CN103064063B - Poly-phase code radar signal waveform automatic identification method based on continuous wave Doppler (CWD) feature - Google Patents

Abstract

The invention relates to a poly-phase code radar signal waveform automatic identification method based on continuous wave Doppler (CWD) feature and belongs to the technical field of information countermeasures. According to the poly-phase code radar signal waveform automatic identification method based on CWD feature, a discrete sampling type Choi-Williams conversion is used as a basic tool, a CWD image of poly-phase code pulse compression radar signal is used as a feature extraction object, a Pseudo-Zernike moment of the CWD image, a target number of an image, a time position of a peak power in a CWD and a poly-phase code waveform symmetrical property are taken as features to identify a poly-phase code pulse compression radar waveform, and a neural network which is composed of 10 perceptrons and stops in advance of overall average is set up for automatic waveform identification. The poly-phase code radar signal waveform automatic identification method based on CWD feature has the advantages that the identification precision of the poly-phase code radar signal waveform is improved, the requirement of a signal to noise ratio is further decreased, and a new way can be developed for the design of radar signal identification and sorting by popularized and used in a poly-phase code continuous wave radar signal.

Description

Polyphase codes radar signal Waveform Auto-specification method based on CWD features

Technical field

The present invention relates to a kind of polyphase codes radar signal Waveform Auto-specification method based on CWD features, belongs to information Countermeasure techniques field.

Background technology

In recent years, with deepening continuously to polyphase codes radar signal research, occur in that Frank codes and P1, P2, P3 and P4 code signals.In a sense, Frank codes and P1～P4 code signals belong to polyphase codes signal (Polyphase Coded).Traditional reconnaissance receiver cannot realize the effective identification to it, and how research is effectively known to this kind of signal Theoretical significance that Ju You be unimportant and engineering application are worth.

The concept of Fractional Fourier Transform is suggested early in nineteen twenty-nine, and in the eighties in 20th century optics neck is applied to Domain, becomes one of study hotspot of field of signal processing from the nineties.Fractional Fourier Transform can be understood as Chirp Base decomposes, therefore is particularly suitable for processing Chirp class signals.Using linear frequency modulation (LFM) signal (namely Chirp signals) not The characteristic of different energy accumulatings is presented with the Fractional Fourier Domain of order, by doing peak in Fractional Fourier Domain Value two-dimensional search can just realize the detection to LFM signals and parameter estimation.And triangular linear Continuous Wave with frequency modulation may be considered It is made up of multi-component LFM signalt, Fractional Fourier Transform is linear transformation, without cross term interference, with additive noise In the case of more advantage.

At present the method for parameter estimation to triangular linear Continuous Wave with frequency modulation, can only estimate the partial parameters of signal mostly, Some requirement signal to noise ratios are higher, and requirement also is exactly a modulation period to signal sampling, and these methods are all without fine The characteristic parameter extraction for solving the problems, such as such signal.

The present invention relates to a kind of polyphase codes radar signal Waveform Auto-specification method based on CWD features, belongs to information Countermeasure techniques field.The present invention is transformed to basic tool with discrete sampling type Choi-Williams, by polyphase codes pulse compression The CWD images of radar signal are proposed the mesh in Pseudo-Zernike squares, the image of CWD images as feature extraction object The time location and polyphase code waveform symmetry property of peak power is used as identification polyphase codes pulse compression thunder in mark number, CWD Up to the feature of waveform, using polyphase code signal difference characteristically, a population mean being made up of 10 perceptrons is set up The neutral net for stopping in advance carrying out automatic waveform recognition.Method proposed by the present invention improves polyphase codes radar signal waveform Recognition accuracy, reduce further the requirement of signal to noise ratio, and may also pass through and promote the use in polyphase codes continuous wave Radar signal, a new approach is provided for Radar Signal Recognition with the design of sorting.

Based on the polyphase codes radar signal Waveform Auto-specification method of CWD features, be divided into polyphase codes radar signal from The normalized of dispersion CWD image, signal characteristic abstraction and signal classifier design 3 parts, altogether 4 process steps (Fig. 1).

Beneficial effect

1. the polyphase codes radar signal Waveform Auto-specification method based on CWD features proposed by the present invention can be with high precision The identification for realizing polyphase codes radar signal of degree.

2. the present invention does not have particular/special requirement substantially to sampling time of signal, can start point from any time of signal Analysis, still has higher recognition accuracy under low signal-to-noise ratio.

3. parallel multilayer neural network waveform recognition device proposed by the present invention, can apply to polyphase codes radar signal Identification, can also apply to the identification of other radar signals, it is critical only that the selection of signal characteristic.

Description of the drawings

Polyphase codes radar signal Waveform Auto-specification scheme schematic diagrams of the Fig. 1 based on CWD features

Five kinds of waveform recognition accuracy of Fig. 2 and total recognition correct rate

Specific embodiment

It is assumed that the radar signal that reconnaissance receiver is received is contaminated with additive white Gaussian noise (AWGN), and signal is The complex envelope for becoming radar signal y (t) that baseband signal is then received through process is as follows：

Y (t)=x (t)+ω (t) (1)

Wherein x (t) is the complex envelope (only including a code-element period) of radar emission signal, and ω (t) is that circulation additivity is answered White Gaussian noise.

The phase code complex signal of radar emission is expressed as follows：

Wherein, A is signal amplitude, f_cIt is signal(-) carrier frequency, φ_iIt is signal discrete phase sequence, each phase place has phase The same persistent period.The mathematical model of 5 kinds of polyphase codes radar signals being studied is given below.

Frank code signals are that a kind of stepping to LFM signals is approached, and it employs N number of step frequency, and in each frequency N times sampling is carried out on rate point.Therefore, total hits of a Frank code is N².The i-th of j-th frequency of one Frank code The phase place of individual sampling is as follows：

Wherein, i=1,2 ..., N, j=1,2 ..., N.Then the pulse compression ratio of this Frank code is N²。

P1 code signals are also that the stepping to LFM signals is approached, and it employs N number of step frequency, and in each Frequency point On carry out n times sampling.The phase place of the ith sample of j-th frequency of one P1 code is as follows：

Wherein, i=1,2 ..., N, j=1,2 ..., N.Then the pulse compression ratio of this P1 code is N²。

The positive and negative of the characteristics of P2 codes have the palindrome, i.e. P2 codes is identical.I-th of j-th frequency of one P2 code is adopted The phase place of sample is as follows：

Wherein, i=1,2 ..., N, j=1,2 ..., N.Then the pulse compression ratio of this P2 code is N².It is pointed out that N is necessary for even number in P2 codes, if N is odd number, the numerical value of the autocorrelation sidelobe of this P2 code can be too high.

P3 codes carry out evolution of sampling to a LFM signal.The following institute of phase place of the ith sample of one P3 code Show：

Wherein i=1,2 ..., ρ, ρ are pulse compression ratio.

P4 codes carry out evolution of sampling to P3 code identical signals.The phase place of the ith sample of one P4 code is as follows It is shown：

Wherein i=1,2 ..., ρ, ρ are pulse compression ratio.

The step of realizing polyphase codes radar signal Waveform Auto-specification method is as follows：

Step one, observation signal y (t)=x (the t)+ω (t) to any one section of polyphase codes radar signal sample, Obtain discrete form y (n)=x (n)+ω (n), sample frequency f_s, sampling time T_s；Then the discrete CWD of signal calculated y (n) becomes Change.

Wherein, σ (σ ＞ 0) is scale factor.

Step 2, the impact next to signal CWD picture strips in order to minimize signal bandwidth and sample frequency, need to signal CWD images be normalized.The step of normalized, is as follows：

(1) threshold test process is carried out to the CWD images of signal；

(2) time gated and frequency domain filtering is carried out to the image after threshold test process, i.e., is removed not from image border Region containing signal；

(3) final bianry image depth-width ratio is normalized to 1.

Threshold value gating is processed vital effect for whole normalization algorithm.After the process of threshold value gating View data should only comprising signal component and not including has any independent noise spot because the result pair of second step These noise spots are very sensitive.For the process of threshold value gating, the selection of threshold value plays a crucial role for the output of the first step.This In text global threshold T is solved using iterative algorithm, specific algorithm is as follows：

(1) initial estimate of a T is selected, the numerical value is how by the maximum grey level to CWD images and minimum Grey level is averaging and obtains；

(2) CWD image division is G by the selected T value of basis₁And G₂Two parts, wherein G₁It is higher than comprising all grey levels The point of T, G₂The point of T is equal to or less than comprising all grey levels；

(3) G is calculated respectively₁And G₂Average intensity level μ in two parts₁And μ₂；

(4) according to T=0.5 (μ₁+μ₂) calculate new threshold value T；

(5) the step of repeating (2) to (4), until the numerical value of T reaches the requirement of convergence.

The numerical value of global threshold is only set it cannot be guaranteed that removing completely for independent noise point, therefore in the choosing of second step time Before logical and frequency domain filtering, first have to process CWD images, to reject harmful noise spot.Hazardous noise point is rejected logical Cross following steps to complete：

(1) bianry image is corroded first and expansion process, bianry image is corroded and expansion process not only CWD images can be smoothed, and can be removed under Low SNR due to putting down that Choi-Williams and formula (8) are produced Row or vertical spectral line；

(2) image and then to processing is marked, and the object with obvious distinction in bianry image is entered into rower Note；

(3) finally reject the target in labelling target less than certain threshold value (e.g., to reject less than maximum target 10% in image All targets).If rejecting the sufficiently high of the threshold value setting of Small object, then in P1, P2 and P4 signal CWD images Non-principal composition also can be weeded out as Small object.

In the second step of normalized, the image-region without signal component is removed from whole CWD images, the The image-region depth-width ratio normalization containing signal component by residue of three steps.Bianry image size after treatment is M × M, Wherein M is the minimum dimension of image after normalization process second step is processed.

The signal characteristic with obvious distinction is extracted in step 3, the signal CWD bianry images after normalized, For realizing the waveform recognition of different type polyphase codes signal.The CWD signal characteristics for being extracted and its following institute of calculation Show：

(1) Pseudo-Zernike squares：Pseudo-Zernike squares have translation invariance, scaling invariance, rotation not Degeneration and mirror invariant performance.

The p+q rank geometric moments of one digital picture f (x, y) are defined as follows：

Translation invariant and scaling permanent center geometric moment are defined as follows：

Wherein,

Translation invariant and the constant radial direction geometric moment of scaling are defined as follows：

Wherein,

The n rank Pseudo-Zernike squares of m circulation can be by translation invariant and scaling permanent center geometric moment peace Move the constant and constant radial direction geometric moment of scaling to be calculated, specific algorithm is as follows：

Wherein,

By to Pseudo-Zernike square Z_nmTake absolute value and obtain rotational invariance, and entered by taking the logarithm to it Mobile state Ratage Coutpressioit.More than synthesis, it can be deduced that final extraction is characterized as：

Wherein, the spy of the following Pseudo-Zernike squares as waveform recognition of bianry image after normalized is chosen Levy：With

(2) the target number after normalized in bianry image：On the basis of normalization is successfully completed, Frank codes And have 2 signal target components in the two-value CWD image of P3 code signals, and the two-value CWD image of other 3 polyphase codes signals In only 1 signal target component.In order to improve the robustness of feature, by less than the signal of maximum target component of signal 20% point Amount is all removed.

(3) in CWD peak power time location：The peak power of P1, P2 and P4 code signal and the distance of encoding centre Relative close, and Frank codes and P3 codes have highest peak power in coding end.This feature is fallen into a trap from bianry image Draw, so just need not can realize only by time gated process to the complete normalization of original CWD images. The method that this feature is calculated in CWD images is as follows：

Wherein, x express times axle, y represents frequency axiss, and N represents W_CW(x, y) length on a timeline.Purpose It is that the numerical value for making this feature is normalized between 0～1.

(4) identification for Frank codes, the block structure of the CWD images of P1 and P2 code signals is proposed by calculating two-value The standard deviation of target component width in image, can distinguish P3 and P4 codes signal with other 3 kinds of encoded signals, concrete to calculate Method is as follows：

After signal object component in labelling CWD images, individually located for each component of signal object Reason, i.e., every time remove all component of signals outside required component to be processed.In one bianry image B (x, y) it is main into Point it is the characteristic vector of its covariance matrix, its computational methods is as follows：

Wherein, bianry image size is N × N, z=(x, y)^T, WithFor the center horizontal stroke of image, vertical seat Mark, can be calculated by formula (11).

Bianry image is rotated so that primary axis is parallel with the vertical or axis of abscissas of image.Due to image from Scattered coordinate feature, this rotary course needs to carry out interpolation calculation, using arest neighbors differential technique.The standard deviation of image object width can To be calculated by postrotational binary image data.It is assumed that first master corresponding with energy highest main constituent in image Coordinate axess rotate to it is parallel with the longitudinal axis of image, then need calculate image line and value

Wherein,Represent postrotational bianry image.

Normalized r (x) is expressed as follows, and it is interval that it is limited to 0～1.

More than synthesis, the standard deviation computing formula of target component width is as follows in bianry image：

Wherein, M is representedNon- small and weak sampling quantity, the summation in above formula is aiming at non-small and weak adopt Sample summation.Because small and weak sampling has a strong impact on the quality of standard deviation estimate, especially when the row or column of image (depends on rotation side To) do not contain any signal component when, so will be excluded before the computation.Setting T_objValue be 0.3, will ownSmall and weak sampling exclude outside read group total.

The numerical value of final feature is exactly the standard deviation sigma of all component of signals in image_objMeansigma methodss.

(5) the 5th signal characteristics make use of the different coding symmetry characteristic of encoded signal, by calculating symbol rate sampling The cross-correlation function of the time energizing signal of pulse and the pulse is obtained.The time delay size of the maximum of the cross-correlation function It is a key character for recognizing above-mentioned different coding signal, its computational methods is as follows：

Wherein, y (n), n=0,1 ..., N-1 is the discrete time complex envelope signal of single symbol rate sampling, | τ |≤N-1.Then The time delay size of the maximum of final cross-correlation function is expressed as：

There is this feature constant to rotate (i.e. y (n>Middle n=0, rotational steps are identical during 1 ..., N-1) invariance is to obtain With time-reversal signal identical feature, can also be by | τ_max| it is identified as feature.

Step 4, a kind of combined classifier of neural network of design, to improve neutral net from accuracy of identification and efficiency Recognition performance.Designed neural network classifier is as follows：

Using weighting to posterior probability, by voting modulation type is determined.

If the classification number of signal to be sorted is K, grader number is N, for input feature vector vector X, then n-th grader Be output as k-th

O_nk(X)=P (c_k|X)+e_nk(X) (21)

Wherein, P (c_k| X) represent the posterior probability for being judged as kth class when input is X, e_nk(X) n-th grader is represented The output error of k-th node.Weight vector ω_k={ ω_1k, ω_2k..., ω_nkBe n-th grader, k-th node output Weights.Then each grader judges that same category of output weighted sum can be expressed as follows：

Wherein, k=1,2 ..., K.

Increase constraintsWithThen have

S_k(X)=P (c_k|X) (23)

WhenWhen, judge that kth class signal is present.

Emulation explanation is done to the present invention with reference to example：

When SNR is -2dB～31dB, 1000 feature samples altogether are produced to each modulated signal interval 3dB, carried out Monte Carlo emulation emulation, and average is calculated as test result.Each training set and checking collection are to enter checking data The different segmentation of row collects the data comprising original training set 10% come what is set wherein verifying.

Fig. 2 points out that this grader reliably performs waveform recognition function.Overall correct classification rate is higher than 97%, in noise Than for 3dB when belong to independent modulation type correct recognition rata be higher than 91%.However, in the case where signal to noise ratio is higher still Occur some it is trickle obscure, have about 1%～2% P2 encoded signals to be identified as P1 encoded signals by mistake.This obscures Come from the error occurred during estimate symbol rate.Additionally, about 1% P1 encoded signals are identified as P4 coding letters by mistake Number.Table 1 have recorded classification percentage ratio when signal to noise ratio is 3dB.

The unlike signal of table 1 recognizes crossing-over rate

Above-mentioned simulation result shows that the present invention is higher to the recognition correct rate of polyphase codes signal；In Low SNR Under, still there is higher correct identification probability to polyphase codes radar signal.

Claims (1)

1. the polyphase codes radar signal Waveform Auto-specification method based on CWD features, is divided into polyphase codes radar signal discrete Normalized, signal characteristic abstraction and the signal classifier for changing CWD images designs 3 parts, altogether 4 process steps；

It is assumed that the radar signal that reconnaissance receiver is received is contaminated with additive white Gaussian noise (AWGN), and signal is passed through The complex envelope that process becomes radar signal y (t) that baseband signal is then received is as follows：

Y (t)=x (t)+ω (t) (1)

Wherein x (t) is the complex envelope of radar emission signal, only includes a code-element period, and ω (t) is that circulation additivity multiple Gauss is white Noise；

The phase code complex signal of radar emission is expressed as follows：

$x\left(t\right)={\mathrm{Ae}}^{j(2{\mathrm{\πf}}_{c}t+{\mathrm{\φ}}_t)}---\left(2\right)$

Wherein, A is signal amplitude, f_cIt is signal(-) carrier frequency, φ_iIt is signal discrete phase sequence, each phase place has identical Persistent period, the mathematical model of 5 kinds of polyphase codes radar signals being studied is given below；

Frank code signals are that a kind of stepping to LFM signals is approached, and it employs N number of step frequency, and in each Frequency point On carry out n times sampling, therefore, total hits of a Frank code is N², i-th of j-th frequency of a Frank code adopt The phase place of sample is as follows：

${\mathrm{\φ}}_{i,j}=\frac{2\mathrm{\π}}{N}(i-1)(j-1)---\left(3\right)$

Wherein, i=1,2 ..., N, j=1,2 ..., N, then the pulse compression ratio of this Frank code is N²；

P1 code signals are also that the stepping to LFM signals is approached, and it employs N number of step frequency, and enterprising in each Frequency point Row n times are sampled, and the phase place of the ith sample of j-th frequency of a P1 code is as follows：

${\mathrm{\φ}}_{i,j}=-\frac{\mathrm{\π}}{N}\[N-(2j-1)\]\[(j-1)N+(i-1)\]---\left(4\right)$

Wherein, i=1,2 ..., N, j=1,2 ..., N, then the pulse compression ratio of this P1 code is N²；

The positive and negative of the characteristics of P2 codes have the palindrome, i.e. P2 codes is identical, the ith sample of j-th frequency of a P2 code Phase place is as follows：

${\mathrm{\φ}}_{i,j}=\[\frac{\mathrm{\π}}{2}\·\frac{N-1}{N}\·\frac{\mathrm{\π}}{N}(i-1)\](N+1-2j)---\left(5\right)$

Wherein, i=1,2 ..., N, j=1,2 ..., N, then the pulse compression ratio of this P2 code is N², it should be pointed out that in P2 codes Middle N is necessary for even number, if N is odd number, the numerical value of the autocorrelation sidelobe of this P2 code can be too high；

P3 codes carry out evolution of sampling to a LFM signal, and the phase place of the ith sample of a P3 code is as follows：

${\mathrm{\φ}}_i=\frac{\mathrm{\π}}{\mathrm{\ρ}}{(i-1)}^2---\left(6\right)$

Wherein i=1,2 ..., ρ, ρ are pulse compression ratio；

P4 codes carry out evolution of sampling to P3 code identical signals, and the phase place of the ith sample of a P4 code is as follows：

${\mathrm{\φ}}_i=\frac{\mathrm{\π}}{\mathrm{\ρ}}{(i-1)}^2-\mathrm{\π}(i-1)---\left(7\right)$

Wherein i=1,2 ..., ρ, ρ are pulse compression ratio；

The step of realizing polyphase codes radar signal Waveform Auto-specification method is as follows：

Step one, observation signal y (t)=x (the t)+ω (t) to any one section of polyphase codes radar signal sample, and obtain Discrete form y (n)=x (n)+ω (n), sample frequency f_s, sampling time T_s；Then the discrete CWD conversion of signal calculated y (n),

$W(t,\mathrm{\ω})=\∫\∫\frac{1}{\sqrt{4{\mathrm{\π\τ}}^2/\mathrm{\σ}}}\exp (-\frac{{(\mathrm{\μ}-t)}^2}{4{\mathrm{\τ}}^2/\mathrm{\σ}})\·y(\mathrm{\μ}+\frac{\mathrm{\τ}}{2})\·y^{*}(\mathrm{\μ}-\frac{r}{2})\exp (-j\mathrm{\ω}\mathrm{\τ})d\mathrm{\μ}d\mathrm{\τ}---\left(8\right)$

Wherein, σ (σ ＞ 0) is scale factor；

Step 2, the impact next to signal CWD picture strips in order to minimize signal bandwidth and sample frequency, need to signal CWD images are normalized, as follows the step of normalized：

(1) threshold test process is carried out to the CWD images of signal；

(2) time gated and frequency domain filtering is carried out to the image after threshold test process, i.e., is removed without letter from image border Number region；

(3) final bianry image depth-width ratio is normalized to 1；

Threshold value gating is processed vital effect for whole normalization algorithm, the figure after the process of threshold value gating As data should not including has any independent noise spot only comprising signal component, because the result of second step is to these Noise spot is very sensitive, and for the process of threshold value gating, the selection of threshold value plays a crucial role for the output of the first step, herein Global threshold T is solved using iterative algorithm, specific algorithm is as follows：

(1) initial estimate of a T is selected, the numerical value is how by the maximum grey level to CWD images and minimal gray Level is averaging and obtains；

(2) CWD image division is G by the selected T value of basis₁And G₂Two parts, wherein G₁It is higher than T's comprising all grey levels Point, G₂The point of T is equal to or less than comprising all grey levels；

(3) G is calculated respectively₁And G₂Average intensity level μ in two parts₁And μ₂；

(4) according to T=0.5 (μ₁+μ₂) calculate new threshold value T；

(5) the step of repeating (2) to (4), until the numerical value of T reaches the requirement of convergence；

The numerical value of global threshold is only set it cannot be guaranteed that removing completely for independent noise point, thus second step it is time gated and Before frequency domain filtering, first have to process CWD images, to reject harmful noise spot, hazardous noise point reject by with Lower step is completed：

(1) bianry image is corroded first and expansion process, bianry image is corroded and expansion process not only can Smooth CWD images, and can remove under Low SNR due to produce parallel of Choi-Williams and formula (8) or Vertical spectral line；

(2) image and then to processing is marked, and the object with obvious distinction in bianry image is marked；

(3) finally reject less than the target of certain threshold value in labelling target, if rejecting the sufficiently high of the threshold value setting of Small object, So for the non-principal composition in P1, P2 and P4 signal CWD images also can be weeded out as Small object；

In the second step of normalized, the image-region without signal component is removed from whole CWD images, the 3rd step The image-region depth-width ratio normalization containing signal component by residue, bianry image size after treatment is M × M, wherein M It is the minimum dimension of image after normalization process second step is processed；

The signal characteristic with obvious distinction is extracted in step 3, the signal CWD bianry images after normalized, is used for The waveform recognition of different type polyphase codes signal is realized, the CWD signal characteristics for being extracted and its calculation are as follows：

(1) Pseudo-Zernike squares：Pseudo-Zernike squares have translation invariance, scaling invariance, rotational invariance And mirror invariant performance,

The p+q rank geometric moments of one digital picture f (x, y) are defined as follows：

$m_{pq}=\underset{x}{\Σ}\underset{y}{\Σ}f(x,y)x^p{y}^q---\left(9\right)$

Translation invariant and scaling permanent center geometric moment are defined as follows：

$G_{pq}=\frac{1}{m_{00}^{(p+q+2)/2}}\underset{x}{\Σ}\underset{y}{\Σ}f(x,y){(x-\stackrel{\‾}{x})}^p{(y-\stackrel{\‾}{y})}^q---\left(10\right)$

Wherein,

$\stackrel{\‾}{x}=\frac{m_{10}}{m_{00}},\stackrel{\‾}{y}=\frac{m_{01}}{m_{00}}$

Translation invariant and the constant radial direction geometric moment of scaling are defined as follows：

$G_{pq}=\frac{1}{m_{00}^{(p+q+3)/2}}\underset{x}{\Σ}\underset{y}{\Σ}f(x,y){({\tilde{x}}^2-{\tilde{y}}^2)}^{1/2}{\tilde{x}}^p{\tilde{y}}^q---\left(11\right)$

Wherein,

The n rank Pseudo-Zernike squares of m circulation can be by translation invariant and scaling permanent center geometric moment with translation not Become and scale constant radial direction geometric moment and calculated, specific algorithm is as follows：

$\begin{array}{c}{Z}_{nm}=\frac{n+1}{\mathrm{\π}}\underset{n-s-m=even}{\overset{n-\left|m\right|}{\underset{s=0}{\Σ}}}{D}_{nms}\\ \underset{a=0}{\overset{k}{\Σ}}\underset{b=0}{\overset{m}{\Σ}}{(-j)}^b\left(\begin{array}{c}k\\ a\end{array}\right)\left(\begin{array}{c}m\\ b\end{array}\right)B_{nms}{G}_{2k-2a+m-b,2a+b}\\ +\frac{n+1}{\mathrm{\π}}\underset{n-s-m=odd}{\overset{n-\left|m\right|}{\underset{s=0}{\Σ}}}{D}_{nms}\underset{a=0}{\overset{d}{\Σ}}\underset{b=0}{\overset{m}{\Σ}}{(-j)}^b\left(\begin{array}{c}k\\ a\end{array}\right)\left(\begin{array}{c}m\\ b\end{array}\right)B_{nms}{G}_{2d-2a+m-b,2a+b}\end{array}---\left(12\right)$

Wherein,

$k=\frac{n-s-m}{2},$

$d=\frac{n-s-m-1}{2}$

By to Pseudo-Zernike square Z_nmTake absolute value and obtain rotational invariance, and enter action by taking the logarithm to it State Ratage Coutpressioit, more than synthesis, it can be deduced that final extraction is characterized as：

${\hat{Z}}_{nm}={\log }_e\left|Z_{nm}\right|---\left(13\right)$

Wherein, the feature of the following Pseudo-Zernike squares as waveform recognition of bianry image after normalized is chosen：With

(2) the target number after normalized in bianry image：On the basis of normalization is successfully completed, Frank codes and P3 There are 2 signal target components in the two-value CWD image of code signal, and in the two-value CWD image of other 3 polyphase codes signals only There is 1 signal target component, in order to improve the robustness of feature, will be complete less than the component of signal of maximum target component of signal 20% Portion removes；

(3) in CWD peak power time location：The peak power of P1, P2 and P4 code signal is relative with the distance of encoding centre It is relatively near, and Frank codes and P3 codes have highest peak power in coding end, this feature is calculated from bianry image Go out, so need not be to the complete normalization of original CWD images, only by time gated process it is achieved that in CWD The method that this feature is calculated in image is as follows：

$t_{\max }=\frac{1}{N-1}\underset{x}{\arg \max }\left\{W_{CW}(x,y)\right\}---\left(14\right)$

Wherein, x express times axle, y represents frequency axiss, and N represents W_CW(x, y) length on a timeline,Purpose be to make The numerical value of this feature is normalized between 0～1；

(4) identification for Frank codes, the block structure of the CWD images of P1 and P2 code signals is proposed by calculating bianry image The standard deviation of middle target component width, can distinguish P3 and P4 codes signal with other 3 kinds of encoded signals, circular It is as follows：

After signal object component in labelling CWD images, individual processing is carried out for each component of signal object, i.e., The all component of signals outside required component to be processed are removed every time, the main constituent in bianry image B (x, y) is it The characteristic vector of covariance matrix, its computational methods are as follows：

$C=\underset{x=0}{\overset{N-1}{\Σ}}\underset{y=0}{\overset{N-1}{\Σ}}(z-c){(z-c)}^{T}B(x,y)---\left(15\right)$

Wherein, bianry image size is N × N, z=(x, y)^T, WithFor image center is horizontal, vertical coordinate, can To be calculated by formula (11)；

Bianry image is rotated so that primary axis is parallel with the vertical or axis of abscissas of image, due to the discrete seat of image Mark feature, this rotary course needs to carry out interpolation calculation, and using arest neighbors differential technique, the standard deviation of image object width can lead to Cross postrotational binary image data to be calculated, it is assumed that first principal coordinate corresponding with energy highest main constituent in image Axle rotate to it is parallel with the longitudinal axis of image, then need calculate image line and value

$r\left(x\right)=\underset{y=0}{\overset{N-1}{\Σ}}\hat{B}(x,y),x=0,1,\mathrm{...},N-1---\left(16\right)$

Wherein,Represent postrotational bianry image；

Normalized r (x) is expressed as follows, it be limited to it is 0～1 interval,

$\hat{r}\left(x\right)\frac{r\left(x\right)}{\max r\left(x\right)}---\left(17\right)$

More than synthesis, the standard deviation computing formula of target component width is as follows in bianry image：

${\mathrm{\σ}}_{obj}=\sqrt{\frac{1}{M}\underset{x}{\Σ}{\hat{r}}^2\left(x\right)-{\left(\frac{1}{M}\underset{x}{\Σ}\hat{r}\right(x\left)\right)}^2}---\left(18\right)$

Wherein, M is representedNon- small and weak sampling quantity, the summation in above formula be aiming at it is non-it is small and weak sampling ask Sum, because small and weak sampling has a strong impact on the quality of standard deviation estimate, especially when the row or column (depending on direction of rotation) of image When not containing any signal component, so will be excluded before the computation, T is set_objValue be 0.3, will ownSmall and weak sampling exclude outside read group total；

The numerical value of final feature is exactly the standard deviation sigma of all component of signals in image_objMeansigma methodss；

(5) the 5th signal characteristics make use of the different coding symmetry characteristic of encoded signal, by calculating symbol rate sampling pulse Obtain with the cross-correlation function of the time energizing signal of the pulse, the time delay size of the maximum of the cross-correlation function is to know One key character of not above-mentioned different coding signal, its computational methods are as follows：

${\hat{r}}_y\left(\mathrm{\&tau;}\right)=\left\{\begin{array}{cc}\underset{n=0}{\overset{N-\mathrm{\&tau;}-1}{\&Sigma;}}y(n+\mathrm{\&tau;})y^{*}(N-1-n),& \mathrm{\&tau;}\&GreaterEqual;0\\ \underset{n=-\mathrm{\&tau;}}{\overset{N-1}{\&Sigma;}}y(n+\mathrm{\&tau;})y^{*}(N-1-n),& \mathrm{\&tau;}<0\end{array}\right.---\left(19\right)$

Wherein, y (n), n=0,1 ..., N-1 is the discrete time complex envelope signal of single symbol rate sampling, | τ |≤N-1, then finally The time delay size of maximum of cross-correlation function be expressed as：

${\mathrm{\&tau;}}_{\max }=\underset{\mathrm{\&tau;}}{\mathrm{argmax}}\left({\hat{r}}_y\right(\mathrm{\&tau;}\left)\right)---\left(20\right)$

This feature has n=0 in constant rotational invariance, i.e. y (n), and rotational steps are identical during 1 ..., N-1, in order to obtain and when Between reverse signal identical feature, can also be by | τ_max| it is identified as feature；

Step 4, a kind of combined classifier of neural network of design, to the knowledge for improving neutral net from accuracy of identification and efficiency Other performance, designed neural network classifier is as follows：

Using weighting to posterior probability, by voting modulation type is determined；

If the classification number of signal to be sorted is K, grader number is N, for input feature vector vector X, then the of n-th grader K is output as

O_nk(X)=P (c_k|X)+e_nk(X) (21)

Wherein, P (c_k| X) represent the posterior probability for being judged as kth class when input is X, e_nk(X) n-th grader kth is represented The output error of individual node, weight vector ω_k={ ω_1k, ω_2k..., ω_nkBe n-th grader, k-th node output power It is worth, then each grader judges that same category of output weighted sum can be expressed as follows：

$S_k\left(X\right)=\underset{n=1}{\overset{N}{\&Sigma;}}{\mathrm{\&omega;}}_{nk}{O}_{nk}\left(X\right)---\left(22\right)$

Wherein, k=1,2 ..., K；

Increase constraintsWithThen have

S_k(X)=P (c_k|X) (23)

WhenWhen, judge that kth class signal is present.