CN109067489A - The calculation method of the UWOC-MD communication system bit error rate and handling capacity based on LN distribution - Google Patents
The calculation method of the UWOC-MD communication system bit error rate and handling capacity based on LN distribution Download PDFInfo
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Abstract
The invention discloses the calculation methods of the UWOC-MD communication system bit error rate and handling capacity that are distributed based on LN, mathematical channel mode is established, the probability density function and cumulative distribution function about instantaneous electric signal-to-noise ratio under LN turbulent flow and path loss collective effect are derived；Theoretical average throughput is calculated, maximum signal to noise ratio scheduling strategy average throughput and selection scheduling strategy average throughput are obtained；The flat bit error rate of computational theory obtains maximum signal to noise ratio scheduling strategy and selection scheduling strategy average error rate；Monte Carlo simulation obtains the system average error rate and handling capacity of proportional fair scheduling and improved adaptive threshold proportional fair scheduling.Change system parameter and seawater characteristics parameter, obtains the parameter to the influence using scheduling strategy UWOC-MD system performance not of the same race.This method has effectively comprehensively considered a variety of factors for influencing system performance, more tallies with the actual situation.
Description
Technical field
The invention belongs to underwater wireless technical field of photo communication, specially examine using BPSK subcarrier intensity modulated and directly
The method of survey derives UWOC-MD communication system in considering oceanic turbulence and the coefficient composite channel model of path loss
The calculation method of system average error rate and handling capacity under different scheduling strategies.
Background technique
Underwater wireless optic communication (Underwater Wireless Optical Communication, UWOC) relative to
Traditional underwater acoustic communication (Underwater Acoustic Communication, UAC) and radio communication (Radio
Frequency, RF) have many advantages, such as high bandwidth, low time delay and better safety in short distance.These are unique
Feature makes UWOC can satisfy high-speed, the imaging of large-capacity data transmission demand, real-time video transmission and high-throughput biography
The submerged applications scene such as sensor network.But UWOC system is influenced to generate path loss by absorbing and scatter, while ocean is rapid
Stream is so that the refractive index of water changes, and the light signal strength that causes receiver end to receive, amplitude and phase change at random, shape
At light intensity scintillation effect, this effect causes the reduction of UWOC communication system channel capacity and the raising of average error rate, sternly
Interference communication again operates normally.To alleviate influence of the light intensity scintillation effect to laser signal transmission, the researcher of related fields
A variety of countermeasures are proposed, wherein the diversity technique introduced from RF application is due to its biggish application prospect by domestic and international
The concern of researcher.
Multi-user diversity in diversity technique is a kind of communication mode of point-to-multipoint, utilizes the difference of multiuser channel
Property, only allowing a user to access in each time slot and realizes information transmission, the essence of multi-user diversity is optimized allocation of resources,
Target does not promote the performance of certain sole user instead of, and all users of base station and receiving end are regarded as an entirety or are
System, selects different users to carry out data transmission for the purpose of realizing system resource peak use rate.
In view of the demand of Time Delay of Systems, handling capacity and fairness, related scholar has been proposed being suitable for MD system
A variety of scheduling strategies, consider selection have maximum throughput maximum signal to noise ratio scheduling strategy, mitigate system load selection
Scheduling strategy of the proportional fair scheduling of scheduling strategy and consideration time delay influence as UWOC-MD system.
Current problem is: since underwater wireless optic communication is the emerging field for solving underwater wireless communication issue, very
Rare research is related to the performance evaluation under turbulent flow and path loss collective effect to UWOC system.Meanwhile underwater wireless optic communication
There is not been reported for the middle performance evaluation for alleviating turbulence effect using multi-user diversity technology.Therefore, the UWOC- based on LN distribution
The characteristic research of the bit error rate and handling capacity under different scheduling strategies of MD communication system is current highly important research direction.
Summary of the invention
The purpose of the present invention is to propose to a kind of calculating of UWOC-MD communication system bit error rate and handling capacity based on LN distribution
Method.Alleviate turbulence effect in wireless light communication using multi-user diversity technology under water, and to using maximum signal to noise ratio tune
The throughput of system and error ratio characteristic of degree strategy and selection scheduling strategy carry out theoretical closure expression formula respectively and derive.Meanwhile
The system of Monte Carlo simulation proportional fair scheduling and improved adaptive threshold proportional fair scheduling is averagely missed
Code rate and handling capacity.
The purpose of the present invention is what is realized by following technical proposals.
The calculating side of UWOC-MD communication system error rate of system and handling capacity under different scheduling strategies based on LN distribution
Method includes the following steps:
1) it is based on LN fading channel, establishes the mathematical channel mode for being suitable for UWOC system, and derive LN turbulent flow and road
Probability density function and iterated integral of the UWOC system composite channel model under collective effect about instantaneous electric signal-to-noise ratio is lost in diameter
Cloth function；
2) it is considered as maximum signal to noise ratio scheduling strategy and selection scheduling strategy respectively, derives LN turbulent flow and path loss connection
Cooperate probability density function and cumulative distribution letter of the UWOC-MD system composite channel model about instantaneous electric signal-to-noise ratio under
Number；
3) according to shannon formula, the theory for calculating LN turbulent flow and the UWOC-MD system under path loss collective effect is average
Handling capacity, and abbreviation obtains maximum signal to noise ratio scheduling strategy average throughput and selection scheduling strategy average throughput respectively；
4) the condition bit error rate according to the UWOC system under BPSK modulation system under Gaussian channel calculates LN turbulent flow and road
The flat bit error rate of theory of the UWOC-MD system under collective effect is lost in diameter, and utilizes Generalized Gaussian Laguerre polynomials
Letter respectively obtains maximum signal to noise ratio scheduling strategy and selection scheduling strategy average error rate；
5) ratio contributed receiving aperture, temperature difference of seawater dissipative shock wave, ocean temperature and salinity to power spectrum and transmission
Distance parameter substitutes into the average throughput and average error rate theoretical expression derived, while obtaining according to Monte Carlo simulation
To proportional fair scheduling and the system average error rate of adaptive threshold proportional fair scheduling redefined and gulp down
The amount of spitting obtains the parameter to the influence using scheduling strategy UWOC-MD system performance not of the same race.
The invention has the following advantages that
Present invention firstly provides a kind of calculating sides of UWOC-MD communication system bit error rate and handling capacity based on LN distribution
Method.Consider the composite channel model under path loss and oceanic turbulence collective effect, and then Monte Carlo simulation analysis compared
Receiving aperture, seawater characteristics and transmission range parameter to use including maximum signal to noise ratio, selection scheduling, Proportional Fair with
And the influence of the UWOC-MD system performance of improved adaptive threshold Proportional Fair strategy.Therefore, this method is effectively comprehensive
It closes and considers a variety of factors for influencing system performance, more tally with the actual situation.
Detailed description of the invention
Fig. 1 is the multi-user diversity mode of underwater wireless optical communication system；
Fig. 2 a), Fig. 2 b) and Fig. 2 c) be fair using maximum signal to noise ratio dispatching algorithm, selection scheduling algorithm and ratio respectively
When the UWOC-MD system of dispatching algorithm changes receiving aperture, the handling capacity comparison diagram based on LN turbulent flow；
Fig. 3 a), Fig. 3 b) and Fig. 3 c) be fair using maximum signal to noise ratio dispatching algorithm, selection scheduling algorithm and ratio respectively
When the UWOC-MD system of dispatching algorithm changes temperature difference of seawater dissipative shock wave, the handling capacity comparison diagram based on LN turbulent flow；
Fig. 4 a), Fig. 4 b) and Fig. 4 c) be fair using maximum signal to noise ratio dispatching algorithm, selection scheduling algorithm and ratio respectively
When the UWOC-MD system of dispatching algorithm changes the ratio that ocean temperature and salinity contribute power spectrum, based on handling up for LN turbulent flow
Measure comparison diagram；
Fig. 5 a) and Fig. 5 b) it is to consider path loss and LN turbulent flow collective effect in littoral seawater and limpid seawater respectively
When, using the handling capacity comparison diagram of the UWOC-MD system of maximum signal to noise ratio dispatching algorithm；
Fig. 6 a) and Fig. 6 b) it is to consider path loss and LN turbulent flow collective effect in littoral seawater and limpid seawater respectively
When, using the handling capacity comparison diagram of the UWOC-MD system of proportional fair scheduling；
Fig. 7 a) and Fig. 7 b) be respectively system user number be 5 and 25 when, using maximum signal to noise ratio dispatching algorithm, selection scheduling
Bit error rate comparison diagram of the UWOC-MD system of algorithm and proportional fair scheduling based on LN turbulent flow.
Specific embodiment
To make the object, technical solutions and advantages of the present invention clearer, with reference to the accompanying drawings and detailed description into
One step is described in detail.The present embodiment only indicates not represent any limitation of the invention to the principle of the present invention explanation.
Step 1, it is based on LN fading channel, considers the influence of path loss, establishes the mathematical channel biography for being suitable for UWOC system
Defeated model.
The multi-user diversity mode of underwater wireless optical communication system is as shown in Figure 1, for simplicity, remember base station and number
M is designated as under path between the user of m ∈ { 1,2,3 ..., M }, it is assumed that institute is access point to any receiving node to system
Equidistant non-homogeneous system, different links are mutually indepedent.Then the discrete-time channel model of link m can indicate are as follows:
ym=RpLpImxm+nm (1)
Wherein, RpFor the response constant of receiving end photoelectric detector, LpIt is damaged to be transmitted by the optical power for absorbing and scattering generation
Consume invariant, i.e. path loss；xm∈ { -1,1 } is the modulated symbol modulated through binary phase shift keying, average emitted function
Rate is Pav；nmFor with the independent additive white Gaussian noise of signal, mean value 0；Variance isN0For bilateral power spectrum
Density；ImFor the optical power random fading factor as caused by oceanic turbulence.
And then derive the UWOC system composite channel model under LN turbulent flow and path loss collective effect about instantaneous electricity
The probability density function and cumulative distribution function of signal-to-noise ratio:
1a) provide the probability density function and path loss function of LN channel model；
Wherein, the probability density function of LN channel modelAre as follows:
WhereinWithThe respectively mean value and variance of the variable z=lnIm of Normal Distribution considers that plane wave passes
Defeated, then the relational expression of any variance and scintillation index isWherein scintillation indexThere is following calculating
Formula:
Wherein ξ is normalized cumulant parameter, and κ is spatial domain wave number size, and the Fresnel ratio Λ at the L of range transmission end is equal to
It is wave wave number, turbulence power spectrum Φ that 0, beam curvature Θ, which are equal to 1, k=2 π/λ,n(κ) calculates as follows:
Wherein ε is unit seawater kinetic energy dissipation rate, χTFor temperature difference of seawater dissipative shock wave, w is ocean temperature and salinity to power
Compose the ratio of contribution, AT=1.863 × 10-2, AS=1.9 × 10-4, ATS=9.41 × 10-2, δ=8.284 (κ η)4/3+12.987
(κη)2, η=10-3。
Path loss function are as follows:
Lp(λ, L)=exp (- c (λ) L) (5)
Wherein, c (λ) indicates that extinction coefficient, L indicate communication distance；
The exemplary reference value of 1 absorption and scattering coefficienth of table
1b) obtain combined channel fading coefficients h of the UWOC system in the case where considering LN turbulent flow and path loss collective effectm=
Im×LpProbability density function are as follows:
1c) based on intensity modulated/method that directly detects, for arbitrarily numbering the link for being m, instantaneous electricity signal-to-noise ratio
It is defined as follows:
Wherein, N0For the bilateral power spectral density of white Gaussian noise.
To guarantee that turbulent flow does not have an impact mean power, neither amplifies nor reduce, we normalize fading factorAbbreviation obtainsThe mean value that instantaneous signal-to-noise ratio can be obtained at this time isWhereinIt is modulation
Index.Combined channel of the UWOC system in the case where considering LN turbulent flow and path loss collective effect can then be obtained about instantaneous electric signal-to-noise ratio
γmProbability density function are as follows:
Instantaneous electricity signal-to-noise ratio γmCumulative distribution function are as follows:
Step 2, it is considered as maximum signal to noise ratio scheduling strategy and selection scheduling strategy respectively, derives LN turbulent flow and path damage
Consume probability density function and cumulative distribution of the UWOC-MD system composite channel model about instantaneous electric signal-to-noise ratio under synergy
Function.
According to the combined channel under LN turbulent flow and path loss collective effect the considerations of being provided in step 1 about instantaneous telecommunications
It makes an uproar and compares γmProbability density function and cumulative distribution function, be considered as maximum signal to noise ratio scheduling strategy and selection scheduling strategy
When, UWOC-MD system composite channel model derives such as about the probability density function and cumulative distribution function of instantaneous electric signal-to-noise ratio
Under:
2a) in UWOC-MD system, it is assumed that all users' to base station is equidistant, and LN having the same is distributed, noteThen when all users undergo the distribution of identical signal-to-noise ratio, selected in any time slot
It selects and accesses channel with the user of maximum signal to noise ratio or maximum throughput, mathematic(al) representation is expressed as follows:
Accordingly, it is considered to the cumulative distribution function about instantaneous electric signal-to-noise ratio when using maximum signal to noise ratio scheduling strategy are as follows:
Derivation obtains probability density function are as follows:
2b) in UWOC-MD system, it is assumed that all users' to base station is equidistant, and LN having the same is distributed, it is assumed that
Biggish observation time is selected, for arbitrarily numbering the link for being m, average signal-to-noise ratioProportional Fair at this time
Being equivalent to selection has maximum signal to noise ratioUser as the optimal user in kth slot transmissionTherefore, we to
Lower mathematic(al) representation obtains the signal-to-noise ratio of optimal user
Wherein, γm,kFor the signal-to-noise ratio of kth time slot user m；S (k) is the number of users in k time slot feedback CQI to base station.For
Reduced mechanical model remembers γ*For the signal-to-noise ratio of user after scheduling, Cumulative Distribution FunctionFor γ*The probability of < x.For
Calculating CDF considers that two kinds of situations calculate respectively.As x < γthWhen, the signal-to-noise ratio of all users is all unsatisfactory for threshold condition,
Scheduler randomly chooses a user and carries out data transmission at this time；In addition as x >=γthWhen, it is selected most in feedback user subset
Thus good user obtains following cumulative distribution function:
Derivation obtains probability density function are as follows:
Wherein, l is the number of users more than given threshold, γthFor the threshold value for effectively reducing channel-quality feedback setting.
Step 3, according to shannon formula, the theory of LN turbulent flow and the UWOC-MD system under path loss collective effect is calculated
Average throughput, and abbreviation obtains the closure expression formula and selection scheduling plan of maximum signal to noise ratio scheduling strategy average throughput respectively
Slightly the part of average throughput is closed expression formula, and is verified by Monte Carlo simulation.
3a) according to shannon formula, obtain averagely gulping down when maximum signal to noise ratio scheduling strategy and selection scheduling strategy is respectively adopted
The integral expression for the amount of spitting:
3b) to formula (14) and (15) abbreviation, it is as follows to obtain closed approximation expression formula:
Wherein, μzWithThe respectively mean value and variance of the variable z=lnI of Normal Distribution, yiRepresent Gauss-
The polynomial H of Hermiten(x) i-th, corresponding weight HiIt is calculated using following formula:
Erfc () is complementary error function, erfcx (x)=exp
(x2) erfc (x) is built-in function in MATLAB.Obviously the Section 2 of desired precise calculation (17) sum term then needs
It sums to infinite multiple algebraic expressions, and with the increase of sum term, the evaluated error of integral formula constantly reduces, verified to work as t
=8 we can obtain sufficiently accurate estimated value.It can calculation formula (17) first using adaptive Gauss-Kronrod integral
Integrating range is the definite integral of semo-infinite in.
Step 4, the condition BER formulas according to the UWOC system under BPSK modulation system under Gaussian channel calculates LN
The flat bit error rate of theory of UWOC-MD system under turbulent flow and path loss collective effect, and it is multinomial using Generalized Gaussian Laguerre
Formula carries out abbreviation, respectively obtains the closure expression formula of maximum signal to noise ratio scheduling strategy and selection scheduling strategy average error rate, and
It is verified by Monte Carlo simulation.
4a) the condition BER formulas according to UWOC system under BPSK modulation system in Gaussian channel, is adopted respectively
With the integral expression of average error rate when maximum signal to noise ratio scheduling strategy and selection scheduling strategy are as follows:
4b) utilize general Gauss-Laguerre quadrature functionTo formula (18) and
(19) abbreviation, the approximate expression for obtaining system average error rate are as follows:
Wherein, μzWithThe respectively mean value and variance of the variable z=lnI of Normal Distribution, xiIndicate broad sense
Gauss-Laguerre multinomial LN(x) i-th, corresponding weight wiIt can use following formula to calculate:
Step 5, ratio receiving aperture, temperature difference of seawater dissipative shock wave, ocean temperature and salinity contributed power spectrum and
Transmission range parameter substitutes into the theoretical expression of the average throughput and average error rate that derive, while Monte Carlo simulation point
It analyses the system average error rate of proportional fair scheduling and improved adaptive threshold proportional fair scheduling and handles up
Amount obtains the parameter to the influence using scheduling strategy UWOC-MD system performance not of the same race.
Correctness and advantage of the invention can be compared by following notional result and be further illustrated:
In the method for the present invention, analytical Calculation is carried out by MATLAB and carries out simulating, verifying using Monte Carlo simulation.It is first
First, the formula that accurate description is derived；Then, change the value of wherein various variables；Finally under a certain specific parameter value,
The error rate of system performance of Monte Carlo simulation comparative analysis four kinds of scheduling strategies mentioned in the present invention.
Theoretical and simulation result
Fig. 2 a), Fig. 2 b) and Fig. 2 c) give under 0mm, 10mm and 24mm receiving aperture, maximum signal to noise ratio tune is respectively adopted
The UWOC-MD system of algorithm, selection scheduling algorithm and proportional fair scheduling is spent based on the handling capacity comparison diagram of LN turbulent flow.It can
To find out, the result of analytical Calculation and MC emulation is coincide preferably, to show the accurate of throughput of system model in the present invention
Property.In addition, receiving aperture is bigger under identical number of users, the handling capacity of same dispatching algorithm is substantially reduced.Identical receiver hole
Under diameter, as the handling capacity of the same dispatching algorithm of increase of number of users is continuously increased.
Fig. 3 a), Fig. 3 b) and Fig. 3 c) give temperature difference of seawater dissipative shock wave be 10-5、10-6With 10-7Under, maximum is respectively adopted
The UWOC-MD system of signal-to-noise ratio dispatching algorithm, selection scheduling algorithm and proportional fair scheduling is based on the handling capacity of LN turbulent flow
Comparison diagram.As can be seen that three kinds of dispatching algorithms, under identical number of users, throughput of system all can be with temperature difference of seawater dissipative shock wave
Increase and increase.And temperature difference of seawater dissipative shock wave is bigger, maximum signal to noise ratio dispatching algorithm, selection are adjusted in the increase of system user number
The influence for spending algorithm diversity gain is also increasing.
Fig. 4 a), Fig. 4 b) and Fig. 4 c) to give the ratio that ocean temperature and salinity contribute power spectrum be -4.5, -2.5
Under -0.5, the UWOC-MD system of maximum signal to noise ratio dispatching algorithm, selection scheduling algorithm and proportional fair scheduling is respectively adopted
Handling capacity comparison diagram of the system based on LN turbulent flow.As can be seen that the ratio that ocean temperature and salinity contribute power spectrum is bigger, three kinds
The handling capacity of dispatching algorithm is also bigger.Meanwhile the ratio that ocean temperature and salinity contribute power spectrum is increased with identical step-length
When, the increase of throughput of system is also more and more obvious.
Fig. 5 a) and Fig. 5 b) be set forth in littoral seawater and limpid seawater, consider that path loss and LN turbulent flow are common
When effect, using the handling capacity comparison diagram of the UWOC-MD system of maximum signal to noise ratio dispatching algorithm；As can be seen that whether clear
Clear seawater is still in littoral seawater, and the handling capacity of system is constantly promoted with the increase of signal-to-noise ratio, and in same subscriber number
In the case where, communication distance is shorter, and the handling capacity of user is bigger；Under identical transmission range, number of users is bigger, and system gulps down
The amount of spitting is bigger.Moreover, by data comparison we have found that transmission range is shorter in littoral seawater, the promotion of signal-to-noise ratio is to being
The influence for handling capacity of uniting is more significant, but the signal-to-noise ratio increase of system is either short to the influence degree of handling capacity in limpid seawater
Distance or long range are substantially the same.
Fig. 6 a) and Fig. 6 b) it is to consider path loss and LN turbulent flow collective effect in littoral seawater and limpid seawater respectively
When, using the handling capacity comparison diagram of the UWOC-MD system of proportional fair scheduling；It is available basic with Fig. 5 a) and Fig. 5 b)
Consistent conclusion.Unlike, in the handling capacity of the UWOC-MD system using proportional fair scheduling and the relationship of signal-to-noise ratio
It is found in curve, influence very little of the number of users to handling capacity, and with the shortening of communication distance, the handling capacity of system is by user
Several influences can be ignored substantially.
Fig. 7 a) and Fig. 7 b) be respectively system user number be 5 and 25 when, using maximum signal to noise ratio dispatching algorithm, selection scheduling
Bit error rate comparison diagram of the UWOC-MD system of algorithm and proportional fair scheduling based on LN turbulent flow.It can be seen that analytical Calculation
It coincide with the result of MC emulation preferably, to show the accuracy of error rate of system model in the present invention.In addition, working as number of users
When smaller, maximum signal to noise ratio scheduling strategy has best error performance, when number of users is larger, maximum signal to noise ratio and adaptive
The bit error rate of the selection scheduling strategy of threshold value is consistent, and error performance is best.
The present invention is not limited to the above embodiments, on the basis of technical solution disclosed by the invention, the skill of this field
For art personnel according to disclosed technology contents, one can be made to some of which technical characteristic by not needing creative labor
A little replacements and deformation, these replacements and deformation are within the scope of the invention.
Claims (7)
1. the calculation method of the UWOC-MD communication system bit error rate and handling capacity based on LN distribution, which is characterized in that including following
Step:
1) it is based on LN fading channel, establishes the mathematical channel mode for being suitable for UWOC system, and derives LN turbulent flow and path damage
Consume probability density function and cumulative distribution letter of the UWOC system composite channel model about instantaneous electric signal-to-noise ratio under collective effect
Number；
2) it is considered as maximum signal to noise ratio scheduling strategy and selection scheduling strategy respectively, derives LN turbulent flow and path loss joint is made
Probability density function and cumulative distribution function of the UWOC-MD system composite channel model about instantaneous electric signal-to-noise ratio under；
3) according to shannon formula, the theoretical average throughput of LN turbulent flow and the UWOC-MD system under path loss collective effect is calculated
Amount, and abbreviation obtains maximum signal to noise ratio scheduling strategy average throughput and selection scheduling strategy average throughput respectively；
4) the condition bit error rate according to the UWOC system under BPSK modulation system under Gaussian channel calculates LN turbulent flow and path damage
The flat bit error rate of theory of the UWOC-MD system under collective effect is consumed, and utilizes Generalized Gaussian Laguerre polynomials abbreviation, respectively
To maximum signal to noise ratio scheduling strategy and selection scheduling strategy average error rate；
5) ratio and transmission range contributed receiving aperture, temperature difference of seawater dissipative shock wave, ocean temperature and salinity to power spectrum
Parameter substitutes into the average throughput and average error rate theoretical expression derived, while being compared according to Monte Carlo simulation
The system average error rate and handling capacity of example fair scheduling algorithm and the adaptive threshold proportional fair scheduling redefined,
The parameter is obtained to the influence using scheduling strategy UWOC-MD system performance not of the same race.
2. the calculation method of the UWOC-MD communication system bit error rate and handling capacity according to claim 1 based on LN distribution,
It is characterized in that, being established as follows suitable for the mathematical channel mode of UWOC system in the step 1):
M is designated as under note base station and the path that number is between the user of m ∈ { 1,2,3 ..., M }, it is assumed that institute is access to system
The point non-homogeneous system equidistant to any receiving node, different links are mutually indepedent, then the discrete-time channel model table of link m
It is shown as:
ym=RpLpImxm+nm (1)
Wherein, RpFor the response constant of receiving end photoelectric detector；LpIt is normal by the optical power transmission loss for absorbing and scattering generation
The number factor；xm∈ { -1,1 } is the modulated symbol modulated through binary phase shift keying；nmFor with the independent additive Gaussian white noise of signal
Sound；ImFor the optical power random fading factor as caused by oceanic turbulence.
3. the calculation method of the UWOC-MD communication system bit error rate and handling capacity according to claim 1 based on LN distribution,
It is characterized in that, in the step 1), UWOC system composite channel model under LN turbulent flow and path loss collective effect it is general
Rate density function and cumulative distribution function, are realized by following step:
1a) provide the probability density function and path loss function of LN channel model；
Wherein, the probability density function of LN channel modelAre as follows:
WhereinWithThe respectively variable z=lnI of Normal DistributionmMean value and variance, ImTo be caused by oceanic turbulence
The optical power random fading factor；
Path loss function are as follows:
Lp(λ, L)=exp (- c (λ) L) (5)
Wherein, c (λ) indicates that extinction coefficient, L indicate communication distance；
1b) obtain combined channel fading coefficients h of the UWOC system in the case where considering LN turbulent flow and path loss collective effectm=Im×
LpProbability density function are as follows:
1c) based on intensity modulated/method that directly detects, for arbitrarily numbering the link for being m, instantaneous electricity signal-to-noise ratio definition
It is as follows:
Wherein, RpFor the response constant of receiving end photoelectric detector；LpIt is normal by the optical power transmission loss for absorbing and scattering generation
The number factor；PavFor average emitted power；N0For the bilateral power spectral density of additive white Gaussian noise；For average electric signal-to-noise ratio；
Combined channel of the UWOC system in the case where considering LN turbulent flow and path loss collective effect is about instantaneous electric signal-to-noise ratio γmIt is general
Rate density function are as follows:
Instantaneous electricity signal-to-noise ratio γmCumulative distribution function are as follows:
4. the calculation method of the UWOC-MD communication system bit error rate and handling capacity according to claim 1 based on LN distribution,
It is characterized in that, the UWOC-MD system composite channel model under LN turbulent flow and path loss collective effect closes in the step 2)
It is obtained by the following method in the probability density function and cumulative distribution function of instantaneous electric signal-to-noise ratio:
2a) assume that all users are equal to base station distance, and LN having the same is distributed, note Then it is considered as the cumulative distribution function about instantaneous electric signal-to-noise ratio when maximum signal to noise ratio scheduling strategy
Are as follows:
Wherein, M is the total number of users of system；
Derivation obtains probability density function are as follows:
All user's being equidistant to base station 2b) are assumed, and LN having the same is distributed, when being considered as selection scheduling strategy
The cumulative distribution function about instantaneous electric signal-to-noise ratio are as follows:
Derivation obtains probability density function are as follows:
Wherein, l is the number of users more than given threshold, γthFor the threshold value for effectively reducing channel-quality feedback setting.
5. the calculation method of the UWOC-MD communication system bit error rate and handling capacity according to claim 1 based on LN distribution,
It is characterized in that, in the step 3), closed using average throughput when maximum signal to noise ratio scheduling strategy and selection scheduling strategy
Expression formula is closed, is realized by the following method:
3a) according to shannon formula, average throughput when obtaining that maximum signal to noise ratio scheduling strategy and selection scheduling strategy is respectively adopted
Integral expression:
3b) abbreviation (14) and (15), obtain closed approximation expression formula:
Wherein, μzWithThe respectively mean value and variance of the variable z=lnI of Normal Distribution, yiRepresent Gauss-Hermite
Polynomial Hn(x) i-th, HiFor corresponding weight, erfc
() is complementary error function, erfcx (x)=exp (x2) erfc (x) be MATLAB in built-in function；Using adaptive
Gauss-Kronrod integral can in calculation formula (17) first item integrating range be semo-infinite definite integral.
6. the calculation method of the UWOC-MD communication system bit error rate and handling capacity according to claim 1 based on LN distribution,
It is characterized in that, calculating in the UWOC-MD system under LN turbulent flow and path loss collective effect, adopting respectively in the step 4)
With the closure expression formula of average error rate when maximum signal to noise ratio scheduling strategy and selection scheduling strategy, it is realized by the following method:
4a) the condition BER formulas according to UWOC system under BPSK modulation system in Gaussian channel, obtains being respectively adopted most
The integral expression of average error rate when big signal-to-noise ratio scheduling strategy and selection scheduling strategy are as follows:
4b) utilize general Gauss-Laguerre quadrature functionFormula (18) and (19) are changed
Letter, the approximate expression for obtaining system average error rate are as follows:
Wherein, μzWithThe respectively mean value and variance of the variable z=lnI of Normal Distribution, n are general Gauss-
The sum term of Laguerre numerical integration, xiFor general Gauss-Laguerre multinomialI-th, wiFor therewith
Corresponding weight.
7. the calculation method of the UWOC-MD communication system bit error rate and handling capacity according to claim 1 based on LN distribution,
It is characterized in that, considering limpid seawater and littoral seawater, extinction coefficient is respectively 0.151m in the step 5)-1With
0.399m-1。
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