CN106443589B - The method for parameter estimation of SMSP interference based on Radon-WDL transformation - Google Patents
The method for parameter estimation of SMSP interference based on Radon-WDL transformation Download PDFInfo
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- CN106443589B CN106443589B CN201610486369.7A CN201610486369A CN106443589B CN 106443589 B CN106443589 B CN 106443589B CN 201610486369 A CN201610486369 A CN 201610486369A CN 106443589 B CN106443589 B CN 106443589B
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
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Abstract
The technical problem to be solved by the invention is to provide a kind of method for parameter estimation of SMSP interference based on Radon-WDL transformation, and SMSP interference is carried out Radon-WDL transformation on the time-frequency domain of broad sense；Radon transformation is carried out in the WDL distribution interfered SMSP, by the time-frequency domain conversation of broad sense on containing the angled polar domain with radius, cross term can be curbed simultaneously, and spike number estimates the subpulse number for obtaining SMSP interference and angle and radius where maximum sharpness after converting according to Radon；Angle and radius after finally being converted according to Radon where maximum sharpness estimate the carrier frequency and chirp rate of SMSP interference.
Description
Technical field
The present invention relates to Anti-jamming Technology for Radar field, the in particular to parameter estimation techniques of frequency spectrum disperse SMSP interference.
Background technique
Frequency modulation(PFM) is carried out by radar signal of the digital radiofrequency memory DRFM to interception and obtains frequency spectrum disperse SMSP interference,
A string of dressing decoys can be generated in radar receiving end, effectively cheat radar.Also, when jamming power is larger, SMSP
Interfere the double action with deception and compacting.So realizing that the parameter Estimation of SMSP interference has inhibition in future SMSP interference
Important researching value and meaning.
Radon-WDL transformation is a kind of efficient algorithm for estimating SMSP interference parameter.2012, Rui-Feng Bai was proposed
Wigner-Ville Distribution Associated with the Linear Canonical Transform, i.e.,
WDL is distributed the algorithm for estimating to linear frequency-modulated parameter, sees " 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, which has 3 free parameters, has higher flexible
Property；It is oblique to the carrier frequency and frequency modulation of estimation linear FM signal under low signal-to-noise ratio as selection suitable parameter a, b, c, d
Rate has higher precision.However, WDL distribution will generate multiple cross terms, sternly when signal is containing multicomponent SMSP interference
Ghost image rings the parameter Estimation of signal.
Summary of the invention
The technical problem to be solved by the invention is to provide a kind of parameter Estimations of SMSP interference that can curb chiasma type
Method.
The present invention is to solve above-mentioned technical problem the technical scheme adopted is that the SMSP based on Radon-WDL transformation is dry
The method for parameter estimation disturbed, comprising the following steps:
Step 1 interferes SMSP progress WDL distribution transformation:
Wherein, JSMSP(t) SMSP interference when being moment t, τ is time delay, and * is conjugation, KA(ω, τ) is the kernel function of WDL,Exp expression is using natural logrithm e as the exponential function at bottom, a,
B, c, d are four parameters a, b, c, d of WDL transformation, and meet ad-bc=1, and ω is angular frequency, and the π of ω=2 f, f are frequency
Rate；
Step 2 carries out Radon transformation to the WDL distribution of SMSP interference:
Wherein, WDL is the WDL distribution of SMSP interference, and u ', v are the independent variable that Radon converts the domain (u, v), and (u, α) is
The radius and angle acquired after Radon transformation, RWDL (u, α) are integral knot of any rotation α under different radius u
Fruit, δ are impulse function；RWDL (u, α) is that the energy accumulation for the subpulse that SMSP is interfered after Radon is converted indicates；
Spike number in RWDL (u, α) is the subpulse number n of SMSP interference；It is corresponding when RWDL (u, α) is maximized
Radius and angle as Radon convert after SMSP interfere subpulse energy accumulation spike position radius u0With
The angle [alpha] of the energy accumulation spike position for the subpulse that SMSP is interfered after Radon transformation0；
The estimated value of carrier frequency and chirp rate that step 3, the SMSP for calculating Radon-WVD transformation are interfered:
Wherein,It is distributed carrier frequency estimated value for WDL,Chirp rate estimated value is distributed for WDL.
SMSP is interfered and is carried out Radon-WDL transformation on the time-frequency domain of broad sense by the present invention；At the WDL interfered SMSP points
Cloth carries out Radon transformation, by the time-frequency domain conversation of broad sense on containing the angled polar domain with radius, while can curb
Cross term, and where spike number estimates to obtain the subpulse number and maximum sharpness of SMSP interference after being converted according to Radon
Angle and radius；Angle and radius after finally being converted according to Radon where maximum sharpness estimate SMSP interference carrier frequency and
Chirp rate.
The invention has the advantages that WDL distribution is applied in the parameter Estimation of SMSP for the first time, Radon is become for the first time
It changes and is introduced into WDL distribution, to inhibit the chiasma type generated by WDL distribution.It is demonstrated experimentally that under low signal-to-noise ratio, relative to classics
Wigner-Ville distribution algorithm, WDL Distribution Algorithm has higher detection accuracy；Also, due to Radon transformation introducing,
It can be suppressed by the cross term that WDL distribution generates, so that the algorithm more effectively estimates the parameter of SMSP interference.
Detailed description of the invention
Fig. 1 is the algorithm steps of Radon-WDL transformation estimation LFM signal chirp rate k '；
Fig. 2 is the instantaneous autocorrelation analysis of SMSP interference；
Fig. 3 is the principle of Radon transformation；
Fig. 4 is the relationship of the MSE of chirp rate and the angle interval of b, Radon transformation；
Fig. 5 is the MSE of chirp rate and the relationship of b, SNR；
Fig. 6 is that Radon-WVD converts schematic diagram.
Specific embodiment
The parameter to be estimated of parameter Estimation of SMSP interference are as follows: subpulse number, the load of SMSP interference of SMSP interference
Frequency and chirp rate.
As shown in Figure 1, comprising the following steps:
Step 1: SMSP is interfered and carries out WDL distribution transformation:
Assuming that SMSP interference is made of n subpulse, then SMSP interference is represented by
Wherein, JSMSP(t) be moment t when SMSP interference, JSMSP,p(t) pth sub- of SMSP interference when p is moment t
Pulse, p=0,1 ..., n-1；
JSMSP,p(t) subpulse signal are as follows:
Wherein, AJThe amplitude for indicating interference, generally takes AJ=1；Exp is indicated using natural logrithm e as the exponential function at bottom, k '
The chirp rate for indicating SMSP interference, by the production principle of SMSP interference it is found that k '=nk, k are the frequency modulation of radar echo signal
Slope；f0For carrier frequency；The time width of TSMSP interference.
The WDL transformation of SMSP interference are as follows:
Wherein, ω is angular frequency, and τ is time delay, and * is conjugation, KA(ω, τ) is the kernel function of WDL,A, b, c, d are four parameters a, b, c, d of WDL transformation,
And meet ad-bc=1；
By JSMSP,p(t) WDL that subpulse signal expression substitutes into SMSP interference converts expression formula, then the WDL of SMSP interference
Transformation may be expressed as:
JSMSP,pFor p-th of subpulse of SMSP interference, p=0,1 ..., n-1, JSMSP,qQ is p-th of SMSP interference
Subpulse, q=0,1 ..., n-1；
As shown in Figure 2, to the subpulse J for having limit for length SMSPSMSP,p(t) and JSMSP, q(t) carrying out WDL transformation can obtain:
In formula
As a=0, abbreviation above formula can be obtained
In formula
It is rightTaking absolute value can obtain:
In formula
Due toBetween when being mutually independent of each other, formula (1-2) can be expressed as
Subpulse p=0,1 ..., n-1 and q=0,1 ..., the relationship of n-1 is as follows
As the p=q in formula (1-2),For from major event, have n 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 shares 2n-1 straight line in time frequency plane.
It is three-dimensionalDistribution be shaped like fin shape, straight line is distributed on time-frequency planeOn.
Step 2: Radon transformation is carried out to the WDL distribution of SMSP interference
Radon transformation is a kind of projective transformation of straight line integral.Such as Fig. 3, former rectangular co-ordinate (t, ω) rotation alpha is obtained newly
Coordinate (u, v), at this moment by different u values be parallel to v axis integral, acquired results be Radon transformation.
The Radon transformation of the WDL distribution of SMSP interference can be expressed as
WDL is the WDL distribution of SMSP interference in formula, and u ', v are the independent variable that Radon converts the domain (u, v), and (u, α) is
The radius and angle acquired after Radon transformation, u, α known variables.RWDL (u, α) is any rotation α along different u value products
Divide as a result, u can be obtained when RWDL (u, α) is maximized0,α0.RWDL transformation, due to working as δ (u-u '), i.e. when u=u ', RWDL
Just have value, then RWDL transformation u ∈ (- ∞ ,+∞) and α ∈ [0,2 π).
With parameter k ', f0Instead of integral parameter u, α, then RWDL (u, α) can be indicated again are as follows:
Wherein ω0=2 π f0, k ' is the chirp rate of SMSP interference, and b is the parametric variable of WDL, p=0,1 ..., n-1, q
=0,1 ..., n-1.
Step 3: the carrier frequency and chirp rate of the SMSP interference by Radon-WDL transformation are estimated as follows:
Wherein b is the parametric variable of WDL.
Step: 4: obtain carrier frequency and chirp rate estimation mean square error (MSE), estimation Radon-WVD transformation with
The estimated accuracy of Radon-WDL transformation.
The carrier frequency of SMSP interference by Radon-WVD transformation and the MSE of chirp rate estimation are as follows:
The carrier frequency of SMSP interference by Radon-WDL transformation and the MSE of chirp rate estimation are as follows:
WDL transformation, Radon transformation are existing algorithm, and Radon is converted combined with WDL transformation for the first time by the present invention, and
Applied in the parameter identification of SMSP interference；The WDL for having derived SMSP interference for the first time converts limited long form.
Emulation experiment
Time width T=10 μ s, bandwidth B=20MHz, the chirp rate k=B/T sample frequency f of LFMs=60MHz, carrier frequency f0=
300MHz, sampled point N=fix (fs× 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 as σ=1.Here only consider SMSP interference plus noise.
1, parameter a=0, b=0.5:0.01:1, c=-1/b, d=0, t=0: τ/[fs × τ]: τ, the f=0 of WDL transformation:
fs/[fs×τ]:fs.The relative mean square error of chirp rate: by MSEk′,Radon-WDLChemical conversion dB form is MSEk′,dB=10log10
(MSEk′,Radon-WDL/max(MSEk′,Radon-WDL)).Range is set as θ=15:ta:45 between the angle of Radon transformation, between angle
It is dry than being JNR=10dB every respectively ta=[0.01 0.05 0.1], Fig. 4 is obtained, analysis chart can obtain: between equal angular
Every, in b=0.6, the estimation MSE of k 'k′,dBAll there is minimum value, then chooses b=0.6；As b=0.6, it is divided between angle
When 0.05, the estimation MSE of k 'k′,dBMinimum then chooses ta=0.05.
2, parameter a=0, b=0.5:0.01:1, c=-1/b, d=0, t=0: τ/[fs × τ]: τ, the f=0 of WDL transformation:
fs/[fs×τ]:fs.The relative mean square error of chirp rate: by MSEk′,Radon-WDLChemical conversion dB form is MSEk′,dB=10log10
(MSEk′,Radon-WDL/max(MSEk′,Radon-WDL)).Range is set as θ=15:ta:45 between the angle of Radon transformation, between angle
It is dry to make an uproar than JNR=[noiseless -5dB 10dB], 100 Monte Carlo simulations every respectively ta=[0.01 0.05 0.1],
Fig. 5 is obtained, analysis chart can obtain: for identical JNR, in b=0.6, the estimation MSE of chirp rate kk′,dBAll there is minimum value, then
Choose b=0.6.
3, JNR=10dB is taken, angle change is θ=0:0.05:90, is divided into 0.05 between angle, parameter a=0, b=0.6, c
=-1/b, d=0；The comparison for carrying out Radon-WDL transformation is interfered SMSP, can be obtained 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 transformation and radius domain.
Claims (1)
1. the method for parameter estimation of the SMSP interference based on Radon-WDL transformation, which comprises the following steps:
Step 1 interferes SMSP progress WDL distribution transformation:
Wherein, JSMSP(t) SMSP interference when being moment t, τ is time delay, and * is conjugation, KA(ω, τ) is the kernel function of WDL,Exp expression is using natural logrithm e as the exponential function at bottom, a,
B, c, d are four parameters a, b, c, d of WDL transformation, and meet ad-bc=1, and ω is angular frequency, and the π of ω=2 f, f are frequency
Rate；
Step 2 carries out Radon transformation to the WDL distribution of SMSP interference:
Wherein, WDL is the WDL distribution of SMSP interference, and u ', v are the independent variable that Radon converts the domain (u, v), and (u, α) is Radon change
The radius and angle acquired after changing, δ are impulse function；RWDL (u, α) is the energy for the subpulse that SMSP is interfered after Radon is converted
Accumulation indicates, is integral result of any rotation α under different radius u；
Spike number in RWDL (u, α) is the subpulse number n of SMSP interference；RWDL (u, α) is corresponding half when being maximized
The radius u of the energy accumulation spike position for the subpulse that SMSP is interfered after diameter and angle are converted as Radon0With Radon
The angle [alpha] of the energy accumulation spike position for the subpulse that SMSP is interfered after transformation0；
The estimated value of carrier frequency and chirp rate that step 3, the SMSP for calculating Radon-WVD transformation are interfered:
Wherein,It is distributed carrier frequency estimated value for WDL,Chirp rate estimated value is distributed for WDL.
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