A Simulation Method for Optical Pulse Response of Underwater Wireless Optical Channels

Abstract

The present invention discloses a method for simulating the optical pulse response of an underwater wireless optical channel, which includes the following steps: calculating the seawater backscattering probability according to the actually measured seawater parameters; calculating each coefficient in the scattering phase function expression according to the backscattering probability; calculating the root mean square of the scattering angle according to the scattering phase function; calculating the optical pulse transmission delay of the underwater wireless optical channel according to the root mean square of the scattering angle; and obtaining the optical pulse response waveform of the underwater wireless optical channel according to the transmission delay. The present invention combines the photon small-angle approximation scattering model with the TTHG scattering phase function, which can effectively reduce the computational complexity while considering the influence of backscattering on the optical pulse response of the underwater wireless optical channel, making the result as close to the actual situation as possible.

Description

Technical Field

[0001] The present invention relates to the field of wireless optical communication, and particularly to a method for simulating the optical pulse response of an underwater wireless optical channel. Background Art

[0002] Underwater Wireless Optical Communication (UWOC) can provide real-time, high-channel-capacity, secure, and high-speed data transmission services, effectively making up for the defects of traditional underwater acoustic communication, such as limited bandwidth resources, severe spatial selective fading, and low transmission rate. However, when an optical pulse is transmitted in a complex ocean environment, due to the severe multiple scattering effect of seawater on the light beam, the optical pulse response diffuses in time, thus causing inter-symbol interference. The time-domain expansion of the pulse signal brings difficulties to the correct detection of the signal and has a serious impact on the underwater optical communication effect. In an underwater wireless optical channel, the optical pulse response is widely used to describe the time-domain expansion of an optical pulse signal. Currently, most studies use a method that combines the Henyey-Greenstein scattering phase function with the Monte Carlo method to simulate the optical pulse response in an underwater wireless optical channel. This method has a large amount of calculation, and there are certain deviations between the Henyey-Greenstein scattering phase function and the real data when the scattering angle is less than 20° and greater than 130°, and the influence of the backscattering of the underwater wireless optical channel is not considered. Summary of the Invention

[0003] In order to more simply and efficiently simulate the optical pulse response in an underwater wireless optical channel, the present invention provides a method for simulating the optical pulse response of an underwater wireless optical channel, which can more simply and efficiently simulate the optical pulse response in an underwater wireless optical channel.

[0004] The technical solution for achieving the purpose of the present invention is as follows:

[0005] A method for simulating the optical pulse response of an underwater wireless optical channel includes the following steps:

[0006] S1, calculating the seawater backscattering probability according to the actually measured seawater parameters;

[0007] S2, calculating each coefficient in the scattering phase function expression according to the backscattering probability;

[0008] S3, calculating the root mean square of the scattering angle according to the scattering phase function;

[0009] S4, calculating the optical pulse transmission delay of the underwater wireless optical channel according to the root mean square of the scattering angle;

[0010] S5, obtaining the optical pulse response waveform of the underwater wireless optical channel according to the transmission delay.

[0011] Further, in S1, the actually measured seawater parameters include the absorption coefficient a, the forward scattering coefficient b, and the backward scattering coefficient b b and the attenuation coefficient c. The measurement of seawater parameters is not restricted by sea area, time, depth, or acquisition method.

[0012] Further, in S1, the seawater backward scattering probability B is obtained by establishing a relationship with the forward scattering coefficient b and the backward scattering coefficient b b and the relationship is

[0013] Further, in S2, the scattering phase function is the Two-Term Henyey-Greenstein (abbreviated as TTHG) function, and its coefficients are weighted coefficients the forward scattering asymmetry factor g1 and the backward scattering asymmetry factor g2. The TTHG function is an empirical formula for the scattering angle θ, and the expression is:

[0014]

[0015] where

[0016]

[0017]

[0018] In the formula, P HG (θ, g1) represents the forward Henyey-Greenstein scattering phase function, and P HG (θ, g2) represents the backward Henyey-Greenstein scattering phase function.

[0019] Further, in S2, a system of equations is established according to the empirical formula, and the coefficients of the TTHG function are obtained by solving the system of equations with the seawater backward scattering probability B obtained through step S1. The system of equations established by the empirical formula is:

[0020]

[0021]

[0022] g2 = -3.061446 + 1.000568g1 - 0.01826332g1 + 0.03643748g1 2 .

[0023] Further, in S3, the root mean square of the scattering angle θ0 represents the root mean square of the single scattering angle θ i (i = 1, 2, 3...) and θ0 satisfies: d is the differential operator.

[0024] Further, in S4, the process of calculating the optical pulse transmission delay of the underwater wireless optical channel according to the root mean square of the scattering angle is as follows: substituting the root mean square value of the scattering angle into the small-angle approximation scattering model of photons to obtain the optical pulse transmission delay.

[0025] Further, in S4, the small-angle approximation scattering model of photons is:

[0026]

[0027] In the formula, t M represents the transmission delay of the pulsed light beam in the underwater wireless optical channel, z represents the transmission distance, n represents the refractive index of seawater, C represents the speed of light in vacuum, λ represents the optical thickness, and ω0 represents the single-scattering albedo;

[0028] Further, the optical thickness λ is obtained by establishing a relationship through the seawater attenuation coefficient c and the transmission distance z, satisfying λ = cz;

[0029] Further, the single-scattering albedo ω0 is obtained by establishing a relationship through the forward scattering coefficient b and the attenuation coefficient c, satisfying ω0 = b / c;

[0030] The transmission delay of the pulsed light beam in the underwater wireless optical channel is simulated by a single-photon small-angle approximation scattering model.

[0031] Further, S5 includes the following steps:

[0032] S5-1, substituting the transmission delay t M into the mathematical model expression of the optical pulse response of the underwater wireless optical channel to obtain the optical pulse response function of the underwater wireless optical channel. The mathematical model expression of the optical pulse response of the underwater wireless optical channel is:

[0033]

[0034] In the formula, t is the time variable;

[0035] S5-2, according to the optical pulse function of the underwater wireless optical channel, using a drawing tool to draw the waveform of the optical pulse response of the underwater wireless optical channel.

[0036] Compared with the existing technology, the solution disclosed in the present invention has the following advantages:

[0037] The present invention combines the small-angle approximation scattering model of photons with the TTHG scattering phase function, which not only effectively reduces the computational complexity but also considers the influence of backscattering on the optical pulse response of the underwater wireless optical channel, making the result as close to the actual situation as possible. Description of the Drawings

[0038] Figure 1Flow chart of a method for simulating the optical pulse response of an underwater wireless optical channel according to the present invention;

[0039] Figure 2 Schematic diagram of the small-angle approximation scattering model of photons in an embodiment of the present invention;

[0040] Figure 3 Waveform diagram of the optical pulse response function of an underwater wireless optical channel in an embodiment of the present invention. Detailed implementation manners

[0041] The embodiments described below with reference to the accompanying drawings are exemplary and are intended to explain the present invention and should not be construed as limiting the present invention.

[0042] See Figure 1 , a method for simulating the optical pulse response of an underwater wireless optical channel, comprising the following steps:

[0043] S1. Calculate the seawater backscattering probability according to the actually measured seawater parameters;

[0044] S2. Calculate each coefficient in the scattering phase function expression according to the backscattering probability;

[0045] S3. Calculate the root mean square of the scattering angle according to the scattering phase function;

[0046] S4. Calculate the optical pulse transmission delay of the underwater wireless optical channel according to the root mean square of the scattering angle;

[0047] S5. Obtain the optical pulse response waveform of the underwater wireless optical channel according to the transmission delay.

[0048] The following takes the simulation of the optical pulse response in turbid seawater as an example for detailed description:

[0049] Assume that the actually measured turbid seawater parameters are: absorption coefficient a = 0.295 m -1 , forward scattering coefficient b = 1.875 m -1 , backscattering coefficient b b = 0.0076 m -1 , attenuation coefficient c = 2.17 m -1 ;

[0050] (1) Calculate the seawater backscattering probability according to the actually measured seawater parameters: The seawater backscattering probability B is obtained by establishing a relationship between the forward scattering coefficient b and the backscattering coefficient b b That is

[0051] (2) Calculate each coefficient in the scattering phase function expression according to the backscattering probability: The TTHG function is an empirical formula of the scattering angle θ, and the specific expression is:

[0052]

[0053] wherein

[0054]

[0055]

[0056] wherein is a weighting coefficient, g1 is the forward scattering asymmetry factor, g2 is the backward scattering asymmetry factor, θ is the scattering angle, and P HG (θ, g1) is the forward Henyey-Greenstein scattering phase function, and P HG (θ, g2) is the backward Henyey-Greenstein scattering phase function;

[0057] Weighting coefficient The forward scattering asymmetry factor g1, the backward scattering asymmetry factor g2, and the seawater backward scattering probability B satisfy:

[0058]

[0059]

[0060] g2 = -3.061446 + 1.000568g1 - 0.01826332g1 + 0.03643748g1 2 (6)

[0061] By combining equations (4), (5), and (6) into a system of equations, the weighting coefficient The forward scattering asymmetry factor g1 ≈ 0.9958, and the backward scattering asymmetry factor g2 ≈ 0.7081. The specific expression of the TTHG scattering phase function can be obtained as:

[0062]

[0063] wherein

[0064]

[0065]

[0066] In equation (7), is the weighting coefficient, g1 is the forward scattering asymmetry factor, g2 is the backward scattering asymmetry factor, and θ is the scattering angle;

[0067] (3) Calculate the root mean square of the scattering angle according to the scattering phase function: The root mean square of the scattering angle θ0 satisfies:

[0068]

[0069] In the formula, θ is the scattering angle, d is the differential operator, g1 is the forward scattering asymmetry factor, g2 is the backward scattering asymmetry factor. Combining with Equation (7), the root mean square of the scattering angle θ0 = 0.0203 rad is calculated;

[0070] (4) Calculate the optical pulse transmission delay in the underwater wireless optical channel according to the root mean square of the scattering angle: Substitute the root mean square value of the scattering angle into the photon small-angle approximation scattering model to obtain the optical pulse transmission delay. See the photon small-angle approximation scattering model in Figure 2 ; During the transmission process, the photons transmitted along the z-axis will collide with water molecules and other particles, and the movement process is as Figure 2 shown:

[0071]

[0072] In the formula, R is the photon direction, d is the differential operator, is the component of R on the x-axis, is the component of R on the y-axis, is the component of R on the z-axis. Perform mathematical transformation on Equation (9):

[0073]

[0074] In the formula, represents the projection of R on the plane formed by the x-axis and the y-axis, z represents the transmission distance, and the projection angle of the photon scattering is approximated as:

[0075]

[0076] In the formula, the photon single-scattering albedo ω0 = b / c, λ = cz is the optical thickness of seawater, θ0 is the root mean square of the single-scattering angle θ i , b is the forward scattering coefficient, c is the attenuation coefficient. Since the value of is small, the projection of R on the plane formed by the x-axis and the y-axis is approximated as:

[0077]

[0078] Transform Equation (10) into:

[0079]

[0080] d is the differential operator. Integrate both sides of Equation (13) to obtain:

[0081]

[0082] The transmission delay of the pulsed beam in the underwater wireless optical channel is Furthermore, it can be obtained that:

[0083]

[0084] Wherein, z represents the transmission distance, n represents the refractive index of seawater, and C represents the speed of light in vacuum; assuming the transmission distance z = 10 m, the refractive index of seawater n = 1.33, and the speed of light in vacuum C = 3×10 8 m / s, and substituting θ0 = 0.0203 rad into Equation (15) gives: t M = 8.4293 ns;

[0085] (5) Obtain the optical pulse response waveform of the underwater wireless optical channel according to the transmission time delay: The mathematical model expression of the optical pulse response of the underwater wireless optical channel is:

[0086]

[0087] Wherein, t is the time variable. Substituting t M = 8.4293 into Equation (16) gives the optical pulse response function of the underwater wireless optical channel:

[0088]

[0089] Wherein, t is the time variable. Using a plotting tool, plot the optical pulse response function of the underwater wireless optical channel with t as the abscissa and f(t) as the ordinate as Figure 3 shown in the optical pulse response waveform of the underwater wireless optical channel.

[0090] The preferred embodiments of the present invention disclosed above are only helpful in explaining the present invention and do not limit the present invention to the specific embodiments described. Obviously, many modifications and variations can be made according to the content of this specification. These embodiments are selected and specifically described in this specification to better explain the principle and practical application of the present invention, so that those skilled in the art can well understand and utilize the present invention.

Claims

1. A method for simulating the optical pulse response of an underwater wireless optical channel, characterized in that, It includes the following steps: S1. Calculate the seawater backward scattering probability based on the actually measured seawater parameters; S2. Calculate each coefficient in the scattering phase function expression according to the backward scattering probability; In S2, the scattering phase function is the TTHG function, and its coefficients are weighting coefficients , the forward scattering asymmetry factor and the backward scattering asymmetry factor , and the TTHG function is an empirical formula for the scattering angle ; S3. Calculate the root mean square of the scattering angle according to the scattering phase function; In S3, the root mean square of the scattering angle represents the root mean square of the single scattering angle , and satisfies: Satisfy: , is a differential operator; S4. Calculate the optical pulse transmission delay of the underwater wireless optical channel according to the root mean square of the scattering angle; In S4, the process of calculating the optical pulse transmission delay of the underwater wireless optical channel according to the root mean square of the scattering angle is as follows: Substitute the root mean square value of the scattering angle into the small-angle approximation scattering model of photons to obtain the optical pulse transmission delay; The small-angle approximation scattering model of photons is as follows: In the formula, represents the transmission delay of the pulsed beam in the underwater wireless optical channel, represents the transmission distance, represents the refractive index of seawater, represents the speed of light in vacuum, represents the optical thickness, represents the single-scattering albedo; Optical thickness Obtained by establishing a connection through the seawater attenuation coefficient and the transmission distance and satisfies ; Single scattering albedo Obtained by establishing a relationship through the forward scattering coefficient and the attenuation coefficient and satisfying ; S5. Obtain the optical pulse response waveform of the underwater wireless optical channel according to the transmission delay.

2. The underwater wireless optical channel optical pulse response simulation method according to claim 1, characterized in that In S1, the actually measured seawater parameters include the absorption coefficient , the forward scattering coefficient , the backward scattering coefficient and the attenuation coefficient . The measurement of seawater parameters is not restricted by sea area, time, depth or acquisition method.

3. A method for simulating the optical pulse response of an underwater wireless optical channel according to claim 1, characterized in that, In S1, the seawater backscattering probability is obtained by establishing a relationship with the forward scattering coefficient and the backscattering coefficient , and the relationship is .

4. The underwater wireless optical channel optical pulse response simulation method according to claim 1, characterized in that The TTHG function is the empirical formula for the scattering angle and the expression is as follows: Where In the formula, is the forward Henyey-Greenstein scattering phase function, is the backward Henyey-Greenstein scattering phase function.

5. A method for simulating the optical pulse response of an underwater wireless optical channel according to claim 4, characterized in that, In S2, a system of equations is established according to the empirical formula, and the seawater backscattering probability obtained through step S1 is used to solve the system of equations to obtain the coefficients of the TTHG function. The system of equations established by the empirical formula is as follows: In the formula, is the seawater backscattering probability, is the weighting coefficient, is the forward scattering asymmetry factor, is the backscattering asymmetry factor.

6. The underwater wireless optical channel optical pulse response simulation method according to claim 1, wherein S5 includes the following steps: S5-1, bring the transmission delay into the mathematical model expression of the optical pulse response of the underwater wireless optical channel to obtain the optical pulse response function of the underwater wireless optical channel. The mathematical model expression of the optical pulse response of the underwater wireless optical channel is as follows: In the formula, t is the time variable; S5-2. Draw the optical pulse response waveform of the underwater wireless optical channel according to the optical pulse function of the underwater wireless optical channel.

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