MIMO-UWOC system node transmitting power optimal distribution method

Abstract

The invention discloses a method for optimally distributing power of each node at a transmitting end of a multiple-input multiple-output underwater wireless optical communication (MIMO-UWOC) system, and belongs to the field of underwater wireless optical communication. The method comprises the following steps: firstly, modeling a composite fading channel comprising non-fading channel impulse response (FFIR) implicit path loss and generalized Gamma distribution (GGD) turbulence; then performing equal gain combination (EGC) on received signals of each receiving port, and performing approximation on a probability density function (PDF) and a cumulative distribution function (CDF) of the cumulative sum of GGD fading coefficients of each link by adopting a foxH function to obtain an average bit error rate expression of the MIMO-UWOC system; and finally, modeling a mathematical optimization problem which takes minimization of the average bit error rate of the system as an optimization target and takes the transmitting power of each node as a decision variable to be solved, and solving the problem by using a Kuhn-Tucker condition to obtain a transmitting power allocation scheme which enables the average bit error rate of the system to be minimum. The node transmitting power optimal distribution method provided by the invention can provide theoretical guidance for upper-layer network planning of the MIMO-UWOC system.

Description

Technical Field

[0001] The present invention relates to an underwater wireless optical communication (UWOC) system, and to a power optimization allocation problem of each transmitting node when the UWOC system works in a multiple input multiple output (MIMO) transmission and receiving mode. The present invention belongs to the field of wireless optical communication, especially underwater wireless optical communication technology. Background Art

[0002] In recent years, with the increasing frequency of marine environmental monitoring and underwater resource exploration activities, the demand for corresponding underwater high-speed multimedia communications has become increasingly urgent in countries around the world. Compared with traditional underwater acoustic communication technology, UWOC is favored for its many advantages such as high transmission rate, low cost, and strong confidentiality. Experimental results show that the blue-green light waves in the visible spectrum wavelength band of 450nm to 550nm have the smallest absorption and scattering losses in seawater, so UWOC systems often use light waves in this frequency band for underwater communication. However, in practical applications, the fluctuation of the refractive index of seawater caused by changes in seawater temperature and salinity in the marine environment, also known as the "turbulence effect", will seriously reduce the quality of underwater communication, that is, increase the bit error rate of the UWOC system receiving signal, and thus cause the effective communication distance of the UWOC system even in clear ocean water to not exceed 150 meters. A common and effective means to solve this problem and effectively increase the transmission range of the UWOC system in various complex environments is to use the so-called MIMO transmission technology of multi-port transmission and multi-port reception.

[0003] Generally speaking, the MIMO-UWOC system consists of N t A transmitter sends wireless optical signals at the transmitting end, while N rThe receivers receive the signals simultaneously and perform appropriate merging processing. Since the transmission links between different transmitters and receivers will experience relatively independent path fading, the signals from different transmission links can be diversity combined, thereby effectively alleviating the impact of fading factors such as turbulence effects on the UWOC system. In addition, by properly optimizing the resource parameters of the MIMO-UWOC system, the performance of the system can be further improved on the basis of diversity transmission. At present, in the research on the optimal configuration of system parameters with the optimization of the core performance indicators of the MIMO-UWOC system as the optimization target, the work on the optimal allocation of the transmitting power of the transmitter with the minimum system average bit error rate as the optimization target is rarely involved in scientific research reports at home and abroad. Considering the unfavorable underwater working environment and limiting the equipment cost, the primary constraint condition that the total transmitting power of the transmitting end of the UWOC system is limited must be met. The traditional equal power allocation (Equal Power Allocation, EPA) scheme that does not consider any performance optimization and parameter constraints, that is, regardless of the situation, all the transmitting power is evenly distributed to N. t The original allocation method of the transmitters is obviously unable to achieve satisfactory communication results. Therefore, under the premise that the total transmission power of the system is fixed, how to reasonably allocate the total power to the N transmitters of the system? t It becomes a very meaningful task to optimize the optimal power allocation (OPA) of the system transmitter with the core performance indicators such as the average bit error rate of the system as the optimization goal. Summary of the invention

[0004] Purpose of the invention: In view of the lack of research on the optimal allocation method of transmitting power at the transmitting end in the current MIMO-UWOC system in the marine turbulent environment with the optimization of the core performance indicators of the system as the optimization target, the present invention proposes an optimal power allocation scheme for the transmitting end of the system for the MIMO-UWOC system, which takes minimizing the system average bit error rate as the optimization target under the premise of limited total transmission power, so as to achieve the lowest system average bit error rate transmission under the same system total power consumption.

[0005] Technical solution: A method for optimizing the transmission power allocation of nodes in a MIMO-UWOC system, comprising the following steps:

[0006] In view of the complex fading working environment that comprehensively considers the complex fading factors such as the implicit path loss and multipath effect of the fading free channel impulse response (FFIR), and the generalized gamma distribution (GGD) ocean turbulence, a MIMO-UWOC system with equal gain combining (EGC) technology at the receiving end is considered, and a constrained mathematical optimization problem is constructed with the minimization of the system average bit error rate as the optimization goal, the transmission power of each node as the decision variable, and the total transmission power as a fixed value. Next, using the fact that the Q function value in the objective function to be optimized, that is, the average bit error rate formula, is monotonically decreasing in the definition domain, the optimization problem is transformed into an equivalent constrained linear programming problem with the same total power constraint condition and the optimization goal of maximizing the linear combination of the transmission power of each node. Then, the Kuhn-Tucker necessary conditions in mathematical optimization theory are used to transform the linear programming problem into an equivalent form of a set of equations / inequalities. By solving the set of equations, the optimal power allocation method for the transmitting end of the MIMO-UWOC system in the working environment can be obtained.

[0007] As a preferred solution, the power-constrained mathematical optimization problem that minimizes the average bit error rate of the MIMO-UWOC system can be expressed as:

[0008]

[0009]

[0010] In the above formula, min means taking the minimum value of the function; P i is the transmit power of each transmitting node, N t is the number of transmitting nodes at the transmitting end, P total is the total transmit power constraint value, and st is the abbreviation of subject to, which means "subject to". It represents the average bit error rate of the MIMO-UWOC system in the complex fading environment, which has the following mathematical expression:

[0011]

[0012] In the above formula, Indicates that the transmitter i-th transmitter to all N r The N r The sum of the fading coefficients of the independent GGD turbulence fading paths; R f is a constant determined by FFIR but independent of i, is the noise dispersion of the received signal after merging. is the Gaussian Q function; yes The joint probability density function (PDF) of Independent of each other, there are Represents a multiple integral operation.

[0013] As a preferred solution, the average bit error rate formula The constrained linear programming problem with the same power constraint condition and the optimization goal of maximizing the linear combination of the transmission power of each node can be expressed as follows:

[0014]

[0015]

[0016] In the above formula, max means taking the maximum value of the function expression.

[0017] As a preferred solution, the linear programming problem is converted into an equivalent form of equation / inequality equation system using the Kuhn-Tucker necessary conditions in mathematical optimization theory:

[0018]

[0019] In the above formula, L is the Lagrange function constructed using the Kuhn-Tucker necessary conditions; λ0, λ i is the Kuhn-Tucker multiplicative multiplier; dL / dP i It means to find P for L i Derivative. By solving this system of equations, we can get the above linear programming problem. Let the linear function term When the maximum transmission power is reached, P i The allocation method is the OPA method at the transmitting end that minimizes the average bit error rate of the MIMO-UWOC system.

[0020] As a preferred solution, the specific OPA method at the transmitting end that minimizes the average bit error rate of the MIMO-UWOC system is as follows: t Among the transmitters, assume that the i-th max transmitters to all N r N receivers between r The sum of the fading coefficients of the GGD turbulent fading paths is the variable Maximum, then the total power of the system transmitter P total should be allocated to the i maxtransmitter, and the remaining transmitters do not allocate power, that is,

[0021] As a preferred solution, the GGD ocean turbulence fading coefficient experienced by the corresponding signal from the i-th transmitting end to the j-th receiving end in the MIMO-UWOC system is The PDF function expression of It can be expressed as:

[0022]

[0023] In the above formula, a and c are the shape parameters of the GGD distribution model, b is the scale parameter, and Γ(·) represents the gamma function; represents the random variable of the ocean turbulence fading coefficient from the i-th transmitter to the j-th receiver.

[0024] As a preferred solution, the transmitting end i-th transmitter to all N r The sum of the GGD turbulence fading coefficients of the receivers The PDF function of can be approximated by the foxH function, which can be expressed as:

[0025]

[0026] Parameters in the above formula

[0027] in, and They are The first and second origin moments, a j , c j and b j They represent the transmission from a fixed numbered transmitter i to the jth receiver (j=1, ..., N r The shape parameters and scale parameters of the GGD fading distribution experienced by ) are not general and can be assumed to be independent of the specific i and j, so the subscripts of these parameters can be omitted in the calculation; function d n (x, y) = Γ(x+n / y) / Γ(x); For advanced transcendent foxH functions.

[0028] As a preferred solution, the non-fading channel impulse response FFIR data can be obtained by simulating the motion of photons using a computer Monte Carlo method under given system transceiver parameters, such as ocean water quality, transmission distance, receiver aperture, emission light source wavelength, etc.

[0029] Beneficial effects:

[0030] Compared with the prior art, the technical solution of the present invention has the following beneficial technical effects: a method for optimizing the allocation of transmit power at the transmitting end of a MIMO-UWOC system provided by the present invention can determine the optimal transmit power allocation scheme for each transmitting node with the goal of minimizing the system average bit error rate in a communication environment where channel FFIR path loss and multipath effect and GGD ocean turbulence fading exist, thereby providing theoretical guidance for the upper-layer network planning and design of the MIMO-UWOC system. BRIEF DESCRIPTION OF THE DRAWINGS

[0031] Figure 1 It is a schematic diagram of the working structure of the MIMO-UWOC system to which the present invention is applicable.

[0032] Figure 2 It is a block diagram of the principle implementation of the MIMO-UWOC system node transmission power optimization allocation method proposed in the present invention.

[0033] Figure 3 This is a curve of the system average bit error rate changing with the transmission power of each node when the MIMO-UWOC system adopts two different power allocation schemes, equal power allocation (EPA) and the proposed optimal power allocation (OPA), when the total transmission distance is 25 meters in near-shore coastal water quality. DETAILED DESCRIPTION

[0034] 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.

[0035] The present invention is a method for deriving the optimal allocation of the transmission power of each node at the transmitting end of the MIMO-UWOC system through a mathematical optimization method, so as to obtain the lowest average bit error rate of the system under the premise that the total transmission power is a fixed constraint value. The specific implementation method and application examples are described as follows:

[0036] Step 1: Mathematically model the channel model of the complex underwater wireless optical communication MIMO-UWOC system which comprehensively considers the FFIR hidden path loss and multipath effect, as well as the GGD ocean turbulence factor;

[0037] Step 2: Perform EGC combination on the received signals of each receiving port that have experienced FFIR path loss and GGD ocean turbulence fading, and use the advanced transcendental foxH function to mathematically approximate the PDF and cumulative distribution function (CDF) of the sum of fading coefficients, and then obtain a general expression of the average bit error rate of the MIMO-UWOC system;

[0038] Step 3: Model a constrained mathematical optimization problem with the optimization goal of minimizing the system average bit error rate, the transmit power of each transmitting node as the decision variable to be determined, and the total transmit power of each transmitting node as a fixed value. Use the Q function characteristics and Kuhn-Tucker necessary conditions to transform and solve the mathematical optimization problem, and finally obtain the MIMO-UWOC system transmitter power allocation solution that can minimize the system average bit error rate.

[0039] Consider a transmitter consisting of N t The transmitter sends the optical signal, and the receiving end is composed of N r The structure diagram of the MIMO-UWOC system is as follows: Figure 1 As shown. Assuming that the system works in an underwater ocean environment with turbulent fading, each optical link from the transmitter to the receiver will be affected by turbulent fading caused by seawater temperature and salinity gradients in addition to path loss and multipath dispersion caused by seawater absorption and scattering. t ) to the jth receiver (1≤j≤N r ) path loss and multipath dispersion, we use the FFIR obtained by Monte Carlo simulation to describe it; and for the turbulence effect, the GGD statistical distribution model is used to characterize it. Among them, the PDF expression of the GGD turbulence fading from the i-th transmitter to the j-th receiver has the following form:

[0040]

[0041] In the formula, is the GGD turbulence fading coefficient from the i-th transmitter to the j-th receiver in the MIMO link, b is the scale parameter, a and c are the shape parameters, represents the gamma function.

[0042] Secondly, we investigate a UWOC system that uses a MIMO communication architecture. In this system, the optical signal is transmitted by N t The transmitter sends the signal and the receiver receives the signal from N r The transmitter uses On-Off Keying (OOK) modulation, and the receiver uses PIN (Positive-Intrinsic-Negative) photodiode to convert and receive the optical signal.

[0043] Assume that the signal sent by the transmitter in the system is a pulse-shaped signal. If the average power of the 0 / 1 OOK symbol sent by the i-th transmitter at the transmitting end is P i, then the rectangular pulse P emitted by it i (t) can be expressed as:

[0044] P i (t) = 2P i ·M(t) (2) In the formula, M(t) is a value in [0, T b ] unit amplitude gate function in the interval, T b is the OOK symbol width. Then, in the MIMO-UWOC system, the signal sequence s transmitted from the i-th transmitter is i (t), and the optical signal y received at the jth receiving end, which is affected by absorption and scattering effects, as well as ocean turbulence and other factors ij (t) can be expressed as:

[0045]

[0046]

[0047] Where b k is the OOK symbol sent in the kth time slot; represents the FFIR function from the i-th transmitter to the j-th receiver; P represents the pulse shaping function P i (t) The time domain waveform after passing through the FFIR channel and being affected by factors such as path loss and multipath effects; is the multiplicative channel turbulence fading factor The mixed channel impulse response of ; the symbol * represents the convolution operation.

[0048] From formula (4), we can get that N at the receiving end r Among the receivers, the current time domain signal received by the jth receiver can be expressed as:

[0049]

[0050] In the formula, R = ηq / hf is the responsivity of the photodetector, where η, q, h, and f represent the quantum efficiency of the photodetector, the electron charge, the Planck constant, and the underwater light frequency, respectively. j (t) has a mean of 0 and a sampling point variance of σ 2 =4K b T e B / R L The additive Gaussian white noise process, where K b 、T e , B, R L represent the Boltzmann constant, Kelvin temperature, system bandwidth and load resistance respectively.

[0051] Therefore, the current signal at the 0th moment received by the jth receiver at the receiving end after the integrator or matched filtering can be expressed as:

[0052]

[0053] Furthermore, the system receiving end N r The photocurrent signal after EGC combination is taken by each receiver as:

[0054]

[0055] In the above equations (6) and (7), b0 is the OOK transmitted symbol to be detected at time 0; is the matched filter output of the current waveform signal; represents the inter-symbol interference (ISI) caused by multipath dispersion in the FFIR channel; L is the channel memory length; v j is the integrated current noise, with a mean of zero and a variance of T b σ 2 Obviously, the noise term after EGC merging is The mean is 0 and the variance is

[0056] In order to obtain the system bit error rate, the optimal decision threshold of the system can be calculated as follows:

[0057]

[0058] In the formula, σ0 and σ1 are the noise deviations when the receiving end receives 0 and 1 symbols respectively. and are the average current at the receiving end when the transmitted code element b0 is "0" and "1" respectively.

[0059] Therefore, formula (8) can be written as:

[0060]

[0061] On this basis, when b0 is 0 or 1, the conditional bit error rate of the MIMO-UWOC system using the EGC combining technology can be expressed mathematically as follows:

[0062]

[0063] It is not difficult to calculate that the two are equal in value. Therefore, we can further deduce that the mathematical expression of the conditional bit error rate of the system when b0 is 0 or 1 is

[0064]

[0065] In the formula, is the Gaussian Q function.

[0066] Furthermore, the average bit error rate of the MIMO-UWOC system after considering turbulent fading is obtained as follows:

[0067]

[0068] In the formula, is a multiple integral; Assuming that each link from the i-th transmitter to the j-th receiver in the system does not affect each other, then Independent of each other,

[0069] To more intuitively represent the power distribution in the system, we denote u ij (s) Rewrite as Where P i is the transmission power of the ith transmitter, In the actual MIMO-UWOC system, if the layout of different transmitter groups and receiver groups is relatively symmetrical and centralized, the FFIR function from any i-th transmitter to the j-th receiver can be Considered to be approximately equal, It can be regarded as a constant that is independent of i and j and can be recorded as R f In this way, the average bit error rate formula (11) of the MIMO-UWOC system can be written as:

[0070]

[0071] use Indicates that the transmitter i-th transmitter to all N r The N r The sum of the fading coefficients of the independent GGD turbulent fading paths, the system average bit error rate expression (12) can be expressed as:

[0072]

[0073] yes The joint PDF of Independent of each other, according to the relevant knowledge of probability statistics theory, the cumulative sum of They are also independent of each other.

[0074] exist In the case of GGD distribution, As In the form of cumulative sum, its PDF and CDF functions can be approximated mathematically by the foxH function, which can be expressed by the following two formulas:

[0075]

[0076]

[0077] In the above formula, and are the sum of the random variables of GGD turbulence intensity PDF and CDF functions of in, and They are The first and second origin moments, a j , c j and b j They represent the transmission from a fixed numbered transmitter i to the jth receiver (j=1, ..., N r ) is the shape parameter and scale parameter of the GGD fading distribution experienced by , without loss of generality, they are independent of the specific i and j, so the subscripts of these parameters can be omitted in the calculation; function d n (x, y) = Γ(x+n / y) / Γ(x); For advanced transcendent foxH functions.

[0078] The optimization goal is to minimize the average bit error rate of the MIMO-UWOC system expressed in equation (13). The transmission power of each node P i is the decision variable to be determined, and the total transmission power of the system is a fixed value P total As a constraint variable, a mathematical optimization problem with constraints can be modeled as follows:

[0079]

[0080] Solving the constrained mathematical optimization problem (16) can obtain the optimal allocation of the transmitting end power to achieve the goal of minimizing the system bit error rate. Analyzing the average bit error rate expression (13) of the receiving end of the MIMO-UWOC system using the EGC combining technology, it can be seen that if N t The transmission power of each transmitting node is optimally allocated to reduce the system average bit error rate To achieve the minimum, given the Q function is monotonically decreasing in the range [0, +∞], and the noise standard deviation after merging is a constant, it is obvious that as long as the Q function term is The numerator in Therefore, the above transmitter power optimization allocation problem (16) of the MIMO-UWOC system based on the minimum system average bit error rate is transformed into another equivalent mathematical optimization problem as follows:

[0081]

[0082] Obviously, the above optimization problem (17) is actually a linear programming problem containing linear constraints. The Kuhn-Tucker necessary conditions in mathematical optimization theory can be used to transform the optimization problem into the equivalent form of the following set of equations and inequalities:

[0083]

[0084] By solving the equation system composed of this equation and inequality, we can obtain the optimal allocation method of the transmitting power at the transmitting end that minimizes the system bit error rate. The specific allocation method is described as follows:

[0085] In N t Among the transmitters, assume that the i-th max transmitters to all N r N receivers r The sum variable of the GGD turbulent fading paths is Maximum, in order to minimize the system bit error rate, the total power of the system transmitter P total All should be allocated to the i max transmitters, and the remaining transmitters do not allocate power, that is:

[0086]

[0087] Under this optimal power allocation method, the multi-integral formula (13) of the average bit error rate of the MIMO-UWOC system can be simplified to

[0088]

[0089] In the above formula, Represents a random variable PDF function. According to mathematical probability theory, the above formula can be transformed into:

[0090]

[0091] In the above formula, and Denote random variables The CDF and PDF functions of β are calculated by equations (15) and (14) respectively; max is the integral variable. In this way, (20) can be finally written as:

[0092]

[0093] The above formula is a calculation expression for the system average bit error rate of the MIMO-UWOC system using the EGC combining technology under the optimal power allocation strategy considered in the present invention.

[0094] Examples of the application of the optimal power allocation method at the transmitter end in improving the bit error rate performance of the MIMO-UWOC system:

[0095] Next, we conduct computer numerical simulation on the proposed MIMO-UWOC system transmitter power optimization allocation scheme under the GGD ocean turbulence fading and offshore coastal water quality FFIR path loss and multipath transmission channel model, and draw the curves of the average bit error rate of the MIMO-UWOC system using EGC merging technology with the node transmission power under the two schemes of equal power allocation (EPA) and optimal power allocation (OPA) at the transmitter (as shown in Figure 2). Figure 3 The two are compared to verify the effect of the proposed optimal power allocation method on improving the system bit error rate.

[0096] The core simulation parameters are set as follows: the ocean water quality is the coastal seawater quality, and its absorption and scattering coefficients are (a′, b′) = (0.179, 0.219) m -1 , the transceiver is located at a depth of 30m underwater; turbulence scintillation index The wavelength of the light source at the transmitting end is 532nm, and the beam waist radius is W r = 1mm blue-green laser; receiver half divergence angle θ div =40°, receiver aperture radius r a =0.2m; link distance between transmitter and receiver d0 = 25m; system load resistance R L =100Ω.

[0097] Figure 3 In the figure, the horizontal axis represents the average transmission power P allocated to each transmitting node. i Obviously, the total power transmitted by the system is P total =N t ·P i ; The vertical axis represents the average bit error rate of the EGC combined MIMO-UWOC system. From the simulation results in the figure, it can be seen that for both the equal power allocation (EPA) and the optimal power allocation (OPA) methods, although the system average bit error rate decreases with the increase of the transmission power, under the premise of a fixed total transmission power, the OPA scheme obviously has a lower bit error performance than the EPA scheme. Specifically, for the N t =N r =2 and N t =N r=3 MIMO-UWOC systems with two transmission and reception configurations, namely the systems marked with 2×2 and 3×3 links in the figure, under the condition of the same total transmission power, the bit error rate performance of the MIMO-UWOC systems of 2×2 and 3×3 links when using the OPA allocation method is significantly lower than that when using the EPA allocation method. Tables 1 and 2 give examples of the bit error rate numerical performance of the MIMO-UWOC systems of 2×2 and 3×3 links using two power allocation methods under the condition of the same total transmission power. Obviously, the simulation results verify the role and effect of the power optimization allocation strategy of the transmitting node at the transmitting end, which takes minimizing the system average bit error rate as the optimization goal and the fixed total transmission power as the constraint condition.

[0098] Table 1 Variation of system average bit error rate with transmit power when EPA and OPA allocation schemes are used in 2×2 MIMO-UWOC system

[0099]

[0100] Table 2 Variation of system average bit error rate with transmit power when EPA and OPA allocation schemes are used in 3×3 MIMO-UWOC system

[0101]

[0102] 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. A method for optimizing the transmission power allocation of nodes in a multiple input multiple output underwater wireless optical communication (MIMO-UWOC) system, characterized in that: The steps include: In view of the complex fading working environment that comprehensively considers the complex fading factors such as the implicit path loss and multipath effect of the fading free channel impulse response (FFIR), and the generalized gamma distribution (GGD) ocean turbulence, a MIMO-UWOC system with equal gain combining (EGC) technology at the receiving end is considered, and a constrained mathematical optimization problem is constructed with the minimization of the system average bit error rate as the optimization goal, the transmission power of each node as the decision variable, and the total transmission power as a fixed value. Next, using the fact that the Q function value in the objective function to be optimized, that is, the average bit error rate formula, is monotonically decreasing in the definition domain, the optimization problem is transformed into an equivalent constrained linear programming problem with the same total power constraint condition and the optimization goal of maximizing the linear combination of the transmission power of each node. Then, the Kuhn-Tucker necessary conditions in mathematical optimization theory are used to transform the linear programming problem into an equivalent form of a set of equations / inequalities. By solving the set of equations, the optimal power allocation (OPA) method of the transmitting end of the MIMO-UWOC system in the working environment can be obtained.

2. The MIMO-UWOC system node transmission power optimization allocation method according to claim 1 is characterized in that: The power-constrained mathematical optimization problem that minimizes the average bit error rate of the MIMO-UWOC system can be expressed as: In the above formula, min means taking the minimum value of the function; P i is the transmit power of each transmitting node, N t is the number of transmitting nodes at the transmitting end, P total is the total transmit power constraint value, and st is the abbreviation of subject to, which means "subject to"; It represents the average bit error rate of the MIMO-UWOC system in the complex fading environment, which has the following mathematical expression: In the above formula, Indicates that the transmitter i-th transmitter to all N r The N r The sum of the fading coefficients of the independent GGD turbulence fading paths; R f is a constant determined by FFIR but independent of i, is the noise deviation of the received signal after merging, Q(ο) is the Gaussian Q function; yes The joint probability density function (PDF) of Independent of each other, there are Represents a multiple integral operation.

3. The MIMO-UWOC system node transmission power optimization allocation method according to claim 1 is characterized in that: The average bit error rate formula The constrained linear programming problem with the same power constraint condition and the optimization goal of maximizing the linear combination of the transmission power of each node can be expressed as follows: In the above formula, max means taking the maximum value of the function expression.

4. The MIMO-UWOC system node transmission power optimization allocation method according to claim 1 is characterized in that: The constrained linear programming problem is transformed into an equivalent form of equation / inequality equation system using the Kuhn-Tucker necessary conditions in mathematical optimization theory: In the above formula, L is the Lagrange function constructed using the Kuhn-Tucker necessary conditions; λ0, λ i is the Kuhn-Tucker multiplicative factor; dL / dP i It means to find P for L i Derivative. By solving this system of equations, we can get the above linear programming problem. Let the linear function term When the maximum transmission power is reached, P i The allocation method is the OPA method at the transmitting end that minimizes the average bit error rate of the MIMO-UWOC system.

5. The MIMO-UWOC system node transmission power optimization allocation method according to claim 4 is characterized in that: The specific OPA method at the transmitting end to minimize the average bit error rate of the MIMO-UWOC system is as follows: t Among the transmitters, assume that the i-th max transmitters to all N r N receivers between r The sum of the fading coefficients of the GGD turbulent fading paths is the variable Maximum, then the total power of the system transmitter P total should be allocated to the i max transmitter, and the remaining transmitters do not allocate power, that is, 6. The MIMO-UWOC system node transmission power optimization allocation method according to claim 1, characterized in that: GGD ocean turbulence fading coefficient experienced by the corresponding signal from the i-th transmitter to the j-th receiver in the MIMO-UWOC system The PDF function expression of It can be expressed as: In the above formula, a and c are the shape parameters of the GGD distribution model, b is the scale parameter, and Γ(·) represents the gamma function; represents the random variable of the ocean turbulence fading coefficient from the i-th transmitter to the j-th receiver.

7. The MIMO-UWOC system node transmission power optimization allocation method according to claim 2 is characterized in that: In the expression of the average bit error rate of the MIMO-UWOC system, the transmission end i-th transmitter to all N r The sum of the GGD turbulence fading coefficients of the receivers The PDF function of can be approximated by the foxH function, which can be expressed as: In the above formula, the parameters in, and They are The first and second origin moments, a j , c j and b j They represent the transmission from a fixed numbered transmitter i to the jth receiver (j=1, ..., N r ) is the shape parameter and scale parameter of the GGD fading distribution experienced by , without loss of generality, they can be assumed to be independent of the specific i and j, so the subscripts of these parameters can be omitted in the calculation; function d n (x, y) = Γ(x+n / y) / Γ(x); For advanced transcendent foxH functions.

8. The MIMO-UWOC system node transmission power optimization allocation method according to claim 1, characterized in that: The non-fading channel impulse response FFIR data can be obtained by simulating the motion of photons using a computer Monte Carlo method under given system transceiver parameters, such as ocean water quality, transmission distance, receiver aperture, wavelength of the transmitting light source, etc.

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