Error rate calculation method for underwater wireless optical communication system based on carrierless amplitude phase modulation

Abstract

The application provides a kind of underwater wireless optical communication system error rate calculation method based on carrierless amplitude phase modulation, comprising: based on the underwater turbulent channel of lognormal distribution and considering the influence of absorption, scattering effect, establish the underwater wireless optical communication system model using carrierless amplitude phase modulation;Using Gauss-Hermite orthogonal integral formula, the closed expression of system error rate is obtained, and compared with the Monte Carlo simulation result, prove the correctness and effectiveness of expression;The related parameters of different underwater scenes are brought into the closed average error rate expression, and the influence of these parameters on system performance is evaluated.The underwater wireless optical communication system model established by the application comprehensively considers the influence of absorption, scattering and turbulence on performance, and is closer to the real marine environment;The error rate calculation method disclosed by the application can provide theoretical guidance for studying the performance of underwater wireless optical communication system in different scenarios.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of underwater wireless optical communication, in particular, especially relates to a method for calculating the bit error rate of an underwater wireless optical communication system based on a carrierless amplitude and phase modulation. BACKGROUND

[0002] Common underwater wireless communication mainly includes underwater acoustic communication, underwater wireless electromagnetic wave communication and underwater wireless optical communication (UWOC, Underwater Wireless Optical Communication). Among them, underwater wireless electromagnetic wave communication needs a larger antenna size and a larger transmission power, which is not conducive to miniaturization, and can only be used for short distance and low bandwidth. Underwater acoustic communication is more mature and is more widely used. The attenuation of sound waves in seawater is very small, only 2-3 dB / km. At very low frequencies, sound waves can travel hundreds of kilometers in the ocean, with the advantages of long communication distance, high reliability, etc. However, underwater acoustic communication has the disadvantages of large communication delay, limited bandwidth, high power consumption, large volume and poor security, and the reflection of the sea surface and the seabed causes the multipath effect of underwater sound propagation to be more serious. With the development of underwater exploration technology, there is an increasing demand for underwater wireless communication technology, and it is urgent to develop a low-power, high-bandwidth system, which is difficult to meet the requirements of underwater acoustic communication. Compared with underwater wireless electromagnetic wave communication and underwater acoustic communication, underwater wireless optical communication has the advantages of strong information carrying capacity, small communication delay, large communication bandwidth, good security, etc., and plays an important role in the fields of marine resource exploration and marine environment monitoring. Therefore, developing and researching UWOC technology is an important part of building a strong marine country, and has important significance for promoting the rapid and sustainable development of China's marine information technology.

[0003] However, the substances contained in seawater are very complex, and the propagation of wireless light in seawater will be affected by absorption, scattering and turbulence effects. Turbulence effects will cause light intensity flicker during transmission, resulting in signal fading; the absorption and scattering effects of seawater on light are collectively referred to as attenuation effects, in which absorption effects will cause energy loss during underwater wireless light propagation, and scattering effects will change the propagation direction of underwater light signals. Absorption, scattering and turbulence effects will all affect the performance of the received signal light power at the receiving end, thereby affecting the transmission performance of the system.

[0004] In terms of underwater turbulence channel modeling, lognormal distribution can be used to simulate the effects caused by turbulence effects. In terms of absorption and scattering, the absorption and scattering effects of seawater on light waves can be characterized by an exponential distribution as a whole. In addition, the underwater wireless optical communication system usually adopts a direct modulation / direct detection transceiver, and the carrierless amplitude and phase modulation is suitable for the characteristics of the system, and the underwater wireless optical communication system is very sensitive to system nonlinearity, and the carrierless amplitude and phase modulation will not cause the problem of excessive peak-to-average power ratio. The current problem is that:

[0005] In the wireless optical communication system in the complex water environment considering absorption, scattering and turbulence, there are few studies on the bit error rate calculation based on the carrierless amplitude phase modulation. Therefore, based on the lognormal distribution turbulence channel model, and considering the influence of absorption and scattering effect, it is of great significance to carry out the bit error rate calculation based on the carrierless amplitude phase modulation and the bit error rate performance of different underwater scenes. SUMMARY

[0006] According to the technical problems proposed above, a bit error rate calculation method of underwater wireless optical communication system based on carrierless amplitude phase modulation is provided. The present application considers the lognormal distribution ocean turbulence channel model, and establishes a composite channel model combined with the influence of absorption and scattering effect, then adopts carrierless amplitude phase modulation and uses the Gaussian-Hermite orthogonal integral formula to approximate the system bit error rate formula, correctly calculates the closed expression of the average bit error rate of underwater wireless optical communication system, and further studies the influence of different scene parameters on the system transmission performance.

[0007] The technical means adopted by the present application are as follows:

[0008] A bit error rate calculation method of underwater wireless optical communication system based on carrierless amplitude phase modulation, comprising:

[0009] Based on the lognormal distribution, the ocean turbulence channel model is simulated, and the influence of absorption and scattering is considered to establish the transmission model of underwater wireless optical communication channel;

[0010] The signal-to-noise ratio of underwater wireless optical communication system under the combined action of lognormal distribution ocean turbulence and absorption and scattering is derived;

[0011] Using the properties of lognormal distribution, the relationship between the signal-to-noise ratio of underwater wireless optical communication system under the combined action of lognormal distribution ocean turbulence and absorption and scattering and the signal-to-noise ratio considering only absorption and scattering effect is derived;

[0012] Based on the bit error rate formula of carrierless amplitude phase modulation, the Gaussian-Hermite orthogonal integral formula is used to obtain the closed average bit error rate expression of underwater wireless optical system under the combined action of lognormal distribution ocean turbulence and absorption and scattering, and the simulation verification is carried out by Monte Carlo method.

[0013] Further, the lognormal distribution is used to simulate the ocean turbulence channel model, and the influence of absorption and scattering is considered to establish the transmission model of underwater wireless optical communication channel, specifically comprising:

[0014] Let x be the transmitted signal sequence, y be the received signal sequence, and the transmission model y of the electrical signal received by the receiver in the underwater wireless optical communication system is represented as:

[0015]

[0016]

[0017] Where η represents the photoelectric conversion coefficient, x represents the transmitted information, v represents a mean of 0, and the variance represents σ. 2 Additive white Gaussian noise; P t I represents the emitted optical power. i H represents the energy change of the optical signal at the receiver when the i-th channel is affected by turbulence. i The channel gain represents the effect of the i-th channel absorbing scattering, N. t This indicates the number of transmitters.

[0018] Furthermore, the derivation of the signal-to-noise ratio of the underwater wireless optical communication system based on the log-normal distribution under the combined effects of ocean turbulence and absorption / scattering specifically includes:

[0019] Because the distance between transceivers is much greater than the wavelength of light and the coherence length, the I between each channel... i If the fading events are independent and identically distributed, then:

[0020] The average signal-to-noise ratio of an underwater wireless optical communication system, considering only absorption and scattering, is:

[0021]

[0022] The average signal-to-noise ratio of an underwater wireless optical communication system, including absorption, scattering, and turbulence, is:

[0023]

[0024] Where E represents x 2 The mathematical expectation of (t), where N0 represents the one-sided power spectral density of additive Gaussian noise.

[0025] Furthermore, by utilizing the properties of the log-normal distribution, the relationship between the signal-to-noise ratio (SNR) of an underwater wireless optical communication system under the combined effects of ocean turbulence and absorption / scattering based on the log-normal distribution and the SNR considering only absorption and scattering effects is derived, specifically including:

[0026] Since the fading between each branch is independent, another log-normal distribution variable e is used. k It is approximately equal to the weighted sum of the log-normal fading coefficients of each branch, and its expression is:

[0027]

[0028] Where k follows a mean of μ k The variance is σk 2 The normal distribution, mean and variance are respectively:

[0029]

[0030] .

[0031] Further, the properties of the lognormal distribution include:

[0032] If I obeys the lognormal distribution with mean μ ρ and variance σ ρ 2 , and a is a constant, then aI obeys the lognormal distribution with mean μ ρ +lna, and variance σ ρ 2 .

[0033] If I i obeys the lognormal distribution with mean μ i and variance σ i 2 , i=1,2,...,n, and each variable is relatively independent, then ∑I i can be approximated by e k , where e k obeys the lognormal distribution with mean μ k and variance σ k 2 , and k obeys the normal distribution with mean μ k and variance σ k 2 .

[0034] Further, the bit error rate formula based on carrierless amplitude phase modulation uses the Gauss-Hermite orthogonal integral formula to obtain the average bit error rate expression of the underwater wireless optical system under the joint action of the lognormal distribution of the ocean turbulence and absorption and scattering, and the simulation verification is carried out by Monte Carlo method, which specifically includes:

[0035] The conditional bit error rate of carrierless amplitude phase modulation is:

[0036]

[0037] Where M represents the order of carrierless amplitude phase modulation, the Q function formula is g represents the direct current bias coefficient, SNR represents the effective electrical signal-to-noise ratio of each carrierless amplitude phase modulation symbol, and the relationship between SNR and μ A , μ r can be expressed as:

[0038]

[0039]

[0040] Therefore, the conditional BER of the CPAM can be further transformed as:

[0041]

[0042] where e k represents a lognormal distributed variable with mean μ k and variance σ k 2

[0043] The BER of the UWOC system based on the CPAM can be expressed as:

[0044]

[0045] where f k (k) is a normal distributed N(μ k , σ k 2 The variable x is set as:

[0046]

[0047] Substitute x into the BER expression of the UWOC system, and replace k, the final BER can be transformed as:

[0048] P e = P e1 + P e2

[0049]

[0050]

[0051] where P e represents the BER of the UWOC system based on the CPAM, and P e is split into the sum of two terms, P e1 represents the first term, and P e2 represents the second term.

[0052] The Gaussian-Hermite orthogonal integral formula is:

[0053]

[0054] According to the Gaussian-Hermite orthogonal integral formula, the final BER closed-form expression can be expressed as:

[0055] P​e = P e1 + P e2

[0056]

[0057]

[0058] Compared with the prior art, the present application has the following advantages:

[0059] 1. The error rate calculation method for the underwater wireless optical communication system based on the carrierless amplitude phase modulation provided by the present application fully considers the complexity of the underwater optical communication channel environment, comprehensively absorbs the influence of absorption, scattering and turbulence effect on the underwater wireless optical communication system, and establishes a complex underwater optical communication channel model. This model is closer to the complex environment of the ocean and can better realize the simulation research on the real ocean environment.

[0060] 2. The error rate calculation method for the underwater wireless optical communication system based on the carrierless amplitude phase modulation provided by the present application uses the lognormal distribution to simulate the turbulence effect, deduces the closed expression of the error rate based on the carrierless amplitude phase modulation, and provides convenience for analyzing the error rate performance of the underwater wireless optical communication system under different scenarios.

[0061] Based on the above reasons, the present application can be widely popularized in the field of underwater wireless optical communication. BRIEF DESCRIPTION OF DRAWINGS

[0062] In order to more clearly illustrate the technical solutions in the embodiments of the present application or the prior art, the drawings needed to be used in the embodiments or the prior art description will be briefly introduced. Obviously, the drawings in the following description are some embodiments of the present application, and other drawings can also be obtained by those skilled in the art without creative labor.

[0063] Figure 1 The block diagram of the underwater wireless optical communication system based on the carrierless amplitude phase modulation of the present application.

[0064] Fig. 2(a) is a 4CAP error rate curve diagram of clean seawater under different flicker indexes provided by the embodiment of the present application.

[0065] Fig. 2(b) is a 4CAP error rate curve diagram of coastal seawater under different flicker indexes provided by the embodiment of the present application.

[0066] Fig. 2(c) is a 16CAP error rate curve diagram of clean seawater under different flicker indexes provided by the embodiment of the present application.

[0067] Fig. 2(d) is a 16CAP error rate curve diagram of coastal seawater under different flicker indexes provided by the embodiment of the present application.

[0068] Figure 3 The different modulation order under the shore seawater 4CAP, 16CAP error rate curve provided by the embodiment of the application.

[0069] Figure 4 The different transmission distance under the shore seawater 4CAP, 16CAP error rate curve provided by the embodiment of the application. DETAILED DESCRIPTION

[0070] It should be noted that the embodiments in the present application and the features in the embodiments can be combined with each other without conflict. The present application will be described in detail below with reference to the drawings and in combination with the embodiments.

[0071] To make the purpose, technical solutions and advantages of the embodiments of the present application clearer, the technical solutions in the embodiments of the present application will be described clearly and completely below in combination with the drawings of the embodiments of the present application. Obviously, the described embodiments are only a part of the embodiments of the present application, rather than all the embodiments. The description of the at least one exemplary embodiment is actually only illustrative, but not as any limitation on the present application and its application or use. Based on the embodiments in the present application, all other embodiments obtained by those skilled in the art without creative work belong to the scope of protection of the present application.

[0072] It should be noted that the terms used herein are only for describing specific embodiments, and are not intended to limit the exemplary embodiments according to the present application. As used herein, the singular form is intended to include the plural form, unless the context clearly indicates otherwise, and it should also be understood that when the terms "comprise" and / or "include" are used in the specification, there is a presence of the features, steps, operations, devices, components and / or their combinations.

[0073] Unless specifically stated otherwise, the relative arrangement of the components and steps, numerical expressions, and numerical values set forth in the various embodiments described herein are not limiting. It should be understood that for the convenience of description, the sizes of the various parts shown in the drawings are not drawn in accordance with the actual proportion relationship. The technology, methods and devices known to those skilled in the relevant art can not be discussed in detail, but should be considered as part of the authorized specification, if appropriate. In all examples shown and discussed herein, any specific value should be interpreted as merely exemplary, and not as a limitation. Therefore, other examples of exemplary embodiments can have different values. It should be noted that similar reference numbers and letters represent similar items in the following drawings, so once an item is defined in one drawing, it does not need to be further discussed in subsequent drawings.

[0074] In the description of the present application, it should be understood that the orientation words such as "front, back, up, down, left, right", "transverse, vertical, perpendicular, horizontal" and "top, bottom" and the like indicate the orientation or positional relationship shown in the drawings, which are only for the convenience of describing the present application and simplifying the description, and do not indicate and imply that the devices or elements referred to must have a particular orientation or be constructed and operated in a particular orientation, so as not to be construed as a limitation on the scope of protection of the present application: the orientation words "inner, outer" refer to the inner and outer of the contour of each component itself.

[0075] For the convenience of description, spatial relative terms such as "over", "above", "upper surface", "upper" and the like can be used herein to describe the spatial positional relationship of one device or feature with other devices or features as shown in the drawings. It should be understood that the spatial relative terms are intended to include different orientations in use or operation in addition to the orientation of the devices described in the drawings. For example, if the devices in the drawings are inverted, the device described as "above" or "over" other devices or structures will be positioned "below" or "under" other devices or structures. Thus, the exemplary term "above" can include both "above" and "below" orientations. The device can also be positioned in other different ways (rotated 90 degrees or in other orientations), and the spatial relative descriptions used herein are interpreted accordingly.

[0076] In addition, it should be noted that the use of the words "first", "second" and the like to define parts is only for the convenience of distinguishing the corresponding parts, and the above words have no special meaning unless otherwise stated, and therefore cannot be construed as a limitation on the scope of protection of the present application.

[0077] The present application provides a method for calculating the bit error rate of an underwater wireless optical communication system based on carrierless amplitude phase modulation, comprising:

[0078] S1, simulate the ocean turbulent channel model based on the lognormal distribution, and consider the influence of absorption and scattering, establish the transmission model of the underwater wireless optical communication channel;

[0079] S2, deduce the signal-to-noise ratio of the underwater wireless optical communication system under the combined action of the ocean turbulent and absorption and scattering based on the lognormal distribution;

[0080] S3, using the properties of the lognormal distribution, deduce the relationship between the signal-to-noise ratio of the underwater wireless optical communication system under the combined action of the ocean turbulent and absorption and scattering based on the lognormal distribution and the signal-to-noise ratio considering only the absorption and scattering effect;

[0081] S4, based on the bit error rate formula of the carrierless amplitude phase modulation, using the Gauss-Hermite orthogonal integral formula, the average bit error rate expression of the end-to-end closed underwater wireless optical system under the joint action of the lognormal distribution of the ocean turbulence and absorption and scattering is obtained, and the simulation verification is carried out through the Monte Carlo method.

[0082] In specific implementation, as a preferred embodiment of the present application, in the step S1, the transmission model of the underwater wireless optical communication channel is established based on the lognormal distribution simulation of the ocean turbulence channel model and considering the influence of absorption and scattering, and specifically includes:

[0083] Let x be the transmitted signal sequence, y be the received signal sequence, and the transmission model y of the electrical signal received by the receiver in the underwater wireless optical communication system is represented as:

[0084]

[0085]

[0086] Wherein, η represents the photoelectric conversion coefficient, x represents the transmitted information, v represents the additive white Gaussian noise with a mean of 0 and a variance of σ 2 ; P t represents the transmitted optical power, I i represents the energy change of the optical signal at the receiver when the i-th channel is affected by turbulence, H i represents the channel gain when the i-th channel is affected by absorption and scattering, and N t represents the number of transmitters.

[0087] In specific implementation, as a preferred embodiment of the present application, in the step S2, the signal-to-noise ratio of the underwater wireless optical communication system under the joint action of the ocean turbulence and absorption and scattering based on the lognormal distribution is derived, and specifically includes:

[0088] Since the distance between the transceiver and the receiver is much larger than the wavelength and the coherence length of light, the I i fading between the channels is mutually independent and identically distributed, so that:

[0089] When only absorption and scattering are included, the average signal-to-noise ratio of the underwater wireless optical communication system is:

[0090]

[0091] When absorption, scattering and turbulence are included, the average signal-to-noise ratio of the underwater wireless optical communication system is:

[0092]

[0093] Wherein, E represents the mathematical expectation of x 2 (t), and N0 represents the one-sided power spectral density of the additive Gaussian noise.

[0094] In a specific implementation, as a preferred embodiment of the present invention, step S3 utilizes the properties of the log-normal distribution to derive the relationship between the signal-to-noise ratio (SNR) of an underwater wireless optical communication system under the combined effects of ocean turbulence and absorption / scattering based on the log-normal distribution and the SNR considering only absorption and scattering effects. Specifically, this includes:

[0095] In this embodiment, the properties of the log-normal distribution used are mainly the following two:

[0096] 1. If I follows a mean of μ ρ The variance is σ ρ 2 If a follows a log-normal distribution and a is a constant, then aI follows a mean of μ. ρ +lna, with a mean of σ ρ 2 The log-normal distribution;

[0097] II. If I i Follows the mean μ i The variance is σ i 2 Given a log-normal distribution, i = 1, 2, ..., n, and the variables are relatively independent, then ∑I i You can use e k To approximate, where e k Follows the mean μ k The variance is σ k 2 Log-normal distribution, k follows a mean of μ k The variance is σ k 2 It follows a normal distribution.

[0098] Since the fading between each branch is independent, another log-normal distribution variable e is used. k It is approximately equal to the weighted sum of the log-normal fading coefficients of each branch, and its expression is:

[0099]

[0100] μ γ =μ A ·e 2k

[0101] Where k follows a mean of μ k The variance is σ k 2 The normal distribution has the following mean and variance:

[0102]

[0103] .

[0104] In specific implementation, as a preferred embodiment of the present application, in the step S4, based on the bit error rate formula of the carrierless amplitude phase modulation, the Gaussian-Hermite orthogonal integral formula is used to obtain the average bit error rate expression of the end-to-end closed underwater wireless optical system under the combined action of the ocean turbulence and absorption and scattering of the lognormal distribution, and the simulation verification is performed through the Monte Carlo method, and specifically includes:

[0105] The conditional bit error rate of the carrierless amplitude phase modulation is:

[0106]

[0107] Wherein, M represents the order of the carrierless amplitude phase modulation, the Q function formula is g represents the direct current bias coefficient, SNR represents the effective electrical signal-to-noise ratio of each carrierless amplitude phase modulation symbol, and the relationship between SNR and μ A , μ r can be expressed as:

[0108]

[0109] Therefore, the conditional bit error rate of the carrierless amplitude phase modulation can be further transformed as:

[0110]

[0111] Wherein, e k represents a lognormal distribution variable with μ k as the mean value and σ k as the variance. 2

[0112] Therefore, the bit error rate of the underwater wireless optical communication system based on the carrierless amplitude phase modulation can be expressed as:

[0113]

[0114] Wherein, the expression of f k (k) is a normal distribution N(μ k , σ k 2 ), and the variable x is set as:

[0115]

[0116] The x is brought into the bit error rate expression of the underwater wireless optical communication system to replace the variable k, and finally the bit error rate can be transformed as:

[0117] P e = P e1 + Pe2

[0118]

[0119]

[0120] where P e represents the bit error rate of the UWC system based on the carrierless amplitude phase modulation, P e is split into the sum of two terms, P e1 represents the first term, P e2 represents the second term.

[0121] The Gaussian-Hermite orthogonal integral formula is:

[0122]

[0123] According to the Gaussian-Hermite orthogonal integral formula, the final bit error rate closed expression can be represented as:

[0124] P e = P e1 + P e2

[0125]

[0126]

[0127] Embodiment

[0128] The correctness of the application can be verified by comparing the bit error rate curve obtained by the Monte Carlo numerical simulation with the theoretical result to improve the reliability of the system model. The bit error performance of different turbulence intensities, different link distances and different modulation orders is compared in the embodiment of the application.

[0129] Figure 1The block diagram of the underwater wireless optical communication system based on the carrierless amplitude phase modulation is given. Fig. 2 (a), Fig. 2 (b), Fig. 2 (c) and Fig. 2 (d) respectively give the bit error rate characteristics of the underwater wireless optical communication system based on the carrierless amplitude phase modulation under four kinds of flicker indexes, considering the independent and identically distributed. It can be seen that the numerical simulation results have good matching effect with the derived closed-form analytical results, which verifies the correctness of the bit error rate calculation method proposed in the application. It can also be seen that under the same water environment and the same modulation order, the bit error rate performance decreases with the increase of the flicker coefficient, that is, the increase of the turbulence intensity. From Fig. 2 (a) and Fig. 2 (b), it can be seen that when the water environment becomes turbid, that is, the attenuation caused by absorption and scattering effect increases, the system bit error rate increases under the same signal-to-noise ratio condition and the same modulation mode. This conclusion can also be seen from Fig. 2 (c) and Fig. 2 (d). In addition, the modulation order also has a great influence on the system performance. From Fig. 2 (a), Fig. 2 (b), Fig. 2 (c) and Fig. 2 (d), it can be seen that under the same conditions, the system bit error rate increases with the increase of the modulation order. From Fig. 2 (a), Fig. 2 (b), Fig. 2 (c) and Fig. 2 (d), it can be seen that with the increase of the link distance, the fading caused by turbulence effect increases, at the same time, the fading caused by absorption and scattering effect also increases, which leads to the increase of the system bit error rate under the same signal-to-noise ratio condition and the same modulation mode. Figure 3 Figure 4

[0130] Finally, it should be pointed out that: the above embodiments are only used to illustrate the technical solutions of the application, but not to limit it; although the application has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that they can still modify the technical solutions recorded in the foregoing embodiments, or make equivalent replacement for part or all of the technical features; and these modifications or replacements do not make the essence of the corresponding technical solutions deviate from the scope of the technical solutions of the embodiments of the application.​​

Claims

1. A method for calculating the bit error rate of an underwater wireless optical communication system based on a carrierless amplitude phase modulation, characterized in that, The application relates to a method for calculating the bit error rate of an underwater wireless optical communication system, and belongs to the field of underwater wireless optical communication. A transmission model of an underwater wireless optical communication channel is established based on a lognormal distribution simulation of an ocean turbulence channel model and considering the influence of absorption and scattering; A signal-to-noise ratio of an underwater wireless optical communication system under the combined action of ocean turbulence based on a lognormal distribution and absorption and scattering is derived; The relationship between the signal-to-noise ratio of the underwater wireless optical communication system under the combined action of ocean turbulence based on a lognormal distribution and absorption and scattering and the signal-to-noise ratio considering only the effect of absorption and scattering is derived based on the properties of the lognormal distribution; Based on the bit error rate formula of a carrierless amplitude phase modulation, a high Gauss-Hermite orthogonal integral formula is used to obtain an end-to-end closed average bit error rate expression of the underwater wireless optical system under the combined action of ocean turbulence based on a lognormal distribution and absorption and scattering, and simulation verification is carried out through a Monte Carlo method, including: The conditional bit error rate of the carrierless amplitude phase modulation is: wherein denotes the order of the carrierless amplitude and phase modulation, Q the function formula is , denotes the DC bias coefficient, SNR denotes the effective electrical signal-to-noise ratio per carrierless amplitude and phase modulation symbol, SNR and , the relationship can be expressed as: Therefore, the conditional bit error rate of the carrierless amplitude phase modulation can be further transformed as: wherein, denotes a lognormal distributed variable with mean and variance . Therefore, the bit error rate of the underwater wireless optical communication system based on the carrierless amplitude phase modulation can be expressed as: wherein The expression is a normal distribution Setting the variable is: Will x Substitute the variable into the bit error rate expression of the underwater wireless optical communication system, replacing it with... k The final bit error rate can be transformed into: wherein, denotes the bit error rate of a UWOC system based on carrierless amplitude phase modulation, with split into the sum of two terms, denotes the first term, denotes the second term; The Gauss-Hermite orthogonal integral formula is: According to the Gauss-Hermite orthogonal integral formula, the final closed expression of the bit error rate can be expressed as: 。 2. The method of claim 1, wherein the method is a method of calculating a bit error rate of a carrier-less amplitude phase modulation based underwater wireless optical communication system. The application relates to a method for calculating the bit error rate of an underwater wireless optical communication system, and belongs to the field of underwater wireless optical communication. Let for transmitting a signal sequence, for receiving a signal sequence, a transmission model of an electrical signal received by a receiver in an underwater wireless optical communication system is represented as: wherein, denotes the photoelectric conversion coefficient, denotes the transmitted information, denotes additive white Gaussian noise with mean 0 and variance denotes the transmitted information, denotes the transmitted optical power, denotes the energy of the optical signal at the receiver when the th channel is affected by turbulence, denotes the channel gain when the th channel is affected by absorption and scattering, denotes the number of transmitters.

3. The method of claim 2, wherein the method is characterized by: The application relates to a method for calculating the bit error rate of an underwater wireless optical communication system, and belongs to the field of underwater wireless optical communication. Since the distance between transceivers is much larger than the wavelength and coherence length of light, the fading between channels is mutually independent and identically distributed, so that: ​ The average signal-to-noise ratio of the underwater wireless optical communication system only considering absorption and scattering is: The average signal-to-noise ratio of the underwater wireless optical communication system considering absorption, scattering and turbulence is: wherein denotes the mathematical expectation of denotes the one-sided power spectral density of the additive Gaussian noise.

4. The method of claim 2, wherein the method is characterized by: The application relates to a method for calculating the bit error rate of an underwater wireless optical communication system, and belongs to the field of underwater wireless optical communication. Since the fading among the branches is independent, another lognormal variable approximately equals the weighted sum of the lognormal fading coefficients of the branches, expressed as in, Follow the mean The variance is The normal distribution has the following mean and variance: 。 5. The method of claim 4, wherein the method further comprises: The properties of the lognormal distribution include: The properties of the lognormal distribution include: If follows a lognormal distribution with mean and variance and is constant, then follows a lognormal distribution with mean and mean ; like Follow the mean The variance is The log-normal distribution And since each variable is relatively independent, then use To approximate, where Follow the mean The variance is Log-normal distribution Follow the mean The variance is It follows a normal distribution.

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