CN104199028A - Microwave correlated imaging method based on radar rotating emission array - Google Patents

Abstract

The invention discloses a microwave correlated imaging method based on a radar rotating emission array and relates to the technical field of radar information acquisition and processing. The microwave correlated imaging method comprises the step 1 of setting a radar rotating emitting antenna, the step 2 of setting the detection surface of the radar and dividing the detection surface into a plurality of detection units, the step 3 of obtaining time delay, the step 4 of obtaining a steering vector by use of the time delay to obtain an array manifold matrix, the step 5 of setting an echo signal vector, the step 6 of establishing a radiation field vector, the step 7 of establishing the correlation form of an original echo vector under M pulses received by the radar and the radiation field vector, the step 8 of solving the objective function of an objection reflection coefficient vector under the constraint condition of the objective function to obtain the objection reflection coefficient vector, and the step 9 of obtaining a rearranged objection reflection coefficient vector matrix, namely the imaging matrix of an objection. The microwave correlated imaging method based on the radar rotating emission array is capable of improving the space-time randomness and the spatial freedom of the radiation field and realizing high resolution image of a large-scene objection.

Description

Based on the microwave relevance imaging method of radar rotation emission array

Technical field

The invention belongs to that radar information is obtained and processing technology field, relate to microwave relevance imaging technology, relate in particular to a kind of microwave relevance imaging method based on radar rotation emission array.

Technical background

Relevance imaging has been obtained faster development in recent years, relevance imaging is distinguished to some extent with traditional radar imagery, and relevance imaging needs the process of light source participation imaging, and requires light source will have the statistical nature of thermo-optical, i.e. the random fluctuation feature in time and space.In actual experimentation, the general method that adopts counterfeit thermo-optical to substitute true thermo-optical is studied relevance imaging, the people such as Martienssen have proposed the production method of counterfeit thermo-optical, the frosted glass rotating with Ear Mucosa Treated by He Ne Laser Irradiation, counterfeit thermo-optical is produced by the molecule modulated laser place of random distribution in frosted glass, in the time that the rotational speed of frosted glass meets some requirements, the statistical nature of this counterfeit thermo-optical meets the time of thermo-optical and the random fluctuation feature in space.In practice can be with sky time, random radiation field replaces counterfeit thermo-optical, because random radiation field and counterfeit thermo-optical all require to obey stochastic distribution when empty, namely has the random fluctuation feature in time and space.

In the patent " microwave staring imaging correlation method " (application number 201110000698.3) of China Science & Technology University's application, a kind of microwave staring imaging correlation method is disclosed.The method is irradiated target area object by random radiation field, form radiation field distribution at body surface, carry out scattered field reception by hyperchannel or single channel, scattered field and random radiation field are carried out association process and obtained with inverting the imaging of target area object.The deficiency of the method is that the sampling number of requirement is very high, also larger to the requirement of signal to noise ratio (S/N ratio).

In the patent " method of microwave staring imaging " (application number 201110000699.8) of China Science & Technology University application, disclose a kind of based on time, the random radiation field of empty bidimensional and association process microwave staring imaging method.The method by time, empty bidimensional radiation field associated microwave staring imaging, can realize high-resolution microwave staring imaging.When the deficiency of the method is radiation field sky, randomness and spatial degrees of freedom are not high, thereby it is few to cause can recovering pixel in same distance door, are difficult to realize the high-resolution imaging to large scene target.

In the patent " microwave relevance imaging system and formation method based on thinned array " (application number 201310167360.6) of Xian Electronics Science and Technology University's application, a kind of microwave relevance imaging system and formation method based on thinned array disclosed, the imaging effect in the time that radar antenna and target do not have non-radially relative motion that mainly solves prior art is poor, the problem that resolution is low.When the deficiency of this system is radiation field sky, randomness and spatial degrees of freedom are lower, poor to the reconstruct effect of large scene target target scene especially in blocks.

Electromagnetic signal is exactly the process of random radiation field while forming sky from array element bore face to the radiative process in target area.Because the target on test surface is sparse distribution, produce empty time bidimensional random radiation field be also sparse, the space-time correlation of radiation field is smaller, just has identical statistical property with the sensing matrix in compressed sensing.In the middle of the process of compressed sensing, sensing matrix has very important effect, therefore we can utilize compressed sensing in the advantage of processing in sparse sampling signal reconstruction problem, when compressive sensing theory is applied to based on sky in the microwave relevance imaging radar of the random radiation field of bidimensional.

Along with scientific and technological development and the progress in epoch, longer-distance realization of goal high-resolution imaging is become to possibility, because spatial resolution is subject to the restriction of antenna aperture, traditional radar imagery is merely able to be applied to closely imaging or under some lower scenes of resolution requirement, if realize longer-distance high-resolution radar imaging, traditional radar obviously can not meet the demands.In the microwave relevance imaging radar based on compressed sensing, the design of random radiation field is the key that high-resolution imaging can be realized.Why microwave relevance imaging based on compressed sensing can form the radiation field distribution that randomness is larger, mainly used transmit in time with space on randomness.

To large scene, imaging is the typical technology problem of traditional synthetic-aperture radar, is also the difficult point that sparse microwave imaging is urgently captured.Existing radar microwave imaging technique, when empty, random radiation field degree of freedom is low, low to large scene target imaging weak effect, resolution.

Summary of the invention

The object of the invention is to the deficiency for above-mentioned prior art, propose a kind of microwave relevance imaging method based on radar rotation emission array, while improving radiation field sky, randomness and spatial degrees of freedom, realize the high-resolution imaging to large scene target.

For achieving the above object, the present invention is achieved by the following technical solutions.

Based on a microwave relevance imaging method for radar rotation emission array, it is characterized in that, comprise the following steps:

Step 1, radar rotation emission array is the two-dimensional array with N array element, and the array element of radar rotation emission array is distributed on a disc, and the receiver of radar is positioned at the center of circle of disc, the axis that array element place disc is walked around the center of circle rotates with angular velocity omega, and the axis in the described center of circle is perpendicular to disc; N is natural number;

Step 2, radar rotation emission array is launched the microwave signal of M pulse to test surface, and receives the original echo data Y under M pulse; M is natural number;

Described test surface is divided into E × F probe unit, probe unit sum Q=E × F, wherein, E represents horizontal detection unit number, and F represents longitudinal probing unit number, and E, F are respectively natural number, and Q>M, M represents radar rotation emission array transponder pulse number;

Step 3, under m pulse, n array element is s to q probe unit launched microwave signal indication _mn(t) echoed signal that, radar receiver receives q probe unit is expressed as s _mn(t-τ _mnq), ask for launched microwave signal s _mn(t) with echoed signal s _mn(t-τ _mnq) between time delay τ _mnq, wherein, t represents the time, m=1, and 2 ..., M, n=1,2 ..., N, q=1,2 ..., Q, M represents radar rotation emission array transponder pulse number, and N represents the transmitting array number of radar rotation emission array, and Q represents probe unit sum;

Step 4, utilizes time delay τ _mnqask for the steering vector V of N relative q the probe unit of array element under m pulse _mq, V _mqdimension is N × 1; And then obtain the array manifold matrix V of N the relative Q of an array element probe unit under m pulse _m, V _mdimension is N × Q;

Step 5, sets n the microwave signal s that array element is launched to q probe unit under m pulse _mn(t) equal the echoed signal s of q probe unit that receiver receives _mn(t-τ _mnq), i.e. s _mn(t-τ _mnq)=s _mn(t), the echoed signal vector under m pulse:

s _m(t)＝[s _m1(t),s _m2(t),...,s _mn(t),...,s _mN(t)] _1×N；m＝1,2,...,M,n＝1,2,...,N,q＝1,2,...,Q；

Step 6, utilizes the array manifold matrix V of m the relative Q of the array element of the N under a pulse probe unit _mwith the echoed signal vector s under m pulse _m(t), build the radiation field vector A under m pulse _m=s _m(t) V _m, dimension is 1 × Q and then obtains M the radiation field matrix under pulse a dimension is M × Q, wherein [] ^trepresent transposition;

Step 7, the vectorization form of target setting reflection coefficient vector σ is [σ ₁, σ ₂..., σ _q..., σ _q] ^t, wherein [] ^trepresent transposition, σ _qrepresent the target reflection factor of q probe unit, q=1,2 ..., Q;

Utilize M radiation field matrix A and the target reflection factor vector σ under pulse to be write the original echo vector Y under M pulse of radar reception as following form:

Y＝Aσ+w

Wherein, A represents the radiation field matrix of M the probe unit of the Q under pulse, and w represents the white Gaussian noise vector that the dimension of setting is M × 1;

Step 8, sets up the objective function of target reflection factor vector σ, using Y=A σ+w as bound for objective function, solves the objective function of target reflection factor vector σ under bound for objective function, obtains target reflection factor to σ, σ=[σ ₁, σ ₂..., σ _q..., σ _q] ^t=[σ ₁, σ ₂..., σ _e, σ _e+1, σ _e+2..., σ _2E..., σ _{(F-1) E+1}, σ _{(F-1) E+2}..., σ _q] ^t, wherein [] ^trepresent transposition, Q=E × F, E represents horizontal detection unit number, F represents longitudinal probing unit number;

Step 9, is arranged as E × F by target reflection factor vector σ by Q × 1 dimension and ties up matrix, obtains the target reflection factor matrix of resetting $\stackrel{\‾}{\mathrm{\σ}}={\left[\begin{array}{cccc}{\mathrm{\σ}}_1& {\mathrm{\σ}}_{E+1}& ...& {\mathrm{\σ}}_{(F-1)E+1}\\ {\mathrm{\σ}}_2& {\mathrm{\σ}}_{E+2}& ...& {\mathrm{\σ}}_{(F-1)E+2}\\ .& .& & .\\ .& .& & .\\ .& .& & .\\ {\mathrm{\σ}}_E& {\mathrm{\σ}}_{2E}& ...& {\mathrm{\σ}}_Q\end{array}\right]}_{E\×F},$ The target reflection factor matrix of resetting it is the imaging array of target.

The feature of technique scheme and further improvement are:

(1) step 3 comprises:

In rectangular coordinate system in space, the receiver of setting radar is positioned at the center of circle of disc at the initial point place of rectangular coordinate system in space, and the coordinate of q probe unit is (x _q, y _q, z _q), the pass between the coordinate figure of q probe unit is:

z _q ²＝r ₀ ²-x _q ²-y _q ²

The rotational time of setting radar rotation emission array under m pulse is Δ t _m, rotational time is that radar rotation emission array never rotated to the time of rotation, n array element is through rotational time Δ t _mafter coordinate be under m pulse, n array element is to the distance r between q probe unit _mnqfor:

$\begin{array}{c}{r}_{\mathrm{mnq}}=\sqrt{{({\tilde{x}}_{\mathrm{mn}}-x_q)}^2+{({\tilde{y}}_{\mathrm{mn}}-y_q)}^2+{(z_q-0)}^2}\\ =\sqrt{{({\tilde{x}}_{\mathrm{mn}}-x_q)}^2+{({\tilde{y}}_{\mathrm{mn}}-y_q)}^2+{r_0}^2-{x_q}^2-{y_q}^2}\\ =\sqrt{{r_0}^2+{\tilde{x}}_{\mathrm{mn}}^2+{\tilde{y}}_{\mathrm{mn}}^2-{2x}_q{\tilde{x}}_{\mathrm{mn}}-{2y}_q{\tilde{y}}_{\mathrm{mn}}}\end{array}$

Wherein, m=1,2 ..., M, n=1,2 ..., N, q=1,2 ..., Q, M represents radar rotation emission array transponder pulse number, and N represents the transmitting array number of radar rotation emission array, and Q represents probe unit sum;

Set radar test surface in the initial point taking rectangular coordinate system in space as the centre of sphere, radius be r ₀sphere on, set the spherical radius r at test surface place ₀at least be greater than 50 times, with n array element through rotational time Δ t _mafter coordinate for variable, use Taylor series to locate to launch n array element to the distance r between q probe unit at point (0,0,0) _mnq:

$\begin{array}{c}{r}_{\mathrm{mnq}}=r_{\mathrm{mnq}}{|}_{\left(\mathrm{0,0,0}\right)}+{\tilde{x}}_{\mathrm{mn}}\left(\frac{{\∂r}_{\mathrm{mnq}}}{\∂{\tilde{x}}_{\mathrm{mn}}}{|}_{\left(\mathrm{0,0,0}\right)}\right)+{\tilde{y}}_{\mathrm{mn}}\left(\frac{{\∂r}_{\mathrm{mnq}}}{\∂{\tilde{y}}_{\mathrm{mn}}}{|}_{\left(\mathrm{0,0,0}\right)}\right)+O\\ \≈r_0-\frac{x_q{\tilde{x}}_{\mathrm{mn}}+y_q{\tilde{y}}_{\mathrm{mn}}}{r_0}\end{array}$

Wherein, r _mnq| _(0,0,0)represent r _mnqthe value of locating at point (0,0,0), represent r _mnqright ask the value of locating at point (0,0,0) after local derviation, represent r _mnqright ask the value of locating at point (0,0,0) after local derviation, r ₀for the test surface of the radar radius in sphere, be also the initial point of rectangular coordinate system in space to the distance of each probe unit, O represents Lagrangian type remainder;

Under m pulse, n array element launched microwave signal is to q probe unit, with the time delay τ of receiver reception echoed signal _mnqfor:

$\begin{array}{c}{\mathrm{\τ}}_{\mathrm{mnq}}=t_{\mathrm{mnq}}-t_0=\frac{r_{\mathrm{mnq}}-r_0}{c}=-\frac{x_q{\tilde{x}}_{\mathrm{mn}}+y_q{\tilde{y}}_{\mathrm{mn}}}{{\mathrm{cr}}_0}\\ =-R_n\frac{\cos ({\mathrm{\ω\Δt}}_m+{\mathrm{\θ}}_n)x_q+\sin ({\mathrm{\ω\Δt}}_m+{\mathrm{\θ}}_n)y_q}{{\mathrm{cr}}_0}\end{array}$

Wherein, t _mnqrepresent the microwave signal travel-time of n array element to q probe unit, t ₀denotation coordination initial point is to the travel-time of q probe unit, and c represents the light velocity, (x _q, y _q, z _q) represent the coordinate of q probe unit, represent that n array element is through rotational time Δ t _mafter coordinate, R _nrepresent the distance of n array element to true origin, Δ t _mrepresent the rotational time of radar rotation emission array under m pulse, r ₀the initial point of representation space rectangular coordinate system is to the distance of each probe unit, and ω represents to rotate the angular velocity of emission array rotation, θ _nbe n element position and the axial angle of x.

(2) step 4 comprises:

Steering vector V _mqexpression formula be: V _mq=[V _m1q, V _m2q..., V _mnq..., V _mNq] ^t, wherein, [] ^trepresent transposition,

$\begin{array}{c}{V}_{\mathrm{mnq}}=\exp (-j2\mathrm{\π}{f}_c{\mathrm{\τ}}_{\mathrm{mnq}})\\ =\exp \left\{{j2\mathrm{\πf}}_c{R}_n\frac{\cos ({\mathrm{\ω\Δt}}_m+{\mathrm{\θ}}_n)x_q+\sin ({\mathrm{\ω\Δt}}_m+{\mathrm{\θ}}_n)y_q}{{\mathrm{cr}}_0}\right\}\end{array}$

Wherein, f _crepresent carrier frequency, c represents the light velocity, (x _q, y _q, z _q) represent the coordinate of q probe unit, R _nrepresent the distance of n array element to true origin, Δ t _mrepresent the rotational time of radar rotation emission array under m pulse, r ₀the initial point of representation space rectangular coordinate system is to the distance of each probe unit, and ω represents to rotate the angular velocity of emission array rotation, θ _nbe n element position and the axial angle of x;

Under m pulse, the array manifold matrix of N the relative Q of an array element probe unit is V _m, expression formula is:

$V_m={\left[\begin{array}{cccccc}{V}_{m11}& V_{m12}& ...& V_{m1q}& ...& V_{m1Q}\\ V_{m21}& V_{m22}& ...& V_{m2q}& ...& V_{m2Q}\\ .& .& .& .& .& .\\ .& .& .& .& .& .\\ .& .& .& .& .& .\\ V_{\mathrm{mn}1}& V_{\mathrm{mn}1}& ...& V_{\mathrm{mnq}}& ...& V_{\mathrm{mnQ}}\\ .& .& .& .& .& .\\ .& .& .& .& .& .\\ .& .& .& .& .& .\\ V_{\mathrm{mN}1}& V_{\mathrm{mN}2}& ...& V_{\mathrm{mNq}}& ...& V_{\mathrm{mNQ}}\end{array}\right]}_{N\×Q}$

The array manifold matrix V=[V of N the relative Q of an array element probe unit under M pulse ₁, V ₂..., V _m..., V _m] ^t.

(3) step 6 comprises:

Radiation field vector A under m pulse _mexpression formula:

$A_m={[s_{m1}\left(t\right),s_{m2}\left(t\right),...,s_{\mathrm{mn}}\left(t\right),...,s_{\mathrm{mN}}\left(t\right)]}_{1\×N}{\·\left[\begin{array}{cccccc}{V}_{m11}& V_{m12}& ...& V_{m1q}& ...& V_{m1Q}\\ V_{m21}& V_{m22}& ...& V_{m2q}& ...& V_{m2Q}\\ .& .& & .& & .\\ .& .& & .& & .\\ .& .& & .& & .\\ V_{\mathrm{mn}1}& V_{\mathrm{mn}1}& ...& V_{\mathrm{mnq}}& ...& V_{\mathrm{mnQ}}\\ .& .& & .& & .\\ .& .& & .& & .\\ .& .& & .& & .\\ V_{\mathrm{mN}1}& V_{\mathrm{mN}2}& ...& V_{\mathrm{mNq}}& ...& V_{\mathrm{mNQ}}\end{array}\right]}_{N\×Q}$

Wherein, m=1,2 ... M, s _mn(t) represent n the microwave signal that array element is launched under m pulse, V _mnqbe illustrated under m pulse, the steering vector of n relative q the probe unit of array element, " " representing matrix multiplies each other;

Radiation field matrix A=[A under M pulse ₁, A ₂..., A _m... A _m] ^t.

(4) step 8 comprises:

Objective function and the bound for objective function of target reflection factor vector σ are following formula:

$\underset{\mathrm{\σ}}{\min }\{Q-F_{{\mathrm{\α}}_j}\left(\mathrm{\σ}\right)\}$

Constraint condition Y=A σ+w

Wherein, Q represents probe unit sum, $F_{{\mathrm{\α}}_j}\left(\mathrm{\σ}\right)=\underset{q=1}{\overset{Q}{\mathrm{\Σ}}}{f}_{{\mathrm{\α}}_j}\left({\mathrm{\σ}}_q\right),f_{{\mathrm{\α}}_j}\left({\mathrm{\σ}}_q\right)=\exp ({{-\mathrm{\σ}}_q}^2/{{2\mathrm{\α}}_j}^2),$ α _jelement variable in the descending series that represents to set, j=1,2 ..., J, the element number in the descending series that J represents to set, σ is target reflection factor vector, exp represents exponent arithmetic, σ _qrepresent the target reflection factor of q probe unit, A represents the radiation field matrix of M the probe unit of the Q under pulse.

(5) objective function that solves target reflection factor vector σ under bound for objective function specifically comprises:

8a) target setting reflection coefficient vector initial value is σ ₁=A ^h(AA ^h) ^-1y, wherein [] ^-1representing matrix is inverted, and A represents the radiation field matrix of M the probe unit of the Q under pulse;

Set descending series [α ₁, α ₂..., α _j..., α _j], wherein the relation between element meets α _j=η α _j-1, j=2 ..., J, η ∈ (0.5,1] be constant, α ₁=2max (σ ₁), α _j<0.01;

8b) utilize j element α in descending series _jstructure gradient vector

$\underset{j}{{\mathrm{\&Delta;\&sigma;}}_{k-1}}=[\underset{j}{{\mathrm{\&sigma;}}_{k-\mathrm{1,1}}}\exp \left(\frac{-\underset{j}{{\mathrm{\&sigma;}}_{k-\mathrm{1,1}}^2}}{{{2\mathrm{\&alpha;}}_j}^2}\right),\underset{j}{{\mathrm{\&sigma;}}_{k-\mathrm{1,2}}}\exp \left(\frac{-\underset{j}{{\mathrm{\&sigma;}}_{k-\mathrm{1,2}}^2}}{{{2\mathrm{\&alpha;}}_j}^2}\right),...,\underset{j}{{\mathrm{\&sigma;}}_{k-1,q}}\exp \left(\frac{\underset{j}{{-\mathrm{\&sigma;}}_{k-1,q}^2}}{{{2\mathrm{\&alpha;}}_j}^2}\right),...,\underset{j}{{\mathrm{\&sigma;}}_{k-1,Q}}\exp \left(\frac{\underset{j}{{-\mathrm{\&sigma;}}_{k-1,Q}^2}}{{{2\mathrm{\&alpha;}}_j}^2}\right)]$ , wherein exp represents exponent arithmetic, represent to utilize j element α _jthe target reflection factor obtaining is to k-1 iterative value of flow control in q element, q=1,2 ..., Q, Q represents probe unit sum;

8c) structure utilizes j element α _jthe target reflection factor obtaining is to k iterative value of flow control wherein step factor μ=2;

By j element α _jthe target reflection factor obtaining is to k iterative value σ of flow control _kconvert: wherein, [] ^-1representing matrix is inverted, ← represent to use the vector on the right to replace the vector on the left side, and $\underset{j}{{\mathrm{\&sigma;}}_k}=[{\underset{j}{{\mathrm{\&sigma;}}_{k,1}},\underset{j}{{\mathrm{\&sigma;}}_{k,2}},...,\underset{j}{{\mathrm{\&sigma;}}_{k,q}},...,\underset{j}{{\mathrm{\&sigma;}}_{k,Q}}]}^T,$ Wherein [] ^trepresent transposition;

8e) make k from 1 to K, repeating step 8b) to step 8d), obtain j element α _junder target reflection factor vector wherein, the iterations that K sets, is positive integer;

8f) make j from 1 to J, repeating step 8b) to step 8e), obtain J element α _junder target reflection factor vector by J element α _junder target reflection factor vector as target reflection factor vector σ.

Compared with prior art, the present invention has outstanding substantive distinguishing features and significant progressive.The present invention compared with the conventional method, has the following advantages:

(1) formation method restructural target numbers of the present invention has improved more than 10 times than array element number, compared with the existing microwave relevance imaging system based on thinned array, the reconfigurable target numbers of system is more, imaging effect is better, resolution is higher, the spatial degrees of freedom of effectively having expanded random radiation field when empty, can be used for the high-resolution imaging of radar to large scene target.

(2) imaging system of the present invention can be at low signal-to-noise ratio, and the sparse target numbers of target scene exceedes in the situation of array element number, realizes the target imaging of breaking through more than 5 times Rayleigh diffraction-limited, is conducive to the real-time processing of radar to target.

Brief description of the drawings

Below in conjunction with the drawings and specific embodiments, the present invention will be further described.

Fig. 1 is the microwave relevance imaging method flow diagram that the present invention is based on radar rotation emission array;

Fig. 2 is the microwave relevance imaging system schematic that the present invention is based on radar rotation emission array;

Fig. 3 is the movement locus figure of n array element of rotation emission array of the present invention;

Fig. 4 is the original distribution figure of 150 point targets; Horizontal ordinate represents lateral separation unit, and ordinate represents fore-and-aft distance unit, and unit distance unit represents length 1.3m;

Fig. 5 is to be 15 o'clock at transmitting array element number, the simulation result with formation method of the present invention to 150 point targets in Fig. 4; Horizontal ordinate represents lateral separation unit, and ordinate represents fore-and-aft distance unit, and unit distance unit represents length 1.3m;

Fig. 6 is the original distribution figure of 150 targets in blocks; Horizontal ordinate represents lateral separation unit, and ordinate represents fore-and-aft distance unit, and unit distance unit represents length 1.3m;

Fig. 7 is to be 15 o'clock at transmitting array element number, the simulation result with formation method of the present invention to 150 targets in blocks in Fig. 6; Horizontal ordinate represents lateral separation unit, and ordinate represents fore-and-aft distance unit, and unit distance unit represents length 1.3m;

Fig. 8 is the original distribution figure of 90 point targets; Horizontal ordinate represents lateral separation unit, and ordinate represents fore-and-aft distance unit, and unit distance unit represents length 1.3m;

Fig. 9 is to be 25 at transmitting array element number, and signal to noise ratio (S/N ratio) is 10dB, breaks through in the situation of 5 times of Rayleigh diffraction-limited the simulation result with formation method of the present invention to 90 point targets in Fig. 8; Horizontal ordinate represents lateral separation unit, and ordinate represents fore-and-aft distance unit, and unit distance unit represents length 1.3m;

Figure 10 is the original distribution figure of 90 targets in blocks; Horizontal ordinate represents lateral separation unit, and ordinate represents fore-and-aft distance unit, and unit distance unit represents length 1.3m;

Figure 11 is to be 25 at transmitting array element number, and signal to noise ratio (S/N ratio) is 10dB, breaks through in the situation of 5 times of Rayleigh diffraction-limited the simulation result with formation method of the present invention to 90 targets in blocks in Figure 10; Horizontal ordinate represents lateral separation unit, and ordinate represents fore-and-aft distance unit, and unit distance unit represents length 1.3m.

Embodiment

With reference to figure 1 and Fig. 2, the microwave relevance imaging method that the present invention is based on radar rotation emission array is described, can be used for rotating the structure of emission array antenna, the raising of random radiation field randomness and the expansion of degree of freedom while realizing sky.

Step 1, radar rotation emission array is the two-dimensional array with N array element, and the array element of radar rotation emission array is distributed on a disc, and the receiver of radar is positioned at the center of circle of disc, the axis that array element place disc is walked around the center of circle rotates with angular velocity omega, and the axis in the center of circle is perpendicular to disc.

As shown in Figure 2.Radar rotation emission array forms by launching array element 1, and the radius of each array element is different, and each array element is launched different microwave signals and formed microwave radiation field in space non-coherent addition, and this microwave radiation field irradiates test surface 2.The receiver of radar forms by receiving array element 3, for receiving the original echo data that produce after microwave radiation field irradiates target, random radiation field 4 when storage is radiated test surface 2 empty simultaneously, the original echo data that receiver 3 receives and the radiation field 4 prestoring are processed by signal processor 5, adopt the inventive method to obtain the target image of super-resolution.

With reference to figure 3, the movement locus of n array element of rotation emission array, sets the coordinate of n array element in the time that radar rotates emission array and do not rotate and is its coordinate figure is: wherein, R _nbe the distance of n array element to true origin, θ _nbe n element position and the axial angle of x, n=1,2 ..., N.

Radar rotation emission array is to the microwave signal of M pulse of test surface transmitting, and array element number N<M to be set in the rotational time that radar under m pulse rotates emission array be Δ t _m, rotational time is that radar rotation emission array never rotated to the time of rotation,, n array element is through rotational time Δ t _mafter coordinate be its coordinate figure is: ${\tilde{x}}_{\mathrm{mn}}=R_n\cos ({\mathrm{\&omega;\&Delta;t}}_m+{\mathrm{\&theta;}}_n),{\tilde{y}}_{\mathrm{mn}}=R_n\sin ({\mathrm{\&omega;\&Delta;t}}_m+{\mathrm{\&theta;}}_n),$ Wherein ω is that the angular velocity of rotation emission array rotation is array element place disc angular velocity omega, m=1, and 2 ..., M, n=1,2 ..., N.

Step 2, radar rotation emission array is launched the microwave signal of M pulse to test surface, and receives the original echo data Y under M pulse;

Described test surface is divided into E × F probe unit, probe unit sum Q=E × F, and Q>M, wherein E represents horizontal detection unit number, and F represents longitudinal probing unit number, and M represents radar rotation emission array transponder pulse number.

Step 3, under m pulse, n array element is s to q probe unit launched microwave signal indication _mn(t) echoed signal that, radar receiver receives q probe unit is expressed as s _mn(t-τ _mnq), ask for launched microwave signal s _mn(t) with echoed signal s _mn(t-τ _mnq) between time delay τ _mnq, wherein, t represents the time, m=1, and 2 ..., M, n=1,2 ..., N, q=1,2 ..., Q, M represents radar rotation emission array transponder pulse number, and N represents the transmitting array number of radar rotation emission array, and Q represents probe unit sum; .

N the signal s that array element is launched to q probe unit under m pulse _mn(t) be microwave random coding signal n=1,2 ..., N, wherein B _mn(t) be n the amplitude that array element transmits under m pulse, ρ _mnbe n the phase place that array element transmits under m pulse, phase place adopts random coded, and t represents the time.

In rectangular coordinate system in space, the receiver of setting radar is positioned at the center of circle of disc at the initial point place of rectangular coordinate system in space, and the coordinate of q probe unit is (x _q, y _q, z _q), the pass between the coordinate figure of q probe unit is:

z _q ²＝r ₀ ²-x _q ²-y _q ²

Set under m pulse, the rotational time of radar rotation emission array is Δ t _m, rotational time is that radar rotation emission array never rotated to the time of rotation, n array element is through rotational time Δ t _mafter coordinate be under m pulse, n array element is to the distance r between q probe unit _mnqfor:

$\begin{array}{c}{r}_{\mathrm{mnq}}=\sqrt{{({\tilde{x}}_{\mathrm{mn}}-x_q)}^2+{({\tilde{y}}_{\mathrm{mn}}-y_q)}^2+{(z_q-0)}^2}\\ =\sqrt{{({\tilde{x}}_{\mathrm{mn}}-x_q)}^2+{({\tilde{y}}_{\mathrm{mn}}-y_q)}^2+{r_0}^2-{x_q}^2-{y_q}^2}\\ =\sqrt{{r_0}^2+{\tilde{x}}_{\mathrm{mn}}^2+{\tilde{y}}_{\mathrm{mn}}^2-{2x}_q{\tilde{x}}_{\mathrm{mn}}-{2y}_q{\tilde{y}}_{\mathrm{mn}}}\end{array}$

Set radar test surface in the initial point taking rectangular coordinate system in space as the centre of sphere, radius be r ₀sphere on, set the spherical radius at test surface place the spherical radius r at test surface place in the present invention ₀at least be greater than 50 times, with n array element through rotational time Δ t _mafter coordinate for variable, use Taylor series to locate to launch n array element to the distance r between q probe unit at point (0,0,0) _mnq:

$\begin{array}{c}{r}_{\mathrm{mnq}}=r_{\mathrm{mnq}}{|}_{\left(\mathrm{0,0,0}\right)}+{\tilde{x}}_{\mathrm{mn}}\left(\frac{{\&PartialD;r}_{\mathrm{mnq}}}{\&PartialD;{\tilde{x}}_{\mathrm{mn}}}{|}_{\left(\mathrm{0,0,0}\right)}\right)+{\tilde{y}}_{\mathrm{mn}}\left(\frac{{\&PartialD;r}_{\mathrm{mnq}}}{\&PartialD;{\tilde{y}}_{\mathrm{mn}}}{|}_{\left(\mathrm{0,0,0}\right)}\right)+O\\ =r_0-\frac{x_q{\tilde{x}}_{\mathrm{mn}}+y_q{\tilde{y}}_{\mathrm{mn}}}{r_0}\end{array}$

Wherein, r _mnq| _(0,0,0)represent r _mnqthe value of locating at point (0,0,0), represent r _mnqright ask the value of locating at point (0,0,0) after local derviation, represent r _mnqright ask the value of locating at point (0,0,0) after local derviation, r ₀for the test surface of the radar radius in sphere, be also the initial point of rectangular coordinate system in space to the distance of each probe unit, O is Lagrangian type remainder; Under m pulse, n array element launched microwave signal be to q probe unit, receives the time delay τ of echoed signal with receiver 3 _mnqfor:

$\begin{array}{c}{\mathrm{\&tau;}}_{\mathrm{mnq}}=t_{\mathrm{mnq}}-t_0=\frac{r_{\mathrm{mnq}}-r_0}{c}=-\frac{x_q{\tilde{x}}_{\mathrm{mn}}+y_q{\tilde{y}}_{\mathrm{mn}}}{{\mathrm{cr}}_0}\\ =-R_n\frac{\cos ({\mathrm{\&omega;\&Delta;t}}_m+{\mathrm{\&theta;}}_n)x_q+\sin ({\mathrm{\&omega;\&Delta;t}}_m+{\mathrm{\&theta;}}_n)y_q}{{\mathrm{cr}}_0}\end{array}$

Wherein, t _mnqrepresent the microwave signal travel-time of n array element to q probe unit, t ₀denotation coordination initial point is to the travel-time of q probe unit, and c represents the light velocity, (x _q, y _q, z _q) represent the coordinate of q probe unit, represent that n array element is through rotational time Δ t _mafter coordinate, R _nbe the distance of n array element to true origin, Δ t _mrepresent the rotational time of radar rotation emission array under m pulse, r ₀the initial point of representation space rectangular coordinate system is to the distance of each probe unit, and ω represents to rotate the angular velocity of emission array rotation, θ _nbe n element position and the axial angle of x.

Step 4, utilizes time delay τ _mnqask for the steering vector V of N relative q the probe unit of array element under m pulse _mq, dimension is N × 1; And then obtain the array manifold matrix V of N the relative Q of an array element probe unit under m pulse _m, dimension is N × Q.

Steering vector V _mqexpression formula be: V _mq=[V _m1q, V _m2q..., V _mnq..., V _mNq] ^t,

Wherein, [] ^trepresent transposition,

$\begin{array}{c}{V}_{\mathrm{mnq}}=\exp (-j2\mathrm{\&pi;}{f}_c{\mathrm{\&tau;}}_{\mathrm{mnq}})\\ =\exp \left\{{j2\mathrm{\&pi;f}}_c{R}_n\frac{\cos ({\mathrm{\&omega;\&Delta;t}}_m+{\mathrm{\&theta;}}_n)x_q+\sin ({\mathrm{\&omega;\&Delta;t}}_m+{\mathrm{\&theta;}}_n)y_q}{{\mathrm{cr}}_0}\right\}\end{array}$

Wherein, f _crepresent carrier frequency, c represents the light velocity, (x _q, y _q, z _q) represent the coordinate of q probe unit, R _nrepresent the distance of n array element to true origin, Δ t _mthe rotational time of radar rotation emission array under m pulse, r ₀the initial point of representation space rectangular coordinate system is to the distance of each probe unit, and ω represents to rotate the angular velocity of emission array rotation, θ _nbe n element position and the axial angle of x.

Under m pulse, the array manifold matrix of N the relative Q of an array element probe unit is V _m,

$V_m={\left[\begin{array}{cccccc}{V}_{m11}& V_{m12}& ...& V_{m1q}& ...& V_{m1Q}\\ V_{m21}& V_{m22}& ...& V_{m2q}& ...& V_{m2Q}\\ .& .& .& .& .& .\\ .& .& .& .& .& .\\ .& .& .& .& .& .\\ V_{\mathrm{mn}1}& V_{\mathrm{mn}1}& ...& V_{\mathrm{mnq}}& ...& V_{\mathrm{mnQ}}\\ .& .& .& .& .& .\\ .& .& .& .& .& .\\ .& .& .& .& .& .\\ V_{\mathrm{mN}1}& V_{\mathrm{mN}2}& ...& V_{\mathrm{mNq}}& ...& V_{\mathrm{mNQ}}\end{array}\right]}_{N\&times;Q}$

Under M pulse, the array manifold matrix V=[V of N the relative Q of an array element probe unit ₁, V ₂..., V _m..., V _m] ^t.

Step 5, sets n the microwave signal s that array element is launched to q probe unit under m pulse _mn(t) equal the echoed signal s of q probe unit that receiver receives _mn(t-τ _mnq), i.e. s _mn(t-τ _mnq)=s _mn(t), the vector of the echoed signal under m pulse s _m(t)=[s _m1(t), s _m2(t) ..., s _mn(t) ..., s _mN(t)] _{1 × N};

Step 6, utilizes the array manifold matrix V of m the relative Q of the array element of the N under a pulse probe unit _mwith the echoed signal vector s under m pulse _m(t), build the radiation field vector A under m pulse _m=s _m(t) V _m, dimension is 1 × Q, and then obtains M the radiation field matrix under pulse

Radiation field vector A under m pulse _mexpression formula:

$A_m={[s_{m1}\left(t\right),s_{m2}\left(t\right),...,s_{\mathrm{mn}}\left(t\right),...,s_{\mathrm{mN}}\left(t\right)]}_{1\&times;N}{\&CenterDot;\left[\begin{array}{cccccc}{V}_{m11}& V_{m12}& ...& V_{m1q}& ...& V_{m1Q}\\ V_{m21}& V_{m22}& ...& V_{m2q}& ...& V_{m2Q}\\ .& .& & .& & .\\ .& .& & .& & .\\ .& .& & .& & .\\ V_{\mathrm{mn}1}& V_{\mathrm{mn}1}& ...& V_{\mathrm{mnq}}& ...& V_{\mathrm{mnQ}}\\ .& .& & .& & .\\ .& .& & .& & .\\ .& .& & .& & .\\ V_{\mathrm{mN}1}& V_{\mathrm{mN}2}& ...& V_{\mathrm{mNq}}& ...& V_{\mathrm{mNQ}}\end{array}\right]}_{N\&times;Q}$

Wherein, m=1,2 ... M, s _mn(t) represent n the microwave signal that array element is launched under m pulse, V _mnqbe illustrated under m pulse, the steering vector of n relative q the probe unit of array element, " " representing matrix multiplies each other.

Radiation field matrix A=[A under M pulse ₁, A ₂..., A _m... A _m] ^t.

It should be noted that, in prior art, if emission array does not rotate, under each pulse, the array manifold matrix of N array element is constant, and the array manifold matrix of setting N array element is ?

$\stackrel{\&OverBar;}{V}={\left[\begin{array}{cccccc}{V}_{11}& V_{12}& ...& V_{1q}& ...& V_{1Q}\\ V_{21}& V_{22}& ...& V_{2q}& ...& V_{2Q}\\ .& .& & .& & .\\ .& .& & .& & .\\ .& .& & .& & .\\ V_{n1}& V_{n2}& ...& V_{\mathrm{nq}}& ...& V_{\mathrm{nQ}}\\ .& .& & .& & .\\ .& .& & .& & .\\ .& .& & .& & .\\ V_{N1}& V_{N2}& ...& V_{\mathrm{Nq}}& ...& V_{\mathrm{NQ}}\end{array}\right]}_{N\&times;Q}$

Wherein, V _nq=exp (j2 π f _cτ _nq), f _crepresent carrier frequency, τ _nqrepresent the time delay of n array element launched microwave signal to the echoed signal of q probe unit reflection;

Because emission array does not rotate, n array element launched microwave signal is to the time delay τ of the echoed signal of q probe unit reflection _nqfor constant, and then the array manifold matrix of N array element under each pulse constant.

It is radiation field matrix can be expressed as:

$\stackrel{\&OverBar;}{A}={\left[\begin{array}{cccccc}{s}_{11}\left(t\right)& s_{12}\left(t\right)& ...& s_{1n}\left(t\right)& ...& s_{1N}\left(t\right)\\ s_{21}\left(t\right)& s_{22}\left(t\right)& ...& s_{2n}\left(t\right)& ...& s_{2N}\left(t\right)\\ .& .& & .& & .\\ .& .& & .& & .\\ .& .& & .& & .\\ s_{m1}\left(t\right)& s_{m2}\left(t\right)& ...& s_{\mathrm{mn}}\left(t\right)& ...& s_{\mathrm{mN}}\left(t\right)\\ .& .& & .& & .\\ .& .& & .& & .\\ .& .& & .& & .\\ s_{M1}\left(t\right)& s_{M2}\left(t\right)& ...& s_{\mathrm{Mn}}\left(t\right)& ...& s_{\mathrm{MN}}\left(t\right)\end{array}\right]}_{M\&times;N}\&CenterDot;{\left[\begin{array}{cccccc}{V}_{11}& V_{12}& ...& V_{1q}& ...& V_{1Q}\\ V_{21}& V_{22}& ...& V_{2q}& ...& V_{2Q}\\ .& .& & .& & .\\ .& .& & .& & .\\ .& .& & .& & .\\ V_{n1}& V_{n2}& ...& V_{\mathrm{nq}}& ...& V_{\mathrm{nQ}}\\ .& .& & .& & .\\ .& .& & .& & .\\ .& .& & .& & .\\ V_{N1}& V_{N2}& ...& V_{\mathrm{Nq}}& ...& V_{\mathrm{NQ}}\end{array}\right]}_{N\&times;Q},$

Wherein, s _mn(t) represent n the microwave signal that array element is launched under m pulse.

From the character of rank of matrix, the wherein order of R () representing matrix, by setting above, N<M<Q, known radiation field matrix order be N to the maximum.

In the time that emission array rotates, under each pulse, the array manifold matrix of N array element changes, thereby cause the radiation field vector under each pulse to change, therefore, order R (A)≤min (M of the radiation field matrix A under M pulse, Q), wherein M<Q, is also that the order of radiation field matrix A is M to the maximum.Therefore radiation field rank of matrix when radiation field rank of matrix is much smaller than array rotation in the time that array does not rotate.Randomness and spatial degrees of freedom are reasonable when the angle of matrix knowledge has reflected that raising radiation field under rotation array model is empty.

Step 7, the vectorization form of target setting reflection coefficient vector σ is [σ ₁, σ ₂..., σ _q..., σ _q] ^t, σ _qrepresent the target reflection factor of q probe unit, q=1,2 ..., Q;

Utilize M radiation field matrix A and the target reflection factor vector σ under pulse to be write the original echo vector Y under M pulse of radar reception as following form:

Y＝Aσ+w

Wherein, A is the radiation field matrix of M the probe unit of the Q under pulse, and w represents the white Gaussian noise vector that the dimension of setting is M × 1.

In step 7, the form of given original echo vector Y has reflected radiation field matrix A associated of original echo vector Y and Q probe unit under M pulse.

It should be noted that, because test surface is divided into the probe unit of E × F, the target reflection factor matrix σ ' of Q probe unit is expressed as:

${\mathrm{\&sigma;}}^{\&prime;}={\left[\begin{array}{cccccc}{\mathrm{\&sigma;}}_{11}& {\mathrm{\&sigma;}}_{12}& ...& {\mathrm{\&sigma;}}_{1f}& ...& {\mathrm{\&sigma;}}_{1F}\\ {\mathrm{\&sigma;}}_{21}& {\mathrm{\&sigma;}}_{22}& ...& {\mathrm{\&sigma;}}_{2f}& ..& {\mathrm{\&sigma;}}_{2F}\\ .& .& & .& & .\\ .& .& & .& & .\\ .& .& & .& & .\\ {\mathrm{\&sigma;}}_{e1}& {\mathrm{\&sigma;}}_{e2}& ...& {\mathrm{\&sigma;}}_{\mathrm{ef}}& ...& {\mathrm{\&sigma;}}_{\mathrm{eF}}\\ .& .& & .& & .\\ .& .& & .& & .\\ .& .& & .& & .\\ {\mathrm{\&sigma;}}_{E1}& {\mathrm{\&sigma;}}_{E2}& ...& {\mathrm{\&sigma;}}_{\mathrm{Ef}}& ...& {\mathrm{\&sigma;}}_{\mathrm{EF}}\end{array}\right]}_{E\&times;F}$

Wherein, σ _efrepresent the target reflection factor of the capable f row of e probe unit.

Target reflection factor matrix σ ' vectorization processing is obtained to target reflection factor vector σ, and the dimension of σ is Q × 1, σ=[σ ₁, σ ₂..., σ _q..., σ _q] ^t, wherein, [] ^trepresent transposition, σ _qrepresent the target reflection factor of q probe unit.

In same probe unit, think that target reflection factor and radiation field are identical, if aimless words are just set to zero target reflection factor on some probe units.

Step 8, sets up the objective function of target reflection factor vector σ, using Y=A σ+w as bound for objective function, solves the objective function of target reflection factor vector σ under bound for objective function, obtains target reflection factor vector σ.

Objective function and the bound for objective function of target reflection factor vector σ are following formula:

$\underset{\mathrm{\&sigma;}}{\min }\{Q-F_{{\mathrm{\&alpha;}}_j}\left(\mathrm{\&sigma;}\right)\}$

Constraint condition Y=A σ+w

Wherein, Q is probe unit sum, $F_{{\mathrm{\&alpha;}}_j}\left(\mathrm{\&sigma;}\right)=\underset{q=1}{\overset{Q}{\mathrm{\&Sigma;}}}{f}_{{\mathrm{\&alpha;}}_j}\left({\mathrm{\&sigma;}}_q\right),f_{{\mathrm{\&alpha;}}_j}\left({\mathrm{\&sigma;}}_q\right)=\exp ({{-\mathrm{\&sigma;}}_q}^2/{{2\mathrm{\&alpha;}}_j}^2),$ α _jthe element variable in the descending series of setting, j=1,2 ..., J, the element number in the descending series that J sets, σ is target reflection factor vector, σ _qbe the target reflection factor of q probe unit, A is the radiation field matrix of M the probe unit of the Q under pulse.

Under constraint condition Y=A σ+w, solve the objective function of target reflection factor vector σ be equivalent under constraint condition Y=A σ+w and solve and make maximum target reflection factor vector σ.

Under bound for objective function, solve the objective function of target reflection factor vector σ, concrete steps:

8a) target setting reflection coefficient vector initial value is σ ₁=A ^h(AA ^h) ^-1y, wherein A is the radiation field matrix of M the probe unit of the Q under pulse, sets descending series [α ₁, α ₂..., α _j..., α _j], wherein the relation between element meets α _j=η α _j-1, j=2 ..., J, η ∈ (0.5,1] be constant, α ₁=2max (σ ₁), α _j<0.01;

8b) utilize j element α in descending series _jstructure gradient vector $\underset{j}{{\mathrm{\&Delta;\&sigma;}}_{k-1}}=[\underset{j}{{\mathrm{\&sigma;}}_{k-\mathrm{1,1}}}\exp \left(\frac{-\underset{j}{{\mathrm{\&sigma;}}_{k-\mathrm{1,1}}^2}}{{{2\mathrm{\&alpha;}}_j}^2}\right),\underset{j}{{\mathrm{\&sigma;}}_{k-\mathrm{1,2}}}\exp \left(\frac{-\underset{j}{{\mathrm{\&sigma;}}_{k-\mathrm{1,2}}^2}}{{{2\mathrm{\&alpha;}}_j}^2}\right),...,\underset{j}{{\mathrm{\&sigma;}}_{k-1,q}}\exp \left(\frac{\underset{j}{{-\mathrm{\&sigma;}}_{k-1,q}^2}}{{{2\mathrm{\&alpha;}}_j}^2}\right),...,\underset{j}{{\mathrm{\&sigma;}}_{k-1,Q}}\exp \left(\frac{\underset{j}{{-\mathrm{\&sigma;}}_{k-1,Q}^2}}{{{2\mathrm{\&alpha;}}_j}^2}\right)],$ Wherein exp represents exponent arithmetic, represent to utilize j element α _jthe target reflection factor obtaining is to k-1 iterative value of flow control in q element, q=1,2 ..., Q, Q represents probe unit sum, represent to ask the local derviation of function;

8c) structure utilizes j element α _jthe target reflection factor obtaining is to k iterative value of flow control wherein step factor μ=2;

By j element α _jthe target reflection factor obtaining is to k iterative value σ of flow control _kconvert: ← represent to use the vector on the right to replace the vector on the left side, and $\underset{j}{{\mathrm{\&sigma;}}_k}=[{\underset{j}{{\mathrm{\&sigma;}}_{k,1}},\underset{j}{{\mathrm{\&sigma;}}_{k,2}},...,\underset{j}{{\mathrm{\&sigma;}}_{k,q}},...,\underset{j}{{\mathrm{\&sigma;}}_{k,Q}}]}^T;$

8e) make k from 1 to K, repeating step 8b) to step 8d), obtain j element α _junder target reflection factor vector wherein, the iterations that K sets, is positive integer K ∈ [3,20];

8f) make j from 1 to J, repeating step 8b) to step 8e), obtain J element α _junder target reflection factor vector by J element α _junder target reflection factor vector as target reflection factor vector σ.

Step 9, by target reflection factor vector be arranged as E × F by Q × 1 dimension and tie up matrix, obtain the target reflection factor matrix of resetting $\stackrel{\&OverBar;}{\mathrm{\&sigma;}}={\left[\begin{array}{cccc}{\mathrm{\&sigma;}}_1& {\mathrm{\&sigma;}}_{E+1}& ...& {\mathrm{\&sigma;}}_{(F-1)E+1}\\ {\mathrm{\&sigma;}}_2& {\mathrm{\&sigma;}}_{E+2}& ...& {\mathrm{\&sigma;}}_{(F-1)E+2}\\ .& .& & .\\ .& .& & .\\ .& .& & .\\ {\mathrm{\&sigma;}}_E& {\mathrm{\&sigma;}}_{2E}& ...& {\mathrm{\&sigma;}}_Q\end{array}\right]}_{E\&times;F},$ The target reflection factor matrix of resetting it is the imaging array of target.

The above-mentioned embodiment describing by reference to accompanying drawing is exemplary, only for explaining the present invention, and can not be interpreted as limitation of the present invention.

Below in conjunction with emulation experiment, effect of the present invention is described further.

1. simulated conditions

Consider the each array element launched microwave of rotation emission array random coding signal, array aperture D=4m, transponder pulse is counted M=400, carrier frequency f _c=3GHz, carrier wavelength lambda=c/f _c=0.1m, wherein c is the light velocity, array rotation angular velocity is 12 revs/min, the distance r between true origin and probe unit ₀=1km, Rayleigh diffraction-limited α=r ₀λ/D=25m, in this experiment, resolution element size is 1.3m × 1.3m, has broken through more than 5 times Rayleigh diffraction-limited.Receiver adopts single antenna, single, receives array element and is positioned at true origin place.

2. emulation content

Under described simulated conditions, test as follows:

Experiment one, rotation emission array array number is 15, target scene is 150 point targets, wherein every 15 the composition one row bar targets that connect together, totally 10 row.Adopt formation method of the present invention to carry out simulation imaging to 150 point targets in Fig. 4, simulation result as shown in Figure 5.

Simulation result from Fig. 5 can be found out, when 15 array elements are reconstructed 150 point targets, imaging effect is fine, target image is very clear, therefore adopt formation method of the present invention can make system restructural target numbers improve 10 times than array element number, when empty, random radiation field has realized the expansion of 10 times of degree of freedom.

Experiment two, rotation emission array array number is 15, and target scene is 150 targets in blocks, and totally 15 row 10 are listed as.Adopt formation method of the present invention to carry out simulation imaging to 150 targets in blocks in Fig. 6, simulation result as shown in Figure 7.

Simulation result from Fig. 7 can be found out, when 15 array elements are reconstructed 150 targets in blocks, imaging effect is better, and target image is more clear, therefore in the time that target numbers is 10 times of array element number, adopt formation method of the present invention also fine to the recovery effects of target in blocks.

The simulation result of experiment one and experiment two shows, is breaking through in 5 times of Rayleigh diffraction-limited situations, adopts formation method of the present invention can make system restructural target numbers improve 10 times than array element number, has realized the high-resolution imaging to large scene target.

Experiment three, rotation emission array array number is 25, and system signal noise ratio is 10dB, and target scene is 90 point targets, wherein every 9 the composition one row bar targets that connect together, totally 10 row.Adopt formation method of the present invention to carry out simulation imaging to 90 point targets in Fig. 8, simulation result as shown in Figure 9.

Simulation result from Fig. 9 can be found out, is 10dB in signal to noise ratio (S/N ratio), breaks through 5 times of Rayleigh diffraction-limited, the sparse target numbers of scene exceedes in the situation of array element number, while adopting formation method of the present invention to be reconstructed target, imaging effect is better, and target image is very clear.

Experiment four, rotation emission array array number is 25, and system signal noise ratio is 10dB, and target scene is 90 targets in blocks, and totally 9 row 10 are listed as, and adopt formation method of the present invention to carry out simulation imaging to 90 targets in blocks in Figure 10, and simulation result is as shown in figure 11.

Simulation result from Figure 11 can be found out, is 10dB in signal to noise ratio (S/N ratio), breaks through 5 times of Rayleigh diffraction-limited, the sparse target numbers of scene exceedes in the situation of array element number, and while adopting formation method of the present invention to be reconstructed target in blocks, imaging effect is better, target image is more clear

Experiment three and experiment four simulation result show, utilizes the formation method of the present invention can be at low signal-to-noise ratio, and the sparse target numbers of target scene exceedes in the situation of array element number, realizes the target imaging of breaking through more than 5 times Rayleigh diffraction-limited.

To sum up, this simulating, verifying correctness of the present invention, realizability and reliability.

Claims (6)

1. the microwave relevance imaging method based on radar rotation emission array, is characterized in that, comprises the following steps:

Step 1, radar rotation emission array is the two-dimensional array with N array element, and the array element of radar rotation emission array is distributed on a disc, and the receiver of radar is positioned at the center of circle of disc, the axis that array element place disc is walked around the center of circle rotates with angular velocity omega, and the axis in the described center of circle is perpendicular to disc; N is natural number;

Step 2, radar rotation emission array is launched the microwave signal of M pulse to test surface, and receives the original echo data Y under M pulse; M is natural number;

Described test surface is divided into E × F probe unit, probe unit sum Q=E × F, wherein, E represents horizontal detection unit number, and F represents longitudinal probing unit number, and E, F are respectively natural number, and Q>M, M represents radar rotation emission array transponder pulse number;

Step 3, under m pulse, n array element is s to q probe unit launched microwave signal indication _mn(t) echoed signal that, radar receiver receives q probe unit is expressed as s _mn(t-τ _mnq), ask for launched microwave signal s _mn(t) with echoed signal s _mn(t-τ _mnq) between time delay τ _mnq, wherein, t represents the time, m=1, and 2 ..., M, n=1,2 ..., N, q=1,2 ..., Q, M represents radar rotation emission array transponder pulse number, and N represents the transmitting array number of radar rotation emission array, and Q represents probe unit sum;

Step 4, utilizes time delay τ _mnqask for the steering vector V of N relative q the probe unit of array element under m pulse _mq, V _mqdimension is N × 1; And then obtain the array manifold matrix V of N the relative Q of an array element probe unit under m pulse _m, V _mdimension is N × Q;

Step 5, sets n the microwave signal s that array element is launched to q probe unit under m pulse _mn(t) equal the echoed signal s of q probe unit that receiver receives _mn(t-τ _mnq), i.e. s _mn(t-τ _mnq)=s _mn(t), the echoed signal vector under m pulse:

s _m(t)＝[s _m1(t),s _m2(t),...,s _mn(t),...,s _mN(t)] _1×N；m＝1,2,...,M,n＝1,2,...,N,q＝1,2,...,Q；

Step 6, utilizes the array manifold matrix V of m the relative Q of the array element of the N under a pulse probe unit _mwith the echoed signal vector s under m pulse _m(t), build the radiation field vector A under m pulse _m=s _m(t) V _m, dimension is 1 × Q and then obtains M the radiation field matrix under pulse a dimension is M × Q, wherein [] ^trepresent transposition;

Step 7, the vectorization form of target setting reflection coefficient vector σ is [σ ₁, σ ₂..., σ _q..., σ _q] ^t, wherein [] ^trepresent transposition, σ _qrepresent the target reflection factor of q probe unit, q=1,2 ..., Q;

Utilize M radiation field matrix A and the target reflection factor vector σ under pulse to be write the original echo vector Y under M pulse of radar reception as following form:

Y＝Aσ+w

Wherein, A represents the radiation field matrix of M the probe unit of the Q under pulse, and w represents the white Gaussian noise vector that the dimension of setting is M × 1;

Step 8, sets up the objective function of target reflection factor vector σ, using Y=A σ+w as bound for objective function, solves the objective function of target reflection factor vector σ under bound for objective function, obtains target reflection factor to σ, σ=[σ ₁, σ ₂..., σ _q..., σ _q] ^t=[σ ₁, σ ₂..., σ _e, σ _e+1, σ _e+2..., σ _2E..., σ _{(F-1) E+1}, σ _(F-1xE+2..., σ _q] ^t, wherein [] ^trepresent transposition, Q=E × F, E represents horizontal detection unit number, F represents longitudinal probing unit number;

Step 9, is arranged as E × F by target reflection factor vector σ by Q × 1 dimension and ties up matrix, obtains the target reflection factor matrix of resetting $\stackrel{\&OverBar;}{\mathrm{\&sigma;}}={\left[\begin{array}{cccc}{\mathrm{\&sigma;}}_1& {\mathrm{\&sigma;}}_{E+1}& ...& {\mathrm{\&sigma;}}_{(F-1)E+1}\\ {\mathrm{\&sigma;}}_2& {\mathrm{\&sigma;}}_{E+2}& ...& {\mathrm{\&sigma;}}_{(F-1)E+2}\\ .& .& & .\\ .& .& & .\\ .& .& & .\\ {\mathrm{\&sigma;}}_E& {\mathrm{\&sigma;}}_{2E}& ...& {\mathrm{\&sigma;}}_Q\end{array}\right]}_{E\&times;F},$ The target reflection factor matrix of resetting it is the imaging array of target.

2. a kind of microwave relevance imaging method based on radar rotation emission array according to claim 1, is characterized in that, step 3 comprises:

In rectangular coordinate system in space, the receiver of setting radar is positioned at the center of circle of disc at the initial point place of rectangular coordinate system in space, and the coordinate of q probe unit is (x _q, y _q, z _q), the pass between the coordinate figure of q probe unit is:

z _q ²＝r ₀ ²-x _q ²-y _q ²

The rotational time of setting radar rotation emission array under m pulse is Δ t _m, rotational time is that radar rotation emission array never rotated to the time of rotation, n array element is through rotational time Δ t _mafter coordinate be under m pulse, n array element is to the distance r between q probe unit _mnqfor:

$\begin{array}{c}{r}_{\mathrm{mnq}}=\sqrt{{({\tilde{x}}_{\mathrm{mn}}-x_q)}^2+{({\tilde{y}}_{\mathrm{mn}}-y_q)}^2+{(z_q-0)}^2}\\ =\sqrt{{({\tilde{x}}_{\mathrm{mn}}-x_q)}^2+{({\tilde{y}}_{\mathrm{mn}}-y_q)}^2+{r_0}^2-{x_q}^2-{y_q}^2}\\ =\sqrt{{r_0}^2+{\tilde{x}}_{\mathrm{mn}}^2+{\tilde{y}}_{\mathrm{mn}}^2-{2x}_q{\tilde{x}}_{\mathrm{mn}}-{2y}_q{\tilde{y}}_{\mathrm{mn}}}\end{array}$

Wherein, m=1,2 ..., M, n=1,2 ..., N, q=1,2 ..., Q, M represents radar rotation emission array transponder pulse number, and N represents the transmitting array number of radar rotation emission array, and Q represents probe unit sum;

Set radar test surface in the initial point taking rectangular coordinate system in space as the centre of sphere, radius be r ₀sphere on, set the spherical radius r at test surface place ₀at least be greater than 50 times, with n array element through rotational time Δ t _mafter coordinate for variable, use Taylor series to locate to launch n array element to the distance r between q probe unit at point (0,0,0) _mnq:

$\begin{array}{c}{r}_{\mathrm{mnq}}=r_{\mathrm{mnq}}{|}_{\left(\mathrm{0,0,0}\right)}+{\tilde{x}}_{\mathrm{mn}}\left(\frac{{\&PartialD;r}_{\mathrm{mnq}}}{\&PartialD;{\tilde{x}}_{\mathrm{mn}}}{|}_{\left(\mathrm{0,0,0}\right)}\right)+{\tilde{y}}_{\mathrm{mn}}\left(\frac{{\&PartialD;r}_{\mathrm{mnq}}}{\&PartialD;{\tilde{y}}_{\mathrm{mn}}}{|}_{\left(\mathrm{0,0,0}\right)}\right)+O\\ \&ap;r_0-\frac{x_q{\tilde{x}}_{\mathrm{mn}}+y_q{\tilde{y}}_{\mathrm{mn}}}{r_0}\end{array}$

Wherein, r _mnq| _(0,0,0)represent r _mnqthe value of locating at point (0,0,0), represent r _mnqright ask the value of locating at point (0,0,0) after local derviation, represent r _mnqright ask the value of locating at point (0,0,0) after local derviation, r ₀for the test surface of the radar radius in sphere, be also the initial point of rectangular coordinate system in space to the distance of each probe unit, O represents Lagrangian type remainder;

Under m pulse, n array element launched microwave signal is to q probe unit, with the time delay τ of receiver reception echoed signal _mnqfor:

$\begin{array}{c}{\mathrm{\&tau;}}_{\mathrm{mnq}}=t_{\mathrm{mnq}}-t_0=\frac{r_{\mathrm{mnq}}-r_0}{c}=-\frac{x_q{\tilde{x}}_{\mathrm{mn}}+y_q{\tilde{y}}_{\mathrm{mn}}}{{\mathrm{cr}}_0}\\ =-R_n\frac{\cos ({\mathrm{\&omega;\&Delta;t}}_m+{\mathrm{\&theta;}}_n)x_q+\sin ({\mathrm{\&omega;\&Delta;t}}_m+{\mathrm{\&theta;}}_n)y_q}{{\mathrm{cr}}_0}\end{array}$

Wherein, t _mnqrepresent the microwave signal travel-time of n array element to q probe unit, t ₀denotation coordination initial point is to the travel-time of q probe unit, and c represents the light velocity, (x _q, y _q, z _q) represent the coordinate of q probe unit, represent that n array element is through rotational time Δ t _mafter coordinate, R _nrepresent the distance of n array element to true origin, Δ t _mrepresent the rotational time of radar rotation emission array under m pulse, r ₀the initial point of representation space rectangular coordinate system is to the distance of each probe unit, and ω represents to rotate the angular velocity of emission array rotation, θ _nbe n element position and the axial angle of x.

3. a kind of microwave relevance imaging method based on radar rotation emission array according to claim 1, is characterized in that, step 4 comprises:

Steering vector V _mqexpression formula be: V _mq=[V _m1q, V _m2q..., V _mnq..., V _mNq] ^t, wherein, [] ^trepresent transposition,

$\begin{array}{c}{V}_{\mathrm{mnq}}=\exp (-j2\mathrm{\&pi;}{f}_c{\mathrm{\&tau;}}_{\mathrm{mnq}})\\ =\exp \left\{{j2\mathrm{\&pi;f}}_c{R}_n\frac{\cos ({\mathrm{\&omega;\&Delta;t}}_m+{\mathrm{\&theta;}}_n)x_q+\sin ({\mathrm{\&omega;\&Delta;t}}_m+{\mathrm{\&theta;}}_n)y_q}{{\mathrm{cr}}_0}\right\}\end{array}$

Wherein, f _crepresent carrier frequency, c represents the light velocity, (x _q, y _q, z _q) represent the coordinate of q probe unit, R _nrepresent the distance of n array element to true origin, Δ t _mrepresent the rotational time of radar rotation emission array under m pulse, r ₀the initial point of representation space rectangular coordinate system is to the distance of each probe unit, and ω represents to rotate the angular velocity of emission array rotation, θ _nbe n element position and the axial angle of x;

Under m pulse, the array manifold matrix of N the relative Q of an array element probe unit is V _m, expression formula is:

$V_m={\left[\begin{array}{cccccc}{V}_{m11}& V_{m12}& ...& V_{m1q}& ...& V_{m1Q}\\ V_{m21}& V_{m22}& ...& V_{m2q}& ...& V_{m2Q}\\ .& .& .& .& .& .\\ .& .& .& .& .& .\\ .& .& .& .& .& .\\ V_{\mathrm{mn}1}& V_{\mathrm{mn}1}& ...& V_{\mathrm{mnq}}& ...& V_{\mathrm{mnQ}}\\ .& .& .& .& .& .\\ .& .& .& .& .& .\\ .& .& .& .& .& .\\ V_{\mathrm{mN}1}& V_{\mathrm{mN}2}& ...& V_{\mathrm{mNq}}& ...& V_{\mathrm{mNQ}}\end{array}\right]}_{N\&times;Q}$

The array manifold matrix V=[V of N the relative Q of an array element probe unit under M pulse ₁, V ₂..., V _m..., V _m] ^t.

4. a kind of microwave relevance imaging method based on radar rotation emission array according to claim 3, is characterized in that, step 6 comprises:

Radiation field vector A under m pulse _mexpression formula:

$A_m={[s_{m1}\left(t\right),s_{m2}\left(t\right),...,s_{\mathrm{mn}}\left(t\right),...,s_{\mathrm{mN}}\left(t\right)]}_{1\&times;N}{\&CenterDot;\left[\begin{array}{cccccc}{V}_{m11}& V_{m12}& ...& V_{m1q}& ...& V_{m1Q}\\ V_{m21}& V_{m22}& ...& V_{m2q}& ...& V_{m2Q}\\ .& .& & .& & .\\ .& .& & .& & .\\ .& .& & .& & .\\ V_{\mathrm{mn}1}& V_{\mathrm{mn}1}& ...& V_{\mathrm{mnq}}& ...& V_{\mathrm{mnQ}}\\ .& .& & .& & .\\ .& .& & .& & .\\ .& .& & .& & .\\ V_{\mathrm{mN}1}& V_{\mathrm{mN}2}& ...& V_{\mathrm{mNq}}& ...& V_{\mathrm{mNQ}}\end{array}\right]}_{N\&times;Q}$

Wherein, m=1,2 ... M, s _mn(t) represent n the microwave signal that array element is launched under m pulse, V _mnqbe illustrated under m pulse, the steering vector of n relative q the probe unit of array element, " " representing matrix multiplies each other;

Radiation field matrix A=[A under M pulse ₁, A ₂..., A _m... A _m] ^t.

5. a kind of microwave relevance imaging method based on radar rotation emission array according to claim 1, is characterized in that, step 8 comprises:

Objective function and the bound for objective function of target reflection factor vector σ are following formula:

$\underset{\mathrm{\&sigma;}}{\min }\{Q-F_{{\mathrm{\&alpha;}}_j}\left(\mathrm{\&sigma;}\right)\}$

Constraint condition Y=A σ+w

Wherein, Q represents probe unit sum, $F_{{\mathrm{\&alpha;}}_j}\left(\mathrm{\&sigma;}\right)=\underset{q=1}{\overset{Q}{\mathrm{\&Sigma;}}}{f}_{{\mathrm{\&alpha;}}_j}\left({\mathrm{\&sigma;}}_q\right),f_{{\mathrm{\&alpha;}}_j}\left({\mathrm{\&sigma;}}_q\right)=\exp ({{-\mathrm{\&sigma;}}_q}^2/{{2\mathrm{\&alpha;}}_j}^2),$ α _jelement variable in the descending series that represents to set, j=1,2 ..., J, the element number in the descending series that J represents to set, σ is target reflection factor vector, exp represents exponent arithmetic, σ _qrepresent the target reflection factor of q probe unit, A represents the radiation field matrix of M the probe unit of the Q under pulse.

6. a kind of microwave relevance imaging method based on radar rotation emission array according to claim 5, is characterized in that, the objective function that solves target reflection factor vector σ under bound for objective function specifically comprises:

8a) target setting reflection coefficient vector initial value is σ ₁=A ^h(AA ^h) ^-1y, wherein [] ^-1representing matrix is inverted, and A represents the radiation field matrix of M the probe unit of the Q under pulse;

Set descending series [α ₁, α ₂..., α _j..., α _j], wherein the relation between element meets α _j=η α _j-1, j=2 ..., J, η ∈ (0.5,1] be constant, α ₁=2max (σ ₁), α _j<0.01;

8b) utilize j element α in descending series _jstructure gradient vector

$\underset{j}{{\mathrm{\&Delta;\&sigma;}}_{k-1}}=[\underset{j}{{\mathrm{\&sigma;}}_{k-\mathrm{1,1}}}\exp \left(\frac{-\underset{j}{{\mathrm{\&sigma;}}_{k-\mathrm{1,1}}^2}}{{{2\mathrm{\&alpha;}}_j}^2}\right),\underset{j}{{\mathrm{\&sigma;}}_{k-\mathrm{1,2}}}\exp \left(\frac{-\underset{j}{{\mathrm{\&sigma;}}_{k-\mathrm{1,2}}^2}}{{{2\mathrm{\&alpha;}}_j}^2}\right),...,\underset{j}{{\mathrm{\&sigma;}}_{k-1,q}}\exp \left(\frac{\underset{j}{{-\mathrm{\&sigma;}}_{k-1,q}^2}}{{{2\mathrm{\&alpha;}}_j}^2}\right),...,\underset{j}{{\mathrm{\&sigma;}}_{k-1,Q}}\exp \left(\frac{\underset{j}{{-\mathrm{\&sigma;}}_{k-1,Q}^2}}{{{2\mathrm{\&alpha;}}_j}^2}\right)]$ , wherein exp represents exponent arithmetic, represent to utilize j element α _jthe target reflection factor obtaining is to k-1 iterative value of flow control in q element, q=1,2 ..., Q, Q represents probe unit sum;

8c) structure utilizes j element α _jthe target reflection factor obtaining is to k iterative value of flow control wherein step factor μ=2;

By j element α _jthe target reflection factor obtaining is to k iterative value σ of flow control _kconvert: wherein, [] ^-1representing matrix is inverted, ← represent to use the vector on the right to replace the vector on the left side, and $\underset{j}{{\mathrm{\&sigma;}}_k}=[{\underset{j}{{\mathrm{\&sigma;}}_{k,1}},\underset{j}{{\mathrm{\&sigma;}}_{k,2}},...,\underset{j}{{\mathrm{\&sigma;}}_{k,q}},...,\underset{j}{{\mathrm{\&sigma;}}_{k,Q}}]}^T,$ Wherein [] ^trepresent transposition;

8e) make k from 1 to K, repeating step 8b) to step 8d), obtain j element α _junder target reflection factor vector wherein, the iterations that K sets, is positive integer;

8f) make j from 1 to J, repeating step 8b) to step 8e), obtain J element α _junder target reflection factor vector by J element α _junder target reflection factor vector as target reflection factor vector σ.