Method for calculating average bit error rate of vertical layered UWOC system under malicious interference

Abstract

The invention discloses a method for calculating the average bit error rate of a vertical layered UWOC system under malicious interference, and the method comprises the steps: building a composite channel fading model of a legal link and an interference link, and obtaining a probability density function and a cumulative distribution function of a composite channel fading coefficient; obtaining a system error rate under malicious interference based on a threshold detection method, and obtaining an average error rate of an SISO-vertical layering UWOC system under malicious interference; a cumulative distribution function and a probability density function are obtained based on a selective merging scheme, and the average bit error rate of the SIMO-vertical layering UWOC system under malicious interference is obtained; and obtaining a moment generation function and a probability density function based on an equal gain merging scheme, and obtaining an average bit error rate of the SIMO-vertical layering UWOC system under malicious interference. The method can be used for calculating the average bit error rate performance of the vertical layered underwater wireless optical communication system influenced by malicious interference, and provides reference for an interference mitigation scheme.

Description

Technical Field

[0001] The present invention belongs to the technical field of underwater wireless optical communication, and specifically relates to a calculation method for the average bit error rate of a vertical layered UWOC system based on a multi-level cascaded EGG ocean turbulence channel under the influence of malicious interference. Background Art

[0002] With the continuous progress of science and technology and the expansion of the scope of human activities, underwater operations are receiving increasing attention, including ocean data collection, underwater rescue, tactical surveillance, and offshore exploration. To meet these needs, researchers have been committed to exploring efficient and reliable underwater wireless communication technologies. Currently, underwater wireless communication methods can be classified into three categories according to the carriers used: radio frequency (RF) communication, acoustic wave communication, and wireless optical communication. Although RF signals can achieve a transmission rate of several hundred Mbps and cover a distance of dozens of kilometers in the atmosphere, they are severely attenuated in the underwater environment, greatly limiting their transmission distance. As a traditional choice for underwater communication, acoustic wave communication can reach a transmission distance of kilometers, but its low bandwidth and high latency make it difficult to meet the requirements of data transmission. In contrast, underwater wireless optical communication (UWOC) exhibits broad application prospects and has become an important development direction for future underwater communication due to its many advantages such as high transmission rate, low power consumption, high security, and low implementation cost.

[0003] Although UWOC technology has many advantages, its performance is still limited by various factors, mainly including the absorption and scattering of seawater, ocean turbulence, and pointing error. Seawater has a complex composition, and pure seawater, chlorophyll, and particulate matter determine the intensity of the absorption and scattering effects. Ocean turbulence is usually caused by refractive index fluctuations due to changes in seawater temperature and salinity, resulting in random scattering and refraction of optical signals, which significantly affects the performance of UWOC systems. In addition, when the transceiver devices of UWOC systems are affected by factors such as strong winds and waves at sea, they will sway and vibrate, resulting in a random offset between the beam center and the detector center and being unable to be fully aligned, that is, pointing error occurs. These factors jointly affect the reliability of UWOC systems. Therefore, when studying UWOC systems, these limiting factors must be fully considered.

[0004] However, most current UWOC research is based on a common assumption that the turbulence intensity in the entire transmission link is constant. However, this assumption only applies to horizontal transmission links with a fixed depth. In many practical application scenarios, such as data transmission between underwater sensor networks or deep-sea observatories and surface platforms, the underwater communication link is usually a vertical link. Compared with horizontal links, vertical underwater links are more complex because the physical properties of seawater change with depth. Specifically, the seawater temperature and salinity gradients change with depth, forming ocean stratification, which leads to changes in the refractive index and further causes depth dependence of the turbulence intensity. Therefore, the assumption of constant turbulence intensity is no longer applicable to vertical links. To accurately describe the characteristics and laws of vertical underwater links, more accurate modeling needs to be carried out for their depth dependence. In this regard, researchers have proposed a cascaded stratified turbulence model to simulate vertical UWOC links, and this stratified model has been widely recognized in the academic community. In addition, since bubbles and temperature gradients have an important impact on the channel, the mixed exponential-generalized gamma (EGG) distribution is needed to model the turbulence in each layer of the vertical stratified channel model to more accurately characterize its statistical properties.

[0005] With the increasing global deployment of wireless optical communication technology, security and privacy protection in communication networks have become key challenges for the sustainable development of this technology. Since wireless optical communication typically operates in a light-transmitting window with low attenuation, its operating wavelength is easily predictable. In addition, to improve the efficiency of received signals, optical detectors usually need to maintain a wide field of view (FoV), and wireless optical communication relies on line-of-sight transmission, making the positions of transceivers easily detectable by enemies. Due to the influence of these factors, wireless optical communication systems are vulnerable to malicious interference attacks, which pose a serious threat to military applications or other scenarios that require high security. To study the interference mechanism and formulate corresponding interference mitigation strategies to effectively improve the efficiency of wireless optical communication networks, more in-depth research is urgently needed. In terms of the study of interference effects, Pratiti Paul et al. considered the effects of negative exponential turbulence fading and pointing error, and studied the bit error and outage performance of single-input single-output (SISO) and multiple-input single-output (MISO) free space optical communication (FSO) systems under interference. To mitigate the interference effects in FSO communication networks, Ashish Kant Shukla et al. proposed a buffer-assisted relay-based scheme and evaluated the outage probability and average bit error rate of the considered FSO system. Prakriti Saxena et al. considered the combined effects of atmospheric turbulence, pointing error, and angle-of-arrival fluctuations, and studied the impact of malicious jammers on the performance of an unmanned aerial vehicle (UAV)-relayed and intelligent reflecting surface (IRS)-assisted FSO communication system. In addition, Jingyu Wang et al. studied the impact of random interference on the ergodic channel capacity, outage probability, and average bit error rate of an FSO communication system based on a more generalized Málaga statistical distribution model, combined with pointing error and atmospheric attenuation factors.

[0006] The disadvantages of the prior art are as follows:

[0007] (1) Existing research on the impact of malicious interference on wireless optical communication systems has not covered relevant research in the marine environment.

[0008] (2) When quantifying the turbulence effect in existing UWOC systems based on spatial diversity, the complex effects of seawater bubbles and temperature gradients are not considered.

[0009] (3) Existing solutions to mitigate the impact of malicious interference on wireless optical communication systems are still limited. In particular, existing MISO solutions have not achieved a closed-form solution.

[0010] (4) There is a lack of a method for calculating the average bit error rate of a vertically layered UWOC system under the influence of interference, and there is also a lack of a method for calculating the average bit error rate of applying the SIMO technology to a system affected by interference.

[0011] According to the above analysis, it can be seen that the impact of malicious interference on communication systems has attracted wide attention. However, existing work mainly focuses on FSO systems, and there are no relevant reports on the impact of malicious interference on the performance of UWOC systems. Therefore, it is of great significance to study the average bit error rate of a vertically layered UWOC system under malicious interference and explore effective interference mitigation techniques. Summary of the Invention

[0012] To solve the above-mentioned defects in the prior art, the purpose of the present invention is to provide a method for calculating the average bit error rate of a vertically layered UWOC system under the influence of malicious interference. Considering the comprehensive influence of seawater path loss, multi-level cascaded EGG ocean turbulence channel, and pointing error, a composite channel fading model of the legitimate link and the interference link in a vertically layered UWOC system under malicious interference is constructed. Based on the threshold detection method, a method for calculating the average bit error rate of the SISO-vertically layered UWOC system is proposed; and the SIMO technology is introduced to mitigate the influence of the interference effect, and a method for calculating the average bit error rate of the SIMO-vertically layered UWOC system under the selection combining and equal gain combining schemes is proposed, so as to effectively evaluate the influence of malicious interference on the bit error performance of the average bit error rate of the vertically layered UWOC system and the interference mitigation effect of the SIMO technology.

[0013] The present invention is implemented through the following technical solutions.

[0014] One aspect of the present invention provides a method for calculating the average bit error rate of a vertically layered UWOC system under malicious interference, including:

[0015] Considering the SISO-vertically layered UWOC system model affected by a malicious jammer, a composite channel fading model of the legitimate link and the interference link is established, and the probability density function and cumulative distribution function of the composite channel fading coefficient of the legitimate link and the interference link are obtained;

[0016] According to the probability density function of the composite channel fading coefficient of the legitimate link and the interference link, the system bit error rate under malicious interference is obtained based on the threshold detection method, and then the average bit error rate of the SISO-vertically layered UWOC system under malicious interference is obtained;

[0017] Considering the SIMO - vertical layered UWOC system model affected by malicious jammers, based on the selection combining scheme, the cumulative distribution function and probability density function of the end - to - end equivalent channel fading coefficient of the legitimate link when using selection combining are obtained. Furthermore, the average bit error rate of the SIMO - vertical layered UWOC system under malicious interference when using the selection combining scheme is obtained.

[0018] Based on the equal - gain combining scheme, the moment - generating function and probability density function of the end - to - end equivalent channel fading coefficient of the legitimate link when using equal - gain combining are obtained. Furthermore, the average bit error rate of the SIMO - vertical layered UWOC system under malicious interference when using the equal - gain combining scheme is obtained.

[0019] Preferably, a composite channel fading model of the legitimate link and the interference link is established, and the probability density function and cumulative distribution function of the composite channel fading coefficient of the legitimate link and the interference link are obtained, including:

[0020] The input - output relationship of the SISO - vertical layered UWOC system model affected by malicious jammers is established, and a composite channel fading model of the legitimate link and the interference link is established.

[0021] According to the composite channel fading model, the probability density function of the composite channel fading coefficient of the legitimate link and the interference link is obtained.

[0022] From the probability density function of the composite channel fading coefficient, the cumulative distribution function of the composite channel fading coefficient of the legitimate link and the interference link is further obtained by integration.

[0023] Preferably, based on the threshold detection method, the system bit error rate under malicious interference is obtained, and then the average bit error rate of the SISO - vertical layered UWOC system under malicious interference is obtained, including:

[0024] When there is a malicious jammer, according to the possible bit - error events and based on the threshold detection method, the system bit error rate under malicious interference is obtained.

[0025] From the system bit error rate under malicious interference, the average bit error rate of the SISO - vertical layered UWOC system under malicious interference is obtained.

[0026] Preferably, based on the selection combining scheme, the cumulative distribution function and probability density function of the end - to - end equivalent channel fading coefficient of the legitimate link when using selection combining are obtained. Furthermore, the average bit error rate of the SIMO - vertical layered UWOC system under malicious interference when using the selection combining scheme is obtained, including:

[0027] The input - output relationship of the SIMO - vertical layered UWOC system model affected by malicious jammers is established.

[0028] The receiving end adopts a selection combining scheme to receive signals, and obtains the equivalent channel fading coefficient of the legitimate link end-to-end when using selection combining.

[0029] According to the equivalent channel fading coefficient of the legitimate link end-to-end, the cumulative distribution function of the equivalent channel fading coefficient of the legitimate link end-to-end when using selection combining is obtained.

[0030] According to the cumulative distribution function of the equivalent channel fading coefficient of the legitimate link end-to-end, by taking the derivative, the probability density function of the equivalent channel fading coefficient of the legitimate link end-to-end when using selection combining is obtained.

[0031] According to the probability density function of the equivalent channel fading coefficient of the legitimate link end-to-end, the average bit error rate of the SIMO-Vertical Layered UWOC system under malicious interference when using the selection combining scheme is obtained.

[0032] Preferably, based on the equal gain combining scheme, the moment generating function and the probability density function of the equivalent channel fading coefficient of the legitimate link end-to-end when using equal gain combining are obtained, and then the average bit error rate of the SIMO-Vertical Layered UWOC system under malicious interference when using the equal gain combining scheme is obtained, including:

[0033] The receiving end adopts an equal gain combining scheme to receive signals, and obtains the equivalent channel fading coefficient of the legitimate link end-to-end when using equal gain combining.

[0034] According to the equivalent channel fading coefficient of the legitimate link end-to-end, the moment generating function of the equivalent channel fading coefficient of the legitimate link end-to-end when using equal gain combining is obtained.

[0035] According to the moment generating function of the equivalent channel fading coefficient of the legitimate link end-to-end, through the inverse Laplace transform, the probability density function of the equivalent channel fading coefficient of the legitimate link end-to-end when using equal gain combining is obtained.

[0036] According to the probability density function of the equivalent channel fading coefficient of the legitimate link end-to-end, the average bit error rate of the SIMO-Vertical Layered UWOC system under malicious interference when using the equal gain combining scheme is obtained.

[0037] Due to the adoption of the above technical solutions, the present invention has the following beneficial effects:

[0038] 1. The present invention extends the research on the interference effect of the wireless optical communication system from the atmospheric environment to the ocean environment, and considers a UWOC system model affected by a malicious jammer to study the interference effect more comprehensively.

[0039] 2. When modeling the composite channel fading of the interfering link and the legitimate link in the system, the present invention comprehensively considers the path loss caused by the seawater absorption and scattering effects, the multi-level cascaded EGG ocean turbulence, and the influence of pointing errors; in particular, for the ocean turbulence effects caused by bubbles and temperature gradients, and in combination with the depth dependence of the turbulence intensity, a multi-level cascaded EGG ocean turbulence channel is used to simulate the fading caused by ocean turbulence, so as to more accurately simulate the ocean turbulence characteristics in the vertical underwater link.

[0040] 3. The present invention comprehensively considers the influence of seawater path loss, ocean turbulence, and pointing errors, constructs a composite channel fading model for the legitimate link and the interfering link in the system, and provides calculation methods for the average bit error rate of the SISO-vertical layered UWOC system under malicious interference and the average bit error rate of the SIMO-vertical layered UWOC system using selection combining and equal gain combining, which can effectively study the interference effects in the vertical layered UWOC system and provide a reference for interference mitigation schemes.

[0041] 4. The present invention supports the accurate calculation of the average bit error rate under different link layer numbers, interference activity factors, pointing errors of the interfering link and the legitimate link, ocean turbulence parameters, and the number of receiving apertures, expands the calculation method of the average bit error rate of the wireless optical communication system in the ocean environment under interference effects, and provides a theoretical guidance for the design and optimization of the wireless optical communication system under the influence of malicious interference. BRIEF DESCRIPTION OF THE DRAWINGS

[0042] The drawings described herein are used to provide a further understanding of the present invention, form a part of this application, and do not constitute an improper limitation to the present invention. In the drawings:

[0043] Figure 1 is a block diagram for implementing the calculation method of the average bit error rate of the vertical layered UWOC system under malicious interference;

[0044] Figure 2 is a schematic diagram of the vertical layered UWOC system model affected by a malicious jammer;

[0045] Figure 3 is the average bit error rate of the SISO-vertical layered UWOC system affected by a malicious jammer under different link layer numbers;

[0046] Figure 4 is the average bit error rate of the SISO-vertical layered UWOC system affected by a malicious jammer under different interference activity factors and different link layer numbers;

[0047] Figure 5The average bit error rate of a SISO - vertical layered UWOC system affected by a malicious jammer under conditions of different interference link pointing errors and different numbers of link layers;

[0048] Figure 6 The average bit error rate of a SISO - two - layer vertical UWOC system affected by a malicious jammer under conditions of different temperature gradients, bubble levels, and water types;

[0049] Figure 7 The average bit error rate of a SISO - three - layer vertical UWOC system affected by a malicious jammer under conditions of different temperature gradients and different bubble levels in fresh water;

[0050] Figure 8 The average bit error rate of SISO and SIMO - vertical layered UWOC systems affected by a malicious jammer under conditions of different numbers of receiving apertures and different combining schemes;

[0051] Figure 9 The average bit error rate of SISO and 1×2 SIMO - vertical layered UWOC systems affected by a malicious jammer under conditions of different interference activity factors and different combining schemes;

[0052] Figure 10 The average bit error rate of SISO and 1×2 SIMO - vertical layered UWOC systems affected by a malicious jammer under conditions of different legitimate link pointing errors and different combining schemes. Detailed implementation manners

[0053] The present invention will be described in detail below with reference to the accompanying drawings and specific embodiments. Here, the schematic embodiments and descriptions of the present invention are used to explain the present invention, but do not limit the present invention.

[0054] Combined with Figure 1 As shown, an embodiment of the present invention provides a method for calculating the average bit error rate of a vertical layered UWOC system under malicious interference, including the following steps:

[0055] Step 1, considering that a single - input single - output (SISO) - vertical layered UWOC system model is affected by a malicious jammer, establish a composite channel fading model for the legitimate link and the interference link, and obtain the probability density function and cumulative distribution function of the composite channel fading coefficients of the legitimate link and the interference link.

[0056] 1a) Establish the input - output relationship of the SISO - vertical layered UWOC system model affected by a malicious jammer, and establish a composite channel fading model for the legitimate link and the interference link.

[0057] Refer toFigure 2 , the SISO - vertically layered UWOC system model affected by a malicious jammer consists of a legitimate transmitter, a malicious random jammer, and a receiver, where the receiver has a receiving aperture; the underwater link is set as an N - layer cascaded structure, and the total length of the underwater link represents the thickness of the n - th layer, and n represents the n - th layer of the underwater link; the system uses on - off keying (OOK) intensity modulation and direct detection technology to transmit symbols; the malicious jammer disrupts the legitimate link by sending random interference signals. At the same time, considering that interference noise dominates and additive white Gaussian noise can be ignored. The system considering the impact of the malicious jammer is completely different from the traditional UWOC system that only considers additive white Gaussian noise. The interference is random and experiences a random fading channel, thus increasing the complexity of calculating the average bit - error rate performance of the system.

[0058] After photoelectric conversion at the receiving end, the input - output (I / O) relationship of the SISO - vertically layered UWOC system affected by a malicious jammer can be expressed as

[0059]

[0060] where y is the received signal, η is the responsivity of the photodetector, and without loss of generality, its value is taken as 1, P L represents the peak transmit energy of the legitimate transmitter, x is the modulation signal symbol, h L represents the composite channel fading coefficient of the legitimate link, h J is the composite channel fading coefficient of the interference link, P J is the interference signal power, x J is the interference signal, W J represents the state of the jammer, including two operating modes: jammer on (W J = 1) and jammer off (W J = 0), which follows a Bernoulli distribution. The probability of being active within an OOK symbol period is ρ (referred to as the interference activity factor), and the probability of being idle is (1 - ρ), that is:

[0061]

[0062] where P(*) represents the probability function. Let N J be the average interference power. When the jammer is active, it will transmit an interference signal with a power of P J = N J / ρ.

[0063] The composite channel fading models of the legitimate link and the interference link can be expressed as

[0064] h S = h l,S h t,S h p,S (3)

[0065] where h S is the composite channel fading coefficient of the legitimate link and the interference link; h l,S is the path loss of the legitimate link and the interference link, calculated using the Beer-Lambert law; h t,S is the oceanic turbulence fading coefficient of the legitimate link and the interference link, described by the multi-level cascaded EGG oceanic turbulence channel model; h p,S is the fading caused by pointing error in the legitimate link and the interference link, simulated by the zero boresight pointing error model.

[0066] where the path loss h l,S of the legitimate link and the interference link is calculated as

[0067] h l,S = exp(-c w d w ) (4)

[0068] where c w is the attenuation coefficient of seawater, and exp(*) represents the exponential function.

[0069] where the zero boresight pointing error model can be expressed as

[0070]

[0071] where is the power fraction received at a radial displacement of 0 in the legitimate link and the interference link, erf(*) is the error function, v is a function of r, w z , where r is the receiving aperture radius and w z is the beam width; m S = w zeq / (2σ s ) is the pointing error parameter of the legitimate link and the interference link, reflecting the severity of the pointing error, where w zeq is the equivalent beam radius at the receiver, satisfying the equation σ s is the jitter standard deviation.

[0072] where the oceanic turbulence fading coefficient h t,S is obtained by cascading the oceanic turbulence fading coefficients h t,S,n of each layer, that is where N is the number of layers of the legitimate link and the interference link. The multi-level cascaded EGG oceanic turbulence channel model Denoted as

[0073]

[0074] Wherein is a natural number taking 0 or 1, n S represents the n-th layer of the legitimate link and the interfering link, and Γ(*) represents the gamma function and are both parameters of the EGG distribution model in the n-th layer of the legitimate link and the interfering link represents the Fox-H function in the multi-level cascaded EGG ocean turbulence channel model is a coefficient related to the EGG distribution model parameters in the 1st to Nth layers of the legitimate link and the interfering link

[0075] When modeling the composite channel fading of the interfering link and the legitimate link in the UWOC system under malicious interference, a multi-level cascaded EGG ocean turbulence channel is adopted to simulate the ocean turbulence fading. This model not only considers the characteristic that the ocean turbulence intensity varies with depth, but also takes into account the influence of seawater bubbles and temperature gradient on the channel, improving the accuracy of link modeling. At the same time, the influence of seawater absorption and scattering effects and pointing errors is comprehensively considered, further improving the accuracy of link modeling

[0076] 1b) According to the composite channel fading model, obtain the probability density function of the composite channel fading coefficient of the legitimate link and the interfering link

[0077] From the composite channel fading model of formula (3), by deriving the formula

[0078]

[0079] the composite channel fading coefficient h of the legitimate link and the interfering link can be obtained S The expression of the probability density function is

[0080]

[0081] Wherein, Z S is a function of N, n S , and represents the Fox-H function in the probability density function

[0082] 1c) From the probability density function of the composite channel fading coefficient, further integrate to obtain the expression of the cumulative distribution function of the composite channel fading coefficient of the legitimate link and the interfering link

[0083] The expression of the cumulative distribution function of the composite channel fading coefficient h of the legitimate link and the interfering link S is where

[0084]

[0085] in which represents the Fox-H function in the cumulative distribution function.

[0086] Step 2: According to the probability density function of the composite channel fading coefficients of the legitimate link and the interfering link, based on the threshold detection method, obtain the system bit error rate under malicious interference, and then obtain the average bit error rate of the SISO-Vertical Layered UWOC system under malicious interference.

[0087] 2a) When there is a malicious jammer, according to the possible bit error events and based on the threshold detection method, obtain the expression of the system bit error rate under malicious interference.

[0088] The possible bit error events in the UWOC system include four cases: the jammer is active and the legitimate transmitter transmits symbol "0", the jammer is active and the legitimate transmitter transmits symbol "1", the jammer is idle and the legitimate transmitter transmits symbol "0", and the jammer is idle and the legitimate transmitter transmits symbol "1". The system bit error rate P e can be derived by the following formula

[0089]

[0090] where P(W J =1) and P(W J =0) represent the probabilities that the jammer is active and idle, respectively, within an OOK symbol period; P(x = 0) and P(x = 1) represent the probabilities that the legitimate transmitter transmits symbol "0" and "1", respectively. Usually, they are equal, i.e., P(x = 0) = P(x = 1) = 0.5; P(error|x = 0) and P(error|x = 1) represent the bit error rates under the conditions that the legitimate transmitter transmits symbol "0" and "1", respectively.

[0091] According to step 1a), when the jammer is idle, the receiver can correctly receive the legitimate transmission signal without bit errors, and bit errors occur only when the jammer is active (W J =1).

[0092] Furthermore, the system bit error rate P e is:

[0093]

[0094] The receiver uses a threshold-based detection method to detect the received signal with interference, which is expressed as

[0095]

[0096] Among them, th is the decision threshold, which is defined as h L is the composite channel fading coefficient of the legitimate link. When the legitimate transmitter transmits the symbol "1", the system can ensure error-free transmission, and only the bit error rate when the transmitted symbol is "0" needs to be calculated.

[0097] Define a random variable z as

[0098]

[0099] where h J is the composite channel fading coefficient of the interference link.

[0100] According to formula (8) in step 1b), the probability density function f z (z) of z can be expressed as

[0101]

[0102] where m J is the pointing error parameter of the interference link, is a natural number taking 0 or 1, n J represents the nth layer of the interference link, and are both EGG distribution model parameters in the nth layer of the interference link, is the power fraction received at the radial displacement of 0 in the interference link, h l,J is the path loss of the interference link, Z J is a function of N and n J , where and are both EGG distribution model parameters in the nth layer of the interference link, is a coefficient related to the EGG distribution model parameters from the 1st layer to the Nth layer of the interference link.

[0103] According to formula (1) in step 1a), when the jammer is active, there is a relational expression Furthermore, the probability density function f y (y|x) of y is

[0104]

[0105] Then, the expression of the system bit error rate P e under malicious interference is

[0106]

[0107] where γ J = P L / N J represents the average signal-to-jamming ratio (SJR) of each symbol, and represents the Fox-H function in the system bit error rate.

[0108] 2b) From the expression of the system bit error rate under malicious jamming, the average bit error rate of the SISO - vertical layered UWOC system under malicious jamming is obtained.

[0109] The average bit error rate of the SISO - vertical layered UWOC system under malicious jamming is derived through the following formula

[0110]

[0111] where is the probability density function of the composite channel fading coefficient h of the legitimate link L .

[0112] Substitute the formula (8) in step 1b) into formula (17), and apply the Mellin transform of the product of two Fox-H functions, the closed-form expression of the average bit error rate of the SISO - vertical layered UWOC system under malicious jamming can be obtained as

[0113]

[0114] where m L is the pointing error parameter of the legitimate link, is a natural number taking 0 or 1, n L represents the nth layer of the legitimate link, and are both EGG distribution model parameters in the nth layer of the legitimate link, represents the Fox-H function in the average bit error rate, is the power fraction received at the radial displacement of 0 in the legitimate link, h l,L is the path loss of the legitimate link, Z L is a function of N, n L , where and are both exponential - generalized gamma distribution model parameters in the nth layer of the legitimate link, is a coefficient related to the EGG distribution model parameters from the 1st layer to the Nth layer of the legitimate link.

[0115] Step 3: Considering the Single-Input Multiple-Output (SIMO)-vertical layered UWOC system model affected by malicious jammers, establish the input-output relationship of the system; based on the selection combining scheme, obtain the end-to-end equivalent channel fading coefficient of the legitimate link when using selection combining, obtain its cumulative distribution function and probability density function, and further obtain the average bit error rate of the SIMO-vertical layered UWOC system under malicious interference when using the selection combining scheme.

[0116] 3a) Establish the input-output relationship of the SIMO-vertical layered UWOC system model affected by malicious jammers.

[0117] Consider the SIMO-vertical layered UWOC system model with K receiving apertures at the receiver. At this time, after the optoelectronic conversion at the receiving end, the input-output relationship of the SIMO-vertical layered UWOC system affected by malicious jammers is expressed as

[0118]

[0119] where, h L,SIMO represents the end-to-end equivalent channel fading coefficient of the legitimate link in the SIMO-vertical layered UWOC system. Under the selection combining scheme, h L,SIMO is denoted as h L,SC ; under the equal gain combining scheme, h L,SIMO is denoted as h L,EGC .

[0120] 3b) The receiver uses the selection combining scheme to receive signals, and obtain the end-to-end equivalent channel fading coefficient of the legitimate link when using selection combining.

[0121] When the receiver uses the Selection Combining (SC) scheme to receive signals, only the diversity aperture with the maximum received intensity is processed. At this time, the end-to-end equivalent channel fading coefficient h L,SC can be expressed as

[0122] h L,SC = max(h L,1 , h L,2 ,..., h L,K ) (20)

[0123] where, max(*) represents the maximum value function, K is the number of receiving apertures, and h L,1 , h L,2 ,..., h L,K are the composite channel fading coefficients of the 1st to the Kth legitimate links, and the composite channel fading coefficients of each branch are independent of each other.

[0124] 3c) Obtain the cumulative distribution function expression of the end-to-end equivalent channel fading coefficient of the legitimate link when using selection combining according to the end-to-end equivalent channel fading coefficient of the legitimate link.

[0125] The end-to-end equivalent channel fading coefficient h of the legitimate link L,SC Cumulative distribution function expression Is derived from the following formula

[0126]

[0127] where k represents the k-th legitimate link, Represents the cumulative distribution function of the composite channel fading coefficient of the k-th legitimate link.

[0128] From formula (8) in step 1b), the cumulative distribution function expression of the end-to-end equivalent channel fading coefficient h of the legitimate link when using selection combining can be further derived L,SC Cumulative distribution function expression Is

[0129]

[0130] where, Is a natural number taking 0 or 1, m L,k Is the pointing error parameter of the k-th legitimate link, n L,k Represents the n-th layer of the k-th legitimate link, And Are both EGG distribution model parameters in the n-th layer of the k-th legitimate link, Represents the multivariate Fox-H function in the cumulative distribution function, Is a coefficient related to the EGG distribution model parameters from the 1st layer to the Nth layer of the k-th legitimate link, [*] k＝1：K Represents replication in K dimensions, Is a coefficient related to parameters such as path loss, power fraction received at radial displacement of 0, h L,SC etc. among the 1st to Kth legitimate links, where, Are respectively the power fractions received at radial displacement of 0 in the 1st and Kth legitimate links, h l,L,1 , h l,L,K Are respectively the path losses of the 1st and Kth legitimate links, Z L,1 Is a function of N, n L,1 , Among them, n L,1 Represents the n-th layer of the 1st legitimate link, Are both exponential-generalized gamma distribution model parameters in the n-th layer of the 1st legitimate link, Is a natural number taking 0 or 1, ZL,K is a function of N and n L,K , where n L,K represents the n-th layer of the K-th legitimate link, and are all parameters of the exponential-generalized gamma distribution model in the n-th layer of the K-th legitimate link, and is a natural number taking 0 or 1.

[0131] 3d) According to the cumulative distribution function of the end-to-end equivalent channel fading coefficient of the legitimate link, by taking the derivative, the probability density function of the end-to-end equivalent channel fading coefficient of the legitimate link when selection combining is adopted is obtained.

[0132] The probability density function of the end-to-end equivalent channel fading coefficient h L,SC of the legitimate link when selection combining is adopted is

[0133]

[0134] where {*} k＝1:K represents replication in different dimensions, and represents the multivariate Fox-H function in the probability density function when the selection combining scheme is adopted.

[0135] 3e) According to the probability density function of the end-to-end equivalent channel fading coefficient of the legitimate link, the closed-form expression of the average bit error rate of the SIMO-vertically layered UWOC system under malicious interference when the selection combining scheme is adopted is obtained.

[0136] The average bit error rate of the SIMO-vertically layered UWOC system under malicious interference when the selection combining scheme is adopted has the following derived expression

[0137]

[0138] According to the probability density function of the end-to-end equivalent channel fading coefficient of the legitimate link in formula (23) and the derived expression of the average bit error rate in formula (24), the closed-form expression of the average bit error rate of the SIMO-vertically layered UWOC system under malicious interference when the selection combining scheme is adopted can be obtained through integration is

[0139]

[0140] where, represents the multivariate Fox-H function in the average bit error rate when the selection combining scheme is adopted, [*] n＝1:N represents replication in N dimensions, is a coefficient related to parameters such as path loss, power fraction received at a radial displacement of 0, and interference activity factor in the first to the Kth legitimate links, where Ξ 1 is related to Z L,1 , h l,J , Z J , h l,L,1 is a function of, Ξ K is related to Z L,K , h l,J , Z J , h l,L,K is a function of.

[0141] Step 4: Based on the equal gain combining scheme, obtain the end-to-end equivalent channel fading coefficient of the legitimate link when using equal gain combining, obtain its moment generating function and probability density function, and further obtain the average bit error rate of the SIMO - vertical layered UWOC system under malicious interference when using the equal gain combining scheme.

[0142] 4a) The receiving end uses the equal gain combining scheme to receive the signal, and obtains the end-to-end equivalent channel fading coefficient of the legitimate link when using equal gain combining.

[0143] When the receiving end uses the equal gain combining (EGC) scheme, the output signals of each branch are combined with the same gain. At this time, the end-to-end equivalent channel fading coefficient h L,EGC can be expressed as

[0144]

[0145] 4b) According to the end-to-end equivalent channel fading coefficient of the legitimate link, obtain the expression of the moment generating function of the end-to-end equivalent channel fading coefficient of the legitimate link when using equal gain combining.

[0146] The moment generating function (Moment Generating Function, MGF) of the end-to-end equivalent channel fading coefficient h L,EGC of the legitimate link when using equal gain combining is derived through the following formula

[0147]

[0148] where t represents the random variable, represents the moment generating function of the composite channel fading coefficient of the kth legitimate link.

[0149] According to formula (8) in step 1b), using the definition formula of the moment generating function After further derivation, the moment generating function expression of the end-to-end equivalent channel fading coefficient \(h\) of the legitimate link with equal gain combining is obtained. L,EGC is For

[0150]

[0151] where represents the multivariate Fox-H function in the moment generating function, is a coefficient related to parameters such as path loss, power fraction received at radial displacement of 0, and random variable \(t\) in the first to \(K\) legitimate links.

[0152] 4c) According to the moment generating function of the end-to-end equivalent channel fading coefficient of the legitimate link, through the inverse Laplace transform, the probability density function of the end-to-end equivalent channel fading coefficient of the legitimate link with equal gain combining is obtained.

[0153] The probability density function of the end-to-end equivalent channel fading coefficient \(h\) of the legitimate link with equal gain combining L,EGC is For

[0154]

[0155] where represents the multivariate Fox-H function in the probability density function with the equal gain combining scheme.

[0156] 4d) According to the probability density function of the end-to-end equivalent channel fading coefficient of the legitimate link, the closed-form expression of the average bit error rate of the SIMO-Vertical Layered UWOC system under malicious interference with the equal gain combining scheme is obtained.

[0157] The average bit error rate of the SIMO-Vertical Layered UWOC system under malicious interference with the equal gain combining scheme The derived expression is as follows

[0158]

[0159] According to the probability density function of the end-to-end equivalent channel fading coefficient of the legitimate link in formula (29) and the derived expression of the average bit error rate in formula (30), through integration, the closed-form expression of the average bit error rate of the SIMO-Vertical Layered UWOC system under malicious interference with the equal gain combining scheme can be obtained For

[0160]

[0161] where represents the multivariate Fox-H function in the average bit error rate with the equal gain combining scheme.

[0162] Verify the correctness of the average bit error rate calculation expressions for the SISO - vertical layered UWOC system and the SIMO - vertical layered UWOC system under malicious interference through Monte Carlo simulation. Evaluate the effects of the number of link layers, interference activity factor, pointing errors of the interference link and the legitimate link, temperature gradient of seawater, bubble level, and the number of receiving apertures on the average bit error rate performance of the vertical layered UWOC system affected by a malicious jammer.

[0163] The correctness and advantages of the present invention can be further illustrated by the following comparison of theoretical results:

[0164] In the method of the present invention, analytical calculations are performed through MATLAB and simulation verification is carried out using Monte Carlo simulation.

[0165] First, accurately derive the closed - form expressions for the average bit error rate of the SISO - vertical layered UWOC system and the closed - form expressions for the average bit error rate of the SIMO - vertical layered UWOC system adopting the selection combining and equal - gain combining schemes under the influence of malicious interference; subsequently, use MATLAB software to numerically simulate and verify the average bit error rate of the vertical layered UWOC system under malicious interference, verifying the correctness of the proposed calculation method of the present invention. In addition, based on these calculation methods, under different conditions of the number of link layers, interference activity factor, pointing errors of the interference link and the legitimate link, temperature gradient of seawater, bubble level, and the number of receiving apertures, the curves of the average bit error rate of the vertical layered UWOC system affected by malicious interference versus the average signal - to - interference ratio are plotted, and the effects of different parameters on the average bit error performance of the system are studied in detail.

[0166] Theoretical and simulation results

[0167] Figure 2 A schematic diagram of the vertical layered UWOC system model affected by a malicious jammer is given.

[0168] Figure 3 The curves of the average bit error rate of the SISO - vertical layered UWOC system affected by a malicious jammer versus the average SJR under the conditions of single - layer, two - layer, and three - layer cascaded EGG ocean turbulence channels are given. It can be seen that the theoretical results obtained by the calculation method of the present invention are highly consistent with the Monte Carlo simulation results, confirming the correctness of the proposed average bit error rate calculation method. From Figure 3 It can be observed that in the presence of a jammer, compared with two - layer and three - layer UWOC systems, the single - layer system assuming a constant turbulence intensity within the transmission range fails to reveal the vertical non - uniformity of the UWOC link and underestimates the value of the average bit error rate.

[0169] Figure 4Shows the average bit error rate curves of the SISO - vertical layered UWOC system affected by a malicious jammer when the interference activity factor ρ is 0.01, 0.1, and 1 respectively, under different numbers of link layers. It can be seen that the average bit error rate increases significantly with the increase of the interference activity factor ρ, which is caused by the increase in the interference degree of the jammer.

[0170] Figure 5 Gives the interference link pointing error parameter m J When they are 0.5763, 0.8644, and 1.7288 respectively, the curve of the average bit error rate of the SISO - vertical layered UWOC system affected by a malicious jammer changing with the SJR. It can be seen from the figure that with the increase of the interference link pointing error parameter m J the average bit error performance of this UWOC system deteriorates accordingly. This is because a larger interference link pointing error parameter m J represents better alignment of the interference link, thus causing more serious damage to the normal transmission of the legitimate transmission signal.

[0171] Figure 6 Shows the theoretical and simulation results of the average bit error rate of the SISO - two - layer vertical UWOC system affected by a malicious jammer under different temperature gradients, bubble levels, and water types. Among them, scenarios 1 to 3 and scenario 6 are all fresh - water environments, and scenarios 4 and 5 are salt - water environments. In each scenario, the [bubble level, temperature gradient] parameters of each layer are specifically set as follows: scenario 1 is [2.4, 0.05] and [2.4, 0.10], scenario 2 is [2.4, 0.05] and [2.4, 0.20], scenario 3 is [2.4, 0.05] and [4.7, 0.10], scenario 4 is [2.4, 0] and [2.4, 0], scenario 5 is [2.4, 0] and [16.5, 0], scenario 6 is [2.4, 0] and [16.5, 0]. It can be seen that the increase of the temperature gradient or the bubble level will significantly increase the average bit error rate, and the average bit error rate in the fresh - water environment is lower than that in the salt - water environment.

[0172] Figure 7The average bit error rate curves of the SISO - three - layer vertical UWOC system affected by malicious jammers under fresh - water conditions with different temperature gradients and bubble levels are plotted. Specifically, the turbulence parameters for each scenario are as follows: Scenario 1: [2.4, 0.05], [2.4, 0.05], [2.4, 0.10]; Scenario 2: [2.4, 0.05], [2.4, 0.05], [2.4, 0.20]; Scenario 3: [2.4, 0.20], [2.4, 0.20], [2.4, 0.20]; Scenario 4: [2.4, 0.05], [2.4, 0.05], [4.7, 0.10]; Scenario 5: [4.7, 0.05], [4.7, 0.05], [4.7, 0.10]. It can be seen from the figure that the average bit error rate of the system under the influence of jamming is affected by the overall turbulence, and the overall turbulence is jointly determined by the turbulence of each layer. The bubble level and temperature gradient of each layer in Scenario 1 are the smallest, so the performance is the best. In contrast, Scenario 2 and Scenario 4 increase the temperature gradient and bubble level of the third layer respectively, making the average bit error rate higher than that of Scenario 1. The average bit error rates of Scenario 3 and Scenario 5 increase further because they increase the temperature gradient or bubble level in all layers, significantly enhancing the overall turbulence, which leads to a significant increase in the average bit error rate.

[0173] Figure 8 The comparative curves of the average bit error rate of the SIMO - two - layer vertical UWOC system under the influence of jammers for SISO and SC and EGC schemes with two and three receiving apertures are given. It can be clearly seen that under different numbers of receiving apertures and combining schemes, the calculation method proposed in the present invention is highly consistent with the Monte Carlo simulation results, further verifying the effectiveness of the method. It can be seen from the figure that under the influence of malicious jammers, the average bit error rate of the SIMO - vertical layered UWOC system is significantly lower than that of the SISO - vertical layered UWOC system, and as the number of receiving apertures K increases, the average bit error rate decreases significantly. In addition, under the influence of jammers, the SIMO - vertical layered UWOC system using the EGC scheme is superior to the SC scheme in terms of average bit error rate performance.

[0174] Figure 9 The average bit error rate curves of the SISO and 1×2 SIMO - vertical layered UWOC systems affected by malicious jammers when the interference activity factor ρ is 0.01, 0.1, 0.5, and 1 are given. It can be seen that the average bit error rate increases with the increase of the interference activity factor ρ and reaches the worst case when ρ = 1. At the same time, it can be seen that for any ρ value, the SIMO technology can significantly reduce the average bit error rate of this vertical layered UWOC system, and this advantage is particularly obvious in the high SJR region.

[0175] Figure 10shows the average bit error rate of SISO and 1×2 SIMO - vertical - layered UWOC systems affected by malicious jammers under the conditions that the legitimate - link pointing - error parameter m L,k is 1.7288, 0.8644, and 0.5763 respectively. It can be seen from the figure that as m L,k decreases, the average bit error rate increases significantly. This is because a smaller m L,k means that the legitimate link is affected by more severe pointing errors, thus weakening the reliable transmission of the legitimate - transmission signal and leading to an increase in the average bit error rate. In addition, combined with Figures 7 - 9 it can be found that under any channel conditions, the SIMO technology can significantly improve the average bit - error - rate performance of the vertical - layered UWOC system affected by interference, and the SIMO - vertical - layered UWOC system using the EGC scheme has better performance - improvement ability than the SC scheme.

[0176] As can be seen from the above embodiments, a method for calculating the average bit error rate of a vertical - layered UWOC system under malicious interference proposed by the present invention can be used to calculate the average bit error rate of a vertical - layered UWOC system with different link - layer numbers, interference - activity factors, interference - link and legitimate - link pointing errors, seawater - temperature gradients, bubble levels, and receiving - aperture numbers in fresh - water or salt - water environments under the influence of malicious interference. The present invention considers the influence of ocean turbulence caused by bubbles and temperature gradients on the channel, and combines the depth - dependence of the turbulence intensity, uses a multi - level - cascaded EGG ocean - turbulence channel to simulate ocean turbulence, and at the same time comprehensively considers the influence of path loss and pointing errors to construct a more realistic UWOC channel - fading model. The present invention enriches the calculation method of the average bit error rate of a wireless optical - communication system under malicious interference and the interference - mitigation scheme, and provides a theoretical reference for the design and optimization of a wireless optical - communication system affected by a malicious jammer.

[0177] The present invention is not limited to the above - mentioned embodiments. Based on the technical solutions disclosed in the present invention, those skilled in the art can make some substitutions and deformations of some technical features without creative labor according to the disclosed technical content, and these substitutions and deformations are all within the protection scope of the present invention.

Claims

1. A method for calculating the average bit error rate of a vertically layered UWOC system under malicious interference, characterized in that: include: Considering the SISO-vertical layered UWOC system model affected by malicious jammers, a composite channel fading model of legitimate links and interference links is established, and the probability density function and cumulative distribution function of the composite channel fading coefficients of legitimate links and interference links are obtained; According to the probability density function of the composite channel fading coefficients of the legitimate link and the interference link, the system bit error rate under malicious interference is obtained based on the threshold detection method, and then the average bit error rate of the SISO-vertical layered UWOC system under malicious interference is obtained; Considering the SIMO-vertical layered UWOC system model affected by malicious jammers, based on the selective merging scheme, the cumulative distribution function and probability density function of the end-to-end equivalent channel fading coefficient of the legitimate link when the selective merging scheme is adopted are obtained, and then the average bit error rate of the SIMO-vertical layered UWOC system under malicious interference when the selective merging scheme is adopted is obtained; Based on the equal-gain combining scheme, the moment generating function and probability density function of the end-to-end equivalent channel fading coefficient of the legitimate link are obtained when the equal-gain combining scheme is adopted, and then the average bit error rate of the SIMO-vertically layered UWOC system under malicious interference when the equal-gain combining scheme is adopted is obtained.

2. The method for calculating the average bit error rate of a vertically layered UWOC system under malicious interference according to claim 1 is characterized in that: A composite channel fading model of the legitimate link and the interference link is established to obtain the probability density function and cumulative distribution function of the composite channel fading coefficient of the legitimate link and the interference link, including: Establish the input-output relationship of the SISO-vertical layered UWOC system model affected by malicious jammers, and establish the composite channel fading model of legitimate links and interference links; According to the composite channel fading model, the probability density function of the composite channel fading coefficients of the legitimate link and the interference link is obtained; The probability density function of the composite channel fading coefficient is further integrated to obtain the cumulative distribution function of the composite channel fading coefficient of the legal link and the interference link.

3. The method for calculating the average bit error rate of a vertically layered UWOC system under malicious interference according to claim 2 is characterized in that: The composite channel fading model of the legitimate link and the interference link is: h S =h l,S h t,S h p,S Among them, h S is the composite channel fading coefficient of the legitimate link and the interfering link, h l,S is the path loss of the legitimate link and the interfering link, h t,S is the ocean turbulence fading coefficient of the legitimate link and the interference link, h p,S It is the fading caused by pointing errors in the legitimate link and the interfering link; Probability density function of composite channel fading coefficients of legitimate link and interference link for: Among them, m S is the pointing error parameter of the legitimate link and the interfering link, is a natural number that can be 0 or 1, N is the number of layers of legitimate links and interfering links, n S represents the nth layer of legitimate links and interference links, Γ(*) represents the gamma function, and are the parameters of the exponential-generalized gamma distribution model in the nth layer of the legitimate link and the interference link, represents the Fox-H function in the probability density function, is the fraction of power received at the radial displacement of 0 in the legitimate link and the interfering link, Z S About The function of and are the parameters of the exponential-generalized gamma distribution model in the nth layer of the legitimate link and the interference link, are the coefficients related to the parameters of the exponential-generalized gamma distribution model in layers 1 to N of the legitimate and interfering links; Cumulative distribution function of composite channel fading coefficients of legitimate link and interference link for: in, Represents the Fox-H function in the cumulative distribution function.

4. The method for calculating the average bit error rate of a vertically layered UWOC system under malicious interference according to claim 1 is characterized in that: Based on the threshold detection method, the system bit error rate under malicious interference is obtained, and then the average bit error rate of the SISO-vertical layered UWOC system under malicious interference is obtained, including: When there is a malicious jammer, the system bit error rate under malicious interference is obtained based on the possible bit error events and the threshold detection method; The average bit error rate of the SISO-vertically layered UWOC system under malicious interference is obtained from the system bit error rate under malicious interference.

5. The method for calculating the average bit error rate of a vertically layered UWOC system under malicious interference according to claim 4 is characterized in that: System bit error rate P under malicious interference e for: Among them, ρ is the interference activity factor, m J is the pointing error parameter of the interference link, is a natural number that takes 0 or 1, N is the number of layers of legal links and interference links, n J represents the nth layer of the interference link, Γ(*) represents the gamma function, and are the parameters of the exponential-generalized gamma distribution model in the nth layer of the interference link, represents the Fox-H function in the system bit error rate, γ J is the average signal-to-interference ratio for each symbol, h L is the composite channel fading coefficient of the legal link, is the fraction of power received at zero radial displacement in the interfering link, h l,J is the path loss of the interfering link, Z J About The function of and are the parameters of the exponential-generalized gamma distribution model in the nth layer of the interference link, are the coefficients related to the parameters of the exponential-generalized gamma distribution model in the interference link layers 1 to N; Average bit error rate of SISO-vertical layered UWOC system under malicious interference for: Among them, m L is the pointing error parameter of the legal link, is a natural number that takes the value 0 or 1, n L Indicates the nth layer of a legal link, and are the parameters of the exponential-generalized gamma distribution model in the nth layer of the legal link, represents the Fox-H function in the average bit error rate, is the fraction of power received at a radial displacement of 0 in the legal link, h l,L is the path loss of the legal link, Z L About The function of and are the parameters of the exponential-generalized gamma distribution model in the nth layer of the legal link, are coefficients related to the parameters of the exponential-generalized gamma distribution model in layers 1 to N of the legitimate links.

6. The method for calculating the average bit error rate of a vertically layered UWOC system under malicious interference according to claim 1 is characterized in that: Based on the selective merging scheme, the cumulative distribution function and probability density function of the end-to-end equivalent channel fading coefficient of the legal link when the selective merging scheme is adopted are obtained, and then the average bit error rate of the SIMO-vertically layered UWOC system under malicious interference when the selective merging scheme is adopted is obtained, including: Establish the input-output relationship of the SIMO-vertical layered UWOC system model affected by malicious jammers; The receiving end receives the signal by adopting the selective combining scheme, and obtains the end-to-end equivalent channel fading coefficient of the legal link when the selective combining scheme is adopted; According to the end-to-end equivalent channel fading coefficient of the legal link, the cumulative distribution function of the end-to-end equivalent channel fading coefficient of the legal link when the selective combination is adopted is obtained; According to the cumulative distribution function of the end-to-end equivalent channel fading coefficient of the legal link, the probability density function of the end-to-end equivalent channel fading coefficient of the legal link when the selective combination is adopted is obtained by derivation; According to the probability density function of the end-to-end equivalent channel fading coefficient of the legitimate link, the average bit error rate of the SIMO-vertical layered UWOC system under malicious interference when the selective merging scheme is adopted is obtained.

7. The method for calculating the average bit error rate of a vertically layered UWOC system under malicious interference according to claim 6 is characterized in that: The end-to-end equivalent channel fading coefficient h of the legal link when selective combining is used L,SC The cumulative distribution function of for: Where K is the number of receiving apertures, k represents the kth legal link, is a natural number that can be 0 or 1, m L,k is the pointing error parameter of the kth legal link, N is the number of layers of legal links and interference links, n L,k represents the nth layer of the kth legal link, and are the parameters of the exponential-generalized gamma distribution model in the nth layer of the kth legal link, Γ(*) represents the gamma function, represents the multivariate Fox-H function in the cumulative distribution function, is the coefficient related to the parameters of the exponential-generalized gamma distribution model in layers 1 to N of the kth legal link, [*] k＝1:K represents replication in K dimensions, It is about the path loss in the 1st to Kth legal links, the power fraction received at the radial displacement of 0, h L,SC The coefficients related to the parameters are as follows: are the power fractions received at the radial displacement of 0 in the 1st and Kth legal links, respectively, and h l,L,1 、h l,L,K are the path losses of the 1st and Kth legal links, respectively, Z L,1 About A function where n L,1 Indicates the nth layer of the first legal link, are the parameters of the exponential-generalized gamma distribution model in the nth layer of the first legal link, is a natural number that takes 0 or 1, Z L,K About A function where n L,K represents the nth layer of the Kth legal link, are the parameters of the exponential-generalized gamma distribution model in the nth layer of the Kth legal link, is a natural number that takes 0 or 1; The end-to-end equivalent channel fading coefficient h of the legal link when selective combining is used L,SC The probability density function of for: in,{*} k＝1:K represents replication in different dimensions, represents the multivariate Fox-H function in the probability density function when the selective merging scheme is adopted; Average bit error rate of SIMO-vertical layered UWOC system under malicious interference when using selective merging scheme for: Among them, ρ is the interference activity factor, m J is the pointing error parameter of the interference link, is a natural number that takes 0 or 1, N is the number of layers of legal links and interference links, n J represents the nth layer of the interfering link, and are the parameters of the exponential-generalized gamma distribution model in the nth layer of the interference link, represents the multivariate Fox-H function in the average bit error rate when the selective combining scheme is adopted, γ J is the average signal-to-interference ratio for each symbol,[*] n＝1:N represents replication in N dimensions, is a coefficient related to the path loss, the power fraction received at the radial displacement of 0, and the interference activity factor in the 1st to Kth legal links, where Ξ1 is a coefficient related to The function of is the fraction of power received at zero radial displacement in the interfering link, h l,J is the path loss of the interfering link, Z J About A function where n J represents the nth layer of the interfering link, are the parameters of the exponential-generalized gamma distribution model in the nth layer of the interference link, is a natural number that takes the value 0 or 1, K About function.

8. The method for calculating the average bit error rate of a vertically layered UWOC system under malicious interference according to claim 1 is characterized in that: Based on the equal-gain combining scheme, the moment generating function and probability density function of the end-to-end equivalent channel fading coefficient of the legal link when equal-gain combining is adopted are obtained, and then the average bit error rate of the SIMO-vertically layered UWOC system under malicious interference when the equal-gain combining scheme is adopted is obtained, including: The receiving end receives the signal using an equal gain combining scheme, and obtains an end-to-end equivalent channel fading coefficient of a legal link when equal gain combining is used; According to the end-to-end equivalent channel fading coefficient of the legal link, a moment generating function of the end-to-end equivalent channel fading coefficient of the legal link when equal gain combining is adopted is obtained; According to the moment generating function of the end-to-end equivalent channel fading coefficient of the legal link, the probability density function of the end-to-end equivalent channel fading coefficient of the legal link when equal gain combining is adopted is obtained through inverse Laplace transform; According to the probability density function of the end-to-end equivalent channel fading coefficient of the legitimate link, the average bit error rate of the SIMO-vertical layered UWOC system under malicious interference when the equal gain combining scheme is adopted is obtained.

9. The method for calculating the average bit error rate of a vertically layered UWOC system under malicious interference according to claim 7 is characterized in that: The end-to-end equivalent channel fading coefficient h of the legal link when equal gain combining is adopted L,EGC The moment generating function for Where t represents a random variable, represents the multivariate Fox-H function in the moment generating function, It is a coefficient related to the path loss in the 1st to Kth legal links, the power fraction received at the radial displacement of 0, the random variable t and other parameters; The end-to-end equivalent channel fading coefficient h of the legal link when equal gain combining is adopted L,EGC The probability density function of for: in, represents the multivariate Fox-H function in the probability density function when the equal gain combining scheme is adopted; Average bit error rate of SIMO-vertical layered UWOC system under malicious interference when using equal gain combining scheme for in, Represents the multivariate Fox-H function in the average bit error rate when the equal gain combining scheme is adopted.

10. A method for calculating the average bit error rate of a vertically layered UWOC system under malicious interference as described in any one of claims 1 to 9 is applied in an underwater wireless optical communication system affected by a malicious jammer.

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