CN112583480B - Method for realizing high-precision wireless optical communication link - Google Patents
Method for realizing high-precision wireless optical communication link Download PDFInfo
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- CN112583480B CN112583480B CN202011546781.6A CN202011546781A CN112583480B CN 112583480 B CN112583480 B CN 112583480B CN 202011546781 A CN202011546781 A CN 202011546781A CN 112583480 B CN112583480 B CN 112583480B
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Abstract
The invention discloses a method for realizing a high-precision wireless optical communication link, which comprises the following steps: generating an atmospheric turbulence phase screen by adopting a Monte Carlo method; calculating the space Euclidean distance of any two sampling points in the screen and the square of the phase difference at the two points based on the phase screen, and performing curve fitting on the space distance and the square data point pair of the phase difference; and comparing and verifying the fitted curve with a theoretical formula of a phase structure function of the atmospheric optical link, thereby obtaining the high-precision wireless optical communication link.
Description
Technical Field
The invention belongs to the field of optical communication, and particularly relates to a method for realizing a high-precision wireless optical communication link.
Background
Wireless optical communication has a number of advantages over traditional wireless communication: a larger antenna gain, thereby having smaller terminal size, weight and power consumption; the frequency spectrum is not regulated, and authorization is not needed; the divergence angle of the laser beam in the atmosphere channel is extremely small, and the laser beam has excellent anti-interference and anti-eavesdropping capabilities; wireless optical communication may also enable unconditionally secure quantum key distribution. However, random disturbances of the atmospheric channel pose a great challenge for wireless optical communications. Turbulent effects are created in the atmosphere channel due to the influence of temperature differences, humidity gradients, wind, etc. When an optical signal is transmitted in an atmospheric channel, the wavefront phase of the optical signal is distorted, and the phase distortion can seriously affect the performance of wireless optical communication after the accumulation of a section of transmission distance, especially for a wireless optical communication system adopting a multi-system modulation format, the error rate of the system can be obviously increased. Thus, implementing a high-precision wireless optical communication link can provide important technical guidance for system performance evaluation and optimization design.
The prior art and method adopts a Monte Carlo method to generate an optical signal phase distortion matrix caused by atmospheric turbulence, and the matrix (hereinafter referred to as an atmospheric turbulence phase screen) is directly regarded as a wireless optical communication link. The Monte Carlo phase screen method represents the phase distortion caused by atmospheric turbulence as an array of computer random sampling points generated from the phase power spectral density function and the fast Fourier transform/inverse transform of the atmospheric optical link. Obviously, in the actual implementation process of the Monte Carlo phase screen method, the generated atmospheric turbulence phase screen is inconsistent with an actual atmospheric channel due to the limited pseudo-random number and random sampling of a computer, so that a wireless optical communication link cannot be accurately reflected, and the important problem is ignored in the prior art and the method.
In summary, the atmospheric turbulence phase screen generated by the monte carlo method cannot accurately reflect the wavefront phase distortion of the optical signal in the actual atmospheric channel, and there is an error, and contrast verification needs to be performed on the atmospheric turbulence phase screen to realize a high-precision wireless optical communication link conforming to the actual situation.
Disclosure of Invention
The present invention aims to solve the above technical problems. Therefore, the invention provides a Monte Carlo atmospheric turbulence phase screen contrast verification method, so that a high-precision wireless optical communication link which is consistent with reality is realized.
The technical scheme adopted for solving the technical problems is as follows:
the implementation method of the high-precision wireless optical communication link is characterized by comprising the following steps:
(1) Generating an atmospheric turbulence phase screen by adopting a Monte Carlo method: performing phase structure function curve fitting based on the generated Monte Carlo atmospheric turbulence phase screen; the atmospheric turbulence phase screen refers to: the phase distortion caused by the atmospheric turbulence in the wireless channel is expressed as a Fourier series sum, the weight coefficient of each Fourier series is calculated by adopting a Monte Carlo method according to a central limit theorem and a Passatsuma law, and then the atmospheric turbulence phase screen is generated by adopting an inverse fast Fourier transform;
comparing and verifying the fitted curve with a theoretical formula of a phase structure function of the atmospheric optical link, thereby realizing a high-precision wireless optical communication link which is consistent with reality; the method is mainly characterized in that a phase structure function theoretical formula of a fitting curve and an atmospheric optical link is subjected to comparison verification, and relative errors are calculated
/>
Wherein the method comprises the steps of
Respectively represent space distance
the theoretical formula of the phase structure function of the atmospheric optical link is as follows:
wherein the method comprises the steps of𝜅 0 =2π/L Outer part ,𝜅 l =5.92/l Inner part ,L Outer part Andl inner part Respectively representing the outer dimension and the inner dimension of the atmospheric turbulence element;
the atmospheric gas dry diameter is the atmospheric gas dry diameter; />
Representing a gamma function; />
Representing a first class of converging hypergeometric functions.
The form of the fitting curve is as follows:
wherein the method comprises the steps of
In order to fit the parameters of the curve,ris an independent variable.
The invention arranges the space distance vector elements in ascending order, and the phase difference square vector elements corresponding to the space distance are modulated in corresponding order. At the same time, the space distance is covered by the minimum value and the maximum value
Equally dividing, counting the space distance vector elements and the corresponding phase difference square vector elements in each subinterval. And taking the midpoint of each subinterval, and calculating the average value of the phase difference square vector elements in each subinterval. By means of the->
Phase structure function curve fitting is performed on pairs of spatial distance and phase difference squared data points. Generating an atmospheric turbulence phase screen in a circulating way, comparing and verifying a fitting curve with a theoretical formula of a phase structure function until a relative error is +.>
Below the threshold, thereby achieving a high accuracy wireless optical communication link.
The mode of the invention also comprises the following steps: the algorithm of the implementation method is used for outputting a high-precision wireless optical communication link which is consistent with the actual situation.
The invention further discloses application of the implementation method of the high-precision wireless optical communication link in the aspect of providing a wireless optical communication link which is consistent with reality. Experimental results show that the traditional Monte Carlo phase screen method cannot reflect an actual wireless optical communication link, and the method provided by the invention can realize the wireless optical communication link which accords with the actual through comparison with a theoretical formula.
The invention is described in more detail below:
the method adopts a Monte Carlo method to generate a phase distortion matrix caused by atmospheric turbulence, and based on the atmospheric turbulence phase screen, the Euclidean space distance of any two sampling points in the screen and the square of the phase difference of the two points are calculated. And performing curve fitting by using the space distance and the phase difference square data point pair. And finally, comparing and verifying the fitted curve with a theoretical formula of a phase structure function of the atmospheric optical link, thereby realizing the high-precision wireless optical communication link. The specific operation comprises the following steps: the atmospheric turbulence phase screen is generated by a fast fourier transform/inverse transform and a monte carlo random sampling method. The computer generates two groups of random number arrays which are uniformly distributed, and randomly samples the spatial point position of the atmospheric turbulence phase screen and the corresponding phase thereof. The euclidean space distance of any two sampling points in the phase screen and the square of the phase difference at the two points are calculated. And (3) carrying out ascending order arrangement on the space distance vector elements, and carrying out corresponding order change on the phase difference square vector elements corresponding to the space distance vector elements. And performing curve fitting based on the ordered space distance and phase difference square point pairs, obtaining a fitted curve, comparing and verifying with a theoretical formula of a phase structure function of the atmospheric optical link, if the error is higher than a specified threshold, continuously regenerating an atmospheric turbulence phase screen by using a Monte Carlo method, and comparing and verifying the regenerated phase screen until the error is lower than the threshold by using the same steps. The phase screen matched with the actual atmospheric optical link can be obtained by using the algorithm, so that the aim of realizing a high-precision wireless optical communication link is fulfilled.
The invention mainly solves the important problem that the wireless optical communication link generated by the prior Monte Carlo phase screen method does not accord with the actual situation, and mainly examines the phase structure function of the wireless optical communication link, and has the main difficulty that the phase structure function fitting algorithm is designed.
Compared with the prior art, the realization method of the high-precision wireless optical communication link has the following positive effects:
(1) The spatial statistical characteristic of the Monte Carlo atmospheric turbulence phase screen is compared and verified with a theoretical formula of a phase structure function of an atmospheric optical link, so that a high-precision wireless optical communication link which is consistent with reality is realized.
(2) A phase structure function fitting algorithm of the wireless optical communication link is designed, so that the accuracy of the prior art can be quantitatively evaluated.
(3) The spatial statistics of the Monte Carlo atmospheric turbulence phase screen are subjected to sequencing treatment, so that the execution efficiency of the algorithm is greatly improved.
Drawings
FIG. 1 is a two-dimensional pictorial illustration of an atmospheric turbulence phase screen generated by a Monte Carlo method in accordance with an embodiment of the present invention;
FIG. 2 is a flow chart of a method of implementing a high accuracy wireless optical communication link in accordance with one embodiment of the present invention;
FIG. 3 is a schematic diagram of simulation results of an atmospheric turbulence phase screen not conforming to an actual wireless optical communication link, a theoretical formula comparison verification of phase structure functions of the atmospheric turbulence phase screen and the atmospheric optical link, and a relative error, according to an embodiment of the present inventionT=210, much higher thanA threshold value of 5;
FIG. 4 is a schematic diagram of simulation results of a highly compliant atmospheric turbulence phase screen and an actual wireless optical communication link according to one embodiment of the present invention, comparing and verifying the theoretical formulas of phase structure functions of the atmospheric turbulence phase screen and the atmospheric optical link, relative errorsT=4.1, below threshold 5;
fig. 5 is a two-dimensional pictorial illustration of a high accuracy wireless optical communication link, in accordance with an embodiment of the present invention.
Detailed Description
Embodiments of the present invention are described in detail below, examples of which are illustrated in the accompanying drawings, wherein like or similar reference numerals refer to like or similar elements or elements having like or similar functions throughout. The embodiments described below by referring to the drawings are illustrative and intended to explain the present invention and should not be construed as limiting the invention.
Example 1
FIG. 1 is a two-dimensional schematic representation of an atmospheric turbulence phase screen matrix generated using the Monte Carlo method, the phase screen being perpendicular to the optical axis of the laser beam, whereinxShaft and method for producing the sameyThe axes show the size of the phase screen and the gray values in the figure represent the phase of the distortion. Fig. 2 is a flow chart of the algorithm of the present invention. Fig. 3 is a graph of the results of curve fitting based on the phase panel data of fig. 1 and comparing the theoretical formula of the phase structure function with that of the optical link. As can be seen from FIG. 3, because the pseudo-random number and random sampling of the computer are limited, the spatial statistical characteristic of the atmospheric turbulence phase screen generated by the Monte Carlo method is not matched with the phase structure function, the error is large, and the real wireless optical communication link cannot be reflected, so that the real wireless optical communication link needs to be verified to realize the high-accuracy wireless optical communication link. As can be seen from fig. 2, the implementation method of the present invention is implemented by the following steps:
step one: the phase distortion matrix caused by the atmospheric turbulence, namely the atmospheric turbulence phase screen, is generated by utilizing the Monte Carlo method numerical value. The spatial phase distortion can be expressed in terms of a fourier series sum
Wherein the method comprises the steps of
Respectively represent edgesxAndyspatial frequency of sampling in direction>
Is a weight coefficient of the fourier series, which is the key to generating the atmospheric turbulence phase screen. Because the atmospheric turbulence elements are spatially independent of each other, according to the central limit theorem +.>
Obeying the mean value to be zero and the variance to be +.>
Is a normal distribution of (c).
Further, according to the pizza law theorem, the phase energy is equal in the spatial domain and the spatial frequency domain
Wherein the method comprises the steps of
As a function of the phase power spectral density, its physical meaning is the distribution of phase fluctuations over the spatial frequency domain caused by atmospheric turbulence. Its concrete expression is
Wherein the method comprises the steps of
Respectively represent the outer dimension and the inner dimension of the atmospheric turbulence element>
Is of atmospheric dry diameter, +.>
And->
Representing wavenumber, link length and atmospheric refractive index structural parameters, +.>
。
From formulas (1) - (3), it can be calculated
Variance of->
Wherein the method comprises the steps of
Respectively representxAndysampling space interval in the direction. In the process of obtaining
Then, the phase distortion caused by the atmospheric turbulence can be obtained by a Monte Carlo method and inverse fast Fourier transform,
wherein the coefficient A represents a complex random number matrix, and the real part and the imaginary part of the complex random number matrix are both subjected to standard normal distribution and can be generated by a Monte Carlo method;
representing an inverse fourier transform operator.
From the above steps, it can be seen that by using the numerical method described above, the phase distortion caused by atmospheric turbulence is represented by an array of computer random sampling points, the spatial statistics of which can theoretically be consistent with the phase power spectral density function.
Step two: because the pseudo-random number and random sampling of the computer are limited, the atmospheric turbulence phase screen generated by the Monte Carlo method is not in line with the real wireless optical communication system (see figure 3), and further contrast verification is needed, and the specific operation is as follows. The computer generates two groups of random number arrays which are uniformly distributed, and randomly samples the space position of the sampling point and the phase position of the sampling point in the atmospheric turbulence phase screen respectively to form two data pairs, wherein one data pair comprises a position matrix
Using a matrix of positions (x 1 ，y 1 ) And (x) 2 ，y 2 ) Calculating Euclidean space distance between any two sampling points in phase screen
The method comprises the steps of carrying out a first treatment on the surface of the By means of a phase matrix->
Calculating the square of the phase difference at the sampling point
. The space distance vector elements are arranged in an ascending order, and the phase difference square vector elements are correspondingly adjusted along with the space distance.
To further improve algorithm efficiency, the number of spatial position and phase difference square data point pairs is reduced, and quick and accurate curve fitting is realizedThe specific method is as follows. The interval covered by the maximum value and the minimum value of the Euclidean space distance vector calculated by the method
Equally dividing, counting the space distance vector elements and the corresponding phase difference square vector elements in each subinterval. The midpoint of each subinterval is taken while the average of all the squares of the phase differences within each subinterval is calculated. By means of the two ∈thers obtained>
Vector formation +.>
And performing phase structure function curve fitting on the space distance-phase difference square data point pairs to obtain a fitting curve.
Step three: and comparing the fitted curve with a theoretical formula of a phase structure function of the atmospheric optical link, and verifying whether the atmospheric turbulence phase screen accords with the actual wireless optical communication link.
Calculating relative errorT
Wherein the method comprises the steps of
Respectively represent space distance->
And calculating a value and a fitting function value according to a theoretical formula of the phase structure function of the atmospheric optical link.
Wherein the method comprises the steps ofrIs the spatial distance;
representing a first class of converging hypergeometric functions.
Specific judgment criteria are as follows. If it is
Below a prescribed threshold, outputting an atmospheric turbulence phase screen; if->
Above a defined threshold, a Monte Carlo atmospheric turbulence phase screen is cyclically generated until +.>
Below the threshold. Through the algorithm, the atmospheric turbulence phase screen generated by the Monte Carlo method can be compared and verified, so that a high-accuracy wireless optical communication link which is consistent with reality is realized.
For example, simulation parameters are shown in table 1.
Table 1 simulation parameters
As can be seen from table 1, the atmospheric turbulence parameters given are equivalent to typical medium-intensity atmospheric turbulence conditions, the phase screen size is 0.512m×0.512m, and the diffraction-limited spot size after a transmission distance of more than 1500m can be used for the input of the phase structure function fitting algorithm. The parameters of table 1 correspond to an actual medium range wireless optical communication link.
FIG. 3 showsTWhen=210 (far above the threshold value), the theoretical formula of the phase structure function of the atmospheric turbulence phase screen and the atmospheric optical link is compared to verify the result to obtain a schematic diagram, and it can be seen from the diagram that the spatial statistical characteristic of the atmospheric turbulence phase screen generated by the monte carlo method is inconsistent with the actual atmospheric optical link, that is, the spatial statistical characteristic cannot accurately reflect the wireless optical communication link.
FIG. 4 shows
When the phase value is lower than the threshold value, comparing and verifying the phase structure function theoretical formula of the atmospheric turbulence phase screen and the atmospheric optical link to obtain a result schematic diagram, and as can be seen from the diagram, continuously comparing and verifying the generated phase screen space statistical characteristic and the phase structure function theoretical formula of the atmospheric optical link by circularly generating the Monte Carlo atmospheric turbulence phase screen untilTBelow the threshold, an atmospheric turbulence phase screen consistent with the theoretical formula of the phase structure function can be realized, so that a high-precision wireless optical communication link consistent with reality is realized.
FIG. 5 shows when
(below the threshold value), the high-accuracy wireless optical communication link is output.
It should be noted that the embodiments described above are not intended to limit the present invention in any way, and all relevant modifications made in accordance with the technical spirit of the present invention still fall within the scope of the present invention.
Claims (6)
1. The implementation method of the high-precision wireless optical communication link is characterized by comprising the following steps:
generating an atmospheric turbulence phase screen by adopting a Monte Carlo method: performing phase structure function curve fitting based on the generated Monte Carlo atmospheric turbulence phase screen; the atmospheric turbulence phase screen refers to: the phase distortion caused by the atmospheric turbulence in the wireless channel is expressed as a Fourier series sum, the weight coefficient of each Fourier series is calculated by adopting a Monte Carlo method according to a central limit theorem and a Passatsuma law, and then the atmospheric turbulence phase screen is generated by adopting an inverse fast Fourier transform;
comparing and verifying the fitted curve with a theoretical formula of a phase structure function of the atmospheric optical link, thereby realizing a high-precision wireless optical communication link which is consistent with reality; the method is mainly characterized in that a phase structure function theoretical formula of a fitting curve and an atmospheric optical link is subjected to comparison verification, and relative errors are calculated
Wherein the method comprises the steps of
Respectively represent space distance
r i Theoretical formula calculation value and fitting function value of phase structure function of time-atmosphere optical link
The theoretical formula of the phase structure function of the atmospheric optical link is as follows:
wherein the method comprises the steps of
Respectively represent the outer dimension and the inner dimension of the atmospheric turbulence element>
Represents the diameter of the air-drying process,krepresenting wave number, & lt + & gt>
Represents the structural parameters of the refractive index of the atmosphere,Lrepresenting the optical link length; />
Representing a gamma function; />
Representing a first class of converging super-geometric functions;
the form of the fitting curve is as follows:
wherein the method comprises the steps of
In order to fit the parameters of the curve,ris the distance between two points in space.
2. The implementation method according to claim 1, wherein the spatial distance vector elements are arranged in an ascending order, and the phase difference square vector elements corresponding to the spatial distances are modulated in a corresponding order.
3. The implementation method according to claim 1, wherein the intervals covered by the maximum value and the minimum value of the euclidean space distance vector obtained by the computer are
Aliquoting.
4. A method according to claim 3, wherein the mean value of the phase difference squared vector elements in each subinterval is calculated taking the midpoint of each subinterval.
5. A method according to claim 3, characterized in that two obtained are used
Vector formation +.>
And performing phase structure function curve fitting on the space distance-phase difference square data point pairs to obtain a fitting curve.
6. The implementation method of claim 1, wherein the fitting curve is compared with a theoretical formula of a phase structure function by circularly generating an atmospheric turbulence phase screen until a relative errorTBelow the threshold, thereby achieving a high accuracy wireless optical communication link.
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