CN106443589A - SMSP interference parameter estimation method based on Radon-WDL transformation - Google Patents

Abstract

The invention provides an SMSP interference parameter estimation method based on Radon-WDL transformation. According to the method, Radon-WDL transformation of SMSP interference on a generalized time-frequency domain is carried out; Radon transformation for WDL distribution of SMSP interference is carried out, the generalized time-frequency domain is transformed to a polar coordinates domain containing an angle and a radius, cross terms can be further inhibited, and the quantity of sub pulses of SMSP interference and an angle and a radius of the location of a largest peak are acquired according to the quantity of peaks after Radon transformation; carrier frequency and a frequency modulation gradient of SMSP interference can be estimated according to the angle and the radius of the location of the largest peak after Radon transformation.

Description

The method for parameter estimation of the SMSP interference based on Radon-WDL conversion

Technical field

The present invention relates to Anti-jamming Technology for Radar field, particularly to the parameter estimation techniques of frequency spectrum disperse SMSP interference.

Background technology

Frequency modulation(PFM) is carried out by digital radiofrequency memory DRFM to the radar signal intercepting and obtains frequency spectrum disperse SMSP interference, A string dressing decoy can be produced in radar receiving terminal, effectively cheat radar.And, when jamming power is larger, SMSP Interference has deception and the dual function of compacting.So, the parameter estimation realizing SMSP interference has to suppression in future SMSP interference Important researching value and meaning.

Radon-WDL conversion is a kind of efficient algorithm estimating SMSP interference parameter.2012, Rui-Feng Bai proposed Wigner-Ville Distribution Associated with the Linear Canonical Transform, that is, The algorithm for estimating to linear frequency-modulated parameter for the WDL distribution, is shown in " R.F.Bai, B.Z.Li, Q.Y.Cheng.Wigner Ville distribution associated with the linear canonical transform,J.Appl.Math.2012 (2012).14pp.”.Compared with classical Wigner-Ville distribution, this algorithm has 3 free parameters, has higher flexible Property；When choosing suitable parameter a, when b, c, d, under low signal-to-noise ratio, it is oblique to the carrier frequency and frequency modulation estimating linear FM signal Rate has higher precision.However, when signal is to disturb containing multicomponent SMSP, WDL distribution will produce multiple cross terms, sternly Ghost image rings the parameter estimation of signal.

Content of the invention

The technical problem to be solved is to provide a kind of parameter estimation of the SMSP interference that can curb chiasma type Method.

The present invention be employed technical scheme comprise that by solving above-mentioned technical problem, is done based on the SMSP of Radon-WDL conversion The method for parameter estimation disturbed, comprises the following steps：

Step 1, to SMSP interference carry out WDL distribution transformation：

Wherein, J_SMSPT () is SMSP interference during moment t, τ is time delay, and * is conjugation, K_A(ω, τ) is the kernel function of WDL,Exp represents the exponential function with natural logrithm e as bottom, a, Four parameters a that b, c, d convert for WDL, b, c, d, and meet ad-bc=1, ω is angular frequency, and ω=2 π f, and f is frequency Rate；

Step 2, the WDL distribution to SMSP interference carry out Radon conversion：

Wherein, WDL is distributed for the WDL that SMSP disturbs, and u ', v convert the independent variable in (u, v) domain for Radon, and (u, α) is The radius tried to achieve after Radon conversion and angle, RWDL (u, α) is any rotation α along the integration knot under different radius u Really, δ is impulse function；RWDL (u, α) represents for the energy accumulation of the subpulse of SMSP interference after Radon conversion；

Subpulse number n that spike number in RWDL (u, α) is disturbed for SMSP；RWDL (u, α) takes and corresponds to during maximum Radius and angle as Radon conversion after SMSP interference subpulse energy accumulation spike position radius u₀With The angle [alpha] of the energy accumulation spike position of subpulse of SMSP interference after Radon conversion₀；

The estimated value of step 3, the carrier frequency of SMSP interference of calculating Radon-WVD conversion and chirp rate：

Wherein,It is distributed carrier frequency estimated value for WDL,It is distributed chirp rate estimated value for WDL.

SMSP interference is carried out Radon-WDL conversion on the time-frequency domain of broad sense by the present invention；The WDL that SMSP disturbs is being divided Cloth carries out Radon conversion, by the time-frequency domain conversation of broad sense to the polar domain containing angled and radius, can curb simultaneously Cross term, and estimate to obtain subpulse number and the maximum sharpness place of SMSP interference according to spike number after Radon conversion Angle and radius；Finally according to Radon conversion after maximum sharpness be located angle and radius estimate SMSP interference carrier frequency and Chirp rate.

The invention has the beneficial effects as follows, first by WDL distribution applications in the parameter estimation of SMSP, first Radon is become Change and be introduced in WDL distribution, to suppress the chiasma type being produced by WDL distribution.It is demonstrated experimentally that under low signal-to-noise ratio, with respect to classics Wigner-Ville distribution algorithm, WDL Distribution Algorithm has higher accuracy of detection；And, the introducing due to Radon conversion, Can be suppressed by the cross term that WDL distribution produces, so that this algorithm more effectively estimates the parameter of SMSP interference.

Brief description

Fig. 1 converts the algorithm steps estimating LFM signal chirp rate k ' for Radon-WDL；

The instantaneous autocorrelation analysis that Fig. 2 disturbs for SMSP；

The principle that Fig. 3 converts for Radon；

Fig. 4 is the relation with the angle interval of b, Radon conversion for the MSE of chirp rate；

Fig. 5 is the relation with b, SNR for the MSE of chirp rate；

Fig. 6 converts schematic diagram for Radon-WVD.

Specific embodiment

The parameter estimation parameter to be estimated of SMSP interference is：The subpulse number of SMSP interference, the load of SMSP interference Frequency and chirp rate.

As shown in figure 1, comprising the following steps：

Step 1：WDL distribution transformation is carried out to SMSP interference：

Assume that SMSP interference is made up of n subpulse, then SMSP interference is represented by

Wherein, J_SMSPT () is SMSP interference during moment t, J_SMSP,pT () p is the pth sub- of SMSP interference during moment t Pulse, p=0,1 ..., n-1；

J_SMSP,pT () subpulse signal is：

Wherein, A_JRepresent the amplitude of interference, typically take A_J=1；Exp represents the exponential function with natural logrithm e as bottom, k ' Represent the chirp rate of SMSP interference, the generation principle disturbed from SMSP, k '=nk, k are the frequency modulation of radar echo signal Slope；f₀For carrier frequency；The when width of T SMSP interference.

The WDL of SMSP interference is transformed to：

Wherein, ω is angular frequency, and τ is time delay, and * is conjugation, K_A(ω, τ) is the kernel function of WDL,Four parameters a that a, b, c, d convert for WDL, b, c, d, And meet ad-bc=1；

By J_SMSP,pT () subpulse signal expression substitutes into the WDL conversion expression formula of SMSP interference, the then WDL of SMSP interference Conversion is represented by：

J_SMSP,pFor p-th subpulse of SMSP interference, p=0,1 ..., n-1, J_SMSP,qThe pth sub- that q disturbs for SMSP Pulse, q=0,1 ..., n-1；

As shown in Figure 2, to the subpulse J having limit for length SMSP_SMSP,p(t) and J_{SMSP, q}T () carries out WDL conversion and can obtain：

In formula

As a=0, abbreviation above formula can obtain

In formula

RightTake absolute value and can obtain：

In formula

Due toBetween when being mutually independent of each other, formula (1-1) can be expressed as

Subpulse p=0,1 ..., n-1 and q=0,1 ..., the relation of n-1 is as follows

As the p=q in formula (1-2),It is from major event, have n item from major event；As p ≠ q,For cross term, haveItem cross term；When p+q value phase simultaneously as from major event with The superposition of cross term, has 2n-1 bar straight line in time frequency plane.

Three-dimensionalDistribution be shaped like fin shape, straight line is distributed on time-frequency planeOn.

Step 2：WDL distribution to SMSP interference carries out Radon conversion

Radon conversion is a kind of projective transformation of straight line integration.As Fig. 3, former rectangular coordinate (t, ω) rotation alpha is obtained newly Coordinate (u, v), at this moment by different u values parallel to v axle integrate, acquired results be Radon conversion.

The Radon conversion of the WDL distribution of SMSP interference can be expressed as

In formula, WDL is distributed for the WDL that SMSP disturbs, and u ', v convert the independent variable in (u, v) domain for Radon, and (u, α) is The radius tried to achieve after Radon conversion and angle, u, α known variables.RWDL (u, α) is that any rotation α amasss along different u values Divide result, can get u when RWDL (u, α) takes maximum₀,α₀.RWDL converts, due to as δ (u-u '), that is, during u=u ', RWDL Just there is value, then the u ∈ (- ∞ ,+∞) that RWDL converts and α ∈ [0,2 π).

With parameter k ', f₀Replace integral parameter u, α, then RWDL (u, α) can be expressed as again：

Wherein ω₀=2 π f₀, the chirp rate that k ' disturbs for SMSP, b is the parametric variable of WDL, p=0,1 ..., n-1, q =0,1 ..., n-1.

Step 3：It is estimated as follows through the carrier frequency of the SMSP interference of Radon-WDL conversion and chirp rate：

Wherein b is the parametric variable of WDL.

Step:4：Obtain the mean square error (MSE) that carrier frequency and chirp rate are estimated, estimate Radon-WVD conversion with The estimated accuracy of Radon-WDL conversion.

The MSE estimating through carrier frequency and the chirp rate of the SMSP interference of Radon-WVD conversion is as follows：

The MSE estimating through carrier frequency and the chirp rate of the SMSP interference of Radon-WDL conversion is as follows：

WDL conversion, Radon conversion are existing algorithm, and Radon conversion is combined by the present invention first with WDL conversion, and It is applied in the parameter identification of SMSP interference；The WDL of the SMSP that derived first interference converts limited long form.

Emulation experiment

When width T=10 μ s, bandwidth B=20MHz, chirp rate k=B/T sample frequency f of LFM_s=60MHz, carrier frequency f₀= 300MHz, sampled point N=fix (f_s× T)=600.The subpulse number of SMSP interference is n=4, and chirp rate is k '=n*k =4k.The amplitude of noise is set to σ=1.Here only consider SMSP interference plus noise.

1st, parameter a=0 of WDL conversion, b=0.5:0.01:1, c=-1/b, d=0, t=0:τ/[fs×τ]:τ, f=0: fs/[fs×τ]:fs.The relative mean square error of chirp rate：By MSE_{k′,Radon-WDL}Chemical conversion dB form is MSE_k′,dB=10log10 (MSE_{k′,Radon-WDL}/max(MSE_{k′,Radon-WDL})).Between the angle of Radon conversion, scope is set to θ=15:ta:45, between angle Every respectively ta=[0.01 0.05 0.1], ratio is dried for JNR=10dB, obtains Fig. 4, analysis chart can obtain：For between equal angular Every, in b=0.6, the estimation MSE of k '_k′,dBAll there is minima, then choose b=0.6；As b=0.6, angle is spaced apart When 0.05, the estimation MSE of k '_k′,dBMinimum, then choose ta=0.05.

2nd, parameter a=0 of WDL conversion, b=0.5:0.01:1, c=-1/b, d=0, t=0:τ/[fs×τ]:τ, f=0: fs/[fs×τ]:fs.The relative mean square error of chirp rate：By MSE_{k′,Radon-WDL}Chemical conversion dB form is MSE_k′,dB=10log10 (MSE_{k′,Radon-WDL}/max(MSE_{k′,Radon-WDL})).Between the angle of Radon conversion, scope is set to θ=15:ta:45, between angle Every respectively ta=[0.01 0.05 0.1], the dry ratio JNR=[noiseless -5dB 10dB] that makes an uproar, 100 Monte Carlo simulations, Obtain Fig. 5, analysis chart can obtain：For identical JNR, in b=0.6, the estimation MSE of chirp rate k_k′,dBAll there is minima, then Choose b=0.6.

3rd, take JNR=10dB, angle change is θ=0:0.05:90, angle is spaced apart 0.05, parameter a=0, b=0.6, c =-1/b, d=0；SMSP interference is carried out with the comparison of Radon-WDL conversion, can obtain from Fig. 6 analysis, the cross term energy of WDL distribution It is suppressed, only from the energy accumulating of major event in the angle of Radon conversion and radius domain.

Claims (1)

1. the method for parameter estimation of the SMSP interference based on Radon-WDL conversion is it is characterised in that comprise the following steps：

Step 1, to SMSP interference carry out WDL distribution transformation：

${\mathrm{WDL}}_J(t,\mathrm{\ω})={\∫}_{-\mathrm{\∞}}^{+\mathrm{\∞}}{J}_{SMSP}(t+\frac{\mathrm{\τ}}{2})J_{SMSP}^{*}(t-\frac{\mathrm{\τ}}{2})K_A(\mathrm{\ω},\mathrm{\τ})d\mathrm{\τ}$

Wherein, J_SMSPT () is SMSP interference during moment t, τ is time delay, and * is conjugation, K_A(ω, τ) is the kernel function of WDL,Exp represents the exponential function with natural logrithm e as bottom, a, Four parameters a that b, c, d convert for WDL, b, c, d, and meet ad-bc=1, ω is angular frequency, and ω=2 π f, and f is frequency Rate；

Step 2, the WDL distribution to SMSP interference carry out Radon conversion：

$RWDL(u,\mathrm{\α})={\∫}_{-\mathrm{\∞}}^{+\mathrm{\∞}}{\∫}_{-\mathrm{\∞}}^{+\mathrm{\∞}}WDL(u^{\′}cos\mathrm{\α}-vsin\mathrm{\α},u^{\′}sin\mathrm{\α}+vcos\mathrm{\α})\mathrm{\δ}(u-u^{\′}){\mathrm{du}}^{\′}dv$

Wherein, WDL is distributed for the WDL that SMSP disturbs, and u ', v convert the independent variable in (u, v) domain for Radon, and (u, α) becomes for Radon The radius tried to achieve after changing and angle, δ is impulse function；RWDL (u, α) is the energy of the subpulse of SMSP interference after Radon conversion Accumulation represents, is any rotation α along the integral result under different radius u；

Subpulse number n that spike number in RWDL (u, α) is disturbed for SMSP；RWDL (u, α) takes corresponding half during maximum Footpath and angle are as the radius u of the energy accumulation spike position of the subpulse of SMSP interference after Radon conversion₀With Radon The angle [alpha] of the energy accumulation spike position of subpulse of SMSP interference after conversion₀；

The estimated value of step 3, the carrier frequency of SMSP interference of calculating Radon-WVD conversion and chirp rate：

${\hat{f}}_{0,Radon-WVD}=|u_0/{\mathrm{sin\α}}_0|/b$

${\hat{k}}_{Radon-WVD}^{\′}=\left|{\mathrm{cot\α}}_0\right|/b$

Wherein,It is distributed carrier frequency estimated value for WDL,It is distributed chirp rate estimated value for WDL.