CN105807275A - MIMO-OFDM-STAP steady waveform design method based on partial clutter priori knowledge - Google Patents

Abstract

The invention belongs to the field of signal processing and relates to a MIMO-OFDM-STAP steady waveform design method based on partial clutter priori knowledge.By introducing parameter uncertainty into the waveform optimization problem explicitly, sensitivity is relieved.The method comprises the steps of 1, building a MIMO-OFDM-STAP model to obtain an expression of received data; 2, obtaining optimized output SINR through objective function deduction; 3, establishing a steady waveform optimization model under the restraint of a constant modulus and total transmitting power; 4, bringing forward an iterative algorithm, and converting each non-linear optimization problem in iteration into a semi-definite programming problem capable of being efficiently solved based on the diagonal loading (DL) technique, so as to achieve optimal design of a steady waveform.

Description

The sane Waveform Design of MIMO-OFDM-STAP based on part clutter priori

Technical field

The invention belongs to signal processing field, relate to a kind of MIMO-OFDM-STAP based on incomplete clutter priori steady Strong waveform design method.

Background technology

Along with MIMO communication vigorous growth, and radar is to break through self to limit new theory and the demand of new technique, MIMO radar concept is arisen at the historic moment.Compared with the phased-array radar that can only send relevant waveform, MIMO radar can utilize many Individual transmitter unit launches almost random waveform.Based on array antenna spacing, MIMO radar system can be divided into two categories below: (1) Splitting radar, (2) put radar altogether.The former uses the Transmit-Receive Unit split farther out to launch desired signal, sees from different perspectives simultaneously Observation of the eyes mark, thus available space diversity is to overcome the hydraulic performance decline caused due to target glint.On the contrary, the latter uses distance very Near transmitter unit is to increase the virtual aperture of receiving array, so that its performance is better than phased-array radar.

OFDM (Orthogonal frequency division multiplexing, OFDM) signal is low as a kind of broadband Intercepting and capturing radar waveform receives more and more attention.OFDM radar utilizes multiple orthogonal subcarrier to detect parallel, thus The frequency selective fading that multipath transmisstion causes can be effective against, improve the noiseproof feature of system.By OFDM and MIMO Technology combines, and can give full play to the advantage of MIMO and OFDM such that it is able to significantly improve the detection to target Energy.

Space-time adaptive processes (STAP) and grows up from eighties of last century the early 1990s, for airborne radar (airborne Radar) data carry out the technology processed.STAP technology suffers from being widely applied in military and civilian, and such as, geology is monitored, Early warning, Ground moving targets detection (GMTI), moving-target detection (MTI), region investigation etc..For traditional phased array thunder Reaching, STAP fundamental research is the most ripe.Many is used for improving STAP complexity and constringent algorithm was carried already Go out.These algorithms just can apply to MIMO radar past slightly amendment.

MIMO radar transmitted waveform design is typically based on the priori of target and environment and carries out, and this priori is by estimating Obtain, thus inevitably there is estimation difference.Now, Waveform Design is difficult to Optimum Matching, causes system detection property Can decline.It is common self adaptation that diagonal angle loads sample matrix inversion algorithm (loaded sample matrix inversion, LSMI) One of robust method, the method, by sample covariance matrix is carried out diagonal angle loading, can improve the convergence rate of adaptive algorithm And robustness, but its loading capacity is given by empirical parameter, does not has analytic solutions.J.Li etc. have studied based on CRB criterion and improve parameter Estimate the Waveform Design problem of performance.But the explicit value solving some parameter of needs of this Waveform Design problem, such as target position Put, reflection coefficient etc..Therefore, the determination optimizing waveform will depend on these values.In engineer applied, these parameter values are due to logical Cross estimation to obtain, thus there is uncertainty.Owing to the final precision of parameter estimation is more sensitive to these uncertainties, so The optimization waveform being worth to based on certain parameter estimation may cause poor Parameter Estimation Precision.

Summary of the invention

In order to improve the Waveform Design of MIMO radar system performance to some parameter estimating error more sensitive issue, the present invention Propose a kind of STAP improving MIMO-OFDM radar the sane transmitted waveform optimization of ground target detection performance at a slow speed is designed Method, by being explicitly included into waveform optimization problem to slow down this sensitivity by parameter uncertainty.First the method proposes one Plant iterative algorithm and optimize waveform covariance matrix, be then based on diagonal angle and load (DL) technology, by non-for each step of iterative process Linear optimization problem is converted into the Semidefinite Programming that can obtain Efficient Solution, thus the output under maximizing worst condition SINR.Simulation result shows, compared with irrelevant transmitted waveform, what the present invention was remarkably improved under worst parameter estimation performance is System performance.

The technical scheme is that a kind of MIMO-OFDM-STAP based on incomplete clutter priori Sane Waveform Design, comprises the steps:

(1) MIMO-OFDM-STAP system model is set up

1a) MIMO-OFDM-STAP receives signal description

Consider MIMO-OFDM-STAP scene as shown in Fig. 1 of Figure of description.In this scene, the transmitting of MIMO radar Array and receiving array are even linear array, and are placed in parallel, and array number is respectively M and N, and array element distance is respectively d_TAnd d_R。 Radar platform is along being parallel to transmitting, the direction unaccelerated flight of receiving array, and flying height and speed are respectively h and v.Target Edge is θ with transmitting, receiving array normal angle_tStraight line uniform motion, speed is v_t, and it is in same plane with radar platform. In a coherent processing inteval (CPI), each array element of launching radiates the burst waveforms being made up of L pulse, and pulse simultaneously Recurrence interval (PRI) is T.N is turned to by discrete for rang ring_C(N_C＞ ＞ NML) individual junior unit, then the l pulse recurrence interval Reception data in PRI are represented by:

$X_l={\mathrm{\ρ}}_t{e}^{j2{\mathrm{\πf}}_{D}l}{\mathrm{ab}}^{T}S+\underset{i=0}{\overset{N_C-1}{\mathrm{\Σ}}}{\mathrm{\ρ}}_i{e}^{j2{\mathrm{\π\βf}}_{s,i}l}{a}_i{b_i}^{T}S+Z_l$

In formula,And

WithRepresent target respectively and be positioned at θ_iClutter Launch steering vector；Represent transmitted waveform matrix in each PRI,Send out for m-th Penetrating the discrete form of the complex baseband signal that array element is launched in each PRI, K is waveform sampling number；

WithRepresent target respectively and be positioned at θ_iClutter Receive steering vector；ρ_tAnd ρ_i(θ) it is respectively the complex magnitude of the rang ring internal object considered and is positioned at θ_iClutter reflection system Number； Represent the interference that the n-th reception array element receives in the l PRI And noise, we may assume that Z_lEvery string independent same distribution, and to submit to average be 0, and variance is that the Cyclic Symmetry of Q is multiple Gauss distribution.

1b) snap statement during sky in rang ring interested

Utilize S^H(SS^H)^-1/2As matched filtering device, andThen corresponding vector quantization matched filtering output can represent For:

${\tilde{x}}_l={\mathrm{\ρ}}_t{e}^{j2{\mathrm{\πf}}_{D}l}(\mathrm{\Φ}\⊗I_N)(b\⊗a)+\underset{i=0}{\overset{N_C-1}{\mathrm{\Σ}}}{\mathrm{\ρ}}_i{e}^{j2{\mathrm{\π\βf}}_{s,i}l}(\mathrm{\Φ}\⊗I_N)(b_i\⊗a_i)+vec\left({\tilde{Z}}_l\right)$

Wherein,I_NIt is the unit matrix of N × N,

Φ=SS^H(SS^H)^-1/2=diag{ | a₁| |a₂| … |a_M|, diag{ } represent diagonal matrix.

By above formula we in can obtaining interested rang ring total empty time snap be:

$\begin{array}{c}{X}_C={\mathrm{\ρ}}_t{U}_D\⊗\left(\right(\mathrm{\Φ}\⊗I_N\left)\right(b\⊗a\left)\right)+\\ \underset{i=0}{\overset{N_C-1}{\mathrm{\Σ}}}{\mathrm{\ρ}}_i{U}_{D,i}\⊗\left(\right(\mathrm{\Φ}\⊗I_N\left)\right(b_i\⊗a_i\left)\right)+I_L\⊗vec\left({\tilde{Z}}_l\right)\\ ={\mathrm{\ρ}}_t(I_L\⊗\mathrm{\Φ}\⊗I_N)(U_D\⊗b\⊗a)+\\ (I_L\⊗\mathrm{\Φ}\⊗I_N)\underset{i=0}{\overset{N_C-1}{\mathrm{\Σ}}}{\mathrm{\ρ}}_i(U_{D,i}\⊗b_i\⊗a_i)+I_L\⊗vec\left({\tilde{Z}}_l\right)\end{array}$

Wherein,WithRepresent target respectively and be positioned at θ i clutter Doppler's steering vector.

(2) object function is derived

2a) export SINR statement under the conditions of optimum MIMO-OFDM-STAP processor

Based on the undistorted criterion of minimum variance (MVDR), optimum output SINR can be obtained and be represented by:

$SINR={{\mathrm{\ρ}}_t}^2{\[(I_L\⊗\mathrm{\Φ}\⊗I_N)(U_D\⊗b\⊗a)\]}^H{R}_{i+n}^{-1}\[(I_L\⊗{\mathrm{\α}}^T\⊗I_N)(U_D\⊗b\⊗a)\]$

In formula,

$R_{i+n}=E\[\left(\right(I_L\⊗\mathrm{\Φ}\⊗I_N\left)\underset{i=0}{\overset{N_C-1}{\mathrm{\Σ}}}{\mathrm{\ρ}}_i\right(U_{D,i}\⊗b_i\⊗a_i)+I_L\⊗vec({\tilde{Z}}_l\left)\right)$

${\left(\right(I_L\⊗\mathrm{\Φ}\⊗I_N\left)\underset{i=0}{\overset{N_C-1}{\mathrm{\Σ}}}{\mathrm{\ρ}}_i\right(U_{D,i}\⊗b_i\⊗a_i)+I_L\⊗vec({\tilde{Z}}_l\left)\right)}^H\]$

2b) clutter Gauss distribution, and with interference uncorrelated under the conditions of export SINR statement simplify

Assuming clutter independent same distribution, and obedience average is 0, variance isGauss distribution, then at clutter and interference plus noise Under incoherent hypothesis, output SINR can be reduced to following expression:

$SINR={\left|{\mathrm{\ρ}}_t\right|}^2{v_t}^H{(I+\tilde{A}{R}_C)}^{-1}\tilde{A}{v}_t$

Wherein,

$V={\[v_1,v_2,\mathrm{...},v_{N_C}\]}^H,v_i=U_{D,i}\⊗b_i\⊗a_i,\mathrm{\Ξ}=diag({{\mathrm{\σ}}_1}^2,{{\mathrm{\σ}}_2}^2,\mathrm{...},{{\mathrm{\σ}}_{N_C}}^2),\tilde{A}=I_L\⊗\mathrm{\Ψ}\⊗Q^{-1}.$

(3) sane waveform optimization model

Under Gaussian noise environment, may certify that maximization detection probability is equivalent to maximize output Signal to Interference plus Noise Ratio.Thus, based on Upper analysis can obtain, and under permanent mould and total emission power constraint, optimizes waveform covariance matrix (WCM) by one convex set of structure The waveform optimization problem maximizing detection probability can be expressed as

$\begin{array}{ccc}\underset{\mathrm{\ψ}}{max}& \underset{{\mathrm{\ΔR}}_C}{min}& {\tilde{v}}_t^H{(I_{MNL}+\tilde{A}{\tilde{R}}_C)}^{-1}\tilde{A}{\tilde{v}}_t\end{array}$

$a_m^2=D_m$

$\underset{m=1}{\overset{M}{\mathrm{\Σ}}}{a}_m^2=P$

||a_m||²≥0

In formula, P represents total emission power.

We can see that from above formula object function be one considerably complicated aboutAnd R_CNonlinear function, thus this asks Topic is difficult with traditional optimization and solves.

(4) alternative manner based on DL solves sane waveform optimization problem

4a) optimize based on DL internal layer

This optimization problem comprises permanent modular constraint, it is clear that being nonlinear optimization (NP) problem, it is easy to solve during globally optimal solution It is absorbed in locally optimal solution.Simultaneously asWe cannot determineCharacter, therefore, we can not Convex optimization method is enough utilized to solve.For this problem, we use diagonal angle loading method that Ψ is carried out diagonal angle loading so that

In formula, ε ＜ ＜ λ_max(Ψ) it is so-called load factor (loading factor), λ_maxThe eigenvalue of maximum of () representing matrix.Note Meaning arrives, due toCan obtainWillReplace withCan obtain

${(I_{MNL}+\widetilde{\stackrel{~}{A}}{\tilde{R}}_C)}^{-1}\widetilde{\stackrel{~}{A}}={({\widetilde{\stackrel{~}{A}}}^{-1}+{\tilde{R}}_C)}^{-1}$

According to above formula, interior optimization problem can be written as:

$\begin{array}{cc}\underset{{\mathrm{\ΔR}}_C,t}{min}& t\end{array}$

$\begin{array}{cc}s.t.& {\tilde{v}}_t^H{({\widetilde{\stackrel{~}{A}}}^{-1}+{\tilde{R}}_C)}^{-1}{\tilde{v}}_t\≤t\end{array}$

In formula, t is auxiliary variable.

The problems referred to above can be equivalent to following SDP problem:

$\begin{array}{cc}\underset{{\mathrm{\ΔR}}_C,t}{min}& t\end{array}$

4b) solve outer layer optimization based on DL

DL method is used forCan obtain

In formula,Meet ρ=λ_max(R_C)/1000, useReplace R_C, can obtain

$SINR={\left|{\mathrm{\ρ}}_t\right|}^2{v_t}^H{(I+\tilde{A}{\widetilde{\stackrel{~}{R}}}_C)}^{-1}\tilde{A}{\widetilde{\stackrel{~}{R}}}_C{{\widetilde{\stackrel{~}{R}}}_C}^{-1}{v}_t$

Utilizing topology, above formula can be rewritten as

$SINR={\left|{\mathrm{\ρ}}_t\right|}^2{v_t}^H{{\widetilde{\stackrel{~}{R}}}_C}^{-1}{v}_t-{\left|{\mathrm{\ρ}}_t\right|}^2{v_t}^H{({\widetilde{\stackrel{~}{R}}}_C+{\widetilde{\stackrel{~}{R}}}_C\tilde{A}{\widetilde{\stackrel{~}{R}}}_C)}^{-1}{v}_t$

Based on discussed above, waveform optimization problem can be expressed equivalently as following SDP problem:

$\begin{array}{cc}\underset{\mathrm{\Ψ},t}{min}& t\end{array}$

$a_m^2=D_m$

$\underset{m=1}{\overset{M}{\mathrm{\Σ}}}{a}_m^2=P$

||a_m||²≥0

In formula, t is auxiliary optimized variable.Thus, this waveform optimization problem may utilize many ripe optimization toolbox and obtains Efficient Solution.

4c) alternative manner based on DL solves sane waveform optimization problem

Based on discussed above, Δ R_CCan obtain with ψ and solve at a high speed, thus can get iterative algorithm: give waveform covariance matrix Initial value (such as, uncorrelated waveform), Δ R_CAnd ψ can be obtained by following steps alternative optimization:

<1>above-mentioned SDP problem 1 is solved to obtain optimum Δ R_C；

<2>SDP problem 2 is solved to obtain optimum ψ；

Return step<1>iteration again until Signal to Interference plus Noise Ratio (SINR) no longer reduces.

For the space-time joint processing problem of the target at a slow speed of ground under complex environment, the uncertainty of parameter is incorporated optimization by the present invention Model, have studied improve under non-complete prior information MIMO-OFDM radar parameter estimate performance sane waveform optimization ask Topic.Under permanent modular constraint, build sane waveform optimization model, load (DL) technology based on diagonal angle, each by iterative process Step nonlinear optimal problem is converted into the Semidefinite Programming that can obtain Efficient Solution, asks with the optimization tool of comparative maturity Solving, simulating, verifying can be effectively improved output SINR, and then the system of maximization detection performance.The basic ideas of the present invention are, Initially set up MIMO-OFDM-STAP system model, object function is derived, then set up sane waveform optimization mould Type, finally completes solving of sane waveform optimization problem.

The present invention compared with prior art has the advantage that

First, for output SINR, parameter estimating error sensitive issue, the present invention are considered by explicitly that parameter is the most true Determine convex set and be included into waveform optimization model to alleviate the output SINR sensitivity to parameter estimating error, thus improve The detection performance of MIMO-OFDM-STAP system.

Second, propose a kind of alternative manner, based on diagonal angle loading technique, step nonlinear optimal problem each in iteration is converted into The semi definite programming problem of Efficient Solution can be obtained, such that it is able to utilize the optimization toolbox of comparative maturity to obtain Efficient Solution.

Accompanying drawing explanation

Fig. 1 is MIMO-OFDM-STAP model

Fig. 2 is the flow chart that the present invention realizes

Fig. 3 is that MIMO radar A (0.5,0.5) and MIMO radar B (1.5,0.5) obtain under the conditions of ASNR=30dB Optimum launching beam directional diagram；

Fig. 4 be the present invention and launch MIMO radar A (0.5,0.5) and MIMO radar B under uncorrelated waveform scene (1.5, 0.5) obtained by, the output SINR under worst case is with the change curve of ASNR.

Detailed description of the invention

The present invention will be further described for 1, accompanying drawing 2, accompanying drawing 3, accompanying drawing 4 and embodiment below in conjunction with the accompanying drawings:

A kind of based on incomplete clutter priori the sane Waveform Design of MIMO-OFDM-STAP of the present invention, including as follows Step:

(1) MIMO-OFDM-STAP system model is set up

1a) MIMO-OFDM-STAP receives signal description

Consider MIMO-OFDM-STAP scene as shown in Fig. 1 of Figure of description.In this scene, the transmitting of MIMO radar Array and receiving array are even linear array, and are placed in parallel, and array number is respectively M and N, and array element distance is respectively d_TAnd d_R。 Radar platform is along being parallel to transmitting, the direction unaccelerated flight of receiving array, and flying height and speed are respectively h and v.Target Edge is θ with transmitting, receiving array normal angle_tStraight line uniform motion, speed is v_t, and it is in same plane with radar platform. In a coherent processing inteval (CPI), each array element of launching radiates the burst waveforms being made up of L pulse, and pulse simultaneously Recurrence interval (PRI) is T.N is turned to by discrete for rang ring_C(N_C＞ ＞ NML) individual junior unit, then the l pulse recurrence interval Reception data in PRI are represented by:

$X_l={\mathrm{\&rho;}}_t{e}^{j2{\mathrm{\&pi;f}}_{D}l}{\mathrm{ab}}^{T}S+\underset{i=0}{\overset{N_C-1}{\mathrm{\&Sigma;}}}{\mathrm{\&rho;}}_i{e}^{j2{\mathrm{\&pi;\&beta;f}}_{s,i}l}{a}_i{b_i}^{T}S+Z_l$

In formula,And WithRepresent target respectively and be positioned at the clutter of θ i Launch steering vector；Represent transmitted waveform matrix in each PRI,Send out for m-th Penetrating the discrete form of the complex baseband signal that array element is launched in each PRI, K is waveform sampling number；

WithRepresent target respectively and be positioned at the clutter of θ i Receive steering vector；ρ_tAnd ρ_i(θ) it is respectively the complex magnitude of the rang ring internal object considered and is positioned at θ_iClutter reflection system Number； Represent the interference that the n-th reception array element receives in the l PRI And noise, we may assume that Z_lEvery string independent same distribution, and to submit to average be 0, and variance is that the Cyclic Symmetry of Q is multiple Gauss distribution.

1b) snap statement during sky in rang ring interested

Utilize S^H(SSH)^-1/2As matched filtering device, andThen corresponding vector quantization matched filtering output can represent For:

${\tilde{x}}_l={\mathrm{\&rho;}}_t{e}^{j2{\mathrm{\&pi;f}}_{D}l}(\mathrm{\&Phi;}\&CircleTimes;I_N)(b\&CircleTimes;a)+\underset{i=0}{\overset{N_C-1}{\mathrm{\&Sigma;}}}{\mathrm{\&rho;}}_i{e}^{j2{\mathrm{\&pi;\&beta;f}}_{s,i}l}(\mathrm{\&Phi;}\&CircleTimes;I_N)(b_i\&CircleTimes;a_i)+vec\left({\tilde{Z}}_l\right)$

Wherein,I_NIt is the unit matrix of N × N, Φ=SS^H(SS^H)^-1/2=diag{ | a₁| |a₂| … |a_M|, diag{ } represent diagonal matrix.

By above formula we in can obtaining interested rang ring total empty time snap be:

$\begin{array}{c}{X}_C={\mathrm{\&rho;}}_t{U}_D\&CircleTimes;\left(\right(\mathrm{\&Phi;}\&CircleTimes;I_N\left)\right(b\&CircleTimes;a\left)\right)+\\ \underset{i=0}{\overset{N_C-1}{\mathrm{\&Sigma;}}}{\mathrm{\&rho;}}_i{U}_{D,i}\&CircleTimes;\left(\right(\mathrm{\&Phi;}\&CircleTimes;I_N\left)\right(b_i\&CircleTimes;a_i\left)\right)+I_L\&CircleTimes;vec\left({\tilde{Z}}_l\right)\\ ={\mathrm{\&rho;}}_t(I_L\&CircleTimes;\mathrm{\&Phi;}\&CircleTimes;I_N)(U_D\&CircleTimes;b\&CircleTimes;a)+\\ (I_L\&CircleTimes;\mathrm{\&Phi;}\&CircleTimes;I_N)\underset{i=0}{\overset{N_C-1}{\mathrm{\&Sigma;}}}{\mathrm{\&rho;}}_i(U_{D,i}\&CircleTimes;b_i\&CircleTimes;a_i)+I_L\&CircleTimes;vec\left({\tilde{Z}}_l\right)\end{array}$

Wherein,WithRepresent target respectively and be positioned at θ_iClutter Doppler's steering vector.

(2) object function is derived

2a) export SINR statement under the conditions of optimum MIMO-OFDM-STAP processor

Based on the undistorted criterion of minimum variance (MVDR), optimum output SINR can be obtained and be represented by:

$SINR={{\mathrm{\&rho;}}_t}^2{\&lsqb;(I_L\&CircleTimes;\mathrm{\&Phi;}\&CircleTimes;I_N)(U_D\&CircleTimes;b\&CircleTimes;a)\&rsqb;}^H{R}_{i+n}^{-1}\&lsqb;(I_L\&CircleTimes;{\mathrm{\&alpha;}}^T\&CircleTimes;I_N)(U_D\&CircleTimes;b\&CircleTimes;a)\&rsqb;$

In formula,

$R_{i+n}=E\&lsqb;\left(\right(I_L\&CircleTimes;\mathrm{\&Phi;}\&CircleTimes;I_N\left)\underset{i=0}{\overset{N_C-1}{\mathrm{\&Sigma;}}}{\mathrm{\&rho;}}_i\right(U_{D,i}\&CircleTimes;b_i\&CircleTimes;a_i)+I_L\&CircleTimes;vec({\tilde{Z}}_l\left)\right)$

${\left(\right(I_L\&CircleTimes;\mathrm{\&Phi;}\&CircleTimes;I_N\left)\underset{i=0}{\overset{N_C-1}{\mathrm{\&Sigma;}}}{\mathrm{\&rho;}}_i\right(U_{D,i}\&CircleTimes;b_i\&CircleTimes;a_i)+I_L\&CircleTimes;vec({\tilde{Z}}_l\left)\right)}^H\&rsqb;$

2b) clutter Gauss distribution, and with interference uncorrelated under the conditions of export SINR statement simplify

Assuming clutter independent same distribution, and obedience average is 0, variance isGauss distribution, then at clutter and interference plus noise Under incoherent hypothesis, output SINR can be reduced to following expression:

$SINR={\left|{\mathrm{\&rho;}}_t\right|}^2{v_t}^H{(I+\tilde{A}{R}_C)}^{-1}\tilde{A}{v}_t$

Wherein,

$V={\&lsqb;v_1,v_2,\mathrm{...},v_{N_C}\&rsqb;}^H,v_i=U_{D,i}\&CircleTimes;b_i\&CircleTimes;a_i,\mathrm{\&Xi;}=diag({{\mathrm{\&sigma;}}_1}^2,{{\mathrm{\&sigma;}}_2}^2,\mathrm{...},{{\mathrm{\&sigma;}}_{N_C}}^2),\tilde{A}=I_L\&CircleTimes;\mathrm{\&Psi;}\&CircleTimes;Q^{-1}.$

(3) sane waveform optimization model

Under Gaussian noise environment, may certify that maximization detection probability is equivalent to maximize output Signal to Interference plus Noise Ratio.Thus, based on Upper analysis can obtain, and under permanent mould and total emission power constraint, optimizes waveform covariance matrix (WCM) by one convex set of structure The waveform optimization problem maximizing detection probability can be expressed as

$\begin{array}{ccc}\underset{\mathrm{\&psi;}}{max}& \underset{{\mathrm{\&Delta;R}}_C}{min}& {\tilde{v}}_t^H{(I_{MNL}+\tilde{A}{\tilde{R}}_C)}^{-1}\tilde{A}{\tilde{v}}_t\end{array}$

$a_m^2=D_m$

$\underset{m=1}{\overset{M}{\mathrm{\&Sigma;}}}{a}_m^2=P$

||a_m||²≥0

In formula, P represents total emission power.

We can see that from above formula object function be one considerably complicated aboutAnd R_CNonlinear function, thus this asks Topic is difficult with traditional optimization and solves.

(4) alternative manner based on DL solves sane waveform optimization problem

4a) optimize based on DL internal layer

This optimization problem comprises permanent modular constraint, it is clear that being nonlinear optimization (NP) problem, it is easy to solve during globally optimal solution It is absorbed in locally optimal solution.Simultaneously asWe cannot determineCharacter, therefore, we can not Convex optimization method is enough utilized to solve.For this problem, we use diagonal angle loading method that Ψ is carried out diagonal angle loading so that

In formula, ε ＜ ＜ λ_max(Ψ) it is so-called load factor (loading factor), λ_maxThe eigenvalue of maximum of () representing matrix.Note Meaning arrives, due toCan obtainWillReplace withCan obtain

${(I_{MNL}+\widetilde{\stackrel{~}{A}}{\tilde{R}}_C)}^{-1}\widetilde{\stackrel{~}{A}}={({\widetilde{\stackrel{~}{A}}}^{-1}+{\tilde{R}}_C)}^{-1}$

According to above formula, interior optimization problem can be written as:

$\begin{array}{cc}\underset{{\mathrm{\&Delta;R}}_C,t}{min}& t\end{array}$

$\begin{array}{cc}s.t.& {\tilde{v}}_t^H{({\widetilde{\stackrel{~}{A}}}^{-1}+{\tilde{R}}_C)}^{-1}{\tilde{v}}_t\&le;t\end{array}$

In formula, t is auxiliary variable.

The problems referred to above can be equivalent to following SDP problem:

$\begin{array}{cc}\underset{{\mathrm{\&Delta;R}}_C,t}{min}& t\end{array}$

4b) solve outer layer optimization based on DL

DL method is used forCan obtain

In formula,Meet ρ=λ_max(R_C)/1000, useReplace R_C, can obtain

$SINR={\left|{\mathrm{\&rho;}}_t\right|}^2{v_t}^H{(I+\tilde{A}{\widetilde{\stackrel{~}{R}}}_C)}^{-1}\tilde{A}{\widetilde{\stackrel{~}{R}}}_C{{\widetilde{\stackrel{~}{R}}}_C}^{-1}{v}_t$

Utilizing topology, above formula can be rewritten as

$SINR={\left|{\mathrm{\&rho;}}_t\right|}^2{v_t}^H{{\widetilde{\stackrel{~}{R}}}_C}^{-1}{v}_t-{\left|{\mathrm{\&rho;}}_t\right|}^2{v_t}^H{({\widetilde{\stackrel{~}{R}}}_C+{\widetilde{\stackrel{~}{R}}}_C\tilde{A}{\widetilde{\stackrel{~}{R}}}_C)}^{-1}{v}_t$

Based on discussed above, waveform optimization problem can be expressed equivalently as following SDP problem:

$\begin{array}{cc}\underset{\mathrm{\&Psi;},t}{min}& t\end{array}$

$a_m^2=D_m$

$\underset{m=1}{\overset{M}{\mathrm{\&Sigma;}}}{a}_m^2=P$

||a_m||²≥0

In formula, t is auxiliary optimized variable.Thus, this waveform optimization problem may utilize many ripe optimization toolbox and obtains Efficient Solution.

4c) alternative manner based on DL solves sane waveform optimization problem

Based on discussed above, Δ R_CCan obtain with ψ and solve at a high speed, thus can get iterative algorithm: give waveform covariance matrix Initial value (such as, uncorrelated waveform), Δ R_CAnd ψ can be obtained by following steps alternative optimization:

<1>above-mentioned SDP problem 1 is solved to obtain optimum Δ R_C；

<2>SDP problem 2 is solved to obtain optimum ψ；

Return step<1>iteration again until Signal to Interference plus Noise Ratio (SINR) no longer reduces.

The effect of the present invention can be further illustrated by following emulation:

Simulated conditions: MIMO radar is 42 and receives, and reception array element distance is half-wavelength, and launching array element distance is 2 times of wavelength, Umber of pulse is 3, uses two MIMO radar to detect target, respectively A (0.5,0.5), B (1.5,0.5), array The definition of signal to noise ratio isWherein, P refers to always launch power,The variance of the white hot noise attached by finger, array Signal to noise ratio be 10000 from 10 to 50 decibels of changes, clutter block number, miscellaneous noise ratio (CNR) is defined as? In experiment, value is 30dB.Each element in clutter covariance matrix is 0 by an average, varianceGauss make an uproar Sound interference.Interference noise ratio is 60 decibels, and sampling number is 256.Assume there is target in the direction of 4 ° herein, building of clutter Mould uses discrete point, and its RCS is modeled as independent identically distributed gaussian random variable vector, and average is zero, and variance isI=1 ..., N_C, And assume to be fixed on coherent processing inteval.In emulation, algorithm in this paper and uncorrelated waveform are contrasted, it can be seen that The improvement situation of signal to noise ratio.

Emulation content:

Emulation 1: Fig. 3 be the present invention under the conditions of ASNR=30dB MIMO radar A (0.5,0.5) and MIMO radar B (1.5, 0.5) the optimum launching beam directional diagram obtained.It can be seen that institute's extracting method creates a spike near target position. It means that the detection performance of the worst case under convex uncertainty can be improved.In addition, it is also seen that produce in Fig. 3 (b) Having given birth to graing lobe, this is due to the sparse layout of emission array in MIMO radar (1.5,0.5).

Emulation 2: Fig. 4 be the present invention and MIMO radar A (0.5,0.5) launching uncorrelated waveform and MIMO radar B (1.5, 0.5) the output SINR under the worst case obtained by is with the change curve of ASNR.It can be seen that the SINR that two class methods obtain is Increase along with the increase of ASNR.Further, relative to uncorrelated waveform, no matter why ASNR is worth, and institute's extracting method can obtain Output SINR under worst case higher.Additionally, comparison diagram 4 (a) and (b), it is known that MIMO radar (1.5,0.5) The output SINR obtained is greater than MIMO radar (0.5,0.5).This is because the virtual aperture that the former is formed is more than the latter, thus Bigger diversity gain can be obtained.

To sum up, the present invention proposes a kind of sane waveform design method, and Parameter uncertainties convex set is explicitly included into waveform optimization Model is to maximize the output SINR under worst case.For solving the nonlinear optimal problem of complexity, alternative manner of the present invention, base Load (DL) technology in diagonal angle, each step nonlinear optimal problem in iteration is converted into the semidefinite that can obtain Efficient Solution Planning problem, thus maximize output SINR, and then the system of maximization detection performance.Emulation shows, with irrelevant transmitted waveform Comparing, the transmitted waveform that institute of the present invention extracting method obtains can significantly improve system detection performance.Understand based on described above, this Bright institute extracting method can be to be provided that solid theory by the robustness of design transmitted waveform raising radar sensing system in engineer applied With realize foundation.

Claims (1)

1. the sane Waveform Design of MIMO-OFDM-STAP based on part clutter priori, it is characterised in that include walking as follows Rapid:

(1) MIMO-OFDM-STAP system model is set up

1a) MIMO-OFDM-STAP reception signal description:

The emission array of MIMO radar and receiving array are even linear array, and are placed in parallel, and array number is respectively M and N, Array element distance is respectively d_TAnd d_R, radar platform is along being parallel to transmitting, the direction unaccelerated flight of receiving array, flying height Being respectively h and v with speed, target edge is θ with transmitting, receiving array normal angle_tStraight line uniform motion, speed is v_t, and Being in same plane with radar platform, in a coherent processing inteval (CPI), each array element of launching radiates by L pulse simultaneously The burst waveforms of composition, and pulse recurrence interval (PRI) be T, turns to N by discrete for rang ring_C(N_C＞ ＞ NML) individual little list Unit, then the reception data in the l pulse recurrence interval PRI are represented by:

$X_l={\mathrm{\&rho;}}_t{e}^{j2{\mathrm{\&pi;f}}_{D}l}{\mathrm{ab}}^{T}S+\underset{i=0}{\overset{N_C-1}{\mathrm{\&Sigma;}}}{\mathrm{\&rho;}}_i{e}^{j2{\mathrm{\&pi;\&beta;f}}_{s,i}l}{a}_i{b_i}^{T}S+Z_l$

In formula,And

WithRepresent target respectively and be positioned at θ_iClutter Launch steering vector；Represent transmitted waveform matrix in each PRI,Send out for m-th Penetrating the discrete form of the complex baseband signal that array element is launched in each PRI, K is waveform sampling number；

WithRepresent target respectively and be positioned at θ_iClutter Receive steering vector；ρ_tAnd ρ_i(θ) it is respectively the complex magnitude of the rang ring internal object considered and is positioned at θ_iClutter reflection system Number； Represent the interference that the n-th reception array element receives in the l PRI And noise, it will be assumed that Z_lEvery string independent same distribution, and to submit to average be 0, and variance is the multiple Gauss of Cyclic Symmetry of Q Distribution；

1b) snap statement during sky in rang ring interested:

Utilize S^H(SS^H)^-1/2As matched filtering device, andThen corresponding vector quantization matched filtering output can represent For:

${\tilde{x}}_l={\mathrm{\&rho;}}_t{e}^{j2{\mathrm{\&pi;f}}_{D}l}(\mathrm{\&Phi;}\&CircleTimes;I_N)(b\&CircleTimes;a)+\underset{i=0}{\overset{N_C-1}{\mathrm{\&Sigma;}}}{\mathrm{\&rho;}}_i{e}^{j2{\mathrm{\&pi;\&beta;f}}_{s,i}l}(\mathrm{\&Phi;}\&CircleTimes;I_N)(b_i\&CircleTimes;a_i)+vec\left({\tilde{Z}}_l\right)$

Wherein,I_NIt is the unit matrix of N × N, Φ=SS^H(SS^H)^-1/2=diag{ | a₁| |a₂| … |a_M|, diag{ } represent diagonal matrix,

In the most interested rang ring total empty time snap be:

$\begin{array}{c}{X}_C={\mathrm{\&rho;}}_t{U}_D\&CircleTimes;\left(\right(\mathrm{\&Phi;}\&CircleTimes;I_N\left)\right(b\&CircleTimes;a\left)\right)+\\ \underset{i=0}{\overset{N_C-1}{\mathrm{\&Sigma;}}}{\mathrm{\&rho;}}_i{U}_{D,i}\&CircleTimes;\left(\right(\mathrm{\&Phi;}\&CircleTimes;I_N\left)\right(b_i\&CircleTimes;a_i\left)\right)+I_L\&CircleTimes;vec\left({\tilde{Z}}_l\right)\\ ={\mathrm{\&rho;}}_t(I_L\&CircleTimes;\mathrm{\&Phi;}\&CircleTimes;I_N)(U_D\&CircleTimes;b\&CircleTimes;a)+\\ (I_L\&CircleTimes;\mathrm{\&Phi;}\&CircleTimes;I_N)\underset{i=0}{\overset{N_C-1}{\mathrm{\&Sigma;}}}{\mathrm{\&rho;}}_i(U_{D,i}\&CircleTimes;b_i\&CircleTimes;a_i)+I_L\&CircleTimes;vec\left({\tilde{Z}}_l\right)\end{array}$

Wherein,WithRepresent target respectively and be positioned at θ_iClutter Doppler's steering vector；

(2) object function is derived

2a) export SINR statement under the conditions of optimum MIMO-OFDM-STAP processor:

Based on the undistorted criterion of minimum variance, i.e. MVDR, optimum output SINR can be obtained and be represented by:

$SINR={{\mathrm{\&rho;}}_t}^2{\&lsqb;(I_L\&CircleTimes;\mathrm{\&Phi;}\&CircleTimes;I_N)(U_D\&CircleTimes;b\&CircleTimes;a)\&rsqb;}^H{R}_{i+n}^{-1}\&lsqb;(I_L\&CircleTimes;{\mathrm{\&alpha;}}^T\&CircleTimes;I_N)(U_D\&CircleTimes;b\&CircleTimes;a)\&rsqb;$

In formula,

$\begin{array}{c}{R}_{i+n}=E\&lsqb;\left(\right(I_L\&CircleTimes;\mathrm{\&Phi;}\&CircleTimes;I_N\left)\underset{i=0}{\overset{N_C-1}{\mathrm{\&Sigma;}}}{\mathrm{\&rho;}}_i\right(U_{D,i}\&CircleTimes;b_i\&CircleTimes;a_i)+I_L\&CircleTimes;vec({\tilde{Z}}_l\left)\right)\\ {\left(\right(I_L\&CircleTimes;\mathrm{\&Phi;}\&CircleTimes;I_N\left)\underset{i=0}{\overset{N_C-1}{\mathrm{\&Sigma;}}}{\mathrm{\&rho;}}_i\right(U_{D,i}\&CircleTimes;b_i\&CircleTimes;a_i)+I_L\&CircleTimes;vec({\tilde{Z}}_l\left)\right)}^H\&rsqb;\end{array}$

2b) clutter Gauss distribution, and with interference uncorrelated under the conditions of export SINR statement simplify:

Assuming clutter independent same distribution, and obedience average is 0, variance isGauss distribution, then at clutter and interference plus noise Under incoherent hypothesis, output SINR can be reduced to following expression:

$SINR={\left|{\mathrm{\&rho;}}_t\right|}^2{v_t}^H{(I+\tilde{A}{R}_C)}^{-1}\tilde{A}{v}_t$

Wherein,

$V={\&lsqb;v_1,v_2,\mathrm{...},v_{N_C}\&rsqb;}^H,v_i=U_{D,i}\&CircleTimes;b_i\&CircleTimes;a_i,\mathrm{\&Xi;}=diag({{\mathrm{\&sigma;}}_1}^2,{{\mathrm{\&sigma;}}_2}^2,\mathrm{...},{{\mathrm{\&sigma;}}_{N_C}}^2),\tilde{A}=I_L\&CircleTimes;\mathrm{\&Psi;}\&CircleTimes;Q^{-1};$

(3) sane waveform optimization model

Under Gaussian noise environment, may certify that maximization detection probability be equivalent to maximize output Signal to Interference plus Noise Ratio, thus, based on Upper analysis can obtain, and under permanent mould and total emission power constraint, optimizes waveform covariance matrix (WCM) by one convex set of structure The waveform optimization problem maximizing detection probability can be expressed as:

$\begin{array}{ccc}\underset{\mathrm{\&psi;}}{max}& \underset{{\mathrm{\&Delta;R}}_C}{min}& {\tilde{v}}_t^H{(I_{MNL}+\tilde{A}{\tilde{R}}_C)}^{-1}\tilde{A}{\tilde{v}}_t\end{array}$

$a_m^2=D_m$

$\underset{m=1}{\overset{M}{\&Sigma;}}{a}_m^2=P$

||a_m||²≥0

In formula, P represents total emission power,

Can be seen that from above formula object function be one considerably complicated aboutAnd R_CNonlinear function, thus this problem is very Difficulty utilizes traditional optimization to solve；

(4) alternative manner based on DL solves sane waveform optimization problem

4a) optimize based on DL internal layer:

This optimization problem comprises permanent modular constraint, it is clear that being nonlinear optimization (NP) problem, it is easy to solve during globally optimal solution It is absorbed in locally optimal solution, simultaneously as Cannot determineCharacter, it is thus impossible to enough utilize convex Optimization method solves, and for this problem, uses diagonal angle loading method that Ψ is carried out diagonal angle loading so that

$\widetilde{\mathrm{\&Psi;}}=\mathrm{\&Psi;}+\mathrm{\&epsiv;}I>0$

In formula, ε ＜ ＜ λ_max(Ψ) it is so-called load factor (loading factor), λ_maxThe eigenvalue of maximum of () representing matrix, note Meaning arrives, due toCan obtainWillReplace withCan obtain

${(I_{MNL}+\widetilde{\stackrel{~}{A}}{\tilde{R}}_C)}^{-1}\widetilde{\stackrel{~}{A}}={({\widetilde{\stackrel{~}{A}}}^{-1}+{\tilde{R}}_C)}^{-1}$

According to above formula, interior optimization problem can be written as:

$\begin{array}{cc}\underset{{\mathrm{\&Delta;R}}_C,t}{min}& t\end{array}$

$\begin{array}{cc}s.t.& {\tilde{v}}_t^H{({\widetilde{\stackrel{~}{A}}}^{-1}+{\tilde{R}}_C)}^{-1}{\tilde{v}}_t\&le;t\end{array}$

In formula, t is auxiliary variable,

The problems referred to above can be equivalent to following SDP problem:

$\begin{array}{cc}\underset{{\mathrm{\&Delta;R}}_C,t}{min}& t\end{array}$

$\begin{array}{cc}s.t.& \left[\begin{array}{cc}{\mathrm{\&sigma;}}^2& vec\left({\mathrm{\&Delta;R}}_C\right)\\ {\mathrm{vec}}^H\left({\mathrm{\&Delta;R}}_C\right)& I\end{array}\right]\&GreaterEqual;0\end{array}$

$\left[\begin{array}{cc}t& v_t\\ {v_t}^H& {\widetilde{\stackrel{~}{A}}}^{-1}+{\tilde{R}}_C\end{array}\right]>0$

4b) solve outer layer optimization based on DL

DL method is used forCan obtain

${\widetilde{\stackrel{~}{R}}}_C={\tilde{R}}_C+\mathrm{\&rho;}I>0$

In formula,Meet ρ=λ_max(R_C)/1000, useReplace R_C, can obtain

$SINR={\left|{\mathrm{\&rho;}}_t\right|}^2{v_t}^H{(I+\tilde{A}{\widetilde{\stackrel{~}{R}}}_C)}^{-1}\tilde{A}{\widetilde{\stackrel{~}{R}}}_C{{\widetilde{\stackrel{~}{R}}}_C}^{-1}{v}_t$

Utilizing topology, above formula can be rewritten as

$SINR={\left|{\mathrm{\&rho;}}_t\right|}^2{v_t}^H{{\widetilde{\stackrel{~}{R}}}_C}^{-1}{v}_t-{\left|{\mathrm{\&rho;}}_t\right|}^2{v_t}^H{({\widetilde{\stackrel{~}{R}}}_C+{\widetilde{\stackrel{~}{R}}}_C\tilde{A}{\widetilde{\stackrel{~}{R}}}_C)}^{-1}{v}_t$

Based on discussed above, waveform optimization problem can be expressed equivalently as following SDP problem:

$\begin{array}{cc}\underset{\mathrm{\&Psi;},t}{min}& t\end{array}$

$\begin{array}{cc}s.t.& \left[\begin{array}{cc}t& {v_t}^H\\ v_t& {\widetilde{\stackrel{~}{R}}}_C+{\widetilde{\stackrel{~}{R}}}_C\tilde{A}{\widetilde{\stackrel{~}{R}}}_C\end{array}\right]\end{array}\&GreaterEqual;0$

$a_m^2=D_m$

$\underset{m=1}{\overset{M}{\&Sigma;}}{a}_m^2=P$

||a_m||²≥0

In formula, t is auxiliary optimized variable, thus, this waveform optimization problem may utilize many ripe optimization toolbox and obtains Efficient Solution；

4c) alternative manner based on DL solves sane waveform optimization problem:

Based on above-mentioned, Δ R_CCan obtain with ψ and solve at a high speed, thus can get iterative algorithm: given waveform covariance matrix is initial Value, Δ R_CAnd ψ can be obtained by following steps alternative optimization:

<1>above-mentioned SDP problem 1 is solved to obtain optimum Δ R_C；

<2>SDP problem 2 is solved to obtain optimum ψ；

Return step<1>iteration again until Signal to Interference plus Noise Ratio (SINR) no longer reduces.