Performance analysis method of multi-RIS-assisted underwater wireless optical communication system under RIS selection scheme

Abstract

The invention provides a performance analysis method of a multi-RIS-assisted underwater wireless optical communication system under an RIS selection scheme. The performance analysis method comprises the following steps: establishing a multi-RIS-assisted underwater wireless optical communication system model under the RIS selection scheme; the method comprises the following steps: deriving 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 under an RIS selection scheme; deriving a probability density function expression of an instantaneous signal-to-noise ratio between a source node and a destination node; based on the cumulative distribution function and the probability density function expression of the instantaneous signal-to-noise ratio, deriving to obtain an analytical expression of the outage probability and the M-PAM average bit error rate, and based on the obtained analytical expression, analyzing the performance of the outage probability and the M-PAM average bit error rate of the multi-RIS-assisted underwater wireless optical communication system under the RIS selection scheme. The invention shows the potential advantage of integrating multiple RISs into an underwater wireless optical communication system.

Description

Technical Field

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

[0002] Various ocean development and maritime applications, such as marine environmental monitoring, ocean data collection, seabed natural gas and natural mineral exploration, and port and shipping safety, all require underwater wireless communications. There are three main implementation options for underwater wireless communications: underwater acoustic communication, underwater radio frequency communication, and underwater wireless optical communication (UWOC). Compared with underwater acoustic communication and underwater radio frequency communication, UWOC has the highest transmission rate, lowest link latency, and lowest implementation cost. It provides a high-capacity, high-speed, low-latency, environmentally friendly, and secure underwater communication solution with broad application prospects.

[0003] Despite the many advantages mentioned above, UWOC 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. In underwater environments, obstacles such as aquatic organisms, plants, and submarine mountains can block the optical link between the laser source and the photodetector, increasing the probability of information loss. Given the high transmission rate of UWOC, even short-term blocking can cause a sudden interruption of communication, resulting in the loss of a large amount of information, which is fatal for a reliable UWOC system. Integrating optically reconfigurable smart surface (RIS) technology into the UWOC system provides a promising technical solution to address the key challenges of UWOC.

[0004] 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, RIS-assisted UWOC systems have 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, a single RIS has limited service coverage and performance enhancement for UWOC systems. In future practical underwater applications of RIS, deploying multiple RIS to adapt to complex underwater communication environments is inevitable. However, the system design, signal-to-noise ratio statistical characteristics, outage probability, and bit error rate performance of multi-RIS-assisted UWOC systems have not been analyzed, and research on multi-RIS-assisted UWOC systems is still lacking. Summary of the Invention

[0006] In order to solve the technical problem that the system scheme design, signal-to-noise ratio statistical characteristics, interruption probability and bit error rate performance of the multi-RIS assisted UWOC system have not been analyzed, and the multi-RIS assisted UWOC system is still lacking in research, the technical means adopted by the present invention are as follows: A performance analysis method of a multi-RIS assisted underwater wireless optical communication system under a RIS selection scheme, comprising the following steps:

[0007] S1. Considering the fading of ocean turbulence and the aiming error caused by the jitter of the beam reconfigurable smart surface, a multi-RIS-assisted underwater wireless optical communication system model under the RIS selection scheme is established;

[0008] S2. Based on the multi-RIS-assisted underwater wireless optical communication system model under the RIS selection scheme, the cumulative distribution function expression of the instantaneous signal-to-noise ratio between the source node and the destination node is derived;

[0009] S3. Based on the cumulative distribution function expression of the instantaneous signal-to-noise ratio between the source node and the destination node, derive the probability density function expression of the instantaneous signal-to-noise ratio between the source node and the destination node;

[0010] S4. Based on the cumulative distribution function and probability density 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 derived. Based on the obtained analytical expressions, the outage probability and average bit error rate performance of the multi-RIS-assisted underwater wireless optical communication system under the RIS selection scheme are analyzed.

[0011] The specific process of establishing the multi-RIS assisted underwater wireless optical communication system model under the RIS selection scheme is as follows:

[0012] The underwater wireless optical communication system assisted by multiple RIS 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, k = 1, 2, …, K, reflection units, the destination node is equipped with a photodetector, assuming 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;

[0013] During the RIS selection process, the destination node estimates the channel fading coefficient of each RIS channel to determine the maximum instantaneous signal-to-noise ratio. Through the feedback channel, the destination node selects the index of the RIS with the highest instantaneous signal-to-noise ratio and sends it back to the source node. The laser source corresponding to the selected RIS is used as the transmitting laser source, and other laser sources remain silent. The transmitting laser source uses the full transmission power. Under the RIS selection scheme, the destination node can only receive the reflected signal from the selected RIS. Assuming that the kth RIS is the selected RIS, the received signal y of the destination node is expressed as:

[0014]

[0015] 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, 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. 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;

[0016] 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:

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

[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 cumulative distribution function expression of the instantaneous signal-to-noise ratio between the source node and the destination node based on the multi-RIS-assisted underwater wireless optical communication system model under the RIS selection scheme is as follows:

[0029] The instantaneous signal-to-noise ratio between the source node and the destination node is expressed as:

[0030]

[0031] Among them, γ k is the instantaneous signal-to-noise ratio when the kth RIS is the selected RIS. According to formula (1), γ k Calculated as:

[0032]

[0033] 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, substitute equations (2) and (6) into equation (9), γ k Expressed as:

[0034]

[0035] 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 ;definition is the average signal-to-noise ratio, Expressed as Therefore, γ k Calculated as:

[0036]

[0037] h t,k N k The probability density function of the sum of independent and identically distributed Gamma-Gamma random variables can be expressed as:

[0038]

[0039] in, is the Meijer-G function;

[0040] Based on equations (7) and (12), h k The probability density function of is calculated as:

[0041]

[0042] in,

[0043] Using equations (11) and (13), γ k The probability density function of is calculated as:

[0044]

[0045] Based on formula (14), γ k The cumulative distribution function of is calculated as:

[0046]

[0047] Substituting formula (14) into formula (15), we can get γ k The cumulative distribution function expression is:

[0048]

[0049] in,

[0050] Based on equations (8) and (16), the cumulative distribution function of the system end-to-end instantaneous signal-to-noise ratio γ under the RIS selection scheme is calculated as:

[0051]

[0052] By expressing Equation (17) with the multivariate Fox-H function, the cumulative distribution function expression of γ can be obtained as follows:

[0053]

[0054] in,

[0055] Furthermore, the specific implementation process of deriving the probability density function expression of the instantaneous signal-to-noise ratio between the source node and the destination node based on the cumulative distribution function expression of the instantaneous signal-to-noise ratio between the source node and the destination node is as follows:

[0056] Based on the cumulative distribution function of the instantaneous signal-to-noise ratio γ shown in formula (18), the probability density function of the instantaneous signal-to-noise ratio γ is calculated by derivation:

[0057]

[0058] Substituting equation (18) into equation (19), we can obtain the probability density function expression of the instantaneous signal-to-noise ratio γ:

[0059]

[0060] Furthermore, based on the cumulative distribution function and probability density 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 derived. Based on the obtained analytical expressions, the specific implementation process of the outage probability and the average bit error rate performance analysis of the multi-RIS-assisted underwater wireless optical communication system under the RIS selection scheme is as follows:

[0061] 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:

[0062] P out =Pr{γ≤γ th}=F γ (γ th ) (twenty one)

[0063] Among them, γ th is the threshold signal-to-noise ratio;

[0064] Based on equations (21) and (18), the outage probability P of the multi-RIS assisted underwater wireless optical communication system under the RIS selection scheme is obtained out The expression is:

[0065]

[0066] In the underwater wireless optical communication system with intensity modulation direct detection, under M-PAM, the average bit error rate is calculated as:

[0067]

[0068] Wherein, erfc(·) is the complementary error function, B = (M-1) / [Mlog2(M)], and C = 3 / [2(M-1)(2M-1)].

[0069] Based on the average bit error rate calculation formula and the probability density function expression of the instantaneous signal-to-noise ratio γ, the average bit error rate analytical expression P is obtained. e for:

[0070]

[0071] Based on the analytical expressions shown in Equations (22) and (24), 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 under the RIS selection scheme is realized respectively.

[0072] The present invention provides a performance analysis method for a multi-RIS-assisted underwater wireless optical communication system under a RIS selection scheme, focusing on the multi-RIS-assisted underwater wireless optical communication system under the RIS selection scheme. Among multiple RISs, the RIS with the highest instantaneous signal-to-noise ratio is selected for communication. Under the RIS selection scheme, a source node communicates with a destination node with the assistance of the selected RIS. The RIS is equipped with multiple passive reflector units and is placed within the field of view of the destination node. In this system, we consider ocean turbulence and aiming error composite fading channels. Under the RIS selection scheme, we derive a cumulative distribution function expression for the system's end-to-end instantaneous signal-to-noise ratio. Based on the cumulative distribution function expression for the instantaneous signal-to-noise ratio, we derive a probability density function expression for the instantaneous signal-to-noise ratio. Based on the cumulative distribution function and probability density function expressions for the instantaneous signal-to-noise ratio, we use the multivariate Fox-H function to obtain analytical expressions for the system outage probability and the M-PAM average bit error rate. Finally, numerical results demonstrate the closeness and effectiveness of our expression compared to Monte Carlo simulations.

[0073] Compared with the prior art, the present invention has the following advantages:

[0074] A performance analysis method for a multi-RIS-assisted underwater wireless optical communication system under a RIS selection scheme. Compared to a single-RIS-assisted underwater wireless optical communication system, the present invention considers deploying multiple RISs in an underwater environment. Among the multiple RISs, the RIS with the highest instantaneous signal-to-noise ratio is selected for communication. Compared to some previous studies on RIS-assisted underwater wireless optical communication systems, the present invention provides a study of the end-to-end instantaneous signal-to-noise ratio statistical characteristics, system interruption probability, and average bit error rate of a multi-RIS-assisted underwater wireless optical communication system under a RIS selection scheme, which is lacking in previous studies. By deploying multiple RISs underwater and applying the RIS selection scheme, we have achieved a reduction in the interruption probability and bit error rate of the underwater wireless optical communication system, which improves the reliability of the system under conditions of ocean turbulence and aiming errors. The above research is of great significance to the field of underwater wireless optical communications.

[0075] 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

[0076] 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.

[0077] Figure 1Flow chart of the method of the present invention.

[0078] Figure 2 The present invention provides a model structure of a multi-RIS-assisted underwater wireless optical communication system under the RIS selection scheme applicable to the present invention.

[0079] 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.

[0080] 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

[0081] 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.

[0082] 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.

[0083] Figure 1 Flow chart of the method of the present invention.

[0084] A performance analysis method for a multi-RIS-assisted underwater wireless optical communication system with a RIS selection scheme comprises the following steps:

[0085] 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 under the RIS selection scheme is established.

[0086] S2. Based on the multi-RIS-assisted underwater wireless optical communication system model under the RIS selection scheme, the cumulative distribution function expression of the instantaneous signal-to-noise ratio between the source node and the destination node is derived;

[0087] S3. Based on the cumulative distribution function expression of the instantaneous signal-to-noise ratio between the source node and the destination node, derive the probability density function expression of the instantaneous signal-to-noise ratio between the source node and the destination node;

[0088] S4. Based on the cumulative distribution function and probability density 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 derived. Based on the obtained analytical expressions, the outage probability and M-PAM average bit error rate performance of the multi-RIS-assisted underwater wireless optical communication system under the RIS selection scheme are analyzed.

[0089] Steps S1 / S2 / S3 / S4 are executed sequentially;

[0090] 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 under the RIS selection scheme shown in the figure. 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 laser source points to a RIS, and each RIS is equipped with N k (k=1,2,…,K) reflection units, and the destination node is equipped with a photodetector. We assume that the line-of-sight link between the source node and the destination node is blocked by underwater obstacles, and information transmission can only be achieved through RIS. Each RIS reflects the optical signal from the source node to the destination node. Under the RIS selection scheme, the destination node estimates the channel fading coefficient of each RIS channel to determine the maximum instantaneous signal-to-noise ratio. Through the feedback channel, the destination node selects the index of the RIS with the highest instantaneous signal-to-noise ratio and sends it back to the source node. Accordingly, the laser source corresponding to the selected RIS is used as the transmitting laser source, the other laser sources remain silent, and the transmitting laser source uses the full transmission power. Under the RIS selection scheme, the destination node can only receive the reflected signal from the selected RIS. Assuming that the kth RIS is the selected RIS, the received signal of the destination node is expressed as:

[0091]

[0092] 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 nth (n=1,2,…,N k ) reflection coefficient of each reflection unit. l,kn 、ht,kn and h p,kn represent 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.

[0093] 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:

[0094]

[0095] 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:

[0096]

[0097] 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:

[0098]

[0099] Among them, K p (·) denotes the p-order modified Bessel function of the second kind.

[0100] 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:

[0101] h p,kn =h p,k (6)

[0102] For the kth RIS, the aiming error fading coefficient h p,k The probability density function of is:

[0103]

[0104] Among them, A k and ξ k is the aiming error parameter.

[0105] 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 under the RIS selection scheme to derive a cumulative distribution function expression of the instantaneous signal-to-noise ratio between the source node and the destination node. The specific implementation process is as follows:

[0106] Under the RIS selection scheme, the system end-to-end instantaneous signal-to-noise ratio can be expressed as:

[0107] γ=max{γ1,γ2,…,γ k ,…,γ K} (8)

[0108] Among them, γ k is the instantaneous signal-to-noise ratio when the kth RIS is the selected RIS. According to formula (1), γ k It can be calculated as:

[0109]

[0110] 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 (9), γ k It can be expressed as:

[0111]

[0112] 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 hk =h p,k h t,k ;definition is the average signal-to-noise ratio, Expressed as Therefore, γ k It can be calculated as:

[0113]

[0114] h t,k N k The probability density function of the sum of independent and identically distributed Gamma-Gamma random variables can be expressed as:

[0115]

[0116] in, is the Meijer-G function.

[0117] Based on equations (7) and (12), h k The probability density function of can be calculated as:

[0118]

[0119] in,

[0120] Using equations (11) and (13), γ k The probability density function of can be calculated as:

[0121]

[0122] Based on formula (14), γ k The cumulative distribution function of is calculated as:

[0123]

[0124] Substituting formula (14) into formula (15), we can get γ k The cumulative distribution function expression is:

[0125]

[0126] in,

[0127] Based on equations (8) and (16), the cumulative distribution function of the system end-to-end instantaneous signal-to-noise ratio γ under the RIS selection scheme is calculated as:

[0128]

[0129] By expressing Equation (17) with the multivariate Fox-H function, the cumulative distribution function expression of γ can be obtained as follows:

[0130]

[0131] in,

[0132] In specific implementation, as a preferred embodiment of the present invention, step S3 derives a probability density function expression of the instantaneous signal-to-noise ratio between the source node and the destination node based on the cumulative distribution function expression of the instantaneous signal-to-noise ratio between the source node and the destination node. The specific implementation process is as follows:

[0133] Based on the cumulative distribution function of the instantaneous signal-to-noise ratio γ shown in formula (18), the probability density function of the instantaneous signal-to-noise ratio γ can be calculated by differentiation:

[0134]

[0135] Substituting equation (18) into equation (19), we can obtain the probability density function expression of the instantaneous signal-to-noise ratio γ:

[0136]

[0137] In specific implementation, as a preferred embodiment of the present invention, step S4 is based on the cumulative distribution function and probability density function expression of the instantaneous signal-to-noise ratio to derive the analytical expression of the interruption probability and the M-PAM (multi-level pulse amplitude modulation) average bit error rate. 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]

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

[0141] Based on equations (21) and (18), the outage probability expression of the multi-RIS assisted underwater wireless optical communication system under the RIS selection scheme can be obtained as follows:

[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 (20), 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 under the RIS selection scheme 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 and applied a RIS selection scheme. Among the multiple RIS, the RIS with the highest instantaneous signal-to-noise ratio is selected for communication to establish a stable reflected optical link. We use 4-PAM modulation and set the turbulence parameter α k =3.35, β k =3.19, aiming error parameter A k =1, Threshold signal-to-noise ratio γ th =13dB.

[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.

[0154] We observed Figure 3 The Monte Carlo simulation results in are highly consistent with the simulation results based on formula (22) in S4. In addition, Figure 4 The Monte Carlo simulation results are also highly consistent with the simulation results based on formula (24) in S4.

[0155] Depend on Figure 3 and Figure 4 It can be seen that compared with the single-RIS-assisted underwater wireless optical communication system (K = 1), the multi-RIS-assisted underwater wireless optical communication system (K = 2, K = 3) with the RIS selection scheme has lower outage probability and bit error rate. In addition, as the number of RISs in the system increases, the outage probability and average bit error rate both decrease. This shows that by increasing the number of RISs and applying the RIS selection scheme, the reliability of the underwater wireless optical communication system can be improved, achieving better communication service quality.

[0156] 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.

[0157] 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 performance analysis method for a multi-RIS-assisted underwater wireless optical communication system under a RIS selection scheme, characterized in that: The steps include: S1. Considering the fading of ocean turbulence and the aiming error caused by the jitter of the reconfigurable smart surface, a model of underwater wireless optical communication system assisted by multiple reconfigurable smart surfaces under the reconfigurable smart surface selection scheme is established; S2. Based on the underwater wireless optical communication system model assisted by multiple reconfigurable smart surfaces under the reconfigurable smart surface selection scheme, the cumulative distribution function expression of the instantaneous signal-to-noise ratio between the source node and the destination node is derived; S3. Based on the cumulative distribution function expression of the instantaneous signal-to-noise ratio between the source node and the destination node, derive the probability density function expression of the instantaneous signal-to-noise ratio between the source node and the destination node; S4. Based on the cumulative distribution function and probability density function expressions of the instantaneous signal-to-noise ratio, analytical expressions of the interruption probability and the average bit error rate of multi-bit pulse amplitude modulation are derived. Based on the obtained analytical expressions, the interruption probability and the average bit error rate performance of the multi-reconfigurable smart surface-assisted underwater wireless optical communication system under the reconfigurable smart surface selection scheme are analyzed.

2. The performance analysis method of a multi-RIS-assisted underwater wireless optical communication system under a RIS selection scheme according to claim 1 is characterized in that: The specific process of establishing the underwater wireless optical communication system model assisted by multiple reconfigurable smart surfaces under the reconfigurable smart surface selection scheme is as follows: The underwater wireless optical communication system assisted by multiple RIS 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 , k = 1, 2, …, K, reflection units, the destination node is equipped with a photodetector, assuming 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; During the RIS selection process, the destination node estimates the channel fading coefficient of each RIS channel to determine the maximum instantaneous signal-to-noise ratio. Through the feedback channel, the destination node selects the index of the RIS with the highest instantaneous signal-to-noise ratio and sends it back to the source node. The laser source corresponding to the selected RIS is used as the transmitting laser source, and other laser sources remain silent. The transmitting laser source uses the full transmission power. Under the RIS selection scheme, the destination node can only receive the reflected signal from the selected RIS. Assuming that the kth RIS is the selected RIS, the received signal y 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, n=1,2,…,N k , 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. 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; 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, h l,kn Calculated as Assume that for all RIS Then h l,kn Calculated as: h l,kn =exp(-cL)=h l (2) 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 performance analysis method of a multi-RIS-assisted underwater wireless optical communication system under a RIS selection scheme according to claim 1 is characterized in that: The specific implementation process of deriving the cumulative distribution function expression of the instantaneous signal-to-noise ratio between the source node and the destination node based on the multi-reconfigurable smart surface assisted underwater wireless optical communication system model under the reconfigurable smart surface selection scheme is as follows: The instantaneous signal-to-noise ratio between the source node and the destination node is expressed as: γ=max{γ1,γ2,…,γ k ,…,c K } (8) Among them, γ k is the instantaneous signal-to-noise ratio when the kth RIS is the selected RIS. According to formula (1), γ k 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, substitute equations (2) and (6) into equation (9), γ k 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 ;definition is the average signal-to-noise ratio, Expressed as Therefore, γ k Calculated as: h t,k N k The probability density function of the sum of independent and identically distributed Gamma-Gamma random variables can be expressed as: in, is the Meijer-G function; Based on equations (7) and (12), h k The probability density function of is calculated as: in, Using equations (11) and (13), γ k The probability density function of is calculated as: Based on formula (14), γ k The cumulative distribution function of is calculated as: Substituting formula (14) into formula (15), we can get γ k The cumulative distribution function expression is: in, Based on equations (8) and (16), the cumulative distribution function of the system end-to-end instantaneous signal-to-noise ratio γ under the RIS selection scheme is calculated as: By expressing Equation (17) with the multivariate Fox-H function, the cumulative distribution function expression of γ can be obtained as follows: in, 4. The performance analysis method of a multi-RIS-assisted underwater wireless optical communication system under a RIS selection scheme according to claim 1 is characterized in that: The specific implementation process of deriving the probability density function expression of the instantaneous signal-to-noise ratio between the source node and the destination node based on the cumulative distribution function expression of the instantaneous signal-to-noise ratio between the source node and the destination node is as follows: Based on the cumulative distribution function of the instantaneous signal-to-noise ratio γ shown in formula (18), the probability density function of the instantaneous signal-to-noise ratio γ is calculated by derivation: Substituting equation (18) into equation (19), we can obtain the probability density function expression of the instantaneous signal-to-noise ratio γ:

5. The performance analysis method of a multi-RIS-assisted underwater wireless optical communication system under a RIS selection scheme according to claim 1 is characterized in that: Based on the cumulative distribution function and probability density 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 derived. The specific implementation process of analyzing the outage probability and the average bit error rate of multi-bit pulse amplitude modulation performance of the multi-reconfigurable smart surface-assisted underwater wireless optical communication system under the reconfigurable smart surface selection scheme 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 (18), the outage probability P of the multi-RIS assisted underwater wireless optical communication system under the RIS selection scheme is obtained out The expression is: In the underwater wireless optical communication system with intensity modulation direct detection, under M-PAM, the average bit error rate is calculated as: Wherein, erfc(·) is the complementary error function, B = (M-1) / [Mlog2(M)], and C = 3 / [2(M-1)(2M-1)]. Based on the average bit error rate calculation formula and the probability density function expression of the instantaneous signal-to-noise ratio γ, the average bit error rate analytical expression P is obtained. e for: Based on the analytical expressions shown in Equations (22) and (24), 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 under the RIS selection scheme is realized respectively.

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