Method for optimizing number of relay nodes of serial relay UWOC system

Abstract

The invention discloses a method for acquiring the optimal number of relay nodes for a serial relay underwater wireless optical communication (UWOC) system, and belongs to the technical field of wireless optical communication, especially underwater wireless optical communication. The method comprises the following steps of: firstly, modeling a novel aggregation fading transmission channel model which comprehensively considers various factors such as non-fading channel impulse response (FFIR) implicit path loss and multipath effect, generalized Gamma distribution (GGD) ocean turbulence, zero visual axis pointing error and the like; deducing a theoretical closed expression of a point-to-point (P2P) outage probability of the serial relay UWOC system in the aggregation fading channel by using a higher exceeding Meijer-G function; then, the deduced serial relay UWOC system P2P outage probability theory closed form expression is subjected to order reduction, an original Meijer-G function is replaced with a Gamma function, and then a final end-to-end outage probability theory expression is obtained; and finally, making a first-order derivative about the relay node number N for the end-to-end outage probability expression, setting the first-order derivative to be zero, constructing a nonlinear equation about the N, and solving the nonlinear equation to obtain the optimal relay node number. The method for optimizing the number of the relay nodes of the serial relay UWOC system can provide theoretical guidance for upper-layer network planning of the system.

Description

Technical Field

[0001] The present invention relates to an optimization problem of the number of relay nodes in an underwater wireless optical communication (UWOC) system under a serial relay working mode, and belongs to the technical field of wireless optical communication, especially underwater wireless optical communication. Background Art

[0002] In recent years, as countries around the world have increasingly carried out activities such as resource exploration and environmental monitoring facing the ocean, underwater wireless optical communication has become more urgent and important. The UWOC system has the characteristics of high communication rate, low latency, and strong confidentiality. Experimental tests show that the blue / green light beams in the visible light band have the smallest absorption loss in seawater compared to light beams of other frequencies, so blue / green frequency band light sources are often used as carriers for underwater information transmission. Even so, a large amount of salt and suspended matter dissolved in seawater will still have a relatively serious absorption and scattering effect on the blue / green light beams transmitted in the water, resulting in the transmission distance of the light beam in the water (≤150 meters) far from being comparable to the propagation distance in the atmospheric environment. One of the means to solve this problem and effectively expand the coverage of the UWOC system is to use wireless relay transmission technology.

[0003] Existing research results show that the introduction of relay nodes can effectively reduce the risk of communication interruption of UWOC during medium and long distance transmission, that is, effectively reduce the interruption probability of the system. The so-called "interruption probability" is defined as the probability that the signal-to-noise ratio of the receiver output signal is lower than a specified threshold, which is an important indicator for measuring the performance of the communication system. Although the introduction of relay nodes can effectively reduce the interruption risk of UWOC during medium and long distance transmission, it is limited by the total transmission link length of the system and the cost of system equipment. Blindly introducing a large number of relay nodes without mathematical optimization design may not further improve the interruption probability performance of the system while greatly increasing the system industry cost and implementation complexity. Therefore, under conditions such as a fixed underwater transmission environment, it is obviously a very meaningful task to design the optimal number of serial relay nodes for a serial relay UWOC system and obtain the best interruption performance index of the system. Summary of the invention

[0004] Purpose of the invention: In view of the deficiency that the existing serial relay UWOC system is limited to analyzing performance indicators such as system interruption probability and does not involve the optimization of the number of serial relay nodes, the present invention proposes a design method for a serial relay UWOC system to obtain the optimal number of serial relay nodes, in order to achieve optimized transmission of the relay UWOC system under the premise of meeting the system interruption performance indicators.

[0005] Technical solution: An optimization solution for obtaining the optimal number of relay nodes in a serial relay UWOC system, including the following steps

[0006] The theoretical closed-form expression P of the end-to-end (e2e) outage probability of the serial relay UWOC system is based on the mixed channel fading with GGD ocean turbulence and zero-line-of-sight pointing error. e2e , calculate its derivative with respect to the number of relay nodes N, i.e. dP e2e / dN; let the above derivative value be dP e2e / dN is equal to zero to construct a nonlinear equation related to the number of relay nodes N; solving the nonlinear equation related to the number of relay nodes N can obtain the optimal number of serial relay nodes in the serial relay UWOC system;

[0007] As a preferred solution, for the case where the point-to-point (P2P) link distance is equal, the end-to-end interruption probability theoretical closed-form calculation formula P of the serial relay UWOC system is e2e It can be expressed as

[0008] P e2e =1-(1-P P2P ) N+1 .

[0009] In the above formula, N represents the number of serial relay nodes, P P2P Indicates the interruption probability of the P2P link.

[0010] As a preferred solution, the interruption probability P of the point-to-point P2P link is P2P The calculation formula is as follows:

[0011]

[0012] In the formula, where a and c are the shape parameters of the generalized gamma distribution (GGD) ocean turbulence model, b is the scale parameter of the GGD model, represents the gamma function, A0 = [erf(v)] 2 It represents the ratio of the laser beam power collected by the receiver at the detector center r = 0, represents the receiver aperture r a With the beam width ω z The ratio of is the error function, the ratio of positive integers l1 to k1 satisfies l1 / k1=c, represents the equivalent beam width, is the jitter variance of the receiver. is the received signal-to-noise ratio threshold γ th The corresponding upper limit of the integration of the mixed fading signal is, is the variance of the Gaussian integrated noise component, u (s) =Ae Bd +Ce Dd is a variable related to the distance d of the P2P link, representing the non-fading path loss, where the coefficients A, B, C, and D can be obtained by Monte Carlo simulation of the non-fading channel impulse response (FFIR) values ​​at different transmission distances through data fitting operations, and d = Z / (N+1), where Z is the total end-to-end transmission link distance of the serial relay UWOC system. It can be seen that h th It is an implicit function of the number of relay nodes N.

[0013] As a preferred solution, the end-to-end interruption probability P e2e The nonlinear equation constructed by taking the first-order derivative with respect to N is as follows:

[0014]

[0015] In the above formula, P P2P′ Represents the P2P interruption probability formula P P2P Take the first-order derivative with respect to N. By solving the nonlinear equation, the optimal number of relay nodes in the serial relay UWOC system with the optimization goal of optimizing the end-to-end system outage probability can be obtained.

[0016] As a preferred solution, the P2P link interruption probability P P2P Again, find the first-order partial derivative P with respect to N P2P′ The calculation formula is as follows:

[0017]

[0018] Where h th ′ represents the integral upper limit h of the mixed fading signal th The first derivative term with respect to N.

[0019] As a preferred embodiment, the h th The first-order derivative h with respect to N th The calculation formula of ′ is as follows:

[0020]

[0021] As a preferred solution, the probability density function (PDF) of the GGD ocean turbulence fading is expressed as follows:

[0022]

[0023] In the formula, b is the scale parameter, a and c are shape parameters, and h a represents a random variable that follows a GGD distribution.

[0024] Beneficial effects:

[0025] Compared with the prior art, the technical solution of the present invention has the following beneficial technical effects: a method for optimizing the number of relay nodes in a serial relay UWOC system provided by the present invention can determine the optimal number of system serial relay nodes with the optimization goal of minimizing the system end-to-end interruption probability under the complex conditions of GGD ocean turbulence environment and zero line-of-sight pointing error fading in the link, thereby providing theoretical guidance for the upper-level network planning of the system. BRIEF DESCRIPTION OF THE DRAWINGS

[0026] Figure 1 It is a block diagram of the principle implementation of the serial relay UWOC system relay node number optimization solution proposed in the present invention.

[0027] Figure 2 This is a schematic diagram of the structure of the serial relay UWOC system. SN represents the source node, DN represents the destination node, and RN represents the destination node. i represents the i-th relay node; h i (t) represents the mixed fading time domain waveform of the i-th serial branch.

[0028] Figure 3 It is a 40-meter-long serial relay UWOC system for offshore coastal water quality. The system interruption probability varies with the node transmission power under the condition of using different numbers of relay nodes.

[0029] Figure 4 It is a 40-meter-long serial relay UWOC system for offshore coastal water quality. When the transmission power of each node is fixed at 30dBm, the system interruption probability varies with the number of relay nodes. DETAILED DESCRIPTION

[0030] The present invention will be further described below in conjunction with specific embodiments, and it should be understood that these embodiments are only used to illustrate the present invention and are not intended to limit the scope of the present invention. After reading the present invention, those skilled in the art will be able to modify various equivalent forms of the present invention within the scope defined by the appended claims of the present application.

[0031] The present invention is a method of using the closed-form expression of the end-to-end interruption probability of the serial relay UWOC system to find the first-order derivative of the number of nodes N and set it equal to zero, and then solve the nonlinear equation to obtain the optimal number of relay nodes in the serial relay UWOC system. The specific implementation method and application examples are described as follows:

[0032] Step 1: Modeling the aggregate fading transmission channel model that comprehensively considers the fading-free channel impulse response (FFIR) implicit path loss and multipath effect, GGD ocean turbulence, and zero boresight pointing error;

[0033] Step 2: Use the advanced transcendental Meiier-G function to derive the mathematical expression of the hybrid fading joint PDF that takes into account GGD turbulence and zero boresight pointing error, and based on this, derive the theoretical closed-form expression of the P2P outage probability in the serial relay environment of the above-mentioned aggregate fading UWOC system;

[0034] Step 3: Reduce the derived closed-form expression of the P2P interruption probability theory of the serial relay UWOC system, use the Gamma function to replace the original Meiier-G function, and obtain the final end-to-end (e2e) interruption probability closed-form expression. Finally, the closed-form expression is differentiated and set equal to zero to obtain an equivalent nonlinear equation. Solving this equation can obtain the optimal number of serial relay nodes.

[0035] First, the GGD model is used to describe the ocean turbulence effect caused by changes in temperature and salinity. Its PDF has the following mathematical expression:

[0036]

[0037] Where b is the scale parameter, a and c are the shape parameters, represents the gamma function.

[0038] Considering the path loss and multipath effect caused by seawater absorption and scattering, GGD turbulence effect h a , and zero boresight pointing error h p The UWOC system aggregate fading channel model is shown in Figure 1. Among them, the path loss and multipath effect are implicitly reflected in the FFIR function h0(t), which can be obtained by setting the Monte Carlo numerical simulation of the specific communication environment. Therefore, in the description of the mixed fading h expression, only the turbulence effect and pointing error need to be considered, that is,

[0039] h=h p h a , (2)

[0040] In the above formula, the zero boresight pointing error attenuation h with a vertical distance z from the launch point and a radial error r is p It can be approximately expressed as

[0041]

[0042] Where A0 = [erf(v)] 2 It represents the power ratio of the laser beam collected by the receiver at the center of the detector r = 0, represents the equivalent beam width, represents the receiver aperture r a With the beam width ω z The ratio of is the error function. Without loss of generality, under zero boresight jitter error, the radial error r of the received beam obeys the Rayleigh distribution, then the pointing error h p The PDF function of is calculated as

[0043]

[0044] In the formula, is the jitter variance of the receiver.

[0045] Therefore, the joint probability density function of the mixed fading factor h can be expressed as

[0046]

[0047] In the formula, is the conditional probability density function. According to the calculation criteria of the PDF of the random variable function value, we have

[0048]

[0049] It can be obtained that the joint PDF of the mixed fading channel h in the GGD turbulent environment with zero boresight pointing error is:

[0050]

[0051] Using the formula and the operational properties of the Meijer-G function, the joint PDF of h can be written as

[0052]

[0053] Where the integer ratio l1 / k1=c (c is the shape factor of the GGD distribution); is the Meijer-G function, represents a k-dimensional vector. To avoid redundancy in the formula, some of the fixed parameters are summarized: Then the joint PDF of h can be further simplified as

[0054]

[0055] Secondly, a simple P2P UWOC system is examined. When the transmitter uses on-off keying (OOK) modulation to transmit information, and the receiver uses a traditional PIN (positive-intrinsic-negative junction) receiver to achieve photoelectric conversion, the received current time domain signal can be expressed as

[0056] r(t)=R·x(t)+n(t), (10)

[0057] In the formula, R = ηq / hf is the conversion coefficient of the photodetector, where η, q, h, and f represent the quantum efficiency, electron charge, Planck constant, and the frequency of the underwater light signal, respectively. n(t) is an additive white Gaussian noise process, and the mean of the noise at each time sampling point is 0 and the variance is σ 2 =4KTB / R L , where K, T, B, R L They represent the Boltzmann constant, Kelvin temperature, filter bandwidth and system load resistance respectively. x(t) represents the received optical signal affected by the comprehensive fading factors such as FFIR, ocean turbulence and pointing error, that is,

[0058]

[0059] In the formula, Indicates the transmission data sequence, b k ∈{0, 1} is the OOK codeword of the kth time slot, T b =1 / R b Indicates the OOK symbol width, R b is the data rate, P(t)=2P b M(t) is [0, T b ] is the pulse shaping function on the time interval, M(t) is the corresponding unit value gate function, P b is the average transmission power of the OOK signal; F(t) = P(t)*h0(t) represents the distortion and path loss received waveform of the pulse shaping function P(t) after passing through the FFIR channel h0(t), h(t) = h·h0(t) is the aggregate channel impulse response containing the multiplicative mixed channel fading factor h, and the symbol "*" represents the convolution operator. If ISI is not considered, the integrated current of the receiver during the 0th symbol interval can be expressed as

[0060]

[0061] Where b0 is the OOK symbol of the 0th time slot, is the matched filter output of the desired current waveform signal. Obviously, u (s) It is a function of the FFIR waveform h0(t), that is, its value is related to the distance d of the P2P link. Let u (s) =Ae Bd +Ce Dd After fitting the FFIR data, the fitting coefficients are A=42.35, B=-0.3983, C=-7.017, and D=-0.7177, where d represents the P2P distance. is zero and has a variance of Gaussian integrated noise component.

[0062] Since the interruption probability is defined as the probability that the output signal-to-noise ratio is lower than a specified threshold, the interruption probability of the P2P link can be expressed as:

[0063] P P2P (γ th )=Pr(γ<γ th ), (13)

[0064] Where γ th is the signal-to-noise ratio threshold. Define the integration limit The interruption probability of a P2P link can be equivalent to:

[0065]

[0066] Using the operational properties of the Meijer-G function, we can get the closed-form expression of the interruption probability of the P2P link:

[0067]

[0068] When k1=1,l1=c,using the reduction formula and operation properties of Meijer-G function,the above closed-form expression can be further written as

[0069]

[0070] The exact expression of the final end-to-end outage probability of the serial relay UWOC system without considering inter-symbol interference is:

[0071]

[0072] For the case where the distance of each link is equal, the above formula is simplified to:

[0073]

[0074] Taking the derivative of N in the above equation and setting it equal to zero, we can get an equivalent nonlinear equation:

[0075]

[0076] Solving this nonlinear equation can obtain the optimal value of the number of relay nodes, where P P2P′ The derivative of the probability of P2P link interruption

[0077]

[0078] Where h th ′ represents the received signal-to-noise ratio threshold γ th The corresponding upper limit of the integration of the mixed fading signal h is th Derivative with respect to N

[0079]

[0080] An example of application of the serial relay UWOC system relay node number optimization method in numerical simulation of ocean aggregate fading channel environment:

[0081] 1. Comparison of the system end-to-end outage probability with node transmission power under different numbers of serial relay nodes

[0082] The core simulation parameters are assumed as follows: The coastal water quality is selected, and its absorption and scattering coefficients are (0.179, 0.219) m -1 ; The total end-to-end link distance of the serial UWOC system is Z = 40m, and the receiver aperture radius is r a =0.1m, jitter standard deviation σ s =0.15m, light beam width ω z =0.2m. In order to verify the accuracy of the theoretical calculation results of the nonlinear equation expression for solving the optimal number of relay nodes derived from the theory, the present invention provides the theoretical calculation results and Monte Carlo numerical simulation results of the closed-form formula (i.e., Formula 18) of the end-to-end interruption probability of the serial relay UWOC system derived from the theory with the change of the node transmission power under different numbers of serial relay nodes, as shown in the figure. Figure 3 As shown in the figure. From the simulation results, it can be seen that under a fixed number of relay nodes, the system end-to-end outage probability decreases with the increase of node transmission power; however, as the number of relay nodes gradually increases, the year-on-year improvement effect of the system outage probability gradually narrows, especially when the number of serial relay nodes is greater than 8, the outage probability increases slowly instead. This shows that the number of relay nodes in the serial relay UWOC system is not getting better with the increase of the number of nodes N, nor does it gradually converge to a certain limit value, but there is an optimal number of relay nodes. At the same time, when the closed-form expression P of the end-to-end outage probability of the serial relay UWOC system e2e When N is derived and set equal to zero, the nonlinear equation of formula (19) is solved by numerical calculation, and the optimal value of the number of relay nodes is 8.1051. Since the number of nodes is an integer, the number of relay nodes that makes the serial relay UWOC system perform best is 8, which is the theoretical calculation value and Figure 3 The results are consistent.

[0083] In order to more intuitively show the variation of the end-to-end interruption probability of the serial relay UWOC system with the number of relay nodes, Figure 4The curve of the interruption probability of the serial relay UWOC system changing with the number of relay nodes under a fixed transmission power of 30dBm is given, and Table 1 summarizes the interruption probability of the serial relay UWOC system under different numbers of relay nodes in the graph. It can be seen from the data in the table that when N < 8, the interruption probability of the serial relay UWOC system gradually decreases, and the system performance improves; when N > 8, the interruption probability of the serial relay UWOC system gradually increases, and the system performance becomes worse. Therefore, for the serial relay UWOC system under the simulation conditions of the present invention, the value of the relay node with the best performance is 8, which is consistent with the theoretical calculation results and is also consistent with Figure 3 The curve trend of the outage probability changing with the transmission power under different numbers of relay nodes is consistent.

[0084] Table 1. Interruption probability of serial relay UWOC system under different numbers of relay nodes at fixed transmission power

[0085] N 1 2 3 4 5 6 7 8 Pout(10^-4) 30 9.6505 5.9631 4.7080 4.1658 3.9146 3.8075 3.7812 N 9 10 11 12 13 14 15 16 Pout(10^-4) 3.8046 3.8605 3.9388 4.0332 4.1395 4.2549 4.3773 4.5053

[0086] The above is only a preferred embodiment of the present invention. It should be pointed out that for ordinary technicians in this technical field, several improvements and modifications can be made without departing from the principle of the present invention. These improvements and modifications should also be regarded as the scope of protection of the present invention.

Claims

1. An optimization scheme for obtaining the optimal number of relay nodes in a serial relay UWOC system, characterized in that: The steps include: The theoretical closed-form expression P of the end-to-end (e2e) outage probability of the serial relay UWOC system is based on the mixed channel fading with GGD ocean turbulence and zero-line-of-sight pointing error. e2e , calculate its derivative with respect to the number of relay nodes N, i.e. dP e2e / dN; let the above derivative value be dP e2e / dN is equal to zero to construct a nonlinear equation related to the number of relay nodes N; by solving the nonlinear equation related to the number of relay nodes N, the optimal number of serial relay nodes in the serial relay UWOC system can be obtained.

2. The optimization scheme for obtaining the optimal number of relay nodes in a serial relay UWOC system according to claim 1 is characterized in that: For the case where the point-to-point (P2P) link distance is equal, the theoretical closed-form calculation formula for the end-to-end interruption probability of the serial relay UWOC system is P e2e It can be expressed as P e2e =1-(1-P P2P ) N+1 . In the above formula, N represents the number of serial relay nodes, P P2P Indicates the interruption probability of the P2P link.

3. The optimization scheme for obtaining the optimal number of relay nodes in a serial relay UWOC system according to claim 2 is characterized in that: The interruption probability P of the point-to-point P2P link P2P The calculation formula is as follows: In the formula, Where a and c are the shape parameters of the generalized gamma distribution (GGD) turbulence model, b is the scale parameter of the GGD model, represents the gamma function, A0 = [erf(v)] 2 It represents the ratio of the laser beam power collected by the receiver at the detector center r = 0, represents the receiver aperture r a With the beam width ω z The ratio of is the error function, the ratio of positive integers l1 to k1 satisfies l1 / k1=c, represents the equivalent beam width, is the jitter variance of the receiver. is the receiving signal-to-noise ratio threshold γ th The corresponding upper limit of the integration of the mixed fading signal is, is the variance of the Gaussian integrated noise component, u (s) =Ae Bd +Ce Dd is a variable related to the distance d of the P2P link, representing the non-fading path loss, where the coefficients A, B, C, and D can be obtained by Monte Carlo simulation of the non-fading channel impulse response (FFIR) values ​​at different transmission distances through data fitting operations, and d = Z / (N+1), where Z is the total end-to-end transmission link distance of the serial relay UWOC system. It can be seen that h th It is an implicit function of the number of relay nodes N.

4. The optimization scheme for obtaining the optimal number of relay nodes in a serial relay UWOC system according to claim 1 is characterized in that: The end-to-end outage probability P e2e The nonlinear equation constructed by taking the first-order derivative with respect to N is as follows: In the above formula, P P2P′ Represents the P2P interruption probability formula P P2P Take the first-order derivative with respect to N. By solving the nonlinear equation, the optimal number of relay nodes in the serial relay UWOC system with the optimization goal of optimizing the end-to-end system outage probability can be obtained.

5. The optimization scheme for obtaining the optimal number of relay nodes in a serial relay UWOC system according to claim 4 is characterized in that: The P2P link interruption probability P P2P Again, find the first-order partial derivative P with respect to N P2P′ The calculation formula is as follows: Where h th ′ represents the integral upper limit h of the mixed fading signal th The first derivative term with respect to N.

6. The optimization scheme for obtaining the optimal number of relay nodes in a serial relay UWOC system according to claim 5 is characterized in that: The h th The first-order derivative h with respect to N th The calculation formula of ′ is as follows:

7. The optimization scheme for obtaining the optimal number of relay nodes in a serial relay UWOC system according to claim 1 is characterized in that: The probability density function (PDF) of the GGD ocean turbulence fading is expressed as follows: In the formula, b is the scale parameter, a and c are shape parameters, and h a represents a random variable that follows a GGD distribution.

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