CN103197284A - 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 auto-correlation, quadrature and the doppler tolerance constraint

Technical field

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

Background technology

In the electromagnetic wave communication process, the time dependent mode of spatial orientation of electric field intensity is called polarization on a certain point of fixity in space.Target is equivalent to a polarization device, and its polarization information can characterize the full detail of its scattering properties, so the utilization of polarization information can improve target detection, tracking and the recognition performance of radar.Adopting Polarization technique to also help ground/extra large clutter suppresses.The prerequisite of polarization information utilization is that radar possesses the polarization measurement ability.Instantaneous complete polarization measurement requires horizontal polarization and vertical polarization transmitted waveform to have good auto-correlation and simple crosscorrelation (quadrature) performance.Autocorrelation performance is undesirable will to cause distance side lobe height after the pulse compression, be unfavorable for detecting little target; The undesirable receiving cable isolation that will cause of quadrature performance reduces, and produces to intersect and disturbs.

The form of orthogonal waveforms has a lot, comprises frequency orthogonal, phase encoding quadrature etc.The PARSAX radar of Holland Delft Polytechnics development adopts the Continuous Wave with frequency modulation system of bistatic, has instantaneous complete polarization measurement capability.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 accurate quadrature, go tiltedly to handle to have produced the cross aisle interference, be presented as the linear FM signal item.The time wide bandwidth long-pending more big, cross aisle disturbs more serious.The Hai Deng of University of New Orleans in 2004 as cost function, adopts simulated annealing that the frequency coding sequence is optimized combination with signal autocorrelation side-lobe energy and simple crosscorrelation energy.The people such as Wang Dunyong of radar institute of air force cost function to waveform on the basis of Hai Deng work improves, and has added auto-correlation side lobe peak and cross-correlation peak value, and genetic algorithm is carried out the wave sequence optimizing as optimizing algorithm.

But face Doppler's tender subject when adopting the phase modulation waveform, for high-speed target, the Doppler shift that echo exists sharply reduces the signal to noise ratio (S/N ratio) of pulse pressure output.Therefore when the design object function, also be necessary to increase doppler tolerance constraint condition.

Desirable transmitted waveform is that separately matched filtering output will have enough low secondary lobe (autocorrelation performance), also want pairwise orthogonal to measure requirement (their cross correlation) to be fit to instantaneous complete polarization between the waveform, each waveform should have enough big doppler tolerance (matched filter as pulse compression can not be too responsive to frequency displacement) as far as possible simultaneously, but does not also have a kind of waveform design method to consider autocorrelation, cross correlation and the constraint of doppler tolerance three aspects simultaneously before.

Summary of the invention

The invention provides a kind of waveform design method of taking all factors into consideration autocorrelation, cross correlation and the doppler tolerance performance of waveform, this method by regulating above-mentioned 3 elements in the cost function weight and use the Greedy random search to optimize algorithm, design the various phase modulation waveforms that satisfy the demands.

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

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

The 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* simple crosscorrelation cost+λ _Dt* doppler tolerance cost (10)

λ wherein _AcThe weighting coefficient of expression auto-correlation constraint, λ _CcThe weighting coefficient of expression interrelational constraint, λ _DtBe the weighting coefficient of doppler tolerance constraint, the doppler tolerance cost is expressed as E _Dt:

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

2) measure requirement according to the radar complete polarization, in cost function, set the weighting coefficient of auto-correlation, quadrature and three performance correspondences of doppler tolerance;

3) be cost function with formula (10), utilize the optimization algorithm in the encoding phase span, phasing matrix to be optimized, obtain the phasing matrix value of minimum cost functional value correspondence at last, and then be met the optimum waveform that the radar complete polarization is measured requirement.

Beneficial effect of the present invention:

1. designed the cost function of the stable performance of taking all factors into consideration waveform autocorrelation, cross correlation and the requirement of doppler tolerance three aspects

These 3 performances retrain by each self-corresponding weighting coefficient in the cost function in the Waveform Design.The relative value that changes each weighting coefficient in the cost function can be adjusted the performance of waveform, and weighting coefficient is more big, shows more to stress corresponding performance.

2. utilize the Greedy random search to optimize algorithm, can design the quadrature phase modulation wave sequence that the radar complete polarization is measured demand that satisfies of any phase and random length expeditiously: after phasing matrix is carried out initialization, exchange phase place disturbance in effective value space of each subcode of facies-suite, calculate the change amount Δ E of disturbance front and back cost function.Only when Δ E＜0, accept disturbance.Through iteration repeatedly, when no longer accepting any phase change, system obtained to satisfy the Waveform Design that the radar complete polarization is measured demand.

Description of drawings

Fig. 1 is the Waveform Design process flow diagram with the 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 done to describe in further detail.

The invention provides a kind of radar waveform method for designing, flow process as shown in Figure 1, basic ideas are to design the cost function of the stable performance of taking all factors into consideration waveform autocorrelation, cross correlation and the requirement of doppler tolerance three aspects, these 3 performances retrain by each self-corresponding weighting coefficient in the cost function, and the performance of waveform can be controlled by the relative value that changes each weighting coefficient in the cost function; Utilize the Greedy random search to optimize the quadrature phase modulation wave sequence that the radar complete polarization is measured demand that satisfies that algorithm design goes out any phase and random length then.Specific as follows:

At first, determine cost function.

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

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

The 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

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

The autocorrelation function of orthogonal signal and cross correlation function should satisfy 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

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

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

Associating code character signal matrix can get

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

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

Utilize conventional method, auto-correlation cost and simple crosscorrelation cost can be expressed as

With $\underset{p=1}{\overset{L-1}{\mathrm{\&Sigma;}}}\underset{q=p+1}{\overset{L}{\mathrm{\&Sigma;}}}\underset{k=-(N-1)}{\overset{N-1}{\mathrm{\&Sigma;}}}{\left|C({\mathrm{\&phi;}}_p,{\mathrm{\&phi;}}_q,k)\right|}^2;$

Frequency separation when doppler tolerance is defined as ambiguity function peak value decline 3dB or 6dB, the mode by the Greedy random search obtains.The doppler tolerance of note signal is f _Dt, express doppler tolerance key element in the cost function with following formula:

λ wherein _DtBe the weighting coefficient of doppler tolerance constraint, B is signal bandwidth, and target setting speed is high-speed target more than or equal to 200m/s's, and target velocity is slower-velocity target less than 200m/s's.Survey for high-speed target, cost was more little when doppler tolerance was more big.For slower-velocity target, owing to do not need to pursue big doppler tolerance, and the more for a short time velocity resolution that means of doppler tolerance is more high, is conducive to distinguish low-speed motion target and clutter, therefore makes doppler tolerance that more hour cost is more little.

Take all factors into consideration the requirement of autocorrelation, cross correlation, doppler tolerance three aspects, cost function is designed to

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

λ wherein _AcThe weighting coefficient of expression auto-correlation constraint, λ _CcThe weighting coefficient of expression interrelational constraint, λ _DtThe weighting coefficient of expression doppler tolerance.Change each weighting coefficient relative value and can adjust the performance of waveform.Weighting coefficient is more big, shows more to stress corresponding performance.

Secondly, adopt the Greedy algorithm that phase sequence is optimized, algorithm flow as shown in Figure 1.

As previously mentioned, establish total L burst in the orthogonal signal code character, each sequence code length N, the encoding phase number is M, 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) measures requirement according to the radar complete polarization, in cost function, set the weighting coefficient of auto-correlation, quadrature and three performance correspondences of doppler tolerance, and in the encoding phase span, the block signal matrix is carried out random initializtion;

2) at the phase of the 1st subcode of the 1st burst ₁(1), replace with the residue encoding phase value except the initialization phase value in the encoding phase span successively, and the cost function value after the each replacement of calculating, with the φ of minimum cost functional value correspondence ₁(1) phase value as a result of is fixed up;

3) to the operation of step 2 again of the individual sub-code weights of all the other N-1 of the 1st burst;

4) all the other L-1 bursts repeat and the 1st sequence identical operations, obtain the phasing matrix value of minimum cost functional value correspondence in the whole burst, namely satisfy the radar complete polarization and measure the optimum waveform that requires.

This optimization method is specially: after phasing matrix is carried out initialization, to the disturbance in effective value space of the phase place of each subcode of each burst, calculate the change amount Δ E of disturbance front and back cost function, only when Δ E＜0, accept disturbance, up to the phase place of each subcode of each burst no longer disturbance namely be met the radar complete polarization and measure the optimum waveform that requires.

Greedy algorithm operation efficiency is very high.Owing to only accept the phase perturbation that cost function reduces, therefore might be absorbed in local minimum, but can be met the waveform of requirement by emulation repeatedly.

Specify the improvement of optimizing back waveform performance below in conjunction with simulation example:

Adopt the Greedy algorithm that the Frank code phase sequences is optimized.Use 4 the 4 Frank sign indicating numbers of 16 subcodes mutually in the emulation, bandwidth B=1MHz, sample frequency f _s=20MHz, doppler tolerance are defined as the frequency separation of ambiguity function peak value decline 3dB.The performance of each sequence of Frank sign indicating number sees Table 1 before optimizing.Weighting coefficient λ for the doppler tolerance factor in the cost function _AcBe respectively 1 and 10 situation, the waveform performance after the optimization sees 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 sign indicating number of table 1

Optimize back auto-correlation PSL(dB)	-17.0927	-17.0927	-21.0721	-17.0927	----	----
							Optimize back cross-correlation peak value (dB)	-23.5218	-23.5218	-18.0618	-22.9226	-19.0849	-19.0849
Optimize back doppler tolerance (kHz)	283.69	267.71	267.71	268.38	----	----

Waveform performance (the λ of the Frank sign indicating number after table 2 is optimized _Ac=1 λ _Cc=1 λ _Dt=1)

Optimize back auto-correlation PSL(dB)	-12.9430	-12.9430	-10.1030	-14.0824	----	----
							Optimize back cross-correlation peak value (dB)	-20.8279	-21.8469	-18.0618	-21.1394	-18.1291	-19.0849
Optimize back doppler tolerance (kHz)	297.79	297.79	290.34	278.73	----	----

Waveform performance (the λ of the Frank sign indicating number after table 3 is optimized _Ac=1 λ _Cc=1 λ _Dt=10)

By the waveform performance before and after the contrast optimization, can find that the weight that increases the doppler tolerance factor can improve the doppler tolerance of optimizing waveform.

To sum up, waveform design method provided by the invention adopts Greedy random search algorithm to carry out the waveform optimization design, weighting by element in the cost function, can take into account autocorrelation, cross correlation and the doppler tolerance performance of waveform, and the weight that can regulate the three arbitrarily, thereby can satisfy the demand (quadrature performance) of channel separation, can take into account the demand that weak target is measured (the low side lobe performance of autocorrelation function) and high-speed target measurement (doppler tolerance performance) again.

In sum, more than be preferred embodiment of the present invention only, be not for limiting protection scope of the present invention.Within the spirit and principles in the present invention all, any modification of doing, be equal to replacement, improvement etc., all should be included within protection scope of the present invention.

Claims (2)

1. the radar waveform method for designing under an auto-correlation, quadrature and doppler tolerance retrain is characterized in that,

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

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

The 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

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

Cost function is:

E=λ _Ac* auto-correlation cost+λ _Cc* simple crosscorrelation cost+λ _Dt* doppler tolerance cost (10)

λ wherein _AcThe weighting coefficient of expression auto-correlation constraint, λ _CcThe weighting coefficient of expression interrelational constraint, λ _DtBe the weighting coefficient of doppler tolerance constraint, the doppler tolerance cost is expressed as E _Dt:

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

2) measure requirement according to the radar complete polarization, in cost function, set the weighting coefficient of auto-correlation, quadrature and three performance correspondences of doppler tolerance;

3) be cost function with formula (10), utilize the optimization algorithm in the encoding phase span, phasing matrix to be optimized, obtain the phasing matrix value of minimum cost functional value correspondence at last, and then be met the optimum waveform that the radar complete polarization is measured requirement.

2. the radar waveform method for designing under a kind of auto-correlation as claimed in claim 1, quadrature and the doppler tolerance constraint is characterized in that, adopts Greedy to optimize algorithm and is optimized, and is specially:

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

Two, at the phase place of the 1st subcode of the 1st burst _φ1 (1), replace with the residue encoding phase value except the initialization phase value in the encoding phase span successively, and the cost function value after the each replacement of calculating, with the φ of minimum cost functional value correspondence ₁(1) phase value as a result of is fixed up;

Three, to the operation of step 2 again of the individual sub-code weights of all the other N-1 of the 1st burst;

Four, all the other L-1 bursts repeat and the 1st sequence identical operations, obtain the phasing matrix value of whole burst minimum cost functional value correspondence, namely satisfy the radar complete polarization and measure the optimum waveform that requires.

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