CN105162740B - A kind of single channel time-frequency blind Signal Separation of Overlapped Signals - Google Patents

A kind of single channel time-frequency blind Signal Separation of Overlapped Signals Download PDF

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CN105162740B
CN105162740B CN201510570107.4A CN201510570107A CN105162740B CN 105162740 B CN105162740 B CN 105162740B CN 201510570107 A CN201510570107 A CN 201510570107A CN 105162740 B CN105162740 B CN 105162740B
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陈晓
支亚京
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Nanjing University of Information Science and Technology
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Abstract

The present invention provides a kind of single channel time-frequency blind Signal Separation of Overlapped Signals, comprises the following steps：Step 1, signal model is established, the mixed signal received is converted into being made up of several Gauss amplitude modulation source signals；Step 2, the joint maximum likelihood function of mixed signal is calculated, the solution procedure of mixed signal is changed into the process for solving multidimensional variable parameter；Step 3, according to characteristics of signals, estimate the temporal center and time width modulation parameter of each source signal；Step 4, calculate the initial value of multidimensional variable parameter；Step 5, calculate the optimal value of multidimensional variable parameter；Step 6, calculate Gauss amplitude modulation source signal.The present invention is a kind of multidimensional variable method for parameter estimation of the blending heredity minimum value searching algorithm with pre-estimation, first the temporal center t0 of the time width modulation parameter P to source signal and source signal carries out pre-estimation, then genetic algorithm and minimum value searching algorithm are mixed again and calculates other parameters, so improve convergence rate and computational accuracy.

Description

A kind of single channel time-frequency blind Signal Separation of Overlapped Signals
Technical field
The present invention relates to signal of communication process field, and in particular to a kind of side of single channel time-frequency overlapped signal blind separation Method.
Background technology
In the present information epoch, with the development of the communication technology and increasing rapidly for global traffic so that communication loop Border complicates, and frequency spectrum resource utilizes anxietyization, interference noise wide variety；Since so, generally for acquisition individual signals Component is, it is necessary to the communication such as the co-channel interference of frequency aliasing signal in the communications when carrying out the separation of component of signal and then causing single channel Generally existing in application environment.Utilize the traditional blind source separation algorithm and time-frequency domain of the processing of array signal mimo system, spatial domain All no longer it is applicable with the method for code domain filtering, thus needs to carry out blind separation to this kind of single channel time-frequency overlapped signal.
It was found from domestic and international substantial amounts of document, polynomial fitting method (Barbarossa S, Scaglione A, Giannakis G B.Product high-order ambiguity function for multicomponent polynomial-phase signal modeling,IEEE Trans Signal Process,vol.46,Issue 3, 1998, p.691-708), energy operator is utilized to calculate the amplitude of each signal and method (Cai X W, the Wei P, Xiao of phase X C.The single channel of time-frequency overlapping signal blind source separation method based on energy operator,China science letter E:information science,2008,38:607-619), parametric technique (Li M Z, Zhao H is estimated using a variety of time-frequency distributions C.Research on parameters extraction of pseudo code phase modulation-carry frequency modulation combined fuse signal based on the adaptive window length of improved B distribution,Acta Armamentarii,2011,32:543-547) and various tunnel methods Etc. can be separated to the overlapping Gauss amplitude modulation communication signal of single channel time-frequency.Conventional method is tunnel in recent years Method, including wavelet-ICA and EMD-ICA methods.Hong Hoonbin etc. first carry out small echo point to the mixed signal received Solution, ICA processing then is carried out for obtained component, the method is used in mechanical fault diagnosis, although this method is not Limited by signal type, the effect separated for unifrequent signal is preferable, but can not be thorough for bandwidth signal Separation, still remain the information of mixed signal, it is impossible to isolate each source signal well, separating effect is less desirable (Hong H,Liang M.Separation of fault features from a single-channel mechanical signal mixture using wavelet decomposition,Mechanical Systems and Signal Processing,2007,21:2025-2040).The it is proposeds such as unliterary peak, which are mixed single channel using overall experience mode decomposition EMD, to be believed Number multiple intrinsic mode functions are decomposed into, intrinsic mode function component is carried out into ICA separation recovers, by empirical mode decomposition EMD- ICA single channel blind source separation method is used for the simulation study of bearing and gear, properly separates out bearing and gear source signal, this Method improves relative to the separation positive effect such as space-time method, wavelet decomposition method, however, for the excessive signal of spectrum overlapping, each Intrinsic mode functions component covers a wide frequency range, causes bad (Wu W F, Chen X H, the Su X of separating effect J.Blind Source Separation of Single-channel Mechanical Signal Based on Empirical Mode Decomposition,Chinese Journal of Mechanical Engineering,2011, 47:12-16).In practice, for the signal of particular model, the method for model estimation can be used to carry out blind separation, that is, established The model of signal, the parameter of signal in model is estimated using some methods of estimation.Wang Shiyuan etc. uses parameter Estimation Method solve the problems, such as the blind separation of original chaotic signal, using a kind of weighted integral letter of the approximate mapping of volume criterion Number, based on the parameter modeled by state-space model, it is proposed that a kind of new parameter Estimation, effectively realize the weight of chaotic signal Structure.Due to the shortcomings that must establishing suitable state-space model, this method is caused not to be suitable for the overlapping height of single channel time-frequency Blind separation (Wang S Y, the Feng J C.A novel method of estimating parameter of this amplitude-modulated signal and its application to blind separation of chaotic signals,Acta Phys.Sin., 2012,61:170508).Zhang Shuning etc. proposes separation and the ginseng of the single channel sine FM mixed signal based on particle filter Number estimation, for feature of the sine FM mixing frequency signal without saltus step, it is proposed that a kind of phase difference solution based on particle filter Aliasing algorithm, and solve the problems, such as particle filter dimensional state space dimensionality reduction in algorithm by source signal phase difference, it is proposed that one The likelihood function model in the suitable dimensional state space of kind, compares regular length particle estimate and actual value error, and then accurately Particle weights is weighed by introducing MCMC transfers after resampling, particle diversity reduction problem under static parameter is solved, has Effect improves particle filter iterative convergence speed, completes the parameter extraction to single channel sine FM mixed signal, and pass through reconstruct Signal completes sine FM mixed signal separation (Zhang S N, Zhao H C, Xiong G.Separation and parameter estimation of single channel sinusoidal frequency modulated signal Mixture sources based on particle filtering.Acta Phys.Sin., 2014,63:158401).
The content of the invention
The present invention is in order to solve drawbacks described above present in prior art and deficiency, there is provided a kind of single channel time-frequency is overlapping The method of blind signal separation, the blind separation of the overlapping Gauss amplitude-modulated signal of single channel time-frequency can be effectively realized, The present invention gives A kind of blending heredity with pre-estimation-minimum value search Blind Signal Separation method.This method is the modulation system according to signal, The model of signal is established, using the unique mixed signal received, the joint maximum likelihood function of estimation parameter required for obtaining, I.e. this problem treats the object function of optimizing parameter；According to the characteristic of signal in itself, pre-estimation is carried out to time width and temporal center；Profit Searched with blending heredity-minimum value searching algorithm be object function optimal value；Finally gone out with the Parameter reconstruction having been estimated that Each Gauss amplitude-modulated signal.
In order to solve the above technical problems, a kind of single channel time-frequency blind Signal Separation of Overlapped Signals of present invention offer, including with Lower step：
Step 1, signal model is established, the mixed signal received is converted into by several Gauss amplitude modulation source signal groups Into；
Step 2, calculates the joint maximum likelihood function of mixed signal, and the solution procedure of mixed signal is changed into solution The process of multidimensional variable parameter；
Step 3, according to characteristics of signals, estimate the temporal center and time width modulation parameter of each source signal；
Step 4, calculate the initial value of multidimensional variable parameter；
Step 5, calculate the optimal value of multidimensional variable parameter；
Step 6, calculate Gauss amplitude modulation source signal.
In the step 1, the mixed signal x (t) received is converted into being made up of M Gauss amplitude modulation source signal, expressed Formula is as follows：
Wherein,Represent the amplitude modulation(PAM) coefficient of each source signal component, t0In the time domain for representing each source signal component The heart, ωiThe time width of each source signal component is represented, P is the modulation parameter of each source signal component time width,Believe for each source The carrier frequency of number component, θiRepresent the initial phase of each source signal component, t is instantaneous time, and j is the imaginary part unit of imaginary number, f0To be each The centre frequency of individual source signal.
In the step 2, the expression formula for setting multidimensional variable parameter lambda is as follows：
Wherein,Represent the amplitude modulation(PAM) coefficient of each source signal component, t0In the time domain for representing each source signal component The heart, ωiThe time width of each source signal component is represented, P is the modulation parameter of each source signal component time width,Believe for each source The carrier frequency of number component, θiRepresent the initial phase of each source signal component；
Then, the expression formula of mixed signal x joint maximum likelihood function is：
Wherein, N is sampling number, and Q is total sampling number, and σ is the standard deviation of noise, TsFor the sampling interval of signal, y Signal used when instantaneously mixing the estimation of composition for several model signals, x represent the mixed signal received.
The optimal value expression of multidimensional variable parameter lambda is：
In the step 3, the mixed signal x (t) received data are substituted into following expression formula, obtain each source The modulation parameter P of component of signal time width and each source signal component temporal center t0Estimate evaluationWith
Wherein, t represents instantaneous time, f0Represent the centre frequency of each source signal.
In the step 4, by the expression formula of the multidimensional variable parameter lambda of setting,In P and t0Use respectivelyWithGeneration Replace, wherein,Represent the amplitude modulation(PAM) coefficient of each source signal component, t0Represent the temporal center of each source signal component, ωi The time width of each source signal component is represented, P is the modulation parameter of each source signal component time width,For each source signal component Carrier frequency, θiRepresent the initial phase of each source signal component；Meanwhile multidimensional variable λ is encoded using binary system, completely with The binary string of machine generation m fixed length is as the initial population that population size is m, and each the excursion of variable is [λ in λmin λmax], represented, then had with q bits p：
According to the expression formula of ideal adaptation angle valueThe fitness value of each individual is calculated, wherein, xj For individual, x is mixed signal, then carries out genetic manipulation to individual, after obtaining new population, another wheel computing is carried out, when most When big iterations is more than 50, the parameter of output is the initial value X0 of multidimensional variable parameter lambda, otherwise, recalculates ideal adaptation Genetic manipulation is carried out after angle value.
Initial point using the initial value X0 of multidimensional variable parameter lambda as search, utilizes the vertex function of given simplex It is worth size, it is determined that the highs and lows of simple shape function, the reflection passed through, extension and squeeze operation form newly simple Shape, when the absolute error E of estimate and mixed signal is less than 1e-6, the solution X1 of output is multidimensional variable λ optimal value；
The calculation expression of absolute error is E=| xj- x |, wherein, xjFor individual, x is mixed signal；
Reflection, compression and spreading coefficient are a, and b, c are constant, then reflect, compression and extended operation are respectively：
Wherein, n is the dimension of variable, and k is iterations,The functional value of the simplex centre of form is represented,Point Biao Shi not be by the functional value after reflection, compression, extension, x(k) hRepresent letter at the functional value and (n+1) point after reflecting Minimum value in numerical value.
Parameter in the optimal value X1 of multidimensional variable parameter lambda is substituted into source signal expression formula：
Each Gauss amplitude modulation source signal can be obtained, wherein,Represent the amplitude modulation(PAM) coefficient of each source signal component, t0 Represent the temporal center of each source signal component, ωiThe time width of each source signal component is represented,For each source signal component Carrier frequency, θiRepresent the initial phase of each source signal component, t is instantaneous time, and j is the imaginary part unit of imaginary number, f0Believe for each source Number centre frequency.
Foregoing genetic manipulation includes selecting duplication, intersection and mutation operation, wherein, carry out selection and replicate and crossover operation The probability of individual is more than the probability for carrying out mutation operation individual.
The advantageous effects that the present invention is reached：The present invention is that a kind of blending heredity-minimum value with pre-estimation is searched The multidimensional variable method for parameter estimation of rope algorithm, first the temporal center t of the time width modulation parameter P to source signal and source signal0Enter Row pre-estimation, then genetic algorithm and minimum value searching algorithm are mixed calculate other parameters again, so improve convergence rate with Computational accuracy.Blind separation effectively can be carried out to the overlapping Gauss amplitude-modulated signal of single channel time-frequency, not chosen by initial value is influenceed, and is estimated Count value precision is high, fast convergence rate.
Brief description of the drawings
Fig. 1 schematic flow sheets of the present invention；
The raw Gaussian amplitude modulation communication signal that test acts in Fig. 2 specific embodiment of the invention；
The mixed signal figure mixed in Fig. 3 specific embodiment of the invention by three source signals；
Fig. 4 is using the source signal figure after the method separation of the present invention；
Methods of the Fig. 5 using the present invention and the convergence rate comparison diagram using mixed search algorithm.
Embodiment
In order to be better understood by technical characteristic, technology contents and its technique effect reached of the present invention, now this is sent out Bright accompanying drawing is described in detail in conjunction with the embodiments.
Patent of the present invention is further illustrated with reference to the accompanying drawings and examples.
As shown in figure 1, the present invention provides a kind of method of single channel time-frequency overlapped signal blind separation, comprise the following steps：
Step 1, signal model is established, the mixed signal x (t) received is converted into by M Gauss amplitude modulation source signal group Into expression formula is as follows：
Wherein,Represent the amplitude modulation(PAM) coefficient of each source signal component, t0In the time domain for representing each source signal component The heart, ωiThe time width of each source signal component is represented, P is the modulation parameter of each source signal component time width,Believe for each source The carrier frequency of number component, θiThe initial phase of each source signal component is represented, t represents instantaneous time, and j represents the imaginary part unit of imaginary number, f0 Represent the centre frequency of each source signal.
Step 2, calculates the joint maximum likelihood function of mixed signal, and the solution procedure of mixed signal is changed into solution The process of multidimensional variable parameter, the expression formula for setting multidimensional variable parameter lambda are as follows：
Then, the expression formula of mixed signal x joint maximum likelihood function is：
Wherein, N is sampling number, and Q is total sampling number, and σ is the standard deviation of noise, and Ts is the sampling interval of signal, y Signal used when representing instantaneously to mix the estimation formed by several model signals, the mixed signal that x expressions receive.
The optimal value expression of multidimensional variable parameter lambda is：
Step 3, according to characteristics of signals, estimate the temporal center and time width modulation parameter of each source signal：
The mixed signal x (t) received data are substituted into following expression formula, obtain each source signal component time width Modulation parameter P and each source signal component temporal center t0Estimate evaluationWith
Wherein, t represents instantaneous time, f0Represent the centre frequency of each source signal.
Step 4, calculate the initial value X0 of multidimensional variable parameter：By the expression formula of the multidimensional variable parameter lambda of setting,In P and t0Use respectivelyWithGeneration Replace, meanwhile, multidimensional variable λ is encoded using binary system, the binary string of completely random generation m fixed length is as population size For m initial population, the excursion of each variable is [λ in λmin λmax], represented, then had with q bits p：
According to the expression formula of ideal adaptation angle valueThe fitness value of each individual is calculated, wherein, xj For individual, x is mixed signal, and then to individual progress genetic manipulation, the genetic manipulation, which includes selection, to be replicated, intersect and make a variation Operation, wherein, carry out selection and replicate the probability for being more than with the individual probability of crossover operation and carrying out mutation operation individual, obtain new Population after, carry out another wheel computing, when maximum iteration is more than 50, the parameter of output for multidimensional variable parameter lambda just Initial value X0, otherwise, genetic manipulation is carried out after recalculating ideal adaptation angle value.
Step 5, calculate the optimal value X1 of multidimensional variable parameter：Using the initial value X0 of multidimensional variable parameter lambda as search Initial point, using the vertex function value size of given simplex, it is determined that the highs and lows of simple shape function, pass through Reflection, extension and squeeze operation form new simplex, defeated when the absolute error E of estimate and mixed signal is less than 1e-6 The solution X1 gone out is multidimensional variable λ optimal value；
The calculation expression of absolute error is E=| xj- x |, wherein, xjFor individual, x is mixed signal；
Reflection, compression and spreading coefficient are a, and b, c are constant, then reflect, compression and extended operation are respectively：
Wherein, n is the dimension of variable, and k is iterations,The functional value of the simplex centre of form is represented,Point Biao Shi not be by the functional value after reflection, compression, extension, x(k) hRepresent letter at the functional value and (n+1) point after reflecting Minimum value in numerical value.
Step 6, calculate Gauss amplitude modulation source signal：Parameter in the optimal value X1 of multidimensional variable parameter lambda is substituted into source signal Expression formula：
Each Gauss amplitude modulation source signal can be obtained.
In order to verify the effect of the inventive method, the inventive method, and and initial value are realized on matlab software platforms The minimum value search method within away from actual value 5% and blending heredity-minimum value searching algorithm is controlled to be contrasted.Contrast As a result it is as shown in table 1.
The parameters separated Comparative result of table 1
It can be drawn according to the data of table 1, the hybrid search algorithm with pre-estimation is searched for compared to minimum value in the present invention Algorithm and hybrid search algorithm, root-mean-square error are obviously reduced, and its estimated accuracy is higher, and are not influenceed by initial value selection.
Frequency is respectively 2MHz, 2.2MHz, 2.4MHz single Gauss amplitude modulation communication signal centered on Fig. 2.It is received Mixed signal x (t) it is as shown in Figure 3.It is as shown in Figure 4 that separation recovers each source signal.Fig. 4 and Fig. 2 contrasts can be seen that Method separating effect provided by the invention is fine.Convergence curve comparison diagram with pre-estimation searching method and mixed search algorithm is such as Shown in Fig. 5.From figure 5 it can be seen that compared to mixed search algorithm, method convergence rate provided by the invention faster, can be more Effectively recover each source signal component.
The present invention is disclosed with preferred embodiment above, so it is not intended to limiting the invention, all to take equivalent substitution Or the technical scheme that the scheme of equivalent transformation is obtained, all fall within protection scope of the present invention.

Claims (2)

  1. A kind of 1. single channel time-frequency blind Signal Separation of Overlapped Signals, it is characterised in that：Comprise the following steps：
    Step 1, signal model is established, the mixed signal received when reality is measured is converted into by several Gauss amplitude modulation sources Signal forms；
    The mixed signal x received during by actual measuring is converted into being made up of M Gauss amplitude modulation source signal, signal model expression formula It is as follows：
    <mrow> <mi>x</mi> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>=</mo> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>M</mi> </munderover> <msub> <mi>k</mi> <msub> <mi>a</mi> <mi>i</mi> </msub> </msub> <mi>exp</mi> <mo>&amp;lsqb;</mo> <mo>-</mo> <msup> <mrow> <mo>(</mo> <mi>t</mi> <mo>-</mo> <msub> <mi>t</mi> <mn>0</mn> </msub> <mo>)</mo> </mrow> <mn>2</mn> </msup> <mo>/</mo> <msup> <msub> <mi>&amp;omega;</mi> <mi>i</mi> </msub> <mn>2</mn> </msup> <mo>&amp;rsqb;</mo> <mi>exp</mi> <mo>&amp;lsqb;</mo> <mi>j</mi> <mn>2</mn> <mi>&amp;pi;</mi> <mrow> <mo>(</mo> <msub> <mi>f</mi> <mn>0</mn> </msub> <mo>+</mo> <msub> <mi>&amp;Delta;f</mi> <msub> <mi>c</mi> <mi>i</mi> </msub> </msub> <mo>)</mo> </mrow> <mrow> <mo>(</mo> <mi>t</mi> <mo>-</mo> <msub> <mi>t</mi> <mn>0</mn> </msub> <mo>)</mo> </mrow> <mo>+</mo> <msub> <mi>j&amp;theta;</mi> <mi>i</mi> </msub> <mo>&amp;rsqb;</mo> </mrow>
    Wherein, x (t) represents the signal synthesized by M Gauss amplitude modulation source signal；
    Step 2, calculates the joint maximum likelihood function of mixed signal, and the solution procedure of mixed signal is changed into solution multidimensional The process of variable parameter；
    The expression formula for setting multidimensional variable parameter lambda is as follows：
    <mrow> <mi>&amp;lambda;</mi> <mo>=</mo> <mrow> <mo>(</mo> <msub> <mi>t</mi> <mn>0</mn> </msub> <mo>,</mo> <mi>P</mi> <mo>,</mo> <msub> <mi>&amp;omega;</mi> <mn>1</mn> </msub> <mo>,</mo> <mn>...</mn> <msub> <mi>&amp;omega;</mi> <mi>i</mi> </msub> <mo>,</mo> <mo>(</mo> <mrow> <msub> <mi>f</mi> <mn>0</mn> </msub> <mo>+</mo> <msub> <mi>&amp;Delta;f</mi> <msub> <mi>c</mi> <mn>1</mn> </msub> </msub> </mrow> <mo>)</mo> <mo>,</mo> <mn>...</mn> <mo>,</mo> <mo>(</mo> <mrow> <msub> <mi>f</mi> <mn>0</mn> </msub> <mo>+</mo> <msub> <mi>&amp;Delta;f</mi> <msub> <mi>c</mi> <mi>i</mi> </msub> </msub> </mrow> <mo>)</mo> <mo>,</mo> <msub> <mi>k</mi> <msub> <mi>a</mi> <mn>1</mn> </msub> </msub> <mo>,</mo> <mn>...</mn> <mo>,</mo> <msub> <mi>k</mi> <msub> <mi>a</mi> <mi>i</mi> </msub> </msub> <mo>,</mo> <msub> <mi>&amp;theta;</mi> <mn>1</mn> </msub> <mo>,</mo> <mn>...</mn> <mo>,</mo> <msub> <mi>&amp;theta;</mi> <mi>i</mi> </msub> <mo>)</mo> </mrow> </mrow>
    Then, the expression formula of the mixed signal x received during actual measurement joint maximum likelihood function is：
    <mrow> <mi>f</mi> <mrow> <mo>(</mo> <mi>&amp;lambda;</mi> <mo>|</mo> <mi>x</mi> <mo>)</mo> </mrow> <mo>=</mo> <munderover> <mo>&amp;Pi;</mo> <mrow> <mi>N</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>Q</mi> </munderover> <mfrac> <mn>1</mn> <mrow> <msup> <mi>&amp;pi;&amp;sigma;</mi> <mn>2</mn> </msup> </mrow> </mfrac> <mi>exp</mi> <mrow> <mo>(</mo> <mo>-</mo> <mfrac> <mrow> <mo>|</mo> <mi>x</mi> <mrow> <mo>(</mo> <msub> <mi>NT</mi> <mi>s</mi> </msub> <mo>)</mo> </mrow> <mo>-</mo> <mi>y</mi> <mrow> <mo>(</mo> <msub> <mi>NT</mi> <mi>s</mi> </msub> <mo>,</mo> <mi>&amp;lambda;</mi> <mo>)</mo> </mrow> <msup> <mo>|</mo> <mn>2</mn> </msup> </mrow> <msup> <mi>&amp;sigma;</mi> <mn>2</mn> </msup> </mfrac> <mo>)</mo> </mrow> </mrow>
    The optimal value expression of multidimensional variable parameter lambda is：
    <mrow> <mtable> <mtr> <mtd> <mrow> <msub> <mi>&amp;lambda;</mi> <mrow> <mi>o</mi> <mi>p</mi> <mi>t</mi> </mrow> </msub> <mo>=</mo> <mi>arg</mi> <munder> <mi>max</mi> <mi>&amp;lambda;</mi> </munder> <mi>ln</mi> <mrow> <mo>(</mo> <mi>ln</mi> <mi>f</mi> <mo>(</mo> <mrow> <mi>&amp;lambda;</mi> <mo>|</mo> <mi>x</mi> </mrow> <mo>)</mo> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mo>=</mo> <mi>arg</mi> <munder> <mi>min</mi> <mi>&amp;lambda;</mi> </munder> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>n</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>N</mi> </munderover> <mo>|</mo> <mi>x</mi> <mrow> <mo>(</mo> <msub> <mi>nT</mi> <mi>s</mi> </msub> <mo>)</mo> </mrow> <mo>-</mo> <mi>y</mi> <mrow> <mo>(</mo> <msub> <mi>nT</mi> <mi>s</mi> </msub> <mo>,</mo> <mi>&amp;lambda;</mi> <mo>)</mo> </mrow> <msup> <mo>|</mo> <mn>2</mn> </msup> </mrow> </mtd> </mtr> </mtable> <mo>;</mo> </mrow>
    Step 3, according to characteristics of signals, estimate the temporal center and time width modulation parameter of each source signal；By M Gauss amplitude modulation The signal x (t) of source signal synthesis data are substituted into following expression formula, obtain the modulation parameter P of each source signal component time width With the temporal center t of each source signal component0Estimate evaluationWith
    <mrow> <mover> <msub> <mi>t</mi> <mn>0</mn> </msub> <mo>^</mo> </mover> <mo>=</mo> <msubsup> <mo>&amp;Integral;</mo> <mrow> <mo>-</mo> <mi>&amp;infin;</mi> </mrow> <mi>&amp;infin;</mi> </msubsup> <mo>|</mo> <mi>x</mi> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <msup> <mo>|</mo> <mn>2</mn> </msup> <mi>t</mi> <mi>d</mi> <mi>t</mi> <mo>/</mo> <msubsup> <mo>&amp;Integral;</mo> <mrow> <mo>-</mo> <mi>&amp;infin;</mi> </mrow> <mi>&amp;infin;</mi> </msubsup> <mo>|</mo> <mi>x</mi> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <msup> <mo>|</mo> <mn>2</mn> </msup> <mi>d</mi> <mi>t</mi> </mrow>
    <mrow> <mover> <mi>P</mi> <mo>^</mo> </mover> <mo>=</mo> <mrow> <mo>(</mo> <msub> <mi>f</mi> <mn>0</mn> </msub> <msqrt> <mrow> <msubsup> <mo>&amp;Integral;</mo> <mrow> <mo>-</mo> <mi>&amp;infin;</mi> </mrow> <mi>&amp;infin;</mi> </msubsup> <mo>|</mo> <mi>x</mi> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <msup> <mo>|</mo> <mn>2</mn> </msup> <msup> <mrow> <mo>(</mo> <mi>t</mi> <mo>-</mo> <mover> <msub> <mi>t</mi> <mn>0</mn> </msub> <mo>^</mo> </mover> <mo>)</mo> </mrow> <mn>2</mn> </msup> <mi>d</mi> <mi>t</mi> </mrow> </msqrt> <mo>)</mo> </mrow> <mo>/</mo> <mn>2</mn> <msqrt> <mrow> <msubsup> <mo>&amp;Integral;</mo> <mrow> <mo>-</mo> <mi>&amp;infin;</mi> </mrow> <mi>&amp;infin;</mi> </msubsup> <mo>|</mo> <mi>x</mi> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <msup> <mo>|</mo> <mn>2</mn> </msup> <mi>d</mi> <mi>t</mi> </mrow> </msqrt> <mo>;</mo> </mrow>
    Step 4, calculate the initial value of multidimensional variable parameter；
    By the expression formula of the multidimensional variable parameter lambda of setting, In P and t0Respectively with estimating evaluationWithInstead of；Meanwhile multidimensional variable λ is encoded using binary system, completely random The binary string of m fixed length is generated as the initial population that population size is m, each the excursion of variable is [λ in λmin, λmax], wherein λminIt is λ lower limit, λmaxIt is λ higher limit, is represented, then had with q bits p：
    <mrow> <mi>&amp;lambda;</mi> <mo>=</mo> <msub> <mi>&amp;lambda;</mi> <mi>min</mi> </msub> <mo>+</mo> <mfrac> <mi>p</mi> <mrow> <msup> <mn>2</mn> <mi>q</mi> </msup> <mo>-</mo> <mn>1</mn> </mrow> </mfrac> <mrow> <mo>(</mo> <msub> <mi>&amp;lambda;</mi> <mi>max</mi> </msub> <mo>-</mo> <msub> <mi>&amp;lambda;</mi> <mi>min</mi> </msub> <mo>)</mo> </mrow> </mrow>
    According to the expression formula of ideal adaptation angle valueThe fitness value of each individual is calculated, wherein, xjTo be individual Body, x are the mixed signal received during actual measurement, then carry out genetic manipulation to individual, after obtaining new population, are carried out another One wheel computing, when maximum iteration is more than 50, the parameter of output is the initial value X0 of multidimensional variable parameter lambda, otherwise, again Genetic manipulation is carried out after calculating ideal adaptation angle value；
    Step 5, calculate the optimal value of multidimensional variable parameter；
    Initial point using the initial value X0 of multidimensional variable parameter lambda as search is big using the vertex function value of given simplex It is small, it is determined that the highs and lows of simple shape function, the reflection passed through, extension and squeeze operation form new simplex, when When the absolute error E of estimate and mixed signal is less than 1e-6, the solution X1 of output is multidimensional variable λ optimal value；
    The calculation expression of absolute error is E=| xj- x |, wherein, xjFor individual, x is the mixing letter received during actual measurement Number；
    Reflectance factor a, compressed coefficient b and spreading coefficient c are constant, then reflect, compression and extended operation are respectively：
    <mrow> <msubsup> <mi>x</mi> <mi>r</mi> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> </msubsup> <mo>=</mo> <msup> <mover> <mi>x</mi> <mo>&amp;OverBar;</mo> </mover> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> </msup> <mo>+</mo> <mi>a</mi> <mrow> <mo>(</mo> <msup> <mover> <mi>x</mi> <mo>&amp;OverBar;</mo> </mover> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> </msup> <mo>-</mo> <msubsup> <mi>x</mi> <mrow> <mi>n</mi> <mo>+</mo> <mn>1</mn> </mrow> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> </msubsup> <mo>)</mo> </mrow> </mrow>
    <mrow> <msubsup> <mi>x</mi> <mi>c</mi> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> </msubsup> <mo>=</mo> <msup> <mover> <mi>x</mi> <mo>&amp;OverBar;</mo> </mover> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> </msup> <mo>+</mo> <mi>b</mi> <mrow> <mo>(</mo> <msubsup> <mi>x</mi> <mi>h</mi> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> </msubsup> <mo>-</mo> <msup> <mover> <mi>x</mi> <mo>&amp;OverBar;</mo> </mover> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> </msup> <mo>)</mo> </mrow> </mrow>
    <mrow> <msubsup> <mi>x</mi> <mi>e</mi> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> </msubsup> <mo>=</mo> <msup> <mover> <mi>x</mi> <mo>&amp;OverBar;</mo> </mover> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> </msup> <mo>+</mo> <mi>c</mi> <mrow> <mo>(</mo> <msubsup> <mi>x</mi> <mrow> <mi>n</mi> <mo>+</mo> <mn>1</mn> </mrow> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> </msubsup> <mo>-</mo> <msup> <mover> <mi>x</mi> <mo>&amp;OverBar;</mo> </mover> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> </msup> <mo>)</mo> </mrow> </mrow>
    <mrow> <msubsup> <mi>x</mi> <mi>h</mi> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> </msubsup> <mo>=</mo> <mi>min</mi> <mo>{</mo> <msubsup> <mi>x</mi> <mrow> <mi>n</mi> <mo>+</mo> <mn>1</mn> </mrow> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> </msubsup> <mo>,</mo> <msubsup> <mi>x</mi> <mi>r</mi> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> </msubsup> <mo>}</mo> </mrow>
    Wherein, n is the dimension of variable, and k is iterations,The functional value of the simplex centre of form is represented,Table respectively Show through reflection, compress, extend after functional value, x(k) hRepresent functional value at the functional value and (n+1) point after reflecting In minimum value；
    Step 6, calculate each Gauss amplitude modulation source signal；
    Parameter in the optimal value X1 of multidimensional variable parameter lambda is substituted into source signal expression formula, you can obtain each Gauss amplitude modulation source Signal si(t),：
    <mrow> <msub> <mi>s</mi> <mi>i</mi> </msub> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>=</mo> <msub> <mi>k</mi> <msub> <mi>a</mi> <mi>i</mi> </msub> </msub> <mi>exp</mi> <mo>&amp;lsqb;</mo> <mo>-</mo> <msup> <mrow> <mo>(</mo> <mi>t</mi> <mo>-</mo> <msub> <mi>t</mi> <mn>0</mn> </msub> <mo>)</mo> </mrow> <mn>2</mn> </msup> <mo>/</mo> <msubsup> <mi>&amp;omega;</mi> <mi>i</mi> <mn>2</mn> </msubsup> <mo>&amp;rsqb;</mo> <mi>exp</mi> <mo>&amp;lsqb;</mo> <mi>j</mi> <mn>2</mn> <mi>&amp;pi;</mi> <mrow> <mo>(</mo> <msub> <mi>f</mi> <mn>0</mn> </msub> <mo>+</mo> <msub> <mi>&amp;Delta;f</mi> <msub> <mi>c</mi> <mi>i</mi> </msub> </msub> <mo>)</mo> </mrow> <mrow> <mo>(</mo> <mi>t</mi> <mo>-</mo> <msub> <mi>t</mi> <mn>0</mn> </msub> <mo>)</mo> </mrow> <mo>+</mo> <msub> <mi>j&amp;theta;</mi> <mi>i</mi> </msub> <mo>&amp;rsqb;</mo> </mrow>
    In above-mentioned expression formula：Represent the amplitude modulation(PAM) coefficient of each source signal component；t0Represent the time domain of each source signal component Center；ωiRepresent the time width of each source signal component；θiRepresent the initial phase of each source signal component；T is instantaneous time；J is The imaginary part unit of imaginary number；f0For the centre frequency of each source signal；ΔfciIt is the carrier frequency and reference frequency of each source signal component Difference；P is the modulation parameter of each source signal component time width；For the carrier frequency of each source signal component；N is sampling number； Q is total sampling number；σ is the standard deviation of noise；TsFor the sampling interval of signal；Y is several model signals when instantaneous Between t when mixing form estimation when signal used, i.e. y is t function, y (NTs) represent in t=NTSWhen y value；x(NTs) Represent t=NTSWhen value, the signal x (t) synthesized by M Gauss amplitude modulation source signal expression formula is calculated.
  2. 2. single channel time-frequency blind Signal Separation of Overlapped Signals according to claim 1, it is characterised in that：The genetic manipulation Including selection replicate, intersect and mutation operation, wherein, carry out selection replicate and crossover operation individual probability be more than become The probability of ETTHER-OR operation individual.
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