CN105785361A - MIMO radar imaging method on condition of array element failure - Google Patents

Abstract

The invention discloses an MIMO radar imaging method on condition of array element failure. A fine random disturbance amount which obeys Gaussian distribution is superposed on a line element that corresponds with a failure array element position in an MIMO radar echo signal matrix. Matrix filling technology can be used for recovering a non-uniform sampled MIMO radar echo data matrix to a complete uniform sampling data matrix. Then an iterative weighting lq least method is used for estimating an objective scene vector. Because the echo data of the failed array element are not effectively utilized, a relatively large error exists in the reconstructed objective scene, thereby reducing the imaging quality of the object. For further improving the reconstruction precision of the objective scene vector, lost object receiving data of the failure array element are reconstructed by means of the coarse estimated value of the objective scene vector and a perception matrix. Then a matrix filling method and an iterative weighting lq least method are utilized for obtaining a high-precision objective scene vector estimated value, thereby settling an MIMO radar imaging problem on condition of array element failure.

Description

A kind of MIMO radar formation method when element failure

Technical field

The present invention relates to MIMO radar formation method when a kind of element failure, belong to MIMO radar technical field of imaging.

Background technology

MIMO (MultipleInputMultipleOutput, multiple-input and multiple-output) radar, as a kind of new system radar technology, is subject to showing great attention to and studying of scientific research personnel recently.Compared with traditional phased-array radar, MIMO radar can significantly improve recognizable ability and the angular resolution of parameter, improves the motility of beam designing；There is more excellent target detection performance and parameter estimation performance；By virtual-antenna array extending aperture, promote the upper limit of the recognizable number of target.

Target imaging has become one of important branch of MIMO radar system development.In recent years, compressed sensing (compressedsensing, CS) theory is widely used in MIMO radar target imaging.Compressed sensing is a kind of new data compression, re-construction theory and algorithm, it is possible to obtain the signal reconstruction of high probability from a small amount of non-self-adapting accidental projection measured value.In actual radar detection scene, target number only occupies a small amount of resolution cell, so the echo-signal received is sparse.Therefore, it is possible to use CS theoretical treatment MIMO radar imaging problem.

Document [1] proposes based on iteration weighting l_qThe MIMO radar formation method minimized, the method is by setting up weighting l_qThe MIMO radar imaging model minimized, and utilize the closed solutions of target scene vector that lagrange's method of multipliers solves in each iteration, the three-dimensional image of target can be gone out with higher accurate reconstruction.In order to improve the real-time of MIMO radar imaging, document [2] have studied the MIMO radar formation method based on SL0 algorithm, and the method utilizes more precipitous hyperbolic tangent function to replace Gaussian function to approach l₀The shortcoming that norm, " crenellated phenomena " existed in order to avoid steepest descent method and convergence rate are slow, adopts modified newton method to carry out solving approximate l₀Norm minimum problem, improves imaging precision and the speed of MIMO radar.

In order to improve image quality, MIMO radar is generally adopted bigger signal bandwidth to improve target range resolving power, higher sample rate is needed during now conventional uniform sampling, and data rate memory differs nearly 100 times with sample rate, huge speed is not mated can cause that data overflow loss, affecting the overall performance of radar system, therefore uniform sampling is significantly high to the hardware requirement of radar system；And echo-signal is carried out nonuniform sampling and can substantially reduce the requirement of hardware system, but there is the loss of sampled data, cause that the image error of MIMO radar is bigger.Matrix fill-in (MatrixCompletion, MC) is a kind of new technique grown up on compressive sensing theory basis, and the echo matrix of nonuniform sampling effectively can be reverted to complete uniform sampling data matrix by it.The echo-signal of MIMO radar generally represents in the matrix form, if signal matrix meets low-rank requirement, namely the eigenvalue of this matrix has sparse characteristic, then can recover complete signal matrix by the Partial Elements of acquisition matrix.Document [3] have studied the MIMO radar target component algorithm for estimating based on matrix fill-in technology, each reception antenna is carried out matched filtering with a small amount of dictionary waveform or carries out nonuniform sampling to received signal by this algorithm, then result is passed to fusion center, matrix fill-in technology is utilized to recover complete signal matrix at fusion center, then MUSIC (MultipleSignalClassification, multiple signal classification) algorithm is adopted to estimate DOA and the Doppler frequency of target from the signal matrix recovered.

In actual environment, numerous impacts such as the service life due to severe natural environment, artificial interference and hardware, it is possible that the part reception antenna of MIMO radar is closed or is damaged, the receiving array antenna being turned off or damage will be unable to obtain target echo data, and this situation is defined as element failure.In element failure situation, reception antenna output signal is zero, now in MIMO radar echo-signal matrix there is the loss situation of full line element and full line element is zero in corresponding inefficacy element position place, thus causing that signal matrix no longer has strong incoherence, therefore cannot utilize matrix fill-in technology that the data of nonuniform sampling revert to complete uniform sampling data, cause that MIMO radar imaging exists a degree of deterioration.

[1]GongP,ShaoZ.Targetestimationbyiterativereweightedl_qminimizationforMIMOradar[J].SignalProcessing,SignalProcessing,2014,101:35-41.

[2]FengJJ,ZhangG,WenFQ.MIMORadarImagingBasedonSmoothedNorm[J].MMathematicalProblemsinEngineering,2015,2015:1-10.

[3]Sun,S,Bajwa,W.U,Petropulu,A.P.MIMO-MCRadar:AMIMORadarApproachBasedonMatrixCompletion[J].IEEETransactionsonAerospaceandElectronicSystems,2015,51(3):1839-1852.

Summary of the invention

Purpose: when there is reception element failure situation for MIMO radar, owing to there is full line shortage of data in its sampled data matrix, to be full line element be zero, causing matrix fill-in to lose efficacy and then affect the problem of MIMO radar image quality, the present invention provides MIMO radar formation method when a kind of element failure.

Technical scheme: for solving above-mentioned technical problem, the technical solution used in the present invention is:

Step one: set up the nonuniform sampling MIMO radar echo signal model under element failure；

Step 2: at the reception signal matrix Y of MIMO radar nonuniform sampling_SThe random disturbance quantity of the Gaussian distributed that superposition is small on the row element at middle corresponding inefficacy element position place, it is thus achieved that the nonuniform sampling echo matrix Y' after the small random disturbance quantity of superposition_SSo that Y'_SMatrix fill-in condition can be met；

Step 3: utilize matrix fill-in technology by the nonuniform sampling echo matrix Y' after small for superposition random disturbance quantity_SRevert to complete fully sampled reception echo signal matrix

Step 4: utilize iteration weighting l_qThe method that minimizes is from signal matrixMiddle acquisition target scene vector rough estimate evaluation；

Step 5: utilize acquired target scene vector rough estimate evaluation and perception matrix reconstruction to go out the intended recipient data of the array element that lost efficacy, and receive signal matrix Y with MIMO radar_SRow data corresponding to middle inefficacy element position are replaced, and can obtain the target echo signal matrix Y after inefficacy array element data are repaired "_S；

Step 6: to target echo signal matrix Y "_SAgain with matrix fill-in and iteration weighting l_qThe method that minimizes obtains high-precision target scene vector estimated value.

Beneficial effect: MIMO radar formation method when a kind of element failure provided by the invention, the random disturbance quantity of the Gaussian distributed that superposition is small on the row element at corresponding inefficacy element position place in MIMO radar echo-signal matrix, enable it to meet matrix fill-in condition, then utilize matrix fill-in technology the MIMO radar echo data matrix of nonuniform sampling can be reverted to complete uniform sampling data matrix, then utilize iteration weighting l_qThe method of minimizing estimates target scene vector.Owing to the echo data of inefficacy array element failing effectively utilize, there is bigger error in the target scene therefore reconstructed, have impact on the image quality of target.In order to improve the reconstruction accuracy of target scene vector further, acquired target scene vector rough estimate evaluation and perception matrix reconstruction is utilized to go out the intended recipient data of the array element that lost efficacy, again with matrix fill-in and iteration weighting l_qThe method that minimizes obtains high-precision target scene vector estimated value, solves MIMO radar imaging problem when element failure.

Present invention have the advantage that

(1), in actual environment, nonuniform sampling MIMO radar is closed because of bay or damages, echo-signal matrix exists the loss of full line element, causes utilizing matrix fill-in technology to obtain complete sampled data, and then affect the quality of target three-dimensional image；The inventive method can make MIMO radar echo matrix meet matrix fill-in condition to obtain complete sampled data, and make full use of the inefficacy array element echo data reconstructed to obtain high-quality high resolution target three-dimensional image, thus MIMO radar imaging problem when efficiently solving element failure.

(2), the inventive method is when ensureing to be changed without damaging reception antenna, enable to MIMO radar imaging system and remain to normal operation, therefore play a significant role in the occasion that some inconvenient maintenance or cost are huge, there is important military significance.

Accompanying drawing explanation

Fig. 1 is three kinds of methods distance-angle imaging results when sample rate N=0.85；

Fig. 2 is three kinds of methods Range-Doppler Imaging results when sample rate N=0.85；

Fig. 3 is the variation relation of the reconstruction SNR of three kinds of methods and sample rate when signal to noise ratio is SNR=20dB；

Fig. 4 is the variation relation of the reconstruction SNR of three kinds of methods and echo signal to noise ratio as sample rate N=0.85.

Detailed description of the invention

Below in conjunction with accompanying drawing, the present invention is further described.

A kind of MIMO radar formation method when element failure,

Step one: set up the nonuniform sampling MIMO radar echo signal model under element failure；

1a. assumes that centralized MIMO radar has M_tIndividual transmitting antenna and M_rIndividual reception antenna, M_tThe transmitting signal waveform matrix of individual antenna is

$X=\[x_1,x_2...,x_{M_t}\]---\left(1\right)$ In formula, x_m=[x_m(1),x_m(2),...,x_m(L)]^TRepresent the transmitting signal of m-th transmitting antenna；L is the length launching signal；

Target scene region is divided into P distance unit, K angle-unit and H doppler cells by 1b.；Then target scene region is divided into D discrete distance-angle-doppler cells { (τ altogether_p,θ_k,ω_h), D=P K H, wherein 1≤p≤P, 1≤k≤K, 1≤h≤H；

1c. assumes that the h doppler cells is expressed as ω_h, then the signal of corresponding h doppler cells is definedWith Doppler frequency shift vector d (ω_h) respectively

$d\left({\mathrm{\ω}}_h\right)={\[1,e^{{\mathrm{j\ω}}_h},...,e^{j(L-1){\mathrm{\ω}}_h}\]}^T,h=1,...,H---\left(3\right)$

So doppler shifted signal matrix is represented by

$X_d=\[{\tilde{x}}_1\left({\mathrm{\ω}}_h\right),...{\tilde{x}}_m\left({\mathrm{\ω}}_h\right),...{\tilde{x}}_{M_t}\left({\mathrm{\ω}}_h\right)\]---\left(4\right)$

1d. is divided into P distance unit due to target scene, so P-1 represents ultimate range unit between target echo, is first and receives the time delay of maximum possible between signal and different distance unit reflected signal；

Therefore, the transmitting signal matrix of zero padding can be expressed as

${\stackrel{\‾}{X}}_d={\left[\begin{array}{c}{X}_d\\ 0_{(P-1)\×M_t}\end{array}\right]}_{(L+P-1)\×M_t}---\left(5\right)$

In formula,It it is the transmitting signal matrix of zero padding；It is a dimension for (P-1) × M_tNull matrix；

1e. is because target scene region is divided into K angle-unit, then the angle of the target area divided is θ_k, k=1 ..., K；The then steering vector of receiving array and emission arrayWithRespectively

$a_R\left({\mathrm{\θ}}_k\right)={\[1,e^{-j2{\mathrm{\πd}}_{r}sin\left({\mathrm{\θ}}_k\right)/{\mathrm{\λ}}_0},...,e^{-j2\mathrm{\π}(M_r-1)d_{r}sin\left({\mathrm{\θ}}_k\right)/{\mathrm{\λ}}_0}\]}^T---\left(6\right)$

$a_T\left({\mathrm{\θ}}_k\right)={\[1,e^{-j2{\mathrm{\πd}}_{t}sin\left({\mathrm{\θ}}_k\right)/{\mathrm{\λ}}_0},...,e^{-j2\mathrm{\π}(M_t-1)d_{t}sin\left({\mathrm{\θ}}_k\right)/{\mathrm{\λ}}_0}\]}^T---\left(7\right)$

In formula, d_rAnd d_tRepresent receiving antenna array column pitch and launching antenna array column pitch respectively；λ₀For carrier wavelength；

The reception echo signal matrix of 1f.MIMO radarCan be expressed as

$Y=\underset{p=1}{\overset{P}{\mathrm{\Σ}}}\underset{k=1}{\overset{K}{\mathrm{\Σ}}}\underset{h=1}{\overset{H}{\mathrm{\Σ}}}{\mathrm{\α}}_{p,k,h}{a}_R\left({\mathrm{\θ}}_k\right)a_T{\left({\mathrm{\θ}}_k\right)}^T{\stackrel{\‾}{X}}_d^H\left({\mathrm{\ω}}_h\right)J_p+N---\left(8\right)$

In formula, ()^HRepresent conjugate transpose；For additive noise matrix；α_p,k,h, p=1 ..., P, k=1 ..., K, h=1 ..., H represents the complex scattering coefficients of target in target scene region, if the complex scattering coefficients zero setting of this position during driftlessness in the region divided；J_pThe transfer matrix adopted when representing and be used for describing the signal reflected apart from unit from pth, namely

If the reception echo signal matrix Y of MIMO radar is carried out nonuniform sampling with sample rate N by 1g., it is thus achieved that to the reception signal matrix of nonuniform sampling be designated as Y_S；Reception signal matrix Y at nonuniform sampling_SIn element value at the data place of sampling be all zero, represent the coordinate set of data that sampling obtains with Ω, thenThen Y and Y_SMeet following relation:

P_Ω(Y)=P_Ω(Y_S)(10)

In formula, P_ΩFor projection operator, it is defined as:

1h. assumes that MIMO radar occurs that r reception antenna is closed or damaged, their position number respectively n₁,n₂,…,n_r, then signal matrix Y is received_SIt is zero entirely in the r row element value corresponding with inefficacy element position, namely

Y_S(n_i:)=0_1×(L+P-1), i=1,2 ..., r (12)

In formula, 0_1×(L+P-1)It is the row vector of zero entirely for element.

Step 2: at the reception signal matrix Y of MIMO radar nonuniform sampling_SThe random disturbance quantity of the Gaussian distributed that superposition is small on the row element at middle corresponding inefficacy element position place, it is thus achieved that the nonuniform sampling echo matrix Y' after the small random disturbance quantity of superposition_SSo that Y'_SMatrix fill-in condition can be met；

2a. is due to the reception signal matrix Y at MIMO radar nonuniform sampling_SThere is the loss situation of full line element in middle corresponding inefficacy element position place and full line element is the situation of zero, thus causing receiving signal matrix Y_SNo longer there is strong incoherence, matrix fill-in technology therefore cannot be utilized the reception signal matrix Y of nonuniform sampling_SRevert to the reception echo signal matrix Y of complete uniform sampling data；

2b. is receiving signal matrix Y_SMiddle be entirely zero row element on the small random disturbance quantity of superposition, it is thus achieved that the nonuniform sampling echo matrix Y' after the small random disturbance quantity of superposition_SSo that Y'_SMatrix fill-in condition can be met, namely

In formula,For obeying zero-mean variance it isMultiple gaussian random distributing vector.

Step 3: utilize matrix fill-in technology by the nonuniform sampling echo matrix Y' after small for superposition random disturbance quantity_SRevert to complete fully sampled reception echo signal matrix

3a. under high s/n ratio, additive noise matrix N ≈ 0, and the element number of array that generally MIMO radar lost efficacy simultaneously receives array number much smaller than it, therefore additive noise matrix N and random disturbance quantity e_i, i=1 ..., the order being received back to ripple signal matrix Y is substantially free of impact by r；

3b. is sparse due to echo signal number, therefore receives echo signal matrix Y and meets low-rank characteristic, then utilizes matrix fill-in method from signal matrix Y'_SIn recover fully sampled reception echo signal matrixCorresponding matrix fill-in model is

$\underset{Y}{min}rank\left(Y\right),s.t.P_{\mathrm{\Ω}}\left(Y\right)=P_{\mathrm{\Ω}}\left(Y_S^{\′}\right)---\left(14\right)$

Owing to rank of matrix function is non-convex, discrete, direct solution order minimization problem is relatively difficult, hence with nuclear norm minimize method replace order minimize method come solution matrix fill problem, formula (14) can be converted to convex optimization problem:

min||Y||_*,s.t.P_Ω(Y)=P_Ω(Y'_S)(15)

In formula, | | | |_*The nuclear norm of representing matrix, its value is equal to the singular value sum of matrix, it is thus possible to estimate fully sampled reception echo signal matrix

Step 4: utilize iteration weighting l_qThe method that minimizes is from signal matrixMiddle acquisition target scene vector rough estimate evaluation；

4a. is in order to construct the expression-form of compressed sensing radar, by fully sampled reception echo signal matrixIt is rewritten into vector form；OrderWherein vec () representing matrix vector quantities operation；Definition perception matrixWith target scene vectorFor

A=[v_1,1,1,v_1,1,2,…,v_P,K,H](16)

α=[α_1,1,1,α_1,1,2,…,α_P,K,H]^T(17)

In formula,Considering the error that data are recovered, received signal vector y can approximate representation be following form

y≈Aα+n(18)

In formula, n=vec (N)；

4b. adopts iteration weighting l_qMinimize algorithm to estimate MIMO radar target scene vector, the estimated value of target scene vector α can be obtained by solving the object function of formula (19)

$\underset{{\mathrm{\α}}_R,w}{min}f(\mathrm{\α},w)=\frac{1}{2\mathrm{\μ}}\left|\right|y-A\mathrm{\α}|{|}_2^2+\underset{i=1}{\overset{D}{\Σ}}\frac{w_i}{q}|{\mathrm{\α}}_i{|}^q---\left(19\right)$

In formula, D=P × K × H；μ represents regularization parameter；0 < q≤1；W=[w₁,w₂,…,w_D]^TFor weighing vector；Solve formula (19) and target scene vector estimated value can be obtainedClosed solutions

$\widehat{\mathrm{\&alpha;}}={\mathrm{QA}}^H{\&lsqb;{\mathrm{AQA}}^H+\mathrm{\&mu;}I\&rsqb;}^{-1}y---\left(20\right)$

In formula,For unit matrix；Owing to Q is the nonlinear function of α and w, then it is not easy the formula that directly utilizes (20) and calculates the estimated value of αTherefore available iterative manner solves the rough estimate evaluation of target scene vectorNamely Q and the w that last iteration obtains is utilized to solve current iterationValue.

Step 5: utilize acquired target scene vector rough estimate evaluation and perception matrix reconstruction to go out the intended recipient data of the array element that lost efficacy, and receive signal matrix Y with MIMO radar_SRow data corresponding to middle inefficacy element position are replaced, and can obtain the target echo signal matrix Y after inefficacy array element data are repaired "_S；

5a. utilizes acquired target scene vector rough estimate evaluationWith the intended recipient data that perception matrix A reconstructs inefficacy array element；Perception matrix A and target scene vector rough estimate evaluationIt is multiplied and obtains the reception signal phasor y of reconstruct_R, namely

$y_R=A\widehat{\mathrm{\&alpha;}}---\left(21\right)$

Reception signal phasor y by reconstruct_RIt is rewritten into matrix form, namely by moment of a vector array computing

$Y_R=\left[\begin{array}{ccc}{y}_{R_1}& ...& y_{R_{M_r\&times;(L+P)+1}}\\ \begin{array}{c}.\\ .\\ .\end{array}& \begin{array}{c}.\\ .\\ .\end{array}& \begin{array}{c}.\\ .\\ .\end{array}\\ y_{R_{M_r}}& ...& y_{R_{M_r\&times;(L+P-1)}}\end{array}\right]---\left(22\right)$

By formula (22) it can be seen that reconstruct reception signal matrix Y_RThe middle row data corresponding to reception element position that lost efficacy are regarded as the lost target echo data of inefficacy array element, extract restructuring matrix Y_RIn these row data and replace the reception signal matrix Y of MIMO radar_SThe row data of middle same position, namely obtain the target echo signal matrix Y after inefficacy array element data are repaired "_S,

Step 6: to target echo signal matrix Y "_SAgain with matrix fill-in and iteration weighting l_qThe method that minimizes obtains high-precision target scene vector estimated value.

6a. is again with SVT algorithm and iteration weighting l_qMinimize the target echo signal matrix Y after algorithm can be repaired from inefficacy array element data "_SIn estimate high accuracy target scene vector, thus the MIMO radar image quality that improve in element failure situation.

The detailed description of the invention of MIMO radar formation method when a kind of element failure that the present invention proposes can be provided by following emulation embodiment and result further.In emulation embodiment, iteration weighting l_qMethod representation directly adopts iteration weighting l_qMethod estimates target scene vector to in the nonuniform sampling MIMO radar echo-signal under array element failure condition；MC_l_qMethod representation utilizes matrix fill-in technology that the MIMO radar echo data matrix of nonuniform sampling reverts to complete uniform sampling data matrix, recycles iteration weighting l_qMethod estimates target scene vector.

Simulation parameter is arranged: the transmitting antenna number M of MIMO radar system_t=5, reception antenna number M_r=25, the aerial array of MIMO radar is pressed even linear array and is arranged, launching antenna array column pitch is d_t=2.5 λ₀, receiving antenna array column pitch is d_r=0.5 λ₀；Launch signal and choose noise FM signal, the employing number L=32 of transmitted waveform；Echo noise choose average be zero, variance be σ²Additive white Gaussian noise, echo signal to noise ratio is defined as

$SNR=10{\log }_{10}\left(\frac{tr\left(X^{*}X\right)}{{\mathrm{L\&sigma;}}^2}\right)---\left(24\right)$

In formula, matrix trace is sought in tr () expression.The distance unit number P=12 of target scene；The angular range [-30 °, 30 °] of radar scanning, angular divisions is spaced apart 1 °, then the angle-unit number K=61 after dividing；The Doppler frequency shift angle of target represents, i.e. Φ_h=ω_hL (180 °/π), Doppler spread is [-25 °, 25 °], and doppler angle divides and is spaced apart 5 °, then the doppler cells number H=11 after dividing.Assuming the 7th and the 18th reception antenna inefficacy in receiving array, the data namely receiving the 7th row in signal matrix and the 18th row are zero entirely.The inventive method and MC_l_qIn method in echo matrix the small random disturbance quantity variance of superposition on corresponding inefficacy element position place row elementAt iteration weighting l_qMinimizing in method, choose q=0.3, iterations is 5.

Definition reconstruction SNR is as follows,

$RSNR=10{\log }_{10}\left(\frac{\left|\right|\mathrm{\&alpha;}|{|}_2}{\left|\right|\widehat{\mathrm{\&alpha;}}-\mathrm{\&alpha;}|{|}_2}\right)---\left(25\right)$

In formula, α is real goal scene vector；Target scene vector estimated value；||·||₂RepresentNorm.

Emulation content 1:MIMO distance by radar-angle imaging

Fig. 1 is distance-angle imaging that MIMO radar is located doppler cells 5 °.The actual distance that Fig. 1 (a) is target place-angle-resolved cell distribution figure, Fig. 1 (b), Fig. 1 (c) and Fig. 1 (d) be iteration weighting l respectively_qMethod, MC_l_qMethod and context of methods estimate the target place distance-angle image obtained, and wherein echo signal to noise ratio is 20dB, sample rate N=0.85.As shown in Figure 1, there is sampled data and inefficacy array element event of data loss, iteration weighting l due to echo-signal_qThe distance of method-angle imaging sidelobe level is higher, and there is many false targets near real goal, causes that the distance-angle image quality suppression ratio of target is more serious；MC_l_qMethod utilizes matrix fill-in method that non-uniform sampling data can revert to complete uniform sampling data, and therefore its imaging sidelobe level will lower than iteration weighting l_qMethod, but the echo data of inefficacy array element is failed effectively to utilize by the method, causes that relatively large deviation still occurs in the target range-angle picture of the method；The inventive method can go out distance and the angle information of target with higher Accuracy extimate, it is thus possible to obtain high-quality target picture.

Emulation content 2:MIMO distance by radar-doppler imaging

Fig. 2 is the Range-Doppler Imaging figure that MIMO radar is located angle-unit-10 °.Fig. 2 (a) is actual distance-Doppler's resolution cell scattergram at target place；Fig. 2 (b), Fig. 2 (c) and Fig. 2 (d) adopt iteration weighting l_qMethod, MC_l_qTarget range-doppler imaging result figure that method and context of methods obtain, wherein echo signal to noise ratio is 20dB, sample rate N=0.85.As shown in Figure 2, compared to iteration weighting l_qMethod and MC_l_qMethod, the inventive method can effectively recover sampled data and the inefficacy array element data of loss, it is thus possible to effectively reconstruct the target two-dimensional image of higher precision, and substantially keeps consistent with target real information.

The reconstruction SNR of emulation 3: three kinds of methods of content and the variation relation of sample rate

Choose echo samples rate even variation between 0.5-1, echo signal to noise ratio snr=20dB, repeat 100 Monte Carlo Experiments.Fig. 3 is the reconstruction SNR variation relation with echo signal sample rate of three kinds of methods.From the figure 3, it may be seen that the inventive method reconstruction SNR that target scene vector is estimated is apparently higher than iteration weighting l_qMethod and MC_l_qMethod；MC_l_qThe reconstruction SNR of method tends to stable after sample rate N=0.6, and this is owing to when echo samples rate is more than 0.6, non-homogeneous data just successfully can be reverted to complete uniform sampling data by matrix fill-in method；When as sample rate N=1, now the echo-signal of MIMO radar shows as complete uniform sampling data, from the figure 3, it may be seen that MC_l_qMethod and iteration weighting l_qMethod has similar reconstruction SNR, but owing to they underuse the loss data of inefficacy array element, causes the reconstruction property of target scene vector to be still inferior to the inventive method.

The reconstruction SNR of emulation 4: three kinds of methods of content and the variation relation of echo signal to noise ratio

Choose echo signal to noise ratio to change between 0dB-25dB, echo signal sample rate N=0.85, repeat 100 Monte Carlo Experiments.Fig. 4 is the reconstruction SNR variation relation with echo signal to noise ratio of three kinds of methods.As shown in Figure 4, although the target scene vector error of the inventive method and MC_l under low echo signal to noise ratio_qMethod and iteration weighting l_qMethod is more or less the same, but is as the increase of echo signal to noise ratio, and the inventive method can rely on the lost target data of inefficacy array element recovered, so that its reconstruction SNR is much better than MC_l_qMethod and iteration weighting l_qMethod, can go out distance-angle-Doppler's three-dimensional image of target with higher accurate reconstruction.

The above is only the preferred embodiment of the present invention; it is noted that, for those skilled in the art; under the premise without departing from the principles of the invention, it is also possible to make some improvements and modifications, these improvements and modifications also should be regarded as protection scope of the present invention.

Claims (7)

1. a MIMO radar formation method when element failure, it is characterised in that: comprise the following steps that

Step one: set up the nonuniform sampling MIMO radar echo signal model under element failure；

Step 2: at the reception signal matrix Y of MIMO radar nonuniform sampling_SThe random disturbance quantity of the Gaussian distributed that superposition is small on the row element at middle corresponding inefficacy element position place, it is thus achieved that the nonuniform sampling echo matrix Y ' after the small random disturbance quantity of superposition_SSo that Y '_SMatrix fill-in condition can be met；

Step 3: utilize matrix fill-in technology by the nonuniform sampling echo matrix Y ' after small for superposition random disturbance quantity_SRevert to complete fully sampled reception echo signal matrix

Step 4: utilize iteration weighting l_qThe method that minimizes is from signal matrixMiddle acquisition target scene vector rough estimate evaluation；

Step 5: utilize acquired target scene vector rough estimate evaluation and perception matrix reconstruction to go out the intended recipient data of the array element that lost efficacy, and receive signal matrix Y with MIMO radar_SRow data corresponding to middle inefficacy element position are replaced, and can obtain the target echo signal matrix Y after inefficacy array element data are repaired "_S；

Step 6: to target echo signal matrix Y "_SAgain with matrix fill-in and iteration weighting l_qThe method that minimizes obtains high-precision target scene vector estimated value.

2. MIMO radar formation method when a kind of element failure according to claim 1, it is characterised in that: described step one comprises the following steps that

1a. assumes that centralized MIMO radar has M_tIndividual transmitting antenna and M_rIndividual reception antenna, M_tThe transmitting signal waveform matrix of individual antenna is

In formula, x_m=[x_m(1),x_m(2),...,x_m(L)]^TRepresent the transmitting signal of m-th transmitting antenna；L is the length launching signal；

Target scene region is divided into P distance unit, K angle-unit and H doppler cells by 1b.；Then target scene region is divided into D discrete distance-angle-doppler cells { (τ altogether_p,θ_k,ω_h), D=P K H, wherein 1≤p≤P, 1≤k≤K, 1≤h≤H；

1c. assumes that the h doppler cells is expressed as ω_h, then the signal of corresponding h doppler cells is definedWith Doppler frequency shift vector d (ω_h) respectively

So doppler shifted signal matrix is represented by

1d. is divided into P distance unit due to target scene, so P-1 represents ultimate range unit between target echo, is first and receives the time delay of maximum possible between signal and different distance unit reflected signal；

Therefore, the transmitting signal matrix of zero padding can be expressed as

In formula,It it is the transmitting signal matrix of zero padding；It is a dimension for (P-1) × M_tNull matrix；

1e. is because target scene region is divided into K angle-unit, then the angle of the target area divided is θ_k, k=1 ..., K；The then steering vector of receiving array and emission arrayWithRespectively

In formula, d_rAnd d_tRepresent receiving antenna array column pitch and launching antenna array column pitch respectively；λ₀For carrier wavelength；

The reception echo signal matrix of 1f.MIMO radarCan be expressed as

In formula, ()^HRepresent conjugate transpose；For additive noise matrix；α_p,k,h, p=1 ..., P, k=1 ..., K, h=1 ..., H represents the complex scattering coefficients of target in target scene region, if the complex scattering coefficients zero setting of this position during driftlessness in the region divided；J_pThe transfer matrix adopted when representing and be used for describing the signal reflected apart from unit from pth, namely

If the reception echo signal matrix Y of MIMO radar is carried out nonuniform sampling with sample rate N by 1g., it is thus achieved that to the reception signal matrix of nonuniform sampling be designated as Y_S；Reception signal matrix Y at nonuniform sampling_SIn element value at the data place of sampling be all zero, represent the coordinate set of data that sampling obtains with Ω, thenThen Y and Y_SMeet following relation:

P_Ω(Y)=P_Ω(Y_S)(10)

In formula, P_ΩFor projection operator, it is defined as:

1h. assumes that MIMO radar occurs that r reception antenna is closed or damaged, their position number respectively n₁,n₂,…,n_r, then signal matrix Y is received_SIt is zero entirely in the r row element value corresponding with inefficacy element position, namely

Y_S(n_i:)=0_1×(L+P-1), i=1,2 ..., r (12)

In formula, 0_1×(L+P-1)It is the row vector of zero entirely for element.

3. MIMO radar formation method when a kind of element failure according to claim 1, it is characterised in that: described step 2 comprises the following steps that

2a. is due to the reception signal matrix Y at MIMO radar nonuniform sampling_SThere is the loss situation of full line element in middle corresponding inefficacy element position place and full line element is the situation of zero, thus causing receiving signal matrix Y_SNo longer there is strong incoherence, matrix fill-in technology therefore cannot be utilized the reception signal matrix Y of nonuniform sampling_SRevert to the reception echo signal matrix Y of complete uniform sampling data；

2b. is receiving signal matrix Y_SMiddle be entirely zero row element on the small random disturbance quantity of superposition, it is thus achieved that the nonuniform sampling echo matrix Y ' after the small random disturbance quantity of superposition_SSo that Y '_SMatrix fill-in condition can be met, namely

In formula,For obeying zero-mean variance it isMultiple gaussian random distributing vector.

4. MIMO radar formation method when a kind of element failure according to claim 1, it is characterised in that: described step 3 comprises the following steps that

3a. under high s/n ratio, additive noise matrix N ≈ 0, and the element number of array that generally MIMO radar lost efficacy simultaneously receives array number much smaller than it, therefore additive noise matrix N and random disturbance quantity e_i, i=1 ..., the order being received back to ripple signal matrix Y is substantially free of impact by r；

3b. is sparse due to echo signal number, therefore receives echo signal matrix Y and meets low-rank characteristic, then utilizes matrix fill-in method from signal matrix Y '_SIn recover fully sampled reception echo signal matrixCorresponding matrix fill-in model is

Owing to rank of matrix function is non-convex, discrete, direct solution order minimization problem is relatively difficult, hence with nuclear norm minimize method replace order minimize method come solution matrix fill problem, formula (14) can be converted to convex optimization problem:

min||Y||_*,s.t.P_Ω(Y)=P_Ω(Y′_S)(15)

In formula, | | | |_*The nuclear norm of representing matrix, its value is equal to the singular value sum of matrix, it is thus possible to estimate fully sampled reception echo signal matrix

5. MIMO radar formation method when a kind of element failure according to claim 1, it is characterised in that: described step 4 comprises the following steps that

4a. is in order to construct the expression-form of compressed sensing radar, by fully sampled reception echo signal matrixIt is rewritten into vector form；OrderWherein vec () representing matrix vector quantities operation；Definition perception matrixWith target scene vectorFor

A=[v_1,1,1, v_1,1,2..., v_{P, K, H}](16)

α=[α_1,1,1, α_1,1,2..., α_{P, K, H}]^T(17)

In formula,Considering the error that data are recovered, received signal vector y can approximate representation be following form

y≈Aα+n(18)

In formula, n=vec (N)；

4b. adopts iteration weighting l_qMinimize algorithm to estimate MIMO radar target scene vector, the estimated value of target scene vector α can be obtained by solving the object function of formula (19)

In formula, D=P × K × H；μ represents regularization parameter；0 < q≤1；W=[w₁,w₂,…,w_D]^TFor weighing vector；Solve formula (19) and target scene vector estimated value can be obtainedClosed solutions

In formula, For unit matrix；Owing to Q is the nonlinear function of α and w, then it is not easy the formula that directly utilizes (20) and calculates the estimated value of αTherefore available iterative manner solves the rough estimate evaluation of target scene vectorNamely Q and the w that last iteration obtains is utilized to solve current iterationValue.

6. MIMO radar formation method when a kind of element failure according to claim 1, it is characterised in that: described step 5 comprises the following steps that

5a. utilizes acquired target scene vector rough estimate evaluationWith the intended recipient data that perception matrix A reconstructs inefficacy array element；Perception matrix A and target scene vector rough estimate evaluationIt is multiplied and obtains the reception signal phasor y of reconstruct_R, namely

Reception signal phasor y by reconstruct_RIt is rewritten into matrix form, namely by moment of a vector array computing

By formula (22) it can be seen that reconstruct reception signal matrix Y_RThe middle row data corresponding to reception element position that lost efficacy are regarded as the lost target echo data of inefficacy array element, extract restructuring matrix Y_RIn these row data and replace the reception signal matrix Y of MIMO radar_SThe row data of middle same position, namely obtain the target echo signal matrix Y after inefficacy array element data are repaired "_S,

。

7. MIMO radar formation method when a kind of element failure according to claim 1, it is characterised in that: described step 6 comprises the following steps that

6a. is again with SVT algorithm and iteration weighting l_qMinimize the target echo signal matrix Y after algorithm can be repaired from inefficacy array element data "_SIn estimate high accuracy target scene vector, thus the MIMO radar image quality that improve in element failure situation.