CN104993867A - Filter parameter optimization method based on visible light communication - Google Patents

Abstract

The invention provides a filter parameter optimization method based on visible light communication, comprising: firstly utilizing a spectrometer to detect the spectrum data of each monochromatic light, and employing a gauss or Lorentzen function for fitting to obtain a spectral fitting function; in dependence on a real system, determining the spectral function of a bias light and the total noise power of a receiving terminal; using the signal to interference ratio of each color light at the receiving terminal as an objective function, and meanwhile determining constraint conditions of filter parameters; first using a signal to interference ratio function to solve the partial derivative of each variable, and setting a partial derivative result to be zero, then fixing a variable, and optimizing another variable under the constraint conditions, and successively performing rounds of iteration to obtain the optimal solution of the filter parameters; and respectively solving objective functions of color lights to obtain the optimal value of parameters of each colored filter. The method is suitable for a plurality of filters, has a fast convergence rate in operation, and can better reduce interference among light colors.

Description

A kind of optical filtering parameter optimization method based on visible light communication

Technical field

The invention belongs to visible light communication field, the optimization method of optical filtering parameter in a kind of polychromatic light communication system.

Background technology

Along with socioeconomic development, the requirement of people to the quality of life is also more and more higher, and meanwhile, the communications field starts to pursue a kind of " green " and " two-forty " communication technology.Visible light communication technology becomes the focus of research field just gradually as above-mentioned alternative.It utilizes Laser Devices or LED component, by realizing high speed information transmission to the modulation of intensity of illumination, while guarantee routine work illumination, also meets the demand that people are transmitted high speed information.

White light in current visible light communication has two kinds of generation types, and one utilizes blue light to coordinate with fluorescent material to form white light, and another kind is the mode of multiple monochromatic light mixing.Adopt the method for polychromatic light mixing to compare with the simple white light that uses, can significantly promote message capacity and traffic rate, become the focus of future studies especially.

For existing polychromatic light communication system, transmitting terminal utilizes the LED of multiple coloured light to send multiple signals, and then blend together white light emission and go out, receiving terminal will be separated each coloured light in white light with the multiple optical filtering of correspondence.

Testing research shows, the LED light spectral shape of transmitting terminal is similar to Gaussian function, just inevitably there is cross jamming between each coloured light.At receiving terminal, each road signal accuracy of receiving be made high as far as possible, and the cross jamming between each coloured light just must be made little as far as possible, is a kind of approach avoiding cross jamming to the optimization of optical filtering parameter.

Under normal circumstances, the shape of optical filtering pass-band performance has rectangle, Gaussian function, Lorentzian etc. several, the parameter of different optical filtering is also different, can provide the method finding optimum optical filtering parameter in theory, and calculate the optimal value of optical filtering parameter.Thus directive function is played to the design and production of actual optical filtering.But, about how obtaining optimum optical filtering parameter, the research that academia is also not relevant.

Summary of the invention

Goal of the invention: the present invention is directed to problems of the prior art, propose the optimization method of a set of receiving terminal optical filtering, utilize the method can find optimum optical filtering parameter, thus making the cross jamming between each coloured light of receiving little as far as possible, the optical filtering going out to be applicable to polychromatic light communication for actual production provides guidance.

Technical scheme: a kind of receiving terminal optical filtering parameter optimization method based on visible light communication, comprises the steps: 1) utilize spectrometer to measure each monochromatic spectroscopic data, carry out matching with Gaussian function or Lorentzian, obtain the fitting function of spectrum; 2) spectral function of bias light and the total noise power of receiving terminal is determined; 3) with each coloured light at the signal interference ratio of receiving terminal for target function, determine the constraints of optical filtering parameter simultaneously; 4) with signal interference ratio function, local derviation is asked to each variable, and make local derviation result equal 0; 5) each parameter of initialization optical filtering, then fixes a parameter, optimizes another one parameter under constraints, carries out successively taking turns iteration more; 6) after iteration meets certain number of times, stop iteration, namely convergence result is the optimal solution of optical filtering parameter; 7) respectively above-mentioned steps (3) ~ (6) are repeated to the optical filtering of each color, export the optimum results of shades of colour optical filtering parameter.

Further, described overall noise comprises Johnson noise and thermal noise.

Further, the pass-band performance of optical filtering is rectangle, and right boundary wavelength is α, β, and described optimization method is specially:

(1) first, measure the spectroscopic data of the LED of four kinds of coloured light with spectrometer, use Gaussian function fitting respectively, expression formula is as follows:

S _r(λ)＝a ₁exp[-(λ-λ ₁) ²/σ ₁ ²]

S _a(λ)＝a ₂exp[-(λ-λ ₂) ²/σ ₂ ²]

S _g(λ)＝a ₃exp[-(λ-λ ₃) ²/σ ₃ ²]

S _b(λ)＝a ₄exp[-(λ-λ ₄) ²/σ ₄ ²]

Wherein, α ₁-α ₄, λ ₁-λ ₄, σ ₁-σ ₄being the fitting parameter of Gaussian function, is real constant; S _r(λ) be the spectral function of ruddiness, S _a(λ) be the spectral function of gold-tinted, S _g(λ) be the spectral function of green glow, S _b(λ) be the spectral function of blue light;

(2) according to the system of reality, suppose that the spectrum amplitude of bias light is equally distributed, determine the spectral function S of bias light _back(λ)=P and receiving terminal total noise power N _t, wherein P and N _tit is real constant;

(3) calculate the signal interference ratio of each coloured light of receiving terminal, the signal interference ratio of ruddiness is as follows:

$\begin{array}{c}\mathrm{SINR}=\\ \frac{{[a_1{\mathrm{\σ}}_1\mathrm{erfc}\left(\frac{\mathrm{\α}-{\mathrm{\λ}}_1}{{\mathrm{\σ}}_1}\right)-a_1{\mathrm{\σ}}_1\mathrm{erfc}\left(\frac{\mathrm{\β}-{\mathrm{\λ}}_1}{{\mathrm{\σ}}_1}\right)]}^2}{{[a_2{\mathrm{\σ}}_2\mathrm{erfc}\left(\frac{\mathrm{\α}-{\mathrm{\λ}}_2}{{\mathrm{\σ}}_2}\right)-a_2{\mathrm{\σ}}_2\mathrm{erfc}\left(\frac{\mathrm{\β}-{\mathrm{\λ}}_2}{{\mathrm{\σ}}_2}\right)+a_3{\mathrm{\σ}}_3\mathrm{erfc}\left(\frac{\mathrm{\α}-{\mathrm{\λ}}_3}{{\mathrm{\σ}}_3}\right)-a_3{\mathrm{\σ}}_3\mathrm{erfc}\left(\frac{\mathrm{\β}-{\mathrm{\λ}}_3}{{\mathrm{\σ}}_3}\right)+a_4{\mathrm{\σ}}_4\mathrm{erfc}\left(\frac{\mathrm{\α}-{\mathrm{\λ}}_4}{{\mathrm{\σ}}_4}\right)-a_4{\mathrm{\σ}}_4\mathrm{erfc}\left(\frac{\mathrm{\β}-{\mathrm{\λ}}_4}{{\mathrm{\σ}}_4}\right)+P(\mathrm{\β}-\mathrm{\α})]}^2+\frac{{{4N}_t}^2}{\mathrm{\π}}}\end{array}$

Constraints is: 380≤α < β≤780;

(4) ask local derviation to α, β respectively with signal interference ratio function, make local derviation result equal 0, abbreviation result is

$\begin{array}{c}\frac{\&PartialD;\mathrm{SINR}}{\&PartialD;\mathrm{\&alpha;}}=0\&DoubleLeftRightArrow;\\ a_1\exp [-{(\mathrm{\&alpha;}-{\mathrm{\&lambda;}}_1)}^2/{{\mathrm{\&sigma;}}_1}^2]\&CenterDot;(B^2+4N_t^2/\mathrm{\&pi;})-\\ \mathrm{AB}\left(a_2\exp \right[-{(\mathrm{\&alpha;}-{\mathrm{\&lambda;}}_2)}^2/{{\mathrm{\&sigma;}}_2}^2]+a_3\exp [-{(\mathrm{\&alpha;}-{\mathrm{\&lambda;}}_3)}^2/{{\mathrm{\&sigma;}}_3}^2]+a_4\exp [-{(\mathrm{\&alpha;}-{\mathrm{\&lambda;}}_4)}^2/{{\mathrm{\&sigma;}}_4}^2]+\frac{\sqrt{\mathrm{\&pi;}}}{2}P)=0\end{array}---\left(1\right)$

$\begin{array}{c}\frac{\&PartialD;\mathrm{SINR}}{\&PartialD;\mathrm{\&beta;}}=0\&DoubleLeftRightArrow;\\ a_1\exp [-{(\mathrm{\&beta;}-{\mathrm{\&lambda;}}_1)}^2/{{\mathrm{\&sigma;}}_1}^2]\&CenterDot;(B^2+4N_t^2/\mathrm{\&pi;})-\\ \mathrm{AB}\left(a_2\exp \right[-{(\mathrm{\&beta;}-{\mathrm{\&lambda;}}_2)}^2/{{\mathrm{\&sigma;}}_2}^2]+a_3\exp [-{(\mathrm{\&beta;}-{\mathrm{\&lambda;}}_3)}^2/{{\mathrm{\&sigma;}}_3}^2]+a_4\exp [-{(\mathrm{\&beta;}-{\mathrm{\&lambda;}}_4)}^2/{{\mathrm{\&sigma;}}_4}^2]+\frac{\sqrt{\mathrm{\&pi;}}}{2}P)=0\end{array}---\left(2\right)$

Wherein, $A=a_1{\mathrm{\&sigma;}}_1\mathrm{erfc}\left(\frac{\mathrm{\&alpha;}-{\mathrm{\&lambda;}}_1}{{\mathrm{\&sigma;}}_1}\right)-a_1{\mathrm{\&sigma;}}_1\mathrm{erfc}\left(\frac{\mathrm{\&beta;}-{\mathrm{\&lambda;}}_1}{{\mathrm{\&sigma;}}_1}\right)$

$B=a_2{\mathrm{\&sigma;}}_2\mathrm{erfc}\left(\frac{\mathrm{\&alpha;}-{\mathrm{\&lambda;}}_2}{{\mathrm{\&sigma;}}_2}\right)-a_2{\mathrm{\&sigma;}}_2\mathrm{erfc}\left(\frac{\mathrm{\&beta;}-{\mathrm{\&lambda;}}_2}{{\mathrm{\&sigma;}}_2}\right)+a_3{\mathrm{\&sigma;}}_3\mathrm{erfc}\left(\frac{\mathrm{\&alpha;}-{\mathrm{\&lambda;}}_3}{{\mathrm{\&sigma;}}_3}\right)-a_3{\mathrm{\&sigma;}}_3\mathrm{erfc}\left(\frac{\mathrm{\&beta;}-{\mathrm{\&lambda;}}_3}{{\mathrm{\&sigma;}}_3}\right)+a_4{\mathrm{\&sigma;}}_4\mathrm{erfc}\left(\frac{\mathrm{\&alpha;}-{\mathrm{\&lambda;}}_4}{{\mathrm{\&sigma;}}_4}\right)-a_4{\mathrm{\&sigma;}}_4\mathrm{erfc}\left(\frac{\mathrm{\&beta;}-{\mathrm{\&lambda;}}_4}{{\mathrm{\&sigma;}}_4}\right)+P(\mathrm{\&beta;}-\mathrm{\&alpha;})$

(5) initialization α, β, first preset parameter β Optimal Parameters α, obtain in the solution meeting the α under constraints according to local derviation formula (1); Then upgrade the value of α, fixing α optimizes β, obtains in the solution meeting the β under constraints, carry out successively taking turns iteration more according to local derviation formula (2);

(6) after iteration meets certain number of times, stop iteration, namely convergence result is the optimal solution of red filter parameter;

(7) repeat above-mentioned steps (3) ~ (6) to yellow, green, blue optical filtering respectively, wherein the constraints of α, β is identical; Export the optimum results of multiple color optical filtering parameter.

The parameter optimization that pass-band performance is the optical filtering of rectangle can be realized by above-mentioned steps.

Further, the pass-band performance of optical filtering is F (λ)=exp [-(λ-λ meeting Gaussian function ₀) ²/ σ ₀ ²], need wavelength X centered by Optimal Parameters ₀and variances sigma ₀, described method is specially:

(1) first, measure the spectroscopic data of the LED of four kinds of coloured light with spectrometer, use Gaussian function fitting respectively, expression formula is as follows:

S _r(λ)＝a ₁exp[-(λ-λ ₁) ²/σ ₁ ²]

S _a(λ)＝a ₂exp[-(λ-λ ₂) ²/σ ₂ ²]

S _g(λ)＝a ₃exp[-(λ-λ ₃) ²/σ ₃ ²]

S _b(λ)＝a ₄exp[-(λ-λ ₄) ²/σ ₄ ²]

Wherein, α ₁-α ₄, λ ₁-λ ₄, σ ₁-σ ₄being the fitting parameter of Gaussian function, is real constant; S _r(λ) be the spectral function of ruddiness, S _a(λ) be the spectral function of gold-tinted, S _g(λ) be the spectral function of green glow, S _b(λ) be the spectral function of blue light;

(2) according to the system of reality, suppose that the spectrum amplitude of bias light is equally distributed, determine the spectral function S of bias light _back(λ)=P and receiving terminal total noise power N _t, wherein P and N _tit is real constant;

(3) calculate the signal interference ratio of each coloured light of receiving terminal, the signal interference ratio of ruddiness is as follows:

$\begin{array}{c}\mathrm{SINR}={\left(\frac{a_1}{\sqrt{1/{\mathrm{\&sigma;}}_0^2+1/{\mathrm{\&sigma;}}_1^2}}\exp \right[-{({\mathrm{\&lambda;}}_1-{\mathrm{\&lambda;}}_0)}^2/({\mathrm{\&sigma;}}_0^2+{\mathrm{\&sigma;}}_1^2)\left]\right)}^2/(\left(\frac{a_2}{\sqrt{1/{\mathrm{\&sigma;}}_0^2+1/{\mathrm{\&sigma;}}_2^2}}\exp \right[-{({\mathrm{\&lambda;}}_2-{\mathrm{\&lambda;}}_0)}^2/({\mathrm{\&sigma;}}_0^2+{\mathrm{\&sigma;}}_2^2)]\\ +\frac{a_3}{\sqrt{1/{\mathrm{\&sigma;}}_0^2+1/{\mathrm{\&sigma;}}_3^2}}\exp [-{({\mathrm{\&lambda;}}_3-{\mathrm{\&lambda;}}_0)}^2/({\mathrm{\&sigma;}}_0^2+{\mathrm{\&sigma;}}_3^2)]+\frac{a_4}{\sqrt{1/{\mathrm{\&sigma;}}_0^2+1/{\mathrm{\&sigma;}}_4^2}}\exp [-{({\mathrm{\&lambda;}}_4-{\mathrm{\&lambda;}}_0)}^2/({\mathrm{\&sigma;}}_0^2+{\mathrm{\&sigma;}}_4^2)+P{\&CenterDot;{\mathrm{\&sigma;}}_0)}^2+\frac{N_t^2}{\mathrm{\&pi;}})\end{array}$

Constraints is: 380≤λ ₀≤ 780,0< σ ₀

(4) use signal interference ratio function respectively to λ ₀, σ ₀ask local derviation, make local derviation result equal 0, abbreviation result is:

$\frac{\&PartialD;\mathrm{SINR}}{{\&PartialD;\mathrm{\&lambda;}}_0}=0\&DoubleLeftRightArrow;\frac{{\mathrm{\&lambda;}}_1-{\mathrm{\&lambda;}}_0}{{\mathrm{\&sigma;}}_0^2+{\mathrm{\&sigma;}}_1^2}\&CenterDot;(B^2+N_t^2/\mathrm{\&pi;})-B\&CenterDot;(B_2\&CenterDot;\frac{{\mathrm{\&lambda;}}_2-{\mathrm{\&lambda;}}_0}{{\mathrm{\&sigma;}}_0^2+{\mathrm{\&sigma;}}_2^2}+B_3\&CenterDot;\frac{{\mathrm{\&lambda;}}_3-{\mathrm{\&lambda;}}_0}{{\mathrm{\&sigma;}}_0^2+{\mathrm{\&sigma;}}_3^2}+B_4\&CenterDot;\frac{{\mathrm{\&lambda;}}_4-{\mathrm{\&lambda;}}_0}{{\mathrm{\&sigma;}}_0^2+{\mathrm{\&sigma;}}_4^2})=0---\left(1\right)$

$\begin{array}{c}\frac{\&PartialD;\mathrm{SINR}}{{\&PartialD;\mathrm{\&sigma;}}_0}=0\&DoubleLeftRightArrow;(\frac{1}{{\mathrm{\&sigma;}}_0}-\frac{{\mathrm{\&sigma;}}_0}{{\mathrm{\&sigma;}}_0^2+{\mathrm{\&sigma;}}_1^2}+\frac{{2\mathrm{\&sigma;}}_0{({\mathrm{\&lambda;}}_1-{\mathrm{\&lambda;}}_0)}^2}{{({\mathrm{\&sigma;}}_0^2+{\mathrm{\&sigma;}}_1^2)}^2})\&CenterDot;(B^2+N_t^2/\mathrm{\&pi;})-\\ B\&CenterDot;(B_2\&CenterDot;(\frac{1}{{\mathrm{\&sigma;}}_0}-\frac{{\mathrm{\&sigma;}}_0}{{\mathrm{\&sigma;}}_0^2+{\mathrm{\&sigma;}}_2^2}+\frac{{2\mathrm{\&sigma;}}_0{({\mathrm{\&lambda;}}_2-{\mathrm{\&lambda;}}_0)}^2}{{({\mathrm{\&sigma;}}_0^2+{\mathrm{\&sigma;}}_2^2)}^2})+B_3\&CenterDot;(\frac{1}{{\mathrm{\&sigma;}}_0}-\frac{{\mathrm{\&sigma;}}_0}{{\mathrm{\&sigma;}}_0^2+{\mathrm{\&sigma;}}_3^2}+\frac{{2\mathrm{\&sigma;}}_0{({\mathrm{\&lambda;}}_3-{\mathrm{\&lambda;}}_0)}^2}{{({\mathrm{\&sigma;}}_0^2+{\mathrm{\&sigma;}}_3^2)}^2})+\\ B_4\&CenterDot;(\frac{1}{{\mathrm{\&sigma;}}_0}-\frac{{\mathrm{\&sigma;}}_0}{{\mathrm{\&sigma;}}_0^2+{\mathrm{\&sigma;}}_4^2}+\frac{{2\mathrm{\&sigma;}}_0{({\mathrm{\&lambda;}}_4-{\mathrm{\&lambda;}}_0)}^2}{{({\mathrm{\&sigma;}}_0^2+{\mathrm{\&sigma;}}_4^2)}^2})+P)=0\end{array}---\left(2\right)$

Wherein:

$B_2=\frac{a_2}{\sqrt{1/{\mathrm{\&sigma;}}_0^2+1/{\mathrm{\&sigma;}}_2^2}}\exp [-{({\mathrm{\&lambda;}}_2-{\mathrm{\&lambda;}}_0)}^2/({\mathrm{\&sigma;}}_0^2+{\mathrm{\&sigma;}}_2^2)],B_3=\frac{a_3}{\sqrt{1/{\mathrm{\&sigma;}}_0^2+1/{\mathrm{\&sigma;}}_3^2}}\exp [-{({\mathrm{\&lambda;}}_3-{\mathrm{\&lambda;}}_0)}^2/({\mathrm{\&sigma;}}_0^2+{\mathrm{\&sigma;}}_3^2)],$

$B_4=\frac{a_4}{\sqrt{1/{\mathrm{\&sigma;}}_0^2+1/{\mathrm{\&sigma;}}_4^2}}\exp [-{({\mathrm{\&lambda;}}_4-{\mathrm{\&lambda;}}_0)}^2/({\mathrm{\&sigma;}}_0^2+{\mathrm{\&sigma;}}_4^2)],B=B_2+B_3+B_4+P\&CenterDot;{\mathrm{\&sigma;}}_0$

(5) initialization λ ₀, σ ₀, first fix σ ₀parameter optimization parameter lambda ₀, obtain according to local derviation formula (1) and meeting the λ under constraints ₀solution; Then λ is upgraded ₀value, fixing λ ₀optimize σ ₀, obtain according to local derviation formula (2) and meeting the σ under constraints ₀solution, carry out successively taking turns iteration more;

(6) after iteration meets certain number of times, stop iteration, namely convergence result is the optimal solution of red filter parameter;

(7) respectively above-mentioned steps (3) ~ (6), wherein λ is repeated to yellow, green, blue optical filtering ₀, σ ₀constraints identical; Export the optimum results of multiple color optical filtering parameter.

The parameter optimization that pass-band performance is the optical filtering meeting Gaussian function can be realized by above-mentioned steps.

Further, the pass-band performance of optical filtering is F (λ)=1/ (1+ (λ-λ meeting Lorentzian ₀) ²/ σ ₀ ²), need wavelength X centered by Optimal Parameters ₀and variances sigma ₀, described method is specially:

(1) first, measure the spectroscopic data of the LED of four kinds of coloured light with spectrometer, use Lorentzian matching respectively, expression formula is as follows:

S _r(λ)＝a ₁/(1+(λ-λ ₁) ²/σ ₁ ²)

S _a(λ)＝a ₂/(1+(λ-λ ₂) ²/σ ₂ ²)

S _g(λ)＝a ₃/(1+(λ-λ ₃) ²/σ ₃ ²)

S _b(λ)＝a ₄/(1+(λ-λ ₄) ²/σ ₄ ²)

Wherein, α ₁-α ₄, λ ₁-λ ₄, σ ₁-σ ₄being the fitting parameter of Lorentzian, is real constant; S _r(λ) be the spectral function of ruddiness, S _a(λ) be the spectral function of gold-tinted, S _g(λ) be the spectral function of green glow, S _bb spectral function that () is blue light;

(2) according to the system of reality, suppose that the spectrum amplitude of bias light is equally distributed, determine the spectral function S of bias light _back(λ)=P and receiving terminal total noise power N _t, wherein P and N _tit is real constant;

(3) calculate the signal interference ratio of each coloured light of receiving terminal, the signal interference ratio of ruddiness is as follows:

$\begin{array}{c}\mathrm{SINR}=\\ {\left(\frac{a_1{\mathrm{\&sigma;}}_0{\mathrm{\&sigma;}}_1({\mathrm{\&sigma;}}_0+{\mathrm{\&sigma;}}_1)}{{({\mathrm{\&lambda;}}_0-{\mathrm{\&lambda;}}_1)}^2+{({\mathrm{\&sigma;}}_0+{\mathrm{\&sigma;}}_1)}^2}\right)}^2/({(\frac{a_2{\mathrm{\&sigma;}}_0{\mathrm{\&sigma;}}_2({\mathrm{\&sigma;}}_0+{\mathrm{\&sigma;}}_2)}{{({\mathrm{\&lambda;}}_0-{\mathrm{\&lambda;}}_2)}^2+{({\mathrm{\&sigma;}}_0+{\mathrm{\&sigma;}}_2)}^2}+\frac{a_3{\mathrm{\&sigma;}}_0{\mathrm{\&sigma;}}_3({\mathrm{\&sigma;}}_0+{\mathrm{\&sigma;}}_3)}{{({\mathrm{\&lambda;}}_0-{\mathrm{\&lambda;}}_3)}^2+{({\mathrm{\&sigma;}}_0+{\mathrm{\&sigma;}}_3)}^2}+\frac{a_4{\mathrm{\&sigma;}}_0{\mathrm{\&sigma;}}_4({\mathrm{\&sigma;}}_0+{\mathrm{\&sigma;}}_4)}{{({\mathrm{\&lambda;}}_0-{\mathrm{\&lambda;}}_4)}^2+{({\mathrm{\&sigma;}}_0+{\mathrm{\&sigma;}}_4)}^2}+P\&CenterDot;{\mathrm{\&sigma;}}_0)}^2+\frac{N_t^2}{{\mathrm{\&pi;}}^2})\end{array}$

Constraints is: 380≤λ ₀≤ 780,0< σ ₀

(4) use signal interference ratio function respectively to λ ₀, σ ₀ask local derviation, make local derviation result equal 0, abbreviation result is:

$\begin{array}{c}\frac{\&PartialD;\mathrm{SINR}}{{\&PartialD;\mathrm{\&lambda;}}_0}=0\&DoubleLeftRightArrow;\frac{{\mathrm{\&lambda;}}_1-{\mathrm{\&lambda;}}_0}{{({\mathrm{\&lambda;}}_0-{\mathrm{\&lambda;}}_1)}^2+{({\mathrm{\&sigma;}}_0+{\mathrm{\&sigma;}}_1)}^2}\&CenterDot;(B^2+N_t^2/{\mathrm{\&pi;}}^2)-\\ B\&CenterDot;(B_2\&CenterDot;\frac{{\mathrm{\&lambda;}}_2-{\mathrm{\&lambda;}}_0}{{({\mathrm{\&lambda;}}_0-{\mathrm{\&lambda;}}_2)}^2+{({\mathrm{\&sigma;}}_0+{\mathrm{\&sigma;}}_2)}^2}+B_3\&CenterDot;\frac{{\mathrm{\&lambda;}}_3-{\mathrm{\&lambda;}}_0}{{({\mathrm{\&lambda;}}_0-{\mathrm{\&lambda;}}_3)}^2+{({\mathrm{\&sigma;}}_0+{\mathrm{\&sigma;}}_3)}^2}+B_4\&CenterDot;\frac{{\mathrm{\&lambda;}}_4-{\mathrm{\&lambda;}}_0}{{({\mathrm{\&lambda;}}_0-{\mathrm{\&lambda;}}_4)}^2+{({\mathrm{\&sigma;}}_0+{\mathrm{\&sigma;}}_4)}^2})=0\end{array}---\left(1\right)$

$\begin{array}{c}\frac{\&PartialD;\mathrm{SINR}}{{\&PartialD;\mathrm{\&sigma;}}_0}=0\&DoubleLeftRightArrow;(\frac{{\mathrm{\&sigma;}}_1+2{\mathrm{\&sigma;}}_0}{({\mathrm{\&sigma;}}_1+{\mathrm{\&sigma;}}_0){\mathrm{\&sigma;}}_0}-\frac{2({\mathrm{\&sigma;}}_1+{\mathrm{\&sigma;}}_0)}{{({\mathrm{\&lambda;}}_0-{\mathrm{\&lambda;}}_1)}^2+{({\mathrm{\&sigma;}}_0+{\mathrm{\&sigma;}}_1)}^2})\&CenterDot;(B^2+N_t^2/{\mathrm{\&pi;}}^2)-\\ B\&CenterDot;(B_2\&CenterDot;(\frac{{\mathrm{\&sigma;}}_2+2{\mathrm{\&sigma;}}_0}{({\mathrm{\&sigma;}}_2+{\mathrm{\&sigma;}}_0){\mathrm{\&sigma;}}_0}-\frac{2({\mathrm{\&sigma;}}_2+{\mathrm{\&sigma;}}_0)}{{({\mathrm{\&lambda;}}_0-{\mathrm{\&lambda;}}_2)}^2+{({\mathrm{\&sigma;}}_0+{\mathrm{\&sigma;}}_2)}^2})+B_3\&CenterDot;(\frac{{\mathrm{\&sigma;}}_3+2{\mathrm{\&sigma;}}_0}{({\mathrm{\&sigma;}}_3+{\mathrm{\&sigma;}}_0){\mathrm{\&sigma;}}_0}-\frac{2({\mathrm{\&sigma;}}_3+{\mathrm{\&sigma;}}_0)}{{({\mathrm{\&lambda;}}_0-{\mathrm{\&lambda;}}_3)}^2+{({\mathrm{\&sigma;}}_0+{\mathrm{\&sigma;}}_3)}^2})+\\ B_4\&CenterDot;(\frac{{\mathrm{\&sigma;}}_4+{2\mathrm{\&sigma;}}_0}{({\mathrm{\&sigma;}}_4+{\mathrm{\&sigma;}}_0){\mathrm{\&sigma;}}_0}-\frac{2({\mathrm{\&sigma;}}_4+{\mathrm{\&sigma;}}_0)}{{({\mathrm{\&lambda;}}_0-{\mathrm{\&lambda;}}_4)}^2+{({\mathrm{\&sigma;}}_0+{\mathrm{\&sigma;}}_4)}^2})+P)=0\end{array}$

Wherein: $B_2=\frac{a_2{\mathrm{\&sigma;}}_0{\mathrm{\&sigma;}}_2({\mathrm{\&sigma;}}_0+{\mathrm{\&sigma;}}_2)}{{({\mathrm{\&lambda;}}_0-{\mathrm{\&lambda;}}_2)}^2+{({\mathrm{\&sigma;}}_0+{\mathrm{\&sigma;}}_2)}^2},B_3=\frac{a_3{\mathrm{\&sigma;}}_0{\mathrm{\&sigma;}}_3({\mathrm{\&sigma;}}_0+{\mathrm{\&sigma;}}_3)}{{({\mathrm{\&lambda;}}_0-{\mathrm{\&lambda;}}_3)}^2+{({\mathrm{\&sigma;}}_0+{\mathrm{\&sigma;}}_3)}^2}$

$B_4=\frac{a_4{\mathrm{\&sigma;}}_0{\mathrm{\&sigma;}}_4({\mathrm{\&sigma;}}_0+{\mathrm{\&sigma;}}_4)}{{({\mathrm{\&lambda;}}_0-{\mathrm{\&lambda;}}_4)}^2+{({\mathrm{\&sigma;}}_0+{\mathrm{\&sigma;}}_4)}^2},B=B_2+B_3+B_4+P\&CenterDot;{\mathrm{\&sigma;}}_0$

(5) initialization λ ₀, σ ₀, first fix σ ₀parameter optimization parameter lambda ₀, obtain according to local derviation formula (1) and meeting the λ under constraints ₀solution; Then λ is upgraded ₀value, fixing λ ₀optimize σ ₀, obtain according to local derviation formula (2) and meeting the σ under constraints ₀solution, carry out successively taking turns iteration more;

(6) after iteration meets certain number of times, stop iteration, namely convergence result is the optimal solution of red filter parameter;

(7) respectively above-mentioned steps (3) ~ (6), wherein λ is repeated to yellow, green, blue filter ₀, σ ₀constraints identical; Export the optimum results of multiple color optical filtering parameter.

The parameter optimization that pass-band performance is the optical filtering meeting Lorentzian can be realized by above-mentioned steps.

Core concept of the present invention be each coloured light between cross jamming minimum to be equivalent to each coloured light maximum at the signal interference ratio of receiving terminal, be target function with each coloured light at the signal interference ratio of receiving terminal, thus provide possibility for analysis and solution quantitatively; In solution procedure, due to directly comparatively difficult to polytomy variable optimization, the solution procedure proposed here is: first fix a variable, optimize another one variable under constraints, carries out successively taking turns iteration more.This mode that solves can restrain rapidly and accurately, and convergence result is hardly by the impact of iterative initial value.

Beneficial effect: the optical filtering parameter optimization method based on visible light communication that the present invention proposes, preferably optical filtering parameter can be designed, reduce the cross jamming between each coloured light of receiving terminal as much as possible, the optical filtering that can go out be applicable to polychromatic light communication for actual production provides guidance.

Accompanying drawing explanation

Fig. 1 is FB(flow block) of the present invention;

Fig. 2 is the spectrum with Gaussian function fitting LZ4-00MA00 model four look LED;

Fig. 3 is the spectrum with Lorentzian matching LZ4-00MA00 model four look LED;

The optical filtering parameter optimization result of Fig. 4 to be passband be rectangle;

The optical filtering parameter optimization result of Fig. 5 to be passband be Gaussian function;

The optical filtering parameter optimization result of Fig. 6 to be passband be Lorentzian;

Embodiment:

Below in conjunction with Figure of description and embodiment, the present invention program is described in further detail.As shown in Figure 1, algorithm flow block diagram of the present invention is illustrated.In an embodiment, for four coloured light communication systems, that transmitting terminal adopts is the four look LED of LZ4-00MA00 model that LED Engin company produces, and under identical drive current 700mA, measures the spectrum of R, A, G, B tetra-kinds of coloured light respectively.Be the result adopting Gaussian function spectrum to be carried out to matching as shown in Figure 2, "-" represents the actual spectrum measured, and "---" represents the spectrum of matching, and from left to right four crests are followed successively by blueness, green, yellow, red spectrum; Be the result adopting Lorentzian spectrum to be carried out to matching as shown in Figure 3, "-" represents the actual spectrum measured, and "---" represents the spectrum of matching, and from left to right four crests are followed successively by blueness, green, yellow, red spectrum.Relatively can find, Gaussian function fitting result is out comparatively accurate, so under same condition, prioritizing selection Gaussian function carries out matching.If but with Lorentzian carry out matching can significantly simplified operation time, can suitably sacrifice fitting precision, change to do and use Lorentzian matching.

Actual test finds, for four look LED of LZ4-00MA00 model, under identical drive current 700mA, the radiant flux of R, A, G, B tetra-kinds of coloured light is respectively 428mW, 122mW, 218mW, 674mW.So in an embodiment, suppose that the total noise power of receiving terminal is 10mW.For the spectrum amplitude of bias light, can be assumed to equally distributed, the present embodiment is not having bias light and is having spectrum amplitude to be that the situation of the bias light of 0.5mW/nm calculates respectively.Provide below 3 specific embodiments respectively with pass-band performance be rectangle, the optical filtering of gaussian sum Lorentz calculates for 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:

S _r(λ)＝a ₁exp[-(λ-λ ₁) ²/σ ₁ ²]

S _a(λ)＝a ₂exp[-(λ-λ ₂) ²/σ ₂ ²]

S _g(λ)＝a ₃exp[-(λ-λ ₃) ²/σ ₃ ²]

S _b(λ)＝a ₄exp[-(λ-λ ₄) ²/σ ₄ ²]

The result obtained with matlab fitting tool is:

S _r(λ)＝23.86exp[-(λ-630.5) ²/11.6 ²]

S _a(λ)＝7.177exp[-(λ-599) ²/11.6 ²]

S _g(λ)＝4.734exp[-(λ-523.7) ²/27.38 ²]

S _b(λ)＝28exp[-(λ-453.3) ²/14.3 ²]

(2) spectral function (supposing that the spectrum amplitude of bias light is uniform here) of bias light:

Get S respectively _back(λ)=P=0 and S _back(λ)=P=0.5mW/nm

The total noise power (comprising Johnson noise, thermal noise etc.) of receiving terminal: N _t=10mW

(3) optical filtering pass-band performance is rectangle, assuming that right boundary wavelength is α, β;

(4) determine the signal interference ratio of assorted optical receiving end, be expressed as follows (for ruddiness, lower same)

Defining integration function $Q_r\left(\mathrm{\&alpha;}\right)={\&Integral;}_{\mathrm{\&alpha;}}^{\&infin;}{S}_r\left(\mathrm{\&lambda;}\right)\mathrm{d\&lambda;}={\&Integral;}_{\mathrm{\&alpha;}}^{\&infin;}{a}_1\exp [-{(\mathrm{\&lambda;}-{\mathrm{\&lambda;}}_1)}^2/{{\mathrm{\&sigma;}}_1}^2]\mathrm{d\&lambda;}=\frac{a_1{\mathrm{\&sigma;}}_1\sqrt{\mathrm{\&pi;}}}{2}\mathrm{erfc}\left(\frac{\mathrm{\&alpha;}-{\mathrm{\&lambda;}}_1}{{\mathrm{\&lambda;}}_1}\right)$

$\mathrm{SINR}=\frac{S}{I+N_t}=\frac{{[Q_r\left(\mathrm{\&alpha;}\right)-Q_r\left(\mathrm{\&beta;}\right)]}^2}{[Q_b\left(\mathrm{\&alpha;}\right)-Q_b\left(\mathrm{\&beta;}\right)+Q_a\left(\mathrm{\&alpha;}\right)-Q_b\left(\mathrm{\&beta;}\right)+Q_g\left(\mathrm{\&alpha;}\right)-Q_g\left(\mathrm{\&beta;}\right)+Q_{\mathrm{back}}\left(\mathrm{\&alpha;}\right)-Q_{\mathrm{back}}\left(\mathrm{\&beta;}\right){]}^2+{N_t}^2}$

Q function is brought in SINR function, and the result obtained is as follows:

$\begin{array}{c}\mathrm{SINR}=\frac{S}{I+N_t}=\frac{{[Q_r\left(\mathrm{\&alpha;}\right)-Q_r\left(\mathrm{\&beta;}\right)]}^2}{{[Q_b\left(\mathrm{\&alpha;}\right)-Q_b\left(\mathrm{\&beta;}\right)+Q_a\left(\mathrm{\&alpha;}\right)-Q_a\left(\mathrm{\&beta;}\right)+Q_g\left(\mathrm{\&alpha;}\right)-Q_g\left(\mathrm{\&beta;}\right)+Q_{\mathrm{back}}\left(\mathrm{\&alpha;}\right)-Q_{\mathrm{back}}\left(\mathrm{\&beta;}\right)]}^2+{N_t}^2}\\ =\frac{{[a_1{\mathrm{\&sigma;}}_1\mathrm{erfc}\left(\frac{\mathrm{\&alpha;}-{\mathrm{\&lambda;}}_1}{{\mathrm{\&sigma;}}_1}\right)-a_1{\mathrm{\&sigma;}}_1\mathrm{erfc}\left(\frac{\mathrm{\&beta;}-{\mathrm{\&lambda;}}_1}{{\mathrm{\&sigma;}}_1}\right)]}^2}{{[a_2{\mathrm{\&sigma;}}_2\mathrm{erfc}\left(\frac{\mathrm{\&alpha;}-{\mathrm{\&lambda;}}_2}{{\mathrm{\&sigma;}}_2}\right)-a_2{\mathrm{\&sigma;}}_2\mathrm{erfc}\left(\frac{\mathrm{\&beta;}-{\mathrm{\&lambda;}}_2}{{\mathrm{\&sigma;}}_2}\right)+a_3{\mathrm{\&sigma;}}_3\mathrm{erfc}\left(\frac{\mathrm{\&alpha;}-{\mathrm{\&lambda;}}_3}{{\mathrm{\&sigma;}}_3}\right)-a_3{\mathrm{\&sigma;}}_3\mathrm{erfc}\left(\frac{\mathrm{\&beta;}-{\mathrm{\&lambda;}}_3}{{\mathrm{\&sigma;}}_3}\right)+a_4{\mathrm{\&sigma;}}_4\mathrm{erfc}\left(\frac{\mathrm{\&alpha;}-{\mathrm{\&lambda;}}_4}{{\mathrm{\&sigma;}}_4}\right)-a_4{\mathrm{\&sigma;}}_4\mathrm{erfc}\left(\frac{\mathrm{\&beta;}-{\mathrm{\&lambda;}}_4}{{\mathrm{\&sigma;}}_4}\right)+P(\mathrm{\&beta;}-\mathrm{\&alpha;})]}^2+\frac{{{4N}_t}^2}{\mathrm{\&pi;}}}\end{array}$

(5) SINR differentiate: in order to derive conveniently, order

$A=a_1{\mathrm{\&sigma;}}_1\mathrm{erfc}\left(\frac{\mathrm{\&alpha;}-{\mathrm{\&lambda;}}_1}{{\mathrm{\&sigma;}}_1}\right)-a_1{\mathrm{\&sigma;}}_1\mathrm{erfc}\left(\frac{\mathrm{\&beta;}-{\mathrm{\&lambda;}}_1}{{\mathrm{\&sigma;}}_1}\right)$

$B=a_2{\mathrm{\&sigma;}}_2\mathrm{erfc}\left(\frac{\mathrm{\&alpha;}-{\mathrm{\&lambda;}}_2}{{\mathrm{\&sigma;}}_2}\right)-a_2{\mathrm{\&sigma;}}_2\mathrm{erfc}\left(\frac{\mathrm{\&beta;}-{\mathrm{\&lambda;}}_2}{{\mathrm{\&sigma;}}_2}\right)+a_3{\mathrm{\&sigma;}}_3\mathrm{erfc}\left(\frac{\mathrm{\&alpha;}-{\mathrm{\&lambda;}}_3}{{\mathrm{\&sigma;}}_3}\right)-a_3{\mathrm{\&sigma;}}_3\mathrm{erfc}\left(\frac{\mathrm{\&beta;}-{\mathrm{\&lambda;}}_3}{{\mathrm{\&sigma;}}_3}\right)+a_4{\mathrm{\&sigma;}}_4\mathrm{erfc}\left(\frac{\mathrm{\&alpha;}-{\mathrm{\&lambda;}}_4}{{\mathrm{\&sigma;}}_1}\right)-a_4{\mathrm{\&sigma;}}_4\mathrm{erfc}\left(\frac{\mathrm{\&beta;}-{\mathrm{\&lambda;}}_4}{{\mathrm{\&sigma;}}_4}\right)+P(\mathrm{\&beta;}-\mathrm{\&alpha;})$

Then $\mathrm{SINR}=\frac{A^2}{B^2+{4N}_t^2/\mathrm{\&pi;}}$

Ask local derviation to α, β respectively, result is as follows:

$\frac{\&PartialD;\mathrm{SINR}}{\&PartialD;\mathrm{\&alpha;}}=\frac{2A\&CenterDot;\frac{\&PartialD;A}{\&PartialD;\mathrm{\&alpha;}}\&CenterDot;(B^2+4N_t^2/\mathrm{\&pi;})-A^2\&CenterDot;2B\&CenterDot;\frac{\&PartialD;B}{\&PartialD;\mathrm{\&alpha;}}}{{(B^2+{4N}_t^2/\mathrm{\&pi;})}^2}=0\&DoubleLeftRightArrow;\frac{\&PartialD;A}{\&PartialD;\mathrm{\&alpha;}}\&CenterDot;(B^2+{4N}_t^2/\mathrm{\&pi;})=A\&CenterDot;B\&CenterDot;\frac{\&PartialD;B}{\&PartialD;\mathrm{\&alpha;}}$

$\frac{\&PartialD;\mathrm{SINR}}{\&PartialD;\mathrm{\&beta;}}=\frac{2A\&CenterDot;\frac{\&PartialD;A}{\&PartialD;\mathrm{\&beta;}}\&CenterDot;(B^2+4N_t^2/\mathrm{\&pi;})-A^2\&CenterDot;2B\&CenterDot;\frac{\&PartialD;B}{\&PartialD;\mathrm{\&beta;}}}{{(B^2+{4N}_t^2/\mathrm{\&pi;})}^2}=0\&DoubleLeftRightArrow;\frac{\&PartialD;A}{\&PartialD;\mathrm{\&beta;}}\&CenterDot;(B^2+{4N}_t^2/\mathrm{\&pi;})=A\&CenterDot;B\&CenterDot;\frac{\&PartialD;B}{\&PartialD;\mathrm{\&beta;}}$

According to $\frac{\&PartialD;\mathrm{erfc}\left(\mathrm{\&alpha;}\right)}{\&PartialD;\mathrm{\&alpha;}}=-\frac{2}{\sqrt{\mathrm{\&pi;}}}\exp (-{\mathrm{\&alpha;}}^2),$ Abbreviation is arranged to local derviation result:

$\begin{array}{c}\frac{\&PartialD;\mathrm{SINR}}{\&PartialD;\mathrm{\&alpha;}}=0\&DoubleLeftRightArrow;\\ a_1\exp [-{(\mathrm{\&alpha;}-{\mathrm{\&lambda;}}_1)}^2/{{\mathrm{\&sigma;}}_1}^2]\&CenterDot;(B^2+4N_t^2/\mathrm{\&pi;})-\\ \mathrm{AB}\left(a_2\exp \right[-{(\mathrm{\&alpha;}-{\mathrm{\&lambda;}}_2)}^2/{{\mathrm{\&sigma;}}_2}^2]+a_3\exp [-{(\mathrm{\&alpha;}-{\mathrm{\&lambda;}}_3)}^2/{{\mathrm{\&sigma;}}_3}^2]+a_4\exp [-{(\mathrm{\&alpha;}-{\mathrm{\&lambda;}}_4)}^2/{{\mathrm{\&sigma;}}_4}^2]+\frac{\sqrt{\mathrm{\&pi;}}}{2}P)=0\end{array}---\left(1\right)$

$\begin{array}{c}\frac{\&PartialD;\mathrm{SINR}}{\&PartialD;\mathrm{\&beta;}}=0\&DoubleLeftRightArrow;\\ a_1\exp [-{(\mathrm{\&beta;}-{\mathrm{\&lambda;}}_1)}^2/{{\mathrm{\&sigma;}}_1}^2]\&CenterDot;(B^2+4N_t^2/\mathrm{\&pi;})-\\ \mathrm{AB}\left(a_2\exp \right[-{(\mathrm{\&beta;}-{\mathrm{\&lambda;}}_2)}^2/{{\mathrm{\&sigma;}}_2}^2]+a_3\exp [-{(\mathrm{\&beta;}-{\mathrm{\&lambda;}}_3)}^2/{{\mathrm{\&sigma;}}_3}^2]+a_4\exp [-{(\mathrm{\&beta;}-{\mathrm{\&lambda;}}_4)}^2/{{\mathrm{\&sigma;}}_4}^2]+\frac{\sqrt{\mathrm{\&pi;}}}{2}P)=0\end{array}---\left(2\right)$

(6) initialization α, β.First preset parameter β Optimal Parameters α, obtains in the solution meeting the α under constraints according to local derviation formula (1); Then upgrade the value of α, fixing α optimizes β, obtains in the solution meeting the β under constraints according to local derviation formula (2).Carry out successively taking turns iteration more.

(7) respectively above-mentioned steps (4) ~ (6) are repeated to the optical filtering of each color, export the convergence optimum results of multiple color optical filtering parameter.

As shown in Figure 4, "---" represents the condition of light of having powerful connections, " ... " represent the condition without bias light, "-" represents actual spectrum, and from left to right four crests are followed successively by blueness, green, yellow, red spectrum.Iteration result is:

As the spectral function S of bias light _back(λ) when=0, iteration convergence in

	Left margin (nm)	Right margin (nm)
			Red	616	700
Yellow	579	611
			Green	484	575
Blue	380	476

As the spectral function S of bias light _back(λ)=0.5mW/nm time, iteration convergence in

	Left margin (nm)	Right margin (nm)
			Red	621	641
Yellow	588	607
			Green	506	541
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:

S _r(λ)＝a ₁exp[-(λ-λ ₁) ²/σ ₁ ²]

S _a(λ)＝a ₂exp[-(λ-λ ₂) ²/σ ₂ ²]

S _g(λ)＝a ₃exp[-(λ-λ ₃) ²/σ ₃ ²]

S _b(λ)＝a ₄exp[-(λ-λ ₄) ²/σ ₄ ²]

The result obtained with matlab fitting tool is:

S _r(λ)＝23.86exp[-(λ-630.5) ²/11.6 ²]

S _a(λ)＝7.177exp[-(λ-599) ²/11.6 ²]

S _g(λ)＝4.734exp[-(λ-523.7) ²/27.38 ²]

S _b(λ)＝28exp[-(λ-453.3) ²/14.3 ²]

(2) spectral function (supposing that the spectrum amplitude of bias light is uniform here) of bias light:

Get S respectively _back(λ)=P=0 and S _back(λ)=P=0.5mW/nm

The total noise power (comprising Johnson noise, thermal noise etc.) of receiving terminal: N _t=10mW

(3) pass-band performance of optical filtering is Gauss, and expression formula is F (λ)=exp [-(λ-λ ₀) ²/ σ ₀ ²]

(4) determine the signal interference ratio of assorted optical receiving end, be expressed as follows (for ruddiness, lower same)

$\mathrm{SINR}=\frac{S}{I+N_t}=\frac{{(\&Integral;{\mathrm{FS}}_r\mathrm{d\&lambda;})}^2}{{({\&Integral;\mathrm{FS}}_a\mathrm{d\&lambda;}+{\&Integral;\mathrm{FS}}_g\mathrm{d\&lambda;}+{\&Integral;\mathrm{FS}}_b\mathrm{d\&lambda;}+{\&Integral;\mathrm{FS}}_{\mathrm{back}}\mathrm{d\&lambda;})}^2+{N_t}^2}$

Due to ${\&Integral;\mathrm{FS}}_r\left(\mathrm{\&lambda;}\right)\mathrm{d\&lambda;}=\&Integral;\exp [-{(\mathrm{\&lambda;}-{\mathrm{\&lambda;}}_0)}^2/{{\mathrm{\&sigma;}}_0}^2]\&CenterDot;a_1\exp [-{(\mathrm{\&lambda;}-{\mathrm{\&lambda;}}_1)}^2/{{\mathrm{\&sigma;}}_1}^2]\mathrm{d\&lambda;}$

$=a_1\sqrt{\mathrm{\&pi;}}/\sqrt{1/{\mathrm{\&sigma;}}_0^2+1/{\mathrm{\&sigma;}}_1^2}\exp [-{({\mathrm{\&lambda;}}_1-{\mathrm{\&lambda;}}_0)}^2/({\mathrm{\&sigma;}}_0^2+{\mathrm{\&sigma;}}_1^2)]$

Have again simultaneously

${\&Integral;\mathrm{FS}}_{\mathrm{bacl}}\mathrm{d\&lambda;}=\exp [-{\left({\mathrm{\&lambda;}-\mathrm{\&lambda;}}_0\right)}^2/{{\mathrm{\&sigma;}}_0}^2]\&CenterDot;\mathrm{Fd\&lambda;}=P\&CenterDot;{\mathrm{\&sigma;}}_0\sqrt{\mathrm{\&pi;}}$

The result of integral function is brought in SINR function, obtains as follows:

$\begin{array}{c}\mathrm{SINR}=\frac{S}{I+N_t}=\frac{{(\&Integral;{\mathrm{FS}}_r\mathrm{d\&lambda;})}^2}{{({\&Integral;\mathrm{FS}}_a\mathrm{d\&lambda;}+{\&Integral;\mathrm{FS}}_g\mathrm{d\&lambda;}+{\&Integral;\mathrm{FS}}_b\mathrm{d\&lambda;}+{\&Integral;\mathrm{FS}}_{\mathrm{back}}\mathrm{d\&lambda;})}^2+{N_t}^2}\\ ={\left(\frac{a_1}{\sqrt{1/{\mathrm{\&sigma;}}_0^2+1/{\mathrm{\&sigma;}}_1^2}}\exp \right[-{({\mathrm{\&lambda;}}_1-{\mathrm{\&lambda;}}_0)}^2/({\mathrm{\&sigma;}}_0^2+{\mathrm{\&sigma;}}_1^2)\left]\right)}^2\left(\right(\frac{a_2}{\sqrt{1/{\mathrm{\&sigma;}}_0^2+1/{\mathrm{\&sigma;}}_2^2}}\exp [-{({\mathrm{\&lambda;}}_2-{\mathrm{\&lambda;}}_0)}^2/({\mathrm{\&sigma;}}_0^2+{\mathrm{\&sigma;}}_2^2)]\\ +\frac{a_3}{\sqrt{1/{\mathrm{\&sigma;}}_0^2+1/{\mathrm{\&sigma;}}_3^2}}\exp [-{({\mathrm{\&lambda;}}_3-{\mathrm{\&lambda;}}_0)}^2/({\mathrm{\&sigma;}}_0^2+{\mathrm{\&sigma;}}_3^2)]+\frac{a_4}{\sqrt{1/{\mathrm{\&sigma;}}_0^2+1/{\mathrm{\&sigma;}}_4^2}}\exp [-{({\mathrm{\&lambda;}}_4-{\mathrm{\&lambda;}}_0)}^2/({\mathrm{\&sigma;}}_0^2+{\mathrm{\&sigma;}}_4^2)]+P\&CenterDot;{\mathrm{\&sigma;}}_0{)}^2+\frac{N_t^2}{\mathrm{\&pi;}})\end{array}$

(5) SINR differentiate: in order to derive conveniently, order

$A=\frac{a_1}{\sqrt{1/{\mathrm{\&sigma;}}_0^2+1/{\mathrm{\&sigma;}}_1^2}}\exp [-{({\mathrm{\&lambda;}}_1-{\mathrm{\&lambda;}}_0)}^2/({\mathrm{\&sigma;}}_0^2+{\mathrm{\&sigma;}}_1^2)],B_2=\frac{a_2}{\sqrt{1/{\mathrm{\&sigma;}}_0^2+1/{\mathrm{\&sigma;}}_2^2}}\exp [-{({\mathrm{\&lambda;}}_2-{\mathrm{\&lambda;}}_0)}^2/({\mathrm{\&sigma;}}_0^2+{\mathrm{\&sigma;}}_2^2)]$

$B_3=\frac{a_3}{\sqrt{1/{\mathrm{\&sigma;}}_0^2+1/{\mathrm{\&sigma;}}_3^2}}\exp [-{({\mathrm{\&lambda;}}_3-{\mathrm{\&lambda;}}_0)}^2/({\mathrm{\&sigma;}}_0^2+{\mathrm{\&sigma;}}_3^2)],B_4=\frac{a_4}{\sqrt{1/{\mathrm{\&sigma;}}_0^2+1/{\mathrm{\&sigma;}}_4^2}}\exp [-{({\mathrm{\&lambda;}}_4-{\mathrm{\&lambda;}}_0)}^2/({\mathrm{\&sigma;}}_0^2+{\mathrm{\&sigma;}}_4^2)]$

B＝B ₂+B ₃+B ₄+P·σ ₀

Then $\mathrm{SINR}=\frac{A^2}{B^2+N_t^2/\mathrm{\&pi;}}$

Respectively to λ ₀, σ ₀ask local derviation, result is as follows:

$\frac{\&PartialD;\mathrm{SINR}}{{\&PartialD;\mathrm{\&lambda;}}_0}=\frac{2A\&CenterDot;\frac{\&PartialD;A}{{\&PartialD;\mathrm{\&lambda;}}_0}\&CenterDot;(B^2+N_t^2/\mathrm{\&pi;})-A^2\&CenterDot;2B\&CenterDot;\frac{\&PartialD;B}{{\&PartialD;\mathrm{\&lambda;}}_0}}{{(B^2+N_t^2/\mathrm{\&pi;})}^2}=0\&DoubleLeftRightArrow;\frac{\&PartialD;A}{{\&PartialD;\mathrm{\&lambda;}}_0}\&CenterDot;(B^2+N_t^2/\mathrm{\&pi;})=A\&CenterDot;B\&CenterDot;\frac{\&PartialD;B}{{\&PartialD;\mathrm{\&lambda;}}_0}$

$\frac{\&PartialD;\mathrm{SINR}}{{\&PartialD;\mathrm{\&sigma;}}_0}=\frac{2A\&CenterDot;\frac{\&PartialD;A}{{\&PartialD;\mathrm{\&sigma;}}_0}\&CenterDot;(B^2+N_t^2/\mathrm{\&pi;})-A^2\&CenterDot;2B\&CenterDot;\frac{\&PartialD;B}{{\&PartialD;\mathrm{\&sigma;}}_0}}{{(B^2+N_t^2/\mathrm{\&pi;})}^2}=0\&DoubleLeftRightArrow;\frac{\&PartialD;A}{{\&PartialD;\mathrm{\&sigma;}}_0}\&CenterDot;(B^2+N_t^2/\mathrm{\&pi;})=A\&CenterDot;B\&CenterDot;\frac{\&PartialD;B}{{\&PartialD;\mathrm{\&sigma;}}_0}$

Arrange abbreviation to local derviation result to obtain:

$\frac{\&PartialD;\mathrm{SINR}}{{\&PartialD;\mathrm{\&lambda;}}_0}=0\&DoubleLeftRightArrow;\frac{{\mathrm{\&lambda;}}_1-{\mathrm{\&lambda;}}_0}{{\mathrm{\&sigma;}}_0^2+{\mathrm{\&sigma;}}_1^2}\&CenterDot;(B^2+N_t^2/\mathrm{\&pi;})-B\&CenterDot;(B_2\&CenterDot;\frac{{\mathrm{\&lambda;}}_2-{\mathrm{\&lambda;}}_0}{{\mathrm{\&sigma;}}_0^2+{\mathrm{\&sigma;}}_2^2}+B_3\&CenterDot;\frac{{\mathrm{\&lambda;}}_3-{\mathrm{\&lambda;}}_0}{{\mathrm{\&sigma;}}_0^2+{\mathrm{\&sigma;}}_3^2}+B_4\&CenterDot;\frac{{\mathrm{\&lambda;}}_4-{\mathrm{\&lambda;}}_0}{{\mathrm{\&sigma;}}_0^2+{\mathrm{\&sigma;}}_4^2})=0$

$\begin{array}{c}\frac{\&PartialD;\mathrm{SINR}}{{\&PartialD;\mathrm{\&sigma;}}_0}=0\&DoubleLeftRightArrow;(\frac{1}{{\mathrm{\&sigma;}}_0}-\frac{{\mathrm{\&sigma;}}_0}{{\mathrm{\&sigma;}}_0^2+{\mathrm{\&sigma;}}_1^2}+\frac{{2\mathrm{\&sigma;}}_0{({\mathrm{\&lambda;}}_1-{\mathrm{\&lambda;}}_0)}^2}{{({\mathrm{\&sigma;}}_0^2+{\mathrm{\&sigma;}}_1^2)}^2})\&CenterDot;(B^2+N_t^2/\mathrm{\&pi;})-\\ B\&CenterDot;(B_2\&CenterDot;(\frac{1}{{\mathrm{\&sigma;}}_0}-\frac{{\mathrm{\&sigma;}}_0}{{\mathrm{\&sigma;}}_0^2+{\mathrm{\&sigma;}}_2^2}+\frac{{2\mathrm{\&sigma;}}_0{({\mathrm{\&lambda;}}_2-{\mathrm{\&lambda;}}_0)}^2}{{({\mathrm{\&sigma;}}_0^2+{\mathrm{\&sigma;}}_2^2)}^2})+B_3\&CenterDot;(\frac{1}{{\mathrm{\&sigma;}}_0}-\frac{{\mathrm{\&sigma;}}_0}{{\mathrm{\&sigma;}}_0^2+{\mathrm{\&sigma;}}_3^2}+\frac{{2\mathrm{\&sigma;}}_0{({\mathrm{\&lambda;}}_3-{\mathrm{\&lambda;}}_0)}^2}{{({\mathrm{\&sigma;}}_0^2+{\mathrm{\&sigma;}}_3^2)}^2})+\\ B_4\&CenterDot;(\frac{1}{{\mathrm{\&sigma;}}_0}-\frac{{\mathrm{\&sigma;}}_0}{{\mathrm{\&sigma;}}_0^2+{\mathrm{\&sigma;}}_4^2}+\frac{{2\mathrm{\&sigma;}}_0{({\mathrm{\&lambda;}}_4-{\mathrm{\&lambda;}}_0)}^2}{{({\mathrm{\&sigma;}}_0^2+{\mathrm{\&sigma;}}_4^2)}^2})+P)=0\end{array}$

(6) initialization λ ₀, σ ₀.First σ is fixed ₀parameter optimization parameter lambda ₀, obtain according to local derviation formula (1) and meeting the λ under constraints ₀solution; Then λ is upgraded ₀value, fixing λ ₀optimize σ ₀, obtain according to local derviation formula (2) and meeting the σ under constraints ₀solution.Carry out successively taking turns iteration more.

(7) respectively above-mentioned steps (4) ~ (6) are repeated to the optical filtering of each color, export the convergence optimum results of multiple color optical filtering parameter.

As shown in Figure 5, "---" represents the condition of light of having powerful connections, " ... " represent the condition without bias light, "-" represents actual spectrum, and from left to right four crests are followed successively by blueness, green, yellow, red spectrum.Iteration result is:

As the spectral function S of bias light _back(λ) when=0, iteration convergence in

	Centre wavelength (nm)	Variance (nm)
			Red	633	14
Yellow	596	11.5
			Green	528	27.5
Blue	450	24.5

As the spectral function S of bias light _back(λ)=0.5mW/nm time, iteration convergence in

	Centre wavelength (nm)	Variance (nm)
			Red	632	9.5
Yellow	597	8.5
			Green	524	17.5

Blue

453

12

Embodiment 3: pass-band performance is the optical filtering of Lorentz

The expression formula of (1) four color light source Lorentzian matching is as follows:

(calculate for the ease of deriving, light source light spectrum uses Lorentzian matching here, can accept in the scope that error allows.)

S _r(λ)＝a ₁/(1+(λ-λ ₁) ²/σ ₁ ²)

S _a(λ)＝a ₂/(1+(λ-λ ₂) ²/σ ₂ ²)

S _g(λ)＝a ₃/(1+(λ-λ ₃) ²/σ ₃ ²)

S _b(λ)＝a ₄/(1+(λ-λ ₄) ²/σ ₄ ²)

The result obtained with matlab fitting tool is:

S _r(λ)＝26.56/(1+(λ-630.9) ²/7.507 ²)

S _a(λ)＝8.033/(1+(λ-599.2) ²/7.135 ²)

S _g(λ)＝5.214/(1+(λ-523.1) ²/17.82 ²)

S _b(λ)＝31.36/(1+(λ-453.1) ²/9.132 ²)

(2) spectral function (supposing that the spectrum amplitude of bias light is uniform here) of bias light:

Get S respectively _back(λ)=P=0 and S _back(λ)=P=0.5mW/nm

The total noise power (comprising Johnson noise, thermal noise etc.) of receiving terminal: N _t=10mW

(3) pass-band performance of optical filtering is Lorentz, and pass-band performance function is F (λ)=1/ (1+ (λ-λ ₀) ²/ σ ₀ ²) (4) determine assorted optical receiving end signal interference ratio, be expressed as follows (for ruddiness, lower with)

$\begin{array}{c}\mathrm{SINR}=\frac{S}{I+N_t}=\frac{{\left({\&Integral;\mathrm{FS}}_r\mathrm{d\&lambda;}\right)}^2}{{(\&Integral;{\mathrm{FS}}_a\mathrm{d\&lambda;}+\&Integral;{\mathrm{FS}}_g\mathrm{d\&lambda;}+\&Integral;{\mathrm{FS}}_b\mathrm{d\&lambda;}+\&Integral;{\mathrm{FS}}_{\mathrm{back}}\mathrm{d\&lambda;})}^2+{N_t}^2}\\ \&Integral;{\mathrm{FS}}_r\left(\mathrm{\&lambda;}\right)\mathrm{d\&lambda;}=\&Integral;1/(1+{\left({\mathrm{\&lambda;}-\mathrm{\&lambda;}}_0\right)}^2/{{\mathrm{\&sigma;}}_0}^2)\&CenterDot;a_1/(1+{(\mathrm{\&lambda;}-{\mathrm{\&lambda;}}_1)}^2/{{\mathrm{\&sigma;}}_1}^2)\mathrm{d\&lambda;}\\ =\frac{a_1{\mathrm{\&sigma;}}_0{\mathrm{\&sigma;}}_1({\mathrm{\&sigma;}}_0+{\mathrm{\&sigma;}}_1)\mathrm{\&pi;}}{{({\mathrm{\&lambda;}}_0-{\mathrm{\&lambda;}}_1)}^2+{({\mathrm{\&sigma;}}_0+{\mathrm{\&sigma;}}_1)}^2}\end{array}$

Have again simultaneously

∫FS _backdλ＝∫1/(1+(λ-λ ₀) ²/σ ₀ ²)·Pdλ＝P·σ ₀π

The result of integral function is brought in SINR function, obtains as follows:

$\begin{array}{c}\mathrm{SINR}=\frac{S}{I+N_t}=\frac{{\left({\&Integral;\mathrm{FS}}_r\mathrm{d\&lambda;}\right)}^2}{{({\&Integral;\mathrm{FS}}_a\mathrm{d\&lambda;}+{\&Integral;\mathrm{FS}}_g\mathrm{d\&lambda;}+{\&Integral;\mathrm{FS}}_b\mathrm{d\&lambda;}+{\&Integral;\mathrm{FS}}_{\mathrm{bacl}}\mathrm{d\&lambda;})}^2+{N_t}^2}\\ ={\left(\frac{a_1{\mathrm{\&sigma;}}_0{\mathrm{\&sigma;}}_1({\mathrm{\&sigma;}}_0+{\mathrm{\&sigma;}}_1)}{{({\mathrm{\&lambda;}}_0-{\mathrm{\&lambda;}}_1)}^2+{({\mathrm{\&sigma;}}_0+{\mathrm{\&sigma;}}_1)}^2}\right)}^2/({(\frac{a_2{\mathrm{\&sigma;}}_0{\mathrm{\&sigma;}}_2({\mathrm{\&sigma;}}_0+{\mathrm{\&sigma;}}_2)}{{({\mathrm{\&lambda;}}_0-{\mathrm{\&lambda;}}_2)}^2+{({\mathrm{\&sigma;}}_0+{\mathrm{\&sigma;}}_2)}^2}+\frac{a_3{\mathrm{\&sigma;}}_0{\mathrm{\&sigma;}}_3({\mathrm{\&sigma;}}_0+{\mathrm{\&sigma;}}_3)}{{({\mathrm{\&lambda;}}_0-{\mathrm{\&lambda;}}_3)}^2+{({\mathrm{\&sigma;}}_0+{\mathrm{\&sigma;}}_3)}^2}+\frac{a_4{\mathrm{\&sigma;}}_0{\mathrm{\&sigma;}}_4({\mathrm{\&sigma;}}_0+{\mathrm{\&sigma;}}_4)}{{({\mathrm{\&lambda;}}_0-{\mathrm{\&lambda;}}_4)}^2+{({\mathrm{\&sigma;}}_0+{\mathrm{\&sigma;}}_4)}^2}+P\&CenterDot;{\mathrm{\&sigma;}}_0)}^2+\frac{N_t^2}{{\mathrm{\&pi;}}^2})\end{array}$

(5) SINR differentiate: in order to derive conveniently, order

$A=\frac{a_1{\mathrm{\&sigma;}}_0{\mathrm{\&sigma;}}_1({\mathrm{\&sigma;}}_0+{\mathrm{\&sigma;}}_1)}{{({\mathrm{\&lambda;}}_0-{\mathrm{\&lambda;}}_1)}^2+{({\mathrm{\&sigma;}}_0+{\mathrm{\&sigma;}}_1)}^2},B_2=\frac{a_2{\mathrm{\&sigma;}}_0{\mathrm{\&sigma;}}_2({\mathrm{\&sigma;}}_0+{\mathrm{\&sigma;}}_2)}{{({\mathrm{\&lambda;}}_0-{\mathrm{\&lambda;}}_2)}^2+{({\mathrm{\&sigma;}}_0+{\mathrm{\&sigma;}}_2)}^2}$

$B_3=\frac{a_3{\mathrm{\&sigma;}}_0{\mathrm{\&sigma;}}_3({\mathrm{\&sigma;}}_0+{\mathrm{\&sigma;}}_3)}{{({\mathrm{\&lambda;}}_0-{\mathrm{\&lambda;}}_3)}^2+{({\mathrm{\&sigma;}}_0+{\mathrm{\&sigma;}}_3)}^2},B_4=\frac{a_4{\mathrm{\&sigma;}}_0{\mathrm{\&sigma;}}_4({\mathrm{\&sigma;}}_0+{\mathrm{\&sigma;}}_4)}{{({\mathrm{\&lambda;}}_0-{\mathrm{\&lambda;}}_4)}^2+{({\mathrm{\&sigma;}}_0+{\mathrm{\&sigma;}}_4)}^2}$

B＝B ₂+B ₃+B ₄+P·σ ₀

Then $\mathrm{SINR}=\frac{A^2}{B^2+N_t^2/{\mathrm{\&pi;}}^2}$

Respectively to λ ₀, σ ₀ask local derviation, result is as follows:

$\frac{\&PartialD;\mathrm{SINR}}{{\&PartialD;\mathrm{\&lambda;}}_0}=\frac{2A\&CenterDot;\frac{\&PartialD;A}{{\&PartialD;\mathrm{\&lambda;}}_0}\&CenterDot;(B^2+N_t^2/\mathrm{\&pi;})-A^2\&CenterDot;2B\&CenterDot;\frac{\&PartialD;B}{{\&PartialD;\mathrm{\&lambda;}}_0}}{{(B^2+N_t^2/\mathrm{\&pi;})}^2}=0\&DoubleLeftRightArrow;\frac{\&PartialD;A}{{\&PartialD;\mathrm{\&lambda;}}_0}\&CenterDot;(B^2+N_t^2/\mathrm{\&pi;})=A\&CenterDot;B\&CenterDot;\frac{\&PartialD;B}{{\&PartialD;\mathrm{\&lambda;}}_0}$

$\frac{\&PartialD;\mathrm{SINR}}{{\&PartialD;\mathrm{\&sigma;}}_0}=\frac{2A\&CenterDot;\frac{\&PartialD;A}{{\&PartialD;\mathrm{\&sigma;}}_0}\&CenterDot;(B^2+N_t^2/\mathrm{\&pi;})-A^2\&CenterDot;2B\&CenterDot;\frac{\&PartialD;B}{{\&PartialD;\mathrm{\&sigma;}}_0}}{{(B^2+N_t^2/\mathrm{\&pi;})}^2}=0\&DoubleLeftRightArrow;\frac{\&PartialD;A}{{\&PartialD;\mathrm{\&sigma;}}_0}\&CenterDot;(B^2+N_t^2/\mathrm{\&pi;})=A\&CenterDot;B\&CenterDot;\frac{\&PartialD;B}{{\&PartialD;\mathrm{\&sigma;}}_0}$

Arrange abbreviation to local derviation result to obtain:

$\begin{array}{c}\frac{\&PartialD;\mathrm{SINR}}{{\&PartialD;\mathrm{\&lambda;}}_0}=0\&DoubleLeftRightArrow;\frac{{\mathrm{\&lambda;}}_1-{\mathrm{\&lambda;}}_0}{{({\mathrm{\&lambda;}}_0-{\mathrm{\&lambda;}}_1)}^2+{({\mathrm{\&sigma;}}_0+{\mathrm{\&sigma;}}_1)}^2}\&CenterDot;(B^2+N_t^2/{\mathrm{\&pi;}}^2)-\\ B\&CenterDot;(B_2\&CenterDot;\frac{{\mathrm{\&lambda;}}_2-{\mathrm{\&lambda;}}_0}{{({\mathrm{\&lambda;}}_0-{\mathrm{\&lambda;}}_2)}^2+{({\mathrm{\&sigma;}}_0+{\mathrm{\&sigma;}}_2)}^2}+B_3\&CenterDot;\frac{{\mathrm{\&lambda;}}_3-{\mathrm{\&lambda;}}_0}{{({\mathrm{\&lambda;}}_0-{\mathrm{\&lambda;}}_3)}^2+{({\mathrm{\&sigma;}}_0+{\mathrm{\&sigma;}}_3)}^2}+B_4\&CenterDot;\frac{{\mathrm{\&lambda;}}_4-{\mathrm{\&lambda;}}_0}{{({\mathrm{\&lambda;}}_0-{\mathrm{\&lambda;}}_4)}^2+{({\mathrm{\&sigma;}}_0+{\mathrm{\&sigma;}}_4)}^2})=0\end{array}$

$\begin{array}{c}\frac{\&PartialD;\mathrm{SINR}}{{\&PartialD;\mathrm{\&sigma;}}_0}=0\&DoubleLeftRightArrow;(\frac{{\mathrm{\&sigma;}}_1+2{\mathrm{\&sigma;}}_0}{({\mathrm{\&sigma;}}_1+{\mathrm{\&sigma;}}_0){\mathrm{\&sigma;}}_0}-\frac{2({\mathrm{\&sigma;}}_1+{\mathrm{\&sigma;}}_0)}{{({\mathrm{\&lambda;}}_0-{\mathrm{\&lambda;}}_1)}^2+{({\mathrm{\&sigma;}}_0+{\mathrm{\&sigma;}}_1)}^2})\&CenterDot;(B^2+N_t^2/{\mathrm{\&pi;}}^2)-\\ B\&CenterDot;(B_2\&CenterDot;(\frac{{\mathrm{\&sigma;}}_2+2{\mathrm{\&sigma;}}_0}{({\mathrm{\&sigma;}}_2+{\mathrm{\&sigma;}}_0){\mathrm{\&sigma;}}_0}-\frac{2({\mathrm{\&sigma;}}_2+{\mathrm{\&sigma;}}_0)}{{({\mathrm{\&lambda;}}_0-{\mathrm{\&lambda;}}_2)}^2+{({\mathrm{\&sigma;}}_0+{\mathrm{\&sigma;}}_2)}^2})+B_3\&CenterDot;(\frac{{\mathrm{\&sigma;}}_3+2{\mathrm{\&sigma;}}_0}{({\mathrm{\&sigma;}}_3+{\mathrm{\&sigma;}}_0){\mathrm{\&sigma;}}_0}-\frac{2({\mathrm{\&sigma;}}_3+{\mathrm{\&sigma;}}_0)}{{({\mathrm{\&lambda;}}_0-{\mathrm{\&lambda;}}_3)}^2+{({\mathrm{\&sigma;}}_0+{\mathrm{\&sigma;}}_3)}^2})+\\ B_4\&CenterDot;(\frac{{\mathrm{\&sigma;}}_4+{2\mathrm{\&sigma;}}_0}{({\mathrm{\&sigma;}}_4+{\mathrm{\&sigma;}}_0){\mathrm{\&sigma;}}_0}-\frac{2({\mathrm{\&sigma;}}_4+{\mathrm{\&sigma;}}_0)}{{({\mathrm{\&lambda;}}_0-{\mathrm{\&lambda;}}_4)}^2+{({\mathrm{\&sigma;}}_0+{\mathrm{\&sigma;}}_4)}^2})+P)=0\end{array}$

(6) initialization λ ₀, σ ₀.First σ is fixed ₀parameter optimization parameter lambda ₀, obtain according to local derviation formula (1) and meeting the λ under constraints ₀solution; Then λ is upgraded ₀value, fixing λ ₀optimize σ ₀, obtain according to local derviation formula (2) and meeting the σ under constraints ₀solution.Carry out successively taking turns iteration more.

(7) respectively above-mentioned steps (4) ~ (6) are repeated to the optical filtering of each color, export the convergence optimum results of multiple color optical filtering parameter.

As shown in Figure 6, "---" represents the condition of light of having powerful connections, " ... " represent the condition without bias light, "-" represents actual spectrum, and from left to right four crests are followed successively by blueness, green, yellow, red spectrum.Iteration result is:

As the spectral function S of bias light _back(λ) when=0, iteration convergence in

	Centre wavelength (nm)	Variance (nm)
			Red	632.36	4.12
Yellow	598.09	2.09
			Green	525	4.02
Blue	451	6.05

As the spectral function S of bias light _back(λ)=0.5mW/nm time, iteration convergence in

	Centre wavelength (nm)	Variance (nm)
			Red	631.77	3.15
Yellow	598.29	1.90
			Green	525	3.44
Blue	452.5	4.22

Claims (5)

1., based on a receiving terminal optical filtering parameter optimization method for visible light communication, it is characterized in that, the method comprises the steps:

(1) utilize spectrometer to measure each monochromatic spectroscopic data, carry out matching with Gaussian function or Lorentzian, obtain the fitting function of spectrum;

(2) spectral function of bias light and the total noise power of receiving terminal is determined;

(3) with each coloured light at the signal interference ratio of receiving terminal for target function, determine the constraints of optical filtering parameter simultaneously;

(4) with signal interference ratio function, local derviation is asked to each variable, and make local derviation result equal 0;

(5) each parameter of initialization optical filtering, then fixes a parameter, optimizes another one parameter under constraints, carries out successively taking turns iteration more;

(6) after iteration meets certain number of times, stop iteration, namely convergence result is the optimal solution of optical filtering parameter;

(7) respectively above-mentioned steps (3) ~ (6) are repeated to the optical filtering of each color, export the optimum results of shades of colour optical filtering parameter.

2., as claimed in claim 1 based on the optical filtering parameter optimization method of visible light communication, it is characterized in that: described overall noise comprises Johnson noise and thermal noise.

3., as claimed in claim 1 or 2 based on the optical filtering parameter optimization method of visible light communication, it is characterized in that: the pass-band performance of optical filtering is rectangle, right boundary wavelength is α, β, and described optimization method is specially:

(1) first, measure the spectroscopic data of the LED of four kinds of coloured light with spectrometer, use Gaussian function fitting respectively, expression formula is as follows:

S _r(λ)＝a ₁exp[-(λ-λ ₁) ²/σ ₁ ²]

S _a(λ)＝a ₂exp[-(λ-λ ₂) ²/σ ₂ ²]

S _g(λ)＝a ₃exp[-(λ-λ ₃) ²/σ ₃ ²]

S _b(λ)＝a ₄exp[-(λ-λ ₄) ²/σ ₄ ²]

Wherein, a ₁-a ₄, λ ₁-λ ₄, σ ₁-σ ₄being the fitting parameter of Gaussian function, is real constant; S _r(λ) be the spectral function of ruddiness, S _a(λ) be the spectral function of gold-tinted, S _g(λ) be the spectral function of green glow, S _b(λ) be the spectral function of blue light;

(2) according to the system of reality, suppose that the spectrum amplitude of bias light is equally distributed, determine the spectral function S of bias light _back(λ)=P and receiving terminal total noise power N _t, wherein P and N _tit is real constant;

(3) calculate the signal interference ratio of each coloured light of receiving terminal, the signal interference ratio of ruddiness is as follows:

$\begin{array}{c}\mathrm{SINR}=\\ \frac{[a_1{\mathrm{\&sigma;}}_1\mathrm{erfc}\left(\frac{\mathrm{\&alpha;}-{\mathrm{\&lambda;}}_1}{{\mathrm{\&sigma;}}_1}\right)-a_1{\mathrm{\&sigma;}}_1\mathrm{erfc}{\left(\frac{\mathrm{\&beta;}-{\mathrm{\&lambda;}}_1}{{\mathrm{\&sigma;}}_1}\right)]}^2}{{[a_2{\mathrm{\&sigma;}}_2\mathrm{erfc}\left(\frac{a-{\mathrm{\&lambda;}}_2}{{\mathrm{\&sigma;}}_2}\right)-a_2{\mathrm{\&sigma;}}_2\mathrm{erfc}\left(\frac{\mathrm{\&beta;}-{\mathrm{\&lambda;}}_2}{{\mathrm{\&sigma;}}_2}\right)+a_3{\mathrm{\&sigma;}}_3\mathrm{erfc}\left(\frac{\mathrm{\&alpha;}-{\mathrm{\&lambda;}}_3}{{\mathrm{\&sigma;}}_3}\right)-a_3{\mathrm{\&sigma;}}_3\mathrm{erfc}\left(\frac{\mathrm{\&beta;}-{\mathrm{\&lambda;}}_3}{{\mathrm{\&sigma;}}_3}\right)+a_4{\mathrm{\&sigma;}}_4\mathrm{erfc}\left(\frac{\mathrm{\&alpha;}-{\mathrm{\&lambda;}}_4}{{\mathrm{\&sigma;}}_4}\right)-a_4{\mathrm{\&sigma;}}_4\mathrm{erfc}\left(\frac{\mathrm{\&beta;}-{\mathrm{\&lambda;}}_4}{{\mathrm{\&sigma;}}_4}\right)+P(\mathrm{\&beta;}-\mathrm{\&alpha;})]}^2+\frac{4N_t^2}{\mathrm{\&pi;}}}\end{array}$

Constraints is: 380≤α < β≤780;

(4) ask local derviation to α, β respectively with signal interference ratio function, make local derviation result equal 0, abbreviation result is

$\begin{array}{c}\frac{\&PartialD;\mathrm{SINR}}{\&PartialD;\mathrm{\&alpha;}}=0\&DoubleLeftRightArrow;\\ a_1\exp [+{(\mathrm{\&alpha;}-{\mathrm{\&lambda;}}_1)}^2/{{\mathrm{\&sigma;}}_1}^2]\&CenterDot;(B^2+4N_t^2/\mathrm{\&pi;})-\\ \mathrm{AB}\left(a_2\exp \right[-{(\mathrm{\&alpha;}-{\mathrm{\&lambda;}}_2)}^2/{{\mathrm{\&sigma;}}_2}^2]+a_3\exp [-{(\mathrm{\&alpha;}-{\mathrm{\&lambda;}}_3)}^2/{{\mathrm{\&sigma;}}_3}^2]+a_4\exp [-{(\mathrm{\&alpha;}-{\mathrm{\&lambda;}}_4)}^2/{{\mathrm{\&sigma;}}_4}^2]+\frac{\sqrt{\mathrm{\&pi;}}}{2}P)=0\end{array}---\left(1\right)$

$\begin{array}{c}\frac{\&PartialD;\mathrm{SINR}}{\&PartialD;\mathrm{\&beta;}}=0\&DoubleLeftRightArrow;\\ a_1\exp [+{(\mathrm{\&beta;}-{\mathrm{\&lambda;}}_1)}^2/{{\mathrm{\&sigma;}}_1}^2]\&CenterDot;(B^2+4N_t^2/\mathrm{\&pi;})-\\ \mathrm{AB}\left(a_2\exp \right[-{(\mathrm{\&beta;}-{\mathrm{\&lambda;}}_2)}^2/{{\mathrm{\&sigma;}}_2}^2]+a_3\exp [-{(\mathrm{\&beta;}-{\mathrm{\&lambda;}}_3)}^2/{{\mathrm{\&sigma;}}_3}^2]+a_4\exp [-{(\mathrm{\&beta;}-{\mathrm{\&lambda;}}_4)}^2/{{\mathrm{\&sigma;}}_4}^2]+\frac{\sqrt{\mathrm{\&pi;}}}{2}P)=0\end{array}---\left(2\right)$ Wherein, $A=a_1{\mathrm{\&sigma;}}_1\mathrm{erfc}\left(\frac{\mathrm{\&alpha;}-{\mathrm{\&lambda;}}_1}{{\mathrm{\&sigma;}}_1}\right)-a_1{\mathrm{\&sigma;}}_1\mathrm{erfc}\left(\frac{\mathrm{\&beta;}-{\mathrm{\&lambda;}}_1}{{\mathrm{\&sigma;}}_1}\right)$

$B=a_2{\mathrm{\&sigma;}}_2\mathrm{erfc}\left(\frac{\mathrm{\&alpha;}-{\mathrm{\&lambda;}}_2}{{\mathrm{\&sigma;}}_2}\right)-a_2{\mathrm{\&sigma;}}_2\mathrm{erfc}\left(\frac{\mathrm{\&beta;}-{\mathrm{\&lambda;}}_2}{{\mathrm{\&sigma;}}_2}\right)+a_3{\mathrm{\&sigma;}}_3\mathrm{erfc}\left(\frac{\mathrm{\&alpha;}-{\mathrm{\&lambda;}}_3}{{\mathrm{\&sigma;}}_3}\right)-a_3{\mathrm{\&sigma;}}_3\mathrm{erfc}\left(\frac{\mathrm{\&beta;}-{\mathrm{\&lambda;}}_3}{{\mathrm{\&sigma;}}_3}\right)+a_4{\mathrm{\&sigma;}}_4\mathrm{erfc}\left(\frac{\mathrm{\&alpha;}-{\mathrm{\&lambda;}}_4}{{\mathrm{\&sigma;}}_4}\right)-a_4{\mathrm{\&sigma;}}_4\mathrm{erfc}\left(\frac{\mathrm{\&beta;}-{\mathrm{\&lambda;}}_4}{{\mathrm{\&sigma;}}_4}\right)+P(\mathrm{\&beta;}-\mathrm{\&alpha;})$

(5) initialization α, β, first preset parameter β Optimal Parameters α, obtain in the solution meeting the α under constraints according to local derviation formula (1); Then upgrade the value of α, fixing α optimizes β, obtains in the solution meeting the β under constraints, carry out successively taking turns iteration more according to local derviation formula (2);

(6) after iteration meets certain number of times, stop iteration, namely convergence result is the optimal solution of red filter parameter;

(7) repeat above-mentioned steps (3) ~ (6) to yellow, green, blue optical filtering respectively, wherein the constraints of α, β is identical; Export the optimum results of multiple color optical filtering parameter.

4., as claimed in claim 1 or 2 based on the optical filtering parameter optimization method of visible light communication, it is characterized in that: the pass-band performance of optical filtering is F (λ)=exp [-(λ-λ meeting Gaussian function ₀) ²/ σ ₀ ²], wavelength X centered by the parameter that needs are optimized ₀and variances sigma ₀, described method is specially:

(1) first, measure the spectroscopic data of the LED of four kinds of coloured light with spectrometer, use Gaussian function fitting respectively, expression formula is as follows:

S _r(λ)＝a ₁exp[-(λ-λ ₁) ²/σ ₁ ²]

S _a(λ)＝a ₂exp[-(λ-λ ₂) ²/σ ₂ ²]

S _g(λ)＝a ₃exp[-(λ-λ ₃) ²/σ ₃ ²]

S _b(λ)＝a ₄exp[-(λ-λ ₄) ²/σ ₄ ²]

Wherein, a ₁-a ₄, λ ₁-λ ₄, σ ₁-σ ₄being the fitting parameter of Gaussian function, is real constant; S _r(λ) be the spectral function of ruddiness, S _a(λ) be the spectral function of gold-tinted, S _g(λ) be the spectral function of green glow, S _b(λ) be the spectral function of blue light;

(2) according to the system of reality, suppose that the spectrum amplitude of bias light is equally distributed, determine the spectral function S of bias light _back(λ)=P and receiving terminal total noise power N _t, wherein P and N _tit is real constant;

(3) calculate the signal interference ratio of each coloured light of receiving terminal, the signal interference ratio of ruddiness is as follows:

$\begin{array}{c}\mathrm{SINR}={\left(\frac{a_1}{\sqrt{1/{\mathrm{\&sigma;}}_0^2+1/{\mathrm{\&sigma;}}_1^2}}\exp \right[-{({\mathrm{\&lambda;}}_1-{\mathrm{\&lambda;}}_0)}^2/({\mathrm{\&sigma;}}_0^2+{\mathrm{\&sigma;}}_1^2)\left]\right)}^2/\left(\left(\frac{a_2}{\sqrt{1/{\mathrm{\&sigma;}}_0^2+1/{\mathrm{\&sigma;}}_2^2}}\exp \right[-{({\mathrm{\&lambda;}}_2-{\mathrm{\&lambda;}}_0)}^2/{\mathrm{\&sigma;}}_0^2+{\mathrm{\&sigma;}}_2^2)\right]\\ +\frac{a_3}{\sqrt{1/{\mathrm{\&sigma;}}_0^2+1/{\mathrm{\&sigma;}}_3^2}}\exp [-{({\mathrm{\&lambda;}}_3-{\mathrm{\&lambda;}}_0)}^2/({\mathrm{\&sigma;}}_0^2+{\mathrm{\&sigma;}}_3^2)]+\frac{a_4}{\sqrt{1/{\mathrm{\&sigma;}}_0^2+1/{\mathrm{\&sigma;}}_4^2}}\exp [-{({\mathrm{\&lambda;}}_4-{\mathrm{\&lambda;}}_0)}^2/({\mathrm{\&sigma;}}_0^2+{\mathrm{\&sigma;}}_4^2)]+P\&CenterDot;{\mathrm{\&sigma;}}_0{)}^2+\frac{N_t^2}{\mathrm{\&pi;}})\end{array}$

Constraints is: 380≤λ ₀≤ 780,0< σ ₀

(4) use signal interference ratio function respectively to λ ₀, σ ₀ask local derviation, make local derviation result equal 0, abbreviation result is:

$\frac{\&PartialD;\mathrm{SINR}}{\&PartialD;{\mathrm{\&lambda;}}_0}=0\&DoubleLeftRightArrow;\frac{{\mathrm{\&lambda;}}_1-{\mathrm{\&lambda;}}_0}{{\mathrm{\&sigma;}}_0^2+{\mathrm{\&sigma;}}_1^2}\&CenterDot;(B^2+N_t^2/\mathrm{\&pi;})-B\&CenterDot;(B_2\&CenterDot;\frac{{\mathrm{\&lambda;}}_2-{\mathrm{\&lambda;}}_0}{{\mathrm{\&sigma;}}_0^2+{\mathrm{\&sigma;}}_2^2}+B_3\&CenterDot;\frac{{\mathrm{\&lambda;}}_3-{\mathrm{\&lambda;}}_0}{{\mathrm{\&sigma;}}_0^2+{\mathrm{\&sigma;}}_3^2}+B_4\&CenterDot;\frac{{\mathrm{\&lambda;}}_4-{\mathrm{\&lambda;}}_0}{{\mathrm{\&sigma;}}_0^2+{\mathrm{\&sigma;}}_4^2})=0---\left(1\right)$

$\begin{array}{c}\frac{\&PartialD;\mathrm{SINR}}{\&PartialD;{\mathrm{\&sigma;}}_0}=0\&DoubleLeftRightArrow;(\frac{1}{{\mathrm{\&sigma;}}_0}-\frac{{\mathrm{\&sigma;}}_0}{{\mathrm{\&sigma;}}_0^2+{\mathrm{\&sigma;}}_1^2}+\frac{2{\mathrm{\&sigma;}}_0{({\mathrm{\&lambda;}}_1-{\mathrm{\&lambda;}}_0)}^2}{{({\mathrm{\&sigma;}}_0^2+{\mathrm{\&sigma;}}_1^2)}^2})\&CenterDot;(B^2+N_t^2/\mathrm{\&pi;})-\\ B\&CenterDot;(B_2\&CenterDot;(\frac{1}{{\mathrm{\&sigma;}}_0}-\frac{{\mathrm{\&sigma;}}_0}{{\mathrm{\&sigma;}}_0^2+{\mathrm{\&sigma;}}_2^2}+\frac{2{\mathrm{\&sigma;}}_0{({\mathrm{\&lambda;}}_2-{\mathrm{\&lambda;}}_0)}^2}{{({\mathrm{\&sigma;}}_0^2+{\mathrm{\&sigma;}}_2^2)}^2})+B_3\&CenterDot;(\frac{1}{{\mathrm{\&sigma;}}_0}-\frac{{\mathrm{\&sigma;}}_0}{{\mathrm{\&sigma;}}_0^2+{\mathrm{\&sigma;}}_3^2}+\frac{2{\mathrm{\&sigma;}}_0{({\mathrm{\&lambda;}}_3-{\mathrm{\&lambda;}}_0)}^2}{{({\mathrm{\&sigma;}}_0^2+{\mathrm{\&sigma;}}_3^2)}^2})+\\ B_4\&CenterDot;(\frac{1}{{\mathrm{\&sigma;}}_0}-\frac{{\mathrm{\&sigma;}}_0}{{\mathrm{\&sigma;}}_0^2+{\mathrm{\&sigma;}}_4^2}+\frac{2{\mathrm{\&sigma;}}_0{({\mathrm{\&lambda;}}_4-{\mathrm{\&lambda;}}_0)}^2}{{({\mathrm{\&sigma;}}_0^2+{\mathrm{\&sigma;}}_4^2)}^2}+P)=0\end{array}---\left(2\right)$

Wherein:

$B_2=\frac{a_2}{\sqrt{1/{\mathrm{\&sigma;}}_0^2+1/{\mathrm{\&sigma;}}_2^2}}\exp [-{({\mathrm{\&lambda;}}_2-{\mathrm{\&lambda;}}_0)}^2/({\mathrm{\&sigma;}}_0^2+{\mathrm{\&sigma;}}_2^2)],B_3=\frac{a_3}{\sqrt{1/{\mathrm{\&sigma;}}_0^2+1/{\mathrm{\&sigma;}}_3^2}}\exp [-{({\mathrm{\&lambda;}}_3-{\mathrm{\&lambda;}}_0)}^2/({\mathrm{\&sigma;}}_0^2+{\mathrm{\&sigma;}}_3^2)],$

$B_4=\frac{a_4}{\sqrt{1/{\mathrm{\&sigma;}}_0^2+1/{\mathrm{\&sigma;}}_4^2}}\exp [-{({\mathrm{\&lambda;}}_4-{\mathrm{\&lambda;}}_0)}^2/({\mathrm{\&sigma;}}_0^2+{\mathrm{\&sigma;}}_4^2)],$ B＝B ₂+B ₃+B ₄+P·σ ₀

(5) initialization λ ₀, σ ₀, first fix σ ₀parameter optimization parameter lambda ₀, obtain according to local derviation formula (1) and meeting the λ under constraints ₀solution; Then λ is upgraded ₀value, fixing λ ₀optimize σ ₀, obtain according to local derviation formula (2) and meeting the σ under constraints ₀solution, carry out successively taking turns iteration more;

(6) after iteration meets certain number of times, stop iteration, namely convergence result is the optimal solution of red filter parameter;

(7) respectively above-mentioned steps (3) ~ (6), wherein λ is repeated to yellow, green, blue optical filtering ₀, σ ₀constraints identical; Export the optimum results of multiple color optical filtering parameter.

5., as claimed in claim 1 or 2 based on the optical filtering parameter optimization method of visible light communication, it is characterized in that: the pass-band performance of optical filtering is F (λ)=1/ (1+ (λ-λ meeting Lorentzian ₀) ²/ σ ₀ ²), wavelength X centered by the parameter that needs are optimized ₀and variances sigma ₀, described method is specially:

(1) first, measure the spectroscopic data of the LED of four kinds of coloured light with spectrometer, use Lorentzian matching respectively, expression formula is as follows:

S _r(λ)＝a ₁/(1+(λ-λ ₁) ²/σ ₁ ²)

S _a(λ)＝a ₂/(1+(λ-λ ₂) ²/σ ₂ ²)

S _g(λ)＝a ₃/(1+(λ-λ ₃) ²/σ ₃ ²)

S _b(λ)＝a ₄/(1+(λ-λ ₄) ²/σ ₄ ²)

Wherein, a ₁-a ₄, λ ₁-λ ₄, σ ₁-σ ₄being the fitting parameter of Lorentzian, is real constant; S _r(λ) be the spectral function of ruddiness, S _a(λ) be the spectral function of gold-tinted, S _g(λ) be the spectral function of green glow, S _b(λ) be the spectral function of blue light;

(2) according to the system of reality, suppose that the spectrum amplitude of bias light is equally distributed, determine the spectral function S of bias light _back(λ)=P and receiving terminal total noise power N _t, wherein P and N _tit is real constant;

(3) calculate the signal interference ratio of each coloured light of receiving terminal, the signal interference ratio of ruddiness is as follows:

$\begin{array}{c}\mathrm{SINR}=\\ {\left(\frac{a_1{\mathrm{\&sigma;}}_0{\mathrm{\&sigma;}}_1({\mathrm{\&sigma;}}_0+{\mathrm{\&sigma;}}_1)}{{({\mathrm{\&lambda;}}_0-{\mathrm{\&lambda;}}_1)}^2+{({\mathrm{\&sigma;}}_0+{\mathrm{\&sigma;}}_1)}^2}\right)}^2/{\left((\frac{a_2{\mathrm{\&sigma;}}_0{\mathrm{\&sigma;}}_2({\mathrm{\&sigma;}}_0+{\mathrm{\&sigma;}}_2)}{{({\mathrm{\&lambda;}}_0-{\mathrm{\&lambda;}}_2)}^2+{({\mathrm{\&sigma;}}_0+{\mathrm{\&sigma;}}_2)}^2}+\frac{a_3{\mathrm{\&sigma;}}_0{\mathrm{\&sigma;}}_3({\mathrm{\&sigma;}}_0+{\mathrm{\&sigma;}}_3)}{{({\mathrm{\&lambda;}}_0-{\mathrm{\&lambda;}}_3)}^2+{({\mathrm{\&sigma;}}_0+{\mathrm{\&sigma;}}_3)}^2}+\frac{a_4{\mathrm{\&sigma;}}_0{\mathrm{\&sigma;}}_4({\mathrm{\&sigma;}}_0+{\mathrm{\&sigma;}}_4)}{{({\mathrm{\&lambda;}}_0-{\mathrm{\&lambda;}}_4)}^2+{({\mathrm{\&sigma;}}_0+{\mathrm{\&sigma;}}_4)}^2}+P\&CenterDot;{\mathrm{\&sigma;}}_0\right)}^2+\frac{N_t^2}{{\mathrm{\&pi;}}^2})\end{array}$

Constraints is: 380≤λ ₀≤ 780,0< σ ₀

(4) use signal interference ratio function respectively to λ ₀, σ ₀ask local derviation, make local derviation result equal 0, abbreviation result is:

$\begin{array}{c}\frac{\&PartialD;\mathrm{SINR}}{\&PartialD;{\mathrm{\&lambda;}}_0}=0\&DoubleLeftRightArrow;\frac{{\mathrm{\&lambda;}}_1-{\mathrm{\&lambda;}}_0}{{({\mathrm{\&lambda;}}_0-{\mathrm{\&lambda;}}_1)}^2+{({\mathrm{\&sigma;}}_0+{\mathrm{\&sigma;}}_1)}^2}\&CenterDot;(B^2+N_t^2/{\mathrm{\&pi;}}^2)-\\ B\&CenterDot;(B_2\&CenterDot;\frac{{\mathrm{\&lambda;}}_2-{\mathrm{\&lambda;}}_0}{{({\mathrm{\&lambda;}}_0-{\mathrm{\&lambda;}}_2)}^2+{({\mathrm{\&sigma;}}_0+{\mathrm{\&sigma;}}_2)}^2}+B_3\&CenterDot;\frac{{\mathrm{\&lambda;}}_3-{\mathrm{\&lambda;}}_0}{{({\mathrm{\&lambda;}}_0-{\mathrm{\&lambda;}}_3)}^2{+({\mathrm{\&sigma;}}_0+{\mathrm{\&sigma;}}_3)}^2}+B_4\&CenterDot;\frac{{\mathrm{\&lambda;}}_4-{\mathrm{\&lambda;}}_0}{{({\mathrm{\&lambda;}}_0-{\mathrm{\&lambda;}}_4)}^2+{({\mathrm{\&sigma;}}_0+{\mathrm{\&sigma;}}_4)}^2})=0\end{array}---\left(1\right)$

$\begin{array}{c}\frac{\&PartialD;\mathrm{SINR}}{{\&PartialD;\mathrm{\&sigma;}}_0}=0\&DoubleLeftRightArrow;(\frac{{\mathrm{\&sigma;}}_1+{2\mathrm{\&sigma;}}_0}{({\mathrm{\&sigma;}}_1+{\mathrm{\&sigma;}}_0){\mathrm{\&sigma;}}_0}-\frac{2({\mathrm{\&sigma;}}_1+{\mathrm{\&sigma;}}_0)}{{({\mathrm{\&lambda;}}_0-{\mathrm{\&lambda;}}_1)}^2+{({\mathrm{\&sigma;}}_0+{\mathrm{\&sigma;}}_1)}^2})\&CenterDot;(B^2+N_t^2/{\mathrm{\&pi;}}^2)-\\ B\&CenterDot;(B_2\&CenterDot;(\frac{{\mathrm{\&sigma;}}_2+{2\mathrm{\&sigma;}}_0}{({\mathrm{\&sigma;}}_2+{\mathrm{\&sigma;}}_0){\mathrm{\&sigma;}}_0}-\frac{2({\mathrm{\&sigma;}}_2+{\mathrm{\&sigma;}}_0)}{{({\mathrm{\&lambda;}}_0-{\mathrm{\&lambda;}}_2)}^2+{({\mathrm{\&sigma;}}_0+{\mathrm{\&sigma;}}_2)}^2})+B_3\&CenterDot;(\frac{{\mathrm{\&sigma;}}_3+{2\mathrm{\&sigma;}}_0}{({\mathrm{\&sigma;}}_3+{\mathrm{\&sigma;}}_0){\mathrm{\&sigma;}}_0}-\frac{2({\mathrm{\&sigma;}}_3+{\mathrm{\&sigma;}}_0)}{{({\mathrm{\&lambda;}}_0-{\mathrm{\&lambda;}}_3)}^2+{({\mathrm{\&sigma;}}_0+{\mathrm{\&sigma;}}_3)}^2})+\\ B_4\&CenterDot;(\frac{{\mathrm{\&sigma;}}_4+{2\mathrm{\&sigma;}}_0}{({\mathrm{\&sigma;}}_4+{\mathrm{\&sigma;}}_0){\mathrm{\&sigma;}}_0}-\frac{2({\mathrm{\&sigma;}}_4+{\mathrm{\&sigma;}}_0)}{{({\mathrm{\&lambda;}}_0-{\mathrm{\&lambda;}}_4)}^2+{({\mathrm{\&sigma;}}_0+{\mathrm{\&sigma;}}_4)}^2})+P)=0\end{array}---\left(2\right)$

Wherein: $B_2=\frac{a_2{\mathrm{\&sigma;}}_0{\mathrm{\&sigma;}}_2({\mathrm{\&sigma;}}_0+{\mathrm{\&sigma;}}_2)}{{({\mathrm{\&lambda;}}_0-{\mathrm{\&lambda;}}_2)}^2+{({\mathrm{\&sigma;}}_0+{\mathrm{\&sigma;}}_2)}^2},B_3=\frac{a_3{\mathrm{\&sigma;}}_0{\mathrm{\&sigma;}}_3({\mathrm{\&sigma;}}_0+{\mathrm{\&sigma;}}_3)}{{({\mathrm{\&lambda;}}_0-{\mathrm{\&lambda;}}_3)}^2+{({\mathrm{\&sigma;}}_0+{\mathrm{\&sigma;}}_3)}^2}$

$B_4=\frac{a_4{\mathrm{\&sigma;}}_0{\mathrm{\&sigma;}}_4({\mathrm{\&sigma;}}_0+{\mathrm{\&sigma;}}_4)}{{({\mathrm{\&lambda;}}_0-{\mathrm{\&lambda;}}_4)}^2+{({\mathrm{\&sigma;}}_0+{\mathrm{\&sigma;}}_4)}^2},$ B＝B ₂+B ₃+B ₄+P·σ ₀

(5) initialization λ ₀, σ ₀, first fix σ ₀parameter optimization parameter lambda ₀, obtain according to local derviation formula (1) and meeting the λ under constraints ₀solution; Then λ is upgraded ₀value, fixing λ ₀optimize σ ₀, obtain according to local derviation formula (2) and meeting the σ under constraints ₀solution, carry out successively taking turns iteration more;

(6) after iteration meets certain number of times, stop iteration, namely convergence result is the optimal solution of red filter parameter;

(7) respectively above-mentioned steps (3) ~ (6), wherein λ is repeated to yellow, green, blue filter ₀, σ ₀constraints identical; Export the optimum results of multiple color optical filtering parameter.