19)
When the probability density function of OAM factor statistical distribution in the FSO system is attenuated to GGD and | m-n | ≧ 1, the optimization problem of solving the statistical model parameters of the OAM factor in the FSO system according to the formula (14) can be decomposed into two parts:
a first part:
wherein
A second part:
when the probability density function of OAM factor statistical distribution in the FSO system is attenuated to GGD and | m-n | ≧ 1, the optimization algorithm for solving the statistical model parameters of the OAM factor in the FSO system:
according to the formula (22)Calculating a from (23)m→n；
In the formula (22) are such that
Respectively calculated according to the formulas (24) and (25)
when the probability density function of the statistical distribution of the OAM factors in the FSO system decays to exponential distribution, the optimization problem of solving the statistical model parameters of the OAM factors in the FSO system according to the formula (15) can be decomposed into two parts:
a first part:
whereinAs a statistical distribution parameter of the OAM attenuation factor, i.e. whenParameters of equation (3).
A second part:
when the probability density function of the OAM factor statistical distribution in the FSO system is attenuated to the exponential distribution, the optimization algorithm for solving the statistical model parameters of the OAM factor in the FSO system is as follows:
firstly, the formula (26) is solved to obtainThen, the formula (27) is solved to obtain the parameters
For the solving methods of equations (13) - (27), a confidence domain algorithm and a maximum likelihood algorithm can be used for solving.
And 4, step 4: based on a statistical model of OAM factors in the FSO system, combining a QPSK modulation OAM multiplexing FSO system transmission model, deducing a system error rate expression, simulating and verifying the practicability of the statistical model of the OAM factors in the FSO system, bringing turbulence intensity into the obtained error rate expression, and comparing the influence of different turbulence intensities on the system performance.
The transmission model of the QPSK modulation OAM multiplexing FSO system is as follows:
let s (t) be the transmission signal, g (t) be the reception signal, QPSK modulation OAM multiplexing FSO system
wherein the content of the first and second substances,is as followsThe number of OAM modes of a channel,is in OAM modeToP is the transmitted optical power, ζ is the photoelectric conversion coefficient, n (t) is the variance σ2White gaussian noise.
The QPSK modulation OAM multiplexing FSO system bit error rate expression is realized by the following steps:
4a) a signal-to-noise ratio expression of the QPSK modulation OAM multiplexing FSO system considering noise influence;
wherein the content of the first and second substances,
4b) First, theBit error rate expression for each channel:
the correctness and advantages of the invention can be further illustrated by comparing the following theoretical results:
in the method, the solution optimization process is carried out through MATLAB, and Monte Carlo is used for simulation verification.
Firstly, the proposed method of calculating OAM factors is accurately described; then, under different turbulence conditions, the degree of fitting of the EGG and the GGD to the probability distribution of the attenuation factors is compared; thirdly, under different turbulence conditions, the degree of fitting of the EGG and the exponential distribution function to the probability distribution of the crosstalk factors is compared; secondly, comparing the probability density function and the simulation data of the OAM factors obtained by model calculation under different OAM transfer intervals and turbulence conditions; meanwhile, under the condition of turbulence, the influence of different channels and average signal-to-noise ratio on the bit error rate of the OAM multiplexing FSO communication system is researched; and finally, under the conditions of different signal-to-noise ratios, the influence of turbulence on the error code performance of the system is researched.
Theoretical and simulation results
Fig. 1 shows a diagram of an OAM multiplexing transmission model under atmospheric turbulence conditions in an FSO communications system. Fig. 2a), 2b) and 2c) respectively show the probability distribution and exponential distribution fitting effects of the GGD fitting based on OAM attenuation and crosstalk factors under the atmospheric turbulence condition of the FSO communication system under three different OAM transfer interval conditions. From fig. 2a) it can be seen that the EGG distribution fits well to the PDF of the OAM attenuation factor and has a better matching degree compared to the GGD function. It can be seen from fig. 2b) that when the OAM transfer interval is 1, the GGD function can well fit the PDF of the OAM crosstalk factor, and has a better fitting effect than the exponential distribution function. From fig. 2c) it can be seen that the exponential distribution function and the GGD function both fit the PDF of the OAM crosstalk factor well when the OAM transfer interval is 2. Whereas the GGD function is a special case of the EGG distribution function, while the exponential distribution function is a special case of the GGD function. Thus, the EGG function may uniformly represent the statistical distribution of OAM attenuation and crosstalk factors, which gradually decays from EGG to GGD, exponential, when the OAM transfer interval is gradually increased from 0 to 1, or even 2. Fig. 3a), 3b) and 3c) respectively show probability density functions of OAM attenuation and crosstalk factors based on the atmospheric turbulence condition of the FSO communication system, which are obtained by model calculation under three different OAM transfer interval conditions. It can be seen that under different OAM transfer intervals, turbulence intensity and OAM mode numbers, the OAM attenuation and crosstalk factor statistical distribution function obtained by model calculation can well represent the statistical characteristics of simulation data. Fig. 4a) and 4b) show different channel error rates of the OAM mode {3,4,5,6} multiplexing FSO communication system under two different turbulence conditions. It can be seen that under the same conditions, the turbulence intensity is increased to reduce the system performance, and the average signal-to-noise ratio is increased to improve the system performance. And as the average signal-to-noise ratio increases, the error rate of
The present invention is not limited to the above-mentioned embodiments, and based on the technical solutions disclosed in the present invention, those skilled in the art can make some substitutions and modifications to some technical features without creative efforts according to the disclosed technical contents, and these substitutions and modifications are all within the protection scope of the present invention.
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