CN103852751B - Based on the centralized MIMO radar waveform method for designing receiving Wave beam forming - Google Patents

Abstract

The invention discloses a kind of based on the centralized MIMO radar waveform method for designing receiving Wave beam forming, mainly solve existing method and can not reduce centralized MIMO radar and be received back to ripple distance side lobe and the problem of angle secondary lobe.It realizes process: (1) is according to actual radar system and needs, it is determined that the antenna number of centralized MIMO radar and waveform number and Baud Length；(2) according to radar detection demand, it is determined that detection angle and suppression angle, and by its normalization；(3) according to detection angle, it is determined that expectation transmitting pattern；(4) parameter obtained according to above procedure, builds object function and constraints that MIMO radar waveform optimizes；(5) according to the object function built and constraints, use optimized algorithm to solve and obtain MIMO radar waveform.The present invention has and can reduce centralized MIMO radar and be received back to ripple distance side lobe and the advantage of angle secondary lobe, can be used for the design of centralized MIMO radar waveform.

Description

Based on the centralized MIMO radar waveform method for designing receiving Wave beam forming

Technical field

The invention belongs to Radar Technology field, specifically a kind of MIMO radar waveform method for designing, receive distance side lobe and the angle secondary lobe of echo for reducing centralized MIMO radar, approach desired transmitting pattern.

Background technology

MIMO radar is a kind of emerging active detection technology, has now become a study hotspot in Radar Technology field.Spacing size according to transmitting antenna and reception antenna, it is possible to MIMO radar is divided into distributed MIMO radar and centralized MIMO radar two class.For centralized MIMO radar, it is characterized in that dual-mode antenna or array element distance are less.Compared with phased-array radar, centralized MIMO radar has and freely designs each array element and launch the ability of signal waveform, thus having the resolution that extraterrestrial target is higher, to the better sensitivity of low-speed motion target with to general objectives parameter recognition ability more preferably.Additionally, centralized MIMO radar can design transmitting pattern more neatly, so that the mode of operation of radar system is very flexible, and the design of transmitting pattern is also realized by Waveform Design.Therefore, study the Waveform Design of centralized MIMO radar, have great importance.

Currently for the research of centralized MIMO radar waveform design, focus primarily upon the design of transmitting pattern, namely design one group of MIMO radar waveform to approach desired transmitting pattern.Such as, first according to desired transmitting pattern, use convex optimization method, matrix disassembling method or positive semidefinite quadratic programming method to try to achieve the covariance matrix of MIMO radar waveform, then use according to covariance matrix the method designs such as round-robin algorithm to obtain MIMO radar shape；Or the method using linear programming directly designs according to desired transmitting pattern and obtains MIMO radar shape.But above method, only considered and approach this factor of desired transmitting pattern, in reality, not only require that the MIMO radar waveform that design obtains has desired transmitting pattern, and require that designing the MIMO radar waveform obtained can reduce distance side lobe and the angle secondary lobe of centralized MIMO radar reception echo.Therefore, the MIMO radar waveform that the design of existing method obtains causes that centralized MIMO radar receives echo and has too high distance side lobe and angle secondary lobe, reduces the detection performance of centralized MIMO radar.

Summary of the invention

Present invention aims to above-mentioned existing methods shortcoming, propose a kind of based on the centralized MIMO radar waveform method for designing receiving Wave beam forming, to reduce distance side lobe and the angle secondary lobe of centralized MIMO radar reception echo, improve the detection performance of centralized MIMO radar.

The technical thought realizing the object of the invention is: receives distance side lobe and the angle secondary lobe of echo according to minimizing centralized MIMO radar and approaches desired transmitting pattern the two criterion, with MIMO radar waveform for optimized variable, using optimized algorithm to solve and obtain MIMO radar waveform, it implements step and includes as follows:

1) according to actual centralized MIMO radar system, it is determined that the transmitting antenna number N of centralized MIMO radar_tWith reception antenna number N_r, the number of MIMO radar waveform is equal to the transmitting antenna number N of centralized MIMO radar_t, according to actual needs, it is determined that the Baud Length N of MIMO radar waveform_s；

2) according to the detection needs that centralized MIMO radar is actual, it is determined that N_θIndividual detection angle θ_m, m=1,2 ..., N_θ, and N '_θIndividual suppression angle, θ '_n, n=1,2 ..., N '_θ, and then obtain N_θIndividual normalized search angle frequency f_m=0.5sin (θ_m) and N '_θIndividual normalized suppression angular frequency f '_n=0.5sin (θ '_n), wherein, m=1,2 ..., N_θ, n=1,2 ..., N '_θ；

3) according to N_θIndividual detection angle θ_m, it is determined that expectation transmitting pattern B_p, this transmitting pattern B_pIt is a N_bThe vector of dimension；

4) object function and the constraints that MIMO radar waveform optimizes is built:

A 4a) given MIMO radar waveform matrix S, according to transmitting antenna number N_t, reception antenna number N_r、N_θIndividual search angle frequency, N '_θIndividual suppression angular frequency, MIMO radar waveform number N_t, Baud Length N_sWith expectation transmitting pattern B_p, obtain centralized MIMO radar be received back to ripple distance side lobe and angle secondary lobe maximum D and MIMO radar waveform matrix S transmitting pattern with expectation transmitting pattern maximum difference C:

$D=\max |\frac{a_r^H\left(f_m\right)a_r\left(f_n^{\′}\right)}{N_r}\·\frac{a_t^H\left(f_m\right){\mathrm{SJ}}_k{S}^H{a}_t\left(f_n^{\′}\right)}{a_t^H\left(f_m\right){\mathrm{SS}}^H{a}_t\left(f_m\right)}|,$

$C=\max |\mathrm{diag}\left(\frac{A^H{\mathrm{SS}}^{H}A}{N_s}\right)-\mathrm{\γ}\·B_p|,$

Wherein, | | represent each element delivery value to input vector, ()^HRepresent conjugate transpose；f_mFor search angle frequency, m=1,2 ..., N_θ；f′_nFor suppressing angular frequency, n=1,2 ..., N '_θ；a_r(f_m) expression angular frequency is f_mTime reception Wave beam forming guiding vector；a_t(f_m) expression angular frequency is f_mTime launching beam formed guiding vector；MIMO radar waveform matrix S is N_tRow N_sThe matrix of row；J_kFor slip matrix, the span of its subscript k and search angle frequency f_mWith suppression angular frequency f '_nRelevant, if search angle frequency f_m=f '_n, then k=1,2 ..., N_s-1, if search angle frequency f_m≠f′_n, then k=0, ± 1, ± 2 ..., ± (N_s-1)；Diag () represents the diagonal entry of input matrix, and A is a N_tRow N_bThe matrix of row, γ is a weight coefficient variable；

4b) according to step 4a) the secondary lobe maximum D that obtains and transmitting pattern maximum difference C, build object function and constraints that MIMO radar waveform optimizes:

$\begin{array}{cc}\underset{\mathrm{\γ},P}{\min }& \max [D,\mathrm{\α}\·C]\\ s.t.& S=\exp \left(\mathrm{jP}\right)\\ & 0\≤P_{x,y}\≤2\mathrm{\π},x=\mathrm{1,2},\·\·\·,N_t,y=\mathrm{1,2},\·\·\·,N_s\end{array},$

Wherein, s.t. represents constraints, and exp () represents index, and j is imaginary unit, and α is a weight coefficient, and P is the phasing matrix of MIMO radar waveform matrix S, P_x,yRepresent the element that the xth row y row of phasing matrix P are corresponding；

5) according to the object function built in step 4) and constraints, use optimized algorithm Program, obtain final MIMO radar waveform matrix

Due to the fact that according to minimizing distance side lobe and the angle secondary lobe of centralized MIMO radar reception echo and approaching desired transmitting pattern structure object function, and design MIMO radar waveform according to this objective function optimization, therefore design the MIMO radar waveform obtained and reduce distance side lobe and the angle secondary lobe of centralized MIMO radar reception echo.

Accompanying drawing explanation

Fig. 1 be the present invention realize general flow chart；

Sub-process figure when Fig. 2 is to use optimized algorithm to solve MIMO radar waveform by the present invention；

Fig. 3 is distance side lobe and the angle side lobe pattern that the centralized MIMO radar that the MIMO radar waveform with present invention design is corresponding receives echo；

Fig. 4 is the transmitting pattern of the MIMO radar waveform with present invention design.

Detailed description of the invention

With reference to Fig. 1, the present invention to realize step as follows:

Step 1, it is determined that the number of centralized MIMO radar antenna number and MIMO radar waveform and length.

Owing to having used launching beam formation in the design process of waveform and having received Wave beam forming in the present invention, it is therefore desirable to determine transmitting antenna number and the reception antenna number of centralized MIMO radar.And application claims transmitting antenna array and receiving antenna array are all the even linear arrays of half wave space.For given centralized MIMO radar system, its transmitting antenna number and reception antenna number are known.

According to actual centralized MIMO radar system, obtain transmitting antenna number N_tWith reception antenna number N_r；

The number of MIMO radar waveform, equal to the number of centralized MIMO radar transmitting antenna, is designated as N by the number according to MIMO radar waveform_t；

According in practical application to radar waveform bandwidth B and radar waveform time width T_pRequirement, it is determined that the Baud Length N of MIMO radar waveform_s=B T_p。

Step 2, it is determined that the normalization search angle frequency of centralized MIMO radar and suppression angular frequency.

According to actual needs, the angle number of detection is needed to be designated as N centralized MIMO radar system_θ, each detection angle is designated as θ_m, m=1,2 ..., N_θ, and then obtain N_θIndividual normalized search angle frequency f_m=0.5sin (θ_m), m=1,2 ..., N_θ；

Centralized MIMO radar system need the angle number carrying out angle suppression be designated as N '_θ, each suppression angle is designated as θ '_n, n=1,2 ..., N '_θ, and then obtain N '_θIndividual normalized suppression angular frequency f '_n=0.5sin (θ '_n), n=1,2 ..., N '_θ。

It should be noted that suppress angular frequency to be likely to identical with search angle frequency, it is also possible to different；But, it is suppressed that angular frequency includes at least search angle frequency.

Step 3, according to detection angle, it is determined that expectation transmitting pattern.

3a) two factors of Approximation effect according to amount of calculation and transmitting pattern, first determine expectation transmitting pattern B_pDimension N_b, dimension N_bValue more than detection angle number N_θ, then by angular interval [-90 °, 90 °] discretization equably, obtain N_bIndividual discrete angularWith walk-off angle frequency ${\stackrel{\‾}{f}}_l=0.5\sin \left({\stackrel{\‾}{\mathrm{\θ}}}_l\right),l=\mathrm{1,2},\·\·\·,N_b;$

3b) to each detection angle θ_m, it is determined that a launching beam width F_m, m=1,2 ..., N_θ；

3c) according to detection angle θ_mWith discrete angularDifference, it is determined that expectation transmitting pattern B_pIn the value of each element, if i.e. inequalitySet up, then expectation transmitting pattern B_pIn the value of l element be 1, otherwise, it is desirable to transmitting pattern B_pIn the value of l element be 0, wherein, m=1,2 ..., N_θ, l=1,2 ..., N_b；

In particular cases, if it is desired to transmitting pattern is theaomni-directional transmission directional diagram, then transmitting pattern B is expected_pIt it is the vector of complete 1.

Step 4, builds object function and constraints that MIMO radar waveform optimizes.

A 4a) given MIMO radar waveform matrix S, according to transmitting antenna number N_t, reception antenna number N_r、N_θIndividual search angle frequency, N '_θIndividual suppression angular frequency, MIMO radar waveform number N_t, Baud Length N_sWith expectation transmitting pattern B_p, obtain centralized MIMO radar be received back to ripple distance side lobe and angle secondary lobe maximum D and MIMO radar waveform matrix S transmitting pattern with expectation transmitting pattern maximum difference C:

$D=\max |\frac{a_r^H\left(f_m\right)a_r\left(f_n^{\′}\right)}{N_r}\·\frac{a_t^H\left(f_m\right){\mathrm{SJ}}_k{S}^H{a}_t\left(f_n^{\′}\right)}{a_t^H\left(f_m\right){\mathrm{SS}}^H{a}_t\left(f_m\right)}|,$

$C=\max |\mathrm{diag}\left(\frac{A^H{\mathrm{SS}}^{H}A}{N_s}\right)-\mathrm{\γ}\·B_p|,$

Wherein, | | represent each element delivery value to input vector, ()^HRepresent conjugate transpose；f_mFor search angle frequency, m=1,2 ..., N_θ；f′_nFor suppressing angular frequency, n=1,2 ..., N '_θ；MIMO radar waveform matrix S is N_tRow N_sThe matrix of row, diag () represents the diagonal entry of input matrix, and γ is a weight coefficient variable；a_r(f_m) expression angular frequency is f_mTime reception Wave beam forming guiding vector, its expression formula is:

a_r(f_m)=[1, exp (j2 π f_m),…,exp(j2π(N_r-1)f_m)]^T, in formula, ()^TRepresent transposition；a_t(f_m) expression angular frequency is f_mTime launching beam formed guiding vector, its expression formula is:

a_t(f_m)=[1, exp (j2 π f_m),…,exp(j2π(N_t-1)f_m)]^T；J_kFor slip matrix, the span of its subscript k and search angle frequency f_mWith suppression angular frequency f '_nRelevant, if search angle frequency f_m=f '_n, then k=1,2 ..., N_s-1, if search angle frequency f_m≠f′_n, then k=0, ± 1, ± 2 ..., ± (N_s-1), slip matrix J_kExpression formula be:

$J_k=J_{-k}^T=\left[\begin{array}{cc}{0}_{(N_s-k)\×k}& I_{N_s-k}\\ 0_{k\×k}& 0_{k\×(N_s-k)}\end{array}\right],$

Wherein, 0 represents full null matrix, I representation unit matrix, 0 and the dimension of subscript representing matrix of I；A is a N_tRow N_bThe matrix of row, matrix A is by N_bIndividual launching beam forms guiding vector composition, and its concrete form is:

$A=[a_t\left({\stackrel{\‾}{f}}_1\right),a_t\left({\stackrel{\‾}{f}}_2\right),\·\·\·,a_t\left({\stackrel{\‾}{f}}_{N_b}\right)],$

Wherein,For walk-off angle frequency, l=1,2 ..., N_b；

4b) according to step 4a) the secondary lobe maximum D that obtains and transmitting pattern maximum difference C, build object function and constraints that MIMO radar waveform optimizes:

$\begin{array}{cc}\underset{\mathrm{\γ},P}{\min }& \max [D,\mathrm{\α}\·C]\\ s.t.& S=\exp \left(\mathrm{jP}\right)\\ & 0\≤P_{x,y}\≤2\mathrm{\π},x=\mathrm{1,2},\·\·\·,N_t,y=\mathrm{1,2},\·\·\·,N_s\end{array},$

Wherein, s.t. represents constraints, and exp () represents index, and j is imaginary unit, and α is a weight coefficient, and P is the phasing matrix of MIMO radar waveform matrix S, P_x,yRepresent the element that the xth row y row of phasing matrix P are corresponding.

It may be noted that the approximation ratio choosing the suppression degree that should consider centralized MIMO radar echo distance side lobe and angle secondary lobe and MIMO radar waveform transmitting pattern and expectation transmitting pattern of weight coefficient α.Weight coefficient α chooses too small, although the distance side lobe of centralized MIMO radar echo and angle secondary lobe can be made farthest to be suppressed, but, the transmitting pattern causing MIMO radar waveform cannot well be approached desired transmitting pattern.Weight coefficient α chooses excessive, although the transmitting pattern of MIMO radar shape can be made well to approach desired transmitting pattern, but, by the sidelobe level of the distance side lobe of centralized for lifting MIMO radar echo and angle secondary lobe.And find in simulation process, different parameters is arranged, it is necessary to choose different α values.Therefore in the design process, it is possible to choose multiple different α value, obtain corresponding design result, then therefrom choose one optimum as final design result.

Step 5, uses optimized algorithm to solve and obtains MIMO radar waveform

For the object function obtained in step 4 and constraints, it is possible to use multiple optimized algorithm solves, for instance, simulated annealing, genetic algorithm and sequential quadratic programming algorithm etc..Compared with simulated annealing and genetic algorithm, faster, therefore this example uses sequential quadratic programming algorithm to solve MIMO radar waveform to the optimal speed of sequential quadratic programming algorithm

Reference Fig. 2, being implemented as follows of this step:

5a) determine cycle-index N, least cost function value F is set_minFor infinity, a provisional matrix T is set, and to arrange all elements in provisional matrix T be all 0；

5b) waveform of initialization phasing matrix P and weight coefficient variable γ, namely first arranges a random value for each element in phasing matrix P, and the span of random value is 0～2 π, then arranges a random value for weight coefficient variable γ, and the span of random value is 0～1；

5c) intialization phase matrix P and weight coefficient variable γ is substituted into the object function in step 4), according to constraints, call phasing matrix P and weight coefficient variable γ that optimized algorithm search makes target function value minimum, obtain the optimum results of this circulation, the phasing matrix P ' after namely optimizing；

5d) compare target function value and the least cost function value F of this optimum results_minSize, if the target function value of this optimum results is less than least cost function value F_min, then empty provisional matrix T, preserve this optimum results, i.e. provisional matrix T=P ', and make least cost function value F_minTarget function value equal to current optimum results；Otherwise, this optimum results is ignored；

5e) return step 5b) until terminating after circulation n times, obtain final phasing matrixAnd then obtain final MIMO radar waveform matrixWherein, exp () represents index, and j is imaginary unit.

The effect of the present invention is further illustrated by following emulation experiment:

Following emulation experiment all carries out on MATLAB software.

1. simulation parameter:

Transmitting antenna number N is set_t=10, reception antenna number N_r=12, detection angle 3, respectively [-45 °, 0 °, 45 °], it is suppressed that angle is identical with detection angle, the Baud Length N of MIMO radar waveform_s=128, it is desirable to transmitting pattern B_pThere are 3 main lobes, the center of main lobe is respectively at 3 detection angle places, and the width of 3 main lobes is 20 °, weight coefficient α=0.008, and cycle-index is 10 times.

2. emulation content

Emulation 1, emulates centralized MIMO radar and receives distance side lobe and the angle secondary lobe of echo.

Arranging according to above parameter, the step program shown in step 5 solves, and obtains desired MIMO radar waveformThe MIMO radar waveform that will obtainRespectively 3 detection angles [-45 °, 0 °, 45 °] place carries out launching beam formation, pulse compression and reception Wave beam forming, then the result after receiving Wave beam forming is lined up matrix, it is drawn as 3-D graphic, as shown in Figure 3 after element in matrix is taken absolute value.The value of the Labeling Coordinate " correlation combiner " in Fig. 3 presses formula (m-1) N_θ+ n calculates, and wherein, m and n represents that m-th search angle frequency and n-th suppresses angular frequency respectively.

As shown in Figure 3, distance side lobe and the angle secondary lobe of centralized MIMO radar reception echo have been suppressed to-25.1743dB, and the amplitude of distance side lobe and angle secondary lobe is very smooth, it is seen that present invention reduces centralized MIMO radar and receive distance side lobe and the angle secondary lobe of echo.

Emulation 2, the transmitting pattern of emulation MIMO radar waveform.

The MIMO radar waveform that will obtainIn angular interval [-90 °, 90 °], carry out launching beam formation, obtain a column vector, the element value in column vector is drawn as X-Y scheme, as shown by the bold lines in fig；Expectation transmitting pattern B during parameter is arranged_pIt is drawn as X-Y scheme, as shown in phantom in figure 4.

As shown in Figure 4, the MIMO radar waveform of present invention designTransmitting pattern can be good at approaching desired transmitting pattern at main lobe place, the effect approached at secondary lobe place is poor.Generally, the MIMO radar waveform of present invention designTransmitting pattern can approach desired transmitting pattern.

Complex chart 3 and Fig. 4 are it can be seen that the present invention designs the MIMO radar waveform obtainedDesired transmitting pattern can be approached, and reduce distance side lobe and the angle secondary lobe of centralized MIMO radar reception echo.

Claims (4)

1., based on the centralized MIMO radar waveform method for designing receiving Wave beam forming, comprise the steps:

1) according to actual centralized MIMO radar system, it is determined that the transmitting antenna number N of centralized MIMO radar_tWith reception antenna number N_r, the number of MIMO radar waveform is equal to the transmitting antenna number N of centralized MIMO radar_t, according to actual needs, it is determined that the Baud Length N of MIMO radar waveform_s；

2) according to the detection needs that centralized MIMO radar is actual, it is determined that N_θIndividual detection angle θ_m, m=1,2 ..., N_θ, and N '_θIndividual suppression angle, θ '_n, n=1,2 ..., N '_θ, and then obtain N_θIndividual normalized search angle frequency f_m=0.5sin (θ_m) and N '_θIndividual normalized suppression angular frequency f_n'=0.5sin (θ '_n), wherein, m=1,2 ..., N_θ, n=1,2 ..., N '_θ；

3) according to N_θIndividual detection angle θ_m, it is determined that expectation transmitting pattern B_p, this transmitting pattern B_pIt is a N_bThe vector of dimension；

4) object function and the constraints that MIMO radar waveform optimizes is built:

A 4a) given MIMO radar waveform matrix S, according to transmitting antenna number N_t, reception antenna number N_r、N_θIndividual search angle frequency, N '_θIndividual suppression angular frequency, MIMO radar waveform number N_t, Baud Length N_sWith expectation transmitting pattern B_p, obtain centralized MIMO radar be received back to ripple distance side lobe and angle secondary lobe maximum D and MIMO radar waveform matrix S transmitting pattern with expectation transmitting pattern maximum difference C:

$D=max|\frac{a_r^H\left(f_m\right)a_r\left(f_n^{\′}\right)}{N_r}\·\frac{a_t^H\left(f_m\right){\mathrm{SJ}}_k{S}^H{a}_t\left(f_n^{\′}\right)}{a_t^H\left(f_m\right){\mathrm{SS}}^H{a}_t\left(f_m\right)}|,$

$C=max|diag\left(\frac{A^H{\mathrm{SS}}^{H}A}{N_s}\right)-\mathrm{\γ}\·B_p|,$

Wherein, | | represent each element delivery value to input vector, ()^HRepresent conjugate transpose；f_mFor search angle frequency, m=1,2 ..., N_θ；f′_nFor suppressing angular frequency, n=1,2 ..., N '_θ；a_r(f_m) expression angular frequency is f_mTime reception Wave beam forming guiding vector；a_t(f_m) expression angular frequency is f_mTime launching beam formed guiding vector；MIMO radar waveform matrix S is N_tRow N_sThe matrix of row；J_kFor slip matrix, the span of its subscript k and search angle frequency f_mWith suppression angular frequency f '_nRelevant, if search angle frequency f_m=f '_n, then k=1,2 ..., N_s-1, if search angle frequency f_m≠f′_n, then k=0, ± 1, ± 2 ..., ± (N_s-1)；Diag () represents the diagonal entry of input matrix, and γ is a weight coefficient variable, and A is a N_tRow N_bThe matrix of row, For walk-off angle frequency, l=1,2 ..., N_b；

4b) according to step 4a) the secondary lobe maximum D that obtains and transmitting pattern maximum difference C, build object function and constraints that MIMO radar waveform optimizes:

$\begin{array}{cc}\underset{\mathrm{\γ},P}{\min }& \max \[D,\mathrm{\α}\·C\]\\ s.t.& S=\exp \left(jP\right)\\ & 0\≤P_{x,y}\≤2\mathrm{\π},x=1,2,...,N_t,y=1,2,...,N_s\end{array},$

Wherein, s.t. represents constraints, and exp () represents index, and j is imaginary unit, and α is a weight coefficient, and P is the phasing matrix of MIMO radar waveform matrix S, P_x,yRepresent the element that the xth row y row of phasing matrix P are corresponding；

5) according to step 4) in build object function and constraints, use optimized algorithm Program, obtain final MIMO radar waveform matrix

2. according to claim 1 based on receive Wave beam forming centralized MIMO radar waveform method for designing, wherein step 3) described according to N_θIndividual detection angle θ_m, m=1,2 ..., N_θ, it is determined that expectation transmitting pattern B_p, carry out as follows:

3a) two factors of Approximation effect according to amount of calculation and transmitting pattern, first determine expectation transmitting pattern B_pDimension N_b, dimension N_bValue more than detection angle number N_θ, then by angular interval [-90 °, 90 °] discretization equably, obtain N_bIndividual discrete angularWith walk-off angle frequency

3b) to each detection angle θ_m, it is determined that a launching beam width F_m, m=1,2 ..., N_θ；

3c) according to detection angle θ_mWith discrete angularDifference, it is determined that expectation transmitting pattern B_pIn the value of each element, if i.e. inequalitySet up, then expectation transmitting pattern B_pIn the value of l element be 1, otherwise, it is desirable to transmitting pattern B_pIn the value of l element be 0, wherein, m=1,2 ..., N_θ, l=1,2 ..., N_b。

3. according to claim 1 based on receive Wave beam forming centralized MIMO radar waveform method for designing, wherein said step 4a) in reception Wave beam forming guiding vector a_r(f_m), launching beam formed guiding vector a_t(f_m) and slip matrix J_k, its expression formula is as follows respectively:

a_r(f_m)=[1, exp (j2 π f_m),…,exp(j2π(N_r-1)f_m)]^T,

a_t(f_m)=[1, exp (j2 π f_m),…,exp(j2π(N_t-1)f_m)]^T,

$J_k=J_{-k}^T=\left[\begin{array}{cc}{0}_{(N_s-k)\×k}& I_{N_s-k}\\ 0_{k\×k}& 0_{k\×(N_s-k)}\end{array}\right],$

Wherein, ()^TRepresenting transposition, 0 represents full null matrix, I representation unit matrix, 0 and the dimension of subscript representing matrix of I.

4. according to claim 1 based on receive Wave beam forming centralized MIMO radar waveform method for designing, wherein step 5) described in use optimized algorithm Program, obtain final MIMO radar waveform matrixIts step is as follows:

5a) determine cycle-index N, least cost function value F is set_minFor infinity, a provisional matrix T is set, and to arrange all elements in provisional matrix T be all 0；

5b) waveform of initialization phasing matrix P and weight coefficient variable γ, namely first one random value is set for each element in phasing matrix P, the span of random value is 0～2 π, then arranges a random value for weight coefficient variable γ, and the span of random value is 0～1；

5c) intialization phase matrix P and weight coefficient variable γ are substituted into step 4) in object function, according to constraints, call phasing matrix P and weight coefficient variable γ that optimized algorithm search makes target function value minimum, obtain the optimum results of this circulation, the phasing matrix P ' after namely optimizing；

5d) compare target function value and the least cost function value F of this optimum results_minSize, if the target function value of this optimum results is less than least cost function value F_min, then empty provisional matrix T, preserve this optimum results, i.e. provisional matrix T=P ', and make least cost function value F_minTarget function value equal to current optimum results；Otherwise, this optimum results is ignored；

5e) return step 5b) until terminating after circulation n times, obtain final phasing matrixAnd then obtain final MIMO radar waveform matrix