CN106249208A - Signal detecting method under amplitude modulated jamming based on Fourier Transform of Fractional Order - Google Patents

Abstract

The present invention proposes signal detecting method under a kind of amplitude modulated jamming based on Fourier Transform of Fractional Order, for solving to detect present in signal detecting method under existing amplitude modulated jamming the technical problem that process is complicated and range of application is narrower, the present invention uses Fourier Transform of Fractional Order to process the reception signal of radar receiver adjacent two pulse repetition periods, and determine fractional order optimal value, make the aggregation of linear frequency modulation echo signal after relevant treatment optimum, to realize the detection of signal, concrete steps include: 1, gather and receive signal and set up signal model；2, docking receipts signal model carries out Fourier Transform of Fractional Order；3, Fourier Transform of Fractional Order model is carried out related operation；4, the aggregation of linear frequency modulation echo signal correlation function is optimized.It is simple that the present invention detects process, and is made without parameter estimation, can be used for realizing the detection to linear FM signal under amplitude modulated jamming background.

Description

Signal detecting method under amplitude modulated jamming based on Fourier Transform of Fractional Order

Technical field

The invention belongs to communication technical field, relate to Fourier Transform of Fractional Order and technology that related operation combines, tool Body relates to signal detecting method under a kind of amplitude modulated jamming based on Fourier Transform of Fractional Order, can be used for realizing adjusting linear Frequently the detection of signal (LFM).

Background technology

Radar chaff kind is more, is generally classified as active interference and sourceless seism, and the most active interference includes compacting Formula and Deceiving interference.Pressing type interference mainly floods radar echo signal by stochastic signal, makes radar effectively not obtain Take target echo information.In order to reach the effective compacting to radar in radar electronic warfare, noise modulated mode is generally used to produce dry Disturb signal, including the noise isoparametric modulation of amplitude, phase place, frequency and pulsewidth to signal.According to noise modulated mode not With, typical case's pressing type interference can be divided into the interference of amplitude modulated jamming, noise phase modulation, niose-modulating-frenquency jamming and radio noise to do Disturb.

Amplitude modulated jamming is a kind of important conflicting mode in the interference of radar pressing type, has signal and produces simple, band The features such as width is variable, pressing result is obvious, are applied to radar carries out aiming formula or combined type interference the most widely.Along with The development of perturbation technique, the interference signal energy of entrance radar receiver can exceed radar echo signal and reach more than tens of decibel, Radar echo signal is submerged in interference signal completely, and what the detection of the backscatter signal under strong jamming background was that radar faces important asks Topic.

In current published data, in the case of very noisy AM interference, signal detection performance depends primarily on interference Inhibition, be usually taken and interference carried out parameter estimation, and interference is filtered process, then suppress interference mode, Detect target echo signal, but be because interference is carried out parameter estimation and filtering, signal detection process can be caused the most multiple Miscellaneous, it is being unsatisfactory for the requirements such as Gauss hypothesis, stationary hypothesis or certain prior information especially, and when signal interference ratio is too low, at signal Reason ability is the best, can introduce certain information loss, limits the range of application of detection.

Du Dongping et al. was published in the article on " electronics and information journal " in 2008, and " noise based on phase matched is adjusted The lower LFM signal detection of width interference " a kind of LFM signal detecting method of middle proposition, amplitude modulated jamming signal is carried by the method Frequency is estimated, then realizes LFM signal detection based on least square phase matching method, and it is more complicated that its signal detection realizes step, with Time, be disturbed emission parameter non-stationary property, radar frequency agile and cause interference with the impact of the factor such as frequency agility, noise pixels detection Carrier frequency in interference is the most all time-varying function, and said method needs to disturb signal to have extremely stable carrier frequency and phase place, limit Make the range of the method.

Summary of the invention

It is an object of the invention to the defect overcoming above-mentioned prior art to exist, it is proposed that a kind of based on fractional order Fourier Signal detecting method under the amplitude modulated jamming of conversion, is used for solving to exist in signal detecting method under existing amplitude modulated jamming The technical problem that detection process is complicated and range of application is narrower.

The technical thought of the present invention is: by different fractional orders, two pulses adjacent to radar receiver repeat week The reception signal of phase carries out Fourier Transform of Fractional Order, and the signal after conversion is made related operation so that linear frequency modulation target Signal is positioned at the peak value of correlation function, determines the fractional order that two effects are best, it is achieved the detection to LFM signal.

According to above-mentioned technical thought, it is achieved the technical scheme that the object of the invention is taked is:

Signal detecting method under a kind of amplitude modulated jamming based on Fourier Transform of Fractional Order, comprises the steps:

(1) signal acquiring system receiver device by continuous wave radar, in collection radar antenna, any one section contains The reception signal of linear frequency modulation echo signal and amplitude modulated jamming, and set up the reception of two pulse repetition periods of arbitrary neighborhood Signal model, it is achieved step is:

(1a) signal model receiving signal that foundation gathers:

Wherein, A (t) is the signal amplitude of linear frequency modulation echo signal, f₀For echo signal original frequency；U₀T () is noise The carrier voltage of AM interference, U_nT () is the zoop of interference, ω_jFor carrier frequency,For initial phase；N (t) is white noise Sound；

(1b) from signal model x (t) set up, the reception signal of two pulse repetition periods of arbitrary neighborhood is chosen, and Utilize the reception signal of two pulse repetition periods of arbitrary neighborhood chosen, set up the reception signal mode of two pulse repetition periods Type:

x(t₁)=S (t₁)+N(t₁)+M(t₁)

x(t₂)=S (t₂)+N(t₂)+M(t₂)

Wherein, x (t₁)、S(t₁)、N(t₁) and M (t₁) it is respectively the reception signal model of first pulse repetition period, line Property frequency modulation echo signal model, amplitude modulated jamming signal model and white noise signal model, x (t₂)、S(t₂)、N(t₂) and M (t₂) it is respectively the reception signal model of second pulse repetition period, linear frequency modulation echo signal model, amplitude modulated jamming Signal model and white noise signal model；

(2) the reception signal model x (t to first pulse repetition period₁) and the reception of second pulse repetition period Signal model x (t₂) carry out Fourier Transform of Fractional Order respectively, obtain the Fourier Transform of Fractional Order of two pulse repetition periods Model:

$X_{{\mathrm{\α}}_1}\left(u_1\right)=X_S\left(u_1\right)+X_N\left(u_1\right)+X_M\left(u_1\right)$

$X_{{\mathrm{\α}}_2}\left(u_2\right)=X_S\left(u_2\right)+X_N\left(u_2\right)+X_M\left(u_2\right)$

Wherein,X_S(u₁)、X_N(u₁) and X_M(u₁) be respectively first pulse repetition period and receive signal, linear The Fourier Transform of Fractional Order model of frequency modulation echo signal, amplitude modulated jamming and white noise,X_S(u₂)、X_N(u₂) and X_M(u₂) it is respectively second pulse repetition period reception signal, linear frequency modulation echo signal, amplitude modulated jamming and white noise Fourier Transform of Fractional Order model；

(3) the Fourier Transform of Fractional Order model to two pulse repetition periodsWithCarry out relevant fortune Calculate, obtain the correlation function X of linear frequency modulation echo signal_S(u₁,u₂)；

(4) to the linear frequency modulation echo signal correlation function X obtained_S(u₁,u₂) aggregation be optimized, when adjacent two The individual pulse repetition period receives the fractional order optimal value group of signal Fourier Transform of Fractional OrderForOrTime, I.e. obtain the linear frequency modulation echo signal correlation function that aggregation is optimum.

The present invention compared with prior art, has the advantage that

Due to the fact that and in signal detection process, processed by Fourier Transform of Fractional Order under carrying out amplitude modulated jamming The reception signal of radar receiver adjacent two pulse repetition periods, and determine the optimal value group of fractional orderMake to be correlated with After process, the aggregation of linear frequency modulation echo signal is optimum, and detection process uses the phase such as Fourier Transform of Fractional Order and relevant treatment To simple calculations method, and be made without parameter estimation, with prior art amplitude modulated jamming carried out parameter estimation and The method detection signal of filtering is compared, and effectively simplifies detection process, the most not by Gauss hypothesis, stationary hypothesis or necessarily first Test the restriction of the requirements such as information, expand range of application.

Accompanying drawing explanation

Fig. 1 be the present invention realize FB(flow block)；

Fig. 2 is the time-frequency conversion schematic diagram of Fourier Transform of Fractional Order of the present invention；

Fig. 3 is the analysis chart that present invention determine that adjacent two pulse repetition periods reception signal fractional order value；

Fig. 4 is that in the present invention, fractional order Fourier when fractional order is 0.5,1.5 of adjacent two pulse repetition periods becomes Reception signal after changing and the simulation result figure of linear frequency modulation echo signal；

Fig. 5 is that in the present invention, fractional order Fourier when fractional order is 0.5,1.5 of adjacent two pulse repetition periods becomes Change the simulation result figure of the correlation function being followed by the collection of letters number and linear frequency modulation echo signal；

Fig. 6 is fractional order when fractional order is 0.8,1.2 and 0.3,1.2 of adjacent two pulse repetition periods in the present invention Fourier transformation is followed by the simulation result figure of the correlation function of the collection of letters number and linear frequency modulation echo signal.

Detailed description of the invention

Below in conjunction with accompanying drawing, the present invention is described in further detail.

With reference to Fig. 1, the present invention comprises the steps:

Step 1, gathers and receives signal and set up signal model.

The signal acquiring system receiver device by continuous wave radar, gathers any one section of reception letter in radar antenna Number, wherein comprise linear frequency modulation echo signal, amplitude modulated jamming and radar receiver equipment with white noise, and set up appoint Anticipate the reception signal model of adjacent two pulse repetition periods, it is achieved step is:

The signal model receiving signal that the foundation of step 1a gathers:

Wherein, A (t) is the signal amplitude of linear frequency modulation echo signal, f₀For echo signal original frequency；U₀T () is noise The carrier voltage of AM interference, U_nT () is the zoop of interference, ω_jFor carrier frequency,For initial phase；N (t) is white noise Sound；

Step 1b, from signal model x (t) set up, chooses the reception signal of two pulse repetition periods of arbitrary neighborhood, And utilize the reception signal of two pulse repetition periods of arbitrary neighborhood chosen, set up the reception signal of two pulse repetition periods Model:

x(t₁)=S (t₁)+N(t₁)+M(t₁)

x(t₂)=S (t₂)+N(t₂)+M(t₂)

Wherein, x (t₁)、S(t₁)、N(t₁) and M (t₁) it is respectively the reception signal model of first pulse repetition period, line Property frequency modulation echo signal model, amplitude modulated jamming signal model and white noise signal model, x (t₂)、S(t₂)、N(t₂) and M (t₂) it is respectively the reception signal model of second pulse repetition period, linear frequency modulation echo signal model, amplitude modulated jamming Signal model and white noise signal model；

Step 2, docking is received signal model and is carried out Fourier Transform of Fractional Order.

Reception signal model x (t to first pulse repetition period₁) and the reception signal of second pulse repetition period Model x (t₂) carry out Fourier Transform of Fractional Order respectively:

$X_{{\mathrm{\α}}_1}\left(u_1\right)=F^{p_1}\[x\left(t_1\right)\]={\∫}_{-\mathrm{\∞}}^{+\mathrm{\∞}}x\left(t_1\right)K_{{\mathrm{\α}}_1}(t_1,u_1){\mathrm{dt}}_1$

$X_{{\mathrm{\α}}_2}\left(u_2\right)=F^{p_2}\[x\left(t_2\right)\]={\∫}_{-\mathrm{\∞}}^{+\mathrm{\∞}}x\left(t_2\right)K_{{\mathrm{\α}}_2}(t_2,u_2){\mathrm{dt}}_2$

Wherein, α₁=p₁Pi/2, α₂=p₂Pi/2, F^p[] representative score rank Fourier transformation operation, K_α(t u) is fractional order The kernel function of Fourier transformation, it is defined as:

$K_{\mathrm{\α}}(t,u)=\left\{\begin{array}{cc}\sqrt{\frac{1-j\cot \mathrm{\α}}{2\mathrm{\π}}}\exp (j\frac{t^2+u^2}{2}\cot \mathrm{\α}-tu\csc \mathrm{\α}),& \mathrm{\α}\≠n\mathrm{\π}\\ \mathrm{\δ}(t-u),& \mathrm{\α}=2n\mathrm{\π}\\ \mathrm{\δ}(t+u),& \mathrm{\α}=(2n\±1)\mathrm{\π}\end{array}\right.$

Obtain the Fourier Transform of Fractional Order model of two pulse repetition periods:

$X_{{\mathrm{\α}}_1}\left(u_1\right)=X_S\left(u_1\right)+X_N\left(u_1\right)+X_M\left(u_1\right)$

$X_{{\mathrm{\α}}_2}\left(u_2\right)=X_S\left(u_2\right)+X_N\left(u_2\right)+X_M\left(u_2\right)$

Wherein,X_S(u₁)、X_N(u₁) and X_M(u₁) be respectively first pulse repetition period and receive signal, linear The Fourier Transform of Fractional Order model of frequency modulation echo signal, amplitude modulated jamming and white noise,X_S(u₂)、X_N(u₂) and X_M(u₂) it is respectively second pulse repetition period reception signal, linear frequency modulation echo signal, amplitude modulated jamming and white noise Fourier Transform of Fractional Order model；

Step 3, carries out related operation to Fourier Transform of Fractional Order model.

Fourier Transform of Fractional Order model to two pulse repetition periodsWithCarry out related operation, Obtain the correlation function X of linear frequency modulation echo signal_S(u₁,u₂), it is achieved process is:

$\begin{array}{c}{X}_{{\mathrm{\α}}_1}\left(u_1\right)\⊗X_{{\mathrm{\α}}_2}\left(u_2\right)=\[X_S\left(u_1\right)+X_N\left(u_1\right)+X_M\left(u_1\right)\]\⊗\\ \[X_S\left(u_2\right)+X_N\left(u_2\right)+X_M\left(u_2\right)\]\\ =X_S\left(u_1\right)\⊗X_S\left(u_2\right)+X_S\left(u_1\right)\⊗X_N\left(u_2\right)\\ +X_S\left(u_1\right)\⊗X_M\left(u_2\right)+X_N\left(u_1\right)\⊗X_S\left(u_2\right)\\ +X_N\left(u_1\right)\⊗X_N\left(u_2\right)+X_N\left(u_1\right)\⊗X_M\left(u_2\right)\\ +X_M\left(u_1\right)\⊗X_S\left(u_2\right)+X_M\left(u_1\right)\⊗X_N\left(u_2\right)\\ +X_M\left(u_1\right)\⊗X_M\left(u_2\right)\\ =X_S\left(u_1\right)\⊗X_S\left(u_2\right)\\ =X_S(u_1,u_2)\end{array}$

WhereinFor related operation symbol.

Because N is amplitude modulated jamming, M is white noise, then X_S(u_i) and X_N(u_i) uncorrelated, X_S(u_i) and X_M(u_i) not phase Close, X_N(u_i) and X_M(u_i) uncorrelated, X_N(u₁) and X_N(u₂) uncorrelated, X_M(u₁) and X_M(u₂) uncorrelated.And linear frequency modulation target Signal is relevant within adjacent two pulse repetition periods, then X_S(u₁) and X_S(u₂) it is relevant.If at these adjacent two arteries and veins In rushing the repetition period, linear frequency modulation echo signal exists, thenWithCorrelation function just have maximum.

Therefore, under amplitude modulated jamming environment, the Fourier Transform of Fractional Order correlation function of only LFM signal just occurs Peak value, thus can carry out signal detection analysis.But for adjacent two pulse repetition periods, the fractional order p used₁With p₂The aggregation of LFM signal after relevant treatment can be affected, in order to preferably carry out signal detection and analysis, it should be determined that fractional order Number p₁With p₂Value, the aggregation making LFM signal is best.

Step 4, is optimized the aggregation of linear frequency modulation echo signal correlation function.

In time-frequency two-dimensional plane, time shaft and frequency axis are generally represented by two mutually orthogonal straight lines.If with time Between be that the x (t) of independent variable represents along the signal representation of time shaft t, and its corresponding conventional Fourier transformation X (ω) represents Signal is along the signal representation of frequency axis f, then can regard the conventional Fourier transformation of signal as a two-dimentional time-frequency and put down Rotation operator on face, and it is to rotate pi/2 arrival rate axle counterclockwise from time shaft t.The time-frequency of Fourier Transform of Fractional Order Shift theory is as shown in Figure 2.

Owing to α=p pi/2 only occurs on the parameter position of trigonometric function, therefore with the p (or α) mark as parameter The definition of rank Fourier transformation with 4 (or 2 π) as cycle.So have only to investigate interval p ∈ (-2,2] (or α ∈ (-π, π]).For the jamming pattern of the present invention, use Fourier Transform of Fractional Order and related operation, p ∈ (-2,0] and p ∈ (0,2] Result is identical, therefore, the present invention only discuss p ∈ (0,2] situation.

P is divided into (1.5,2) two intervals of (0.5,1.5) and (0,0.5) ∪ discuss compare.If p₁And p₂It is in Interval (0.5,1.5) or in being in interval (0,0.5) ∪ (1.5,2), such as 0.8 and 1.2, thenWithFrequency domain Dependency is the most forward in the time and relative locating rearward becomes big, and linear frequency modulation echo signal aggregation is deteriorated；If p₁And p₂Locate respectively In interval (0.5,1.5) and (0,0.5) ∪ (1.5,2), such as 0.3 and 1.2, then the p being in interval (0.5,1.5) also can make Frequency domain dependency within corresponding time pulse repetition period becomes big, and linear frequency modulation echo signal aggregation is deteriorated.When adjacent two The individual pulse repetition period receives the fractional order of signal Fourier Transform of Fractional OrderTake optimal value groupOrTime, I.e. obtain the linear frequency modulation echo signal correlation function X that aggregation is optimum_S(u₁,u₂), reach the purpose of signal detection.Adjacent Two pulse repetition periods receive the analysis of signal fractional order value as shown in Figure 3.

With reference to Fig. 2, Fourier Transform of Fractional Order can be construed on two dimension time-frequency plane from time shaft t to frequency axis f edge The counterclockwise operator of rotation alpha angle, wherein time shaft t and frequency axis f rotates to the u in Fourier Transform of Fractional Order territory respectively Axle and v axle, Fourier Transform of Fractional Order has merged signal in time domain and the information of frequency domain simultaneously.

With reference to Fig. 3, if p₁And p₂It is in interval (0,0.5) ∪ (0.5,1.5) ∪ (1.5,2), such as 0.8 and 1.2, or 0.3 With 1.2, then linear frequency modulation echo signal correlation function aggregation is deteriorated, and receives signal mark when adjacent two pulse repetition periods The fractional order of rank Fourier transformationTake optimal value groupOrTime, linear frequency modulation echo signal correlation function gathers Collection property is optimum.

Below in conjunction with emulation experiment, the technique effect of the present invention is further described.

1. simulated conditions.

The operation system of emulation experiment of the present invention is Intel (R) Core (TM) i5CPU [email protected], 32 Windows operating system, simulation software uses MATLAB R (2010a), and simulation parameter arranges as follows.

Assuming the radar of some amplitude modulated jamming machine one L-band of interference, radar wavelength is 0.15m, and pulse repeats Cycle is 500 μ s.Radar emission signal is LFM signal, and during signal, a width of 20 μ s, carry a width of 10MHz, and signal center frequency is 0MHz, sample frequency is 40MHz.The fundamental frequency of jammer is equal to the operating frequency of radar, and the pulse repetition period is 500 μ s, initially Phase placeThe index of modulation is 1000.In the presence of frequency modulation echo signal linear in radar signal, it is assumed that echo signal quilt Noise floods, if power signal interference ratio is-15dB, signal to noise ratio is 6dB.

2. emulation content and interpretation of result.

2.1 pairs of adjacent two pulse repetition periods connecing after Fourier Transform of Fractional Order when fractional order is 0.5,1.5 The collection of letters number and linear frequency modulation echo signal emulate, and its simulation result is as shown in Figure 4；

2.2 pairs of adjacent two pulse repetition periods receive after Fourier Transform of Fractional Order when fractional order is 0.5,1.5 The correlation function of signal and linear frequency modulation echo signal emulates, and its simulation result is as shown in Figure 5；

2.3 pairs of fractional order Fouriers when fractional order is 0.8,1.2 and 0.3,1.2 of adjacent two pulse repetition periods become Changing and be followed by collecting mail number and the correlation function of linear frequency modulation echo signal emulates, its simulation result is as shown in Figure 6.

It is to receive signal graphics after Fourier Transform of Fractional Order with reference to Fig. 4, Fig. 4 (a), does not carry out relevant place Reason；Fig. 4 (b) is only graphics in the case of linear frequency modulation echo signal.Wherein fractional order value respectively is 0.5 He 1.5.From Fig. 4 (a) and Fig. 4 (b), only through Fourier Transform of Fractional Order, and do not carry out relevant treatment, it is more difficult to from receiving letter Identify echo signal in number, do not reach the purpose of signal detection.

With reference to Fig. 5, Fig. 5 (a) for receive signal after Fourier Transform of Fractional Order, the graphics of correlation function；Fig. 5 (b) For the graphics of same treatment in the case of only linear frequency modulation echo signal.Wherein fractional order value respectively is 0.5 He 1.5.From Fig. 5 (a) and Fig. 5 (b), the correlation function aggregation of echo signal is the highest, the most easily detects from receiving signal Go out echo signal.

With reference to the graphics of correlation function under the value that Fig. 6, Fig. 6 are different fractional order.Fig. 6 (a) is adjacent two arteries and veins Rushing the repetition period receives signal fractional order value when being respectively 0.8 and 1.2, receives the graphics of signal correction function；Fig. 6 B () is to receive signal fractional order value adjacent two pulse repetition periods when being respectively 0.8 and 1.2, linear frequency modulation target is believed The graphics of number correlation function；Fig. 6 (c) is adjacent two pulse repetition periods to receive signal fractional order value to be respectively 0.3 During with 1.2, receive the graphics of signal correction function；Fig. 6 (d) is adjacent two pulse repetition periods to receive signal fractional order When value is respectively 0.3 and 1.2, the graphics of linear frequency modulation echo signal correlation function.Compared with Fig. 5, if fractional order Value is 0.8 and 1.2 respectively, or value is 0.3 and 1.2, and the aggregation of echo signal correlation function is poor, is difficult to from receiving letter Detected in number.If fractional order value respectively is 0.5 and 1.5, then the correlation function of echo signal has well Aggregation, can reach detect linear frequency modulation echo signal purpose.Through theory analysis and emulation experiment, it may be determined that phase Adjacent two pulse repetition periods receive the fractional order optimal value group of signalForOrNow linear frequency modulation mesh Mark signal correction function X_S(u₁,u₂) aggregation optimum, reached the purpose of signal detection.

In sum, three emulation experiments three results obtained show, use the present invention effectively to detect Linear frequency modulation echo signal, and reduce detection process complexity, expand range of application.

Claims (4)

1. a signal detecting method under amplitude modulated jamming based on Fourier Transform of Fractional Order, comprises the steps:

(1) signal acquiring system receiver device by continuous wave radar, in collection radar antenna, any one section contains linear The reception signal of frequency modulation echo signal and amplitude modulated jamming, and set up the reception signal of two pulse repetition periods of arbitrary neighborhood Model, it is achieved step is:

(1a) signal model receiving signal that foundation gathers:

Wherein, A (t) is the signal amplitude of linear frequency modulation echo signal, f₀For echo signal original frequency；U₀T () is noise pixels detection The carrier voltage of interference, U_nT () is the zoop of interference, ω_jFor carrier frequency,For initial phase；N (t) is white noise；

(1b) from signal model x (t) set up, choose the reception signal of two pulse repetition periods of arbitrary neighborhood, and utilize The reception signal of two pulse repetition periods of arbitrary neighborhood chosen, sets up the reception signal model of two pulse repetition periods:

x(t₁)=S (t₁)+N(t₁)+M(t₁)

x(t₂)=S (t₂)+N(t₂)+M(t₂)

Wherein, x (t₁)、S(t₁)、N(t₁) and M (t₁) be respectively the reception signal model of first pulse repetition period, linearly adjust Frequently echo signal model, amplitude modulated jamming signal model and white noise signal model, x (t₂)、S(t₂)、N(t₂) and M (t₂) point It is not the reception signal model of second pulse repetition period, linear frequency modulation echo signal model, amplitude modulated jamming signal mode Type and white noise signal model；

(2) the reception signal model x (t to first pulse repetition period₁) and the reception signal mode of second pulse repetition period Type x (t₂) carry out Fourier Transform of Fractional Order respectively, obtain the Fourier Transform of Fractional Order model of two pulse repetition periods:

$X_{{\mathrm{\α}}_1}\left(u_1\right)=X_S\left(u_1\right)+X_N\left(u_1\right)+X_M\left(u_1\right)$

$X_{{\mathrm{\α}}_2}\left(u_2\right)=X_S\left(u_2\right)+X_N\left(u_2\right)+X_M\left(u_2\right)$

Wherein,X_S(u₁)、X_N(u₁) and X_M(u₁) it is respectively first pulse repetition period reception signal, linear frequency modulation The Fourier Transform of Fractional Order model of echo signal, amplitude modulated jamming and white noise,X_S(u₂)、X_N(u₂) and X_M (u₂) it is respectively second pulse repetition period reception signal, linear frequency modulation echo signal, amplitude modulated jamming and white noise Fourier Transform of Fractional Order model；

(3) the Fourier Transform of Fractional Order model to two pulse repetition periodsWithCarry out related operation, Correlation function X to linear frequency modulation echo signal_S(u₁,u₂)；

(4) to the linear frequency modulation echo signal correlation function X obtained_S(u₁,u₂) aggregation be optimized, when adjacent two arteries and veins Rush the fractional order optimal value group of repetition period reception signal Fourier Transform of Fractional OrderForOrTime, to obtain final product To the linear frequency modulation echo signal correlation function that aggregation is optimum.

Signal detecting method under amplitude modulated jamming based on Fourier Transform of Fractional Order the most according to claim 1, its It is characterised by, the reception signal model x (t to first pulse repetition period described in step (2)₁) and second pulse weight The reception signal model x (t in multiple cycle₂) carry out Fourier Transform of Fractional Order respectively, realize as follows:

$X_{{\mathrm{\α}}_1}\left(u_1\right)=F^{p_1}\[x\left(t_1\right)\]={\∫}_{-\mathrm{\∞}}^{+\mathrm{\∞}}x\left(t_1\right)K_{{\mathrm{\α}}_1}(t_1,u_1){\mathrm{dt}}_1$

$X_{{\mathrm{\α}}_2}\left(u_2\right)=F^{p_2}\[x\left(t_2\right)\]={\∫}_{-\mathrm{\∞}}^{+\mathrm{\∞}}x\left(t_2\right)K_{{\mathrm{\α}}_2}(t_2,u_2){\mathrm{dt}}_2$

Wherein, α₁=p₁Pi/2, α₂=p₂Pi/2, F^p[] representative score rank Fourier transformation operation, K_α(t is u) in fractional order Fu The kernel function of leaf transformation, it is defined as:

$K_{\mathrm{\α}}\left(t,u\right)=\left\{\begin{array}{cc}\sqrt{\frac{1-j\cot \mathrm{\α}}{2\mathrm{\π}}}\exp \left(j\frac{t^2+u^2}{2}\cot \mathrm{\α}-tu\csc \mathrm{\α}\right),& \mathrm{\α}\≠n\mathrm{\π}\\ \mathrm{\δ}\left(t-u\right),& \mathrm{\α}=2n\mathrm{\π}\\ \mathrm{\δ}\left(t+u\right),& \mathrm{\α}=\left(2n\±1\right)\mathrm{\π}\end{array}\right..$

Signal detecting method under amplitude modulated jamming based on Fourier Transform of Fractional Order the most according to claim 1, its It is characterised by, the Fourier Transform of Fractional Order model to two pulse repetition periods described in step (3)WithCarry out related operation, it is achieved process is:

$\begin{array}{c}{X}_{{\mathrm{\α}}_1}\left(u_1\right)\⊗X_{{\mathrm{\α}}_2}\left(u_2\right)=\[X_S\left(u_1\right)+X_N\left(u_1\right)+X_M\left(u_1\right)\]\⊗\\ \[X_S\left(u_2\right)+X_N\left(u_2\right)+X_M\left(u_2\right)\]\\ =X_S\left(u_1\right)\⊗X_S\left(u_2\right)+X_S\left(u_1\right)\⊗X_N\left(u_2\right)\\ +X_S\left(u_1\right)\⊗X_M\left(u_2\right)+X_N\left(u_1\right)\⊗X_S\left(u_2\right)\\ +X_N\left(u_1\right)\⊗X_N\left(u_2\right)+X_N\left(u_1\right)\⊗X_M\left(u_2\right)\\ +X_M\left(u_1\right)\⊗X_S\left(u_2\right)+X_M\left(u_1\right)\⊗X_N\left(u_2\right)\\ +X_M\left(u_1\right)\⊗X_M\left(u_2\right)\\ =X_S\left(u_1\right)\⊗X_S\left(u_2\right)\\ =X_S\left(u_1,u_2\right)\end{array}$

WhereinFor related operation symbol.

Signal detecting method under amplitude modulated jamming based on Fourier Transform of Fractional Order the most according to claim 1, its Be characterised by, described in step (4) to linear frequency modulation echo signal correlation function X_S(u₁,u₂) aggregation be optimized, press Following steps realize:

(4a) according to the principle of Fourier Transform of Fractional Order, determine the interval of fractional order p for (0,2]；

(4b) by fractional order p interval (0,2] in the discussion of different values, obtain adjacent two pulse repetition periods Receive the fractional order optimal value group of signal Fourier Transform of Fractional Order