CN103197284B - Radar wave form design method restrained by autocorrelation, orthogonality and Doppler tolerance - Google Patents

Abstract

The invention discloses a radar waveform design method restrained by autocorrelation, orthogonality and Doppler tolerance. Firstly, a cost function with stable properties and with overall consideration of the autocorrelation, the cross correlation and the Doppler tolerance of wave forms is designed. Secondly, by using a Greedy random search optimization algorithm, repeated iterations are carried out until a system no longer receives any phase change, and the wave form design meeting the requirements of the full polarization measurement of radar is obtained.

Description

Radar waveform method for designing under the constraint of auto-correlation, orthogonal and doppler tolerance

Technical field

The present invention relates to radar waveform design field, particularly relate to the radar waveform method for designing under a kind of auto-correlation, the constraint of orthogonal and doppler tolerance.

Background technology

In Electromagnetic Wave Propagation process, on a certain point of fixity in space, the time dependent mode of spatial orientation of electric field intensity is called polarization.Target is equivalent to a Polarization changer, and its polarization information can characterize the full detail of its scattering properties, and therefore the utilization of polarization information can improve the target detection of radar, tracking and recognition performance.Polarization technique is adopted to also help ground/ocean clutter cancellation.The prerequisite that polarization information utilizes is that radar possesses polarization measurement ability.Instantaneous Polarimetry requires that horizontal polarization and vertical polarization transmitted waveform have good auto-correlation and cross-correlation (orthogonal) performance.Autocorrelation performance is undesirable will cause pulse compression after distance side lobe high, be unfavorable for detect Small object; The undesirable receiving cable isolation that will cause of orthogonal performance reduces, and produces cross jamming.

The form of orthogonal waveforms has a lot, comprises frequency orthogonal, phase encoding orthogonal etc.The PARSAX radar of Delft Polytechnics of Holland development adopts the Continuous Wave with frequency modulation system of bistatic, has instantaneous Polarimetry ability.Horizontal polarization (H) transmission channel adopts the LFM waveform of positive frequency modulation slope, and vertical polarization (V) transmission channel adopts the LFM waveform of negative frequency modulation slope.Because positive frequency modulation slope LFM signal and negative frequency modulation slope LFM signal are just accurate orthogonal, go tiltedly process to create cross aisle interference, be presented as linear FM signal item.Timed automata is larger, and cross aisle interference is more serious.The Hai Deng of University of New Orleans in 2004, using signal autocorrelation side-lobe energy and cross-correlation energy as cost function, adopts simulated annealing to be optimized combination to frequency coding sequence.The people such as the Wang Dunyong of Airforce Radar institute improve the cost function of waveform on the basis that Hai Deng works, and add autocorrelation sidelobe peak value and cross-correlation peak value, and genetic algorithm is carried out wave sequence optimizing as optimizing algorithm.

But adopt during phase modulation waveform and face Doppler sensitivity problem, for high-speed target, the signal to noise ratio (S/N ratio) that the Doppler shift that echo exists makes pulse pressure export sharply reduces.Therefore there is a need to when design object function increase doppler tolerance constraint condition.

Desirable transmitted waveform is that respective matched filtering output will have enough low secondary lobe (autocorrelation performance), pairwise orthogonal is also wanted to require (their cross correlation) to be applicable to instantaneous Polarimetry between waveform, simultaneously each waveform should have enough large doppler tolerance (matched filter as pulse compression can not be too responsive to frequency displacement) as far as possible, but does not also have a kind of waveform design method to consider the three aspect constraint of autocorrelation, cross correlation and doppler tolerance before simultaneously.

Summary of the invention

The invention provides a kind of waveform design method of the autocorrelation, cross correlation and the doppler tolerance performance that consider waveform, the method is by the weight of 3 elements above-mentioned in Readjusting cost function and use Greedy Stochastic search optimization algorithm, designs the various phase modulation waveforms satisfied the demands.

The waveform design method taking into account waveform autocorrelation, cross correlation and doppler tolerance performance of the present invention comprises: 1) first design a kind of cost function, if total L burst in orthogonal signal code character, each burst code length N, encoding phase value number is M, each chip in each burst is subcode, then l burst shows by formula (1);

{s _l(n)=exp[jφ _l(n)]，n=1，2，---，N}，l=1，2，---，L (1)

Encoding phase span is

${\mathrm{\φ}}_l\left(n\right)\∈\{0,\frac{2\mathrm{\π}}{M},2\·\frac{2\mathrm{\π}}{M},---,(M-1)\·\frac{2\mathrm{\π}}{M}\}---\left(2\right)$

The phasing matrix of whole orthogonal signal code character can be expressed as

$S(L,N,M)=\left[\begin{array}{c}{\mathrm{\φ}}_1\left(1\right),{\mathrm{\φ}}_1\left(2\right),{\mathrm{\φ}}_1\left(3\right),---,{\mathrm{\φ}}_1\left(N\right)\\ {\mathrm{\φ}}_2\left(1\right),{\mathrm{\φ}}_2\left(2\right),{\mathrm{\φ}}_2\left(3\right),---{\mathrm{\φ}}_2\left(N\right)\\ {\mathrm{\φ}}_3\left(1\right),{\mathrm{\φ}}_3\left(2\right),{\mathrm{\φ}}_3\left(3\right),---,{\mathrm{\φ}}_3\left(N\right)\\ -\\ -\\ -\\ {\mathrm{\φ}}_L\left(1\right),{\mathrm{\φ}}_L\left(2\right),{\mathrm{\φ}}_L\left(3\right),---,{\mathrm{\φ}}_L\left(N\right)\end{array}\right]---\left(3\right)$

Cost function is:

E=λ _ac× auto-correlation cost+λ _cc× cross-correlation cost+λ _dt× doppler tolerance cost (10)

Wherein λ _acrepresent the weighting coefficient of auto-correlation constraint, λ _ccrepresent the weighting coefficient of interrelational constraint, λ _dtbe the weighting coefficient of doppler tolerance constraint, doppler tolerance cost is expressed as E _dt:

Wherein B is signal bandwidth, f _dtfor the doppler tolerance of signal, what target setting speed was more than or equal to 200m/s is high-speed target, and what target velocity was less than 200m/s is slower-velocity target;

2) according to the requirement of radar Polarimetry, in cost function, auto-correlation, the weighting coefficient that orthogonal and doppler tolerance three performances are corresponding is set;

3) with the formula (10) are cost function, optimized algorithm is utilized to be optimized phasing matrix in encoding phase span, finally obtain the phasing matrix value that least cost function value is corresponding, and then be met the optimum waveform of radar Polarimetry requirement.

Beneficial effect of the present invention:

1. have devised and consider waveform autocorrelation, cross correlation and doppler tolerance three cost function of stable performance of requiring of aspect

In Waveform Design, this 3 individual character retrains by self-corresponding weighting coefficient each in cost function.The relative value changing each weighting coefficient in cost function can adjust the performance of waveform, and weighting coefficient is larger, shows more to stress corresponding performance.

2. utilize Greedy Stochastic search optimization algorithm, the orthogonal phase modulation wave sequence meeting radar Polarimetry demand of phase and random length arbitrarily can be designed expeditiously: after initialization is carried out to phasing matrix, exchange phase place disturbance in effective valued space of each subcode of facies-suite, the knots modification Δ E of cost function before and after calculation perturbation.Only accept disturbance as Δ E < 0.Through successive ignition, until obtain the Waveform Design meeting radar Polarimetry demand when system no longer accepts any phase change.

Accompanying drawing explanation

Fig. 1 is the Waveform Design process flow diagram with Greedy algorithm;

Embodiment

In order to understand technical scheme of the present invention better, below in conjunction with drawings and the specific embodiments, the present invention is described in further detail.

The invention provides a kind of radar waveform method for designing, flow process as shown in Figure 1, basic ideas design to consider waveform autocorrelation, cross correlation and doppler tolerance three cost function of stable performance of requiring of aspect, this 3 individual character retrains by self-corresponding weighting coefficient each in cost function, and the performance of waveform controls by the relative value changing each weighting coefficient in cost function; Then Greedy Stochastic search optimization algorithm design is utilized to go out the orthogonal phase modulation wave sequence meeting radar Polarimetry demand of phase and random length arbitrarily.Specific as follows:

First, cost function is determined.

If total L burst in orthogonal signal code character, each sequence code length N, encoding phase value number is M, and each chip in each burst is subcode.Then l burst shows by formula (1);

{s _l(n)=exp[jφ _l(n)]，n=1，2，---，N}，=1，2，---，L (1)

Encoding phase span is

${\mathrm{\&phi;}}_l\left(n\right)\&Element;\{0,\frac{2\mathrm{\&pi;}}{M},2\&CenterDot;\frac{2\mathrm{\&pi;}}{M},---,(M-1)\&CenterDot;\frac{2\mathrm{\&pi;}}{M}\}---\left(2\right)$

The phasing matrix of whole orthogonal signal code character can be expressed as

$S(L,N,M)=\left[\begin{array}{c}{\mathrm{\&phi;}}_1\left(1\right),{\mathrm{\&phi;}}_1\left(2\right),{\mathrm{\&phi;}}_1\left(3\right),---,{\mathrm{\&phi;}}_1\left(N\right)\\ {\mathrm{\&phi;}}_2\left(1\right),{\mathrm{\&phi;}}_2\left(2\right),{\mathrm{\&phi;}}_2\left(3\right),---{\mathrm{\&phi;}}_2\left(N\right)\\ {\mathrm{\&phi;}}_3\left(1\right),{\mathrm{\&phi;}}_3\left(2\right),{\mathrm{\&phi;}}_3\left(3\right),---,{\mathrm{\&phi;}}_3\left(N\right)\\ -\\ -\\ -\\ {\mathrm{\&phi;}}_L\left(1\right),{\mathrm{\&phi;}}_L\left(2\right),{\mathrm{\&phi;}}_L\left(3\right),---,{\mathrm{\&phi;}}_L\left(N\right)\end{array}\right]---\left(3\right)$

The autocorrelation function of orthogonal signal and cross correlation function should meet following two conditions:

$A(s_l,k)=\left\{\begin{array}{cc}\frac{1}{N}\underset{n=1}{\overset{N-k}{\mathrm{\&Sigma;}}}{s}_l\left(n\right)s_l^{*}(n+k)=0,& 0<k<N\\ \frac{1}{N}\underset{n=-k+1}{\overset{N}{\mathrm{\&Sigma;}}}{s}_l\left(n\right)s_l^{*}(n+k)=0,& -N<k<0\end{array}\right.l=\mathrm{1,2},---,L---\left(4\right)$

With

$C(s_p,s_q,k)=\left\{\begin{array}{cc}\frac{1}{N}\underset{n=1}{\overset{N-k}{\mathrm{\&Sigma;}}}{s}_p\left(n\right)s_q^{*}(n+k)=0,& 0\&le;k<N\\ \frac{1}{N}\underset{n=-k+1}{\overset{N}{\mathrm{\&Sigma;}}}{s}_p\left(n\right)s_q^{*}(n+k)=0,& -N<k<0\end{array}\right.pp\&NotEqual;q;p,q=\mathrm{1,2},---,L---\left(5\right)$

Wherein A (s _l, k) represent in l burst be spaced apart k subcode autocorrelation function, C (s _p, s _q, k) represent p burst and q burst be spaced apart k subcode cross correlation function;

Associating code character signal matrix can obtain

$A({\mathrm{\&phi;}}_l,k)=\left\{\begin{array}{cc}\frac{1}{N}\underset{n=1}{\overset{N-k}{\mathrm{\&Sigma;}}}\mathrm{expj}[{\mathrm{\&phi;}}_l\left(n\right)-{\mathrm{\&phi;}}_l(n+k)]=0,& 0<k<N\\ \frac{1}{N}\underset{n=-k+1}{\overset{N}{\mathrm{\&Sigma;}}}\mathrm{expj}[{\mathrm{\&phi;}}_l\left(n\right)-{\mathrm{\&phi;}}_l(n+k)]=0,& -N<k<0\end{array}\right.l=\mathrm{1,2},---L---\left(6\right)$

$C({\mathrm{\&phi;}}_p,{\mathrm{\&phi;}}_q,k)=\left\{\begin{array}{cc}\frac{1}{N}\underset{n=1}{\overset{N-k}{\mathrm{\&Sigma;}}}\mathrm{expj}[{\mathrm{\&phi;}}_q\left(n\right)-{\mathrm{\&phi;}}_p(n+k)]=0,& 0\&le;k<N\\ \frac{1}{N}\underset{n=-k+1}{\overset{N}{\mathrm{\&Sigma;}}}\mathrm{expj}[{\mathrm{\&phi;}}_q\left(n\right)-{\mathrm{\&phi;}}_p(n+k)]=0,& -N<k<0\end{array}\right.pp\&NotEqual;q,p,q=\mathrm{1,2},---L---\left(7\right)$

Utilize conventional method, auto-correlation cost and cross-correlation cost can be expressed as with $\underset{p=1}{\overset{L-1}{\mathrm{\&Sigma;}}}\underset{q=p+1}{\overset{L}{\mathrm{\&Sigma;}}}\underset{k=-(N-1)}{\overset{N-1}{\mathrm{\&Sigma;}}}{\left|C({\mathrm{\&phi;}}_p,{\mathrm{\&phi;}}_q,k)\right|}^2;$

Doppler tolerance is defined as frequency separation during ambiguity function peak value decline 3dB or 6dB, is obtained by the mode of Greedy random search.The doppler tolerance of note signal is f _dt, the doppler tolerance key element in cost function is expressed with following formula:

Wherein λ _dtbe the weighting coefficient of doppler tolerance constraint, B is signal bandwidth, and what target setting speed was more than or equal to 200m/s is high-speed target, and what target velocity was less than 200m/s is slower-velocity target.For high-speed target detection, when doppler tolerance is larger, cost is less.For slower-velocity target, owing to not needing to pursue large doppler tolerance, and doppler tolerance is less means that velocity resolution is higher, and be conducive to distinguishing low-speed motion target and clutter, more hour cost is less therefore to make doppler tolerance.

Consider the requirement of autocorrelation, cross correlation, doppler tolerance three aspect, cost function is designed to

$E={\mathrm{\&lambda;}}_{\mathrm{ac}}\underset{l=1}{\overset{L}{\mathrm{\&Sigma;}}}\underset{k=1}{\overset{N-1}{\mathrm{\&Sigma;}}}{\left|A({\mathrm{\&phi;}}_l,k)\right|}^2+{\mathrm{\&lambda;}}_{\mathrm{cc}}\underset{p=1}{\overset{L-1}{\mathrm{\&Sigma;}}}\underset{q=p+1}{\overset{L}{\mathrm{\&Sigma;}}}\underset{k=-(N-1)}{\overset{N-1}{\mathrm{\&Sigma;}}}{\left|C({\mathrm{\&phi;}}_p,{\mathrm{\&phi;}}_q,k)\right|}^2+{\mathrm{\&lambda;}}_{\mathrm{dt}}\&CenterDot;E_{\mathrm{dt}}---\left(10\right)$

Wherein λ _acrepresent the weighting coefficient of auto-correlation constraint, λ _ccrepresent the weighting coefficient of interrelational constraint, λ _dtrepresent the weighting coefficient of doppler tolerance.Change the performance that each weighting coefficient relative value can adjust waveform.Weighting coefficient is larger, shows more to stress corresponding performance.

Secondly, adopt Greedy algorithm to be optimized phase sequence, algorithm flow as shown in Figure 1.

As previously mentioned, if total L burst in orthogonal signal code character, each sequence code length N, encoding phase number is M, and whole block signal matrix can be expressed as:

$S(L,N,M)=\left[\begin{array}{c}{\mathrm{\&phi;}}_1\left(1\right),{\mathrm{\&phi;}}_1\left(2\right),{\mathrm{\&phi;}}_1\left(3\right),---,{\mathrm{\&phi;}}_1\left(N\right)\\ {\mathrm{\&phi;}}_2\left(1\right),{\mathrm{\&phi;}}_2\left(2\right),{\mathrm{\&phi;}}_2\left(3\right),---{\mathrm{\&phi;}}_2\left(N\right)\\ {\mathrm{\&phi;}}_3\left(1\right),{\mathrm{\&phi;}}_3\left(2\right),{\mathrm{\&phi;}}_3\left(3\right),---,{\mathrm{\&phi;}}_3\left(N\right)\\ -\\ -\\ -\\ {\mathrm{\&phi;}}_L\left(1\right),{\mathrm{\&phi;}}_L\left(2\right),{\mathrm{\&phi;}}_L\left(3\right),---,{\mathrm{\&phi;}}_L\left(N\right)\end{array}\right]$

1) according to the requirement of radar Polarimetry, in cost function, set auto-correlation, the weighting coefficient that orthogonal and doppler tolerance three performances are corresponding, and in encoding phase span, random initializtion is carried out to block signal matrix;

2) for the phase of the 1st subcode of the 1st burst ₁(1), replace by the residue encoding phase value except intialization phase value in encoding phase span successively, and calculate the cost function value after each replacement, by φ corresponding for least cost function value ₁(1) phase value is fixed up as a result;

3) all the other N-1 subcodes of the 1st burst are repeated to the operation of step 2;

4) all the other L-1 bursts repeat and the 1st operation that sequence is identical, obtain the phasing matrix value that least cost function value in whole burst is corresponding, namely meet the optimum waveform of radar Polarimetry requirement.

This optimization method is specially: after carrying out initialization to phasing matrix, to phase place disturbance in effective valued space of each subcode of each burst, the knots modification Δ E of cost function before and after calculation perturbation, only accept disturbance as Δ E < 0, until the phase place of each subcode of each burst no longer disturbance be namely met the optimum waveform that radar Polarimetry requires.

Greedy algorithm operation efficiency is very high.Owing to only accepting the phase perturbation that cost function reduces, be therefore likely absorbed in local minimum, but the waveform of requirement can be met by Multi simulation running.

The improvement optimizing rear waveform performance is illustrated below in conjunction with simulation example:

Greedy algorithm is adopted to be optimized Frank code phase sequences.The Frank code of 44 phase 16 subcodes is used, bandwidth B=1MHz, sample frequency f in emulation _s=20MHz, doppler tolerance is defined as the frequency separation of ambiguity function peak value decline 3dB.Before optimizing, the performance of each sequence of Frank code is in table 1.For the weighting coefficient λ of the doppler tolerance factor in cost function _acbe respectively the situation of 1 and 10, the waveform performance after optimization is in table 2,3;

Original auto-correlation PSL(dB)	-17.0927	-17.0927	-21.0721	-17.0927	----	----
							Original cross-correlation peak value (dB)	-23.5218	23.5218	-18.0618	-22.9226	-19.0849	-19.0849
Original doppler tolerance (kHz)	268.38	267.71	267.71	268.38	----	----

The waveform performance of the original Frank code of table 1

Auto-correlation PSL(dB after optimizing)	-17.0927	-17.0927	-21.0721	-17.0927	----	----
							Cross-correlation peak value (dB) after optimizing	-23.5218	-23.5218	-18.0618	-22.9226	-19.0849	-19.0849
Doppler tolerance (kHz) after optimizing	283.69	267.71	267.71	268.38	----	----

Waveform performance (the λ of the Frank code after table 2 optimization _ac=1 λ _cc=1 λ _dt=1)

Auto-correlation PSL(dB after optimizing)	-12.9430	-12.9430	-10.1030	-14.0824	----	----
							Cross-correlation peak value (dB) after optimizing	-20.8279	-21.8469	-18.0618	-21.1394	-18.1291	-19.0849
Doppler tolerance (kHz) after optimizing	297.79	297.79	290.34	278.73	----	----

Waveform performance (the λ of the Frank code after table 3 optimization _ac=1 λ _cc=1 λ _dt=10)

Waveform performance before and after being optimized by contrast, can find that the weight increasing the doppler tolerance factor can improve the doppler tolerance optimizing waveform.

To sum up, waveform design method provided by the invention adopts Greedy random search algorithm to carry out waveform optimization design, by the weighting of element in cost function, the autocorrelation of waveform, cross correlation and doppler tolerance performance can be taken into account, and the weight of three can be regulated arbitrarily, thus the demand (orthogonal performance) of channel separation can be met, the demand that weak target measures (the low sidelobe performance of autocorrelation function) and high-speed target measurement (doppler tolerance performance) can be taken into account again.

In sum, these are only preferred embodiment of the present invention, be not intended to limit protection scope of the present invention.Within the spirit and principles in the present invention all, any amendment done, equivalent replacement, improvement etc., all should be included within protection scope of the present invention.

Claims (2)

1. the radar waveform method for designing under auto-correlation, the constraint of orthogonal and doppler tolerance, is characterized in that,

1) a kind of cost function is first designed, if total L burst in orthogonal signal code character, each burst code length N, encoding phase value number is M, each chip in each burst is subcode, then l burst shows by formula (1);

{s _i(n)=exp[jφ _i(n)]，n=1，2，---，N)，l=1，2，---，L (1)

Encoding phase span is

${\mathrm{\&phi;}}_l\left(n\right)\{0,\frac{2\mathrm{\&pi;}}{M},2\&CenterDot;\frac{2\mathrm{\&pi;}}{M},---,(M-1)\&CenterDot;\frac{2\mathrm{\&pi;}}{M}\}---\left(2\right)$

The phasing matrix of whole orthogonal signal code character can be expressed as

$S(L,N,M)=\left[\begin{array}{c}{\mathrm{\&phi;}}_1\left(1\right),{\mathrm{\&phi;}}_2\left(2\right),{\mathrm{\&phi;}}_1\left(3\right),---{,\mathrm{\&phi;}}_1\left(N\right)\\ {\mathrm{\&phi;}}_2\left(1\right),{\mathrm{\&phi;}}_2\left(2\right),{\mathrm{\&phi;}}_2\left(3\right),---,{\mathrm{\&phi;}}_2\left(N\right)\\ {\mathrm{\&phi;}}_3\left(1\right),{\mathrm{\&phi;}}_3\left(2\right),{\mathrm{\&phi;}}_3\left(3\right),---,{\mathrm{\&phi;}}_3\left(N\right)\\ -\\ -\\ -\\ {\mathrm{\&phi;}}_L\left(1\right),{\mathrm{\&phi;}}_L\left(2\right),{\mathrm{\&phi;}}_L\left(3\right),---,{\mathrm{\&phi;}}_L\left(N\right)\end{array}\right]---\left(3\right)$

The autocorrelation function of orthogonal signal and cross correlation function should meet following two conditions:

$A(s_l,k)=\left\{\begin{array}{c}\frac{1}{N}\underset{n=1}{\overset{N-k}{\mathrm{\&Sigma;}}}{s}_l\left(n\right)s_l^{*}(n+k)=\mathrm{0,0}<k<N\\ \frac{1}{N}\underset{n=-k+1}{\overset{N}{\mathrm{\&Sigma;}}}{s}_l\left(n\right)s_l^{*}(n+k)=0,-N<k<0\end{array}\right.l=\mathrm{1,2},---,L---\left(4\right)$

With

$C(s_p,s_q,k)=\left\{\begin{array}{c}\frac{1}{N}\underset{n=1}{\overset{N-k}{\mathrm{\&Sigma;}}}{s}_l\left(n\right)s_l^{*}(n+k)=\mathrm{0,0}<k<N\\ \frac{1}{N}\underset{n=-k+1}{\overset{N}{\mathrm{\&Sigma;}}}{s}_l\left(n\right)s_l^{*}(n+k)=0,-N<k<0\end{array}\right.pp\&NotEqual;q;p,q=\mathrm{1,2},---,L---\left(5\right)$

Wherein A (s _l, k) represent in l burst be spaced apart k subcode autocorrelation function, C (s _p, s _q, k) represent p burst and q burst be spaced apart k subcode cross correlation function;

Cost function is:

E=λ _ac× auto-correlation cost+λ _cc× cross-correlation cost+λ _dt× doppler tolerance cost (6)

Wherein λ _acrepresent the weighting coefficient of auto-correlation constraint, λ _ccrepresent the weighting coefficient of interrelational constraint, λ _dtbe the weighting coefficient of doppler tolerance constraint, doppler tolerance cost is expressed as E _dt:

(7)

Wherein B is signal bandwidth, f _dtfor the doppler tolerance of signal, what target setting speed was more than or equal to 200m/s is high-speed target, and what target velocity was less than 200m/s is slower-velocity target;

2) according to the requirement of radar Polarimetry, in cost function, auto-correlation, the weighting coefficient that orthogonal and doppler tolerance three performances are corresponding is set;

3) with the formula (6) are cost function, optimized algorithm is utilized to be optimized phasing matrix in encoding phase span, finally obtain the phasing matrix value that least cost function value is corresponding, and then be met the optimum waveform of radar Polarimetry requirement.

2. the radar waveform method for designing that a kind of auto-correlation as claimed in claim 1, the constraint of orthogonal and doppler tolerance are lower, it is characterized in that, employing Greedy optimized algorithm is optimized, and is specially:

One, in encoding phase span, initialization is carried out to each matrix element in phasing matrix;

Two, for the phase of the 1st subcode of the 1st burst ₁(1), replace by the residue encoding phase value except intialization phase value in encoding phase span successively, and calculate the cost function value after each replacement, by φ corresponding for least cost function value ₁(1) phase value is fixed up as a result;

Three, all the other N-1 subcodes of the 1st burst are repeated to the operation of step 2;

Four, all the other L-1 bursts repeat and the 1st operation that sequence is identical, obtain the phasing matrix value that whole burst least cost function value is corresponding, namely meet the optimum waveform of radar Polarimetry requirement.