CN106102207B - A kind of light-dimming method of indoor white light LEDs - Google Patents
A kind of light-dimming method of indoor white light LEDs Download PDFInfo
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Abstract
The invention discloses a kind of light-dimming method of indoor white light LEDs, dim the method being combined by changing signal element probability of happening with amplitude to adjust luminous intensity：Variable η is taken as DC compensation D in simulation light modulationshiftScale factor, DC compensation Dshift=A | 12 ε |；ε is dim level, and A is LED linear area luminous intensity rated value；When dim level is below 50%, by increasing the probability of happening of the low signal element of light intensity amplitude, probability that the high signal element of reduction light intensity amplitude occurs adjust luminous intensity；When dim level is 50%, no DC compensation Dshift；Luminous intensity is adjusted by changing the probability of high and low magnitude symbols；When dim level is higher than 50%, by reducing the probability of happening of the low signal element of light intensity amplitude, increasing the probability of the high signal element generation of light intensity amplitude and reducing DshiftThe mode of compensation adjusts luminous intensity.The more traditional digital dimming method of the present invention has higher bandwidth availability ratio, it is ensured that traffic rate will not follow the change of dim level and reduce.
Description
Technical field
The present invention relates to LED communication technical field, particularly a kind of light-dimming method of indoor white light LEDs.
Background technology
White light LEDs communication system is in the majority using baseband modulation mode, and the modulator approach of suitable white light LEDs communication has at present:
On-off keying (OOK)；Pulse position modulation (PPM)；Multi-pulse position modulation (VPPM)；Pulse width modulation (PWM)；Digit pulse
Interval modulation (DPIM)；Double end pulse spacing width modulated (DH-PIM) and color keying (CSK).The mesh of these modulator approaches
Be in order under the bandwidth of relative narrower, to obtain higher power utilization and the relatively low bit error rate.In addition, indoor white light
LED communication system also need to respect to illumination and communication double demands, then in order to save the energy, it is necessary to according to the moon/it is fine,
The different background luminous intensity such as day/daytime adjusts light-source brightness at any time, to save the energy, then how different stage illuminance
Under, remain to keep the constant of traffic rate to be vital.According to current modulation technique, OOK, PPM, CSK dimming function
Coding techniques brightness regulation is easily achieved due to its coding, thus recommended by IEEE802.15.7 groups to be used for LED communication
Message sink coding.
Current existing dimming arrangement：(1) OOK is modulated, and when without communication requirement, can effectively be controlled by increasing Redundant time slot
The change of average light power processed and illumination light and shade；If increase compensation time slot, the brightness of light will improve, still, compensation when
The more, valid data position will be reduced gap；(2) impulse modulation PPM, using changing pulse position modulation and pulse width modulation
Feature meets flicker free lighting requirement and brightness control function there is provided constant data rate, the frame length scope of change,
But validity declines；(3) multi-carrier modulation, by changing the size of bias direct current, so as to change the intensity of Output optical power
To adjust brightness, although will not change data transmission rate, but improve transmitting terminal power and receiving terminal decoding when mistake
Code check；(4) CSK (Color shift key) is modulated, and is the light wave Tag ID number in advance to different colours, and by selection not
With the light wave of No. ID, change mapping position of the code element in color-planisphere with reference to multilevel code scheme, to reach regulation
The purpose of brightness, codec complexity is higher.
Above-mentioned modulator approach should meet the requirement of transmission information, also meet the regulatory function of room lighting.If adopting
It is that, to sacrifice a width of cost of code element band, bandwidth shared by reduction signal reduces signal to illumination with traditional OOK, PPM pattern
Influence, but this coded system capacity usage ratio is low, and when transmission rate is relatively low, can there is LED scintillations.It is comprehensive
On, all there is a drawback in these methods, traffic rate can be remarkably decreased with the increase and decrease of light levels.
The content of the invention
The technical problems to be solved by the invention are to overcome the deficiencies in the prior art and provide a kind of tune of indoor white light LEDs
Light method, the present invention is for the moon/fine, day/daytime etc., and under indoor environment, different lighting requirements adjust light-source brightness at any time, with
Save the energy；Simultaneously, it is ensured that the transmission rate of communication is not influenceed by dimming function, a kind of efficient, volume of tunable optical of proposition
Code mode.
The present invention uses following technical scheme to solve above-mentioned technical problem：
According to a kind of light-dimming method of indoor white light LEDs proposed by the present invention, by the probability of happening for changing signal element
Dim the method being combined to adjust luminous intensity with amplitude；It is specific as follows：
Variable η is taken as DC compensation D in simulation light modulationshiftScale factor, DC compensation Dshift=A | 1-2 ε |；ε is dim level, and A is LED linear area luminous intensity rated value；
When dim level is below 50%, by the probability of happening, the reduction light intensity width that increase the low code element of light intensity amplitude
Probability that the high signal element of value occurs adjusts luminous intensity；The low average value referred to less than light intensity amplitude of light intensity amplitude, light intensity
Amplitude height refers to the average value more than light intensity amplitude；
When dim level is 50%, no DC compensation Dshift；By changing the signal that light intensity amplitude is low, light intensity amplitude is high
The probability that code element occurs adjusts luminous intensity；
When dim level is higher than 50%, by the probability of happening, the increase light intensity amplitude that reduce the low code element of light intensity amplitude
The probability of high signal element generation simultaneously reduces the mode of DC compensation to adjust luminous intensity.
As a kind of further prioritization scheme of light-dimming method of indoor white light LEDs of the present invention, adjusted in probability-amplitude
In light method, the probability of the generation of each signal element is also no longer to wait general, will be different according to light modulation demand, each signal code
Member occurs with different probability.
As a kind of further prioritization scheme of light-dimming method of indoor white light LEDs of the present invention, in maximum informational entropy
Under the conditions of, according to the relation between the probability of happening of dim level and each signal element, and according to DshiftThe scale factor η of compensation
Influence to the probability of happening of unlike signal code element, to improve output light intensity.
It is used as a kind of further prioritization scheme of light-dimming method of indoor white light LEDs of the present invention, the hair of signal element
Raw probability PkCircular it is as follows：
The level magnitude of each signal element, the voltage magnitude a of k-th of signal element are determined firstkFor：
Wherein, M is system grade, 1≤k≤M；
Then there is light modulation equation：
Formula (1) is substituted into formula (2), obtained：
Probabilistic constraints：
Using maximum information entropy model, the probability of happening P of each signal element is set upkWith dim level ε relation, it is known that M-
PAM comentropy H (X) is expressed as：
In order to try to achieve maximum informational entropy H (X), extreme value, wherein formula (3) and (4) are asked (5) using Lagrange multiplier formula
For restrictive condition, therefore have：
Wherein, λ1,λ2It is Lagrange factor；
Extreme value is asked to have formula (6)：
Arrangement formula (7)：
Simultaneous formula (8) and (10) are obtained：
Simultaneous formula (9) and (10) are obtained：
λ is solved by simultaneous formula (11) and (12)1,λ2, and real part is taken, then substitute into formula (7), try to achieve Pk。
As a kind of further prioritization scheme of light-dimming method of indoor white light LEDs of the present invention, it is during the η=0
Probability light-modulating mode.
The present invention uses above technical scheme compared with prior art, with following technique effect：
(1) present invention, according to different lighting requirements, light can be adjusted at any time under the indoor environments such as the moon/fine, day/daytime
Source brightness, to save the energy；Simultaneously, it is ensured that the transmission rate of communication is not influenceed by dimming function；
(2) the inventive method is efficient, the coded system of tunable optical, multi-system pulse amplitude modulation (M-PAM)；
(3) the more traditional digital dimming method of light-dimming method of the invention has higher bandwidth availability ratio, it is ensured that communication
Speed will not follow the change of dim level and reduce；
(4) present invention is without complex mechanical equipment, and effectively using existing intelligence software, combination algorithm module extends existing work(
Can, reduce the consuming of hardware resource.
Brief description of the drawings
Fig. 1 is the light modulation of M-PAM amplitudes；Wherein, in (a), 0≤ε ＜ 0.5, i.e. dim level are below 50%, each multi-system
Signal element just concentrates on [0, A-Dshift] in the range of, now DshiftNo longer be DC offset value, but highest amplitude code element away from
The redundancy of the strong peak A of LED light；(b) ε=0.5 in, the light intensity value of each signal element is evenly distributed in [0, A]；(c) in
0.5 ＜ ε≤1, when dim level is higher than 50%, it is necessary to give the compensation D of lowest amplitude code element necessarilyshift, each code element is averaged
Luminous intensity is improved to [Dshift, A] in the range of.
Fig. 2 is M-PAM probability-amplitude light modulation；Wherein, (a) be light adjusting grade below 50% when, increase light intensity amplitude it is low
Signal element probability of happening, the probability that the high signal element of reduction light intensity amplitude occurs；(b) it is that light adjusting grade is 50%
When, each signal element etc. generally occurs, and without DshiftCompensation；(c) when being higher than 50% for light adjusting grade, the low letter of reduction light intensity amplitude
The probability of happening of number member, the probability that the high signal element of increase light intensity amplitude occurs, and reduce η DshiftCompensation.
Fig. 3 is dim level and each signal element probabilistic relation figure；Wherein, (a) is 3-PAM dim levels and each signal code
First probabilistic relation figure, (b) is 4-PAM dim levels and each signal element probabilistic relation figure.
Fig. 4 is η=0,4-PAM dim levels and each signal element probabilistic relation figure.
Fig. 5 is the dim level and each signal element probabilistic relation figure of each signal elements of 4-PAM；Wherein, (a) is signal code
First a1Probability of happening P1Change curve when η is from 0 to 1, (b) is signal element a2Probability of happening P2When η is from 0 to 1
Change curve, (c) is signal element a3Probability of happening P3Change curve when η is from 0 to 1, (d) is signal element a4Hair
Raw probability P4Change curve when η is from 0 to 1.
Embodiment
Technical scheme is described in further detail below in conjunction with the accompanying drawings：
M-PAM coded systems are intended in LED linear area, and by marking, different impulse amplitudes distinguishes multi-system signal code
Member.It follows that system grade M is higher, the significant bit that each code element is carried is more, bandwidth availability ratio increase.But, it is too high
M also bring along problem：1. because LED linear area is limited, electric signal waveform difference is small, causes A/D converter to need higher
Precision；2. bigger SNR, bit error rate increase, sensitivity decrease are needed when receiving terminal reads signal；3. small voltage difference is held very much
Easily die out in ambient noise.Therefore appropriate M is selected to have a major impact PAM coding efficiencies.
The M-PAM of the present invention, that is, have M voltage magnitude.Label L ED linear zone luminous intensities rated value is A, then each signal
The magnitude of voltage of code element is represented by：Code-element period is Tsym.In order to adapt to light intensity modulation, it is desirable to provide certain
DC compensation so that each pulse amplitude is in the LED range of linearity, therefore note DC compensation Dshift.Then M-PAM code elements
Stream is represented by：
X (t)=(ak+Dshift)g(t-kTsym) (1)
From formula (1), shaping pulse g (t) is by TsymDetermine, the T in M-PAM light-modulating modessymImmobilize, i.e.,
G (t) is preset parameter.Each signal element voltage magnitude akIt is related to system grade M and LED light intensity peak A, therefore can not
Change amplitude at any time in communication process.
It is intended to want to change code element stream x (t) in the present invention to adjust brightness, most straightforward approach is exactly to change DC compensation
Dshift, to realize the function of regulation x (t) amplitude.The method that i.e. amplitude is dimmed, such as Fig. 1 shows that note dim level is ε, 0≤ε≤1.
In (a) in Fig. 1,0≤ε ＜ 0.5, i.e. dim level are below 50%, and each multi-system signal element is just concentrated on
[0,A-Dshift] in the range of, now DshiftNo longer it is DC offset value, but highest amplitude code element is away from the superfluous of the strong peak A of LED light
It is remaining.ε=0.5 in (b) in Fig. 1, the light intensity value of each signal element is evenly distributed in [0, A].0.5 in (c) in Fig. 1
＜ ε≤1, when dim level is higher than 50%, it is necessary to give the compensation D of lowest amplitude code element necessarilyshift, make each code element average intensity
Degree is improved to [Dshift, A] in the range of.Only change D in simulation light modulationshift, and the probability of happening of each code element is to wait general, is designated as Pk
Voltage amplitude value difference L between=1/M, and each code element is also identical.Therefore, each signal element level value is added up and just obtained
Output intensity, then have simulation light modulation formula as follows：
Obtained after abbreviation：Dshift=A (1-2 ε)
Obtained after abbreviation：Dshift=A (2 ε -1)
To sum up, D is obtainedshiftRelation with light adjusting grade ε is
From formula (4) it can be seen that the advantage of this amplitude coding mode is light adjusting grade ε and offset DshiftRelation letter
It is single, it is easy to adjust, increase DshiftCompensation.But, because LED range of light intensity [0, A] is limited, the electricity of each signal element
Pressure amplitude value is also required to ensure certain difference, and this results in DshiftCompensation is limited, and with M increase, compensation range is with regard to smaller, this side
Method greatly limit dimming scope.In this regard, the present invention proposes that a kind of signal element probability of happening that changes is combined with amplitude light modulation
Method.
Such as the method that Fig. 2 shows, probability-amplitude is dimmed, variable η is taken as D in simulation light modulationshiftThe scale factor of compensation, η
∈[0,1].As η=0, i.e., no compensating direct current, now PAM adjust output by changing the probability of high and low magnitude symbols
The size of luminous intensity；As η=1, that is, compensate DshiftTotal head, by A | 1-2 ε | determine, now dimmed for amplitude.Therefore it is of the invention
The eta factor of proposition is exactly changed in amplitude light modulation and probability light-modulating mode.
The present invention is in probability-amplitude light-dimming method, and the probability of the generation of each signal element is also no longer to wait general, will
Different according to light modulation demand, each signal element occurs with different probability.Principle is：In (a) in Fig. 2, light adjusting grade exists
When less than 50%, the probability of happening of the low signal element of increase light intensity amplitude, the high signal element of reduction light intensity amplitude occurs
Probability；In (b) in Fig. 2, when light adjusting grade is 50%, each signal element etc. generally occurs, and without DshiftCompensation；(c) in Fig. 2
In, when light adjusting grade is higher than 50%, the probability of happening of the low signal element of reduction light intensity amplitude, the high signal of increase light intensity amplitude
The probability that code element occurs, and reduce η DshiftCompensation.
According to the elaboration in foregoing invention content to light-dimming method in the present invention, to (c) two in (a) in Fig. 2, Fig. 2
Information summary is planted to consider.Firstly the need of the level magnitude for determining each signal element, the voltage magnitude of each signal element can be with
It is expressed as：
Note dim level is ε, and then there is light modulation equation 0≤ε≤1：
(5) are substituted into (6), obtained：
Remember that the probability that each signal element occurs is pk, then have probabilistic constraints：
In order to obtain the maximum information entropy model in the emulation of top performance, the present invention, the generation of each signal element is set up
Probability and pkWith dim level ε relation, it is known that M-PAM comentropy is represented by：
In order to try to achieve maximum informational entropy H (X), extreme value is asked to (9) using Lagrange multiplier formula, wherein (7) and (8) are
Restrictive condition, therefore have：
λ1, λ2For Lagrange factor.And ask extreme value to have to (10)：
(11) are arranged to obtain：
Simultaneous (12) and (14) are obtained：
Simultaneous (13) and (14) are obtained：
(λ can be solved by simultaneous (15) and (16)1, λ2), and take real part.Substitute into again in (11), try to achieve pk.Fig. 3
0≤ε≤1 is simulated, when taking η=0.6, compares 3-, 4-PAM dim level and the relation of each signal element probability of happening.
Understood from (b) analysis in (a) in Fig. 3, Fig. 3 in 0≤ε ＜ 0.5, the signal element that level magnitude is zero
Probability of happening P1 highests, the probability of happening P4 of level magnitude highest signal element is minimum, and this allows for the luminous intensity dimension of output
Hold in relatively low scope；As ε=0.5, Dshift=A | 1-2 ε |=0, so no matter M is how many, each signal element is all to wait general
Rate occurs, and maintains output intensity at half peak value；As 0.5 ＜ ε≤1, the curve in the range of P1 to P4 curves and 0≤ε ＜ 0.5
It is not in symmetric relation, exactly because the effect of this eta factor, in high intensity range, the generation of the signal element of high level amplitude
Probability does not increase significantly, and the signal element probability of relatively low level magnitude is not also significantly reduced, but the general trend such as tends to.
The present invention further probes into the effect of eta factor, provides η from the change of each signal element probability of happening when 0 to 1.Fig. 4
During for η=0,4-PAM dim level and each signal element probabilistic relation figure.By above-mentioned theory, it is known that η=0 when adjusted for probability
Optical mode, P1 is to P4 curves it is also seen that they are the symmetric figures on the axis of ε=0.5 from figure.Because probability is dimmed
In the level magnitude of each signal element be A/M, so the signal element probability of happening of increase high level amplitude can just be improved
Output light intensity, similarly, on the contrary reduction output light intensity.So, it is symmetric relation in the region of ＜ ε of 0≤ε ＜ 0.5 and 0.5≤1.
And in probability-amplitude light modulation, because introducing DshiftCompensation, the level magnitude of each signal element is no longer A/M relations, therefore is adjusted
Light level and symbol probability are no longer symmetric relations.
(a) in Fig. 5 is signal element a1Probability of happening P1(b) in change curve when η is from 0 to 1, Fig. 5 is letter
Number member a2Probability of happening P2(c) in change curve when η is from 0 to 1, Fig. 5 is signal element a3Probability of happening P3
η is from change curve when 0 to 1, and (d) in Fig. 5 is signal element a4Probability of happening P4Change curve when η is from 0 to 1.
During η=1, the probability of happening of each signal element is identical, is 0.25, is now amplitude light-modulating mode, Dshift=A | 1-2 ε |；η=0
When, the curve map of each signal element probability of happening is consistent with Fig. 4.When η is from during 0 to 1 gradual change, that is, probability is dimmed is adjusted to amplitude
Light changes, and the probability of happening P of the less signal element of voltage magnitude is can be seen that from (a), (b) figure1、P2In the scopes of 0≤ε ＜ 0.5
It is interior to be gradually reduced with η increase；It is slowly increased in the range of 0.5 ＜ ε≤1 with η increase, finally to 0.25.But
It is in (c), (d) it can be seen from the figure that, for the probability of happening P of the higher signal element of voltage magnitude3、P4For, this rule
Just with P1、P2On the contrary, but final is also to tend to wait generally.
The present invention proposes a kind of M-PAM coding methods for possessing dimming function, and it compares OOK, PPM method with more
Efficient bandwidth availability ratio.
The present invention gives the technical scheme of M-PAM probability-amplitude light-dimming method, under the conditions of maximum informational entropy, light modulation
Relation between the probability of happening of rank and each signal element, and further analyze DshiftThe scale factor η of compensation is to different letters
The influence of the probability of happening of number member, theoretical foundation is provided to the technical program.
In the present invention, M-PAM has M voltage magnitude.Label L ED linear zone luminous intensities rated value is A, then each letter
The magnitude of voltage of number member is represented by：Code-element period is Tsym.In order to adapt to light intensity modulation, it is desirable to provide one
Fixed DC compensation so that each pulse amplitude is in the LED range of linearity, therefore note DC compensation Dshift.Obtain M-PAM
Code element stream.
It is intended to want to change code element stream x (t) in this programme to adjust brightness, most straightforward approach is exactly to change DC compensation
Dshift, you can realize the function of regulation x (t) amplitude.
Dim level ε defined in the present invention, 0≤ε ＜ 0.5, i.e. dim level is below 50%, each multi-system signal element
Just concentrate on [0, A-Dshift] in the range of, now DshiftNo longer it is DC offset value, but highest amplitude code element is strong away from LED light
The redundancy of peak A.ε=0.5, the light intensity value of each signal element is evenly distributed in [0, A].0.5 ＜ ε≤1, dim level
During higher than 50%, it is necessary to give the compensation D of lowest amplitude code element necessarilyshift, each code element average luminous intensity is improved to [Dshift,
A] in the range of.Only change D in simulation light modulationshift, and the probability of happening of each code element is to wait general, is designated as Pk=1/M, and each code
Voltage amplitude value difference L between member is also identical.
In the present invention, because LED range of light intensity [0, A] is limited, the voltage magnitude of each signal element is also required to ensure
Certain difference, this results in DshiftCompensation is limited, with M increase, and compensation range is just smaller, and this method greatly limit light modulation
Scope.In this regard, the present invention proposes that a kind of signal element probability of happening that changes dims the method being combined with amplitude.
The present invention takes variable η as D in simulation light modulationshiftThe scale factor of compensation, η ∈ [0,1].As η=0, that is, do not have
There is compensating direct current, now PAM adjusts the size of output light intensity by changing the probability of high and low magnitude symbols；As η=1,
Compensate DshiftTotal head, by A | 1-2 ε | determine, now dimmed for amplitude.Therefore eta factor proposed by the present invention is exactly adjusted in amplitude
Changed in light and probability light-modulating mode.
In probability-amplitude light-dimming method, the probability of the generation of each signal element is also no longer to wait general, will be according to tune
Light demand is different, and each signal element occurs with different probability.Principle is：When light adjusting grade is below 50%, increase light intensity width
The probability of happening of the low signal element of value, the probability that the high signal element of reduction light intensity amplitude occurs；When light adjusting grade is 50%,
Each signal element etc. generally occurs, and without DshiftCompensation；When light adjusting grade is higher than 50%, the low signal element of reduction light intensity amplitude
Probability of happening, the probability that the high signal element of increase light intensity amplitude occurs, and reduce DshiftCompensation.
Claims (3)
1. a kind of light-dimming method of indoor white light LEDs, it is characterised in that adjusted by the probability of happening for changing signal element with amplitude
Method that light is combined adjusts luminous intensity；It is specific as follows：
Variable η is taken as DC compensation D in simulation light modulationshiftScale factor, DC compensation Dshift=A | 1-2 ε |；ε is dim level, and A is LED linear area luminous intensity rated value；
When dim level is below 50%, by the probability of happening, the reduction light intensity width that increase the low signal element of light intensity amplitude
Probability that the high signal element of value occurs adjusts luminous intensity；The low average value referred to less than light intensity amplitude of light intensity amplitude, light intensity
Amplitude height refers to the average value more than light intensity amplitude；
When dim level is 50%, no DC compensation Dshift；By changing the signal element that light intensity amplitude is low, light intensity amplitude is high
The probability of generation adjusts luminous intensity；
When dim level is higher than 50%, by the probability of happening, the increase light intensity amplitude that reduce the low signal element of light intensity amplitude
The probability of high signal element generation simultaneously reduces the mode of DC compensation to adjust luminous intensity；
The probability of happening P of signal elementkCircular it is as follows：
The level magnitude of each signal element, the level magnitude a of k-th of signal element are determined firstkFor：
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<mrow>
<mo>(</mo>
<mn>1</mn>
<mo>)</mo>
</mrow>
</mrow>
Wherein, M is system grade, 1≤k≤M；
Then there is light modulation equation：
<mrow>
<munderover>
<mo>&Sigma;</mo>
<mrow>
<mi>k</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>M</mi>
</munderover>
<msub>
<mi>P</mi>
<mi>k</mi>
</msub>
<msub>
<mi>a</mi>
<mi>k</mi>
</msub>
<mo>=</mo>
<mi>&epsiv;</mi>
<mi>A</mi>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>2</mn>
<mo>)</mo>
</mrow>
</mrow>
Formula (1) is substituted into formula (2), obtained：
<mrow>
<munderover>
<mo>&Sigma;</mo>
<mrow>
<mi>k</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>M</mi>
</munderover>
<msub>
<mi>p</mi>
<mi>k</mi>
</msub>
<mrow>
<mo>(</mo>
<mi>k</mi>
<mo>-</mo>
<mn>1</mn>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mfrac>
<mrow>
<mi>&epsiv;</mi>
<mrow>
<mo>(</mo>
<mi>M</mi>
<mo>-</mo>
<mn>1</mn>
<mo>)</mo>
</mrow>
</mrow>
<mrow>
<mn>1</mn>
<mo>-</mo>
<mi>&eta;</mi>
<mrow>
<mo>(</mo>
<mn>1</mn>
<mo>-</mo>
<mn>2</mn>
<mi>&epsiv;</mi>
<mo>)</mo>
</mrow>
</mrow>
</mfrac>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>3</mn>
<mo>)</mo>
</mrow>
</mrow>
Probabilistic constraints：
<mrow>
<munderover>
<mo>&Sigma;</mo>
<mrow>
<mi>k</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>M</mi>
</munderover>
<msub>
<mi>P</mi>
<mi>k</mi>
</msub>
<mo>=</mo>
<mn>1</mn>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>4</mn>
<mo>)</mo>
</mrow>
</mrow>
Using maximum information entropy model, the probability of happening P of each signal element is set upkWith dim level ε relation, it is known that multi-system
Pulse amplitude modulation M-PAM comentropy H (X) is expressed as：
<mrow>
<mi>H</mi>
<mrow>
<mo>(</mo>
<mi>X</mi>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mo>-</mo>
<munderover>
<mo>&Sigma;</mo>
<mrow>
<mi>k</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>M</mi>
</munderover>
<msub>
<mi>P</mi>
<mi>k</mi>
</msub>
<msub>
<mi>log</mi>
<mn>2</mn>
</msub>
<msub>
<mi>P</mi>
<mi>k</mi>
</msub>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>5</mn>
<mo>)</mo>
</mrow>
</mrow>
In order to try to achieve maximum informational entropy H (X), extreme value is asked (5) using Lagrange multiplier formula, wherein formula (3) and (4) are limited
Condition processed, therefore have：
<mrow>
<mi>L</mi>
<mrow>
<mo>(</mo>
<msub>
<mi>p</mi>
<mn>1</mn>
</msub>
<mo>,</mo>
<mo>,</mo>
<mo>,</mo>
<mo>,</mo>
<msub>
<mi>p</mi>
<mi>M</mi>
</msub>
<mo>;</mo>
<msub>
<mi>&lambda;</mi>
<mn>1</mn>
</msub>
<mo>,</mo>
<msub>
<mi>&lambda;</mi>
<mn>2</mn>
</msub>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mo>-</mo>
<munderover>
<mo>&Sigma;</mo>
<mrow>
<mi>k</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>M</mi>
</munderover>
<msub>
<mi>P</mi>
<mi>k</mi>
</msub>
<msub>
<mi>log</mi>
<mn>2</mn>
</msub>
<msub>
<mi>P</mi>
<mi>k</mi>
</msub>
<mo>-</mo>
<msub>
<mi>&lambda;</mi>
<mn>1</mn>
</msub>
<mrow>
<mo>(</mo>
<munderover>
<mo>&Sigma;</mo>
<mrow>
<mi>k</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>M</mi>
</munderover>
<msub>
<mi>P</mi>
<mi>k</mi>
</msub>
<mo>-</mo>
<mn>1</mn>
<mo>)</mo>
</mrow>
<mo>-</mo>
<msub>
<mi>&lambda;</mi>
<mn>2</mn>
</msub>
<mo>&lsqb;</mo>
<munderover>
<mo>&Sigma;</mo>
<mrow>
<mi>k</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>M</mi>
</munderover>
<msub>
<mi>P</mi>
<mi>k</mi>
</msub>
<mrow>
<mo>(</mo>
<mi>k</mi>
<mo>-</mo>
<mn>1</mn>
<mo>)</mo>
</mrow>
<mo>-</mo>
<mfrac>
<mrow>
<mi>&epsiv;</mi>
<mrow>
<mo>(</mo>
<mi>M</mi>
<mo>-</mo>
<mn>1</mn>
<mo>)</mo>
</mrow>
</mrow>
<mrow>
<mn>1</mn>
<mo>-</mo>
<mi>&eta;</mi>
<mrow>
<mo>(</mo>
<mn>1</mn>
<mo>-</mo>
<mn>2</mn>
<mi>&epsiv;</mi>
<mo>)</mo>
</mrow>
</mrow>
</mfrac>
<mo>&rsqb;</mo>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>6</mn>
<mo>)</mo>
</mrow>
</mrow>
Wherein, λ1,λ2It is Lagrange factor；
Extreme value is asked to have formula (6)：
<mrow>
<mfrac>
<mrow>
<mo>&part;</mo>
<mi>L</mi>
</mrow>
<mrow>
<mo>&part;</mo>
<msub>
<mi>P</mi>
<mi>k</mi>
</msub>
</mrow>
</mfrac>
<mo>=</mo>
<mo>-</mo>
<msub>
<mi>log</mi>
<mn>2</mn>
</msub>
<msub>
<mi>P</mi>
<mi>k</mi>
</msub>
<mo>-</mo>
<mfrac>
<mn>1</mn>
<mrow>
<mi>ln</mi>
<mn>2</mn>
</mrow>
</mfrac>
<mo>-</mo>
<msub>
<mi>&lambda;</mi>
<mn>1</mn>
</msub>
<mo>-</mo>
<msub>
<mi>&lambda;</mi>
<mn>2</mn>
</msub>
<mrow>
<mo>(</mo>
<mi>k</mi>
<mo>-</mo>
<mn>1</mn>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mn>0</mn>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>7</mn>
<mo>)</mo>
</mrow>
</mrow>
1
<mrow>
<mfrac>
<mrow>
<mo>&part;</mo>
<mi>L</mi>
</mrow>
<mrow>
<mo>&part;</mo>
<msub>
<mi>&lambda;</mi>
<mn>1</mn>
</msub>
</mrow>
</mfrac>
<mo>=</mo>
<munderover>
<mo>&Sigma;</mo>
<mrow>
<mi>k</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>M</mi>
</munderover>
<msub>
<mi>P</mi>
<mi>k</mi>
</msub>
<mo>-</mo>
<mn>1</mn>
<mo>=</mo>
<mn>0</mn>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>8</mn>
<mo>)</mo>
</mrow>
</mrow>
<mrow>
<mfrac>
<mrow>
<mo>&part;</mo>
<mi>L</mi>
</mrow>
<mrow>
<mo>&part;</mo>
<msub>
<mi>&lambda;</mi>
<mn>2</mn>
</msub>
</mrow>
</mfrac>
<mo>=</mo>
<munderover>
<mo>&Sigma;</mo>
<mrow>
<mi>k</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>M</mi>
</munderover>
<msub>
<mi>P</mi>
<mi>k</mi>
</msub>
<mrow>
<mo>(</mo>
<mi>k</mi>
<mo>-</mo>
<mn>1</mn>
<mo>)</mo>
</mrow>
<mo>-</mo>
<mfrac>
<mrow>
<mi>&epsiv;</mi>
<mrow>
<mo>(</mo>
<mi>M</mi>
<mo>-</mo>
<mn>1</mn>
<mo>)</mo>
</mrow>
</mrow>
<mrow>
<mn>1</mn>
<mo>-</mo>
<mi>&eta;</mi>
<mrow>
<mo>(</mo>
<mn>1</mn>
<mo>-</mo>
<mn>2</mn>
<mi>&epsiv;</mi>
<mo>)</mo>
</mrow>
</mrow>
</mfrac>
<mo>=</mo>
<mn>0</mn>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>9</mn>
<mo>)</mo>
</mrow>
</mrow>
Arrangement formula (7)：
<mrow>
<msub>
<mi>P</mi>
<mi>k</mi>
</msub>
<mo>=</mo>
<msup>
<mn>2</mn>
<mrow>
<mo>-</mo>
<mfrac>
<mn>1</mn>
<mrow>
<mi>ln</mi>
<mn>2</mn>
</mrow>
</mfrac>
<mo>-</mo>
<msub>
<mi>&lambda;</mi>
<mn>1</mn>
</msub>
<mo>-</mo>
<msub>
<mi>&lambda;</mi>
<mn>2</mn>
</msub>
<mrow>
<mo>(</mo>
<mi>k</mi>
<mo>-</mo>
<mn>1</mn>
<mo>)</mo>
</mrow>
</mrow>
</msup>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>10</mn>
<mo>)</mo>
</mrow>
</mrow>
Simultaneous formula (8) and (10) are obtained：
<mrow>
<msup>
<mn>2</mn>
<mrow>
<mo>(</mo>
<mfrac>
<mn>1</mn>
<mrow>
<mi>ln</mi>
<mn>2</mn>
</mrow>
</mfrac>
<mo>+</mo>
<msub>
<mi>&lambda;</mi>
<mn>1</mn>
</msub>
<mo>)</mo>
</mrow>
</msup>
<mo>=</mo>
<mfrac>
<mrow>
<mn>1</mn>
<mo>-</mo>
<msup>
<mn>2</mn>
<mrow>
<mo>-</mo>
<msub>
<mi>&lambda;</mi>
<mn>2</mn>
</msub>
<mrow>
<mo>(</mo>
<mi>M</mi>
<mo>+</mo>
<mo>!</mo>
<mo>)</mo>
</mrow>
</mrow>
</msup>
</mrow>
<mrow>
<mn>1</mn>
<mo>-</mo>
<msup>
<mn>2</mn>
<mrow>
<mo>-</mo>
<msub>
<mi>&lambda;</mi>
<mn>2</mn>
</msub>
</mrow>
</msup>
</mrow>
</mfrac>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>11</mn>
<mo>)</mo>
</mrow>
</mrow>
Simultaneous formula (9) and (10) are obtained：
<mrow>
<mfrac>
<msup>
<mn>2</mn>
<mrow>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mfrac>
<mn>1</mn>
<mrow>
<mi>l</mi>
<mi>n</mi>
<mn>2</mn>
</mrow>
</mfrac>
<mo>+</mo>
<msub>
<mi>&lambda;</mi>
<mn>1</mn>
</msub>
<mo>)</mo>
</mrow>
</mrow>
</msup>
<mrow>
<mn>1</mn>
<mo>-</mo>
<msup>
<mn>2</mn>
<mrow>
<mo>-</mo>
<msub>
<mi>&lambda;</mi>
<mn>2</mn>
</msub>
</mrow>
</msup>
</mrow>
</mfrac>
<mo>{</mo>
<mfrac>
<mrow>
<msup>
<mn>2</mn>
<mrow>
<mo>-</mo>
<msub>
<mi>&lambda;</mi>
<mn>2</mn>
</msub>
</mrow>
</msup>
<mo>&lsqb;</mo>
<mn>1</mn>
<mo>-</mo>
<msup>
<mn>2</mn>
<mrow>
<mo>-</mo>
<msub>
<mi>&lambda;</mi>
<mn>2</mn>
</msub>
<mi>M</mi>
</mrow>
</msup>
<mo>&rsqb;</mo>
</mrow>
<mrow>
<mn>1</mn>
<mo>-</mo>
<msup>
<mn>2</mn>
<mrow>
<mo>-</mo>
<msub>
<mi>&lambda;</mi>
<mn>2</mn>
</msub>
</mrow>
</msup>
</mrow>
</mfrac>
<mo>-</mo>
<msup>
<mn>2</mn>
<mrow>
<mo>-</mo>
<msub>
<mi>&lambda;</mi>
<mn>2</mn>
</msub>
<mrow>
<mo>(</mo>
<mi>M</mi>
<mo>+</mo>
<mn>1</mn>
<mo>)</mo>
</mrow>
</mrow>
</msup>
<mi>M</mi>
<mo>}</mo>
<mo>=</mo>
<mfrac>
<mrow>
<mi>&epsiv;</mi>
<mi>M</mi>
</mrow>
<mrow>
<mn>1</mn>
<mo>-</mo>
<mi>&eta;</mi>
<mrow>
<mo>(</mo>
<mn>1</mn>
<mo>-</mo>
<mn>2</mn>
<mi>&epsiv;</mi>
<mo>)</mo>
</mrow>
</mrow>
</mfrac>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>12</mn>
<mo>)</mo>
</mrow>
</mrow>
λ is solved by simultaneous formula (11) and (12)1,λ2, and real part is taken, then substitute into formula (7), try to achieve Pk。
2. the light-dimming method of a kind of indoor white light LEDs according to claim 1, it is characterised in that in probability-amplitude light modulation
In method, the probability of the generation of each signal element is also no longer to wait general, will be different according to light modulation demand, each signal element
Occur with different probability.
3. the light-dimming method of a kind of indoor white light LEDs according to claim 1, it is characterised in that in maximum informational entropy bar
Under part, according to the relation between the probability of happening of dim level and each signal element, and according to Dshiftη pairs of the scale factor of compensation
The influence of the probability of happening of unlike signal code element, to improve output light intensity.
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