A method and system for estimating parameters of atmospheric turbulence light intensity scintillation model

Abstract

The present invention discloses an atmospheric turbulence light intensity flicker model parameter estimation method, system, device and medium, and relates to the fields of free space optical communication technology and free space quantum communication technology, including: obtaining multiple channel sampling values ​​of atmospheric turbulence, and obtaining initial channel parameters of the channel sampling values; generating multiple groups of light intensity flicker samples according to the estimated channel parameters, and obtaining the light intensity flicker estimation model of each group of light intensity flicker samples by using the nearest neighbor density estimation method; eliminating data that are not within the light intensity flicker sample range in the channel sampling values, and inputting the remaining data into the light intensity flicker estimation model to obtain the average log-likelihood function value; iterating the step of obtaining the average log-likelihood function value, and using the gradient descent method to iterate the values ​​and channel parameters, and obtaining the maximum average log-likelihood function value and channel parameter value. The present invention achieves a trade-off between estimation accuracy and computational complexity, and improves the efficiency of parameter estimation of different channel models.

Description

Technical Field

[0001] The present invention relates to the fields of free-space optical communication technology and free-space quantum communication technology, and in particular to a method and system for estimating parameters of an atmospheric turbulence light intensity scintillation model. Background Art

[0002] With the continuous development of society and the rapid advancement of science and technology, traditional ground communication technology has shortcomings in wide-area coverage, low latency and high-bandwidth transmission, which has led to the development of integrated space-ground communication. In recent years, communication systems based on optical carriers have developed rapidly on free-space channels. In satellite-to-ground laser or optical quantum communications, there is an atmosphere more than 20 kilometers thick. The random changes in temperature and pressure in space will produce atmospheric turbulence, which in turn causes random changes in the refractive index, and ultimately causes the power of light to propagate to the receiving end when it passes through the atmospheric channel. This fading effect is called scintillation. Due to the wave-particle duality of light, the interaction between quantum signals and atmospheric turbulence is consistent with classical light, so the model of the quantum light efficiency at the receiving end changing with time is consistent with classical light.

[0003] In order to effectively evaluate the performance of actual free-space channels and optical quantum communication systems, researchers have proposed many light intensity flicker models, and compared and discussed the adaptability of light intensity flicker models in detail. According to the number of parameters used to determine the model, the existing light intensity flicker models can be divided into single-parameter models, dual-parameter models, and multi-parameter models. Among the single-parameter turbulence models, the lognormal model and the negative exponential model are commonly used, and their scope of application is limited to the weak turbulence and strong turbulence limit areas. Among the dual-parameter turbulence models, the light intensity flicker Gamma-Gamma model and the wireless channel Lognormal-Rician model are commonly used. They have the ability to adapt to the range of changes from weak turbulence to strong turbulence. In some channel scenarios, such as large aperture reception or when the laser transmission mode is spherical wave propagation, the Lognormal-Rician model is more accurate than the Gamma-Gamma model. The multi-parameter turbulence model includes the Malaga model (five-parameter model). Generally speaking, the more complex the light intensity flicker model is, the wider its adaptability and channel conditions are. Since the light intensity flicker model parameters need to be estimated when evaluating the actual system performance, the two-parameter turbulence model is the most studied in terms of trade-offs between complexity and model accuracy.

[0004] In the dual-parameter turbulence model, the parameter estimation of the Gamma-Gamma channel includes moment estimation, expected maximum algorithm, fractional order moment estimation, etc., and the estimation methods of the Lognormal-Rician include generalized order moment estimation method, expected maximum algorithm and saddle point approximation algorithm. However, the parameter estimation method used in the existing dual-parameter turbulence model involves complex functions or integral operations when obtaining a high-precision model, which will cause the estimation process to become complicated, which is not conducive to parameter estimation of different channel models through the model, and even cannot accurately and effectively evaluate the performance of free space channels and optical quantum communication systems. Summary of the invention

[0005] The purpose of the present invention is to address the deficiencies of the above-mentioned prior art and to provide a method and system for estimating the parameters of an atmospheric turbulence light intensity scintillation model, so as to solve the problem that the existing estimation methods in the prior art involve complex functions or integral operations, which will cause the estimation process to become complicated, making it difficult to estimate the parameters of different channel models through the model, and even making it impossible to accurately and effectively evaluate the performance of free space channels and optical quantum communication systems.

[0006] The present invention specifically provides the following technical solution: a method for estimating parameters of an atmospheric turbulence light intensity scintillation model, comprising the following steps:

[0007] Acquire multiple channel sampling values ​​of atmospheric turbulence, and acquire initial channel parameters of the multiple channel sampling values;

[0008] Generate multiple groups of light intensity flicker samples according to the initial channel parameters and the sample number L value, and use the k-nearest neighbor density estimation method to obtain the light intensity flicker estimation model of each group of light intensity flicker samples;

[0009] Eliminate the data that are not in the range of the minimum value to the maximum value of each group of light intensity flicker samples from the channel sampling values, input the remaining channel sampling values ​​into the light intensity flicker estimation model, obtain the log-likelihood function value of each group of light intensity flicker samples, and average multiple log-likelihood function values;

[0010] Iterate the steps of obtaining the average log-likelihood function value to obtain the maximum average log-likelihood function value, and represent the channel parameter value of the light intensity flicker estimation model through the maximum average log-likelihood function value;

[0011] The method of obtaining a plurality of channel sampling values ​​of atmospheric turbulence and obtaining initial channel parameters of the plurality of channel sampling values ​​is specifically as follows:

[0012] Get the parameters r,σ in the channel sampling value z The initial estimate expression of Specifically:

[0013]

[0014] Where, I[l] represents the lth atmospheric turbulence channel sampling value obtained by the photoelectric detector, satisfying I[1]≤I[2]≤…≤I[M], M represents the total sampling size, 1 and 2 represent the first and second sampling samples;

[0015] The method of generating a plurality of groups of light intensity flicker samples according to the initial channel parameters and the sample number L value comprises:

[0016] The specific expressions of multiple groups of light intensity flicker samples are:

[0017]

[0018] where z i [j] The subscript i represents the i-th group of light intensity flicker samples, i∈[1,2,…,N], N represents the total number of groups of light intensity flicker samples, j represents the j-th sample, j∈[1,2,…,L], and each light intensity flicker sample obeys the parameter Lognormal-Rician distribution, L represents the number of light intensity flicker samples in each group;

[0019] The method of obtaining a light intensity flicker estimation model for each group of light intensity flicker samples by using a k-nearest neighbor density estimation method comprises:

[0020] For any set of light intensity flicker sample data, take the i-th set as an example. i [1],z i [2],…,z i [L], using the k nearest neighbor density estimation method and the current k value to obtain the sample point z i [j] Density estimation for:

[0021]

[0022] The variables Γ is the gamma function, d represents the dimension of each data sample, for the Lognormal-Rician channel, d = 1, Represents the sequence z i [1],z i [2],…,z i [L] in z i [j] The kth distance value closest to the target;

[0023] For data points Perform linear interpolation to obtain the light intensity flicker estimation model and obtain the log-likelihood function value f of the light intensity flicker estimation model i (z);

[0024] The data that is not in the range of the minimum value to the maximum value of each group of light intensity flicker samples in the channel sampling values ​​are removed, and the remaining channel sampling values ​​are input into the light intensity flicker estimation model to obtain the logarithmic likelihood function value of each group of light intensity flicker samples, and the multiple logarithmic likelihood function values ​​are averaged, specifically:

[0025] For the i-th group, z i [1],z i [2],…,z i [L], channel sampling sequence After elimination, we get Said satisfy:

[0026] z i [1]≤I[j]≤I[j+1]≤…≤I[O]≤z i [M];

[0027] Where M is the total sample size; for any set of light intensity flicker samples z i [j], satisfying z i [j]≤z i [O], O represents the maximum number of light intensity flicker samples after elimination, and n is the number of samples;

[0028] Will Substitute into f i (z) and calculate the average log-likelihood function value LLR for each group i , the specific expression is:

[0029]

[0030] Among them, c i is the normalization factor, and the specific expression is:

[0031]

[0032] If the light intensity flicker samples are N groups, the average log-likelihood function value LLR is:

[0033]

[0034] The steps of obtaining the average log-likelihood function value are iterated to obtain the maximum average log-likelihood function value, and the channel parameter value of the light intensity flicker estimation model is represented by the maximum average log-likelihood function value, including:

[0035] The k value and channel parameters are iterated by the gradient descent method to obtain the maximum average log-likelihood function value. The specific expression is:

[0036]

[0037] By differentiating the maximum average log-likelihood function value, the first-order derivatives of each parameter k, r, and σ are approximately obtained, specifically:

[0038]

[0039] In the formula, k (j) ,r (j) ,σ (j) represents the j-th estimation result.

[0040] The present invention also includes an atmospheric turbulence light intensity scintillation model parameter estimation system, comprising:

[0041] An acquisition module, used for acquiring multiple channel sampling values ​​of atmospheric turbulence and acquiring initial channel parameters of the multiple channel sampling values;

[0042] A model acquisition module is used to generate multiple groups of light intensity flicker samples according to the initial channel parameters and the sample number L value, and obtain a light intensity flicker estimation model for each group of light intensity flicker samples using a k-nearest neighbor density estimation method;

[0043] An average processing module is used to remove data from the channel sampling values ​​that are not in the range from the minimum value to the maximum value of each group of light intensity flicker samples, input the remaining channel sampling values ​​into the light intensity flicker estimation model, obtain the logarithmic likelihood function value of each group of light intensity flicker samples, and average multiple logarithmic likelihood function values;

[0044] An estimation module, used for iterating the step of obtaining an average of log-likelihood function values ​​to obtain a maximum average log-likelihood function value, and representing a channel parameter value of a light intensity flicker estimation model through the maximum average log-likelihood function value;

[0045] The method of obtaining a plurality of channel sampling values ​​of atmospheric turbulence and obtaining initial channel parameters of the plurality of channel sampling values ​​is specifically as follows:

[0046] Get the parameters r,σ in the channel sampling value z The initial estimate expression of Specifically:

[0047]

[0048] Wherein, I[l] represents the lth atmospheric turbulence channel sampling value obtained by the photoelectric detector, satisfying I[1]≤I[2]≤…≤I[l]≤…≤I[M], M represents the total sampling size, 1 and 2 represent the first and second sampling samples;

[0049] The method of generating a plurality of groups of light intensity flicker samples according to the initial channel parameters and the sample number L value comprises:

[0050] The specific expressions of multiple groups of light intensity flicker samples are:

[0051]

[0052] where z i [j] The subscript i represents the i-th group of light intensity flicker samples, i∈[1,2,…,N], N represents the total number of groups of light intensity flicker samples, j represents the j-th sample, j∈[1,2,…,L], and each light intensity flicker sample obeys the parameter Lognormal-Rician distribution, L represents the number of light intensity flicker samples in each group;

[0053] The light intensity flicker estimation model of each group of light intensity flicker samples is obtained by using the k-nearest neighbor density estimation method, including:

[0054] For any set of light intensity flicker sample data, take the i-th set as an example. i [1],z i [2],…,z i [L], using the k nearest neighbor density estimation method and the current k value to obtain the sample point z i [j] Density estimation for:

[0055]

[0056] The variables Γ is the gamma function, d represents the dimension of each data sample, for the Lognormal-Rician channel, d = 1, Represents the sequence z i [1],z i [2],…,z i [L] in z i [j] The kth distance value closest to the target;

[0057] For data points Perform linear interpolation to obtain the light intensity flicker estimation model and obtain the log-likelihood function value f of the light intensity flicker estimation model i (z);

[0058] The data that is not in the range of the minimum value to the maximum value of each group of light intensity flicker samples in the channel sampling values ​​are removed, and the remaining channel sampling values ​​are input into the light intensity flicker estimation model to obtain the logarithmic likelihood function value of each group of light intensity flicker samples, and the multiple logarithmic likelihood function values ​​are averaged, specifically:

[0059] For the i-th group, z i [1],z i [2],…,z i [L], channel sampling sequence After elimination, we get Said satisfy:

[0060] z i [1]≤I[j]≤I[j+1]≤…≤I[O]≤z i [M];

[0061] Where M is the total sample size; for any set of light intensity flicker samples z i [j], satisfying z i [j]≤z i [O], O represents the maximum number of light intensity flicker samples after elimination, and n is the number of samples;

[0062] Will Substitute into f i (z) and calculate the average log-likelihood function value LLR for each group i , the specific expression is:

[0063]

[0064] Among them, c i is the normalization factor, and the specific expression is:

[0065]

[0066] If the light intensity flicker samples are N groups, the average log-likelihood function value LLR is:

[0067]

[0068] The step of iterating the average log-likelihood function value to obtain the maximum average log-likelihood function value, and characterizing the channel parameter value of the light intensity flicker estimation model by the maximum average log-likelihood function value, comprises:

[0069] The k value and channel parameters are iterated by the gradient descent method to obtain the maximum average log-likelihood function value. The specific expression is:

[0070]

[0071] By differentiating the maximum average log-likelihood function value, the first-order derivatives of each parameter k, r, and σ are approximately obtained, specifically:

[0072]

[0073] In the formula, k (j) ,r (j) ,σ (j) represents the j-th estimation result.

[0074] The present invention provides a storage medium on which a computer program is stored. When the computer program is executed by a processor, the steps of the above-mentioned atmospheric turbulence light intensity scintillation model parameter estimation method are implemented.

[0075] The present invention provides a computer device, comprising a memory and a processor, wherein a program is stored in the memory, and when the program is executed by the processor, the processor executes the steps of the above-mentioned atmospheric turbulence light intensity scintillation model parameter estimation method.

[0076] Compared with the prior art, the present invention has the following significant advantages:

[0077] The present invention estimates the parameters of the light intensity flicker model based on the idea of ​​light intensity flicker samples. During operation, the parameters are not directly estimated according to the specific expression of probability density, but multiple groups of light intensity flicker samples are generated according to the initial channel parameters and the sample number L value, and the data that is not within the light intensity flicker sample range in the channel sampling value is eliminated, so as to obtain high-quality channel sampling values, improve the accuracy of the estimated data, and input the high-quality channel sampling values ​​into the respectively selected light intensity flicker estimation models, output the log-likelihood function value of each group of light intensity flicker samples, and obtain the maximum average log-likelihood function value and channel parameter value through iteration, so as to achieve the effect of directly estimating the log-likelihood function value of each point based on each group of light intensity flicker sample data, avoid the complex functions or integral operations involved in the parameter estimation, achieve the trade-off between the estimation accuracy and the computational complexity, improve the efficiency of the atmospheric turbulence light intensity flicker model parameter estimation, and further improve the accuracy and effect of the free space channel and the optical quantum communication system performance evaluation. BRIEF DESCRIPTION OF THE DRAWINGS

[0078] Figure 1 The present invention provides a simulation diagram of the maximum likelihood based on k nearest neighbors and the minimum KL divergence based on k nearest neighbors in a Lognormal-Rician turbulent channel, and the simulation parameters are L=M=10 4 ,N=50, the number of trials is 30 to calculate the MSE performance;

[0079] Figure 2 The present invention provides a simulation diagram of the maximum likelihood based on k nearest neighbors and the minimum KL divergence based on k nearest neighbors in a Lognormal-Rician turbulent channel, and the simulation parameters are L=M=5×10 4 ,N=50, the number of trials is 30 to calculate the MSE performance;

[0080] Figure 3The present invention provides a simulation diagram of the maximum likelihood based on k nearest neighbors and the minimum KL divergence based on k nearest neighbors in a Lognormal-Rician turbulent channel, and the simulation parameters are L = M = 1 × 10 5 ,N=50, the number of trials is 30 to calculate the MSE performance;

[0081] Figure 4 The present invention provides a simulation diagram of the maximum likelihood based on k nearest neighbors and the minimum KL divergence based on k nearest neighbors in a Lognormal-Rician turbulent channel, with simulation parameters of R=4, L=M=1×10 4 ,N=50, the number of trials is 30 to calculate the MSE performance;

[0082] Figure 5 A flow chart of a method for estimating parameters of an atmospheric turbulence light intensity scintillation model according to the present invention;

[0083] Figure 6 This is a second flow chart of a method for estimating parameters of an atmospheric turbulence light intensity scintillation model according to the present invention. DETAILED DESCRIPTION

[0084] The following is a clear and complete description of the technical solutions of the embodiments of the present invention in conjunction with the drawings in the present invention. Obviously, the described embodiments are part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work should fall within the scope of protection of the present invention.

[0085] For the light intensity flicker model generated by the atmospheric turbulence effect, a two-parameter model is commonly used from the perspectives of model accuracy and model complexity, which are the light intensity flicker Gamma-Gamma model and the wireless channel Lognormal-Rician model. Since the Lognormal-Rician model is more adaptable to a wider channel range than the Gamma-Gamma model, the implementation steps of the present invention are described below using the Lognormal-Rician model as an example.

[0086] The probability density function expression of the Lognormal-Rician light intensity flicker model is:

[0087]

[0088] There are currently three methods for estimating the parameters of the Lognormal-Rician light intensity scintillation model, which are described in detail as follows.

[0089] (1) Prior art solution 1, generalized moment estimation method: X. Song and J. Cheng, ``Joint estimation of the Lognormal-Rician atmospheric turbulence model by the generalized method of moments, ” Opt. Commun., vol. 285, no. 24, pp. 4727-4732, Nov. 2012.

[0090] Step 1: Calculate the moments α1, α2, …, α of the sample values ​​I[1], I[2], …, I[M] s ,Right now:

[0091]

[0092] The error between the theoretical n-th order central moment is expressed as:

[0093] The expression of the n-th order central moment is:

[0094]

[0095] Step 2: Let the weight matrix W (0) =I s (s-dimensional identity matrix), solve the following optimization function to obtain channel parameter estimation The initial value of:

[0096]

[0097] Step 3: Using Initial Estimates Calculate the residual vector, which is expressed as:

[0098]

[0099] And based on the residual vector, calculate the autocovariance matrix:

[0100]

[0101] Thus we get g s The covariance matrix of (θ) can be estimated as:

[0102]

[0103] Let the weight coefficient w j =1-j / (l+1), update the weight matrix W (1) =S -1 .

[0104] Step 4: Solve the following optimization function Get the update of θ Repeat steps 3 and 4, and finally get Estimates.

[0105] (2) Prior Art Solution 2: L. Yang, J. Cheng, and JF Holzman, ``Maximum likelihood estimation of the Lognormal-Rician FSO channel model, IEEE

[0106] Photon.Technol.Lett.,vol.27,no.15,pp.1656-1659,Aug.1,2015.

[0107] Step 1: Initialize parameter estimates in The expression is:

[0108]

[0109] Step 2: Calculate the mean of the following function:

[0110]

[0111] In the formula, I={I[1],I[2],…,I[M]}, z={z[1],z[2],…,z[M]}.

[0112] Step 3: Update parameters in The expressions are:

[0113]

[0114] Repeat steps 2 and 3, and finally get Estimates.

[0115] (3) Existing technology solution 3: MKMiao, and XFLi, ``Parameter Estimation of the Lognormal-Rician Channel Model Using Saddlepoint Approximation, IEEE Access, vol. 8, pp. 152924-152931, 2020.

[0116] Step 1: Initialize parameter estimates in The expression is:

[0117]

[0118] Step 2: Sort the sample values ​​I = {I[1], I[2], ..., I[M]} from small to large, recorded as sequence C = {C[1], C[2], ..., C[M]}, and find the saddle point S[l] of the following function for each sample C[l], that is

[0119] The variables The expression is:

[0120]

[0121] Step 3: Substitute C[l] and saddle point S[l] into the following function to obtain the density approximation f(·):

[0122]

[0123] Then use linear interpolation to get the normalization factor c according to the following formula:

[0124]

[0125] Step 4: Calculate the approximate log-likelihood function

[0126]

[0127] Step 5: Solving Forward and backward differences And use the gradient descent method to iterate the parameters.

[0128] like Figure 5 As shown, the present invention provides a method for estimating parameters of an atmospheric turbulence light intensity scintillation model, specifically:

[0129] Step S1: Acquire multiple channel sampling values ​​of atmospheric turbulence, and acquire initial channel parameters of the multiple channel sampling values.

[0130] Step S1 is as follows: after obtaining the atmospheric turbulence channel sampling values, sort them from small to large, and use the moment estimation method and the light intensity flicker theoretical model to obtain the initial channel parameters, wherein the parameters r, σ in the channel sampling values ​​are obtained. z The initial estimate expression of Specifically:

[0131]

[0132] Wherein, I[l] represents the lth atmospheric turbulence channel sampling value obtained by the photoelectric detector, satisfying I[1]≤I[2]≤…≤I[M], M represents the total sampling size, and 1 and 2 represent the first and second sampling samples.

[0133] Step S2: Generate multiple groups of light intensity flicker samples according to the initial channel parameters and the sample number L value, and use the k-nearest neighbor density estimation method to obtain the light intensity flicker estimation model of each group of light intensity flicker samples.

[0134] Generate multiple groups of light intensity flicker samples according to the initial channel parameters and the sample number L value, including:

[0135] According to the estimated channel parameters, the receiving end processor generates multiple groups of light intensity flicker samples. Each group of generated light intensity flicker samples is sorted in ascending order from small to large. The specific expressions of the multiple groups of light intensity flicker samples are:

[0136]

[0137] where z i [j] The subscript i represents the i-th group of light intensity flicker samples, i∈[1,2,…,N], N represents the total number of groups of light intensity flicker samples, j represents the j-th sample, j∈[1,2,…,L], and each light intensity flicker sample obeys the parameter Lognormal-Rician distribution, L represents the number of light intensity flicker samples in each group.

[0138] The light intensity flicker estimation model of each group of light intensity flicker samples is obtained by using the k-nearest neighbor density estimation method, including:

[0139] For any set of light intensity flicker sample data, take the i-th set as an example. i [1],z i [2],…,z i [L], using the k nearest neighbor density estimation method and the current k value to obtain the sample point z i [j] Density estimation for:

[0140]

[0141] The variables Γ is the gamma function, d represents the dimension of each data sample, for the Lognormal-Rician channel, d = 1, Represents the sequence z i [1],z i [2],…,z i [L] in z i [j] The kth distance value closest to it.

[0142] For data points Perform linear interpolation to obtain the light intensity flicker estimation model and obtain the log-likelihood function value f of the light intensity flicker estimation model i (z), and integrate the interpolated curve to obtain the current normalization factor c using the following formula: i , specifically:

[0143]

[0144] Step S3: Eliminate the data in the channel sampling values ​​that are not in the range of the minimum value to the maximum value of each group of light intensity flicker samples, input the remaining channel sampling values ​​into the light intensity flicker estimation model, obtain the logarithmic likelihood function value of each group of light intensity flicker samples, and average multiple logarithmic likelihood function values. Specifically:

[0145] For the i-th group, z i [1],z i [2],…,z i [L], channel sampling sequence After elimination, we get satisfy:

[0146] z i [1]≤I[j]≤I[j+1]≤…≤I[O]≤z i [M];

[0147] Where M is the total sample size; for any set of light intensity flicker samples z i [j], satisfying z i [j]≤z i [O], O represents the maximum number of light intensity flicker samples after elimination, and n is the number of samples.

[0148] Will Substitute into f i (z) and calculate the average log-likelihood function value LLR for each group i , the specific expression is:

[0149]

[0150] Therefore, if the light intensity flicker samples are N groups, the average log-likelihood function value is:

[0151]

[0152] in, is the log-likelihood function value.

[0153] Step S4: iterate the step of averaging the log-likelihood function values ​​to obtain the maximum average log-likelihood function value, and use the maximum average log-likelihood function value to represent the channel parameter value of the light intensity flicker estimation model.

[0154] S4 includes:

[0155] The k value and channel parameters are iterated by the gradient descent method to obtain the maximum average log-likelihood function value. The specific expression is:

[0156]

[0157] By differentiating the maximum average log-likelihood function value, the first-order derivatives of each parameter k, r, and σ are approximately obtained, specifically:

[0158]

[0159] In the formula, k (j) ,r (j) ,σ (j) represents the j-th estimation result.

[0160] Figure 1 to Figure 4 By depicting the parameter estimation mean square error (MSE) performance in different scenarios, we can draw the following two important conclusions:

[0161] 1) The two parameter estimation methods based on data drive proposed in the present invention are feasible. With the increase of the number of sampled samples and the number of light intensity flicker samples, the parameter estimation MSE is improved. For the case of low sampled samples, for example, L = M = 10 4 , only when the signal amplitude r or variance When is small, the deviation between the estimated result and the true value will not be large.

[0162] 2) For data volume L = M = 10 4 ,5×10 4 , it can be found that the minimum KL divergence estimation method based on k nearest neighbors is The estimation performance is slightly better than the maximum likelihood estimation method based on k nearest neighbors. 5 , two methods Performance in 10 -3 Slight up and down fluctuation.

[0163] Table 1 compares in detail several estimation methods of the Lognormal-Rician light intensity flicker model.

[0164] Table 1 Comparison results between different estimation methods of Lognormal-Rician light intensity flicker model

[0165]

[0166]

[0167] The present invention also includes an atmospheric turbulence light intensity flicker model parameter estimation system, comprising: a collection module, a model acquisition module, an average processing module and an estimation module.

[0168] Among them, the acquisition module is used to obtain multiple channel sampling values ​​of atmospheric turbulence, and obtain the initial channel parameters of the multiple channel sampling values; the sorting module is used to generate multiple groups of light intensity flicker samples according to the initial channel parameters and the sample number L value, and use the k-nearest neighbor density estimation method to obtain the light intensity flicker estimation model of each group of light intensity flicker samples; the average processing module is used to eliminate the data in the channel sampling values ​​that are not in the range of the minimum value to the maximum value of each group of light intensity flicker samples, input the remaining channel sampling values ​​into the light intensity flicker estimation model, obtain the log-likelihood function value of each group of light intensity flicker samples, and average the multiple log-likelihood function values; the estimation module is used to iterate the step of obtaining the average log-likelihood function value, obtain the maximum average log-likelihood function value, and characterize the channel parameter value of the light intensity flicker estimation model by the maximum average log-likelihood function value.

[0169] The present invention provides a storage medium on which a computer program is stored. When the computer program is executed by a processor, the steps of a method for estimating parameters of an atmospheric turbulence light intensity scintillation model are realized.

[0170] According to the disclosed embodiments, the storage medium may be a non-volatile computer-readable storage medium, such as but not limited to: a portable computer disk, a hard disk, a random access memory (RAM), a read-only memory (ROM), an erasable programmable read-only memory (EPROM or flash memory), a portable compact disk read-only memory (CD-ROM), an optical storage device, a magnetic storage device, or any suitable combination thereof. In the present invention, the storage medium may be any tangible medium containing or storing a program that may be used by or in conjunction with an instruction execution system, apparatus, or device.

[0171] The present invention provides a computer device, comprising a memory and a processor. The memory stores a program, and when the program is executed by the processor, the processor executes the steps of a method for estimating parameters of an atmospheric turbulence light intensity flicker model.

[0172] In accordance with the disclosed embodiments, a computing device may communicate with one or more external devices (e.g., keyboards, pointing devices, Bluetooth communications, etc.), or with any device (e.g., routers, modems, etc.) that enables a computing device to communicate with one or more other computing devices.

[0173] like Figure 6As shown, the second estimation method of the atmospheric turbulence light intensity scintillation model parameters is introduced below, which is based on the minimum KL divergence estimation method of k nearest neighbors, including (1) verification of the light intensity scintillation theoretical model to see whether it satisfies four conditional expressions; (2) data operations between atmospheric turbulence channel sampling values ​​(data); (3) calculation of initial (channel) parameter estimates and k values ​​according to the theoretical model; (4) data operations between light intensity scintillation samples and atmospheric turbulence channel sampling values; (5) calculation of the average KL divergence between atmospheric turbulence channel sampling values ​​and generated light intensity scintillation samples. (6) Parameter iteration. The six steps are described in detail below. Specifically:

[0174] Step S1: Check whether η>2 exists so that the constructed light intensity flicker theoretical model satisfies four conditional expressions.

[0175] Among them, it is checked whether there is η>2 so that the constructed light intensity flicker theoretical model meets four conditions, specifically:

[0176]

[0177] Where p(x) and p(y) represent the light intensity flicker sampling model and the light intensity flicker generation model respectively. In the subsequent simulation results, they are both Lognormal-Rician models.

[0178] Step S2: Calculate the distance between each sampling value and other sampling values ​​according to the atmospheric turbulence channel sampling values, sort them from small to large and retain the kth one.

[0179] S2 is specifically:

[0180] Assumptions represents the M atmospheric turbulence channel sampling values ​​obtained by the photoelectric detector. For the nth data I[n], calculate D n =|I[n]-I[m]|,m={1,...,n-1,n+1,...,M}, for D n After sorting from small to large, take the kth distance and get the sequence ρ k,i .

[0181] Step S3: using the moment estimation method and the light intensity scintillation theoretical model to obtain the initial channel parameter estimation of the atmospheric turbulence channel sampling values.

[0182] S3 is specifically:

[0183]

[0184] Step S4: Based on the estimated channel parameters, the receiving end processor generates multiple groups of light intensity flicker samples, calculates the distance between each atmospheric turbulence channel sampling value and each group of generated light intensity flicker samples (or other sampling values), sorts them from small to large, and retains the kth value each time.

[0185] S4 is specifically:

[0186]

[0187] where z i [j] The subscript i represents the i-th group of light intensity flicker samples, which obeys the parameter Lognormal-Rician distribution. For the i-th group of light intensity flicker samples z i [1],z i [2],…,z i [L], calculate D for each sample value I[n] n =|I[n]-z i [m]|,m={1,...,L}, for D n After sorting from small to large, take the kth distance and record the resulting sequence as v k,i .

[0188] Step S5: Calculate the average KL divergence between the atmospheric turbulence channel sampling values ​​and the generated light intensity scintillation samples using a KL divergence estimator.

[0189] S5 is as follows:

[0190] The i-th group of light intensity flicker samples z i [1],z i [2],…,z i [L] and The KL divergence between is estimated as:

[0191]

[0192] Where d represents the dimension of each data sample. Therefore, for N sets of light intensity flicker sample sequences, the average KL divergence expression is:

[0193]

[0194] Step S6: Repeat steps S4-S5, and use the gradient descent method to iterate the k value and channel parameters to minimize the average KL divergence.

[0195] S6 is specifically:

[0196]

[0197] The above optimization problem can be solved using the gradient descent method. The first-order derivatives of each parameter k, r, σ can be approximated by their respective differences, which are:

[0198]

[0199] Where k (j) ,r (j) ,σ (j) represents the j-th estimation result.

[0200] Table 2 compares in detail several estimation methods of the Lognormal-Rician light intensity flicker model.

[0201] Table 2 Comparison results between different estimation methods of Lognormal-Rician light intensity flicker model

[0202]

[0203]

[0204] The above content is a further detailed description of the present invention in combination with a specific preferred embodiment. For technicians in the technical field to which the present invention belongs, several simple deductions or substitutions can be made without departing from the concept of the present invention, which should be regarded as belonging to the protection scope of the present invention.

Claims

1. A method for estimating parameters of an atmospheric turbulence light intensity scintillation model, characterized in that: The steps include: Acquire multiple channel sampling values ​​of atmospheric turbulence, and acquire initial channel parameters of the multiple channel sampling values; Generate multiple groups of light intensity flicker samples according to the initial channel parameters and the number of samples L, and obtain a light intensity flicker estimation model for each group of light intensity flicker samples using a k-nearest neighbor density estimation method; Eliminate the data that are not in the range of the minimum value to the maximum value of each group of light intensity flicker samples from the channel sampling values, input the remaining channel sampling values ​​into the light intensity flicker estimation model, obtain the log-likelihood function value of each group of light intensity flicker samples, and average multiple log-likelihood function values; Iterate the steps of obtaining the average log-likelihood function value to obtain the maximum average log-likelihood function value, and represent the channel parameter value of the light intensity flicker estimation model through the maximum average log-likelihood function value; The method of obtaining a plurality of channel sampling values ​​of atmospheric turbulence and obtaining initial channel parameters of the plurality of channel sampling values ​​is specifically as follows: Get the parameters r,σ in the channel sampling value z The initial estimate expression of Specifically: Wherein, I[l] represents the lth atmospheric turbulence channel sampling value obtained by the photoelectric detector, satisfying I[1]≤I[2]≤…≤I[l]≤…≤I[M], M represents the total sampling size, 1 and 2 represent the first and second sampling samples; The method of generating a plurality of groups of light intensity flicker samples according to the initial channel parameters and the sample number L value comprises: The specific expressions of multiple groups of light intensity flicker samples are: where z i [j] The subscript i represents the i-th group of light intensity flicker samples, i∈[1,2,…,N], N represents the total number of groups of light intensity flicker samples, j represents the j-th sample, j∈[1,2,…,L], and each light intensity flicker sample obeys the parameter Lognormal-Rician distribution, L represents the number of light intensity flicker samples in each group; The light intensity flicker estimation model of each group of light intensity flicker samples is obtained by using the k-nearest neighbor density estimation method, including: For any set of light intensity flicker sample data, take the i-th set as an example. i [1],z i [2],…,z i [L], using the k nearest neighbor density estimation method and the current k value to obtain the sample point z i [j] Density estimation for: The variables Γ is the gamma function, d represents the dimension of each data sample, for the Lognormal-Rician channel, d = 1, Represents the sequence z i [1],z i [2],…,z i [L] in z i [j] The kth distance value closest to the target; For data points Perform linear interpolation to obtain the light intensity flicker estimation model and obtain the log-likelihood function value f of the light intensity flicker estimation model i (z); The data that is not in the range of the minimum value to the maximum value of each group of light intensity flicker samples in the channel sampling values ​​are removed, and the remaining channel sampling values ​​are input into the light intensity flicker estimation model to obtain the logarithmic likelihood function value of each group of light intensity flicker samples, and the multiple logarithmic likelihood function values ​​are averaged, specifically: For the i-th group, z i [1],z i [2],…,z i [L], channel sampling sequence After elimination, we get Said satisfy: z i [1]≤I[j]≤I[j+1]≤…≤I[O]≤z i [M]; Where M is the total sample size; for any set of light intensity flicker samples z i [j], satisfied O represents the maximum number of light intensity flicker samples after elimination, and n is the number of samples; Will Substitute into f i (z) and calculate the average log-likelihood function value LLR for each group i , the specific expression is: Among them, c i is the normalization factor, and the specific expression is: If the light intensity flicker samples are N groups, the average log-likelihood function value LLR is: The step of iterating the average log-likelihood function value to obtain the maximum average log-likelihood function value, and characterizing the channel parameter value of the light intensity flicker estimation model by the maximum average log-likelihood function value, comprises: The k value and channel parameters are iterated by the gradient descent method to obtain the maximum average log-likelihood function value. The specific expression is: By differentiating the maximum average log-likelihood function value, the first-order derivatives of each parameter k, r, and σ are approximately obtained, specifically: In the formula, k (j) ,r (j) ,σ (j) represents the j-th estimation result.

2. An atmospheric turbulence light intensity scintillation model parameter estimation system, characterized in that: include: An acquisition module, used for acquiring multiple channel sampling values ​​of atmospheric turbulence and acquiring initial channel parameters of the multiple channel sampling values; A model acquisition module is used to generate multiple groups of light intensity flicker samples according to the initial channel parameters and the sample number k value, and obtain a light intensity flicker estimation model for each group of light intensity flicker samples using a k-nearest neighbor density estimation method; An average processing module is used to remove data from the channel sampling values ​​that are not in the range from the minimum value to the maximum value of each group of light intensity flicker samples, input the remaining channel sampling values ​​into the light intensity flicker estimation model, obtain the logarithmic likelihood function value of each group of light intensity flicker samples, and average multiple logarithmic likelihood function values; An estimation module, used for iterating the step of obtaining an average of log-likelihood function values ​​to obtain a maximum average log-likelihood function value, and representing a channel parameter value of a light intensity flicker estimation model through the maximum average log-likelihood function value; The method of obtaining a plurality of channel sampling values ​​of atmospheric turbulence and obtaining initial channel parameters of the plurality of channel sampling values ​​is specifically as follows: Get the parameters r,σ in the channel sampling value z The initial estimate expression of Specifically: Wherein, I[l] represents the lth atmospheric turbulence channel sampling value obtained by the photoelectric detector, satisfying I[1]≤I[2]≤…≤I[l]≤…≤I[M], M represents the total sampling size, 1 and 2 represent the first and second sampling samples; The method of generating a plurality of groups of light intensity flicker samples according to the initial channel parameters and the sample number L value comprises: The specific expressions of multiple groups of light intensity flicker samples are: where z i [j] The subscript i represents the i-th group of light intensity flicker samples, i∈[1,2,…,N], N represents the total number of groups of light intensity flicker samples, j represents the j-th sample, j∈[1,2,…,L], and each light intensity flicker sample obeys the parameter Lognormal-Rician distribution, L represents the number of light intensity flicker samples in each group; The light intensity flicker estimation model of each group of light intensity flicker samples is obtained by using the k-nearest neighbor density estimation method, including: For any set of light intensity flicker sample data, take the i-th set as an example. i [1],z i [2],…,z i [L], using the k nearest neighbor density estimation method and the current k value to obtain the sample point z i [j] Density estimation for: The variables Γ is the gamma function, d represents the dimension of each data sample, for the Lognormal-Rician channel, d = 1, Represents the sequence z i [1],z i [2],…,z i [L] in z i [j] The kth distance value closest to the target; For data points Perform linear interpolation to obtain the light intensity flicker estimation model and obtain the log-likelihood function value f of the light intensity flicker estimation model i (z); The data that is not in the range of the minimum value to the maximum value of each group of light intensity flicker samples in the channel sampling values ​​are removed, and the remaining channel sampling values ​​are input into the light intensity flicker estimation model to obtain the logarithmic likelihood function value of each group of light intensity flicker samples, and the multiple logarithmic likelihood function values ​​are averaged, specifically: For the i-th group, z i [1],z i [2],…,z i [L], channel sampling sequence After elimination, we get Said satisfy: z i [1]≤I[j]≤I[j+1]≤…≤I[O]≤z i [M]; Where M is the total sample size; for any set of light intensity flicker samples z i [j], satisfied O represents the maximum number of light intensity flicker samples after elimination, and n is the number of samples; Will Substitute into f i (z) and calculate the average log-likelihood function value LLR for each group i , the specific expression is: Among them, c i is the normalization factor, and the specific expression is: If the light intensity flicker samples are N groups, the average log-likelihood function value LLR is: The step of iterating the average log-likelihood function value to obtain the maximum average log-likelihood function value, and characterizing the channel parameter value of the light intensity flicker estimation model by the maximum average log-likelihood function value, comprises: The k value and channel parameters are iterated by the gradient descent method to obtain the maximum average log-likelihood function value. The specific expression is: By differentiating the maximum average log-likelihood function value, the first-order derivatives of each parameter k, r, and σ are approximately obtained, specifically: In the formula, k (j) ,r (j) ,σ (j) represents the j-th estimation result.

3. A storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, the steps of a method for estimating parameters of an atmospheric turbulence light intensity scintillation model as described in any one of claim 1 are implemented.

4. A computer device, characterized in that: It comprises a memory and a processor, wherein a program is stored in the memory, and when the program is executed by the processor, the processor executes the steps of a method for estimating parameters of an atmospheric turbulence light intensity scintillation model as claimed in any one of claim 1.

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