Multi-RIS-assisted underwater wireless optical communication system performance analysis method

Abstract

The invention provides a multi-RIS-assisted underwater wireless optical communication system performance analysis method. The method comprises the following steps: establishing a multi-RIS-assisted underwater wireless optical communication system model under a composite fading channel; the method comprises the following steps: deriving a probability density function and a cumulative distribution function expression of an instantaneous signal-to-noise ratio between a source node and a destination node based on a multi-RIS-assisted underwater wireless optical communication system model; and obtaining an analytical expression of the outage probability and the M-PAM average bit error rate based on a probability density function and a cumulative distribution function expression of the instantaneous signal-to-noise ratio, and realizing performance analysis of the outage probability and the M-PAM average bit error rate of the multi-RIS-assisted underwater wireless optical communication system based on the obtained analytical expression. According to the method, the accuracy of the performance index expressions is verified through numerical results, the potential advantage of integrating the multiple RISs into the underwater wireless optical communication system is shown, and the research result provides theoretical support for design and application of the underwater wireless optical communication system assisted by the multiple RISs.

Description

Technical Field

[0001] The present invention relates to the technical field of underwater wireless optical communication, and in particular to a multi-RIS-assisted underwater wireless optical communication system performance analysis method. Background Art

[0002] In recent years, with the continuous development of oceans, the underwater Internet of Things (IoUT) has experienced rapid development. The IoUT requires stable underwater wireless communication links to achieve seamless underwater operations and data transmission. Underwater wireless optical communication (UWOC) offers the advantages of high transmission rates, low link latency, high communication security, and low implementation costs. Therefore, UWOC is particularly suitable for high-speed, high-capacity underwater data transmission and has broad application prospects in IoUT systems.

[0003] Although UWOC shows great advantages, it still faces some challenges, including optical signal attenuation caused by ocean turbulence and aiming errors caused by misalignment between the laser source and the photodetector, which can degrade system performance. Another key issue of UWOC is optical link blocking. Since optical signals propagate in a straight line and are not penetrating, they are easily blocked by obstacles such as marine animals and plants, seamounts, and some marine equipment, causing link blocking. Given the high transmission rate of UWOC, even short-term blocking can lead to sudden interruption of communication, resulting in the loss of a large amount of information, which is fatal for a reliable UWOC system. The emergence of optically reconfigurable smart surfaces (RIS) has opened the door to solving these challenges of UWOC.

[0004] Specifically, RIS is a plane that includes multiple low-cost passive reflective elements, each of which can independently control the intensity and direction of the incident optical signal. RIS has the advantages of low cost, low energy consumption, flexible reconfiguration, and easy deployment. The application of RIS has great potential for optical communication links. In the UWOC system, the application of RIS can reduce the impact of ocean turbulence and aiming errors, and RIS can overcome link blockage by redirecting optical signals, thereby improving the reliability of UWOC. Therefore, the combination of UWOC system and RIS has attracted widespread attention and research in academia and industry to achieve high-speed and reliable underwater wireless communications.

[0005] Although researchers have conducted some research on RIS-assisted UWOC systems in recent years, these studies have only focused on single-RIS-assisted UWOC systems. In fact, the service coverage and performance enhancement of UWOC systems by a single RIS are limited. In the actual underwater application of RIS in the future, it is inevitable to deploy multiple RIS to adapt to the complex underwater communication environment. Multiple RIS can be flexibly deployed on buoys, underwater equipment, underwater reefs and seamounts, providing rich reflected optical links and improving the reliability of UWOC systems. However, the system model, signal-to-noise ratio statistical characteristics, outage probability and average bit error rate performance of multi-RIS-assisted UWOC systems have not been analyzed, and there is still a lack of research on multi-RIS-assisted UWOC systems. Summary of the Invention

[0006] In response to the above technical problems, the present invention provides a multi-RIS-assisted underwater wireless optical communication system performance analysis method, comprising the following steps:

[0007] S1. Considering the fading of ocean turbulence and the aiming error fading caused by the jitter of the light beam and the reconfigurable smart surface, a model of underwater wireless optical communication system assisted by multiple reconfigurable smart surfaces in a composite fading channel is established.

[0008] S2. Based on the underwater wireless optical communication system model assisted by multiple reconfigurable smart surfaces, derive the probability density function and cumulative distribution function expressions of the instantaneous signal-to-noise ratio between the source node and the destination node;

[0009] S3. Based on the probability density function and cumulative distribution function expressions of the instantaneous signal-to-noise ratio, analytical expressions for the outage probability and the average bit error rate of multi-bit pulse amplitude modulation are obtained. Based on the obtained analytical expressions, the outage probability and the average bit error rate performance of the multi-bit pulse amplitude modulation assisted underwater wireless optical communication system with the assistance of multiple reconfigurable smart surfaces are analyzed.

[0010] Furthermore, the specific process of establishing a multi-reconfigurable smart surface-assisted underwater wireless optical communication system model under a composite fading channel, taking into account the fading of ocean turbulence and the aiming error caused by the jitter of the light beam and the reconfigurable smart surface, is as follows:

[0011] Consider a multi-RIS-assisted underwater wireless optical communication system, which consists of a source node, K optical reconfigurable smart surfaces (RISs), and a destination node. The source node is equipped with K laser sources, each of which points to a RIS. Each RIS is equipped with N k reflection units, the destination node is equipped with a photodetector, k = 1, 2, ..., K;

[0012] Assume that the line-of-sight link between the source node and the destination node is blocked by underwater obstacles. Information transmission can only be achieved through RIS. Each RIS reflects the optical signal from the source node to the destination node. The photodetector of the destination node has a large enough field of view to receive signals from multiple RIS. The received signal of the destination node is expressed as:

[0013]

[0014] Where x represents the emission signal of the source node, η is the responsivity of the photodetector, is additive white Gaussian noise, ρ kn is the reflection coefficient of the nth reflection unit of the kth RIS, h l,kn 、h t,kn and h p,kn denote the path loss, ocean turbulence fading coefficient, and aiming error fading coefficient from the source node through the nth reflection unit of the kth RIS to the destination node, respectively. They represent the path losses from the source node to the nth reflection unit of the kth RIS and from the nth reflection unit of the kth RIS to the destination node, respectively. are the turbulence fading coefficients from the source node to the nth reflection unit of the kth RIS and from the nth reflection unit of the kth RIS to the destination node, respectively, n = 1, 2, ..., N k ;

[0015] According to the Beer-Lambert law, and Calculated as and Where c is the extinction coefficient of seawater, and are the link distances from the source node to the kth RIS and from the kth RIS to the destination node, respectively. Therefore, Calculated as

[0016] Assume that for all RIS Then h l,kn Calculated as:

[0017]

[0018] Assume that the channels between the source node and RIS and between RIS and the destination node are Gamma turbulent fading channels. and Obey the Gamma distribution, and The probability density functions are:

[0019]

[0020] Among them, Γ(·) is the Gamma function, α k is the turbulence parameter of the channel between the source node and the kth RIS, β k is the turbulence parameter of the channel between the kth RIS and the destination node, which can be obtained from equations (3) and (4). It obeys the Gamma-Gamma distribution, and its probability density function is:

[0021]

[0022] Among them, K p (·) represents the p-order modified Bessel function of the second kind;

[0023] In addition, the jitter of the beam and RIS will cause aiming errors, which will also introduce channel fading. Assuming that the reflection units on the same RIS have the same aiming errors, that is:

[0024]

[0025] For the kth RIS, the aiming error fading coefficient h p,k The probability density function of is:

[0026]

[0027] Among them, A k and ξ k is the aiming error parameter.

[0028] Furthermore, the specific implementation process of deriving the probability density function and cumulative distribution function expressions of the instantaneous signal-to-noise ratio between the source node and the destination node based on the underwater wireless optical communication system model assisted by multiple reconfigurable intelligent surfaces is as follows:

[0029] According to formula (1), the instantaneous signal-to-noise ratio between the source node and the destination node of the underwater wireless optical communication system assisted by multiple reconfigurable intelligent surfaces can be calculated as:

[0030]

[0031] Among them, E x For the transmitted signal energy, it is assumed that the reflection coefficients of all RIS reflection units are the same, that is, ρ kn =ρ, substituting equations (2) and (6) into equation (8), the instantaneous signal-to-noise ratio can be expressed as:

[0032]

[0033] Define h t,k is the turbulent channel fading coefficient from the source node to the destination node through the kth RIS, ht,k Expressed as Define h k is the composite channel fading coefficient from the source node through the kth RIS to the destination node, h k Represented as h k =h p,k h t,k ; Define h as the total channel fading coefficient from the source node through K RIS to the destination node, h is expressed as definition is the average signal-to-noise ratio, Expressed as Therefore, the instantaneous signal-to-noise ratio can be calculated as:

[0034]

[0035] h t,k N k The probability density function of the sum of independent and identically distributed Gamma-Gamma random variables is expressed as:

[0036]

[0037] in, is the Meijer-G function;

[0038] Based on equations (7) and (11), h k The probability density function of is calculated as:

[0039]

[0040] in,

[0041] Using h k The probability density function of h can be calculated k The moment generating function of h. k The moment generating function of is calculated as:

[0042]

[0043] Substituting formula (12) into formula (13), we can get h k The moment generating function of is:

[0044]

[0045] in, is the Fox-H function, a k =[(N k α k ,1),(N k β k ,1)];

[0046] Then, using h k The probability density function of h is calculated by the moment generating function and the inverse Laplace transform. The probability density function of h is calculated as:

[0047]

[0048] in, Denotes the inverse Laplace transform. Substituting equation (14) into equation (15), the probability density function of h is calculated as:

[0049]

[0050] in, is the multivariate Fox-H function,

[0051] Based on equations (10) and (16), the probability density function of the instantaneous signal-to-noise ratio γ is expressed as:

[0052]

[0053] Using h k The moment generating function and the inverse Laplace transform are used to calculate the cumulative distribution function of h. The cumulative distribution function of h is calculated as:

[0054]

[0055] Substituting formula (14) into formula (18), the cumulative distribution function of h is calculated as follows:

[0056]

[0057] Based on equations (10) and (19), the cumulative distribution function of the instantaneous signal-to-noise ratio γ is expressed as:

[0058]

[0059] Furthermore, based on the probability density function and cumulative distribution function expressions of the instantaneous signal-to-noise ratio, analytical expressions for the outage probability and the average bit error rate of multi-ary pulse amplitude modulation are obtained. The specific implementation process of the outage probability and the average bit error rate of multi-ary pulse amplitude modulation based on the obtained analytical expressions for the underwater wireless optical communication system assisted by multiple reconfigurable smart surfaces is as follows:

[0060] The outage probability represents the probability that the instantaneous signal-to-noise ratio is lower than the threshold signal-to-noise ratio. The outage probability is defined as:

[0061]

[0062] Among them, γ th is the threshold signal-to-noise ratio;

[0063] Based on equations (21) and (20), the interruption probability expression is:

[0064]

[0065] Under multi-level pulse amplitude modulation M-PAM, the average bit error rate is calculated as:

[0066]

[0067] Where erfc(·) is the complementary error function, B = (M-1) / [Mlog2(M)], C = 3 / [2(M-1)(2M-1)];

[0068] Based on equations (23) and (17), the analytical expression of the average bit error rate is:

[0069]

[0070] Based on the analytical expressions shown in Equations (22) and (24), the performance analysis of the outage probability and the average bit error rate of the M-PAM underwater wireless optical communication system assisted by multiple RIS is realized respectively.

[0071] The present invention provides a performance analysis method for a multi-RIS-assisted underwater wireless optical communication system. The technical solution employed by the present invention includes: establishing a multi-RIS-assisted underwater wireless optical communication system model for a composite fading channel, taking into account ocean turbulence fading and aiming error fading caused by beam and RIS jitter; deriving the probability density function and cumulative distribution function expressions for the instantaneous signal-to-noise ratio (SNR) between the source and destination nodes based on the multi-RIS-assisted underwater wireless optical communication system model; and deriving analytical expressions for the outage probability and M-PAM average bit error rate (M-PAM) based on the instantaneous SNR P ...

[0072] This paper focuses on a multi-RIS-assisted underwater wireless optical communication system, in which a source node communicates with a destination node with the assistance of several RISs equipped with multiple passive reflectors and placed within the destination node's field of view. In this system, we consider fading due to ocean turbulence and aiming error fading caused by beam and RIS jitter. We derive the probability density function and cumulative distribution function expressions for the instantaneous signal-to-noise ratio (SNR) between the source and destination nodes. Based on these expressions, we use the multivariate Fox-H function to obtain analytical expressions for the system outage probability and the average bit error rate of the M-PAM. Finally, numerical results demonstrate the closeness and effectiveness of our expressions compared to Monte Carlo simulations.

[0073] Under the premise of considering the fading of ocean turbulence and the fading of aiming errors caused by the jitter of the light beam and the RIS, the present invention provides analytical expressions for the outage probability and the M-PAM average bit error rate of the multi-RIS-assisted underwater wireless optical communication system, so as to realize the performance analysis of the outage probability and the M-PAM average bit error rate of the multi-RIS-assisted underwater wireless optical communication system.

[0074] Compared with the prior art, the present invention has the following advantages:

[0075] 1. This invention provides a performance analysis method for underwater wireless optical communication systems assisted by multiple RISs. Compared to underwater wireless optical communication systems assisted by a single RIS, this invention considers deploying multiple RISs in an underwater environment. Multiple RISs simultaneously assist the underwater wireless optical communication system under conditions of fading caused by ocean turbulence and aiming errors caused by beam and RIS jitter. This makes the system model more realistic for RIS applications in underwater environments.

[0076] 2. This invention provides a performance analysis method for a multi-RIS-assisted underwater wireless optical communication system. Compared to previous studies on RIS-assisted underwater wireless optical communication systems, this invention provides research on the statistical characteristics of the instantaneous signal-to-noise ratio, system outage probability, and average bit error rate of multi-RIS-assisted underwater wireless optical communication systems, which is lacking in previous research. By deploying and applying multiple RISs underwater, we achieve a reduction in the outage probability and average bit error rate of the underwater wireless optical communication system, which improves system reliability under conditions of ocean turbulence and aiming errors. This research has important implications for the field of underwater wireless optical communications.

[0077] Based on the above reasons, the present invention can be widely promoted in fields such as underwater wireless optical communication. BRIEF DESCRIPTION OF THE DRAWINGS

[0078] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments or the description of the prior art. Obviously, the drawings described below are some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative labor.

[0079] Figure 1 Flow chart of the method of the present invention.

[0080] Figure 2 The model structure of the multi-RIS-assisted underwater wireless optical communication system to which the solution of the present invention is applicable.

[0081] Figure 3 This is a simulation diagram of the relationship between system outage probability and average signal-to-noise ratio under different RIS numbers provided by an embodiment of the present invention.

[0082] Figure 4 This is a simulation diagram of the relationship between the average bit error rate and the average signal-to-noise ratio of the system under different RIS numbers provided by an embodiment of the present invention. DETAILED DESCRIPTION

[0083] In order to enable those skilled in the art to better understand the solutions of the present invention, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the embodiments described are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts should fall within the scope of protection of the present invention.

[0084] It should be noted that the terms "first", "second", etc. in the description and claims of the present invention and the above-mentioned drawings are used to distinguish similar objects and are not necessarily used to describe a specific order or sequence. It should be understood that the numbers used in this way can be interchanged where appropriate, so that the embodiments of the present invention described herein can be implemented in an order other than those illustrated or described herein. In addition, the terms "including" and "having" and any variations thereof are intended to cover non-exclusive inclusions. For example, a process, method, system, product or device that includes a series of steps or units is not necessarily limited to those steps or units clearly listed, but may include other steps or units that are not clearly listed or inherent to these processes, methods, products or devices.

[0085] Figure 1 Flow chart of the method of the present invention;

[0086] A multi-RIS-assisted underwater wireless optical communication system performance analysis method, characterized by comprising the following steps:

[0087] S1. Considering the fading of ocean turbulence and the aiming error caused by the jitter of the beam and RIS (Reconfigurable Smart Surface), a multi-RIS-assisted underwater wireless optical communication system model is established under a composite fading channel.

[0088] S2. Based on the multi-RIS-assisted underwater wireless optical communication system model, derive the probability density function and cumulative distribution function expressions of the instantaneous signal-to-noise ratio between the source node and the destination node;

[0089] S3. Based on the probability density function and cumulative distribution function expressions of the instantaneous signal-to-noise ratio, analytical expressions for the outage probability and the average bit error rate of M-PAM (multi-ary pulse amplitude modulation) are obtained. Based on the obtained analytical expressions, the outage probability and the average bit error rate performance of the multi-RIS-assisted underwater wireless optical communication system are analyzed.

[0090] Steps S1 / S2 / S3 are performed sequentially;

[0091] During specific implementation, as a preferred embodiment of the present invention, the following is established: Figure 2 The model structure of the multi-RIS-assisted underwater wireless optical communication system is shown in Figure 1. The system consists of a source node, K optical reconfigurable smart surfaces (RIS) and a destination node. The source node is equipped with K laser sources, each of which points to a RIS. Each RIS is equipped with N k There are (k = 1, 2, …, K) reflectors, and the destination node is equipped with a photodetector. We assume that the line-of-sight link between the source and destination nodes is blocked by underwater obstacles, and information transmission can only be achieved through the RIS. Each RIS reflects the optical signal from the source node to the destination node. The photodetector at the destination node has a large enough field of view to receive signals from multiple RIS. The received signal at the destination node is expressed as:

[0092]

[0093] Where x represents the emission signal of the source node, η is the responsivity of the photodetector, Additive white Gaussian noise, ρ kn is the nth (n=1,2,…,N k ) reflection coefficient of each reflection unit. l,kn 、h t,kn and h p,kn are the path loss, ocean turbulence fading coefficient, and pointing error fading coefficient from the source node through the nth reflection unit of the kth RIS to the destination node, respectively. They represent the path losses from the source node to the nth reflection unit of the kth RIS and from the nth reflection unit of the kth RIS to the destination node, respectively. They represent the turbulence fading coefficients from the source node to the nth reflection unit of the kth RIS and from the nth reflection unit of the kth RIS to the destination node, respectively.

[0094] According to the Beer-Lambert law, and It can be calculated as and Where c is the extinction coefficient of seawater, and are the link distances from the source node to the kth RIS and from the kth RIS to the destination node, respectively. Therefore, Calculated as We assume that for all RIS Then h l,kn It can be calculated as:

[0095] h l,kn =exp(-cL)=h l (2)

[0096] We assume that the channels between the source node and RIS and between RIS and the destination node are Gamma turbulent fading channels. and Obeys Gamma distribution. and The probability density functions are:

[0097]

[0098] Among them, Γ(·) is the Gamma function, α k is the turbulence parameter of the channel between the source node and the kth RIS, β k is the turbulence parameter of the channel between the kth RIS and the destination node. From equations (3) and (4), we can get h t,kn It obeys the Gamma-Gamma distribution, and its probability density function is:

[0099]

[0100] Among them, K p (·) denotes the p-order modified Bessel function of the second kind.

[0101] In addition, the jitter of the beam and RIS will cause aiming errors, which will also introduce channel fading. We assume that the reflectors on the same RIS have the same aiming errors, that is:

[0102] h p,kn =h p,k (6)

[0103] For the kth RIS, the aiming error fading coefficient h p,k The probability density function of is:

[0104]

[0105] Among them, A k and ξ k is the aiming error parameter.

[0106] In specific implementation, as a preferred embodiment of the present invention, step S2 is based on a multi-RIS-assisted underwater wireless optical communication system model to derive the probability density function and cumulative distribution function expressions of the instantaneous signal-to-noise ratio between the source node and the destination node. The specific implementation process is as follows:

[0107] According to formula (1), the instantaneous signal-to-noise ratio between the system source node and the destination node can be calculated as:

[0108]

[0109] Among them, E x is the transmitted signal energy. We assume that the reflection coefficients of all RIS reflection units are the same, that is, ρ kn =ρ. Substituting equations (2) and (6) into equation (8), the instantaneous signal-to-noise ratio can be expressed as:

[0110]

[0111] We define h t,k is the turbulent channel fading coefficient from the source node to the destination node through the kth RIS, h t,k Expressed as Define h k is the composite channel fading coefficient from the source node through the kth RIS to the destination node, h k Represented as h k =h p,k h t,k ; Define h as the total channel fading coefficient from the source node through K RIS to the destination node, h is expressed as definition is the average signal-to-noise ratio, Expressed as Therefore, the instantaneous signal-to-noise ratio can be calculated as:

[0112]

[0113] h t,k N kThe probability density function of the sum of independent and identically distributed Gamma-Gamma random variables can be expressed as:

[0114]

[0115] in, is the Meijer-G function.

[0116] Based on equations (7) and (11), h k The probability density function of can be calculated as:

[0117]

[0118] in,

[0119] Using h k The probability density function of h can be calculated k The moment generating function of h. k The moment generating function of can be calculated as:

[0120]

[0121] Substituting formula (12) into formula (13), we can get h k The moment generating function of is:

[0122]

[0123] in, is the Fox-H function, a k =[(N k α k ,1),(N k β k ,1)].

[0124] Then, using h k The probability density function of h is calculated by the moment generating function and the inverse Laplace transform. The probability density function of h can be calculated as:

[0125]

[0126] in, Denotes the inverse Laplace transform. Substituting equation (14) into equation (15), the probability density function of h is calculated as:

[0127]

[0128] in, is the multivariate Fox-H function.

[0129] Based on equations (10) and (16), the probability density function of the instantaneous signal-to-noise ratio γ can be expressed as:

[0130]

[0131] Next, using h k The cumulative distribution function of h is calculated by the moment generating function and the inverse Laplace transform. The cumulative distribution function of h can be calculated as:

[0132]

[0133] Substituting formula (14) into formula (18), the cumulative distribution function of h is calculated as follows:

[0134]

[0135] Based on equations (10) and (19), the cumulative distribution function of the instantaneous signal-to-noise ratio γ can be expressed as:

[0136]

[0137] In specific implementation, as a preferred embodiment of the present invention, step S3 obtains analytical expressions of the outage probability and the M-PAM average bit error rate based on the probability density function and cumulative distribution function expression of the instantaneous signal-to-noise ratio. The specific implementation process is as follows:

[0138] When a multi-RIS-assisted underwater optical wireless communication system experiences ocean turbulence fading and aiming error fading, outage probability and bit error rate are key parameters for evaluating the reliability of the communication system. The outage probability represents the probability that the instantaneous signal-to-noise ratio (SNR) is lower than the threshold SNR. The system outage probability is defined as:

[0139] P out =Pr{γ≤γ th =F γ (γ th ) (twenty one)

[0140] Among them, γ th is the threshold signal-to-noise ratio.

[0141] Based on equations (21) and (20), the system outage probability expression can be obtained as:

[0142]

[0143] We consider an underwater wireless optical communication system with intensity modulation direct detection. Under M-PAM, the average bit error rate of the system is calculated as:

[0144]

[0145] Wherein, erfc(·) is the complementary error function, B = (M-1) / [Mlog2(M)], and C = 3 / [2(M-1)(2M-1)].

[0146] Based on equations (23) and (17), the average bit error rate expression can be obtained as:

[0147]

[0148] Based on the obtained analytical expressions, the outage probability and M-PAM average bit error rate performance analysis of multi-RIS-assisted underwater wireless optical communication systems can be realized.

[0149] Example

[0150] In order to verify the effectiveness of the solution of the present invention, the following simulation experiments were carried out:

[0151] The specific simulation parameters of the multi-RIS-assisted underwater wireless optical communication system are:

[0152] In the simulation setting, an underwater wireless optical communication system consists of a source node, K RISs, and a destination node. Each RIS is equipped with N k (k=1,2,…,K) reflection units. Due to obstacles between the source node and the destination node, the direct optical link between the source node and the destination node is blocked, and the system communication is severely restricted. To solve this problem, we deployed multiple RIS in the underwater environment to establish a stable reflected optical link. We used 4-PAM modulation and set the threshold signal-to-noise ratio γ th =13dB, turbulence parameter α k =3.35, β k =3.19, aiming error parameter A k =1,

[0153] Figure 3 The relationship between the system outage probability and the average signal-to-noise ratio under different RIS numbers is shown. Figure 4 The relationship between the average bit error rate and the average signal-to-noise ratio of the system under different RIS numbers is shown. In order to make a fair comparison, we set the total number of reflection units in the system under different RIS numbers to be equal, and the total number of all RIS reflection units in the system is set to 12. For a single RIS-assisted system (K=1), the number of RIS reflection units is N k = 12. For a dual RIS-assisted system (K = 2), the number of RIS reflection units is N k = 6. For a three-RIS-assisted system (K = 3), the number of RIS reflection units is N k = 4. We observe Figure 3The Monte Carlo simulation results in S3 are highly consistent with the simulation results based on formula (22). In addition, Figure 4 The Monte Carlo simulation results are also highly consistent with the simulation results based on formula (24) in S3. Figure 3 and Figure 4 It can be seen that compared with the underwater wireless optical communication system assisted by a single RIS (K = 1), the underwater wireless optical communication system assisted by multiple RIS (K = 2 and K = 3) has a lower outage probability and average bit error rate. As the number of RIS in the system increases, the outage probability and average bit error rate both decrease. This shows that by increasing the number of RIS, the reliability of the underwater wireless optical communication system can be improved, achieving better communication service quality.

[0154] In summary, the above simulation results verify the accuracy of the expressions for outage probability and average bit error rate derived by the solution of the present invention.

[0155] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it. Although the present invention has been described in detail with reference to the above embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the above embodiments, or replace some or all of the technical features therein with equivalents. However, these modifications or replacements do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A multi-RIS-assisted underwater wireless optical communication system performance analysis method, characterized in that: The steps include: S1. Considering the fading of ocean turbulence and the aiming error fading caused by the jitter of the light beam and the reconfigurable smart surface, a model of underwater wireless optical communication system assisted by multiple reconfigurable smart surfaces in a composite fading channel is established. S2. Based on the underwater wireless optical communication system model assisted by multiple reconfigurable smart surfaces, derive the probability density function and cumulative distribution function expressions of the instantaneous signal-to-noise ratio between the source node and the destination node; S3. Based on the probability density function and cumulative distribution function expressions of the instantaneous signal-to-noise ratio, analytical expressions for the outage probability and the average bit error rate of multi-bit pulse amplitude modulation are obtained. Based on the obtained analytical expressions, the outage probability and the average bit error rate performance of the multi-bit pulse amplitude modulation assisted underwater wireless optical communication system with the assistance of multiple reconfigurable smart surfaces are analyzed.

2. The multi-RIS-assisted underwater wireless optical communication system performance analysis method according to claim 1, characterized in that: The specific process of establishing a multi-reconfigurable smart surface-assisted underwater wireless optical communication system model under a composite fading channel, taking into account the fading of ocean turbulence and the aiming error fading caused by the jitter of the light beam and the reconfigurable smart surface, is as follows: Consider a multi-RIS-assisted underwater wireless optical communication system, which consists of a source node, K optical reconfigurable smart surfaces (RISs), and a destination node. The source node is equipped with K laser sources, each of which points to a RIS. Each RIS is equipped with N k reflection units, the destination node is equipped with a photodetector, k = 1, 2, ..., K; Assume that the line-of-sight link between the source node and the destination node is blocked by underwater obstacles. Information transmission can only be achieved through RIS. Each RIS reflects the optical signal from the source node to the destination node. The photodetector of the destination node has a large enough field of view to receive signals from multiple RIS. The received signal of the destination node is expressed as: Where x represents the emission signal of the source node, η is the responsivity of the photodetector, is additive white Gaussian noise, ρ kn is the reflection coefficient of the nth reflection unit of the kth RIS, h l,kn 、h t,kn and h p,kn denote the path loss, ocean turbulence fading coefficient, and aiming error fading coefficient from the source node through the nth reflection unit of the kth RIS to the destination node, respectively. They represent the path losses from the source node to the nth reflection unit of the kth RIS and from the nth reflection unit of the kth RIS to the destination node, respectively. are the turbulence fading coefficients from the source node to the nth reflection unit of the kth RIS and from the nth reflection unit of the kth RIS to the destination node, respectively, n = 1, 2, ..., N k ; According to the Beer-Lambert law, and Calculated as and Where c is the extinction coefficient of seawater, and are the link distances from the source node to the kth RIS and from the kth RIS to the destination node, respectively. Therefore, Calculated as Assume that for all RIS Then h l,kn Calculated as: Assume that the channels between the source node and RIS and between RIS and the destination node are Gamma turbulent fading channels. and Obey the Gamma distribution, and The probability density functions are: Among them, Γ(·) is the Gamma function, α k is the turbulence parameter of the channel between the source node and the kth RIS, β k is the turbulence parameter of the channel between the kth RIS and the destination node. According to equations (3) and (4), h t,kn It obeys the Gamma-Gamma distribution, and its probability density function is: Among them, K p (·) represents the p-order modified Bessel function of the second kind; In addition, the jitter of the beam and RIS will cause aiming errors, which will also introduce channel fading. Assuming that the reflectors on the same RIS have the same aiming errors, that is: h p,kn =h p,k (6) For the kth RIS, the aiming error fading coefficient h p,k The probability density function of is: Among them, A k and ξ k is the aiming error parameter.

3. The multi-RIS-assisted underwater wireless optical communication system performance analysis method according to claim 1, characterized in that: The specific implementation process of deriving the probability density function and cumulative distribution function expressions of the instantaneous signal-to-noise ratio between the source node and the destination node based on the underwater wireless optical communication system model assisted by multiple reconfigurable intelligent surfaces is as follows: According to formula (1), the instantaneous signal-to-noise ratio between the source node and the destination node of the underwater wireless optical communication system assisted by multiple reconfigurable intelligent surfaces can be calculated as: Among them, E x For the transmitted signal energy, it is assumed that the reflection coefficients of all RIS reflection units are the same, that is, ρ kn =ρ, substituting equations (2) and (6) into equation (8), the instantaneous signal-to-noise ratio can be expressed as: Define h t,k is the turbulent channel fading coefficient from the source node to the destination node through the kth RIS, h t,k Expressed as Define h k is the composite channel fading coefficient from the source node through the kth RIS to the destination node, h k Represented as h k =h p,k h t,k ; Define h as the total channel fading coefficient from the source node through K RIS to the destination node, h is expressed as definition is the average signal-to-noise ratio, Expressed as Therefore, the instantaneous signal-to-noise ratio can be calculated as: h t,k N k The probability density function of the sum of independent and identically distributed Gamma-Gamma random variables is expressed as: in, is the Meijer-G function; Based on equations (7) and (11), h k The probability density function of is calculated as: in, Using h k The probability density function of h can be calculated k The moment generating function of h. k The moment generating function of is calculated as: Substituting formula (12) into formula (13), we can get h k The moment generating function of is: in, is the Fox-H function, a k =[(N k α k ,1),(N k β k ,1)]; Then, using h k The probability density function of h is calculated by the moment generating function and the inverse Laplace transform. The probability density function of h is calculated as: in, Denotes the inverse Laplace transform. Substituting equation (14) into equation (15), the probability density function of h is calculated as: in, is the multivariate Fox-H function, Based on equations (10) and (16), the probability density function of the instantaneous signal-to-noise ratio γ is expressed as: Using h k The moment generating function and the inverse Laplace transform are used to calculate the cumulative distribution function of h. The cumulative distribution function of h is calculated as: Substituting formula (14) into formula (18), the cumulative distribution function of h is calculated as follows: Based on equations (10) and (19), the cumulative distribution function of the instantaneous signal-to-noise ratio γ is expressed as:

4. The multi-RIS-assisted underwater wireless optical communication system performance analysis method according to claim 1, characterized in that: Based on the probability density function and cumulative distribution function expressions of the instantaneous signal-to-noise ratio, analytical expressions for the outage probability and the average bit error rate of multi-ary pulse amplitude modulation are obtained. The specific implementation process of performing the outage probability and the average bit error rate performance analysis of the multi-reconfigurable intelligent surface-assisted underwater wireless optical communication system based on the obtained analytical expressions is as follows: The outage probability represents the probability that the instantaneous signal-to-noise ratio is lower than the threshold signal-to-noise ratio. The outage probability is defined as: P out =Pr{γ≤γ th }=F γ (γ th ) (21) Among them, γ th is the threshold signal-to-noise ratio; Based on equations (21) and (20), the interruption probability expression is: Under multi-level pulse amplitude modulation M-PAM, the average bit error rate is calculated as: Where erfc(·) is the complementary error function, B = (M-1) / [Mlog2(M)], C = 3 / [2(M-1)(2M-1)]; Based on equations (23) and (17), the analytical expression of the average bit error rate is: Based on the analytical expressions shown in Equations (22) and (24), the performance analysis of the outage probability and the average bit error rate of the M-PAM underwater wireless optical communication system assisted by multiple RIS is realized respectively.

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