CN102841335B - Iterative FFT-based quick MIMO radar waveform synthesis method - Google Patents

Abstract

The invention discloses an iterative FFT (Fast Fourier Transform)-based quick MIMO (Multiple Input Multiple Output) radar waveform synthesis method, and aims to solve the problems that a current method, which can not quickly synthesize the waveform meeting empty domain and time domain property. The realization process comprises the following steps: setting an expected emission directional pattern of a radar according to the objective information of a radar return, and determining a discrete azimuth angle based on the inverse Fourier transform relation of the emission directional pattern with a waveform matrix; obtaining a constant modulus waveform matrix of the radar in a way that an iterative FFT manner is adopted to synthesize the directional patterns according to the expected emission directional pattern; utilizing the constant modulus waveform matrix to construct a phase shift constant modulus waveform matrix; and utilizing the iterative manner to optimize sub pulse initial phase of the phase shift constant modulus waveform matrix so as to improve the signal self-correlation property in the objective direction, and finally obtaining the synthetic waveform. According to the invention, the method realizes on-line waveform design and can be used for multi-objective tracking of the MIMO radar.

Description

The quick waveform synthetic method of MIMO radar based on iteration FFT

Technical field

The invention belongs to Radar Technology field, relate to the synthetic of radar waveform, can be used for the online Waveform Design of MIMO radar, with engineering demands.

Background technology

Multiple-input and multiple-output MIMO radar is a kind of emerging active detection technology, has now become a study hotspot in Radar Technology field.

Rabideau in 2003 and Parker use for reference MIMO technology and the sparse array synthetic impulse and aperture radar SIAR in the communications field, MIMO radar concept has been proposed, see [Rabideau D.J.and Parker P..Ubiquitous MIMO Multifunction Digital Array Radar[C] .Conference Record of the 37th Asilomar Conference on Signals, Systems and Computers, 2003, vol.1, pp.1057-1064].Afterwards, this concept has caused people's extensive concern in field of radar.At present, the spacing size according to antenna, can be divided into MIMO radar distributed MIMO radar and centralized MIMO radar two classes.For distributed MIMO radar, because each antenna has different observation visual angles and the independence of target echo to target, under statistical significance, thereby can overcoming the scintillation effect of target, this class MIMO radar improves the detection performance of radar to target.For centralized MIMO radar, be characterized in that array element distance is less, there is the ability that freely designs every slave antenna waveform, i.e. waveform diversity.Compare with phased-array radar, the degree of freedom of centralized MIMO radar has improved, thereby MIMO radar presents more superiority, as better parameter resolving ability, transmitting pattern designed capacity etc. more freely, see [Li J.and Stoica P..MIMO Radar With Colocated Antennas[J] .IEEE Signal Processing Magazine, Sep.2007, vol.24, pp.106-114].The waveform diversity ability of centralized MIMO radar, also makes the mode of operation of radar system more flexible.

At present, the waveform of MIMO radar is synthetic mainly launches research around three aspects such as orthogonal waveforms design, the design of transmitting pattern coupling and transmitted waveform are comprehensive.Wherein, orthogonal waveforms design is mainly for the detection of target; The design of transmitting pattern coupling and transmitted waveform, comprehensively mainly for the tracking of target, solve the distribution problem of radar system dimensional energy.

For the design of transmitting pattern coupling, the comparatively effective method of delivering on international publication is positive semidefinite law of planning (the Semi-defined programming that Stoica Petre and Li Jian propose, SDP), see [Stoica P., Li J., Xie Y..On probing signal design for MIMO radar.IEEE Trans.on Signal Processing.2007, Vol.55 (8) .4151-4161], the method under minimum mean square error criterion, obtains the signal covariance matrix of global optimum according to given transmitting pattern.But computation complexity is higher, especially, in the situation that array element is more, can not obtain fast signal covariance matrix.

Comprehensive for transmitted waveform, effective method is round-robin algorithm (Cyclic Algorithm at present, CA), see [Stoica P., Li J., Zhu X..Waveform Synthesis for Diversity-Based Transmit Beampattern Design.IEEE Trans.on Signal Processing.2008, Vol.56 (6) .2593-2598].This algorithm, in the situation that meeting signal and being permanent mould, stresses to consider the approximation problem of transmitting pattern, and there is no to consider the correlation properties of " space composite signal " or " echoed signal ".

In reality, for radar system, not only wish to transmit to there is constant modulus property, and should there is following characteristic:

1) spatial power that waveform should have an expectation that transmits distributes, and formed transmitting pattern will approach the transmitting pattern of expectation.

2) space composite signal or echoed signal have good pulse pressure characteristic, and the time domain autocorrelation peak sidelobe level of echoed signal is low.

3) different directions echoed signal should have good their cross correlation, and the time domain peak value simple crosscorrelation level of different directions echoed signal is low.

In practice, for moving-target, when their orientation, distance and radial velocity, be engraved in and change.Therefore, their electromagnetic energy is distributed and also will be adaptive to their variation, Waveform Design not only will be considered above characteristic, and should meet real-time.And above-mentioned existing waveform design method had not both been considered the correlation properties of space composite signal or echoed signal, can not reach again the engine request of online design waveform.

Summary of the invention

The object of the invention is to the deficiency for above-mentioned prior art, propose the quick waveform synthetic method of a kind of MIMO radar based on iteration FFT, to guarantee that waveform can approach in real time expectation spatial power and distribute, improve the time domain pulse pressure characteristic of echoed signal.

For achieving the above object, the quick waveform synthetic method of MIMO radar of the present invention, comprises the steps:

(1), according to the target information in radar return, set the expectation transmitting pattern D (θ of radar _n), θ _nrepresent discrete azimuth angle, be defined as follows:

N wherein _srepresent position angle sampling number, λ represents signal wavelength, and d represents the array element distance of radar, and arcsin () represents arcsin function;

(2) according to expectation transmitting pattern D (θ _n), it is comprehensive that employing iteration FFT mode is carried out transmitting pattern, obtains the permanent mould waveform matrix X of radar:

(2a) make iterations k=0, remember that the permanent mould waveform matrix X of the k time iteration is X ^(k); Produce the initial permanent mould waveform matrix X of L * M dimension ^(k), k=0, its concrete form is

l the sub-pulse signal that represents the k time iteration, wherein

the k time permanent mould waveform matrix X ^(k)the capable m column element of l, l=1 ..., L, m=1 ..., M, L represents waveform code length, M represents the element number of array of radar, () ^trepresent transposition, || represent plural mould value;

(2b) set iteration and stop threshold epsilon ₁=0.1; Permanent mould waveform matrix X to the k=0 time iteration ^(k)by row, be N _sthe inverse Fourier transform IFFT of point, obtains

the spatial domain signal Y at place ^(k); Calculate the permanent mould waveform matrix X of the k=0 time iteration ^(k)corresponding transmitting pattern P ^(k)(θ _n), n=0 ..., N _s-1, k=0;

(2c) calculation expectation spatial domain signal Z ^(k)=Y ^(k)Γ ^(k),

Γ wherein ^(k)be scale factor matrix, be expressed as:

${\mathrm{\Γ}}^{\left(k\right)}=\mathrm{diag}\left(\right[\sqrt{D\left({\mathrm{\θ}}_0\right)}/\sqrt{P^{\left(k\right)}\left({\mathrm{\θ}}_0\right)},\·\·\·,\sqrt{D\left({\mathrm{\θ}}_{N_s-1}\right)}/\sqrt{P^{\left(k\right)}\left({\mathrm{\θ}}_{N_s-1}\right)}\left]\right),$

In formula, diag () represents to form diagonal matrix operation according to vector;

(2d) calculate the permanent mould waveform matrix X of the k+1 time iteration ^(k+1)in element:

$x_{l,m}^{(k+1)}=\exp \left(j\arg \left({\left(Z^{\left(k\right)}{F}^H\right)}_{l,m}\right)\right),l=1,\·\·\·,L,m=1,\·\·\·,M,$

Wherein F represents N _sthe IFFT matrix of point, () ^hrepresent conjugate transpose,

represent permanent mould waveform matrix X ^(k+1)the element of the capable m of l row, (Z ^(k)f ^h) _{l, m}representing matrix Z ^(k)f ^hthe element of the capable m of l row, arg () represents to get phase place; Execution step (2e);

(2e) the permanent mould waveform matrix X to the k+1 time iteration ^(k+1)by row, be N _sthe inverse Fourier transform IFFT of point, obtains

the spatial domain signal Y of place ^(k+1); Calculate the permanent mould waveform matrix X of the k+1 time iteration ^(k+1)corresponding transmitting pattern P ^(k+1)(θ _n), n=0 ..., N _s-1; Judgement end condition

whether set up, if set up, permanent mould waveform matrix is X=X ^(k+1), execution step (3), otherwise, make k=k+1, repeating step (2c)-(2d);

(3) utilize permanent mould waveform matrix X, the permanent mould waveform of structure phase shift matrix S

Wherein, x _lthe capable transposition of l of permanent mould waveform matrix X,

the subpulse first phase that represents the permanent mould waveform of phase shift matrix S, represent the transposition mutually of the permanent mould waveform of phase shift matrix S, l=1 ..., L;

(4) the subpulse first phase to the permanent mould waveform of phase shift matrix S

be optimized:

(4a) make iterations t=0, remember that the permanent mould waveform of the phase shift matrix S of the t time iteration is S ^(t); Produce initial phase shift matrix wherein

the permanent mould waveform of the phase shift matrix S that represents the t time iteration ^(t)=Λ ^(t)the subpulse first phase of X, t=0, l=1 ..., L, sets iteration and stops threshold epsilon ₂=10 ^-3;

(4b) calculate the permanent mould waveform of the phase shift matrix S of the t time iteration ^(t)=Λ ^(t)x exists

the frequency spectrum f that 2L in direction is ordered _i, phase shift matrix wherein

be i target direction, i=1 ..., I, I represents total number of target; Calculate the expectation frequency spectrum of signal in direction:

$v_i=\frac{1}{\sqrt{2}}[e^{j{\mathrm{\ψ}}_{1,i}},\·\·\·,e^{j{\mathrm{\ψ}}_{2L,i}}{]}^T,i=1,\·\·\·,I,$

ψ wherein _pi=arg (f _pi) expression expectation frequency spectrum v _iphase place on p frequency, f _pifor frequency spectrum f _ip spectrum value, p=1 ..., 2L, i=1 ..., I;

(4c) right

the expectation frequency spectrum v of signal in direction _icarry out the inverse Fourier transform that 2L is ordered, obtain

wanted signal g in direction _i, i=1 ..., I; Calculate the subpulse first phase of the t+1 time iteration

Wherein () ^*represent conjugation, s _liand g _lirepresent respectively vectorial s _iand g _il element, s _irepresent that the designed permanent mould waveform matrix X of step (2) exists

spatial domain signal in direction, i=1 ..., I; Calculate the phase shift matrix of the t+1 time iteration

execution step (4d);

(4d) judgement end condition

whether set up, if set up, the permanent mould waveform of phase shift matrix is S=Λ ^(t+1)x, using the permanent mould waveform of phase shift matrix S as final synthetic waveform; Otherwise, make t=t+1, repeating step (4b)-(4c).

The present invention has the following advantages:

1) the present invention is based on each subpulse signal is carried out to the identical constant characteristic of phase shift directional diagram, the design of spatial domain beam pattern and time domain waveform is separated, effectively reduce the complexity of time domain spatial domain combined optimization;

2) main operation of the present invention is FFT and IFFT, has therefore greatly reduced the consuming time of algorithm, can meet engineering real-time demand;

3) the present invention carries out in the mode of iteration, and in target tracking stage, the waveform matrix of previous moment of usining upgrades as initial waveform matrix, the redesign to waveform matrix while having avoided wave beam to change.

Accompanying drawing explanation

Fig. 1 is main flow chart of the present invention;

Fig. 2 is the directional diagram in emulation Pattern Synthesis process of the present invention;

Fig. 3 is the directional diagram of the final waveform matrix of emulation of the present invention;

Fig. 4 is the autocorrelation sequence figure in simulation objectives direction of the present invention;

Fig. 5 is the simple crosscorrelation sequence chart in simulation objectives direction of the present invention;

Fig. 6 is the directional diagram in emulation Pattern Synthesis process of the present invention;

Fig. 7 is the autocorrelation sequence figure in simulation objectives direction of the present invention;

Fig. 8 is the simple crosscorrelation sequence chart in simulation objectives direction of the present invention.

Embodiment

With reference to Fig. 1, the specific implementation step of the present embodiment is as follows:

Step 1, sets desired orientation figure, determines Space domain sampling point.

Suppose that MIMO radar array is the even linear array consisting of M array element, define permanent mould waveform matrix and be

X＝[x ₁,x ₂,…x _L] ^T，

X wherein _l=[x _{l, 1}..., x _l,M] ^tbe the capable transposition of l of X, represent l sub-pulse signal, wherein | x _l,m|=1, x _l,mthe capable m column element of l of waveform X, l=1 ..., L, m=1 ..., M, () ^trepresent transposition, || represent plural mould value, L represents code length, and the transmitting pattern of permanent mould waveform matrix X can be expressed as

P(θ)＝a ^H(θ)X ^HXa(θ)/L， <1>

Wherein a (θ)=[1 ..., e ^{j2 π dsin θ/λ}] ^trepresent steering vector, θ represents position angle, and d represents array element distance, and λ represents signal wavelength, () ^hrepresent conjugate transpose;

According to the inverse Fourier transform relation existing between transmitting pattern in <1> formula and permanent mould waveform matrix, can determine discrete azimuth angle θ _nfor:

N wherein _srepresent position angle sampling number, arcsin () represents arcsin function;

Set the expectation transmitting pattern D (θ of radar _n):

First, according to target direction

determine that traditional phased-array radar points to time wave beam P _i(θ _n), θ _nrepresent discrete azimuth angle, n=0 ..., N _s-1, P _i(θ _n) main lobe region be Ω _i, i=1...I, I is target number;

Then, with wave beam P _i(θ _n) main lobe form the expectation transmitting pattern D (θ of radar _n):

θ wherein _nrepresent discrete azimuth angle, w _i>=0 represents weights.

Step 2, according to desired orientation figure, it is comprehensive that employing iteration FFT mode is carried out transmitting pattern.Definition spreading wave form matrix is

wherein

represent L * (N _s-M) the full null matrix of dimension; Definition N _sthe IFFT matrix of point is wherein

$e_p=[1,{\mathrm{<figure-callout\; id="2"\; label="e\; j"\; filenames="201210333070X100003DEST\_PATH\_IMAGE005.png"\; state="\{\{state\}\}">e</figure-callout>}}^j,\&CenterDot;\&CenterDot;\&CenterDot;,{\mathrm{<figure-callout\; id="2"\; label="e\; j"\; filenames="201210333070X100003DEST\_PATH\_IMAGE005.png"\; state="\{\{state\}\}">e</figure-callout>}}^j{]}^T/\sqrt{N_s},p=0,\&CenterDot;\&CenterDot;\&CenterDot;{,N}_s-1$

N _sthe FFT matrix of point is F ^h, according to formula <2>, can obtain θ _nthe steering vector of direction

In order to distinguish permanent mould waveform matrix X corresponding to different iterationses in iterative process, remember that the permanent mould waveform matrix X of the k time iteration is X ^(k), k represents iterations;

Adopt following steps to design permanent mould waveform matrix X, to approach expectation transmitting pattern D (θ _n):

(2.1) make iterations k=0; Produce the initial permanent mould waveform matrix X of L * M dimension ^(k), specifically comprise two kinds of producing methods:

The first, at the initial time of radar work, adopts random fashion to produce;

The second, in target tracking stage, using radar at the waveform matrix of previous moment as initial permanent mould waveform matrix; Initial permanent mould waveform matrix X ^(k)concrete form be

wherein l the sub-pulse signal that represents the k time iteration, k=0, wherein the permanent mould waveform matrix X of the k time iteration ^(k)the capable m column element of l, l=1 ..., L, m=1 ..., M;

(2.2) set iteration and stop threshold epsilon ₁=0.1, the permanent mould waveform matrix X to the k=0 time iteration ^(k)by row, be N _sthe inverse Fourier transform of point, obtains

the spatial domain signal Y at place ^(k):

$Y^{\left(k\right)}=\sqrt{N_s}{\tilde{X}}^{\left(k\right)}F,---<4>$

Wherein

represent spreading wave form matrix, its concrete form is

k=0;

Calculate the permanent mould waveform matrix X of the k=0 time iteration ^(k)corresponding transmitting pattern P ^(k)(θ _n):

$P^{\left(k\right)}\left({\mathrm{\&theta;}}_n\right)={\left|\right|y_n^{\left(k\right)}\left|\right|}^2=N_s{\left|\right|{\tilde{X}}^{\left(k\right)}{e}_n\left|\right|}^2,n=0,\&CenterDot;\&CenterDot;\&CenterDot;,N_s-1,---<5>$

Wherein spatial domain signal Y ^(k)n row, represent permanent mould waveform matrix X ^(k)at direction θ _non signal, k=0;

(2.3) calculate yardstick factor matrix Γ ^(k):

${\mathrm{\&Gamma;}}^{\left(k\right)}=\mathrm{diag}\left(\right[\sqrt{D\left({\mathrm{\&theta;}}_0\right)}/\sqrt{P^{\left(k\right)}\left({\mathrm{\&theta;}}_0\right)},\&CenterDot;\&CenterDot;\&CenterDot;,\sqrt{D\left({\mathrm{\&theta;}}_{N_s-1}\right)}/\sqrt{P^{\left(k\right)}\left({\mathrm{\&theta;}}_{N_s-1}\right)]});---<6>$

Calculation expectation spatial domain signal Z ^(k):

Z ^(k)＝Y ^(k)Γ ^(k)， <7>

Z wherein ^(k)n column vector represent direction θ _non wanted signal, n=0 ..., N _s-1;

(2.4) calculate the permanent mould waveform matrix X of the k+1 time iteration ^(k+1)in element:

$x_{l,m}^{(k+1)}=\exp \left(j\arg \right({\left(Z^{\left(k\right)}{F}^H\right)}_{l,m}\left)\right),l=1,\&CenterDot;\&CenterDot;\&CenterDot;,L,m=1,\&CenterDot;\&CenterDot;\&CenterDot;,M,---<8>$

Wherein

represent permanent mould waveform matrix X ^(k+1)the element of the capable m of l row, (Z ^(k)f ^h) _{l, m}representing matrix Z ^(k)f ^hthe element of the capable m of l row, wherein arg () represents to get phase place; Execution step (2.5);

(2.5) the permanent mould waveform matrix X to the k+1 time iteration ^(k+1) by row, be N _sthe inverse Fourier transform of point, obtains

the spatial domain signal Y of place ^(k+1):

$Y^{(k+1)}=\sqrt{N_s}{\tilde{X}}^{(k+1)}F,---<9>$

Wherein represent the spreading wave form matrix of the k+1 time, its concrete form is

calculate the permanent mould waveform matrix X of the k+1 time iteration ^(k+1)corresponding transmitting pattern P ^(k+1)(θ _n):

$P^{(k+1)}\left({\mathrm{\&theta;}}_n\right)=N_s{\left|\right|{\tilde{X}}^{(k+1)}{e}_n\left|\right|}^2,n=0,\&CenterDot;\&CenterDot;\&CenterDot;,N_s-1;---<10>$

Judgement end condition whether set up, if set up, permanent mould waveform matrix is: X=X ^(k+1), perform step 3, otherwise, k=k+1 made, repeating step (2.3)-(2.4).

Step 3, utilizes permanent mould waveform matrix, the permanent mould waveform of structure phase shift matrix.

Utilize permanent mould waveform matrix X, the permanent mould waveform of structure phase shift matrix S:

Wherein, x _lthe capable transposition of l of permanent mould waveform matrix X, the subpulse first phase that represents the permanent mould waveform of phase shift matrix S, represent the transposition mutually of the permanent mould waveform of phase shift matrix S, l=1 ..., L;

Step 4, adopts iterative manner to optimize the subpulse first phase of the permanent mould waveform of phase shift matrix, obtains final synthetic waveform.

If target direction is

i represents total number of target, and permanent mould waveform matrix X is at i target direction

on normalized signal be:

$s_i=\mathrm{Xa}\left({\widetilde{\mathrm{\&theta;}}}_i\right)/\sqrt{a^H\left({\widetilde{\mathrm{\&theta;}}}_i\right)X^H\mathrm{Xa}\left({\widetilde{\mathrm{\&theta;}}}_i\right)}{;---<12>}^{}$

Definition size is the phase shift matrix of L * L wherein

the subpulse first phase that represents the permanent mould waveform of phase shift matrix S, l=1 ..., L, the permanent mould waveform of phase shift matrix S=Λ X, and there is identical transmitting pattern with permanent mould waveform matrix X;

In order to distinguish the permanent mould waveform of the phase shift matrix S that in iterative process, different iterationses are corresponding, remember that the permanent mould waveform of the phase shift matrix S of the t time iteration is S ^(t), remember that the phase shift matrix Λ of the t time iteration is Λ ^(t), wherein t represents iterations;

The IFFT matrix that definition 2L is ordered is B=[b ₁..., b _2L] ^t, wherein

$b_p=[1,{\mathrm{<figure-callout\; id="2"\; label="e\; j"\; filenames="201210333070X100003DEST\_PATH\_IMAGE005.png"\; state="\{\{state\}\}">e</figure-callout>}}^j\&CenterDot;\&CenterDot;\&CenterDot;,{\mathrm{<figure-callout\; id="2"\; label="e\; j"\; filenames="201210333070X100003DEST\_PATH\_IMAGE005.png"\; state="\{\{state\}\}">e</figure-callout>}}^j{]}^T/\sqrt{2L},p=1,\&CenterDot;\&CenterDot;\&CenterDot;,2L,$

The FFT matrix that 2L is ordered is B ^h;

Subpulse first phase to the permanent mould waveform of phase shift matrix S as follows

be optimized:

(4.1) make iterations t=0, set iteration and stop threshold epsilon ₂=10 ^-3; Produce initial phase shift matrix

wherein

the permanent mould waveform of the phase shift matrix S that represents the t time iteration ^(t)=Λ ^(t)the subpulse first phase of X, t=0, l=1 ..., L;

(4.2) calculate the permanent mould waveform of the phase shift matrix S of the t time iteration ^(t)=Λ ^(t)x exists

normalized signal h in direction _i:

$h_i=S^{\left(t\right)}a\left({\widetilde{\mathrm{\&theta;}}}_i\right)/\sqrt{a^H\left({\widetilde{\mathrm{\&theta;}}}_i\right)X^H\mathrm{Xa}\left({\widetilde{\mathrm{\&theta;}}}_i\right)},i=1,\&CenterDot;\&CenterDot;\&CenterDot;,I;---<13>$

To h _icarry out the Fourier transform that 2L is ordered, obtain

the frequency spectrum f that 2L in direction is ordered _i:

f _i＝B ^Hq _i，i＝1,…,I， <14>

Q wherein _irepresent

spread signal in direction, its concrete form is

0 _{l * 1}complete zero column vector that represents L dimension;

Calculate

the expectation frequency spectrum v of signal in direction _i:

$v_i=[e^{j{\mathrm{\&psi;}}_{1,i}},\&CenterDot;\&CenterDot;\&CenterDot;,e^{j{\mathrm{\&psi;}}_{2L,i}}{]}^T/\sqrt{2},i=1,\&CenterDot;\&CenterDot;\&CenterDot;,I,---<15>$

ψ wherein _pirepresent expectation frequency spectrum v _iphase place on p frequency, its concrete form is ψ _pi=arg (f _pi), f _pifor frequency spectrum f _ip spectrum value, p=1 ..., 2L, i=1 ..., I;

(4.3) right

the expectation frequency spectrum v of signal in direction _icarry out the inverse Fourier transform that 2L is ordered, obtain

wanted signal g in direction _i:

g _i＝Bv _i，i＝1,…,I； <16>

Calculate the subpulse first phase of the t+1 time iteration

Wherein, () ^*represent conjugation, s _lirepresent

normalized signal s in direction _il element, g _lirepresent

wanted signal g in direction _il element, i=1 ..., I;

Calculate the phase shift matrix Λ of the t+1 time iteration ^(t+1):

execution step (4.4);

(4.4) judgement end condition

whether set up, if set up, the permanent mould waveform of final phase shift matrix is: S=Λ ^(t+1)x, using the permanent mould waveform of phase shift matrix S as final synthetic waveform; Otherwise, make t=t+1, repeating step (4.2)-(4.3).

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

1. experiment scene: suppose that MIMO radar system consists of even linear array ULA, its array number is M=16, and array element distance is half-wavelength, and the code length of permanent mould waveform matrix is L=200, and the termination Threshold in transmitting pattern combined process is ε ₁=0.1, the termination Threshold in subpulse first phase optimizing process is ε ₂=10 ^-3, position angle sampling number is N _s=256, target number is I=3, and the weight setting in desired orientation figure is w _i=1, i=1 ..., I.

2. emulation content:

If 3 targets lay respectively at-40 °, 0 ° and 40 °, initial waveform matrix is the random permanent mould waveform matrix producing, remember that existing positive semidefinite planning SDP and round-robin algorithm CA are SDP+CA algorithm, SDP+CA algorithm and the inventive method are carried out to contrast simulation, wherein the directional diagram in Pattern Synthesis process of the present invention as shown in Figure 2, the inventive method directional diagram corresponding with the waveform of SDP+CA algorithm synthesized as shown in Figure 3, the auto-correlation simulation result of the synthetic waveform of two kinds of methods on target direction is as Fig. 4, Fig. 4 (a) wherein, shown in 4 (b) and 4 (c), be respectively-40 °, the autocorrelation sequence figure of signal in 0 ° and 40 ° of directions, the simple crosscorrelation simulation result of the synthetic waveform of two kinds of methods on target direction as shown in Figure 5, wherein Fig. 5 (a) be depicted as-40 ° with 0 ° of direction on the simple crosscorrelation sequence chart of signal, Fig. 5 (b) be depicted as-40 ° with 40 ° of directions on the simple crosscorrelation sequence chart of signal, Fig. 5 (c) be depicted as 0 ° with 40 ° of directions on the simple crosscorrelation sequence chart of signal.

Suppose that 3 targets move to respectively-42 °, 0 ° and 39 °, using the waveform matrix of the present invention's design in experiment above as initial waveform matrix, adopt method of the present invention to carry out emulation to waveform is synthetic, wherein the directional diagram in Pattern Synthesis process is as shown in Figure 6; The auto-correlation simulation result of the synthetic waveform of the present invention on target direction as shown in Figure 7, is wherein respectively-42 ° shown in Fig. 7 (a), 7 (b) and 7 (c), the autocorrelation sequence figure of signal in 0 ° and 39 ° of directions; The simple crosscorrelation simulation result of the synthetic waveform of the present invention on target direction as shown in Figure 8, wherein Fig. 8 (a) be depicted as-42 ° with 0 ° of direction on the simple crosscorrelation sequence chart of signal, Fig. 8 (b) be depicted as-42 ° with 39 ° of directions on the simple crosscorrelation sequence chart of signal, Fig. 8 (c) be depicted as 0 ° with 39 ° of directions on the simple crosscorrelation sequence chart of signal.

3. analysis of simulation result:

As can be seen from Figure 2, the directional diagram in Pattern Synthesis process of the present invention forms 3 wave beams gradually on 3 target directions.

As can be seen from Figure 3, designed directional diagram corresponding to waveform of the present invention and SDP+CA algorithm approaches the directional diagram of expectation very much in main lobe region.

From Fig. 4 (a), 4 (b) and 4 (c), can find out, the waveform that the present invention is designed, the autocorrelation peak sidelobe level APSL on target direction has reduced about 6dB than SDP+CA algorithm.

From Fig. 5 (a), 5 (b) and 5 (c), can find out, the peak value simple crosscorrelation level PCCL of the present invention and SDP+CA algorithm is substantially suitable, because peak value simple crosscorrelation level can further reduce after received beam forms, and autocorrelation peak sidelobe level APSL plays a major role in pulse compression, therefore the inventive method has obviously been improved the performance of pulse compression, and because main operation of the present invention is FFT and IFFT, it is consuming time more much lower than SDP+CA algorithm.

As can be seen from Figure 6, in target tracking stage, adopt previous moment waveform as initial waveform, transmitting pattern is adjusted to the sensing of current expectation gradually from the sensing of previous moment, avoided each redesign to waveform.From Fig. 7 (a), 7 (b) and 7 (c), can find out, the APSL that new waveform that the present invention synthesizes is corresponding with eve waveform is very approaching.From Fig. 8 (a), 8 (b) and 8 (c), can find out, the PCCL that new waveform that the present invention synthesizes is corresponding with eve waveform is very approaching.

Claims (3)

1. the quick waveform synthetic method of the MIMO radar based on iteration FFT, comprises the steps:

(1), according to the target information in radar return, set the expectation transmitting pattern D (θ of radar _n):

1a) according to target direction determine that traditional phased-array radar points to

time wave beam P _i(θ _n),

1b) with wave beam P _i(θ _n) main lobe form the expectation transmitting pattern D (θ of radar _n):

Wherein, θ _nrepresent discrete azimuth angle, n=0 ..., N _s-1, P _i(θ _n) main lobe region be Ω _i, i=1 ... I, I is target number; w _i>=0 represents weights, θ _nbe defined as follows:

N wherein _srepresent position angle sampling number, λ represents signal wavelength, and d represents the array element distance of radar, and arcsin () represents arcsin function;

(2) according to expectation transmitting pattern D (θ _n), it is comprehensive that employing iteration FFT mode is carried out transmitting pattern, obtains the permanent mould waveform matrix X of radar:

(2a) make iterations k=0, remember that the permanent mould waveform matrix X of the k time iteration is X ^(k); Produce the initial permanent mould waveform matrix X of L * M dimension ^(k), k=0, its concrete form is l the sub-pulse signal that represents the k time iteration, wherein

the k time permanent mould waveform matrix X ^(k)the capable m column element of l, l=1 ..., L, m=1 ..., M, L represents waveform code length, M represents the element number of array of radar, () ^trepresent transposition, | | represent plural mould value;

(2b) set iteration and stop threshold epsilon ₁=0.1; Permanent mould waveform matrix X to the k=0 time iteration ^(k)by row, be N _sthe inverse Fourier transform IFFT of point, obtains the spatial domain signal Y at place ^(k); Calculate the permanent mould waveform matrix X of the k=0 time iteration ^(k)corresponding transmitting pattern P ^(k)(θ _n), n=0 ..., N _s-1, k=0;

(2c) calculation expectation spatial domain signal Z ^(k)=Y ^(k)Γ ^(k),

Γ wherein ^(k)be scale factor matrix, be expressed as:

${\mathrm{\&Gamma;}}^{\left(k\right)}=\mathrm{diag}\left(\right[\sqrt{D\left({\mathrm{\&theta;}}_0\right)}/\sqrt{P^{\left(k\right)}\left({\mathrm{\&theta;}}_0\right)},...,\sqrt{D\left({\mathrm{\&theta;}}_{N_s-1}\right)}/\sqrt{P^{\left(k\right)}\left({\mathrm{\&theta;}}_{N_s-1}\right)}\left]\right),$

In formula, diag () represents to form diagonal matrix operation according to vector;

(2d) calculate the permanent mould waveform matrix X of the k+1 time iteration ^(k+1)in element:

$x_{l,m}^{(k+1)}=\exp \left(j\arg \left({\left(Z^{\left(k\right)}{F}^H\right)}_{l,m}\right)\right),l=1,...,L,m=1,...,M,$

Wherein F represents N _sthe IFFT matrix of point, () ^hrepresent conjugate transpose, represent permanent mould waveform matrix X ^(k+1)the element of the capable m of l row, (Z ^(k)f ^h) _l,mrepresenting matrix Z ^(k)f ^hthe element of the capable m of l row, arg () represents to get phase place; Execution step (2e);

(2e) the permanent mould waveform matrix X to the k+1 time iteration ^(k+1) by row, be N _sthe inverse Fourier transform IFFT of point, obtains

the spatial domain signal Y of place ^(k+1); Calculate the permanent mould waveform matrix X of the k+1 time iteration ^(k+1)corresponding transmitting pattern P ^(k+1)(θ _n), n=0, ... N _s-1; Judgement end condition

whether set up, if set up, permanent mould waveform matrix is X=X ^(k+1), execution step (3), otherwise, make k=k+1, repeating step (2c)-(2d);

(3) utilize permanent mould waveform matrix X, the permanent mould waveform of structure phase shift matrix S

Wherein, x _lthe capable transposition of l of permanent mould waveform matrix X,

the subpulse first phase that represents the permanent mould waveform of phase shift matrix S,

represent the transposition mutually of the permanent mould waveform of phase shift matrix S, l=1 ..., L;

(4) the subpulse first phase to the permanent mould waveform of phase shift matrix S

be optimized:

(4a) make iterations t=0, remember that the permanent mould waveform of the phase shift matrix S of the t time iteration is S ^(t); Produce initial phase shift matrix

wherein

the permanent mould waveform of the phase shift matrix S that represents the t time iteration ^(t)=Λ ^(t)the subpulse first phase of X, t=0, l=1 ..., L, sets iteration and stops threshold epsilon ₂=10 ^-3;

(4b) calculate the permanent mould waveform of the phase shift matrix S of the t time iteration ^(t)=Λ ^(t)x exists

the frequency spectrum f that 2L in direction is ordered _i, phase shift matrix wherein

be i target direction, i=1 ..., I, I represents total number of target; Calculate

the expectation frequency spectrum of signal in direction:

$v_i=\frac{1}{\sqrt{2}}{[e^{j{\mathrm{\&psi;}}_{1,i}},...,e^{j{\mathrm{\&psi;}}_{2L,i}}]}^T,i=1,....,I,$

ψ wherein _pi=arg (f _pi) expression expectation frequency spectrum v _iphase place on p frequency, f _pifor frequency spectrum f _ip spectrum value, p=1 ..., 2L, i=1 ..., I;

(4c) right

the expectation frequency spectrum v of signal in direction _icarry out the inverse Fourier transform that 2L is ordered, obtain wanted signal g in direction _i, i=1 ..., I; Calculate the subpulse first phase of the t+1 time iteration

Wherein () ^*represent conjugation, s _liand g _lirepresent respectively vectorial s _iand g _il element, s _irepresent that the designed permanent mould waveform matrix X of step (2) exists

spatial domain signal in direction, i=1 ..., I; Calculate the phase shift matrix of the t+1 time iteration

execution step (4d);

(4d) judgement end condition

whether set up, if set up, the permanent mould waveform of phase shift matrix is S=Λ ^(t+1)x, using the permanent mould waveform of phase shift matrix S as final synthetic waveform; Otherwise, make t=t+1, repeating step (4b)-(4c).

2. the quick waveform synthetic method of MIMO radar according to claim 1, the wherein initial permanent mould waveform matrix X of the described generation L * M dimension of step (2a) ^(k), k=0, produces as follows:

At the initial time of radar work, adopt random fashion to produce;

In target tracking stage, using radar at the waveform matrix of previous moment as initial permanent mould waveform matrix.

3. the quick waveform synthetic method of MIMO radar according to claim 1, wherein the permanent mould waveform of the phase shift matrix S of step (3) structure has identical transmitting pattern with permanent mould waveform matrix X,

$\begin{array}{c}P\left(\mathrm{\&theta;}\right)=\frac{1}{L}{a}^H\left(\mathrm{\&theta;}\right)X^H\mathrm{Xa}\left(\mathrm{\&theta;}\right)=\frac{1}{L}{a}^H\left(\mathrm{\&theta;}\right)X^H{\mathrm{\&Lambda;}}^H\mathrm{\&Lambda;Xa}\left(\mathrm{\&theta;}\right)\\ =\frac{1}{L}{a}^H\left(\mathrm{\&theta;}\right)S^H\mathrm{Sa}\left(\mathrm{\&theta;}\right)\end{array}$

Wherein P (θ) represents the transmitting pattern of permanent mould waveform matrix X, a (θ)=[1 ..., e ^{j2 π dsin θ/λ}] ^trepresent steering vector, θ represents position angle, phase shift matrix

the subpulse first phase that represents the permanent mould waveform of phase shift matrix S, l=1 ..., L.

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