CN104716927A - Interference canceling method based on improved all-pass fractional delay filter - Google Patents

Abstract

The invention belongs to the technical field of digital filter design and in particular relates to an interference canceling method based on an improved all-pass fractional delay filter. The interference canceling method comprises the specific steps of utilizing a minimum mean square error criterion to construct a mathematic model of the all-pass fractional delay filter, utilizing a particle swarm optimization method based on natural selection to solve the mathematic model of the all-pass fractional delay filter and further construct the all-pass fractional delay filter, obtaining reference signals, utilizing the constructed all-pass fractional delay filter to filter the reference signals and carrying out interference canceling process on the filtered signals and signals received by a radar. The interference canceling method uses a natural-selection particle swarm algorithm, guarantees the solving convergence of the filter, quickens the convergence speed, avoids complex numeric calculation, guarantees the solving numerical stability of the all-pass fractional delay filter and enables design of the variable fractional delay filter to be more flexible.

Description

Based on the interference cancellation method of the wildcard-filter style mark filtering wave by prolonging time device improved

Technical field

The invention belongs to digital filter design technical field, particularly based on the interference cancellation method of the wildcard-filter style mark filtering wave by prolonging time device improved.

Background technology

Fractional sampling time delays is widely used in every field, comprising: the adjustment of digital receiver time delay, the beam steering of array radar, speech coding and comprehensive, musical instrument calibration, sample rate conversion, time delay are estimated, comb filter design and A/D convert etc.The most frequently used is at present the method for designing of wildcard-filter style mark filtering wave by prolonging time device, for the design of wildcard-filter style mark filtering wave by prolonging time device, filter coefficient is carried out fitting of a polynomial, is the optimal design that criterion carries out mark filtering wave by prolonging time device with all square (the WLS:Weighted Least Square) error of weight minimization.Generally there are two kinds of methods to realize solving of best initial weights, are respectively iterative method and non-iterative method.

The Optimization Solution that alternative manner carries out mark filtering wave by prolonging time device is difficult to ensure convergence, and alternative manner all cannot be restrained under its some given design examples.Non-iterative method solves convergence problem, but it is approximate to there is blocking of numerical integration and infinite series in solution procedure.No matter whether iteration, the conventional numeric Optimization Solution of mark filtering wave by prolonging time device all applies in matrix inversion and numerical integration, and matrix inversion operation complexity filter order comparatively Gao Shihui become very high, therefore numerical integration can only could obtain good propinquity effect when filter order is lower.

Summary of the invention

The object of the invention is to the interference cancellation method proposing to propose the wildcard-filter style mark filtering wave by prolonging time device based on improvement for above-mentioned defect, the particle cluster algorithm given based on natural selection carries out design and the method for solving of wildcard-filter style mark filtering wave by prolonging time device, ensure that the convergence that the mark filtering wave by prolonging time device of wildcard-filter style solves and numerical stability.

For realizing above-mentioned technical purpose, the present invention adopts following technical scheme to be achieved.

Interference cancellation method based on the wildcard-filter style mark filtering wave by prolonging time device improved comprises the following steps:

Step 1, adopts the Mathematical Modeling of minimum mean square error criterion structure wildcard-filter style mark filtering wave by prolonging time device;

Step 2, adopts the particle group optimizing method based on natural selection to solve the Mathematical Modeling of described wildcard-filter style mark filtering wave by prolonging time device, and then constructs wildcard-filter style mark filtering wave by prolonging time device;

Step 3, obtain reference signal, the wildcard-filter style mark filtering wave by prolonging time device utilizing step 2 to construct carries out filtering process to reference signal, and the signal after filtering process and the signal utilizing radar to receive are carried out interference cancellation process.

Beneficial effect of the present invention is: the particle cluster algorithm that 1) have employed natural selection, ensure that the convergence that filter solves; 2) have employed the mechanism of natural selection, when ensureing convergence, accelerating convergence rate; 3) adopt particle cluster algorithm to carry out solving of filter and do not need complicated numerical operation, ensure that the numerical stability that wildcard-filter style mark filtering wave by prolonging time device solves.4) adopt minimum weight mean-square error criteria to design variable mark filtering wave by prolonging time device, make the design of variable mark filtering wave by prolonging time device have more flexibility.

Accompanying drawing explanation

Fig. 1 is design and the solution procedure schematic diagram of the wildcard-filter style mark filtering wave by prolonging time device based on improving of the present invention;

Fig. 2 a is the group delay response schematic diagram of 8 rank wildcard-filter style mark filtering wave by prolonging time devices in emulation experiment; Fig. 2 b is the group delay response schematic diagram of 10 rank wildcard-filter style mark filtering wave by prolonging time devices in emulation experiment;

Fig. 3 a is the group delay response of 8 rank wildcard-filter style mark filtering wave by prolonging time devices and the group delay response error curve synoptic diagram of idealized score filtering wave by prolonging time device in emulation experiment; Fig. 3 b is the group delay response of 10 rank wildcard-filter style mark filtering wave by prolonging time devices and the group delay response error curve synoptic diagram of idealized score filtering wave by prolonging time device in emulation experiment;

Fig. 4 a is the phase-frequency response curve synoptic diagram of 8 rank wildcard-filter style mark filtering wave by prolonging time devices in emulation experiment; Fig. 4 b is the phase-frequency response curve synoptic diagram of 10 rank wildcard-filter style mark filtering wave by prolonging time devices in emulation experiment;

Fig. 5 a is the poles and zeros assignment schematic diagram of 8 rank wildcard-filter style mark filtering wave by prolonging time devices in emulation experiment; Fig. 5 b is the poles and zeros assignment schematic diagram of 10 rank wildcard-filter style mark filtering wave by prolonging time devices in emulation experiment;

Fig. 6 a is the filtering actual result of single point-frequency signal and the contrast schematic diagram of ideal filtering result of 8 rank wildcard-filter style mark filtering wave by prolonging time devices in emulation experiment; Fig. 6 b is the filtering actual result of single point-frequency signal and the contrast schematic diagram of ideal filtering result of 10 rank wildcard-filter style mark filtering wave by prolonging time devices in emulation experiment;

Fig. 7 a is the filtering error curve synoptic diagram of single point-frequency signal of 8 rank wildcard-filter style mark filtering wave by prolonging time devices in emulation experiment; Fig. 7 b is the filtering error curve synoptic diagram of single point-frequency signal of 10 rank wildcard-filter style mark filtering wave by prolonging time devices in emulation experiment;

Fig. 8 a is the filtering actual result of linear FM signal and the contrast schematic diagram of ideal filtering result of 8 rank wildcard-filter style mark filtering wave by prolonging time devices in emulation experiment; Fig. 8 b is the filtering actual result of linear FM signal and the contrast schematic diagram of ideal filtering result of 10 rank wildcard-filter style mark filtering wave by prolonging time devices in emulation experiment;

Fig. 9 a is the pulse pressure post filtering error curve schematic diagram of the linear FM signal of 8 rank wildcard-filter style mark filtering wave by prolonging time devices in emulation experiment; Fig. 9 b is the pulse pressure post filtering error curve schematic diagram of the linear FM signal of 10 rank wildcard-filter style mark filtering wave by prolonging time devices in emulation experiment.

Embodiment

Below in conjunction with accompanying drawing, the invention will be further described:

Present invention employs the particle cluster algorithm of natural selection, particle cluster algorithm is a kind of Iterative search algorithm using for reference flock of birds predation.It is different from traditional algorithm, and the optimized algorithm of most of allusion is gradient based on a single metric function (valuation functions) or comparatively high order statistics, to produce a deterministic experiment solution sequence; Particle cluster algorithm does not rely on gradient information, but searches for optimal solution by simulation birds predation process, and it utilizes oneself and the flying experience of companion, upgrades oneself speed and position, follows current optimal particle and search in solution space.Particle cluster algorithm tool has the following advantages: the popularity represented feasible solution; Collective search characteristic; Do not need supplementary; Inherent heuristic random searching characteristic; Particle cluster algorithm is not easy to be absorbed in local optimum in search procedure, even if under defined fitness function is discontinuous, irregular or noisy situation, also can find globally optimal solution with very large probability; Particle cluster algorithm based on natural selection adopts natural evolution mechanism to show complicated phenomenon, the solution of fast and reliable ground can solve very difficult problem; Particle cluster algorithm has intrinsic concurrency and the ability of parallel computation; Particle cluster algorithm has extensibility, is easy to the optimisation technique mixing with other.

With reference to Fig. 1, be design and the solution procedure schematic diagram of the wildcard-filter style mark filtering wave by prolonging time device based on improving of the present invention.In the embodiment of the present invention, the interference cancellation method based on the wildcard-filter style mark filtering wave by prolonging time device improved comprises the following steps:

Step 1, adopts minimum mean square error criterion structure wildcard-filter style mark filtering wave by prolonging time device

Its concrete sub-step is:

(1.1) according to the requirement to group delay precision, the filter order n of wildcard-filter style mark filtering wave by prolonging time device is determined,

Draw the z territory form of wildcard-filter style mark filtering wave by prolonging time device, the z territory form of wildcard-filter style mark filtering wave by prolonging time device is:

$\begin{array}{c}A\left(z\right)=\frac{a_n+a_{n-1}{z}^{-1}+...+a_1{z}^{-(n-1)}+z^{-n}}{1+a_1{z}^{-1}+...a_{n-1}{z}^{-(n-1)}+a_n{z}^{-n}}\\ =\frac{z^{-n}D\left(z^{-1}\right)}{D\left(z\right)}\end{array}---\left(1\right)$

Wherein, a ₁to a _nfor real number, a ₁to a _nrepresent n backward feedback factor of wildcard-filter style mark filtering wave by prolonging time device to be solved, in the z territory form of wildcard-filter style mark filtering wave by prolonging time device, and point submultinomial is the mirror image of denominator polynomials.

By $D\left(z^{-1}\right){|}_{z=e^{\mathrm{j\ω}}}=D\left(e^{-\mathrm{j\ω}}\right)=D^{*}\left(e^{\mathrm{j\ω}}\right)$ ,

$A\left(e^{\mathrm{j\ω}}\right)=\frac{e^{-\mathrm{jn\ω}}{D}^{*}\left(e^{\mathrm{j\ω}}\right)}{D\left(e^{\mathrm{j\ω}}\right)}.$

Wherein, ω represents frequency variable, and * represents and gets conjugation.Significantly, the amplitude-frequency response perseverance of wildcard-filter style mark filtering wave by prolonging time device is 1.

(1.2) the phase-frequency response Θ of n rank all-pass filter can be obtained by formula (1) _a(ω),

Θ _A(ω)＝arg{A(e ^jω)}＝-nω+2Θ _D(ω) (2)

Wherein, ω represents frequency variable, and e is natural Exponents, e ^{{ }}represent the computing asking natural Exponents power, arg{} is for getting phase operation, and the n in formula (2) is identical with the n implication in formula (1), all represents that the exponent number of filter is n, Θ _d(ω) can be expressed as,

$\begin{array}{c}{\mathrm{\Θ}}_D\left(\mathrm{\ω}\right)=\arg \left\{\frac{1}{D\left(e^{\mathrm{j\ω}}\right)}\right\}=\arctan \left\{\frac{\underset{k=0}{\overset{n}{\mathrm{\Σ}}}{a}_k\sin \left(\mathrm{k\ω}\right)}{\underset{k=0}{\overset{n}{\mathrm{\Σ}}}{a}_k\cos \left(\mathrm{k\ω}\right)}\right\}\\ =\arctan \left\{\frac{a^{T}s}{a^{T}c}\right\}\end{array}$

Wherein, k gets 0 to n, the transposition of subscript T representing matrix or vector, a=[a ₀, a ₁..., a _n] ^t, a ₀=1, s=[1, sin (ω) ..., sin (n ω)] ^t, c=[1, cos (ω) ..., cos (n ω)] ^t; Arctan{} is arctan function, a ^ts is real part, a ^tc is imaginary part.

(1.3) frequency response of desirable all-pass filter can be written as:

$A_{\mathrm{id}}\left(e^{\mathrm{j\ω}}\right)=e^{j{\mathrm{\Θ}}_{\mathrm{id}}\left(\mathrm{\ω}\right)}$

Wherein, Θ _id(ω) phase-frequency response of desirable all-pass filter is represented; That is, the amplitude of desirable all-pass filter is 1, and phase-frequency response is Θ _id(ω).

For n rank above-mentioned wildcard-filter style mark filtering wave by prolonging time device, its desirable phase-frequency response Θ _id(ω) be

Θ _id(ω)＝-(l+p)ω

Wherein, l is the integer samples time delays of above-mentioned wildcard-filter style mark filtering wave by prolonging time device, and p is the fractional sampling time delays of above-mentioned wildcard-filter style mark filtering wave by prolonging time device, and ω is frequency variable.

Therefore, the phase-frequency response error delta Θ (ω) of said n rank wildcard-filter style mark filtering wave by prolonging time device is:

$\mathrm{\Δ\Θ}\left(\mathrm{\ω}\right)={\mathrm{\Θ}}_{\mathrm{id}}\left(\mathrm{\ω}\right)-{\mathrm{\Θ}}_A\left(\mathrm{\ω}\right)=2\arctan \left\{\frac{a^T{s}_{\mathrm{\β}}}{a^T{c}_{\mathrm{\β}}}\right\}---\left(3\right)$

Wherein, s _βand c _βbe respectively:

s _β＝[sin{β(ω)},sin{β(ω)-ω},…,sin{β(ω)-nω}] ^T

c _β＝[cos{β(ω)},cos{β(ω)-ω},…,cos{β(ω)-nω}] ^T

Wherein, $\mathrm{\β}\left(\mathrm{\ω}\right)=\frac{1}{2}[{\mathrm{\Θ}}_{\mathrm{id}}\left(\mathrm{\ω}\right)+\mathrm{n\ω}].$

According to calculating, value usually less, so the phase-frequency response error delta Θ (ω) of said n rank wildcard-filter style mark filtering wave by prolonging time device is approximately

$\mathrm{\Δ\Θ}\left(\mathrm{\ω}\right)=2\frac{a^T{s}_{\mathrm{\β}}}{a^T{c}_{\mathrm{\β}}}.$

(1.4) adopt minimum mean square error criterion design all-pass filter, introduce its detailed process below.

Set up the Optimized model that formula (4) describes,

$\underset{a}{\min }\left\{J\right\}=\underset{a}{\min }\left\{{\∫}_0^{\mathrm{\α\π}}W\left(\mathrm{\ω}\right){\left|\mathrm{\Δ\Θ}\left(\mathrm{\ω}\right)\right|}^2\mathrm{d\ω}\right\}---\left(4\right)$

Wherein, represent with vectorial a for variable minimizes the operation of { }.

j represents target function, and in formula (4), the α in upper limit of integral is used for the frequency range of constrained optimization, represents that the frequency range of Optimal Filters Design is [0, α π], 0< α <1.W (ω) represents the weighting function of non-negative, and weight that some frequency retrains can be made comparatively large, thus obtains more accurate phase place and approach.In [0, α π] frequency range, the weight of constraint is comparatively large, so under normal circumstances, weighting function W (ω) is set to 1.Δ Θ (ω) is the phase-frequency response error of said n rank wildcard-filter style mark filtering wave by prolonging time device.

In the embodiment of the present invention, the target function J in discretization formula (4), obtains discretization target function J _c,

$J_c=\underset{\mathrm{\&Omega;}=0}{\overset{\mathrm{\&alpha;\&pi;}}{\mathrm{\&Sigma;}}}W\left(\mathrm{\&Omega;}\right){\left|\mathrm{\&Delta;\&Theta;}\left(\mathrm{\&Omega;}\right)\right|}^2---\left(5\right)$

Wherein, || represent and take absolute value, Ω represents the digital angular frequency of discretization.Now,

So far, the Mathematical Modeling of said n rank wildcard-filter style mark filtering wave by prolonging time device is: with the backward feedback factor a of all-pass filter ₁, a ₂..., a _nfor optimized variable, minimize target function J _c, namely set up following about discretization target function J _coptimized model

$\arg \underset{a}{\min }\left\{J_c\right\}=\underset{\mathrm{\&Omega;}=0}{\overset{\mathrm{\&alpha;\&pi;}}{\mathrm{\&Sigma;}}}\left\{W\left(\mathrm{\&Omega;}\right){\left|\mathrm{\&Delta;\&Theta;}\left(\mathrm{\&Omega;}\right)\right|}^2\right\}$

$\begin{array}{c}{J}_c=4\underset{\mathrm{\&Omega;}=0}{\overset{\mathrm{\&alpha;\&pi;}}{\mathrm{\&Sigma;}}}W\left(\mathrm{\&Omega;}\right){\left|\frac{a^T{s}_{\mathrm{\&beta;}}}{a^T{c}_{\mathrm{\&beta;}}}\right|}^2\\ =4\underset{\mathrm{\&Omega;}=0}{\overset{\mathrm{\&alpha;\&pi;}}{\mathrm{\&Sigma;}}}W\left(\mathrm{\&Omega;}\right)\frac{a^T\mathrm{Sa}}{a^T\mathrm{Ca}}\end{array}.---\left(6\right)$

Wherein, || represent and take absolute value, Ω represents the digital angular frequency of discretization, and Ω gets 0 to α π, and W (Ω) represents the weighting function of non-negative, and under normal circumstances, weighting function W (ω) is set to 1.a＝[a ₀,a ₁,…,a _n] ^T，a ₀＝1， $S=s_{\mathrm{\&beta;}}{s}_{\mathrm{\&beta;}}^T,C=c_{\mathrm{\&beta;}}{c}_{\mathrm{\&beta;}}^T,$ S _βand c _βbe respectively:

s _β＝[sin{β(Ω)},sin{β(Ω)-Ω},…,sin{β(Ω)-nΩ}] ^T

c _β＝[cos{β(Ω)},cos{β(Ω)-Ω},…,cos{β(Ω)-nΩ}] ^T

Wherein, Θ _id(Ω) the desirable phase-frequency response of said n rank wildcard-filter style mark filtering wave by prolonging time device is represented, Θ _id(Ω)=-(l+p) Ω, l is the integer samples time delays of above-mentioned wildcard-filter style mark filtering wave by prolonging time device, and p is the fractional sampling time delays of above-mentioned wildcard-filter style mark filtering wave by prolonging time device.

Step 2, adopts the particle group optimizing method based on natural selection to solve above-mentioned about discretization target function J _coptimized model, draw n the backward feedback factor of wildcard-filter style mark filtering wave by prolonging time device; N the backward feedback factor according to wildcard-filter style mark filtering wave by prolonging time device designs wildcard-filter style mark filtering wave by prolonging time device.

The concrete sub-step of step 2 is:

(2.1) initialized population is set.

Particularly, because the optimized variable in the present invention is without any constraint, therefore initialized population is set in the equally distributed random number of employing, the diversity of population can be strengthened.

Fitness value by calculating particle in the present invention carries out solving above-mentioned optimization problem, does not relate to complex calculations, therefore suitably increases initialized population number of particles m, can increase the diversity of population, accelerates the convergence of particle cluster algorithm.For initialized population number of particles m, its size determines the efficiency of particle evolution and the constringency performance of particle cluster algorithm.If it is smaller that m selects, then the individuality of high fitness is retained, and particle cluster algorithm is restrained soon but is easily absorbed in individual optimal solution; Otherwise, m select larger when, convergence rate can be made to reduce.Consider, in the embodiment of the present invention, m is set to 200.

(2.2) in population, random ergodic sampling is adopted to carry out particle selection.

Particularly, when the particle cluster algorithm of employing natural selection is optimized and solves, need to construct fitness function.In the present invention, based on the discretization target function J that formula (5) provides _c, adopt boundary structured approach structure fitness function, for minimization problem, the present invention constructs fitness function Fit (J _c) be

$\mathrm{Fit}\left(J_c\right)=\left\{\begin{array}{cc}{c}_{\max }-J_c,& J_c<c_{\max }\\ 0,& \mathrm{else}\end{array}\right.$

Wherein, c _maxto discretization target function J _cthe conservative estimation of the upper limit, this is through the estimated result that many experiments draws.

Particle cluster algorithm is in n-dimensional space search, finds optimal solution by iteration.Therefore, in embodiments of the present invention, the position vector of each particle and velocity in random initializtion population, the initial velocity vector representation of i-th particle of n-dimensional space is V ⁱ, the initial position of i-th particle of n-dimensional space is expressed as vectorial X ⁱ, V ⁱ=[v _{i, 1}v _{i, 2}... v _i,n], X ⁱ=[x _{i, 1}x _{i, 2}... x _i,n], i=1,2 ... m, v _i,jrepresent a jth element of the initial velocity vector of i-th particle of n-dimensional space, x _i,jrepresent a jth element of the initial velocity vector of i-th particle of n-dimensional space, j=1,2...n.

According to initial velocity and the initial position of i-th particle of n-dimensional space, solve the discretization target function J of each particle _cvalue; By the discretization target function J of each particle _cvalue substitute into fitness function Fit (J _c) computing formula in, draw the fitness value of each particle.

After the fitness value drawing each particle, the individual optimal solution of each particle of initialization, namely using the initial velocity of each particle and the initial position individual optimal solution as corresponding particle.

Find out the particle that fitness value is the highest, using the globally optimal solution of the individual optimal solution of particle the highest for the fitness value found out as population.

(2.3) upgrading velocity and the position vector of each particle of n-dimensional space, is x by a jth element representation of the position vector needing i-th particle of the n-dimensional space upgraded _i,jt a jth element representation of the velocity needing i-th particle of the n-dimensional space upgraded is v by () _i,j(t).Draw a jth element x of the position vector of i-th particle of the n-dimensional space after renewal _i,j(t+1) a jth element v of the velocity of i-th particle of the n-dimensional space and after upgrading _i,j(t+1),

v _i,j(t+1)＝wv _i,j(t)+c ₁r ₁[p _i,j-x _i,j(t)]+c ₂r ₂[p _g,j-x _i,j(t)]

x _i,j(t+1)＝x _i,j(t)+v _i,j(t+1),j＝1,2...n

Wherein, w represents the Inertia weight factor of setting, c ₁represent the first Studying factors of setting, c ₁for positive number, c ₂represent the second Studying factors of setting, c ₂for positive number.R ₁represent random number (choosing according to being uniformly distributed) between 0-1, r ₂represent random number (choosing according to being uniformly distributed) between 0-1, P _i,jrepresent a jth element of position vector in the individual optimal solution of i-th particle of n-dimensional space, P _g,jrepresent a jth element of position vector in the globally optimal solution of i-th particle of n-dimensional space.Inertia weight factor determines to inherit how many to current particulate, and suitable selection can make the existing spirit of exploration of particulate, can inherit fine tradition again; Studying factors makes particle have oneself to sum up and to the close ability of excellent individual, make the result of each particulate always be tending towards optimal solution, usual c ₁and c ₂all be taken as 2.

(2.4) according to the velocity of each particle of n-dimensional space after upgrading and position vector, the individual optimal solution of each particle of n-dimensional space and globally optimal solution are upgraded.

Particularly, using the velocity of each particle of n-dimensional space after upgrading and the position vector individual optimal solution as the corresponding particle of current time n-dimensional space; According to the individual optimal solution of each particle of current time n-dimensional space, solve the discretization target function J of each particle of current time _cvalue (according to particle position vector, using a jth element of up-to-date particle position vector jth+1 element as vectorial a, thus outgoing vector a; Then according to the vectorial a drawn, the value of discretization target function is drawn); By the discretization target function J of each for current time particle _cvalue substitute into fitness function Fit (J _c) computing formula in, draw the fitness value of each particle of current time; Find the highest particle of fitness value, using the globally optimal solution of the individual optimal solution of particle the highest for the fitness value found out as current time population.

Before the individual optimal solution of each particle of current time n-dimensional space and the corresponding particle of n-dimensional space experience (drawing) individual optimal solution in, select individual optimal solution that fitness value is the highest as the individual optimal solution of the corresponding particle of current time n-dimensional space.

In the individual optimal solution of each particle of current time n-dimensional space and each globally optimal solution of population of drawing by the end of current time, select optimal solution (individual optimal solution or globally optimal solution) that fitness value is the highest as the globally optimal solution of current time population.

(2.5) according to fitness value order from high to low, to current particle, group sorts; In whole population, half particle minimum for fitness value is replaced with the highest half particle of fitness value, and the highest half particle of fitness value retains, passable like this, keep globally optimal solution and individual optimal solution constant, form new population;

The strategy used in sub-step (2.5) ensures that the high-quality individuality obtained up to now is always retained, and this is an important guarantee condition of particle cluster algorithm convergence.

(2.6) judge whether the stopping criterion for iteration reaching setting, if do not reached, be then back to sub-step (2.3); If reached, then according to the up-to-date globally optimal solution drawn, draw up-to-date particle position vector, using a jth element of up-to-date particle position vector jth+1 element as vectorial a, thus obtain outgoing vector a; Then according to the vectorial a drawn, the value of discretization target function is drawn.

In the embodiment of the present invention, the stopping criterion for iteration of setting selects one of following three stopping criterion for iteration:

First stopping criterion for iteration, secondary iteration end condition and the 3rd stopping criterion for iteration.First stopping criterion for iteration is: the number of the value of the discretization target function that sub-step (2.6) solves reaches the termination thresholding ξ preset; Secondary iteration end condition is: the number of times that sub-step (2.3) is repeatedly executed to sub-step (2.6) reaches Np time, and wherein Np is the maximum execution number of times of renewal rewards theory preset; 3rd stopping criterion for iteration is: when sub-step (2.3) is performed continuously 50 times to sub-step (2.6), when the value of the discretization target function that sub-step (2.6) solves all does not change, and stops renewal rewards theory.

Step 3, obtain reference signal, the wildcard-filter style mark filtering wave by prolonging time device utilizing step 2 to design carries out filtering process to reference signal, and the signal after filtering process and the signal utilizing radar to receive are carried out interference cancellation process.In the embodiment of the present invention, reference signal normally the transmitting of radar.

To sum up, the present invention proposes a kind of design and method for solving of wildcard-filter style mark filtering wave by prolonging time device of improvement, be applicable to the technology of adaptive cancellation in Radar Signal Processing, realize the alignment of reference signal and interference signal time, thus reach the object that broadband offsets.If interference signal is broadband signal, carries out adaptive cancellation and can produce very large error.This is because interference signal is different by the time delay of two channels, and the phase modulation in broadband can not change the time delay of signal, and then causes reference signal not alignd with the interference substantially inputted, and offsets poor effect.Therefore before reference signal input adaptive filter, increase all-pass fractional filtering wave by prolonging time device is a very necessary step.

Effect of the present invention is further illustrated by following simulation comparison test:

1) experiment scene: the wildcard-filter style mark filtering wave by prolonging time device designing 8 rank and 10 rank according to the present invention respectively, and respectively the performance of designed Filter and Filltering device for filtering is analyzed.During performance of filter checking, reference signal adopts single point-frequency signal and linear FM signal respectively.For single point-frequency signal, adopt after filtering with idealized score time delay after signal carry out contrasting the performance verifying filter.For linear FM signal, verify the performance of filter with the effect of pulse pressure.The frequency of the single point-frequency signal adopted is f _c=100MHz, the bandwidth B=250MHz of linear FM signal, time wide T=1 μ s, the sample rate under two kinds of signal forms is all f _s=500MHz.

2. emulate content:

Design 8 rank and 10 rank wildcard-filter style mark filtering wave by prolonging time devices, the excursion of mark amount of delay is-0.5 to 0, and frequency band constraint factor α=0.8, the frequency separation namely optimized is [0,0.8 π].Adopt the filtering performance of the mark filtering wave by prolonging time device of single-point frequency signal authentication two kinds of exponent numbers.Linear FM signal is adopted to verify the filtering performance of the mark filtering wave by prolonging time device of two kinds of exponent numbers.

3. analysis of simulation result:

With reference to Fig. 2 a, being the group delay response schematic diagram of 8 rank wildcard-filter style mark filtering wave by prolonging time devices in emulation experiment, with reference to Fig. 2 b, is the group delay response schematic diagram of 10 rank wildcard-filter style mark filtering wave by prolonging time devices in emulation experiment; In Fig. 2 a and Fig. 2 b, transverse axis represents angular frequency, and the longitudinal axis represents that group delay responds, the sampling interval (radar return signal) that different curves is corresponding different.Find out from Fig. 2 a and Fig. 2 b, the group delay response of 10 rank filters is more smooth.With reference to Fig. 3 a, for the group delay response of 8 rank wildcard-filter style mark filtering wave by prolonging time devices in emulation experiment and the group delay response error curve synoptic diagram of idealized score filtering wave by prolonging time device, with reference to Fig. 3 b, be the group delay response of 10 rank wildcard-filter style mark filtering wave by prolonging time devices in emulation experiment and the group delay response error curve synoptic diagram of idealized score filtering wave by prolonging time device; In Fig. 3 a and Fig. 3 b, transverse axis represents angular frequency, and the longitudinal axis represents group delay response error, and unit is dB.As can be seen from the contrast of Fig. 3 a and Fig. 3 b, the group delay response error of 10 rank wildcard-filter style mark filtering wave by prolonging time devices is than low about the 10dB of 8 rank wildcard-filter style mark filtering wave by prolonging time device.In Fig. 3 a and Fig. 3 b, group delay error is lower at low frequency place, and along with the rising of frequency, error becomes large.

With reference to Fig. 4 a, it is the phase-frequency response curve synoptic diagram of 8 rank wildcard-filter style mark filtering wave by prolonging time devices in emulation experiment; With reference to Fig. 4 b, it is the phase-frequency response curve synoptic diagram of 10 rank wildcard-filter style mark filtering wave by prolonging time devices in emulation experiment; In Fig. 4 a and Fig. 4 b, transverse axis represents angular frequency, and the longitudinal axis represents phase-frequency response.With reference to Fig. 5 a, it is the poles and zeros assignment schematic diagram of 8 rank wildcard-filter style mark filtering wave by prolonging time devices in emulation experiment; With reference to Fig. 5 b, it is the poles and zeros assignment schematic diagram of 10 rank wildcard-filter style mark filtering wave by prolonging time devices in emulation experiment; In Fig. 5 a and Fig. 5 b, transverse axis represents real part, and the longitudinal axis represents imaginary part.Fig. 4 a, Fig. 4 b Fig. 5 a and Fig. 5 b are used for verifying the stability of filter designed in emulation experiment.Adopt two kinds of methods to judge the stability of wildcard-filter style mark filtering wave by prolonging time device respectively in emulation experiment, one, is judged by phase-frequency response; Its two, judged by poles and zeros assignment.If the phase-frequency response of mark filtering wave by prolonging time device meets following three conditions, then filter must be stablized: (1) 0 phase theta (0) frequently located is 0; (2) phase theta (π) at the most high frequency points π place of normalization numeral is-N π, when N gets 8, and θ (π)=-8 π=-25.133; (3) phase-frequency characteristic wants monotone decreasing.When adopting poles and zeros assignment to judge the stability of filter, only need to determine that the limit of filter is all positioned at unit circle.As can be seen from Fig. 4 a, Fig. 4 b Fig. 5 a and Fig. 5 b, the wildcard-filter style mark filtering wave by prolonging time device of design of Simulation of the present invention is all stable.

With reference to Fig. 6 a, be the filtering actual result of single point-frequency signal and the contrast schematic diagram of ideal filtering result of 8 rank wildcard-filter style mark filtering wave by prolonging time devices in emulation experiment; With reference to Fig. 6 b, be the filtering actual result of single point-frequency signal and the contrast schematic diagram of ideal filtering result of 10 rank wildcard-filter style mark filtering wave by prolonging time devices in emulation experiment; With reference to Fig. 7 a, it is the filtering error curve synoptic diagram of single point-frequency signal of 8 rank wildcard-filter style mark filtering wave by prolonging time devices in emulation experiment; With reference to Fig. 7 b, it is the filtering error curve synoptic diagram of single point-frequency signal of 10 rank wildcard-filter style mark filtering wave by prolonging time devices in emulation experiment; In Fig. 6 a, Fig. 6 b, Fig. 7 a and Fig. 7 b, transverse axis represents discrete time, and the longitudinal axis represents amplitude.The filtering error of a 10 rank wildcard-filter style mark filtering wave by prolonging time devices order of magnitude lower than 8 rank filters can be found out.

With reference to Fig. 8 a, be the filtering actual result of linear FM signal and the contrast schematic diagram of ideal filtering result of 8 rank wildcard-filter style mark filtering wave by prolonging time devices in emulation experiment; With reference to Fig. 8 b, be the filtering actual result of linear FM signal and the contrast schematic diagram of ideal filtering result of 10 rank wildcard-filter style mark filtering wave by prolonging time devices in emulation experiment; With reference to Fig. 9 a, it is the pulse pressure post filtering error curve schematic diagram of the linear FM signal of 8 rank wildcard-filter style mark filtering wave by prolonging time devices in emulation experiment; With reference to Fig. 9 b, it is the pulse pressure post filtering error curve schematic diagram of the linear FM signal of 10 rank wildcard-filter style mark filtering wave by prolonging time devices in emulation experiment.In Fig. 8 a, Fig. 8 b, Fig. 9 a and Fig. 9 b, transverse axis represents discrete time, and the longitudinal axis represents amplitude.Can find out, adopt 10 rank wildcard-filter style mark filtering wave by prolonging time devices to carry out filtering, pulse pressure performance obviously promotes, and error ratio adopts during 8 rank filter and reduces about 1 order of magnitude.

Obviously, those skilled in the art can carry out various change and modification to the present invention and not depart from the spirit and scope of the present invention.Like this, if these amendments of the present invention and modification belong within the scope of the claims in the present invention and equivalent technologies thereof, then the present invention is also intended to comprise these change and modification.

Claims (7)

1., based on the interference cancellation method of the wildcard-filter style mark filtering wave by prolonging time device improved, it is characterized in that, comprise the following steps:

Step 1, adopts the Mathematical Modeling of minimum mean square error criterion structure wildcard-filter style mark filtering wave by prolonging time device;

Step 2, adopts the particle group optimizing method based on natural selection to solve the Mathematical Modeling of described wildcard-filter style mark filtering wave by prolonging time device, and then constructs wildcard-filter style mark filtering wave by prolonging time device;

Step 3, obtain reference signal, the wildcard-filter style mark filtering wave by prolonging time device utilizing step 2 to construct carries out filtering process to reference signal, and the signal after filtering process and the signal utilizing radar to receive are carried out interference cancellation process.

2., as claimed in claim 1 based on the interference cancellation method of the wildcard-filter style mark filtering wave by prolonging time device improved, it is characterized in that, the concrete sub-step of described step 1 is:

(1.1) determine the filter order n of wildcard-filter style mark filtering wave by prolonging time device, draw the z territory form of wildcard-filter style mark filtering wave by prolonging time device, the z territory form of wildcard-filter style mark filtering wave by prolonging time device is:

$\begin{array}{c}A\left(z\right)=\frac{a_n+a_{n-1}{z}^{-1}+...+a_1{z}^{-(n-1)}+z^{-n}}{1+a_1{z}^{-1}+...a_{n-1}{z}^{-(n-1)}+a_n{z}^{-n}}\\ =\frac{z^{-n}D\left(z^{-1}\right)}{D\left(z\right)}\end{array}$

Wherein, a ₁to a _nfor real number, a ₁to a _nrepresent n backward feedback factor of wildcard-filter style mark filtering wave by prolonging time device to be solved;

(1.2) Mathematical Modeling of following wildcard-filter style mark filtering wave by prolonging time device is set up:

$\arg \underset{a}{\min }\left\{J_c\right\}=\underset{\mathrm{\&Omega;}=0}{\overset{\mathrm{\&alpha;\&pi;}}{\mathrm{\&Sigma;}}}\left\{W\left(\mathrm{\&Omega;}\right){\left|\mathrm{\&Delta;\&Theta;}\left(\mathrm{\&Omega;}\right)\right|}^2\right\}$

$\begin{array}{c}{J}_c=4\underset{\mathrm{\&Omega;}=0}{\overset{\mathrm{\&alpha;\&pi;}}{\mathrm{\&Sigma;}}}W\left(\mathrm{\&Omega;}\right){\left|\frac{a^T{s}_{\mathrm{\&beta;}}}{a^T{c}_{\mathrm{\&beta;}}}\right|}^2\\ =4\underset{\mathrm{\&Omega;}=0}{\overset{\mathrm{\&alpha;\&pi;}}{\mathrm{\&Sigma;}}}W\left(\mathrm{\&Omega;}\right)\frac{a^T\mathrm{Sa}}{a^T\mathrm{Ca}}\end{array}$

Wherein, J _crepresent discretization target function, || represent and take absolute value, Ω represents the digital angular frequency of discretization, and Ω gets 0 to α π, 0< α <1; W (Ω) represents the weighting function of non-negative, a=[a ₀, a ₁..., a _n] ^t, a ₀=1, the transposition of subscript T representing matrix or vector; s _βand c _βbe respectively:

s _β＝[sin{β(Ω)},sin{β(Ω)-Ω},...,sin{β(Ω)-nΩ}] ^T

c _β＝[cos{β(Ω)},cos{β(Ω)-Ω},...,cos{β(Ω)-nΩ}] ^T

Wherein, Θ _id(Ω) the desirable phase-frequency response of described n rank wildcard-filter style mark filtering wave by prolonging time device is represented.

3., as claimed in claim 2 based on the interference cancellation method of the wildcard-filter style mark filtering wave by prolonging time device improved, it is characterized in that, in step 1, described weighting function W (Ω) is set to 1.

4., as claimed in claim 2 based on the interference cancellation method of the wildcard-filter style mark filtering wave by prolonging time device improved, it is characterized in that, the concrete sub-step of described step 2 is:

(2.1) arrange initialized population, initialized population number of particles is expressed as m;

(2.2) fitness function Fit (J is constructed _c) be

Wherein, c _maxto discretization target function J _cthe conservative estimation of the upper limit;

The position vector of each particle and velocity in initialization population, the initial velocity vector representation of i-th particle of n-dimensional space is V ⁱ, the initial position of i-th particle of n-dimensional space is expressed as vectorial X ⁱ, V ⁱ=[v _{i, 1}v _{i, 2}... v _i,n], X ⁱ=[x _{i, 1}x _{i, 2}... x _i,n], i=1,2 ... m, v _i,jrepresent a jth element of the initial velocity vector of i-th particle of n-dimensional space, x _i,jrepresent a jth element of the initial velocity vector of i-th particle of n-dimensional space, j=1,2...n;

According to the initial position of i-th particle of n-dimensional space, solve the discretization target function J of each particle _cvalue; By the discretization target function J of each particle _cvalue substitute into fitness function Fit (J _c) computing formula in, draw the fitness value of each particle;

After the fitness value drawing each particle, using the initial velocity of each particle and the initial position individual optimal solution as corresponding particle; Find out the particle that fitness value is the highest, using the globally optimal solution of the individual optimal solution of particle the highest for the fitness value found out as population;

(2.3) upgrading velocity and the position vector of each particle of n-dimensional space, is x by a jth element representation of the position vector needing i-th particle of the n-dimensional space upgraded _i,jt a jth element representation of the velocity needing i-th particle of the n-dimensional space upgraded is v by () _i,j(t); Draw a jth element x of the position vector of i-th particle of the n-dimensional space after renewal _i,j(t+1) a jth element v of the velocity of i-th particle of the n-dimensional space and after upgrading _i,j(t+1);

(2.4) using the velocity of each particle of n-dimensional space after upgrading and the position vector individual optimal solution as the corresponding particle of current time n-dimensional space; According to the individual optimal solution of each particle of current time n-dimensional space, solve the discretization target function J of each particle of current time _cvalue; By the discretization target function J of each for current time particle _cvalue substitute into fitness function Fit (J _c) computing formula in, draw the fitness value of each particle of current time; Find the highest particle of fitness value, using the globally optimal solution of the individual optimal solution of particle the highest for the fitness value found out as current time population;

In the individual optimal solution experienced before the individual optimal solution of each particle of current time n-dimensional space and the corresponding particle of n-dimensional space, select individual optimal solution that fitness value is the highest as the individual optimal solution of the corresponding particle of current time n-dimensional space; In the individual optimal solution of each particle of current time n-dimensional space and each globally optimal solution of population of drawing by the end of current time, select optimal solution that fitness value is the highest as the globally optimal solution of current time population;

(2.5) according to fitness value order from high to low, to current particle, group sorts; In whole population, half particle minimum for fitness value is replaced with the highest half particle of fitness value, and the half particle reservation that fitness value is the highest;

(2.6) judge whether the stopping criterion for iteration reaching setting, if do not reached, be then back to sub-step (2.3); If reached, then according to the up-to-date globally optimal solution drawn, draw up-to-date particle position vector, using a jth element of up-to-date particle position vector jth+1 element as vectorial a, thus obtain outgoing vector a; Then according to the vectorial a drawn, draw the value of discretization target function and construct wildcard-filter style mark filtering wave by prolonging time device.

5., as claimed in claim 4 based on the interference cancellation method of the wildcard-filter style mark filtering wave by prolonging time device improved, it is characterized in that, in step 2, adopt equally distributed random number to arrange initialized population, initialized population number of particles m is set to 200.

6., as claimed in claim 4 based on the interference cancellation method of the wildcard-filter style mark filtering wave by prolonging time device improved, it is characterized in that, in step 2, a jth element x of the position vector of i-th particle of the n-dimensional space after renewal _i,j(t+1) a jth element v of the velocity of i-th particle of the n-dimensional space and after upgrading _i,j(t+1) be respectively:

v _i,j(t+1)＝wv _i,j(t)+c ₁r ₁[p _i,j-x _i,j(t)]+c ₂r ₂[p _g,j-x _i,j(t)]

x _i,j(t+1)＝x _i,j(t)+v _i,j(t+1),j＝1,2...n

Wherein, w represents the Inertia weight factor of setting, c ₁represent the first Studying factors of setting, c ₁for positive number, c ₂represent the second Studying factors of setting, c ₂for positive number; r ₁represent random number between 0-1, r ₂represent random number between 0-1, P _i,jrepresent a jth element of position vector in the individual optimal solution of i-th particle of n-dimensional space, P _g,jrepresent a jth element of position vector in the globally optimal solution of i-th particle of n-dimensional space.

7. as claimed in claim 4 based on the interference cancellation method of the wildcard-filter style mark filtering wave by prolonging time device improved, it is characterized in that, in step 2, the stopping criterion for iteration of setting selects the one: first stopping criterion for iteration of following three stopping criterion for iteration, secondary iteration end condition and the 3rd stopping criterion for iteration; Described first stopping criterion for iteration is: the number of the value of the discretization target function that sub-step (2.6) solves reaches the termination thresholding ξ preset; Described secondary iteration end condition is: the number of times that sub-step (2.3) is repeatedly executed to sub-step (2.6) reaches Np time, and wherein Np is the maximum execution number of times of renewal rewards theory preset; Described 3rd stopping criterion for iteration is: when sub-step (2.3) is performed continuously 50 times to sub-step (2.6), the value of the discretization target function that sub-step (2.6) solves all does not change.