CN106067004B - 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 a kind of recognition methods of digital modulation signals under impulsive noise, the described method comprises the following steps: calculating the fractional lower-order ambiguity function of digital modulation signals；The section that the Doppler frequency shift of fractional lower-order ambiguity function is zero is intercepted, and converts two dimensional image for the section and fills below the image border, becomes the coloured color image of tool；The normalization of gray processing, binaryzation, image segmentation and image size is carried out to color image, and translation and dimension normalization are carried out to image again；Feature vector of the Zernike square of image as identification is extracted, and digital modulation signals are identified using probabilistic neural network classifier.The present invention has good recognition performance under standard profile impulsive noise, to digital modulation signals 2ASK, 4ASK, 2FSK, 4FSK, BPSK.
Description
Technical field
The invention belongs to a kind of recognition methods of digital modulation signals under field of communication technology more particularly to impulsive noise.
Background technique
The Modulation Identification of signal is a key technology between signal detection and demodulation, is had in military and civilian field
It is widely applied.Traditional digital modulation signal recognizing method is mostly using Gaussian noise as noise model, and making an uproar in the actual environment
Often there is sound the probability density function of spike property and noise to have thicker hangover.The research card of Nikias professor et al.
Bright, Alpha Stable distritation is a kind of effective model for describing this kind of impulse noise signal.Therefore number under research impulsive noise
The recognition methods of modulated signal has certain meaning.
Vinod A P et al. uses the normalization fourth order cumulant based on fractional lower-order statistics under impulsive noise
BPSK, QPSK, 16QAM, 64QAM signal are identified, but recognition performance of this method when mixing noise is 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. is used
Fractional lower-order statistical moment identifies BPSK the and 2FSK signal containing impulsive noise, but this method identification signal type
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. using 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 this 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
The purpose of the present invention is to provide a kind of recognition methods of digital modulation signals under impulsive noise, it is intended to solve existing
Impulsive noise under digital modulation signals recognition methods it is existing mix noise it is relatively low when recognition performance it is poor, identification
Signal kinds are less, the undesirable problem of recognition effect.
The invention is realized in this way under a kind of impulsive noise digital modulation signals recognition methods, the impulsive noise
The recognition methods of lower digital modulation signals the following steps are included:
The fractional lower-order ambiguity function of S1 calculating digital modulation signals；
S2 intercepts the section that the Doppler frequency shift of fractional lower-order ambiguity function is zero, and converts two dimensional image for the section
And fill below the image border, become the coloured color image of tool；
S3 to color image carry out gray processing, binaryzation, image segmentation and image size normalization, and again to image into
Row translation and dimension normalization；
S4 extracts feature vector of the Zernike square of image as identification, and utilizes probabilistic neural network classifier logarithm
Word modulated signal is identified.
It should be noted that the fractional lower-order ambiguity function for calculating digital modulation signals is carried out as follows in step S1:
Receiving signal y (t) can indicate are as follows:
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.For MASK and MPSK tune
The analytical form of system, x (t) indicates are as follows:
Wherein, N is sampling number, anFor the information symbol of transmission, 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) expression rectangle molding pulse, TbIndicate symbol
Number period, fcIndicate carrier frequency, carrier wave initial phaseIt is the equally distributed random number in [0,2 π].For MFSK tune
The analytical form of system, x (t) indicates are as follows:
Wherein, fmFor the offset of m-th of carrier frequency, if MFSK signal carrier shift Δ f, fm=-(M-1) Δ f ,-(M-
3) Δ f ..., (M-3) Δ f, (M-1) Δ f, carrier wave initial phaseIt is the equally distributed random number in [0,2 π].
In addition to special circumstances, closed expression formula, therefore general use is not present in the probability density function of Alpha Stable distritation
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 when γ=1, which is known as standard S α S distribution.
The fractional lower-order ambiguity function of digital modulation signals x (t) indicates are as follows:
Wherein, τ is delay skew, and f is Doppler frequency shift, 0 α/2 < a, b <.x*(t) conjugation of x (t) is indicated.As x (t)
When 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), which only changes the amplitude information of signal, retains its frequency and phase information, can effectively suppressor pulse make an uproar
Sound.
It should be noted that in step S2, the section that the Doppler frequency shift of interception fractional lower-order ambiguity function is zero, and will
The section is converted into two dimensional image and fills below the image border, become the coloured color image of tool by below into
Row:
The section that the Doppler frequency shift of the fractional lower-order ambiguity function of digital modulation signals MASK, MFSK, MPSK is zero can
It indicates are as follows:
Wherein,Be width be TbThe gate function of-τ.
Above three formula only hasCoefficient it is different.MASK signalImpermanent is 1；MFSK signalImpermanent is 1, therefore the section wheel that the Doppler frequency shift of the fractional lower-order ambiguity function of three classes digital modulation signals is zero
It is wide different.For 2ASK signal, an=0,1；For 4ASK signal, an=0,1,2,3, two kinds of signalsDifference, score
The section profile that the Doppler frequency shift of low order ambiguity function is zero is also 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, fractional lower-order ambiguity function it is how general
It is also different to strangle the section profile that frequency displacement is zero.Therefore the fractional lower-order ambiguity function of 2ASK, 4ASK, 2FSK, 4FSK, bpsk signal
Doppler frequency shift be zero section chamfered shape it is different, can be using its shape feature as the feature vector of signal identification.
The section that Doppler frequency shift by fractional lower-order ambiguity function is zero is converted into two dimensional imageAnd it is arranged small
It is in the pixel value of the pixel (s, z) of section maximum valueWhereinξ and λ is respectively to scheme
As the value of Red Green Blue, becomes image and have coloured color image.
It should be noted that carrying out gray processing, binaryzation, image segmentation and image size to color image in step S3
Normalization, and again to image carry out translation and dimension normalization be carried out as follows:
The color three dimensional image that filled image is made of red (R), green (G), blue (B) three primary colors, schemes for convenience
As processing, gray level image usually is converted by color image.The value of tri- components of RGB of each pixel of color image is arrived 0
Between 255, rectangular coordinate system in space is established by reference axis of R, G, B respectively, then the color of each pixel of color image can be with
It is indicated with a point of the three-dimensional space, and each pixel of gray level image can be indicated with the point of straight line R=G=B.It will
RGB three-dimensional space is mapped to the one-dimensional space, and is subject to different weights according to induction of the human eye to color is different, obtains gray scale
Value:
Gray=0.299 × R+0.587 × G+0.114 × B；
It sets each pixel of original color image to the operation result of above formula, has been converted to gray level image.
Image binaryzation, that is, scanning grey pictures pixel value chooses an optimum gradation threshold value, will be greater than the picture of threshold value
Vegetarian refreshments is set to 1, and the pixel less than threshold value is set to 0, divides the image into target (prospect) and background two parts.The present invention is using most
Big Ostu method, selection make the maximum threshold value of the inter-class variance of target and background as optimal threshold.If image is
Size is O × Q, and the segmentation threshold of target and background is l, optimal threshold l*, belong to the total pixel of pixel number Zhan of target
Several ratios is w0, average gray μ0；The ratio for belonging to the total pixel number of pixel number Zhan of background is w1, average gray
For μ1.The overall average gray scale of image is denoted as μ, and the inter-class variance of target and background is denoted asGray value is less than the pixel of threshold value
Number scale makees Ω0, gray scale be greater than threshold value number of pixels be denoted as Ω1, then have:
Ω0+Ω1=O × Q, w0+w1=1；
μ=w0μ0+w1μ1；
The l acquired*As optimal threshold, and then can be by image binaryzation.
Using morphological image processing method, by structural element (minor matrix slided on the image, element 0
Or 1) logical operation is carried out with bianry image, new image is generated, realizes image segmentation.Bianry image can be considered a set,
It is indicated with J, the point that pixel value is 1 in original image is the element of set.If all 1's matrix that structural element S is 3 × 3, works as structural elements
When the central point of element moves on to the point (s, z) in image, it is denoted as Ssz.Morphology basic operation is burn into expansion, opens and be closed.
Erosion operation indicates are as follows:
Dilation operation indicates are as follows:
Opening operation indicates are as follows:
The present invention obtains target image using opening operation, then image background is filled with black, former bianry image and filling
The image of good black background make AND operation and can be divided after target area.
Using arest neighbors interpolation method normalized image Aspect Ratio, it is consistent all image sizes all, is arranged 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 is 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
Relationship between pixel (s ', z ') are as follows:
), s=s'(C/c z=z'(H/h)；
It can be the image of unified size by image normalization by above-mentioned coordinate transform, if the coordinate of target image occurs
Decimal, then the value of the coordinate points is replaced with the binary value of the nearest coordinate points of distance in the original image coordinate points.
A sub-picture is normalized using standard squareIt maps an image in unit circle.Standard square is by following formula meter
It calculates:
By the center of gravity of the available image of standard square:
By the gravity motion of image to the unit circle center of circle, i.e. coordinate origin, so that it may so that image has translation invariance.η00
The area for indicating image object shape, converts image
The size of image object object can be become consistent.To sum up, image is converted:
It should be noted that extracting feature vector of the Zernike square of image as identification, and using generally in step S4
Rate neural network classifier carries out identification to digital modulation signals and is carried out as follows:
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 the distance of former point-to-point (s, z), and θ is the line and the anticlockwise folder of x-axis of former point-to-point (s, z)
Angle.Any image g (s, z) in unit circle with translation and scale invariance can uniquely be indicated with following formula:
Wherein ZrvThat is the heavy Zernike square of the r rank v of image:
Wherein, r=0,1,2 ..., ∞, 0≤| v |≤r and r- | v | it is even number.For discrete digital picture,
Zernike square is acquired by following formula:
Finally using the Zernike square acquired as feature vector.It is modulated signal identification using probabilistic neural network,
Activation primitive is Gaussian function, is expressed as follows:
Wherein, δ is the extension constant of radial basis function.
The recognition methods of digital modulation signals under impulsive noise provided by the invention, the case where considering raised cosine roll off
Under, when mix signal-to-noise ratio in 8dB or more when, 2ASK, 4ASK, 2FSK, 4FSK, bpsk signal discrimination 90% or more, can
See that the present invention has good recognition performance.
Detailed description of the invention
Fig. 1 is the recognition methods flow chart of digital modulation signals under impulsive noise provided in an embodiment of the present invention.
Fig. 2 is the Digital modulation identification performance map provided in an embodiment of the present invention in the case where standard S α S is distributed impulsive noise.
Specific embodiment
In order to make the objectives, technical solutions, and advantages of the present invention clearer, with reference to embodiments, to the present invention
It is further elaborated.It should be appreciated that the specific embodiments described herein are merely illustrative of the present invention, it is not used to
Limit the present invention.
Application principle of the invention is explained in detail with reference to the accompanying drawing.
As shown in Figure 1, under the impulsive noise of the embodiment of the present invention digital modulation signals recognition methods the following steps are included:
S101: the fractional lower-order ambiguity function of digital modulation signals is calculated；
S102: the section that the Doppler frequency shift of interception fractional lower-order ambiguity function is zero, and two dimension is converted by the section
It image and fills below the image border, becomes the coloured color image of tool；
S103: the normalization of gray processing, binaryzation, image segmentation and image size is carried out to color image, and again to figure
As carrying out translation and dimension normalization；
S104: feature vector of the Zernike square of image as identification is extracted, and utilizes probabilistic neural network classifier pair
Digital modulation signals are identified.
Application principle of the invention is further described combined with specific embodiments below.
The fractional lower-order ambiguity function of S1 calculating digital modulation signals；
It should be noted that the fractional lower-order ambiguity function for calculating digital modulation signals is carried out as follows in step S1:
Receiving signal y (t) can indicate are as follows:
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.For MASK and MPSK tune
The analytical form of system, x (t) indicates are as follows:
Wherein, N is sampling number, anFor the information symbol of transmission, 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) expression rectangle molding pulse, TbIndicate symbol
Number period, fcIndicate carrier frequency, carrier wave initial phaseIt is the equally distributed random number in [0,2 π].For MFSK tune
The analytical form of system, x (t) indicates are as follows:
Wherein, fmFor the offset of m-th of carrier frequency, if MFSK signal carrier shift Δ f, fm=-(M-1) Δ f ,-(M-
3) Δ f ..., (M-3) Δ f, (M-1) Δ f, carrier wave initial phaseIt is the equally distributed random number in [0,2 π].
In addition to special circumstances, closed expression formula, therefore general use is not present in the probability density function of Alpha Stable distritation
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 when γ=1, which is known as standard S α S distribution.
The fractional lower-order ambiguity function of digital modulation signals x (t) indicates are as follows:
Wherein, τ is delay skew, and f is Doppler frequency shift, 0 α/2 < a, b <.x*(t) conjugation of x (t) is indicated.As x (t)
When 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), which only changes the amplitude information of signal, retains its frequency and phase information, can effectively suppressor pulse make an uproar
Sound.
S2 intercepts the section that the Doppler frequency shift of fractional lower-order ambiguity function is zero, and converts two dimensional image for the section
And fill below the image border, become the coloured color image of tool；
It should be noted that in step S2, the section that the Doppler frequency shift of interception fractional lower-order ambiguity function is zero, and will
The section is converted into two dimensional image and fills below the image border, become the coloured color image of tool by below into
Row:
The section that the Doppler frequency shift of the fractional lower-order ambiguity function of digital modulation signals MASK, MFSK, MPSK is zero can
It indicates are as follows:
Wherein,Be width be TbThe gate function of-τ.
Above three formula only hasCoefficient it is different.MASK signalImpermanent is 1；MFSK signalImpermanent is 1, therefore the section wheel that the Doppler frequency shift of the fractional lower-order ambiguity function of three classes digital modulation signals is zero
It is wide different.For 2ASK signal, an=0,1；For 4ASK signal, an=0,1,2,3, two kinds of signalsDifference, score are low
The section profile that the Doppler frequency shift of rank ambiguity function is zero is also 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, Doppler's frequency of fractional lower-order ambiguity function
The section profile that shifting is zero is also different.Therefore the fractional lower-order ambiguity function of 2ASK, 4ASK, 2FSK, 4FSK, bpsk signal is more
The general chamfered shape for strangling the section that frequency displacement is zero is different, can be using its shape feature as the feature vector of signal identification.
The section that Doppler frequency shift by fractional lower-order ambiguity function is zero is converted into two dimensional imageAnd it is arranged small
It is in the pixel value of the pixel (s, z) of section maximum valueWhereinξ and λ is respectively to scheme
As the value of Red Green Blue, becomes image and have coloured color image.
S3 to color image carry out gray processing, binaryzation, image segmentation and image size normalization, and again to image into
Row translation and dimension normalization；
It should be noted that carrying out gray processing, binaryzation, image segmentation and image size to color image in step S3
Normalization, and again to image carry out translation and dimension normalization be carried out as follows:
The color three dimensional image that filled image is made of red (R), green (G), blue (B) three primary colors, schemes for convenience
As processing, gray level image usually is converted by color image.The value of tri- components of RGB of each pixel of color image is arrived 0
Between 255, rectangular coordinate system in space is established by reference axis of R, G, B respectively, then the color of each pixel of color image can be with
It is indicated with a point of the three-dimensional space, and each pixel of gray level image can be indicated with the point of straight line R=G=B.It will
RGB three-dimensional space is mapped to the one-dimensional space, and is subject to different weights according to induction of the human eye to color is different, obtains gray scale
Value:
Gray=0.299 × R+0.587 × G+0.114 × B；
It sets each pixel of original color image to the operation result of above formula, has been converted to gray level image.
Image binaryzation, that is, scanning grey pictures pixel value chooses an optimum gradation threshold value, will be greater than the picture of threshold value
Vegetarian refreshments is set to 1, and the pixel less than threshold value is set to 0, divides the image into target (prospect) and background two parts.The present invention is using most
Big Ostu method, selection make the maximum threshold value of the inter-class variance of target and background as optimal threshold.If image is
Size is O × Q, and the segmentation threshold of target and background is l, optimal threshold l*, belong to the total pixel of pixel number Zhan of target
Several ratios is w0, average gray μ0；The ratio for belonging to the total pixel number of pixel number Zhan of background is w1, average gray
For μ1.The overall average gray scale of image is denoted as μ, and the inter-class variance of target and background is denoted asGray value is less than the pixel of threshold value
Number scale makees Ω0, gray scale be greater than threshold value number of pixels be denoted as Ω1, then have:
Ω0+Ω1=O × Q, w0+w1=1；
μ=w0μ0+w1μ1；
The l acquired*As optimal threshold, and then can be by image binaryzation.
Using morphological image processing method, by structural element (minor matrix slided on the image, element 0
Or 1) logical operation is carried out with bianry image, new image is generated, realizes image segmentation.Bianry image can be considered a set,
It is indicated with J, the point that pixel value is 1 in original image is the element of set.If all 1's matrix that structural element S is 3 × 3, works as structural elements
When the central point of element moves on to the point (s, z) in image, it is denoted as Ssz.Morphology basic operation is burn into expansion, opens and be closed.
Erosion operation indicates are as follows:
Dilation operation indicates are as follows:
Opening operation indicates are as follows:
The present invention obtains target image using opening operation, then image background is filled with black, former bianry image and filling
The image of good black background make AND operation and can be divided after target area.
Using arest neighbors interpolation method normalized image Aspect Ratio, it is consistent all image sizes all, is arranged 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 is 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 pixel
Relationship between point (s ', z ') are as follows:
), s=s'(C/c z=z'(H/h)；
It can be the image of unified size by image normalization by above-mentioned coordinate transform, if the coordinate appearance of target image is small
Number, then the value of the coordinate points is replaced with the binary value of the nearest coordinate points of distance in the original image coordinate points.
A sub-picture is normalized using standard squareIt maps an image in unit circle.Standard square is by following formula meter
It calculates:
By the center of gravity of the available image of standard square:
By the gravity motion of image to the unit circle center of circle, i.e. coordinate origin, so that it may so that image has translation invariance.η00
The area for indicating image object shape, converts image
The size of image object object can be become consistent.To sum up, image is converted:
S4 extracts feature vector of the Zernike square of image as identification, and utilizes probabilistic neural network classifier logarithm
Word modulated signal is identified；
It should be noted that extracting feature vector of the Zernike square of image as identification, and using generally in step S4
Rate neural network classifier carries out identification to digital modulation signals and is carried out as follows:
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 the distance of former point-to-point (s, z), and θ is the line and the anticlockwise folder of x-axis of former point-to-point (s, z)
Angle.Any image g (s, z) in unit circle with translation and scale invariance can uniquely be indicated with following formula:
Wherein ZrvThat is the heavy Zernike square of the r rank v of image:
Wherein, r=0,1,2 ..., ∞, 0≤| v |≤r and r- | v | it is even number.For discrete digital picture,
Zernike square is acquired by following formula:
Finally using the Zernike square acquired as feature vector, signal identification is modulated using probabilistic neural network,
Activation primitive is Gaussian function, is expressed as follows:
Wherein, δ is the extension constant of radial basis function.
The foregoing is merely illustrative of the preferred embodiments of the present invention, is not intended to limit the invention, all in essence of the invention
Made any modifications, equivalent replacements, and improvements etc., should all be included in the protection scope of the present invention within mind and principle.
Claims (3)
1. the recognition methods of digital modulation signals under a kind of impulsive noise, which is characterized in that digital modulation under the impulsive noise
The recognition methods of signal the following steps are included:
Step 1 calculates the fractional lower-order ambiguity function of digital modulation signals；
Step 2, the section that the Doppler frequency shift of interception fractional lower-order ambiguity function is zero, and two dimensional image is converted by section
And below filling image border, become the coloured color image of tool；
Step 3 carries out the normalization of gray processing, binaryzation, image segmentation and image size to color image, and again to image
Carry out translation and dimension normalization；
Step 4 extracts feature vector of the Zernike square of image as identification, and utilizes probabilistic neural network classifier logarithm
Word modulated signal is identified.
2. the recognition methods of digital modulation signals under impulsive noise as described in claim 1, which is characterized in that the calculating number
The fractional lower-order ambiguity function of word modulated signal is carried out as follows:
Receiving signal y (t) indicates are as follows:
Y (t)=x (t)+n (t)；
Wherein, t is the duration of signal, and x (t) is digital modulation signals, and n (t) is the impulsive noise of standard S α S distribution；
The analytical form of MASK and MPSK modulation, x (t) indicates are as follows:
Wherein, N is sampling number, anFor the information symbol of transmission, in MASK signal, an=0,1,2 ..., M-1, M are modulation
Order, in mpsk signal, an=ej2πε/M, ε=0,1,2 ..., M-1, g (t) expression rectangle molding pulse, TbIndicate symbol week
Phase, fcIndicate carrier frequency, carrier wave initial phaseIt is the equally distributed random number in [0,2 π]；
The analytical form of MFSK modulation, x (t) indicates are as follows:
Wherein, fmFor the offset of m-th of carrier frequency, if MFSK signal carrier shift Δ f, fm=-(M-1) Δ f ,-(M-3) Δ
F ..., (M-3) Δ f, (M-1) Δ f, carrier wave initial phaseIt is the 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 known as standard S α S distribution；
The fractional lower-order ambiguity function of digital modulation signals x (t) indicates are as follows:
Wherein, τ is delay skew, and f is Doppler frequency shift, 0 < a, b < α/2, x*(t) conjugation of x (t) is indicated；When x (t) is real
When 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 2, which is characterized in that the interception point
The section that the Doppler frequency shift of number low order ambiguity function is zero, and convert two dimensional image for the section and fill the image border
Lower section becomes the coloured color image of tool and carries out by the following method:
The section that the Doppler frequency shift of the fractional lower-order ambiguity function of digital modulation signals MASK, MFSK, MPSK is zero indicates are as follows:
Wherein,Be width be TbThe gate function of-τ；
Above three formula only hasCoefficient it is different, MASK signalImpermanent 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, score are low
The section profile that the Doppler frequency shift of rank ambiguity function is zero is also 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
The section profile for being zero is also different；
The section that Doppler frequency shift by fractional lower-order ambiguity function is zero is converted into two dimensional imageAnd it is arranged to be less than and cuts
The pixel value of the pixel (s, z) of face maximum value be (θ, ξ, λ), θ, ξ, λ ≠ 255, wherein θ, ξ and λ be respectively image it is red, it is green,
The value of primary colors becomes image and has coloured color image.
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