CN104993867B - A kind of optical filtering parameter optimization method based on visible light communication - Google Patents
A kind of optical filtering parameter optimization method based on visible light communication Download PDFInfo
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Abstract
The present invention proposes a kind of optimization method of optical filtering parameter in visible light communication system, and this method measures each monochromatic spectroscopic data first with spectrometer, is fitted with Gauss or Lorentzian, obtains the fitting function of spectrum；According to real system, the spectral function of bias light and the total noise power of receiving terminal are determined；Using each coloured light receiving terminal signal interference ratio as object function, while determine the constraints of optical filtering parameter；Local derviation first is sought with each variable of signal interference ratio function pair, and makes local derviation result be equal to 0, a variable is then fixed, optimizes another variable under constraints, more wheel iteration is carried out successively, obtains the optimal solution of optical filtering parameter；The object function of each coloured light is solved respectively, you can obtain the optimal value of each color filters parameter.The method of the present invention goes for a variety of optical filterings, and convergence rate is very fast during computing, can preferably reduce the interference between white light.
Description
Technical field
The invention belongs to visible light communication field, in particular to optical filtering parameter in a kind of polychrome optical communication system
Optimization method.
Background technology
With the continuous social and economic development, requirement of the people to the quality of life also more and more higher, at the same time, communication
Field starts to pursue a kind of " green " and " high-speed " communication technology.Visible light communication technology as above-mentioned alternative just
It is increasingly becoming the focus of research field.It utilizes laser device or LED component, and letter is realized by the modulation to intensity of illumination
High-speed transfer is ceased, while routine work illumination is ensured, also meets the demand that people are transmitted to high speed information.
The white light in visible light communication has two kinds of generation types at present, one kind be cooperatively formed using blue light with fluorescent material it is white
Light, another kind are the modes of a variety of monochromatic light mixing.Using polychromatic light mixing method with compared using white light merely, Neng Gou great
Amplitude lifts message capacity and traffic rate, the even more focus as future studies.
For existing polychrome optical communication system, transmitting terminal sends multiple signals using the LED of a variety of coloured light, then mixes
Gone out into white light emission, receiving terminal will separate the white light in white light with corresponding a variety of optical filterings.
Testing research shows that the LED light spectral shape of transmitting terminal is analogous to Gaussian function, can not just be kept away between white light
Exempt from there is cross jamming.In receiving terminal, to make each road signal degree of accuracy for receiving as high as possible, must just make white light
Between cross jamming it is as small as possible, the optimization to optical filtering parameter is to avoid a kind of approach of cross jamming.
Under normal circumstances, the shape of optical filtering pass-band performance has that rectangle, Gaussian function, Lorentzian etc. are several, different
The parameter of optical filtering is also different, can provide the method for finding optimal optical filtering parameter in theory, and calculate optical filtering
The optimal value of mirror parameter.So as to which the design to actual optical filtering plays directive function with production.It is however, optimal on how to obtain
Optical filtering parameter, academia also without correlation research.
The content of the invention
Goal of the invention：The present invention is directed to problems of the prior art, it is proposed that the optimization of a set of receiving terminal optical filtering
Method, optimal optical filtering parameter can be found using the method, so that the cross jamming between the white light received is use up
May be small, the optical filtering gone out for actual production suitable for polychrome optic communication provides guidance.
Technical scheme：A kind of receiving terminal optical filtering parameter optimization method based on visible light communication, comprises the following steps：1)
Each monochromatic spectroscopic data is measured using spectrometer, is fitted with Gaussian function or Lorentzian, obtains the plan of spectrum
Close function；2) spectral function of bias light and the total noise power of receiving terminal are determined；3) with each coloured light receiving terminal letter
Dry ratio is object function, while determines the constraints of optical filtering parameter；4) local derviation is sought with each variable of signal interference ratio function pair, and made
Local derviation result is equal to 0；5) each parameter of initial photochemical filter, then fixes a parameter, optimizes another under constraints
Parameter, more wheel iteration are carried out successively；6) after iteration meets certain number, iteration is stopped, convergence result is optical filtering parameter
Optimal solution；7) repeat the above steps (3)~(6) to the optical filtering of each color respectively, output a variety of colors optical filtering ginseng
Several optimum results.
Further, the overall noise includes Johnson noise and thermal noise.
Further, the pass-band performance of optical filtering is rectangle, and right boundary wavelength is α, β, and the optimization method is specific
For：
(1) first, the LED of four kinds of coloured light spectroscopic data is measured with spectrometer, respectively with Gaussian function fitting, expression formula
It is as follows：
Sr(λ)=a1 exp[-(λ-λ1)2/σ1 2]
Sa(λ)=a2 exp[-(λ-λ2)2/σ2 2]
Sg(λ)=a3 exp[-(λ-λ3)2/σ3 2]
Sb(λ)=a4 exp[-(λ-λ4)2/σ4 2]
Wherein, a1-a4、λ1-λ4、σ1-σ4It is the fitting parameter of Gaussian function, is real constant；Sr(λ) is the spectrum letter of feux rouges
Number, Sa(λ) be gold-tinted spectral function, Sg(λ) be green glow spectral function, Sb(λ) is the spectral function of blue light；
(2) according to the system of reality, it is assumed that the spectrum amplitude of bias light is equally distributed, determines the spectrum letter of bias light
Number Sback(λ)=P and receiving terminal total noise power Nt, wherein P and NtIt is real constant；
(3) signal interference ratio of receiving terminal white light is calculated, the signal interference ratio of feux rouges is as follows：
Constraints is：380≤α ＜ β≤780；
(4) local derviation is asked to α, β respectively with signal interference ratio function, makes local derviation result be equal to 0, abbreviation result is
Wherein,
(5) α, β are initialized, preset parameter β Optimal Parameters α first, is obtained according to local derviation formula (1) in the case where meeting constraints
α solution；Then α value is updated, fixed α optimizes β, the solution of the β in the case where meeting constraints is obtained according to local derviation formula (2), according to
Secondary progress takes turns iteration more；
(6) after iteration meets certain number, iteration is stopped, convergence result is the optimal solution of red filter parameter；
(7) repeat the above steps (3)~the constraints of (6), wherein α, β to the optical filtering of yellow, green, blueness respectively
For 380≤α ＜ β≤780；Export the optimum results of multiple color optical filtering parameter.
It can realize that pass-band performance is the parameter optimization of the optical filtering of rectangle by above-mentioned steps.
Further, the pass-band performance of optical filtering is F (λ)=exp [- (λ-λ for meeting Gaussian function0)2/σ0 2], it is necessary to
Wavelength X centered on Optimal Parameters0And variances sigma0, methods described is specially：
(1) first, the LED of four kinds of coloured light spectroscopic data is measured with spectrometer, respectively with Gaussian function fitting, expression formula
It is as follows：
Sr(λ)=a1exp[-(λ-λ1)2/σ1 2]
Sa(λ)=a2exp[-(λ-λ2)2/σ2 2]
Sg(λ)=a3exp[-(λ-λ3)2/σ3 2]
Sb(λ)=a4exp[-(λ-λ4)2/σ4 2]
Wherein, a1-a4、λ1-λ4、σ1-σ4It is the fitting parameter of Gaussian function, is real constant；Sr(λ) is the spectrum letter of feux rouges
Number, Sa(λ) be gold-tinted spectral function, Sg(λ) be green glow spectral function, Sb(λ) is the spectral function of blue light；
(2) according to the system of reality, it is assumed that the spectrum amplitude of bias light is equally distributed, determines the spectrum letter of bias light
Number Sback(λ)=P and receiving terminal total noise power Nt, wherein P and NtIt is real constant；
(3) signal interference ratio of receiving terminal white light is calculated, the signal interference ratio of feux rouges is as follows：
Constraints is：380≤λ0≤ 780,0<σ0
(4) with signal interference ratio function respectively to λ0、σ0Local derviation is sought, makes local derviation result be equal to 0, abbreviation result is：
Wherein：
(5) λ is initialized0、σ0, σ fixed first0Parameter optimization parameter lambda0, obtained according to local derviation formula (1) and meeting to constrain bar
λ under part0Solution；Then λ is updated0Value, fixed λ0Optimize σ0, the σ in the case where meeting constraints is obtained according to local derviation formula (2)0
Solution, carry out more wheel iteration successively；
(6) after iteration meets certain number, iteration is stopped, convergence result is the optimal solution of red filter parameter；
(7) repeat the above steps (3)~(6), wherein λ to the optical filtering of yellow, green, blueness respectively0、σ0Constraint bar
Part is 380≤λ0≤ 780,0<σ0；Export the optimum results of multiple color optical filtering parameter.
It can realize that pass-band performance is the parameter optimization for the optical filtering for meeting Gaussian function by above-mentioned steps.
Further, the pass-band performance of optical filtering is F (λ)=1/ (1+ (λ-λ for meeting Lorentzian0)2/σ0 2), need
Want wavelength X centered on Optimal Parameters0And variances sigma0, methods described is specially：
(1) first, the LED of four kinds of coloured light spectroscopic data is measured with spectrometer, is fitted respectively with Lorentzian, is expressed
Formula is as follows：
Sr(λ)=a1/(1+(λ-λ1)2/σ1 2)
Sa(λ)=a2/(1+(λ-λ2)2/σ2 2)
Sg(λ)=a3/(1+(λ-λ3)2/σ3 2)
Sb(λ)=a4/(1+(λ-λ4)2/σ4 2)
Wherein, a1-a4、λ1-λ4、σ1-σ4It is the fitting parameter of Lorentzian, is real constant；Sr(λ) is the spectrum of feux rouges
Function, Sa(λ) be gold-tinted spectral function, Sg(λ) be green glow spectral function, Sb(λ) is the spectral function of blue light；
(2) according to the system of reality, it is assumed that the spectrum amplitude of bias light is equally distributed, determines the spectrum letter of bias light
Number Sback(λ)=P and receiving terminal total noise power Nt, wherein P and NtIt is real constant；
(3) signal interference ratio of receiving terminal white light is calculated, the signal interference ratio of feux rouges is as follows：
Constraints is：380≤λ0≤ 780,0<σ0
(4) with signal interference ratio function respectively to λ0、σ0Local derviation is sought, makes local derviation result be equal to 0, abbreviation result is：
Wherein：
(5) λ is initialized0、σ0, σ fixed first0Parameter optimization parameter lambda0, obtained according to local derviation formula (1) and meeting to constrain bar
λ under part0Solution；Then λ is updated0Value, fixed λ0Optimize σ0, the σ in the case where meeting constraints is obtained according to local derviation formula (2)0
Solution, carry out more wheel iteration successively；
(6) after iteration meets certain number, iteration is stopped, convergence result is the optimal solution of red filter parameter；
(7) repeat the above steps (3)~(6), wherein λ to yellow, green, blue filter respectively0、σ0Constraints
For 380≤λ0≤ 780,0<σ0；Export the optimum results of multiple color optical filtering parameter.
It can realize that pass-band performance is the parameter optimization for the optical filtering for meeting Lorentzian by above-mentioned steps.
The core concept of the present invention is that the cross jamming minimum between white light is equivalent to each coloured light in receiving terminal
Signal interference ratio it is maximum, in the signal interference ratio of receiving terminal be object function with each coloured light, so as to be provided for quantitatively analysis and solution
May；In solution procedure, due to more difficult directly to polytomy variable optimization, the solution procedure proposed here is：It is first solid
A fixed variable, optimizes another variable under constraints, carries out more wheel iteration successively.This solution mode can be quick
Restrain exactly, convergence result is hardly influenceed by iterative initial value.
Beneficial effect：Optical filtering parameter optimization method proposed by the present invention based on visible light communication, can design compared with
Excellent optical filtering parameter, reduces the cross jamming between receiving terminal white light as much as possible, can go out for actual production applicable
Guidance is provided in the optical filtering of polychrome optic communication.
Brief description of the drawings
Fig. 1 is the FB(flow block) of the present invention；
Fig. 2 is the spectrum with the color LED of Gaussian function fitting LZ4-00MA00 models four；
Fig. 3 is the spectrum with the color LED of Lorentzian fitting LZ4-00MA00 models four；
Fig. 4 is the optical filtering parameter optimization result that passband is rectangle；
Fig. 5 is the optical filtering parameter optimization result that passband is Gaussian function；
Fig. 6 is the optical filtering parameter optimization result that passband is Lorentzian；
Embodiment：
The present invention program is described in further detail with reference to Figure of description and embodiment.As shown in figure 1, exhibition
The algorithm flow block diagram of the present invention is shown.In embodiment, by taking four coloured light communication systems as an example, transmitting terminal is using LED
Engin companies production LZ4-00MA00 models four color LED, under identical driving current 700mA, measure respectively R, A, G,
The spectrum of tetra- kinds of coloured light of B.It is the result being fitted to spectrum using Gaussian function as shown in Figure 2, from left to right four crests
It is followed successively by blueness, green, yellow, red spectrum；It is the result being fitted using Lorentzian to spectrum as shown in Figure 3,
From left to right four crests are followed successively by blueness, green, yellow, red spectrum.Comparison is it can be found that what Gaussian function fitting came out
As a result more accurate, so under conditions of same, prioritizing selection Gaussian function is fitted.But if carried out with Lorentzian
Fitting can notable simplified operation when, can suitably sacrifice fitting precision, be exchanged with and be fitted with Lorentzian.
Actual test is found, for four color LED of LZ4-00MA00 models, under identical driving current 700mA, R, A,
G, the radiation flux of tetra- kinds of coloured light of B is respectively 428mW, 122mW, 218mW, 674mW.So in embodiment, it is assumed that receiving terminal
Total noise power is 10mW.For the spectrum amplitude of bias light, it can be assumed that to be equally distributed, the present embodiment is not having respectively
Have powerful connections light and the situation of bias light that has spectrum amplitude to be 0.5mW/nm is calculated.3 specific implementations are given below
Example respectively using pass-band performance be rectangle, gaussian sum Lorentz optical filtering calculated as optimization object.
Embodiment 1:Pass-band performance is the optical filtering of rectangle
The expression formula of (1) four color light source Gaussian function fitting is as follows：
Sr(λ)=a1exp[-(λ-λ1)2/σ1 2]
Sa(λ)=a2exp[-(λ-λ2)2/σ2 2]
Sg(λ)=a3exp[-(λ-λ3)2/σ3 2]
Sb(λ)=a4exp[-(λ-λ4)2/σ4 2]
The result obtained with matlab fitting tools is：
Sr(λ)=23.86exp [- (λ -630.5)2/11.62]
Sa(λ)=7.177exp [- (λ -599)2/11.62]
Sg(λ)=4.734exp [- (λ -523.7)2/27.382]
Sb(λ)=28exp [- (λ -453.3)2/14.32]
(2) spectral function (it is assumed here that the spectrum amplitude of bias light is uniform) of bias light:
S is taken respectivelyback(λ)=P=0 and Sback(λ)=P=0.5mW/nm
The total noise power (including Johnson noise, thermal noise etc.) of receiving terminal：Nt=10mW
(3) optical filtering pass-band performance is rectangle, it is assumed that right boundary wavelength is α, β；
(4) signal interference ratio of assorted optical receiving end is determined, is represented following (by taking feux rouges as an example, similarly hereinafter)
Defining integration function
Q functions are brought into SINR functions, obtained result is as follows：
(5) SINR derivations：In order to derive conveniently, order
Then
Local derviation is sought α, β respectively, it is as a result as follows：
According toAbbreviation is arranged to local derviation result:
(6) α, β are initialized.Preset parameter β Optimal Parameters α first, obtained according to local derviation formula (1) in the case where meeting constraints
α solution；Then α value is updated, fixed α optimizes β, the solution of the β in the case where meeting constraints is obtained according to local derviation formula (2).According to
Secondary progress takes turns iteration more.
(7) repeat the above steps (4)~(6) to the optical filtering of each color respectively, output multiple color optical filtering ginseng
Several convergence optimum results.
As shown in figure 4, " --- " represents the condition for the light that has powerful connections, " ... " represents the condition without bias light, and "-" represents actual
Spectrum, from left to right four crests be followed successively by blueness, green, yellow, red spectrum.Iteration result is：
As the spectral function S of bias lightbackDuring (λ)=0, iteration convergence in
| Left margin (nm) | Right margin (nm) | |
| It is red | 616 | 700 |
| It is yellow | 579 | 611 |
| It is green | 484 | 575 |
| It is blue | 380 | 476 |
As the spectral function S of bias lightbackDuring (λ)=0.5mW/nm, iteration convergence in
| Left margin (nm) | Right margin (nm) | |
| It is red | 621 | 641 |
| It is yellow | 588 | 607 |
| It is green | 506 | 541 |
| It is blue | 441 | 465 |
Embodiment 2:Pass-band performance is the optical filtering of Gauss
The expression formula of (1) four color light source Gaussian function fitting is as follows：
Sr(λ)=a1 exp[-(λ-λ1)2/σ1 2]
Sa(λ)=a2 exp[-(λ-λ2)2/σ2 2]
Sg(λ)=a3 exp[-(λ-λ3)2/σ3 2]
Sb(λ)=a4 exp[-(λ-λ4)2/σ4 2]
The result obtained with matlab fitting tools is：
Sr(λ)=23.86exp [- (λ -630.5)2/11.62]
Sa(λ)=7.177exp [- (λ -599)2/11.62]
Sg(λ)=4.734exp [- (λ -523.7)2/27.382]
Sb(λ)=28exp [- (λ -453.3)2/14.32]
(2) spectral function (it is assumed here that the spectrum amplitude of bias light is uniform) of bias light:
S is taken respectivelyback(λ)=P=0 and Sback(λ)=P=0.5mW/nm
The total noise power (including Johnson noise, thermal noise etc.) of receiving terminal：Nt=10mW
(3) pass-band performance of optical filtering is Gauss, and expression formula is F (λ)=exp [- (λ-λ0)2/σ0 2]
(4) signal interference ratio of assorted optical receiving end is determined, is represented following (by taking feux rouges as an example, similarly hereinafter)
Due to
Have again simultaneously
The result of integral function is brought into SINR functions, obtained as follows：
(5) SINR derivations：In order to derive conveniently, order
B=B2+B3+B4+P·σ0
Then
Respectively to λ0、σ0Local derviation is sought, it is as a result as follows：
Abbreviation is arranged to local derviation result to obtain：
(6) λ is initialized0、σ0.σ fixed first0Parameter optimization parameter lambda0, obtained according to local derviation formula (1) and meeting to constrain bar
λ under part0Solution；Then λ is updated0Value, fixed λ0Optimize σ0, the σ in the case where meeting constraints is obtained according to local derviation formula (2)0
Solution.More wheel iteration are carried out successively.
(7) repeat the above steps (4)~(6) to the optical filtering of each color respectively, output multiple color optical filtering ginseng
Several convergence optimum results.
As shown in figure 5, " --- " represents the condition for the light that has powerful connections, " ... " represents the condition without bias light, and "-" represents actual
Spectrum, from left to right four crests be followed successively by blueness, green, yellow, red spectrum.Iteration result is：
As the spectral function S of bias lightbackDuring (λ)=0, iteration convergence in
| Centre wavelength (nm) | Variance (nm) | |
| It is red | 633 | 14 |
| It is yellow | 596 | 11.5 |
| It is green | 528 | 27.5 |
| It is blue | 450 | 24.5 |
As the spectral function S of bias lightbackDuring (λ)=0.5mW/nm, iteration convergence in
Embodiment 3：Pass-band performance is the optical filtering of Lorentz
The expression formula that (1) four color light source is fitted with Lorentzian is as follows：
(calculated for the ease of deriving, light source light spectrum is fitted with Lorentzian here, can in the range of error permission
To receive.)
Sr(λ)=a1/(1+(λ-λ1)2/σ1 2)
Sa(λ)=a2/(1+(λ-λ2)2/σ2 2)
Sg(λ)=a3/(1+(λ-λ3)2/σ3 2)
Sb(λ)=a4/(1+(λ-λ4)2/σ4 2)
The result obtained with matlab fitting tools is：
Sr(the 1+ (λ -630.9) of (λ)=26.56/2/7.5072)
Sa(the 1+ (λ -599.2) of (λ)=8.033/2/7.1352)
Sg(the 1+ (λ -523.1) of (λ)=5.214/2/17.822)
Sb(the 1+ (λ -453.1) of (λ)=31.36/2/9.1322)
(2) spectral function (it is assumed here that the spectrum amplitude of bias light is uniform) of bias light:
S is taken respectivelyback(λ)=P=0 and Sback(λ)=P=0.5mW/nm
The total noise power (including Johnson noise, thermal noise etc.) of receiving terminal：Nt=10mW
(3) pass-band performance of optical filtering is Lorentz, and pass-band performance function is F (λ)=1/ (1+ (λ-λ0)2/σ0 2)
(4) assorted optical receiving end signal interference ratio is determined, is represented following (by taking feux rouges as an example, similarly hereinafter)
Have again simultaneously
∫FSback(1+ (λ-the λ of d λ=∫ 1/0)2/σ0 2) Pd λ=P σ0π
The result of integral function is brought into SINR functions, obtained as follows：
(5) SINR derivations：In order to derive conveniently, order
B=B2+B3+B4+P·σ0
Then
Respectively to λ0、σ0Local derviation is sought, it is as a result as follows：(
Abbreviation is arranged to local derviation result to obtain：
6) λ is initialized0、σ0.σ fixed first0Parameter optimization parameter lambda0, obtained according to local derviation formula (1) and meeting constraints
Under λ0Solution；Then λ is updated0Value, fixed λ0Optimize σ0, the σ in the case where meeting constraints is obtained according to local derviation formula (2)0's
Solution.More wheel iteration are carried out successively.
(7) repeat the above steps (4)~(6) to the optical filtering of each color respectively, output multiple color optical filtering ginseng
Several convergence optimum results.
As shown in fig. 6, " --- " represents the condition for the light that has powerful connections, " ... " represents the condition without bias light, and "-" represents actual
Spectrum, from left to right four crests be followed successively by blueness, green, yellow, red spectrum.Iteration result is：
As the spectral function S of bias lightbackDuring (λ)=0, iteration convergence in
| Centre wavelength (nm) | Variance (nm) | |
| It is red | 632.36 | 4.12 |
| It is yellow | 598.09 | 2.09 |
| It is green | 525 | 4.02 |
| It is blue | 451 | 6.05 |
As the spectral function S of bias lightbackDuring (λ)=0.5mW/nm, iteration convergence in
| Centre wavelength (nm) | Variance (nm) | |
| It is red | 631.77 | 3.15 |
| It is yellow | 598.29 | 1.90 |
| It is green | 525 | 3.44 |
| It is blue | 452.5 | 4.22 |
Claims (5)
1. a kind of optical filtering parameter optimization method based on visible light communication, it is characterised in that this method comprises the following steps：
(1) each monochromatic spectroscopic data is measured using spectrometer, is fitted with Gaussian function or Lorentzian, obtains light
The fitting function of spectrum；
(2) spectral function of bias light and the total noise power of receiving terminal are determined；
(3) using each coloured light receiving terminal signal interference ratio as object function, while determine the constraints of optical filtering parameter, its
Middle optical filtering parameter includes right boundary α, β or central wavelength lambda0, variances sigma0；
(4) signal interference ratio function pair each optical filtering parameter alpha, β or λ are used0、σ0Local derviation is sought, and makes local derviation result be equal to 0, obtains local derviation public affairs
Formula (1) and local derviation formula (2)；
(5) be for passband rectangle optical filtering：Initialize α, β, preset parameter β Optimal Parameters α first, according to local derviation formula
(1) solution of the α in the case where meeting constraints is obtained；Then α value is updated, fixed α optimizations β, is obtained according to local derviation formula (2)
Meet the solution of the β under constraints, carry out more wheel iteration successively；
It is the optical filtering of Gaussian function or Lorentzian for passband：Initialize λ0、σ0, σ fixed first0Parameter optimization parameter
λ0, the λ in the case where meeting constraints is obtained according to local derviation formula (1)0Solution；Then λ is updated0Value, fixed λ0Optimize σ0, according to
Local derviation formula (2) obtains the σ in the case where meeting constraints0Solution, carry out more wheel iteration successively；
(6) after iteration meets certain number, iteration is stopped, convergence result is optical filtering parameter alpha, β or λ0、σ0Optimal solution；
(7) repeat the above steps (3)~(6) to the optical filtering of each color respectively, output a variety of colors optical filtering parameter alpha, β
Or λ0、σ0Optimum results.
A kind of 2. optical filtering parameter optimization method based on visible light communication as claimed in claim 1, it is characterised in that：It is described
Overall noise includes Johnson noise and thermal noise.
A kind of 3. optical filtering parameter optimization method based on visible light communication as claimed in claim 1 or 2, it is characterised in that：
The pass-band performance of optical filtering is rectangle, and right boundary wavelength is α, β, and the optimization method is specially：
(1) first, the LED of four kinds of coloured light spectroscopic data is measured with spectrometer, respectively with Gaussian function fitting, expression formula is such as
Under：
Sr(λ)=a1exp[-(λ-λ1)2/σ1 2]
Sa(λ)=a2exp[-(λ-λ2)2/σ2 2]
Sg(λ)=a3exp[-(λ-λ3)2/σ3 2]
Sb(λ)=a4exp[-(λ-λ4)2/σ4 2]
Wherein, a1-a4、λ1-λ4、σ1-σ4It is the fitting parameter of Gaussian function, is real constant；Sr(λ) be feux rouges spectral function, Sa
(λ) be gold-tinted spectral function, Sg(λ) be green glow spectral function, Sb(λ) is the spectral function of blue light；
(2) according to the system of reality, it is assumed that the spectrum amplitude of bias light is equally distributed, determines the spectral function of bias light
Sback(λ)=P and receiving terminal total noise power Nt, wherein P and NtIt is real constant；
(3) signal interference ratio of receiving terminal white light is calculated, the signal interference ratio of feux rouges is as follows：
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<mrow>
<mo>&lsqb;</mo>
<msub>
<mi>a</mi>
<mn>2</mn>
</msub>
<msub>
<mi>&sigma;</mi>
<mn>2</mn>
</msub>
<mi>e</mi>
<mi>r</mi>
<mi>f</mi>
<mi>c</mi>
<mrow>
<mo>(</mo>
<mfrac>
<mrow>
<mi>&alpha;</mi>
<mo>-</mo>
<msub>
<mi>&lambda;</mi>
<mn>2</mn>
</msub>
</mrow>
<msub>
<mi>&sigma;</mi>
<mn>2</mn>
</msub>
</mfrac>
<mo>)</mo>
</mrow>
<mo>-</mo>
<msub>
<mi>a</mi>
<mn>2</mn>
</msub>
<msub>
<mi>&sigma;</mi>
<mn>2</mn>
</msub>
<mi>e</mi>
<mi>r</mi>
<mi>f</mi>
<mi>c</mi>
<mrow>
<mo>(</mo>
<mfrac>
<mrow>
<mi>&beta;</mi>
<mo>-</mo>
<msub>
<mi>&lambda;</mi>
<mn>2</mn>
</msub>
</mrow>
<msub>
<mi>&sigma;</mi>
<mn>2</mn>
</msub>
</mfrac>
<mo>)</mo>
</mrow>
<mo>+</mo>
<msub>
<mi>a</mi>
<mn>3</mn>
</msub>
<msub>
<mi>&sigma;</mi>
<mn>3</mn>
</msub>
<mi>e</mi>
<mi>r</mi>
<mi>f</mi>
<mi>c</mi>
<mrow>
<mo>(</mo>
<mfrac>
<mrow>
<mi>&alpha;</mi>
<mo>-</mo>
<msub>
<mi>&lambda;</mi>
<mn>3</mn>
</msub>
</mrow>
<msub>
<mi>&sigma;</mi>
<mn>3</mn>
</msub>
</mfrac>
<mo>)</mo>
</mrow>
<mo>-</mo>
<msub>
<mi>a</mi>
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</msub>
<msub>
<mi>&sigma;</mi>
<mn>3</mn>
</msub>
<mi>e</mi>
<mi>r</mi>
<mi>f</mi>
<mi>c</mi>
<mrow>
<mo>(</mo>
<mfrac>
<mrow>
<mi>&beta;</mi>
<mo>-</mo>
<msub>
<mi>&lambda;</mi>
<mn>3</mn>
</msub>
</mrow>
<msub>
<mi>&sigma;</mi>
<mn>3</mn>
</msub>
</mfrac>
<mo>)</mo>
</mrow>
<mo>+</mo>
<msub>
<mi>a</mi>
<mn>4</mn>
</msub>
<msub>
<mi>&sigma;</mi>
<mn>4</mn>
</msub>
<mi>e</mi>
<mi>r</mi>
<mi>f</mi>
<mi>c</mi>
<mrow>
<mo>(</mo>
<mfrac>
<mrow>
<mi>&alpha;</mi>
<mo>-</mo>
<msub>
<mi>&lambda;</mi>
<mn>4</mn>
</msub>
</mrow>
<msub>
<mi>&sigma;</mi>
<mn>4</mn>
</msub>
</mfrac>
<mo>)</mo>
</mrow>
<mo>-</mo>
<msub>
<mi>a</mi>
<mn>4</mn>
</msub>
<msub>
<mi>&sigma;</mi>
<mn>4</mn>
</msub>
<mi>e</mi>
<mi>r</mi>
<mi>f</mi>
<mi>c</mi>
<mrow>
<mo>(</mo>
<mfrac>
<mrow>
<mi>&beta;</mi>
<mo>-</mo>
<msub>
<mi>&lambda;</mi>
<mn>4</mn>
</msub>
</mrow>
<msub>
<mi>&sigma;</mi>
<mn>4</mn>
</msub>
</mfrac>
<mo>)</mo>
</mrow>
<mo>+</mo>
<mi>P</mi>
<mrow>
<mo>(</mo>
<mi>&beta;</mi>
<mo>-</mo>
<mi>&alpha;</mi>
<mo>)</mo>
</mrow>
<mo>&rsqb;</mo>
</mrow>
<mn>2</mn>
</msup>
<mo>+</mo>
<mfrac>
<mrow>
<mn>4</mn>
<msubsup>
<mi>N</mi>
<mi>t</mi>
<mn>2</mn>
</msubsup>
</mrow>
<mi>&pi;</mi>
</mfrac>
</mrow>
</mfrac>
</mtd>
</mtr>
</mtable>
</mfenced>
Constraints is：380≤α ＜ β≤780；
(4) local derviation is asked to α, β respectively with signal interference ratio function, makes local derviation result be equal to 0, abbreviation result is
<mrow>
<mtable>
<mtr>
<mtd>
<mrow>
<mfrac>
<mrow>
<mo>&part;</mo>
<mi>S</mi>
<mi>I</mi>
<mi>N</mi>
<mi>R</mi>
</mrow>
<mrow>
<mo>&part;</mo>
<mi>&alpha;</mi>
</mrow>
</mfrac>
<mo>=</mo>
<mn>0</mn>
<mo>&DoubleLeftRightArrow;</mo>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<msub>
<mi>a</mi>
<mn>1</mn>
</msub>
<mi>exp</mi>
<mo>&lsqb;</mo>
<mo>-</mo>
<msup>
<mrow>
<mo>(</mo>
<mi>&alpha;</mi>
<mo>-</mo>
<msub>
<mi>&lambda;</mi>
<mn>1</mn>
</msub>
<mo>)</mo>
</mrow>
<mn>2</mn>
</msup>
<mo>/</mo>
<msup>
<msub>
<mi>&sigma;</mi>
<mn>1</mn>
</msub>
<mn>2</mn>
</msup>
<mo>&rsqb;</mo>
<mo>&CenterDot;</mo>
<mrow>
<mo>(</mo>
<msup>
<mi>B</mi>
<mn>2</mn>
</msup>
<mo>+</mo>
<mn>4</mn>
<msubsup>
<mi>N</mi>
<mi>t</mi>
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</msubsup>
<mo>/</mo>
<mi>&pi;</mi>
<mo>)</mo>
</mrow>
<mo>-</mo>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<mi>A</mi>
<mi>B</mi>
<mrow>
<mo>(</mo>
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<mi>a</mi>
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</msub>
<mi>exp</mi>
<mo>&lsqb;</mo>
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<msup>
<mrow>
<mo>(</mo>
<mrow>
<mi>&alpha;</mi>
<mo>-</mo>
<msub>
<mi>&lambda;</mi>
<mn>2</mn>
</msub>
</mrow>
<mo>)</mo>
</mrow>
<mn>2</mn>
</msup>
<mo>/</mo>
<msup>
<msub>
<mi>&sigma;</mi>
<mn>2</mn>
</msub>
<mn>2</mn>
</msup>
<mo>&rsqb;</mo>
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<mi>a</mi>
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</msub>
<mi>exp</mi>
<mo>&lsqb;</mo>
<mo>-</mo>
<msup>
<mrow>
<mo>(</mo>
<mrow>
<mi>&alpha;</mi>
<mo>-</mo>
<msub>
<mi>&lambda;</mi>
<mn>3</mn>
</msub>
</mrow>
<mo>)</mo>
</mrow>
<mn>2</mn>
</msup>
<mo>/</mo>
<msup>
<msub>
<mi>&sigma;</mi>
<mn>3</mn>
</msub>
<mn>2</mn>
</msup>
<mo>&rsqb;</mo>
<mo>+</mo>
<msub>
<mi>a</mi>
<mn>4</mn>
</msub>
<mi>exp</mi>
<mo>&lsqb;</mo>
<mo>-</mo>
<msup>
<mrow>
<mo>(</mo>
<mrow>
<mi>&alpha;</mi>
<mo>-</mo>
<msub>
<mi>&lambda;</mi>
<mn>4</mn>
</msub>
</mrow>
<mo>)</mo>
</mrow>
<mn>2</mn>
</msup>
<mo>/</mo>
<msup>
<msub>
<mi>&sigma;</mi>
<mn>4</mn>
</msub>
<mn>2</mn>
</msup>
<mo>&rsqb;</mo>
<mo>+</mo>
<mfrac>
<msqrt>
<mi>&pi;</mi>
</msqrt>
<mn>2</mn>
</mfrac>
<mi>P</mi>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mn>0</mn>
</mrow>
</mtd>
</mtr>
</mtable>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>1</mn>
<mo>)</mo>
</mrow>
</mrow>
<mrow>
<mtable>
<mtr>
<mtd>
<mrow>
<mfrac>
<mrow>
<mo>&part;</mo>
<mi>S</mi>
<mi>I</mi>
<mi>N</mi>
<mi>R</mi>
</mrow>
<mrow>
<mo>&part;</mo>
<mi>&beta;</mi>
</mrow>
</mfrac>
<mo>=</mo>
<mn>0</mn>
<mo>&DoubleLeftRightArrow;</mo>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<msub>
<mi>a</mi>
<mn>1</mn>
</msub>
<mi>exp</mi>
<mo>&lsqb;</mo>
<mo>-</mo>
<msup>
<mrow>
<mo>(</mo>
<mi>&beta;</mi>
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<mn>1</mn>
</msub>
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<mi>&sigma;</mi>
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<mn>2</mn>
</msup>
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<mo>&CenterDot;</mo>
<mrow>
<mo>(</mo>
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<mn>2</mn>
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<mtr>
<mtd>
<mrow>
<mi>A</mi>
<mi>B</mi>
<mrow>
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</mrow>
<mn>2</mn>
</msup>
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<msup>
<msub>
<mi>&sigma;</mi>
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</msub>
<mn>2</mn>
</msup>
<mo>&rsqb;</mo>
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<msub>
<mi>a</mi>
<mn>3</mn>
</msub>
<mi>exp</mi>
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<mo>-</mo>
<msup>
<mrow>
<mo>(</mo>
<mrow>
<mi>&beta;</mi>
<mo>-</mo>
<msub>
<mi>&lambda;</mi>
<mn>3</mn>
</msub>
</mrow>
<mo>)</mo>
</mrow>
<mn>2</mn>
</msup>
<mo>/</mo>
<msup>
<msub>
<mi>&sigma;</mi>
<mn>3</mn>
</msub>
<mn>2</mn>
</msup>
<mo>&rsqb;</mo>
<mo>+</mo>
<msub>
<mi>a</mi>
<mn>4</mn>
</msub>
<mi>exp</mi>
<mo>&lsqb;</mo>
<mo>-</mo>
<msup>
<mrow>
<mo>(</mo>
<mrow>
<mi>&beta;</mi>
<mo>-</mo>
<msub>
<mi>&lambda;</mi>
<mn>4</mn>
</msub>
</mrow>
<mo>)</mo>
</mrow>
<mn>2</mn>
</msup>
<mo>/</mo>
<msup>
<msub>
<mi>&sigma;</mi>
<mn>4</mn>
</msub>
<mn>2</mn>
</msup>
<mo>&rsqb;</mo>
<mo>+</mo>
<mfrac>
<msqrt>
<mi>&pi;</mi>
</msqrt>
<mn>2</mn>
</mfrac>
<mi>P</mi>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mn>0</mn>
</mrow>
</mtd>
</mtr>
</mtable>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>2</mn>
<mo>)</mo>
</mrow>
</mrow>
5) α, β are initialized, preset parameter β Optimal Parameters α first, obtains α's in the case where meeting constraints according to local derviation formula (1)
Solution；Then α value is updated, fixed α optimizations β, the solution of the β in the case where meeting constraints is obtained according to local derviation formula (2), is carried out successively
More wheel iteration；
(6) after iteration meets certain number, iteration is stopped, convergence result is the optimal solution of red filter parameter；
(7) repeat the above steps (3)~(6) to the optical filtering of yellow, green, blueness respectively, and wherein α, β constraints are
380≤α ＜ β≤780；Export the optimum results of multiple color optical filtering parameter.
A kind of 4. optical filtering parameter optimization method based on visible light communication as claimed in claim 1 or 2, it is characterised in that：
The pass-band performance of optical filtering is F (λ)=exp [- (λ-λ for meeting Gaussian function0)2/σ0 2], it is necessary to ripple centered on the parameter of optimization
Long λ0And variances sigma0, methods described is specially：
(1) first, the LED of four kinds of coloured light spectroscopic data is measured with spectrometer, respectively with Gaussian function fitting, expression formula is such as
Under：
Sr(λ)=a1exp[-(λ-λ1)2/σ1 2]
Sa(λ)=a2exp[-(λ-λ2)2/σ2 2]
Sg(λ)=a3exp[-(λ-λ3)2/σ3 2]
Sb(λ)=a4exp[-(λ-λ4)2/σ4 2]
Wherein, a1-a4、λ1-λ4、σ1-σ4It is the fitting parameter of Gaussian function, is real constant；Sr(λ) be feux rouges spectral function, Sa
(λ) be gold-tinted spectral function, Sg(λ) be green glow spectral function, Sb(λ) is the spectral function of blue light；
(2) according to the system of reality, it is assumed that the spectrum amplitude of bias light is equally distributed, determines the spectral function of bias light
Sback(λ)=P and receiving terminal total noise power Nt, wherein P and NtIt is real constant；
(3) signal interference ratio of receiving terminal white light is calculated, the signal interference ratio of feux rouges is as follows：
<mfenced open = "" close = "">
<mtable>
<mtr>
<mtd>
<mrow>
<mi>S</mi>
<mi>I</mi>
<mi>N</mi>
<mi>R</mi>
<mo>=</mo>
<msup>
<mrow>
<mo>(</mo>
<mfrac>
<msub>
<mi>a</mi>
<mn>1</mn>
</msub>
<msqrt>
<mrow>
<mn>1</mn>
<mo>/</mo>
<msubsup>
<mi>&sigma;</mi>
<mn>0</mn>
<mn>1</mn>
</msubsup>
<mo>+</mo>
<mn>1</mn>
<mo>/</mo>
<msubsup>
<mi>&sigma;</mi>
<mn>1</mn>
<mn>2</mn>
</msubsup>
</mrow>
</msqrt>
</mfrac>
<mi>exp</mi>
<mo>&lsqb;</mo>
<mo>-</mo>
<msup>
<mrow>
<mo>(</mo>
<mrow>
<msub>
<mi>&lambda;</mi>
<mn>1</mn>
</msub>
<mo>-</mo>
<msub>
<mi>&lambda;</mi>
<mn>0</mn>
</msub>
</mrow>
<mo>)</mo>
</mrow>
<mn>2</mn>
</msup>
<mo>/</mo>
<mo>(</mo>
<mrow>
<msubsup>
<mi>&sigma;</mi>
<mn>0</mn>
<mn>2</mn>
</msubsup>
<mo>+</mo>
<msubsup>
<mi>&sigma;</mi>
<mn>1</mn>
<mn>2</mn>
</msubsup>
</mrow>
<mo>)</mo>
<mo>&rsqb;</mo>
<mo>)</mo>
</mrow>
<mn>2</mn>
</msup>
<mo>/</mo>
<mrow>
<mo>(</mo>
<mo>(</mo>
<mfrac>
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<mi>a</mi>
<mn>2</mn>
</msub>
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<mrow>
<mn>1</mn>
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<mo>+</mo>
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<msubsup>
<mi>&sigma;</mi>
<mn>2</mn>
<mn>2</mn>
</msubsup>
</mrow>
</msqrt>
</mfrac>
<mi>exp</mi>
<mo>&lsqb;</mo>
<mo>-</mo>
<msup>
<mrow>
<mo>(</mo>
<msub>
<mi>&lambda;</mi>
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</msub>
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<mn>2</mn>
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</msubsup>
<mo>+</mo>
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<mi>&sigma;</mi>
<mn>2</mn>
<mn>2</mn>
</msubsup>
<mo>)</mo>
</mrow>
<mo>&rsqb;</mo>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<mo>+</mo>
<mfrac>
<msub>
<mi>a</mi>
<mn>3</mn>
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<mi>&sigma;</mi>
<mn>0</mn>
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<mo>/</mo>
<msubsup>
<mi>&sigma;</mi>
<mn>3</mn>
<mn>2</mn>
</msubsup>
</mrow>
</msqrt>
</mfrac>
<mi>exp</mi>
<mo>&lsqb;</mo>
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<msup>
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<msub>
<mi>&lambda;</mi>
<mn>3</mn>
</msub>
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</mrow>
<mn>2</mn>
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<mn>2</mn>
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<mn>3</mn>
<mn>2</mn>
</msubsup>
<mo>)</mo>
</mrow>
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<mo>+</mo>
<mfrac>
<msub>
<mi>a</mi>
<mn>4</mn>
</msub>
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<mn>0</mn>
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<mn>1</mn>
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<msubsup>
<mi>&sigma;</mi>
<mn>4</mn>
<mn>2</mn>
</msubsup>
</mrow>
</msqrt>
</mfrac>
<mi>exp</mi>
<mo>&lsqb;</mo>
<mo>-</mo>
<msup>
<mrow>
<mo>(</mo>
<msub>
<mi>&lambda;</mi>
<mn>4</mn>
</msub>
<mo>-</mo>
<msub>
<mi>&lambda;</mi>
<mn>0</mn>
</msub>
<mo>)</mo>
</mrow>
<mn>2</mn>
</msup>
<mo>/</mo>
<mrow>
<mo>(</mo>
<msubsup>
<mi>&sigma;</mi>
<mn>0</mn>
<mn>2</mn>
</msubsup>
<mo>+</mo>
<msubsup>
<mi>&sigma;</mi>
<mn>4</mn>
<mn>2</mn>
</msubsup>
<mo>)</mo>
</mrow>
<mo>&rsqb;</mo>
<mo>+</mo>
<mi>P</mi>
<mo>&CenterDot;</mo>
<msub>
<mi>&sigma;</mi>
<mn>0</mn>
</msub>
<msup>
<mo>)</mo>
<mn>2</mn>
</msup>
<mo>+</mo>
<mfrac>
<msubsup>
<mi>N</mi>
<mi>t</mi>
<mn>2</mn>
</msubsup>
<mi>&pi;</mi>
</mfrac>
<mo>)</mo>
</mrow>
</mtd>
</mtr>
</mtable>
</mfenced>
2
Constraints is：380≤λ0≤ 780,0<σ0
(4) with signal interference ratio function respectively to λ0、σ0Local derviation is sought, makes local derviation result be equal to 0, abbreviation result is：
<mrow>
<mfrac>
<mrow>
<mo>&part;</mo>
<mi>S</mi>
<mi>I</mi>
<mi>N</mi>
<mi>R</mi>
</mrow>
<mrow>
<mo>&part;</mo>
<msub>
<mi>&lambda;</mi>
<mn>0</mn>
</msub>
</mrow>
</mfrac>
<mo>=</mo>
<mn>0</mn>
<mo>&DoubleLeftRightArrow;</mo>
<mfrac>
<mrow>
<msub>
<mi>&lambda;</mi>
<mn>1</mn>
</msub>
<mo>-</mo>
<msub>
<mi>&lambda;</mi>
<mn>0</mn>
</msub>
</mrow>
<mrow>
<msubsup>
<mi>&sigma;</mi>
<mn>0</mn>
<mn>2</mn>
</msubsup>
<mo>+</mo>
<msubsup>
<mi>&sigma;</mi>
<mn>1</mn>
<mn>2</mn>
</msubsup>
</mrow>
</mfrac>
<mo>&CenterDot;</mo>
<mrow>
<mo>(</mo>
<msup>
<mi>B</mi>
<mn>2</mn>
</msup>
<mo>+</mo>
<msubsup>
<mi>N</mi>
<mi>t</mi>
<mn>2</mn>
</msubsup>
<mo>/</mo>
<mi>&pi;</mi>
<mo>)</mo>
</mrow>
<mo>-</mo>
<mi>B</mi>
<mo>&CenterDot;</mo>
<mrow>
<mo>(</mo>
<msub>
<mi>B</mi>
<mn>2</mn>
</msub>
<mo>&CenterDot;</mo>
<mfrac>
<mrow>
<msub>
<mi>&lambda;</mi>
<mn>2</mn>
</msub>
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<msub>
<mi>&lambda;</mi>
<mn>0</mn>
</msub>
</mrow>
<mrow>
<msubsup>
<mi>&sigma;</mi>
<mn>0</mn>
<mn>2</mn>
</msubsup>
<mo>+</mo>
<msubsup>
<mi>&sigma;</mi>
<mn>2</mn>
<mn>2</mn>
</msubsup>
</mrow>
</mfrac>
<mo>+</mo>
<msub>
<mi>B</mi>
<mn>3</mn>
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<mfrac>
<mrow>
<msub>
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<msub>
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<mrow>
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<mi>&sigma;</mi>
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<mn>2</mn>
</msubsup>
<mo>+</mo>
<msubsup>
<mi>&sigma;</mi>
<mn>3</mn>
<mn>2</mn>
</msubsup>
</mrow>
</mfrac>
<mo>+</mo>
<msub>
<mi>B</mi>
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</mfrac>
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<mi>I</mi>
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<mi>R</mi>
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</mfrac>
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<mo>&DoubleLeftRightArrow;</mo>
<mrow>
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<mfrac>
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<mfrac>
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<mn>2</mn>
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</mfrac>
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<mi>P</mi>
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</mtd>
</mtr>
</mtable>
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<mo>-</mo>
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<mrow>
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</mrow>
</mrow>
Wherein：
<mrow>
<msub>
<mi>B</mi>
<mn>2</mn>
</msub>
<mo>=</mo>
<mfrac>
<msub>
<mi>a</mi>
<mn>2</mn>
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<msqrt>
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<msubsup>
<mi>&sigma;</mi>
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<mo>/</mo>
<msubsup>
<mi>&sigma;</mi>
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<mn>2</mn>
</msubsup>
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</msqrt>
</mfrac>
<mi>exp</mi>
<mo>&lsqb;</mo>
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<msup>
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<mi>P</mi>
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</mrow>
(5) λ is initialized0、σ0, σ fixed first0Parameter optimization parameter lambda0, obtained according to local derviation formula (1) in the case where meeting constraints
λ0Solution；Then λ is updated0Value, fixed λ0Optimize σ0, the σ in the case where meeting constraints is obtained according to local derviation formula (2)0Solution, according to
Secondary progress takes turns iteration more；
(6) after iteration meets certain number, iteration is stopped, convergence result is the optimal solution of red filter parameter；
(7) repeat the above steps (3)~(6), wherein λ to the optical filtering of yellow, green, blueness respectively0、σ0Constraints be
380≤λ0≤ 780,0<σ0；Export the optimum results of multiple color optical filtering parameter.
A kind of 5. optical filtering parameter optimization method based on visible light communication as claimed in claim 1 or 2, it is characterised in that：
The pass-band performance of optical filtering is F (λ)=1/ (1+ (λ-λ for meeting Lorentzian0)2/σ0 2), it is necessary to centered on the parameter of optimization
Wavelength X0And variances sigma0, methods described is specially：
(1) first, the LED of four kinds of coloured light spectroscopic data is measured with spectrometer, is fitted respectively with Lorentzian, expression formula is such as
Under：
Sr(λ)=a1/(1+(λ-λ1)2/σ1 2)
Sa(λ)=a2/(1+(λ-λ2)2/σ2 2)
Sg(λ)=a3/(1+(λ-λ3)2/σ3 2)
Sb(λ)=a4/(1+(λ-λ4)2/σ4 2)
Wherein, a1-a4、λ1-λ4、σ1-σ4It is the fitting parameter of Lorentzian, is real constant；Sr(λ) is the spectral function of feux rouges,
Sa(λ) be gold-tinted spectral function, Sg(λ) be green glow spectral function, Sb(λ) is the spectral function of blue light；
(2) according to the system of reality, it is assumed that the spectrum amplitude of bias light is equally distributed, determines the spectral function of bias light
Sback(λ)=P and receiving terminal total noise power Nt, wherein P and NtIt is real constant；
(3) signal interference ratio of receiving terminal white light is calculated, the signal interference ratio of feux rouges is as follows：
<mfenced open = "" close = "">
<mtable>
<mtr>
<mtd>
<mrow>
<mi>S</mi>
<mi>I</mi>
<mi>N</mi>
<mi>R</mi>
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</mrow>
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<mtr>
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<mrow>
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<mi>a</mi>
<mn>1</mn>
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<mi>&sigma;</mi>
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<mn>1</mn>
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</mfenced>
3
Constraints is：380≤λ0≤ 780,0<σ0
(4) with signal interference ratio function respectively to λ0、σ0Local derviation is sought, makes local derviation result be equal to 0, abbreviation result is：
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</mtable>
<mo>-</mo>
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</mrow>
Wherein：
B=B2+B3+B4+P·σ0
(5) λ is initialized0、σ0, σ fixed first0Parameter optimization parameter lambda0, obtained according to local derviation formula (1) in the case where meeting constraints
λ0Solution；Then λ is updated0Value, fixed λ0Optimize σ0, the σ in the case where meeting constraints is obtained according to local derviation formula (2)0Solution, according to
Secondary progress takes turns iteration more；
(6) after iteration meets certain number, iteration is stopped, convergence result is the optimal solution of red filter parameter；
(7) repeat the above steps (3)~(6), wherein λ to yellow, green, blue filter respectively0、σ0Constraints be 380
≤λ0≤ 780,0<σ0；Export the optimum results of multiple color optical filtering parameter.
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