CN106646421A - Joint designing method for MIMO radar waveform based on three-dimensional heterogeneous array - Google Patents

Abstract

The invention discloses a joint designing method for MIMO radar waveform based on three-dimensional heterogeneous array. The method mainly comprises: determining a MIMO radar wherein the MIMO radar is a three-dimensional heterogeneous array; dividing the three-dimensional heterogeneous array into N layers; setting the range of the azimuth (theta) of a to-be-observed target as Omega and the range of the pitch angle (shown in the figure) of the to-be-observed target as Gamma respectively; then dividing the Omega into Kaz grids and Gamma into Kel grids; making t represented from the set of 1, 2, ..., N; calculating the acquisition probability of the transmitted signal (shown in the figure) of the Kel-th grid of the t-th layer matrix in the Z-axis direction and calculating the acquisition probability of the fundamental beam transmission signal (shown in the figure) at the kaz-th grid of the t-th layer matrix in the X-axis direction so as to calculate the transmission signal St of the t-th layer matrix; making t added by 1 until the transmission signal SN of the N-th layer matrix is obtained; and in such a case, based on the transmission signal S1 of the first layer matrix to the transmission signal SN of the N-th layer matrix, calculating the MIMO radar waveform of the three-dimensional heterogeneous array.

Description

MIMO radar waveform co-design method based on three-dimensional nonuniform noise

Technical field

It is more particularly to a kind of based on three-dimensional nonuniform noise the invention belongs to MIMO radar waveform design field MIMO radar combines waveform design method, it is adaptable to the detection of airborne radar target and tracking, lifts airborne cubical array radar The flexibility of mode of operation and detection performance, and the diversity ability of signal is improved on the premise of adaptation airborne platform.

Background technology

In recent years, MIMO radar is the study hotspot in current Radar Technology field, is characterized in that each transmitting antenna can The different waveform of independent transmission, compared with all array element transmitting identical waveforms of traditional phased-array radar, MIMO radar has The ability of waveform diversity, can bring more transmitting frees degree, can neatly design expectation by design transmitted waveform and send out Penetrate the shape of directional diagram.

The research work of existing MIMO radar waveform method for designing at present is mainly based upon what even linear array was studied, And to even more seldom having research based on the MIMO radar waveform method for designing of face battle array and three-dimensional matrix structure so that traditional base There is no extensive practical application condition in the MIMO radar waveform method for designing of even linear array.

The content of the invention

For the deficiency of above-mentioned prior art, present invention aim at proposing a kind of MIMO radar of three-dimensional nonuniform noise Joint waveform design method, the MIMO radar joint waveform design method of this kind of three-dimensional nonuniform noise can be in array structure more Plus by Waveform Design in the case of adaptation practical application condition, to improve the detection performance of MIMO radar.

For achieving the above object, technical scheme mainly comprises the steps：

A kind of MIMO radar based on three-dimensional nonuniform noise combines waveform design method, comprises the following steps：

Step 1, determines MIMO radar, and the MIMO radar is three-dimensional nonuniform noise, and the three-dimensional nonuniform noise Be the length of side be D square；Simultaneously in three-dimensional system of coordinate XYZ, X-axis and Z axis include respectively M array element, Y-axis to the square Comprising N number of array element；Target to be observed is included in the three-dimensional system of coordinate XYZ, the position of the target to be observed isθ tables Show the azimuth of target to be observed in three-dimensional system of coordinate,Represent the angle of pitch of target to be observed in three-dimensional system of coordinate；D is nature Number；

The three-dimensional nonuniform noise along Y-axis is divided into into N layers and is numbered, the 1st aspect battle array is designated as respectively to n-th layer face battle array, Then using the steering vector at all element positions in the 1st aspect battle array as reference array element steering vector, to the 2nd aspect battle array extremely Steering vector at all element positions of n-th layer face battle array carries out respectively phase compensation, respectively obtains after Y direction phase compensation Steering vector at 2 aspect battle arrays to all element positions of n-th layer face battle array, and respectively with the 1st aspect battle array in all element positions The steering vector at place is identical, is designated asAnd the steering vector of the MIMO radar as three-dimensional nonuniform noise；

Step 2, the two dimension for determining target to be observed expects transmitting patternθ represents to be observed in three-dimensional system of coordinate The azimuth of target,The angle of pitch of target to be observed in three-dimensional system of coordinate is represented, and respectively by the side of the target to be observed The range set of parallactic angle θ is Ω, by the angle of pitch of the target to be observedRange set be Γ, then respectively by setting Scope Ω of the azimuth angle theta of target to be observed is divided into K_azIndividual grid, by the angle of pitch of the target to be observed of settingScope Γ is divided into K_elIndividual grid, subscript az represents the angle of pitch, and subscript el represents azimuth, K_azAnd K_elRespectively natural number；

Step 3, initialization：T ∈ { 1,2 ..., N }, t is made to represent t aspect battle arrays, the initial value of t is represented three-dimensional for 1, N The face battle array number of plies that nonuniform noise is included after being layered；

Step 4, calculates successively the angle of pitch desired orientation figure that t aspect battle arrays synthesize in the Z-axis directionWith t layers Face battle array kth in the Z-axis direction_elThe transmission signal of fundamental wave beam at individual gridAnd then t aspect battle arrays are calculated in Z-direction Upper kth_elThe transmission signal of fundamental wave beam at individual gridAcquisition probability

Step 5, calculates successively t aspects battle array kth in the X-axis direction_azFundamental wave beam transmission signal at individual grid With t aspects battle array kth in the X-axis direction_azFundamental wave beam transmission signal at individual gridAcquisition probability

Step 6, determines that Signal coding length L is penetrated in t aspect paroxysms^t, and calculate t aspects battle array sensing kth_azIndividual grid side Parallactic angleKth_elThe individual grid angle of pitchThe fundamental wave beam transmission signal at placeFurther calculate sending out for t aspect battle arrays Penetrate signal S^t；

Step 7, makes t plus 1, repeat step 4 to step 6, transmission signal S until obtaining n-th layer face battle array^N, now obtain Transmission signal S of the 1st aspect battle array¹Transmission signal S in face to n-th layer face battle array^N；

Step 8, according to transmission signal S of the 1st aspect battle array¹Transmission signal S in face to n-th layer face battle array^N, it is calculated three-dimensional The MIMO radar waveform of nonuniform noise

Beneficial effects of the present invention：The inventive method is in combination with software and first non-homogeneous to three-dimensional by the hardware of radar The MIMO radar of array is designed, and then designs waveform using MIMO radar waveform method for designing, can not only ensure MIMO Adaptability of the radar arrangement to platform, and there is less complexity in waveform design method, while lifting airborne three-dimensional battle array The flexibility of row MIMO radar mode of operation and detection performance.

Description of the drawings

The present invention is described in further detail with reference to the accompanying drawings and detailed description.

Fig. 1 is that a kind of MIMO radar based on three-dimensional nonuniform noise of the present invention combines waveform design method flow chart；

Fig. 2 is three-dimensional nonuniform noise schematic diagram；

Fig. 3 is three-dimensional nonuniform noise layering schematic diagram；

Fig. 4 is display schematic diagram of the position of target to be observed in the 1st aspect battle array；

Fig. 5 is the MIMO radar simple beam directional diagram obtained using the inventive method；

Fig. 6 is the MIMO radar multi-beam directional diagram obtained using the inventive method.

Specific embodiment

It is that a kind of MIMO radar based on three-dimensional nonuniform noise of the present invention combines waveform design method stream with reference to Fig. 1 Cheng Tu；The MIMO radar based on three-dimensional nonuniform noise combines waveform design method, comprises the following steps：

Step 1, determines MIMO radar, and the MIMO radar is three-dimensional nonuniform noise, is three-dimensional non-homogeneous with reference to Fig. 2 Array schematic diagram；And the three-dimensional nonuniform noise is the square that the length of side is D；Simultaneously the square is in three-dimensional system of coordinate In XYZ, X-axis and Z axis include respectively M array element, and Y-axis includes N number of array element；Mesh to be observed is included in the three-dimensional system of coordinate XYZ Mark, the position of the target to be observed isθ represents the azimuth of target to be observed in three-dimensional system of coordinate,Represent three-dimensional The angle of pitch of target to be observed in coordinate system；D is natural number.

The steering vector of array element p is at any one position in the three-dimensional system of coordinateIts Middle x represents position of array element p in X-axis in three-dimensional system of coordinate, and y represents position of array element p in Y-axis in three-dimensional system of coordinate Put, z represents position of array element p on Z axis in three-dimensional system of coordinate, θ represents the azimuth of target to be observed in three-dimensional system of coordinate, Represent the angle of pitch of target to be observed in three-dimensional system of coordinate, p ∈ D³, D represents the length of side of three-dimensional nonuniform noise.

It is three-dimensional nonuniform noise layering schematic diagram with reference to Fig. 3；The three-dimensional nonuniform noise is divided into into N layers simultaneously along Y-axis Numbering, is designated as respectively the 1st aspect battle array to n-th layer face battle array；Then by the steering vector at all element positions in the 1st aspect battle array As reference array element steering vector, phase is multiplied by respectively to the steering vector at the 2nd aspect battle array to all element positions of n-th layer face battle array Position compensating factorPhase place in compensate three-dimensional system of coordinate in Y direction, obtains the 2nd aspect battle array to n-th layer Steering vector at all element positions of face battle array is respectivelyX' is represented the 2nd layer after Y direction phase compensation Position of the array element of face battle array to n-th layer face battle array any position in X-axis, z' represents the 2nd aspect battle array after Y direction phase compensation To the position of the array element on Z axis of n-th layer face battle array any position, and then respectively obtain the 2nd aspect after Y direction phase compensation Battle array to the steering vector at all element positions of n-th layer face battle array, respectively with the 1st aspect battle array in all element positions at guiding Vector is identical, is designated asAnd the steering vector of the MIMO radar as three-dimensional nonuniform noise, its expression formula is：

Wherein,Represent the position of target to be observedGuiding vector in X-axis,Represent to be observed The angle of pitch of targetGuiding vector on Z axis, f_cThe transmission signal carrier frequency of MIMO radar is represented, c represents the light velocity, Z_iRepresent I-th element position in three-dimensional system of coordinate on Z axis, X_jRepresent j-th element position in X-axis, i ∈ in three-dimensional system of coordinate { 1,2 ..., M }, j ∈ { 1,2 ..., M }, M represents the element number of array that X-axis or Z axis are included respectively in three-dimensional system of coordinate XYZ, subscript T Transposition is represented, e represents exponential function.

Because the position of target to be observed isAnd the target to be observed is located in three-dimensional nonuniform noise, by institute State three-dimensional nonuniform noise along Y-axis be divided into N layers and number after, the 1st aspect battle array for obtaining is able to embodiment and treats to n-th layer face battle array The position of observed objectIt is display schematic diagram of the position of target to be observed in the 1st aspect battle array with reference to Fig. 4；Wherein, M_X1Represent element number of array of the position of target to be observed in X-axis in the 1st aspect battle array, M_Z1The position for representing target to be observed exists Element number of array in 1st aspect battle array on Z axis, θ represents the azimuth of target to be observed in three-dimensional system of coordinate,Represent three-dimensional coordinate The angle of pitch of target to be observed in system, and the azimuth angle theta of target to be observed is the coordinate of three-dimensional system of coordinate XYZ in three-dimensional system of coordinate In the projection of XOY and the angle of Y-axis, target to be observed bows line between origin O and target to be observed in three-dimensional system of coordinate The elevation angleThe angle of the line between origin of coordinates O and target to be observed and Z axis for three-dimensional system of coordinate XYZ.

Step 2, the two dimension for determining target to be observed expects transmitting patternθ is represented and wait in three-dimensional system of coordinate and see The azimuth of target is surveyed,The angle of pitch of target to be observed in three-dimensional system of coordinate is represented, and respectively by the target to be observed The range set of azimuth angle theta is Ω, by the angle of pitch of the target to be observedRange set be Γ, then respectively will setting Scope Ω of azimuth angle theta of target to be observed be divided into K_azIndividual grid, by the angle of pitch of the target to be observed of settingModel Enclose Γ and be divided into K_elIndividual grid, subscript az represents the angle of pitch, and subscript el represents azimuth, K_azAnd K_elRespectively natural number；This reality The scope of azimuth angle theta of the target to be observed set in example is applied as [- 45 °, 45 °], the angle of pitch of the target to be observed of setting's Scope is [45 °, 135 °].

Step 3, initialization：T ∈ { 1,2 ..., N }, t is made to represent t aspect battle arrays, the initial value of t is represented three-dimensional for 1, N The face battle array number of plies that nonuniform noise is included after being layered.

Step 4, calculates successively the angle of pitch desired orientation figure that t aspect battle arrays synthesize in the Z-axis directionWith t layers Face battle array kth in the Z-axis direction_elThe transmission signal of fundamental wave beam at individual gridAnd then t aspect battle arrays are calculated in Z-direction Upper kth_elThe transmission signal of fundamental wave beam at individual gridAcquisition probability

(4a) angle of pitch desired orientation figure that t aspect battle arrays synthesize in the Z-axis direction is calculatedIts expression formula is：

Wherein,Represent t aspects battle array kth in the Z-axis direction_azIndividual grid azimuthKth_elIndividual grid The lattice angle of pitchThe desired orientation figure at place, k_el∈{1,2,…,K_el, k_az∈{1,2,…,K_az, K_azRepresent by setting wait see Survey the grid number that scope Ω of the azimuth angle theta of target is divided, K_elRepresent the angle of pitch of the target to be observed of settingModel Enclose the grid number of Γ divisions.

(4b) t aspects battle array kth in the Z-axis direction is calculated_elThe transmission signal of fundamental wave beam at individual gridIts expression Formula is：

Wherein,T aspects battle array array element weighing vector in the Z-axis direction is represented,Represent t aspect battle arrays in Z Kth on direction of principal axis_elThe individual grid angle of pitchThe guiding vector at place, ⊙ represents that Hadamard is accumulated.

(4c) t aspects battle array kth in the Z-axis direction is calculated_elThe transmission signal of fundamental wave beam at individual gridAcquisition ProbabilityIts calculating process is：

Wherein,T aspects battle array expectation figure amplitude factor in the Z-axis direction is represented,Represent t aspect battle arrays The angle of pitch desired orientation figure for synthesizing in the Z-axis direction,Represent t aspects battle array kth in the Z-axis direction_elIndividual grid is bowed The elevation angleThe guiding vector at place,Represent t aspects battle array kth in the Z-axis direction_elThe transmitting letter of fundamental wave beam at individual grid NumberCovariance matrix,Represent t aspects battle array kth in the Z-axis direction_elThe transmitting of fundamental wave beam at individual grid Signal, k_el∈{1,2,…,K_el, K_elRepresent the angle of pitch of the target to be observed of settingThe grid that divides of scope Γ Number；When expression makes minimum with regard to functional expression, s.t. represents constraints, | | | |₂Represent 2- norms, subscript H tables Show conjugate transposition.

Step 5, calculates successively t aspects battle array kth in the X-axis direction_azFundamental wave beam transmission signal at individual grid With t aspects battle array kth in the X-axis direction_azFundamental wave beam transmission signal at individual gridAcquisition probability

(5a) t aspects battle array kth in the X-axis direction is calculated_azFundamental wave beam transmission signal at individual gridIts table It is up to formula：

Wherein,T aspects battle array array element weighing vector in the X-axis direction is represented,Represent t aspects Battle array kth in the X-axis direction_azIndividual grid azimuthKth_elThe individual grid angle of pitchThe guiding vector at place, ⊙ is represented Hadamard is accumulated.

(5b) t aspects battle array kth in the X-axis direction is calculated_azFundamental wave beam transmission signal at individual gridAcquisition ProbabilityIts calculating process is：

Wherein,T aspects battle array expectation figure amplitude factor in the X-axis direction is represented,Represent t aspects Battle array kth in the X-axis direction_azIndividual grid azimuthKth_elThe individual grid angle of pitchThe desired orientation figure at place,Represent t aspects battle array kth in the X-axis direction_azIndividual grid azimuthKth_elThe individual grid angle of pitch The guiding vector at place,Represent t aspects battle array kth in the X-axis direction_azFundamental wave beam transmission signal at individual gridCovariance matrix,Represent t aspects battle array kth in the X-axis direction_azBase beam transmission letter at individual grid Number, k_az∈{1,2,…,K_az, K_azRepresent the grid number for dividing scope Ω of the azimuth angle theta of the target to be observed of setting；When expression makes minimum with regard to functional expression, s.t. represents constraints, | | | |₂2- norms are represented, subscript H is represented Conjugate transposition.

Step 6, determines that Signal coding length L is penetrated in t aspect paroxysms^t, and calculate t aspects battle array sensing kth_azIndividual grid side Parallactic angleKth_elThe individual grid angle of pitchThe fundamental wave beam transmission signal at placeFurther calculate sending out for t aspect battle arrays Penetrate signal S^t。

(6a) determine that Signal coding length L is penetrated in t aspect paroxysms^t, and calculate t aspects battle array sensing kth_azIndividual grid orientation AngleKth_elThe individual grid angle of pitchThe fundamental wave beam transmission signal at placeIts expression formula is：

Wherein, vec represents that vectorization is operated,Represent t aspects battle array kth in the Z-axis direction_elBase at individual grid The transmission signal of wave beam,Represent t aspects battle array kth in the X-axis direction_azFundamental wave beam transmission signal at individual grid, on Mark T represents transposition.

(6b) kth is pointed in t aspects battle array_azIndividual grid azimuthKth_elThe individual grid angle of pitchThe fundamental wave beam at place Transmission signalF satisfaction of middle selection imposes a conditionFundamental wave beam transmission signal, point Wei not t aspects battle array sensing kth_azIndividual grid azimuthKth_elThe individual grid angle of pitchThe 1st base beam transmission letter at place NumberKth is pointed to t aspects battle array_azIndividual grid azimuthKth_elThe individual grid angle of pitchThe F base at place Beam transmission signalIts process is：

WhenWhen, correspond to obtain t aspects battle array kth in the X-axis direction respectively_azAt individual grid F-th fundamental wave beam transmission signalWith t aspects battle array kth in the Z-axis direction_elF-th of fundamental wave beam at individual grid Penetrate signalFurther it is calculated t aspects battle array and points to kth_azIndividual grid azimuthKth_elThe individual grid angle of pitch F-th fundamental wave beam transmission signal at placeThe t aspects battle array points to kth_azIndividual grid azimuthKth_elIt is individual The grid angle of pitchF-th fundamental wave beam transmission signal at placeLength be

Further respectively obtain t aspects battle array and point to kth_azIndividual grid azimuthKth_elThe individual grid angle of pitchPlace 1st fundamental wave beam transmission signalKth is pointed to t aspects battle array_azIndividual grid azimuthKth_elIndividual grid is bowed The elevation angleThe F fundamental wave beam transmission signal at placeAnd t aspects battle array points to kth_azIndividual grid azimuthKth_elThe individual grid angle of pitchThe 1st fundamental wave beam transmission signal at placeLengthRefer to t aspect battle arrays To kth_azIndividual grid azimuthKth_elThe individual grid angle of pitchThe F fundamental wave beam transmission signal at place's Length

Wherein,Expression is rounded downwards, f ∈ { 1,2 ..., F }, and F represents that t aspects battle array points to kth_azIndividual grid azimuth Kth_elThe individual grid angle of pitchThe fundamental wave beam transmission signal at placeMiddle satisfaction imposes a condition Fundamental wave beam transmission signal number,Represent t aspects battle array kth in the Z-axis direction_elThe transmitting letter of fundamental wave beam at individual grid NumberAcquisition probability,Represent t aspects battle array kth in the X-axis direction_azBase beam transmission letter at individual grid NumberAcquisition probability.

(6c) kth is pointed to according to t aspects battle array_azIndividual grid azimuthKth_elThe individual grid angle of pitchThe fundamental wave at place Beam transmission signalMiddle F satisfaction imposes a conditionFundamental wave beam transmission signal, calculate Obtain transmission signal S of t aspect battle arrays^t, its expression formula is：

Λ₁+…+Λ_f+…+Λ_F=L^t

Step 7, makes t plus 1, repeat step 4 to step 6, transmission signal S until obtaining n-th layer face battle array^N, now obtain Transmission signal S of the 1st aspect battle array¹Transmission signal S in face to n-th layer face battle array^N。

Step 8, according to transmission signal S of the 1st aspect battle array¹Transmission signal S in face to n-th layer face battle array^N, it is calculated three-dimensional The MIMO radar waveform of nonuniform noiseIts expression formula is：

Wherein, the face battle array number of plies that N is included after representing and being layered three-dimensional nonuniform noise, L represents three-dimensional nonuniform array The MIMO radar waveform of rowLength,Represent the steering vector of the MIMO radar of three-dimensional nonuniform noise, θ tables Show the azimuth of target to be observed,The angle of pitch of target to be observed in three-dimensional system of coordinate is represented, subscript H represents conjugate transposition.

Further checking explanation is made to effect of the present invention by the test of following simulation comparison.

(1) experiment scene：

MIMO radar is three-dimensional nonuniform noise, and the three-dimensional nonuniform array is listed in three-dimensional system of coordinate XYZ and three-dimensional non-equal Even array includes target to be observed, and X-axis and Z axis include respectively 16 array elements, and Y-axis includes 4 array elements；The transmitting letter of MIMO radar Number wavelengthC=3.0 × 10⁸M/s, f_c=3.0 × 10⁸Hz；The MIMO radar waveform of three-dimensional nonuniform noiseLength L=256；The angle of pitch of target to be observed in three-dimensional system of coordinateDraw according to 0.5 ° of interval Divide and formed the conjunction of first fundamental wave constriction, azimuth angle theta ∈ [45 °, 135 °] of target to be observed in three-dimensional system of coordinate, between 0.5 ° Close every dividing and forming second fundamental wave constriction, then three-dimensional nonuniform noise is divided into into 4 layers.

16 element positions in X-direction are：

[0 0.708619 1.53777 2.26888 2.80559 3.4345 4.0567 4.6738 5.17387 5.67594 6.22344 6.73955 7.47585 8.17668 9.14359 10]×λ

16 element positions in Z-direction are：

[0 0.708619 1.53777 2.26888 2.80559 3.4345 4.0567 4.6738 5.17387 5.67594 6.22344 6.73955 7.47585 8.17668 9.14359 10]×λ

Simple beam simulating scenes are：First fundamental wave constriction close and second fundamental wave constriction close beam center be respectively (90 °, 0 °), beam angle is respectively 15 °；

Multi-beam simulating scenes are：The beam center that first fundamental wave constriction is closed and second fundamental wave constriction is closed is respectively： (70 °, -20 °), (90 °, 0 °) and (110 °, 20 °), beam shape width is respectively：6 °, 10 ° and 6 °.

(2) emulation mode

For the method that the checking present invention is adopted, the simple beam that first fundamental wave constriction is closed and second fundamental wave constriction is closed is carried out respectively Beam pattern and multi-beam beam pattern, and carry out MATLAB simulation analysis

(3) emulation content

Emulation 1, with the inventive method simple beam beam pattern is carried out, and simulation result is as shown in figure 5, Fig. 5 is using this The MIMO radar simple beam directional diagram that inventive method is obtained.

Emulation 2, with the inventive method multi-beam beam pattern is carried out, and simulation result is as shown in fig. 6, Fig. 6 is using this The MIMO radar multi-beam directional diagram that inventive method is obtained.

(4) interpretation

The inventive method is can be seen that by simulation result Fig. 5 and Fig. 6 simple beam and multi-beam Waveform Design are delivered and had Good effect, and then there is good applicability to three-dimensional nonuniform noise.

Emulation experiment shows that the MIMO radar based on three-dimensional nonuniform noise of the present invention combines waveform design method by three Dimension nonuniform noise is combined with Waveform Design, improves the adaptability of three-dimensional nonuniform noise, and to airborne MIMO radar Object detecting and tracking have great importance.

In sum, emulation experiment demonstrates the correctness of the present invention, validity and reliability.

Obviously, those skilled in the art can carry out the essence of various changes and modification without deviating from the present invention to the present invention God and scope；So, if these modifications of the present invention and modification belong to the scope of the claims in the present invention and its equivalent technologies Within, then the present invention is also intended to comprising these changes and modification.

Claims (9)

1. a kind of MIMO radar based on three-dimensional nonuniform noise combines waveform design method, it is characterised in that including following step Suddenly：

Step 1, determines MIMO radar, and the MIMO radar is three-dimensional nonuniform noise, and the three-dimensional nonuniform noise is side The square of a length of D；Simultaneously in three-dimensional system of coordinate XYZ, X-axis and Z axis include respectively M array element to the square, and Y-axis is included N number of array element；Target to be observed is included in the three-dimensional system of coordinate XYZ, the position of the target to be observed isθ represents three The azimuth of target to be observed in dimension coordinate system,Represent the angle of pitch of target to be observed in three-dimensional system of coordinate；D is natural number；

The three-dimensional nonuniform noise along Y-axis is divided into into N layers and is numbered, the 1st aspect battle array is designated as respectively to n-th layer face battle array, then Using the steering vector at all element positions in the 1st aspect battle array as reference array element steering vector, to the 2nd aspect battle array to N Steering vector at all element positions of aspect battle array carries out respectively phase compensation, respectively obtains the 2nd layer after Y direction phase compensation Steering vector at face battle array to all element positions of n-th layer face battle array, and respectively with the 1st aspect battle array in all element positions at Steering vector is identical, is designated asAnd the steering vector of the MIMO radar as three-dimensional nonuniform noise；

Step 2, the two dimension for determining target to be observed expects transmitting patternθ represents target to be observed in three-dimensional system of coordinate Azimuth,The angle of pitch of target to be observed in three-dimensional system of coordinate is represented, and respectively by the azimuth angle theta of the target to be observed Range set be Ω, by the angle of pitch of the target to be observedRange set be Γ, then respectively by setting it is to be observed Scope Ω of the azimuth angle theta of target is divided into K_azIndividual grid, by the angle of pitch of the target to be observed of settingScope Γ divide For K_elIndividual grid, subscript az represents the angle of pitch, and subscript el represents azimuth, K_azAnd K_elRespectively natural number；

Step 3, initialization：T ∈ { 1,2 ..., N }, t is made to represent t aspect battle arrays, the initial value of t represents that three-dimensional is non-for 1, N The face battle array number of plies that even array is included after being layered；

Step 4, calculates successively the angle of pitch desired orientation figure that t aspect battle arrays synthesize in the Z-axis directionWith t aspect battle arrays Kth in the Z-axis direction_elThe transmission signal of fundamental wave beam at individual gridAnd then calculate t aspects battle array in the Z-axis direction the k_elThe transmission signal of fundamental wave beam at individual gridAcquisition probability

Step 5, calculates successively t aspects battle array kth in the X-axis direction_azFundamental wave beam transmission signal at individual gridWith t Aspect battle array kth in the X-axis direction_azFundamental wave beam transmission signal at individual gridAcquisition probability

Step 6, determines that Signal coding length L is penetrated in t aspect paroxysms^t, and calculate t aspects battle array sensing kth_azIndividual grid azimuthKth_elThe individual grid angle of pitchThe fundamental wave beam transmission signal at placeAnd then the transmitting letter of calculating t aspect battle arrays Number S^t；

Step 7, makes t plus 1, repeat step 4 to step 6, transmission signal S until obtaining n-th layer face battle array^N, now obtain the 1st layer Transmission signal S of face battle array¹Transmission signal S in face to n-th layer face battle array^N；

Step 8, according to transmission signal S of the 1st aspect battle array¹Transmission signal S in face to n-th layer face battle array^N, it is calculated three-dimensional non-equal The MIMO radar waveform of even array

2. a kind of MIMO radar based on three-dimensional nonuniform noise as claimed in claim 1 combines waveform design method, and it is special Levy and be, in step 1, the three-dimensional nonuniform noise is the square that the length of side is D, is also included：In the three-dimensional system of coordinate The steering vector of array element p is at any one positionWherein x represents battle array in three-dimensional system of coordinate Positions of first p in X-axis, y represents position of array element p in Y-axis in three-dimensional system of coordinate, and z represents battle array in three-dimensional system of coordinate Positions of first p on Z axis, θ represents the azimuth of target to be observed in three-dimensional system of coordinate,Represent to be observed in three-dimensional system of coordinate The angle of pitch of target, p ∈ D³, D represents the length of side of three-dimensional nonuniform noise.

3. a kind of MIMO radar based on three-dimensional nonuniform noise as claimed in claim 2 combines waveform design method, and it is special Levy and be, in step 1, the steering vector at the 2nd aspect battle array to all element positions of n-th layer face battle array carries out respectively phase Position compensation, specially：

Phase compensating factor is multiplied by respectively to the steering vector at the 2nd aspect battle array to all element positions of n-th layer face battle arrayPhase place in compensate three-dimensional system of coordinate in Y direction, obtains the 2nd aspect battle array all to n-th layer face battle array Steering vector at element position is respectivelyX' represents that the 2nd aspect battle array is extremely after Y direction phase compensation Position of the array element of n-th layer face battle array any position in X-axis, z' represents after Y direction phase compensation the 2nd aspect battle array to N Position of the array element of aspect battle array any position on Z axis.

4. a kind of MIMO radar based on three-dimensional nonuniform noise as claimed in claim 1 combines waveform design method, and it is special Levy and be, in step 1, the steering vector of the MIMO radar of the three-dimensional nonuniform noise, its expression formula is：

Wherein,Represent the position of target to be observedGuiding vector in X-axis,Represent target to be observed The angle of pitchGuiding vector on Z axis, f_cThe transmission signal carrier frequency of MIMO radar is represented, c represents the light velocity, Z_iRepresent three-dimensional I-th element position in coordinate system on Z axis, X_jJ-th element position in expression three-dimensional system of coordinate in X-axis, i ∈ 1, 2 ..., M }, j ∈ { 1,2 ..., M }, M represents the element number of array that X-axis or Z axis are included respectively in three-dimensional system of coordinate XYZ, subscript T tables Show transposition, e represents exponential function.

5. a kind of MIMO radar based on three-dimensional nonuniform noise as claimed in claim 1 combines waveform design method, and it is special Levy and be, the sub-step of step 4 is：

(4a) angle of pitch desired orientation figure that t aspect battle arrays synthesize in the Z-axis direction is calculatedIts expression formula is：

Wherein,Represent t aspects battle array kth in the Z-axis direction_azIndividual grid azimuthKth_elIndividual grid is bowed The elevation angleThe desired orientation figure at place, k_el∈{1,2,…,K_el, k_az∈{1,2,…,K_az, K_azRepresent the mesh to be observed of setting The grid number that scope Ω of target azimuth angle theta is divided, K_elRepresent the angle of pitch of the target to be observed of settingScope Γ The grid number of division；

(4b) t aspects battle array kth in the Z-axis direction is calculated_elThe transmission signal of fundamental wave beam at individual gridIts expression formula For：

Wherein,T aspects battle array array element weighing vector in the Z-axis direction is represented,Represent t aspect battle arrays in Z axis side Kth upwards_elThe individual grid angle of pitchThe guiding vector at place, ⊙ represents that Hadamard is accumulated；

(4c) t aspects battle array kth in the Z-axis direction is calculated_elThe transmission signal of fundamental wave beam at individual gridAcquisition probabilityIts calculating process is：

$\begin{array}{cc}s.t.& R_Z^t\left(k_{el}\right)=\underset{k_{el}=1}{\overset{K}{\Σ}}{P}_Z^t\left(k_{el}\right)S_Z^t\left(k_{el}\right)S_Z^{tH}\left(k_{el}\right)\end{array}$

$\underset{k_{el}=1}{\overset{K_{el}}{\Σ}}{P}_Z^t\left(k_{el}\right)=1$

$0\≤P_Z^t\left(k_{el}\right)\≤1$

Wherein,T aspects battle array expectation figure amplitude factor in the Z-axis direction is represented,Represent t aspect battle arrays in Z axis The angle of pitch desired orientation figure synthesized on direction,Represent t aspects battle array kth in the Z-axis direction_elThe individual grid angle of pitchThe guiding vector at place,Represent t aspects battle array kth in the Z-axis direction_elThe transmission signal of fundamental wave beam at individual gridCovariance matrix,Represent t aspects battle array kth in the Z-axis direction_elThe transmitting letter of fundamental wave beam at individual grid Number, k_el∈{1,2,…,K_el, K_elRepresent the angle of pitch of the target to be observed of settingScope Γ divide grid number；When expression makes minimum with regard to functional expression, s.t. represents constraints, | | | |₂2- norms are represented, subscript H is represented Conjugate transposition.

6. a kind of MIMO radar based on three-dimensional nonuniform noise as claimed in claim 1 combines waveform design method, and it is special Levy and be, the sub-step of step 5 is：

(5a) t aspects battle array kth in the X-axis direction is calculated_azFundamental wave beam transmission signal at individual gridIts expression formula For：

Wherein,T aspects battle array array element weighing vector in the X-axis direction is represented,Represent t aspect battle arrays in X Kth on direction of principal axis_azIndividual grid azimuthKth_elThe individual grid angle of pitchThe guiding vector at place, ⊙ represents Hadamard Product；

(5b) t aspects battle array kth in the X-axis direction is calculated_azFundamental wave beam transmission signal at individual gridAcquisition probabilityIts calculating process is：

$\begin{array}{cc}s.t.& R_X^t\left(k_{az}\right)=\underset{k_{az}=1}{\overset{K_{az}}{\Σ}}{P}_X^t\left(k_{az}\right)S_X^t\left(k_{az}\right){S_X^t}^H\left(k_{az}\right)\end{array}$

$\underset{K}{\overset{K_{az}}{\Σ}}{P}_X^t\left(k_{az}\right)=1$

$0\≤P_X^t\left(k_{az}\right)\≤1$

Wherein,T aspects battle array expectation figure amplitude factor in the X-axis direction is represented,Represent that t aspect battle arrays exist Kth in X-direction_azIndividual grid azimuthKth_elThe individual grid angle of pitchThe desired orientation figure at place,Table Show t aspects battle array kth in the X-axis direction_azIndividual grid azimuthKth_elThe individual grid angle of pitchThe guiding vector at place,Represent t aspects battle array kth in the X-axis direction_azFundamental wave beam transmission signal at individual gridCovariance square Battle array,Represent t aspects battle array kth in the X-axis direction_azFundamental wave beam transmission signal at individual grid, k_az∈{1,2,…, K_az, K_azRepresent the grid number for dividing scope Ω of the azimuth angle theta of the target to be observed of setting；Expression makes minimum When with regard to functional expression, s.t. represents constraints, | | | |₂2- norms are represented, subscript H represents conjugate transposition.

7. a kind of MIMO radar based on three-dimensional nonuniform noise as claimed in claim 1 combines waveform design method, and it is special Levy and be, the sub-step of step 6 is：

(6a) determine that Signal coding length L is penetrated in t aspect paroxysms^t, and calculate t aspects battle array sensing kth_azIndividual grid azimuthKth_elThe individual grid angle of pitchThe fundamental wave beam transmission signal at placeIts expression formula is：

Wherein, vec represents that vectorization is operated,Represent t aspects battle array kth in the Z-axis direction_elFundamental wave beam at individual grid Transmission signal,Represent t aspects battle array kth in the X-axis direction_azFundamental wave beam transmission signal at individual grid, subscript T tables Show transposition；

(6b) kth is pointed in t aspects battle array_azIndividual grid azimuthKth_elThe individual grid angle of pitchThe base beam transmission at place SignalF satisfaction of middle selection imposes a conditionFundamental wave beam transmission signal, respectively T aspects battle array points to kth_azIndividual grid azimuthKth_elThe individual grid angle of pitchThe 1st fundamental wave beam transmission signal at placeKth is pointed to t aspects battle array_azIndividual grid azimuthKth_elThe individual grid angle of pitchThe F fundamental wave at place Beam transmission signal

(6c) kth is pointed to according to t aspects battle array_azIndividual grid azimuthKth_elThe individual grid angle of pitchThe fundamental wave beam at place is sent out Penetrate signalMiddle F satisfaction imposes a conditionFundamental wave beam transmission signal, be calculated Transmission signal S of t aspect battle arrays^t, its expression formula is：

Λ₁+…+Λ_f+…+Λ_F=L^t

Wherein, f ∈ { 1,2 ..., F }, F represent that t aspects battle array points to kth_azIndividual grid azimuthKth_elThe individual grid angle of pitchThe fundamental wave beam transmission signal at placeMiddle satisfaction imposes a conditionBase beam transmission letter Number number.

8. a kind of MIMO radar based on three-dimensional nonuniform noise as claimed in claim 7 combines waveform design method, and it is special Levy and be, the t aspects battle array points to kth_azIndividual grid azimuthKth_elThe individual grid angle of pitch1st fundamental wave at place Beam transmission signalKth is pointed to t aspects battle array_azIndividual grid azimuthKth_elThe individual grid angle of pitchPlace The F fundamental wave beam transmission signalIt obtains process：

WhenWhen, correspond to obtain t aspects battle array kth in the X-axis direction respectively_azF at individual grid Individual fundamental wave beam transmission signalWith t aspects battle array kth in the Z-axis direction_elF-th transmitting letter of fundamental wave beam at individual grid NumberFurther it is calculated t aspects battle array and points to kth_azIndividual grid azimuthKth_elThe individual grid angle of pitchPlace F-th fundamental wave beam transmission signalThe t aspects battle array points to kth_azIndividual grid azimuthKth_elIndividual grid The angle of pitchF-th fundamental wave beam transmission signal at placeLength be

Further respectively obtain t aspects battle array and point to kth_azIndividual grid azimuthKth_elThe individual grid angle of pitchThe 1st of place Fundamental wave beam transmission signalKth is pointed to t aspects battle array_azIndividual grid azimuthKth_elThe individual grid angle of pitch The F fundamental wave beam transmission signal at placeAnd t aspects battle array points to kth_azIndividual grid azimuthKth_elIt is individual The grid angle of pitchThe 1st fundamental wave beam transmission signal at placeLengthKth is pointed to t aspects battle array_azIndividual grid Lattice azimuthKth_elThe individual grid angle of pitchThe F fundamental wave beam transmission signal at placeLength

Wherein,Expression is rounded downwards, f ∈ { 1,2 ..., F }, and F represents that t aspects battle array points to kth_azIndividual grid azimuthThe k_elThe individual grid angle of pitchThe fundamental wave beam transmission signal at placeMiddle satisfaction imposes a condition Fundamental wave beam transmission signal number,Represent t aspects battle array kth in the Z-axis direction_elThe transmitting letter of fundamental wave beam at individual grid NumberAcquisition probability,Represent t aspects battle array kth in the X-axis direction_azFundamental wave beam transmission signal at individual gridAcquisition probability.

9. a kind of MIMO radar based on three-dimensional nonuniform noise as claimed in claim 1 combines waveform design method, and it is special Levy and be, in step 8, the MIMO radar waveform of the three-dimensional nonuniform noiseIts expression formula is：

Wherein, the face battle array number of plies that N is included after representing and being layered three-dimensional nonuniform noise, L represents three-dimensional nonuniform noise MIMO radar waveformLength,The steering vector of the MIMO radar of three-dimensional nonuniform noise is represented, θ is represented and treated The azimuth of observed object,The angle of pitch of target to be observed in three-dimensional system of coordinate is represented, subscript H represents conjugate transposition.