CN106067004A - The recognition methods of digital modulation signals under a kind of impulsive noise - Google Patents
The recognition methods of digital modulation signals under a kind of impulsive noise Download PDFInfo
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Abstract
The invention discloses the recognition methods of digital modulation signals under a kind of impulsive noise, said method comprising the steps of: calculate the fractional lower-order ambiguity function of digital modulation signals；Intercept the tangent plane that Doppler frequency shift is zero of fractional lower-order ambiguity function, and this tangent plane is converted into two dimensional image and fills below this image border so that it is become the coloured coloured image of tool；Coloured image is carried out gray processing, binaryzation, image segmentation and the normalization of image size, and again image is translated and dimension normalization；Extract the Zernike square characteristic vector as identification of image, and utilize probabilistic neural network grader that digital modulation signals is identified.The present invention, under standard profile impulsive noise, has good recognition performance to digital modulation signals 2ASK, 4ASK, 2FSK, 4FSK, BPSK.
Description
Technical field
The invention belongs to communication technical field, particularly relate to the recognition methods of digital modulation signals under a kind of impulsive noise.
Background technology
The Modulation Identification of signal is a key technology between signal detection and demodulation, has in military and civilian field
Extensively application.Traditional digital modulation signal recognizing method is many with Gaussian noise as noise model, and making an uproar in actual environment
Sound often has the probability density function of spike character and noise and has thicker hangover.The research card of professor Nikias et al.
Bright, Alpha Stable distritation is a kind of effective model describing this kind of impulse noise signal.Therefore numeral under research impulsive noise
The recognition methods of modulated signal has certain meaning.
Vinod A P et al. have employed normalization fourth order cumulant based on fractional lower-order statistics under impulsive noise
BPSK, QPSK, 16QAM, 64QAM signal is identified, but the recognition performance that the method is when mixing signal to noise ratio and being relatively low is poor
(Vinod A P, Madhukumar A S, Krishna A K, Automatic Modulation Classification for
Cognitive Radios using Cumulants based on Fractional Lower Order Statistics
[J], URSI on General Assembly and Scientific Symposium, 2011:1-4.).He Tao et al. uses
BPSK and 2FSK signal containing impulsive noise is identified by fractional lower-order statistical moment, but the method identification signal kinds
Less (He Tao, Zhou Zheng ' ou, Modulation Classification in Alpha-Stable Noise [C],
International Conference on Communications, Circuits and Systems, ICCCAS, 2007:
193-196.).Fanggang WANG et al. utilize the Kolmogorov-Smirnov method of inspection to MQAM under impulsive noise and
Mpsk signal is identified, but undesirable (WANG FG, the WANG X D.Fast of the method recognition effect under low mixing signal to noise ratio
and Robust Modulation Classification via Kolmogorov-Smirnov Test[J].IEEE
Transaction on Communications, 2010,58 (8): 2324-2332.).
Summary of the invention
It is an object of the invention to provide the recognition methods of digital modulation signals under a kind of impulsive noise, it is intended to solve existing
Impulsive noise under digital modulation signals recognition methods exist mix signal to noise ratio relatively low time recognition performance poor, identify
Signal kinds is less, the problem that recognition effect is undesirable.
The present invention is achieved in that the recognition methods of digital modulation signals under a kind of impulsive noise, described impulsive noise
The recognition methods of lower digital modulation signals comprises the following steps:
S1 calculates the fractional lower-order ambiguity function of digital modulation signals；
S2 intercepts the tangent plane that Doppler frequency shift is zero of fractional lower-order ambiguity function, and this tangent plane is converted into two dimensional image
And fill below this image border so that it is become the coloured coloured image of tool；
S3 carries out gray processing, binaryzation, image segmentation and the normalization of image size to coloured image, and enters image again
Row translation and dimension normalization；
S4 extracts the Zernike square characteristic vector as identification of image, and utilizes probabilistic neural network grader logarithm
Word modulated signal is identified.
It should be noted that in step S1, the fractional lower-order ambiguity function calculating digital modulation signals is carried out as follows:
Receive signal y (t) can be expressed as:
Y (t)=x (t)+n (t)；
Wherein, x (t) is digital modulation signals, and n (t) is the impulsive noise of standard S α S distribution.Adjust for MASK and MPSK
System, the analytical form of x (t) is expressed as:
Wherein, N is sampling number, anFor the information symbol sent, in MASK signal, an=0,1,2 ..., M-1, M are
Order of modulation, in mpsk signal, an=ej2πε/M, ε=0,1,2 ..., M-1, g (t) represent rectangle molding pulse, TbRepresent symbol
Number cycle, fcRepresent carrier frequency, carrier wave initial phaseIt it is equally distributed random number in [0,2 π].Adjust for MFSK
System, the analytical form of x (t) is expressed as:
Wherein, fmFor the side-play amount of m-th carrier frequency, if MFSK is signal carrier shift Δ f, then fm=-(M-1) Δ f ,-(M-
3) Δ f ..., (M-3) Δ f, (M-1) Δ f, carrier wave initial phaseIt it is equally distributed random number in [0,2 π].
In addition to special circumstances, there is not the expression formula of closing in the probability density function of Alpha Stable distritation, the most typically uses
Following characteristics function describes its distribution character:
WhereinFor sign function,
α (0 ＜ α≤2) is characterized index, and γ is the coefficient of dispersion, and β is symmetric parameter, and ζ is location parameter.When ζ=0, β=0
And during γ=1, this distribution is referred to as standard S α S distribution.
The fractional lower-order ambiguity function of digital modulation signals x (t) is expressed as:
Wherein, τ is delay skew, and f is Doppler frequency shift, 0 ＜ a, b ＜ α/2.x*T () represents the conjugation of x (t).As x (t)
During for real signal, x (t)＜ p ＞=| x (t) |＜ p ＞sgn(x(t))；When x (t) is time multiplexed signal, [x (t)]＜ p ＞=| x (t) |p-1x*
T (), this nonlinear operation only changes the amplitude information of signal, retains its frequency and phase information, can make an uproar by effectively suppressor pulse
Sound.
It should be noted that in step S2, intercept the tangent plane that Doppler frequency shift is zero of fractional lower-order ambiguity function, and will
This tangent plane is converted into two dimensional image and fills below this image border so that it is become tool coloured coloured image by following enter
OK:
The tangent plane that Doppler frequency shift is zero of the fractional lower-order ambiguity function of digital modulation signals MASK, MFSK, MPSK can
It is expressed as:
Wherein,Be width be TbThe gate function of-τ.
Above three formulas are onlyCoefficient different.MASK signalThe most permanent is 1；MFSK signalThe most permanent is 1, therefore the tangent plane that Doppler frequency shift is zero wheel of the fractional lower-order ambiguity function of three class digital modulation signals
Wide different.For 2ASK signal, an=0,1；For 4ASK signal, an=0,1,2,3, two kinds of signalsDifference, mark
The Doppler frequency shift of low order ambiguity function be zero tangent plane profile the most different.For 2FSK signal, fm=-Δ f, Δ f；For
4FSK signal, fm=-3 Δ f ,-Δ f, Δ f, 3 Δ f, two kinds of signalsDifference, the Doppler of fractional lower-order ambiguity function
Frequency displacement be zero tangent plane profile the most different.Therefore the fractional lower-order ambiguity function of 2ASK, 4ASK, 2FSK, 4FSK, bpsk signal
Doppler frequency shift is that the contour shape of the tangent plane of zero is different, can be using its shape facility as the characteristic vector of signal identification.
The tangent plane that Doppler frequency shift is zero of fractional lower-order ambiguity function is converted into two dimensional imageAnd arrange little
In the pixel of tangent plane maximum, (s, pixel value z) isWhereinξ and λ is respectively figure
As the value of Red Green Blue, image is made to become the coloured coloured image of tool.
It should be noted that in step S3, coloured image is carried out gray processing, binaryzation, image segmentation and image size
Normalization, and again image is translated and dimension normalization is carried out as follows:
The color three dimensional image that image after filling is made up of red (R), green (G), blue (B) three primary colors, schemes for convenience
As processing, generally coloured image is converted into gray level image.The value of tri-components of RGB of each pixel of coloured image arrives 0
Between 255, set up rectangular coordinate system in space with R, G, B for coordinate axes respectively, then the color of each pixel of coloured image is permissible
Represent with this three-dimensional point, and each pixel of gray level image can represent with the point of straight line R=G=B.Will
RGB three dimensions is mapped to the one-dimensional space, and according to human eye, color senses different in addition different weight, obtains gray scale
Value:
Gray=0.299 × R+0.587 × G+0.114 × B；
Each pixel by original color image is set to the operation result of above formula, has been converted to gray level image.
The image binaryzation i.e. pixel value of scanning grey pictures, chooses an optimum gradation threshold value, will be greater than the picture of threshold value
Vegetarian refreshments is set to 1, is set to 0 less than the pixel of threshold value, divides the image into target (prospect) and background two parts.The present invention utilizes
Big Ostu method, chooses the threshold value of the inter-class variance maximum making target and background as optimal threshold.If image is
Size is O × Q, and the segmentation threshold of target and background is l, and optimal threshold is l*, the pixel number belonging to target accounts for total pixel
The ratio of number is w0, its average gray μ0；Belong to the pixel number of background accounting for the ratio of total pixel number is w1, its average gray
For μ1.The grand mean gray scale of image is designated as μ, and the inter-class variance of target and background is designated asGray value is less than the pixel of threshold value
Number scale makees Ω0, gray scale is denoted as Ω more than the number of pixels of threshold value1, then have:
Ω0+Ω1=O × Q, w0+w1=1；
μ=w0μ0+w1μ1；
The l tried to achieve*It is optimal threshold, and then can be by image binaryzation.
Using morphological image processing method, by structural element, (minor matrix slided on image, its element is 0
Or 1) carry out logical operations with bianry image, produce new image, it is achieved image is split.Bianry image can be considered a set,
Represent with J, in original image pixel value be the point of 1 be set element.If structural element S is all 1's matrix of 3 × 3, work as structural elements
The central point of element moves on to the point in image, and (s, time z), is denoted as Ssz.Morphology elementary operation is that burn into expands, opens and close.
Erosion operation is expressed as:
Dilation operation is expressed as:
Opening operation is expressed as:
The present invention utilizes opening operation to obtain target image, then image background is filled to black, former bianry image and filling
The image of good black background makees the target area after AND operation just can be split.
Use arest neighbors interpolation method normalized image Aspect Ratio, make all image sizes all keep consistent, arrange here
Length-width ratio is 1:1.If image isIts value is the binary value of pixel,For the target figure after normalization
Picture.If H, C are the height and width of original image, h, c are the height and width of target image, then original image pixel (s, z) and target image
Relation between pixel (s ', z ') is:
S=s'(C/c), z=z'(H/h)；
Can be by the image that image normalization is unified size through above-mentioned coordinate transform, if the coordinate of target image occurs
Decimal, then in the value original image of this coordinate points, the binary value of the coordinate points that this coordinate points of distance is nearest replaces.
Employing standard square carrys out normalization one sub-pictureMap an image in unit circle.Standard square is by following formula meter
Calculate:
The center of gravity of image can be obtained by standard square:
By the gravity motion of image to the unit circle center of circle, i.e. zero, so that it may so that image has translation invariance.η00
Represent the area of image object shape, image is converted
The size of image object thing can be become consistent.To sum up, image is converted:
It should be noted that in step S4, extract the Zernike square characteristic vector as identification of image, and utilize general
Digital modulation signals is identified being carried out as follows by rate neural network classifier:
Zernike proposes one group of manifold { V that writes a letter in reply being defined on unit circlerv(s, z) }:
Vrv(s, z)=Vrv(ρ,θ)；
Wherein ρ is that (θ is former point-to-point (s, line z) and the anticlockwise folder of x-axis to former point-to-point for s, distance z)
Angle.Have in unit circle translation and scale invariance any image g (s, z) can represent by unique following formula:
Wherein ZrvThe i.e. r rank v weight Zernike square of image:
Wherein, r=0,1,2 ..., ∞, 0≤| v |≤r and r-| v | is even number.For discrete digital picture,
Zernike square is tried to achieve by following formula:
Finally using the Zernike square tried to achieve as characteristic vector.Probabilistic neural network is utilized to be modulated signal identification, its
Activation primitive is Gaussian function, is expressed as follows:
Wherein, δ is the extension constant of RBF.
The recognition methods of digital modulation signals under the impulsive noise that the present invention provides, in the situation considering raised cosine roll off
Under, when mix signal to noise ratio at more than 8dB time, 2ASK, 4ASK, 2FSK, 4FSK, bpsk signal discrimination more than 90%, can
See that the present invention has good recognition performance.
Accompanying drawing explanation
Fig. 1 is the recognition methods flow chart of digital modulation signals under the impulsive noise that the embodiment of the present invention provides.
Fig. 2 is the Digital modulation identification performance map under standard S α S distribution impulsive noise that the embodiment of the present invention provides.
Detailed description of the invention
In order to make the purpose of the present invention, technical scheme and advantage clearer, below in conjunction with embodiment, to the present invention
It is further elaborated.Should be appreciated that specific embodiment described herein, only in order to explain the present invention, is not used to
Limit the present invention.
Below in conjunction with the accompanying drawings the application principle of the present invention is explained in detail.
As it is shown in figure 1, the recognition methods of digital modulation signals comprises the following steps under the impulsive noise of the embodiment of the present invention:
S101: calculate the fractional lower-order ambiguity function of digital modulation signals；
S102: intercept the tangent plane that Doppler frequency shift is zero of fractional lower-order ambiguity function, and this tangent plane is converted into two dimension
Image and filling below this image border so that it is become the coloured coloured image of tool；
S103: coloured image is carried out gray processing, binaryzation, image segmentation and the normalization of image size, and again to figure
As carrying out translating and dimension normalization；
S104: extract the Zernike square characteristic vector as identification of image, and utilize probabilistic neural network grader pair
Digital modulation signals is identified.
Below in conjunction with specific embodiment, the application principle of the present invention is further described.
S1 calculates the fractional lower-order ambiguity function of digital modulation signals；
It should be noted that in step S1, the fractional lower-order ambiguity function calculating digital modulation signals is carried out as follows:
Receive signal y (t) can be expressed as:
Y (t)=x (t)+n (t)；
Wherein, x (t) is digital modulation signals, and n (t) is the impulsive noise of standard S α S distribution.Adjust for MASK and MPSK
System, the analytical form of x (t) is expressed as:
Wherein, N is sampling number, anFor the information symbol sent, in MASK signal, an=0,1,2 ..., M-1, M are
Order of modulation, in mpsk signal, an=ej2πε/M, ε=0,1,2 ..., M-1, g (t) represent rectangle molding pulse, TbRepresent symbol
Number cycle, fcRepresent carrier frequency, carrier wave initial phaseIt it is equally distributed random number in [0,2 π].Adjust for MFSK
System, the analytical form of x (t) is expressed as:
Wherein, fmFor the side-play amount of m-th carrier frequency, if MFSK is signal carrier shift Δ f, then fm=-(M-1) Δ f ,-(M-
3) Δ f ..., (M-3) Δ f, (M-1) Δ f, carrier wave initial phaseIt it is equally distributed random number in [0,2 π].
In addition to special circumstances, there is not the expression formula of closing in the probability density function of Alpha Stable distritation, the most typically uses
Following characteristics function describes its distribution character:
WhereinFor sign function,
α (0 ＜ α≤2) is characterized index, and γ is the coefficient of dispersion, and β is symmetric parameter, and ζ is location parameter.When ζ=0, β=0
And during γ=1, this distribution is referred to as standard S α S distribution.
The fractional lower-order ambiguity function of digital modulation signals x (t) is expressed as:
Wherein, τ is delay skew, and f is Doppler frequency shift, 0 ＜ a, b ＜ α/2.x*T () represents the conjugation of x (t).As x (t)
During for real signal, x (t)＜ p ＞=| x (t) |＜ p ＞sgn(x(t))；When x (t) is time multiplexed signal, [x (t)]＜ p ＞=| x (t) |p-1x*
T (), this nonlinear operation only changes the amplitude information of signal, retains its frequency and phase information, can make an uproar by effectively suppressor pulse
Sound.
S2 intercepts the tangent plane that Doppler frequency shift is zero of fractional lower-order ambiguity function, and this tangent plane is converted into two dimensional image
And fill below this image border so that it is become the coloured coloured image of tool；
It should be noted that in step S2, intercept the tangent plane that Doppler frequency shift is zero of fractional lower-order ambiguity function, and will
This tangent plane is converted into two dimensional image and fills below this image border so that it is become tool coloured coloured image by following enter
OK:
The tangent plane that Doppler frequency shift is zero of the fractional lower-order ambiguity function of digital modulation signals MASK, MFSK, MPSK can
It is expressed as:
Wherein,Be width be TbThe gate function of-τ.
Above three formulas are onlyCoefficient different.MASK signalThe most permanent is 1；MFSK signalThe most permanent is 1, therefore the tangent plane profile that Doppler frequency shift is zero of the fractional lower-order ambiguity function of three class digital modulation signals
Different.For 2ASK signal, an=0,1；For 4ASK signal, an=0,1,2,3, two kinds of signalsDifference, fractional lower-order
The Doppler frequency shift of ambiguity function be zero tangent plane profile the most different.For 2FSK signal, fm=-Δ f, Δ f；4FSK is believed
Number, fm=-3 Δ f ,-Δ f, Δ f, 3 Δ f, two kinds of signalsDifference, the Doppler frequency shift of fractional lower-order ambiguity function is
The tangent plane profile of zero is the most different.Therefore the Doppler of the fractional lower-order ambiguity function of 2ASK, 4ASK, 2FSK, 4FSK, bpsk signal
Frequency displacement is that the contour shape of the tangent plane of zero is different, can be using its shape facility as the characteristic vector of signal identification.
The tangent plane that Doppler frequency shift is zero of fractional lower-order ambiguity function is converted into two dimensional imageAnd arrange little
In the pixel of tangent plane maximum, (s, pixel value z) isWhereinξ and λ is respectively figure
As the value of Red Green Blue, image is made to become the coloured coloured image of tool.
S3 carries out gray processing, binaryzation, image segmentation and the normalization of image size to coloured image, and enters image again
Row translation and dimension normalization；
It should be noted that in step S3, coloured image is carried out gray processing, binaryzation, image segmentation and image size
Normalization, and again image is translated and dimension normalization is carried out as follows:
The color three dimensional image that image after filling is made up of red (R), green (G), blue (B) three primary colors, schemes for convenience
As processing, generally coloured image is converted into gray level image.The value of tri-components of RGB of each pixel of coloured image arrives 0
Between 255, set up rectangular coordinate system in space with R, G, B for coordinate axes respectively, then the color of each pixel of coloured image is permissible
Represent with this three-dimensional point, and each pixel of gray level image can represent with the point of straight line R=G=B.Will
RGB three dimensions is mapped to the one-dimensional space, and according to human eye, color senses different in addition different weight, obtains gray scale
Value:
Gray=0.299 × R+0.587 × G+0.114 × B；
Each pixel by original color image is set to the operation result of above formula, has been converted to gray level image.
The image binaryzation i.e. pixel value of scanning grey pictures, chooses an optimum gradation threshold value, will be greater than the picture of threshold value
Vegetarian refreshments is set to 1, is set to 0 less than the pixel of threshold value, divides the image into target (prospect) and background two parts.The present invention utilizes
Big Ostu method, chooses the threshold value of the inter-class variance maximum making target and background as optimal threshold.If image is
Size is O × Q, and the segmentation threshold of target and background is l, and optimal threshold is l*, the pixel number belonging to target accounts for total pixel
The ratio of number is w0, its average gray μ0；Belong to the pixel number of background accounting for the ratio of total pixel number is w1, its average gray
For μ1.The grand mean gray scale of image is designated as μ, and the inter-class variance of target and background is designated asGray value is less than the pixel of threshold value
Number scale makees Ω0, gray scale is denoted as Ω more than the number of pixels of threshold value1, then have:
Ω0+Ω1=O × Q, w0+w1=1；
μ=w0μ0+w1μ1；
The l tried to achieve*It is optimal threshold, and then can be by image binaryzation.
Using morphological image processing method, by structural element, (minor matrix slided on image, its element is 0
Or 1) carry out logical operations with bianry image, produce new image, it is achieved image is split.Bianry image can be considered a set,
Represent with J, in original image pixel value be the point of 1 be set element.If structural element S is all 1's matrix of 3 × 3, work as structural elements
The central point of element moves on to the point in image, and (s, time z), is denoted as Ssz.Morphology elementary operation is that burn into expands, opens and close.
Erosion operation is expressed as:
Dilation operation is expressed as:
Opening operation is expressed as:
The present invention utilizes opening operation to obtain target image, then image background is filled to black, former bianry image and filling
The image of good black background makees the target area after AND operation just can be split.
Use arest neighbors interpolation method normalized image Aspect Ratio, make all image sizes all keep consistent, arrange here
Length-width ratio is 1:1.If image isIts value is the binary value of pixel,For the target image after normalization.
If H, C are the height and width of original image, h, c are the height and width of target image, then (s, z) with target image pixel for original image pixel
Relation between point (s ', z ') is:
S=s'(C/c), z=z'(H/h)；
Can be by the image that image normalization is unified size through above-mentioned coordinate transform, if the coordinate of target image occurs little
Number, then in the value original image of this coordinate points, the binary value of the coordinate points that this coordinate points of distance is nearest replaces.
Employing standard square carrys out normalization one sub-pictureMap an image in unit circle.Standard square is by following formula meter
Calculate:
The center of gravity of image can be obtained by standard square:
By the gravity motion of image to the unit circle center of circle, i.e. zero, so that it may so that image has translation invariance.η00
Represent the area of image object shape, image is converted
The size of image object thing can be become consistent.To sum up, image is converted:
S4 extracts the Zernike square characteristic vector as identification of image, and utilizes probabilistic neural network grader logarithm
Word modulated signal is identified；
It should be noted that in step S4, extract the Zernike square characteristic vector as identification of image, and utilize general
Digital modulation signals is identified being carried out as follows by rate neural network classifier:
Zernike proposes one group of manifold { V that writes a letter in reply being defined on unit circlerv(s, z) }:
Vrv(s, z)=Vrv(ρ,θ)；
Wherein ρ is that (θ is former point-to-point (s, line z) and the anticlockwise folder of x-axis to former point-to-point for s, distance z)
Angle.Have in unit circle translation and scale invariance any image g (s, z) can represent by unique following formula:
Wherein ZrvThe i.e. r rank v weight Zernike square of image:
Wherein, r=0,1,2 ..., ∞, 0≤| v |≤r and r-| v | is even number.For discrete digital picture,
Zernike square is tried to achieve by following formula:
Finally the Zernike square tried to achieve is modulated signal identification as characteristic vector, employing probabilistic neural network, its
Activation primitive is Gaussian function, is expressed as follows:
Wherein, δ is the extension constant of RBF.
The foregoing is only presently preferred embodiments of the present invention, not in order to limit the present invention, all essences in the present invention
Any amendment, equivalent and the improvement etc. made within god and principle, should be included within the scope of the present invention.
Claims (3)
1. the recognition methods of digital modulation signals under an impulsive noise, it is characterised in that digital modulation under described impulsive noise
The recognition methods of signal comprises the following steps:
Step one, calculates the fractional lower-order ambiguity function of digital modulation signals；
Step 2, intercepts the tangent plane that Doppler frequency shift is zero of fractional lower-order ambiguity function, and tangent plane is converted into two dimensional image
And below filling image border, become the coloured coloured image of tool；
Step 3, carries out gray processing, binaryzation, image segmentation and the normalization of image size to coloured image, and again to image
Carry out translating and dimension normalization；
Step 4, extracts the Zernike square characteristic vector as identification of image, and utilizes probabilistic neural network grader logarithm
Word modulated signal is identified.
2. the recognition methods of digital modulation signals under impulsive noise as claimed in claim 1, it is characterised in that described calculating number
The fractional lower-order ambiguity function of word modulated signal is carried out as follows:
Receive signal y (t) to be expressed as:
Y (t)=x (t)+n (t)；
Wherein, x (t) is digital modulation signals, and n (t) is the impulsive noise of standard S α S distribution；MASK and MPSK modulates, x's (t)
Analytical form is expressed as:
Wherein, N is sampling number, anFor the information symbol sent, in MASK signal, an=0,1,2 ..., M-1, M are modulation
Exponent number, in mpsk signal, an=ej2πε/M, ε=0,1,2 ..., M-1, g (t) represent rectangle molding pulse, TbRepresent symbol week
Phase, fcRepresent carrier frequency, carrier wave initial phaseIt it is equally distributed random number in [0,2 π]；
MFSK modulates, and the analytical form of x (t) is expressed as:
Wherein, fmFor the side-play amount of m-th carrier frequency, if MFSK is signal carrier shift Δ f, then fm=-(M-1) Δ f ,-(M-3) Δ
F ..., (M-3) Δ f, (M-1) Δ f, carrier wave initial phaseIt it is equally distributed random number in [0,2 π]；
Following characteristics function describes distribution character:
WhereinFor sign function,
α (0 ＜ α≤2) is characterized index, and γ is the coefficient of dispersion, and β is symmetric parameter, and ζ is location parameter；As ζ=0, β=0 and γ
When=1, distribution is referred to as standard S α S distribution；
The fractional lower-order ambiguity function of digital modulation signals x (t) is expressed as:
Wherein, τ is delay skew, and f is Doppler frequency shift, 0 ＜ a, b ＜ α/2, x*T () represents the conjugation of x (t)；When x (t) is real
During signal, x (t)＜ p ＞=| x (t) |＜ p ＞sgn(x(t))；When x (t) is time multiplexed signal, [x (t)]＜ p ＞=| x (t) |p-1x*(t)。
3. the recognition methods of digital modulation signals under impulsive noise as claimed in claim 1, it is characterised in that described intercepting divides
The tangent plane that Doppler frequency shift is zero of number low order ambiguity function, and this tangent plane is converted into two dimensional image and fills this image border
Lower section so that it is become the coloured coloured image of tool and carry out by the following method:
The tangent plane that Doppler frequency shift is zero of the fractional lower-order ambiguity function of digital modulation signals MASK, MFSK, MPSK is expressed as:
Wherein,Be width be TbThe gate function of-τ；
Above three formulas are onlyCoefficient different, MASK signalThe most permanent is 1；MFSK signalNo
Perseverance is 1；For 2ASK signal, an=0,1；For 4ASK signal, an=0,1,2,3, two kinds of signalsDifference, mark is low
The Doppler frequency shift of rank ambiguity function be zero tangent plane profile the most different；For 2FSK signal, fm=-Δ f, Δ f；For 4FSK
Signal, fm=-3 Δ f ,-Δ f, Δ f, 3 Δ f, two kinds of signalsDifference, the Doppler frequency shift of fractional lower-order ambiguity function
Be zero tangent plane profile the most different；
The tangent plane that Doppler frequency shift is zero of fractional lower-order ambiguity function is converted into two dimensional imageAnd arrange less than cutting
The pixel of face maximum (s, pixel value z) is (θ, ξ, λ), (θ, ξ, λ ≠ 255), wherein θ, ξ and λ be respectively image red,
Green, the value of primary colors, makes image become the coloured coloured image of tool.
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